diff --git "a/batch_s000018.csv" "b/batch_s000018.csv" new file mode 100644--- /dev/null +++ "b/batch_s000018.csv" @@ -0,0 +1,10268 @@ +source,target + For us letter we consider that accretion occurs over a range of radii within the corotation radius., For this letter we consider that accretion occurs over a range of radii within the corotation radius. +" Εις is equivalent to the ipproach taken previously by 27... ὃν, 2. and ? who have emonstrated that such an assumption reproduces observed μα»ectral line profiles ancl variability."," This is equivalent to the approach taken previously by \citet*{har94}, \citet*{muz01}, \citet*{sym05} and \citet{aze06} who have demonstrated that such an assumption reproduces observed spectral line profiles and variability." + It should also be noted iu the accreting field geometries which we consider here are only snap-shots in time. and in reality will evolve due to the interaction with the disc.," It should also be noted that the accreting field geometries which we consider here are only snap-shots in time, and in reality will evolve due to the interaction with the disc." + The accretion filling factors are 0.9% for the AB Dor-like field and 1.2% for the LO 1να- field. smaller than would be expected for accretion to a dipole. but consistent with observationally inferred. values (e.g. 7)).," The accretion filling factors are $0.9\%$ for the AB Dor-like field and $1.2\%$ for the LQ Hya-like field, smaller than would be expected for accretion to a dipole, but consistent with observationally inferred values (e.g. \citealt{val04}) )." + We assume that material is supplied. by the disc. and accretes onto the star at a constant rate., We assume that material is supplied by the disc and accretes onto the star at a constant rate. + For a. dipolar magnetic field. accretion occurs into two rings in opposite, For a dipolar magnetic field accretion occurs into two rings in opposite +There απο two objections to accepting the above arguments as disproof of the idea of flowing space.,There are two objections to accepting the above arguments as disproof of the idea of flowing space. + One is that the derivatious here are cutirely Newtonian. aud so of course will uot show au effect which is relativistic iu origin: that problem will be addressed below.," One is that the derivations here are entirely Newtonian, and so of course will not show an effect which is relativistic in origin; that problem will be addressed below." + The secoud is that an origin placed a finite distance away from the test particle is not appropriate. aud one should really consider the problem to be that of a particle eiven an initial peculiar velocity.," The second is that an origin placed a finite distance away from the test particle is not appropriate, and one should really consider the problem to be that of a particle given an initial peculiar velocity." + In that case. the Dubble flow could be thought of as exerting a sort of viscous force.," In that case, the Hubble flow could be thought of as exerting a sort of viscous force." + One would then not necessarily expect the expansion of space to act inmiediatelv and overwheliinglv., One would then not necessarily expect the expansion of space to act immediately and overwhelmingly. + While a leaf placed in a river iuight become part of the flow at once. a ship has inertia. aud ouce the engines are stopped will continue to move with respect to the water for some time (as anvoue who has attempted fine maneuvering knows very well).," While a leaf placed in a river might become part of the flow at once, a ship has inertia, and once the engines are stopped will continue to move with respect to the water for some time (as anyone who has attempted fine maneuvering knows very well)." + Aud it does appear. since peculiar velocity is know to decay with tine. that the free particle indeed joius the Hubble flow after passing through the origin.," And it does appear, since peculiar velocity is known to decay with time, that the free particle indeed joins the Hubble flow after passing through the origin." + It is to the matter of joining the IIubble flow that we now turn., It is to the matter of joining the Hubble flow that we now turn. + It is a general property of expauding universes that anv motion which departs from the general flow decreases with time. the familiar decay of peculiarvelocity.," It is a general property of expanding universes that any motion which departs from the general flow decreases with time, the familiar decay of peculiar." + In the solutions above (and in the Appendix) it is readily seen that the time derivatives of the e» functions are all monotonically decreasing (with the exception of the overdense universe i some phases). aud iudeed decreasing more quickly than the ey (Iubble flow) fictions.," In the solutions above (and in the Appendix) it is readily seen that the time derivatives of the $c_2$ functions are all monotonically decreasing (with the exception of the overdense universe in some phases), and indeed decreasing more quickly than the $c_1$ (Hubble flow) functions." + From this it seems clear that all particles nist eventually join the IHubble Sow as their velocity away from it vanishes., From this it seems clear that all particles must eventually join the Hubble flow as their velocity away from it vanishes. +" However. this is worth investigating quantitatively,"," However, this is worth investigating quantitatively." + Considering the motion of a free particle iu a critical universe without a cosmological coustaut. its asvinptotic speed is The backerouud particle with this same asviuptotic speed has as its equation of notion The spatial distance between these two particles is thusunbounded.," Considering the motion of a free particle in a critical universe without a cosmological constant, its asymptotic speed is The background particle with this same asymptotic speed has as its equation of motion The spatial distance between these two particles is thus." + Fox an uuderdeuse universe. the distance between the free particle aud the backerouud particle with the same asviuptotic speed (we might call it a ‘peculiar distance’) is more complicated. but as time becomes large approaches a constaut.," For an underdense universe, the distance between the free particle and the background particle with the same asymptotic speed (we might call it a `peculiar distance') is more complicated, but as time becomes large approaches a constant." + That is. the free particle stavs at least this far from its correspouding backgound particle. even at infinite times.," That is, the free particle stays at least this far from its corresponding backgound particle, even at infinite times." +" A particle which keeps a distauce frou its ""proper place in the Uubble flow. even after an infinitely long time. caunot really be said to join it."," A particle which keeps a distance from its `proper' place in the Hubble flow, even after an infinitely long time, cannot really be said to join it." +reutralino signal obviously may chanec this result.,neutralino signal obviously may change this result. + Actually we show here that in a Ον scenario. even. in case of a finite antiproton lifetime. we can produce uodels which give at the same time a very good fit of he existing data aud whose spectral features are oeculiar Chough to be distiuguished. from the standard jckerounud once measurements at higher energies will be available.," Actually we show here that in a clumpy scenario, even in case of a finite antiproton lifetime, we can produce models which give at the same time a very good fit of the existing data and whose spectral features are peculiar enough to be distinguished from the standard background once measurements at higher energies will be available." + Iu Fie., In Fig. + 5 we compare three such models with he case of standard backerouud aud iufiuite rz., \ref{fig:spectau} we compare three such models with the case of standard background and infinite $\tau_{\bar{p}}$. +" Model 5 is à 51 GeV eate10-like neutralino whose autiproton flux iis been scaledby £6=19 aac for 7,=0.82 Myr."," Model 5 is a 51 GeV gaugino-like neutralino whose antiproton flux has been scaled by $f\,\delta = 49$ and for $\tau_{\bar{p}} = 0.82$ Myr." +" Also shown in the figure is the reduction in the background flux luneed In:"" cousidering rz,=0.82 Myr (dashed nue abelledby 5 3b).", Also shown in the figure is the reduction in the background flux induced by considering $\tau_{\bar{p}} = 0.82$ Myr (dashed line labelled by $5b$ ). +" Model7 is the heaviest model for which the oxedieted Buiis stillin excellent agreement with existiug data C.L. fit for i,=1017 GeV. fó=12:H and 7,=2.92 My»). while model 6 is some intermediate case (Gn.=188 GeV. fó=T8 aud 7,= Alvr)."," Model 7 is the heaviest model for which the predicted flux is still in excellent agreement with existing data C.L. fit for $m_{\chi} = 477$ GeV, $f\,\delta = 1.2 \cdot 10^4$ and $\tau_{\bar{p}} = 2.92$ Myr), while model 6 is some intermediate case $m_{\chi} = 188$ GeV, $f\,\delta = 78$ and $\tau_{\bar{p}} = 1.32$ Myr)." + The trend is that for heavier ueutralinos there is a larger overproduction of autiprotous in the high energy ranec., The trend is that for heavier neutralinos there is a larger overproduction of antiprotons in the high energy range. + Applving the largest possible rescalings consistent with -rav lneasurements we fud that a 56 CV ueutralino model gives a flux which is consistent with data at CLL. in case the autiproton lifetime is as low as Ty=045 Myr., Applying the largest possible rescalings consistent with $\gamma$ -ray measurements we find that a 56 GeV neutralino model gives a flux which is consistent with data at C.L. in case the antiproton lifetime is as low as $\tau_{\bar{p}} = 0.15$ Myr. + The bound of Ceer Ixeuucdy (1998) as clearly violated., The bound of Geer Kennedy (1998) is clearly violated. + Notice that we are comparing with a more aboundant data set than in that reference 97 data were not included there) and that we used our standard values for the parameters which define the diffusion model aud solar iiodulation., Notice that we are comparing with a more aboundant data set than in that reference 97 data were not included there) and that we used our standard values for the parameters which define the diffusion model and solar modulation. +" If uncertainties were included the lower bound we would ect with this method would probably be very close to the most stringent direct experimental bounud z,>0.05 Myr or lower.", If uncertainties were included the lower bound we would get with this method would probably be very close to the most stringent direct experimental bound $\tau_{\bar{p}} > 0.05$ Myr or lower. + To conclude. we have shown that there is a chance of detecting ueutralino dark iwatter im upcoming nieasurenaents of the cosmic autiprotou flux at hieh energies.," To conclude, we have shown that there is a chance of detecting neutralino dark matter in upcoming measurements of the cosmic antiproton flux at high energies." + The signatures we propose here are alternative to the signature of au exotic component low kinetic enereies. which secius not to be required by present data.," The signatures we propose here are alternative to the signature of an exotic component at low kinetic energies, which seems not to be required by present data." +" We have aso discussed the possibility that antiprotous have a finite lifetime and shown that the lini ou 7, which is possible to set ou the basis of cosmic rav measurements is comparable to those iu direct experiments.", We have also discussed the possibility that antiprotons have a finite lifetime and shown that the limit on $\tau_{\bar{p}}$ which is possible to set on the basis of cosmic ray measurements is comparable to those in direct experiments. + I an eratefulrateful to LLars BerestBerestrouun audL JoakimJoal EdEdsyo for αμα useful discussions., I am grateful to Lars Bergströmm and Joakim Edsjö for many useful discussions. + I thauk Paolo Coudolo for collaboration ou thenumerical. supersviuuuetry calculations., I thank Paolo Gondolo for collaboration on thenumerical supersymmetry calculations. +We processed 5.030 sessions of the permanent geodetic and astrometric VLBI program since 1979. totalling 7.285.312 group delay measurements at 84 GHz.,"We processed 5,030 sessions of the permanent geodetic and astrometric VLBI program since 1979, totalling 7,285,312 group delay measurements at 8.4 GHz." + Radio source coordinates Were estimated once per session. together with Earth orientation parameters and station coordinates.," Radio source coordinates were estimated once per session, together with Earth orientation parameters and station coordinates." + The off elevation angle was set to 5°., The cut-off elevation angle was set to $^{\circ}$. + A priori zenith delays were determined from local pressure values (Saastamoinen 1972). which were then mapped to the elevation of the observation using the Vienna mapping functions (Bóhhm et al.," A priori zenith delays were determined from local pressure values (Saastamoinen 1972), which were then mapped to the elevation of the observation using the Vienna mapping functions (Böhhm et al." + 2006)., 2006). + Zenith wet delays were estimated as a continuous piecewise linear function at 30-min intervals., Zenith wet delays were estimated as a continuous piecewise linear function at 30-min intervals. + Troposphere gradients were estimated às 8-hr east and north piecewise functions at all stations except a set of 110 stations with short observational histories., Troposphere gradients were estimated as 8-hr east and north piecewise functions at all stations except a set of 110 stations with short observational histories. + Statior heights were corrected for atmospheric pressure and oceanic tidal loading., Station heights were corrected for atmospheric pressure and oceanic tidal loading. + The relevant loading quantities were deduced from surface pressure grids from the U. 5. NCEP/NCAR reanalysis project atmospheric global circulation model (Kalnay et al., The relevant loading quantities were deduced from surface pressure grids from the U. S. NCEP/NCAR reanalysis project atmospheric global circulation model (Kalnay et al. + 1996. Petrov Boy 2004) and from the FES 2004 ocean tide model (Lyard et al.," 1996, Petrov Boy 2004) and from the FES 2004 ocean tide model (Lyard et al." + 2004)., 2004). + No-net rotation (NR) and translation constraints per session were applied to the positions of all stations. excluding Fort Davis (Texas). Pie Town (New Mexico). Fairbanks (Alaska). and the TIGO antenna at Concepeiónn. Chile because of strong non linear displacements (These two sites experienced post-seismic relaxation effects after large earthquakes on the Denali fault in 2003. and between Talca and Concepeiónn in early 2010).," No-net rotation (NNR) and translation constraints per session were applied to the positions of all stations, excluding Fort Davis (Texas), Pie Town (New Mexico), Fairbanks (Alaska), and the TIGO antenna at Concepciónn, Chile because of strong non linear displacements (These two sites experienced post-seismic relaxation effects after large earthquakes on the Denali fault in 2003, and between Talca and Concepciónn in early 2010)." + A priori precession and nutation comply with the [AU 2000/2006 resolutions. which include the nutation model of Mathews et al. (," A priori precession and nutation comply with the IAU 2000/2006 resolutions, which include the nutation model of Mathews et al. (" +2002). the improved precession model of Capitaine et al. (,"2002), the improved precession model of Capitaine et al. (" +2003b). and the non rotating origin-based coordinate. transformation. between terrestrial and celestial coordinate systems (Capitaine et al.,"2003b), and the non rotating origin-based coordinate transformation between terrestrial and celestial coordinate systems (Capitaine et al." + 2003a)., 2003a). + Usually. an NNR constraint is used to fix the ICRS axes.," Usually, an NNR constraint is used to fix the ICRS axes." + However. Titov (2010) argues that application of a tight NNR constraint may wipe out all systemtic effects in the proper motion of reference radio sources.," However, Titov (2010) argues that application of a tight NNR constraint may wipe out all systemtic effects in the proper motion of reference radio sources." + Therefore. we tied the celestial frame to the ICRF? using a loose NNR constraint uniformly applied for each session.," Therefore, we tied the celestial frame to the ICRF2 using a loose NNR constraint uniformly applied for each session." + More details are discussed later in Section 3.2., More details are discussed later in Section 3.2. + The calculations used the Cale 10.0/Solve 2010.05.21 geodetic VLBI analysis software package. which was developed and maintained at NASA Goddard Space Flight Center. and were carried out at the Paris Observatory IVS Analysis Center (Gontier et al.," The calculations used the Calc 10.0/Solve 2010.05.21 geodetic VLBI analysis software package, which was developed and maintained at NASA Goddard Space Flight Center, and were carried out at the Paris Observatory IVS Analysis Center (Gontier et al." + 2008)., 2008). + Before 1990. the general deficiency of the VLBI networks. including the number of observed sources and observing antennas per session. makes the VLBI products less reliable (see. e.g.. Gontier et al.," Before 1990, the general deficiency of the VLBI networks, including the number of observed sources and observing antennas per session, makes the VLBI products less reliable (see, e.g., Gontier et al." + 2001. Malkin 2004. Feissel-Vernier et al.," 2001, Malkin 2004, Feissel-Vernier et al." + 2004. Lambert Gontier 2009 who reports interesting statistical results and remarks about the VLBI evolution over the past two decades).," 2004, Lambert Gontier 2009 who reports interesting statistical results and remarks about the VLBI evolution over the past two decades)." + For this reason we removed data before 1990., For this reason we removed data before 1990. + A treatment of the full data base over 1979-2010 1s nevertheless presented later for comparison., A treatment of the full data base over 1979–2010 is nevertheless presented later for comparison. + In the coordinate time series. data points resulting from fewer than three reliable observations within à session. were removed. and outliers were eliminated so that the y is reasonably close to unity.," In the coordinate time series, data points resulting from fewer than three reliable observations within a session were removed, and outliers were eliminated so that the $\chi^2$ is reasonably close to unity." + Then. proper motions were computed by weighted least-squares for time series containing at least ten points and longer than ten years.," Then, proper motions were computed by weighted least-squares for time series containing at least ten points and longer than ten years." + Weights were taken as the inverse of the squared formal error., Weights were taken as the inverse of the squared formal error. +" A set of 39 sources showing significant non linear positional variations due to large-scale variations in their structure (including 3C84. 3C273B. 3C279, 3C345. 3C454.3. and 1C39.25) were isolated in the ICRF2 work and treated in such a manner that they did not perturb the geodetic solutions (Fey et al."," A set of 39 sources showing significant non linear positional variations due to large-scale variations in their structure (including 3C84, 3C273B, 3C279, 3C345, 3C454.3, and 4C39.25) were isolated in the ICRF2 work and treated in such a manner that they did not perturb the geodetic solutions (Fey et al." + 2009)., 2009). + We removed these 39 sources from our data set., We removed these 39 sources from our data set. + The final sample contains proper motions of 555 sources and is made available electronically., The final sample contains proper motions of 555 sources and is made available electronically. + Figure | displays the distribution of sources and proper motion formal errors in declination., Figure \ref{fig00} displays the distribution of sources and proper motion formal errors in declination. + Near the polar areas. the number of sources decreases proportionally to the cosine of the declination.," Near the polar areas, the number of sources decreases proportionally to the cosine of the declination." + It also shows the nonuniformity of the sample and a lack of sources at declinations under —407., It also shows the nonuniformity of the sample and a lack of sources at declinations under $-40^{\circ}$. +" Figure 2 displays 45,cos0 versus a for 40 sources observed in more than 1.000 sessions (see Section 3.2 for details)."," Figure \ref{fig20} displays $\mu_{\alpha}\cos\delta$ versus $\alpha$ for 40 sources observed in more than 1,000 sessions (see Section 3.2 for details)." + The apparent motions of these sources are estimated very accurately thanks to a large number of observations., The apparent motions of these sources are estimated very accurately thanks to a large number of observations. + A systematic in sinc of magnitude less than 10 uas clearly shows up., A systematic in $\sin\alpha$ of magnitude less than 10 $\mu$ as clearly shows up. + Tiny underlying aberrational drift is indicative even for a limited number of well-observed radio sources., Tiny underlying aberrational drift is indicative even for a limited number of well-observed radio sources. + This section comprises our results of the dipole component estimation., This section comprises our results of the dipole component estimation. + We start with a main solution including all 555 radio sources., We start with a main solution including all 555 radio sources. + Then we consider different subsets of radio sources to verify the robustness of the main solution., Then we consider different subsets of radio sources to verify the robustness of the main solution. + First. dipole and rotation coefficients. were fitted by weighted least-squares following Eqs. (," First, dipole and rotation coefficients were fitted by weighted least-squares following Eqs. (" +3)}-(4) and (6)-(7) (Table .. column DR).,"3)–(4) and (6)–(7) (Table \ref{tab01}, column DR)." + Reported errors are standard formal errors., Reported errors are standard formal errors. + The fit produces correlations of ~O.4 between dj and r» and between d» and r|., The fit produces correlations of $\sim$ 0.4 between $d_1$ and $r_2$ and between $d_2$ and $r_1$. + Figure 3 displays both the proper motions of the 555 sources and the estimated dipole component of the velocity field., Figure \ref{fig01} displays both the proper motions of the 555 sources and the estimated dipole component of the velocity field. + Within error bars. the dipole amplitude and direction agree with predictions from measurements of the Galactic parameters.," Within error bars, the dipole amplitude and direction agree with predictions from measurements of the Galactic parameters." + The corresponding, The corresponding +niaxiumui of 6045WOkkinss | atrτο ppc.,maximum of $v_{rot}=160$ $^{-1}$ at $r=375$ pc. + The rotation curve (ο) aud the related principal frequencies derived in the epieyclie approximation (Q and 0-4/2) are represented iu Fig., The rotation curve $v_{rot}$ ) and the related principal frequencies derived in the epicyclic approximation $\Omega$ and $\Omega$ $\kappa$ /2) are represented in Fig. + 7 for the immer ppc., \ref{fig:omega} for the inner pc. + A laree amount of eas is detected at velocities lower than deterinined by the ridge o‘terminal velocities shown in Fie. 6.., A large amount of gas is detected at velocities lower than determined by the ridge of terminal velocities shown in Fig. \ref{fig:posvel}. + There Is an S-shaped feature in the p-v diaeranuue gonig across the vuanucal centre (denoted as SP in Fie. 6))., There is an S-shaped feature in the p-v diagramme going across the dynamical centre (denoted as SP in Fig. \ref{fig:posvel}) ). + The characteristic pattern of SP sugeests the presence of a ioni-axisviunetrie distribution of inolecular gas 1i the form o clear nünirspiral aris. which extend froui the cenre to r~300 ppc.," The characteristic pattern of SP suggests the presence of a non-axisymmetric distribution of molecular gas in the form of nuclear mini-spiral arms, which extend from the centre to $r\sim 300$ pc." +" ALorcover. the ""figure-cielit xivttern of the p-v diagranune formed by SP and the curve of termiwl velocities is typical of a burriven eas fiow (Ixuijiken Merrifield 1995j)."," Moreover, the `figure-eight' pattern of the p-v diagramme formed by SP and the curve of terminal velocities is typical of a bar-driven gas flow (Kuijken Merrifield \cite{kuijken}) )." +" The existeice of a nucear stellar bar of kk)c diameter was iready establishec w Telesco Cezari 19923). base Ol Learifrared observations 1 ithe J. Is iux Thanes,"," The existence of a nuclear stellar bar of kpc diameter was already established by Telesco Gezari \cite{telesco9}) ), based on near-infrared observations in the J, K and I bands." + Driven by alxw potential. eas clotds follow nonu sclfintersecting elipsoiclal orbits.," Driven by a bar potential, gas clouds follow non self-intersecting ellipsoidal orbits." + TiC snajex axes of these orbits precess as a netion of radius. axl hence eud up delineating niviral wis. owlne o orbi crowding.," The major axes of these orbits precess as a function of radius, and hence end up delineating spiral arms, owing to orbit crowding." + The precession of eas OFits is due to tI !dissipative nature of eas: uolecular Coud-oud collisions aud the implied viscosiv of tie pTOCeSS οιπο a smooth trasition between the har-criven + orbits (parallel to the bar major axis) towards ο orbits serpendicular to bar major axis). when we go across t1C Imer Lindblad Resouance (IER).," The precession of gas orbits is due to the dissipative nature of gas: molecular cloud-cloud collisions and the implied viscosity of the process cause a smooth transition between the bar-driven $x_1$ orbits (parallel to the bar major axis) towards $x_2$ orbits (perpendicular to bar major axis), when we go across the Inner Lindblad Resonance (ILR)." +" Therefore. the presence ) fa nuclear bar potential and a spiral eas response are ""PSituaatelv related."," Therefore, the presence of a nuclear bar potential and a spiral gas response are intimately related." + The existence of two ILBs in the nucleus of is clearly sugecsted by our observations (see Fig. 7))., The existence of two ILRs in the nucleus of is clearly suggested by our observations (see Fig. \ref{fig:omega}) ). +identification.,identification. +" As can be seen from Figure 2,, however, also passively evolving or dusty galaxies at intermediate redshifts 2.5—4) can exhibit similarly red colors in ὅπου(z—Hi69."," As can be seen from Figure \ref{fig:colsel}, however, also passively evolving or dusty galaxies at intermediate redshifts $z\sim2.5-4$ ) can exhibit similarly red colors in $J_{125}-H_{160}$ ." +" While the requirement of optical non-detections removes the bulk of lower redshift contamination, certain intermediate redshift galaxies with evolved or dusty stellar populations can still be included due to the fact that the optical data does not reach deep enough, if at similar depth as the IR (see Fig. 3))."," While the requirement of optical non-detections removes the bulk of lower redshift contamination, certain intermediate redshift galaxies with evolved or dusty stellar populations can still be included due to the fact that the optical data does not reach deep enough, if at similar depth as the IR (see Fig. \ref{fig:maglim}) )." + Deep Spitzer IRAC data provides a way to identify contaminating galaxies., Deep Spitzer IRAC data provides a way to identify contaminating galaxies. +" These are expected to exhibit very red Hiso—[3.6m] colors, which discriminates them from genuine z~10 candidates."," These are expected to exhibit very red $H_{160}-[3.6\micron]$ colors, which discriminates them from genuine $z\sim10$ candidates." +" To exclude possible low-redshift contamination, we thus use two steps to select z=9.5 galaxy candidates."," To exclude possible low-redshift contamination, we thus use two steps to select $z\gtrsim9.5$ galaxy candidates." +" For the first step, the primary criteria are based on HST data only: Additional to excluding objects that are detected in any band blueward of Jj25 at more than 20, we include a cut in the optical X2pt value of a galaxy (seee.g.Bouwensetal.2011b; 2011a)."," For the first step, the primary criteria are based on HST data only: Additional to excluding objects that are detected in any band blueward of $J_{125}$ at more than $2\sigma$, we include a cut in the optical $\chi^2_{opt}$ value of a galaxy \citep[see e.g.][]{Bouwens10c,Bouwens11}." +". This is computed from the 0725 radius aperture fluxes as =sign(fi)(fioi), where the sum runs over all X2ptthe bands5 available in the given data set blueward of J125, i.e. it includes all the available optical data as well as the NIR band Yos for the HUDF09 data, and Yoos in the ERS."," This is computed from the $0\farcs25$ radius aperture fluxes as $\chi^2_{opt} = \sum_i\mathrm{sign}(f_i)\left(f_i/\sigma_i\right)^2$, where the sum runs over all the bands available in the given data set blueward of $J_{125}$, i.e. it includes all the available optical data as well as the NIR band $Y_{105}$ for the HUDF09 data, and $Y_{098}$ in the ERS." + The relatively large apertures were chosen in order sample >7096 of the light of point-like sources., The relatively large apertures were chosen in order sample $>70\%$ of the light of point-like sources. +" The limiting x2,, are derived from photometric scatter simulations.", The limiting $\chi^2_{cut}$ are derived from photometric scatter simulations. +" They are set to exclude the majority of interlopers which remain undetected at 2σ purely due to photometric noise, but not to cut a substantial fraction of galaxies with real zero flux in the optical bands."," They are set to exclude the majority of interlopers which remain undetected at $2\sigma$ purely due to photometric noise, but not to cut a substantial fraction of galaxies with real zero flux in the optical bands." +" The scatter simulations utilize all galaxies in our catalogs that are 1—3 mag above the completeness limit, applying photometric Gaussian noise from 1 mag fainter sources."," The scatter simulations utilize all galaxies in our catalogs that are $1-3$ mag above the completeness limit, applying photometric Gaussian noise from 1 mag fainter sources." +" From these simulations it is clear that contamination is mainly an issue at 0.75 mag above the completeness limits, but that ~60—80% of contaminants can be eliminated by using a limit of x2,,=2.8 or 2.4, for 5 filters or 4 filters, respectively."," From these simulations it is clear that contamination is mainly an issue at 0.75 mag above the completeness limits, but that $\sim60-80$ of contaminants can be eliminated by using a $\chi^2_{opt}$ limit of $\chi^2_{cut}=2.8$ or 2.4, for 5 filters or 4 filters, respectively." +"X2pt In the HUDFO09 data, the resulting number of expected contaminants due to photometric scatter is thus reduced from ~0.5 source per WFC3/IR field to 0.1 source."," In the HUDF09 data, the resulting number of expected contaminants due to photometric scatter is thus reduced from $\sim0.5$ source per WFC3/IR field to $\sim0.1$ source." +" On the other hand, the adopted x2,, limits do remove an additional ~20% of sources with real zero flux, simply due to Gaussian statistics."," On the other hand, the adopted $\chi^2_{cut}$ limits do remove an additional $\sim20$ of sources with real zero flux, simply due to Gaussian statistics." + This reduction of the real galaxy sample is reflected in our subsequent analysis in the reduction of the selection volume., This reduction of the real galaxy sample is reflected in our subsequent analysis in the reduction of the selection volume. +" All galaxies passing the above selection criteria, using both the ACS and WFC3/IR data, are retained and analyzed individually."," All galaxies passing the above selection criteria, using both the ACS and WFC3/IR data, are retained and analyzed individually." +" These total to 17 sources with Hi60,AB in the range 23.6—28.8 mag; one source in the HUDF, none in the parallel HUDFO09 fields, three in the ERS and 8 and 5 in the CANDELS Deep and Wide, respectively Tables 2 and A4))."," These total to 17 sources with $H_{160,AB}$ in the range $23.6-28.8$ mag; one source in the HUDF, none in the parallel HUDF09 fields, three in the ERS and 8 and 5 in the CANDELS Deep and Wide, respectively (see Tables \ref{tab:phot} and \ref{tab:photContamin}) )." +" Interestingly, (seeonly one source previously reported galaxy with Heo~29 mag from (theBouwens et al."," Interestingly, only one source (the previously reported galaxy with $H_{160}\sim29$ mag from Bouwens et al." +" 2011) did pass our selection in the three deep HUDF09 fields,"," 2011) did pass our selection in the three deep HUDF09 fields," +"annuli, and fits the data to flattened sinusoidal models as a function of position angle.","annuli, and fits the data to flattened sinusoidal models as a function of position angle." +" For the discrete velocity data (GCs), rotation and dispersion are fitted simultaneously through a maximum likelihood method (Figs."," For the discrete velocity data (GCs), rotation and dispersion are fitted simultaneously through a maximum likelihood method (Figs." + 2a-d)., 2a–d). +" 'The position angles and ellipticities of the rotation field and the sampling bins (PAkin, €kin) are part of the fit for the SKiMS data but are not well constrained for the discrete velocity data, which we assume follows the stellar isophotes (PA=43.5°, e=0.5)."," The position angles and ellipticities of the rotation field and the sampling bins $\rm{PA_{kin}}$ , $\rm{\epsilon_{kin}}$ ) are part of the fit for the SKiMS data but are not well constrained for the discrete velocity data, which we assume follows the stellar isophotes $^{\circ}$, $\epsilon$ =0.5)." + Our results are insensitive to reasonable variations in these parameters., Our results are insensitive to reasonable variations in these parameters. + Uncertainties are estimated via Monte Carlo fitting of mock data-sets., Uncertainties are estimated via Monte Carlo fitting of mock data-sets. + The resulting rotation profiles for the different subcomponents are shown in Figs., The resulting rotation profiles for the different subcomponents are shown in Figs. +" 2e and 2f, where rolling fits with radius are used to capture the details of any radial kinematic transitions from the inner to outer bulge/halo)."," 2e and 2f, where rolling fits with radius are used to capture the details of any radial kinematic transitions (e.g from the inner to outer bulge/halo)." +" Within ~ 1.5 (e.gΠο the MRGC system rotates nearly as rapidly as the stellar bulge, supporting the coevolution of these two components, as also inferred from their similar ages and metallicities [2006).."," Within $\sim$ 1.5 $R_{\rm e}$ the MRGC system rotates nearly as rapidly as the stellar bulge, supporting the coevolution of these two components, as also inferred from their similar ages and metallicities \citep{2006MNRAS.367..815N}." +" At larger radii, this rotation decreases dramatically (see also Figs."," At larger radii, this rotation decreases dramatically (see also Figs." +" 2a,b)."," 2a,b)." +" The MPGCs have moderate rotation with a decline outside ~4R,.", The MPGCs have moderate rotation with a decline outside $\sim 4 R_{\rm e}$. + An alternative rotation profile for the MRGCs is shown in Fig., An alternative rotation profile for the MRGCs is shown in Fig. +" 2g, after normalizing by the local velocity dispersion."," 2g, after normalizing by the local velocity dispersion." +" The photometric ellipticity profile is also plotted, showing a decrease with radius that parallels the rotational gradient."," The photometric ellipticity profile is also plotted, showing a decrease with radius that parallels the rotational gradient." +" The overall implication is for a bulge that has a high degree of rotational flattening in its central regions, while becoming rounder and dispersion-dominated in its outskirts."," The overall implication is for a bulge that has a high degree of rotational flattening in its central regions, while becoming rounder and dispersion-dominated in its outskirts." +" Having found kinematic transitions in both GC subpopulations, we look for analogous transitions in the radial metallicity profiles."," Having found kinematic transitions in both GC subpopulations, we look for analogous transitions in the radial metallicity profiles." + First we summarize the overall color distribution of the GCs in Fig., First we summarize the overall color distribution of the GCs in Fig. +" 3a, which shows a classic bimodality."," 3a, which shows a classic bimodality." +" We will assume that this bimodality persists with increasing radius, but that the location of the color peaks may shift."," We will assume that this bimodality persists with increasing radius, but that the location of the color peaks may shift." +" At large radii we must cope with the contaminating effects of foreground stars, whose color distribution we also show in Fig."," At large radii we must cope with the contaminating effects of foreground stars, whose color distribution we also show in Fig." +" 3a, and use to construct Monte Carlo mock datasets to iteratively correct for the contaminant bias on the color peak locations."," 3a, and use to construct Monte Carlo mock datasets to iteratively correct for the contaminant bias on the color peak locations." + Fig., Fig. +" 3c shows color versus radius, both for individual GC candidates and for the fitted peak locations."," 3c shows color versus radius, both for individual GC candidates and for the fitted peak locations." +" Both GC subpopulations have radially-decreasing colors, whichwe quantify as power-law color gradients with slopes of —0.05 and —0.07 mag per dex for MPGCs and MRGCs, respectively."," Both GC subpopulations have radially-decreasing colors, whichwe quantify as power-law color gradients with slopes of $-0.05$ and $-0.07$ mag per dex for MPGCs and MRGCs, respectively." +" Using our own empirical calibration to the (g—z) color used in ACS surveys (Pengal.[2006),, the gradients are —0.07 and —0.10 mag peret dex."," Using our own empirical calibration to the $(g-z)$ color used in ACS surveys \citep{2006ApJ...639...95P}, the gradients are $-0.07$ and $-0.10$ mag per dex." +" onverting to [Fe/H] metallicity 2006),, we estimate gradients of —0.38+0.06 and —0.17+0.04 dex per dex."," Converting to [Fe/H] metallicity \citep{2006ApJ...639...95P}, we estimate gradients of $-0.38\pm 0.06$ and $-0.17\pm 0.04$ dex per dex." +" To our knowledge, this is the first time that metallicity gradients in both GC subpopulations have been measured to large radii in any galaxy besides a few very massive ellipticals (see Section ??))."," To our knowledge, this is the first time that metallicity gradients in both GC subpopulations have been measured to large radii in any galaxy besides a few very massive ellipticals (see Section \ref{intro}) )." + It is also one of the first cases of any galaxy type where joint rotation and metallicity gradients are observed in the halo (see also NGC 4697: 2009}; and NGC 4125: 3010).," It is also one of the first cases of any galaxy type where joint rotation and metallicity gradients are observed in the halo (see also NGC 4697: \citealt{2005ApJ...627..767M,2009ApJ...691..228M}; and NGC 4125: \citealt{2010A&A...516A...4P}) )." + We now consider some possible implications of the rotation and metallicity gradients for NGC 3115’s assembly history., We now consider some possible implications of the rotation and metallicity gradients for NGC 3115's assembly history. +" The central bulge properties are generally consistent with a standard major merger picture, with the very high amount of rotation in this case indicative of a gas-rich merger with an uneven mass-ratio (og.⋅⋅"," The central bulge properties are generally consistent with a standard major merger picture, with the very high amount of rotation in this case indicative of a gas-rich merger with an uneven mass-ratio \citep[e.g.,][]{2005A&A...437...69B,2006MNRAS.372..839N}." +" Alternatively, the inner bulge might have formed via the inward migration of giant star forming clumps within a turbulent disk fed by cold streams from the cosmicweb at early epochs (e. al.||2009)).."," Alternatively, the inner bulge might have formed via the inward migration of giant star forming clumps within a turbulent disk fed by cold streams from the cosmicweb at early epochs \citep[e.g.,][]{1999ApJ...514...77N,2008ApJ...688...67E,2009ApJ...703..785D}. ." +" In either case, the exceptionally high inner-bulge rotation in NGC 3115 may require a residual thick disk component"," In either case, the exceptionally high inner-bulge rotation in NGC 3115 may require a residual thick disk component" +We used different methods for the ealeulation of the column density.,We used different methods for the calculation of the column density. +" In fact. for (he NU, (1.1) and (3-2) transitions the optical depth and the excitation temperature have been derived from the hyperline fitting whilst for the other lines these two crucial parameters cannot be derived. therefore we must assume the optical thin and LTE approximation."," In fact, for the (1-0), $_3$ (1,1) and (3-2) transitions the optical depth and the excitation temperature have been derived from the hyperfine fitting whilst for the other lines these two crucial parameters cannot be derived, therefore we must assume the optical thin and LTE approximation." +" For (1-0) and (3-2) the column density is given by the following formula (from Casellietal. (2002b))) valid lor optically thick transitions where Ar is the line width. ν is lrequeney of the observed transition. μι is the Einstein coellicient. g, are the statistical weight of the upper level. 7 is the optical depth.Zi, is the excitation temperature. Q is the partition function. £; is the energy of the lower level."," For (1-0) and (3-2) the column density is given by the following formula (from \cite{caselli02b}) ) valid for optically thick transitions where $\Delta v$ is the line width, $\nu$ is frequency of the observed transition, $A_{ul}$ is the Einstein coefficient, $g_u$ are the statistical weight of the upper level, $\tau$ is the optical depth,$T_{ex}$ is the excitation temperature, Q is the partition function, $E_l$ is the energy of the lower level." + In parüeular. for the NII; (1.1) line we used an approximated formula derived by (1987).. also valid for optically thin lines," In particular, for the $_3$ (1,1) line we used an approximated formula derived by \cite{bachiller87}, also valid for optically thin lines" +lue ratio and we discuss their implications.,line ratio and we discuss their implications. + Finally. we give a brief smunnuw in 5 5.," Finally, we give a brief summary in $\S$ 5." +" Wo assume the following ACDAM cosmology throughout the paper: | 1204, =0.3. and Q4=0.72007)."," We assume the following $\Lambda$ CDM cosmology throughout the paper: $H_0=70 \ $ $ \ $ $^{-1} \ $ $^{-1}$, $\Omega_M=0.3$, and $\Omega_\Lambda +=0.7$." +. Our sample is composed of 22 targets: 3 new spectra observed with VET-ISAAC (see Tab. 1)), Our sample is composed of 22 targets: 3 new spectra observed with VLT-ISAAC (see Tab. \ref{new_source}) ) + aud 19 sources from the literature (see Tab. 2)).," and 19 sources from the literature (see Tab. \ref{lit_spec}) )," + kindly provided by the respective authors., kindly provided by the respective authors. + Ten of the literature sourceshave redshift L50«τς5.702002).. while the remaining 9 have 5.70<2«6.12 and z-band maguitudes apo20.9 GQuagnitudes are taken from the discovery papers).," Ten of the literature sourceshave redshift $4.50 \,\sim$ 2.8 for 16 bursts by \citealp{jakobsson06}) )." +" The distributions of the BAT duration 75, both in the observer and vest frame are shown in Figure 1..", The distributions of the BAT duration $T_{90}$ both in the observer and rest frame are shown in Figure \ref{fig:t90}. + The mean value of Z5) in observers frame is 80.4 s. consistent with that deduced in a sample of 237 bursts bv Sakamotoetal.(2008).," The mean value of $T_{90}$ in observer's frame is 80.4 s, consistent with that deduced in a sample of 237 bursts by \citet{sakamoto08}." +. With the 150 measured redshifts in our sample. we find (hat (he mean value of Loy in the rest [rame is 29.2 s. Shorter bursts increase significantly in munber. but no positive classification can be made.," With the 150 measured redshifts in our sample, we find that the mean value of $T_{90}$ in the rest frame is 29.2 s. Shorter bursts increase significantly in number, but no positive classification can be made." +" Even so. as indicated in Figure 1.. there is an apparent oddball. GRBO50509B. which has an extremely short curation Z5,~0.04 s in the rest frame."," Even so, as indicated in Figure \ref{fig:t90}, there is an apparent oddball, GRB050509B, which has an extremely short duration $T_{90}\sim 0.04$ s in the rest frame." +" To view the overall behaviors of GRBs in their rest frame. we take advantage of theSwift Burst Analyser. which provides the combined DAT-XRT light curves in the form of Πας density F,,(77) at LO keV in the observers rest frame (Evansetal.2010)."," To view the overall behaviors of GRBs in their rest frame, we take advantage of the Burst Analyser, which provides the combined BAT-XRT light curves in the form of flux density $F_\nu(\nu)$ at 10 keV in the observer's rest frame \citep{evans10}." +. With the measured redshift z. the isotropic spectral luminosity al a given photon [frequency vy (which is 10 keV in this work) in the rest frame can be calculated by where νι.= m(l-4zi)is the emitted photon energy in the rest. frame for the observed photonenergv mj amd /= fg/(lo:)is the time measured in the rest. frame related (o (he time /j measured in the observers frame.," With the measured redshift $z$, the isotropic spectral luminosity at a given photon frequency $\nu_0$ (which is 10 keV in this work) in the rest frame can be calculated by where $\nu_e=\nu_0(1+z)$ is the emitted photon energy in the rest frame for the observed photonenergy $\nu_0$ and $t=t_0/(1+z)$ is the time measured in the rest frame related to the time $t_0$ measured in the observer's frame." +" Here. a single power-law spectrum has been assumed F(t)xpl1HU, where P(/) is the time-dependent photon index. which is available bv the Burst Analyser (Evansetal.2010)."," Here, a single power-law spectrum has been assumed $F_\nu(\nu,t)\propto\nu^{1-\Gamma(t)}$, where $\Gamma(t)$ is the time-dependent photon index, which is available by the Burst Analyser \citep{evans10}." +". Throughout this work. the luminosity distance Dj(2) is caleulated by assuming the cosmological parameters 44,=7lkims!Mpe. t. Oy,=0.27. and O4=0.73."," Throughout this work, the luminosity distance $D_{\rm L}(z)$ is calculated by assuming the cosmological parameters $H_0=71\,{\rm km}\, {\rm s}^{-1}\, {\rm Mpc}^{-1}$ , $\Omega_M=0.27$, and $\Omega_\Lambda=0.73$." + According to the error propagation rule. the uncertainty in (he isolropic spectral luminosity can be given by where σι: and gp are the uncertainties in (he measured fIux density and photon index. respectively. and the uncertainty in GRB redshift measurements is considered negligible.," According to the error propagation rule, the uncertainty in the isotropic spectral luminosity can be given by where $\sigma_{F_\nu}$ and $\sigma_\Gamma$ are the uncertainties in the measured flux density and photon index, respectively, and the uncertainty in GRB redshift measurements is considered negligible." + In Figure 2.. the calculated. X-ray light curves from 0.01 s to 10* s after BAT trigger al 10 keV in the rest frame with the spectral evolution of 150 GRBs are plotted together.," In Figure \ref{fig:restframelc}, the calculated X-ray light curves from 0.01 s to $10^7$ s after BAT trigger at 10 keV in the rest frame with the spectral evolution of 150 GRBs are plotted together." + Interestingly. some underlyingglobal features are revealed in both the light curves," Interestingly, some underlyingglobal features are revealed in both the light curves" +"black hole would accrete al a rate corresponding to a higher effective ambient temperature ol a stationary black hole such that: where{τους is (he actual ambient temperature and 77,,,—0 is Lhe ambient temperature (and corresponding sound speed) (that woulcl give (he proper accretion rate in the calculations of Park&Ricotti(2011). lor stationary black holes.","black hole would accrete at a rate corresponding to a higher effective ambient temperature of a stationary black hole such that: where$T_{ism,v>0}$ is the actual ambient temperature and $T_{ism,v=0}$ is the ambient temperature (and corresponding sound speed) that would give the proper accretion rate in the calculations of \citet{PR11} for stationary black holes." +" I. for a given. ambient temperature. the accretion rate for a moving black hole corresponds to accretion al effectively a higher ambient temperature for a stationary black hole. then the values of the radiative feedback parameter derived by Park&Ricotti(2011) for a given ambient temperature must also be scaled to that same. higher effective temperature or. from Equation 15:: where _0$ is the radiative feedback efficiency parameter for the same value of $T_{ism}$, but for a stationary black hole from \cite{PR11}." +". We can thus write for a black hole moving with a velocitv. v: The results of (Park&Ricotti2011) for a given ambient temperature are thus equivalent (o those of a somewhat higher ""effec(ive ambient temperature for a moving black hole."," We can thus write for a black hole moving with a velocity, v: The results of \citep{PR11} for a given ambient temperature are thus equivalent to those of a somewhat higher “effective"" ambient temperature for a moving black hole." + This correctionfactor is quantitatively important. but not qualitatively important for eSe.," This correctionfactor is quantitatively important, but not qualitatively important for $v \lesssim c_{s}$." + The steep dependence on this [actor may become significant if the black holes move supersonically through the ambient medium., The steep dependence on this factor may become significant if the black holes move supersonically through the ambient medium. + With Equations 10.. 18.. 13. and 14. we can write: where the factor. F. is: Or," With Equations \ref{bondi}, \ref{mdot1}, , \ref{rad1} and \ref{rad2}, , we can write: where the factor, F, is: or" +"void volume function of the L model more or less catches up those in the N models, as is evident in the upper left panel of Fig. 2..","void volume function of the L model more or less catches up those in the N models, as is evident in the upper left panel of Fig. \ref{vvf}." +" We also note that at a—1.0 there are less small voids in the N4 model than in the L and other N models, which is likely because of the fact that small voids have been used up to merge to form bigger ones."," We also note that at $a=1.0$ there are less small voids in the N4 model than in the L and other N models, which is likely because of the fact that small voids have been used up to merge to form bigger ones." +" For the C models, the suppress of the fifth force means that the clustering of matter and growth of voids are less affected by it*."," For the C models, the suppress of the fifth force means that the clustering of matter and growth of voids are less affected by it." +". This is easily seen in the a=0.5 case (Fig. 2,,"," This is easily seen in the $a=0.5$ case (Fig. \ref{vvf}," +" lower right panel), which shows that the void volume functions for the C models do not deviate much from that for the L model (one might appreciate the effect of the suppress in the fifth force by considering that the ratio between the magnitudes of fifth force and gravity is 24? if the former is not suppressed, and y~O(0.1) for N models while y~O(1) for C models)."," lower right panel), which shows that the void volume functions for the C models do not deviate much from that for the L model (one might appreciate the effect of the suppress in the fifth force by considering that the ratio between the magnitudes of fifth force and gravity is $2\gamma^2$ if the former is not suppressed, and $\gamma\sim\mathcal{O}(0.1)$ for N models while $\gamma\sim\mathcal{O}(1)$ for C models)." +" We could also have an examination of the void filling factor, defined as the fraction of total space that is filled by voids which are either bigger or smaller than V."," We could also have an examination of the void filling factor, defined as the fraction of total space that is filled by voids which are either bigger or smaller than $V$." +" Because our algorithm leaves the very small voids undetected, we choose to show the former, and the results are given in Fig. 3.."," Because our algorithm leaves the very small voids undetected, we choose to show the former, and the results are given in Fig. \ref{ff}." + It turns out that this plot shows more clearly the effects of the scalar coupling., It turns out that this plot shows more clearly the effects of the scalar coupling. +" As our first example, for the L model at a=0.5 (Fig. 3,,"," As our first example, for the L model at $a=0.5$ (Fig. \ref{ff}," +" lower left panel), we notice that only of the total space is filled by voids larger than 35)ὃ Mpc’, in contrast to more than and for the models N3 and N4 respectively."," lower left panel), we notice that only of the total space is filled by voids larger than $35h^{-3}$ $^3$, in contrast to more than and for the models N3 and N4 respectively." +" At a=1.0, as a result of void growth and mergers, the numbers for these three models are changed to25%,, and respectively."," At $a=1.0$, as a result of void growth and mergers, the numbers for these three models are changed to, and respectively." +" In both cases, the scalar field coupling dramatically changes the total volume of void"," In both cases, the scalar field coupling dramatically changes the total volume of void" +that the PCI chip with its strong backeround light gradient was the only area where | was a significant function of radius: on the WE chips a single function. (11) could be used.,that the PC1 chip with its strong background light gradient was the only area where $f$ was a significant function of radius; on the WF chips a single function $f(m)$ could be used. + The instrumental magnitudes were converted to (he Johnson-Cousins J svstem with the stancard transformations for ΕΣΕΤ found in Holtzmanetal.(1995)., The instrumental magnitudes were converted to the Johnson-Cousins $I$ system with the standard transformations for $F814W$ found in \citet{Hol95}. +". For the four individual BCGs. Galactic exlinclion corrections of A,= 0.16. 0.10. 0.11 and 0.06 respectively have been adopted (.1, is given by A,=1.532Byy. where the Eg\ values are obtained Dor each ealaxv [rom NASA/IPAC Extragalactie Database (NED))."," For the four individual BCGs, Galactic extinction corrections of $A_I =\;$ 0.16, 0.10, 0.11 and 0.06 respectively have been adopted $A_I$ is given by $A_I=1.82 \; E_{B-V}$, where the $E_{B-V}$ values are obtained for each galaxy from NASA/IPAC Extragalactic Database (NED))." + To emplov the transformation equations and also to step back and forth between { and the (more normally used) V magnitude scale for globular clusters. we have simply assumed a color index of 1.10.1. typical of moderately metal-rich globular clusters in giant E galaxies (e.g. (1999))).," To employ the transformation equations and also to step back and forth between $I$ and the (more normally used) $V$ magnitude scale for globular clusters, we have simply assumed a color index of $(V-I)_0 = 1.1 \pm 0.1$ , typical of moderately metal-rich globular clusters in giant E galaxies (e.g. \citet{Kun99}) )." + The intrinsic range in (V.— Z)s. folded through the trausformation equations. will not introduce uncertainties larger than £0.03 in the calibration of J.," The intrinsic range in $(V-I)_0$ , folded through the transformation equations, will not introduce uncertainties larger than $\pm 0.03$ in the calibration of $I$." + The assumed (V—η value is (he mean value representative of most other gE galaxies. ancl if the GCSs were entirely metal-rich or metal-poor. (he error introduced by (he assumption would be at most 0.1 mae.," The assumed $(V-I)_0$ value is the mean value representative of most other gE galaxies, and if the GCSs were entirely metal-rich or metal-poor, the error introduced by the assumption would be at most 0.1 mag." + The projected number density σ of detected objects around each galaxy plainly reveals an extensive GCS concentrated around (he galaxy center in each case., The projected number density $\sigma$ of detected objects around each galaxy plainly reveals an extensive GCS concentrated around the galaxy center in each case. + The profile is reasonably well represented by a simple power-law form o(r)=eut(r)+OngephTig. Where σε 1s the background number density of starlike objects (mostly faint. small galaxies which passed through the image classification routines. plus a few foreground Galactic stus).," The profile is reasonably well represented by a simple power-law form $ \sigma(r) = \sigma_{cl}(r) + \sigma_{bg} = a +\;r^b + \sigma_{bg} $, where $\sigma_{bg}$ is the background number density of starlike objects (mostly faint, small galaxies which passed through the image classification routines, plus a few foreground Galactic stars)." + To obtain the profile parameters of the GCS for each galaxy. we subdivided the WEDPC? fields into annuli 50 pixels wide. centered on the DCGs.," To obtain the profile parameters of the GCS for each galaxy, we subdivided the WFPC2 fields into annuli 50 pixels wide, centered on the BCGs." + The number densitv of objects was then calculated down to a cutoff magnitude at which incompleteness corrections were still small., The number density of objects was then calculated down to a cutoff magnitude at which incompleteness corrections were still small. + The projected number density is then just &.=N/A. where N is the number of detected objects within each annulus and ο is the area of that annulus which falls within the ΝΕΟΣ boundaries (minus (he small masked-out areas).," The projected number density is then just $\sigma = N/A$, where $N$ is the number of detected objects within each annulus and $A$ is the area of that annulus which falls within the WFPC2 boundaries (minus the small masked-out areas)." + Completeness corrections. (hough small. were explicitly accounted for.," Completeness corrections, though small, were explicitly accounted for." +" Finally. the background density 05, on each of the four fields was delined as the mean of the outermost eight annuli. which fall on the outskirts of the WF chips."," Finally, the background density $\sigma_{bg}$ on each of the four fields was defined as the mean of the outermost eight annuli, which fall on the outskirts of the WF chips." +" This corresponds to a radial distance greater than 105"" (or about 30 kpe) from the centers of the DCGs.", This corresponds to a radial distance greater than $105''$ (or about 30 kpc) from the centers of the BCGs. + Although the GCSs probably extend at trace amounts farther out than this boundary. the directly observed o(r) curves (Figure 1)) have plainlyalmost leveled off there. indicating that we are already including the main portion of the GCS.," Although the GCSs probably extend at trace amounts farther out than this boundary, the directly observed $\sigma(r)$ curves (Figure \ref{rad_plot}) ) have plainlyalmost leveled off there, indicating that we are already including the main portion of the GCS." +The estimates of £45. Dy; and mi obtained in equations (4). (5) for the shell model are valid in (his case as well. (,"The estimates of $R_{15}$ , $D_{15}$ and $n_{15}$ obtained in equations (4), (5) for the shell model are valid in this case as well. (" +Recall that ej; refers to the projected radius of the emitüng region. and that 7 refers to the optical depth parallel to the line of sieht. not perpendicular to the inclined. funnel surface.),"Recall that $R_{15}$ refers to the projected radius of the emitting region, and that $\tau$ refers to the optical depth parallel to the line of sight, not perpendicular to the inclined funnel surface.)" + In this model there is no longer any clilficeult with having a very small value of d/D., In this model there is no longer any difficult with having a very small value of $d/D$. + The ionizing photons trom the GRB impinge on the inner surface of the funnel aud (he line photons are also emitted from (he same surface., The ionizing photons from the GRB impinge on the inner surface of the funnel and the line photons are also emitted from the same surface. + Thus. the radiating region can be an arbitrarily thin laver (unlike in the case of the shell model).," Thus, the radiating region can be an arbitrarily thin layer (unlike in the case of the shell model)." + There is. however. a problem with the amount of mass required in the model.," There is, however, a problem with the amount of mass required in the model." + Let us assume (hat (he funnel is carved oul of a roughly quasi-spherical external medium (11651 probably the supernova ejecta)., Let us assume that the funnel is carved out of a roughly quasi-spherical external medium (most probably the supernova ejecta). + Given (he electron densitv. à». ancl the radius of the sphere D. we estimate the external mass to be For 8H~1. the mass is unacceptable large.," Given the electron density $n_e$ and the radius of the sphere $D$, we estimate the external mass to be For $\theta_{-1}\sim1$, the mass is unacceptable large." +oS Even if we take ϐH~10. 1.e.. no beamineg.5 ihe mass is still much too large.," Even if we take $\theta_{-1}\sim10$, i.e., no beaming, the mass is still much too large." +5 As in the case of the shell model. we do not have much freedom in choosing the other parameters.," As in the case of the shell model, we do not have much freedom in choosing the other parameters." + One wav lo decrease the mass requirement in the funnel model is to enhance (he density in the funnel wall relative to (he rest of the ejecta., One way to decrease the mass requirement in the funnel model is to enhance the density in the funnel wall relative to the rest of the ejecta. + For example. one could imagine that initiallv there was no funnel. and (hat it was the GRB itself that pushed the material aside to form the Tunnel.," For example, one could imagine that initially there was no funnel, and that it was the GRB itself that pushed the material aside to form the funnel." + It is conceivable that the material pushed aside could have piled up on the walls. giving an enhanced density there.," It is conceivable that the material pushed aside could have piled up on the walls, giving an enhanced density there." + It is not clear that this mechanism can produce the orders of magnitude density enhancement needed (o reduce (he mass estimate to a reasonable value.Model:, It is not clear that this mechanism can produce the orders of magnitude density enhancement needed to reduce the mass estimate to a reasonable value.: + In this model. the photoionization occurs indirectly.," In this model, the photoionization occurs indirectly." + Photons from the GRB travel out to a screen. are scattered. and then irradiate the eas. which is located in the surface lavers of (he supernova ejecta.," Photons from the GRB travel out to a screen, are scattered, and then irradiate the line-emitting gas, which is located in the surface layers of the supernova ejecta." + Because the eeomelry is very cdillerent [rom (he previous(wo moclels. there are (wo important changes.," Because the geometry is very different from the previoustwo models, there are two important changes." + First. the time delay of 104 s between the GRB and the line emission measures (he distance io the scattering screen (>10!! em) but not the size of the line-emitting ejecta.," First, the time delay of $10^4$ s between the GRB and the line emission measures the distance to the scattering screen $> 10^{14}$ cm) but not the size of the line-emitting ejecta." + Therefore. (he estimates given in equation (4) are not valid.," Therefore, the estimates given in equation (4) are not valid." +" Instead. if we assume Chat the ejecta have expanded αἱ speed O.le3.4 for 1047...) s. we estimate that R~Dc1077/1,413,4 em."," Instead, if we assume that the ejecta have expanded at speed $0.1c\beta_{*,-1}$ for $10^4\txg$ s, we estimate that $R\sim +D\sim 10^{13.5}\txg\beta_{*,-1}$ cm." +" Second. the irradiation occurs for a (ime ~10,4; s ratherthan 107 s. and so we expect lo~ 10011."," Second, the irradiation occurs for a time $\sim10^4\txg$ s ratherthan $10^2$ s, and so we expect $t_2\sim100\txg$ ." + Both changes help to ease some of the constraints., Both changes help to ease some of the constraints. +Galactic plane as measured with extragalactic radio sources is where 1607 7 £10 per cent rans.,"Galactic plane as measured with extragalactic radio sources is where =1607 $^{-2}$ $\pm$ 10 per cent r.m.s.," + 462.17 (Cleggοἱal.1986)., $^\circ$ \citep{clegg92}. +.. WT5N is al the galactic longitude 81.97. and [rom (7) one has A544 7.," W75N is at the galactic longitude $^\circ$, and from (7) one has =–544 $^{-2}$." + At the OIL frequency (A=I8 em) the Faraday rotation is x(0.13)?— 17.6 radizc5.4 rad if one assumes maximum uncertainty 30 per cent., At the OH frequency $\lambda=18$ cm) the Faraday rotation is $\times$ $^2$ =– 17.6 $\pm$ 5.4 rad if one assumes maximum uncertainty 30 per cent. + This is the total Faraday rotation throughout the ealactic disk: W75N is at (he distance of 2 kpe. which is probably about a half of the total effective cistance. and the Faraday rotation to W75N can be a [actor of 2 lower. or 9 racdzE2.7 rad.," This is the total Faraday rotation throughout the galactic disk; W75N is at the distance of 2 kpc, which is probably about a half of the total effective distance, and the Faraday rotation to W75N can be a factor of 2 lower, or –9 $\pm$ 2.7 rad." + This is a large rotation. about 3 full turns. and a correction for the Faraday rotation to the position angle of the linear polarization could be quite uncertain.," This is a large rotation, about 3 full turns, and a correction for the Faraday rotation to the position angle of the linear polarization could be quite uncertain." + Therefore il is not posible to determine the direction of (he magnetic field in OIL maser spots., Therefore it is not posible to determine the direction of the magnetic field in OH maser spots. +" Physical parameters of the maser spots can be estimated [rom maser models. which require gas density nj,-10'cm 7. kinetic temperature LOO IX. dust. temperature. 150. Is. and OL abundance 10? (GrayandField1995)."," Physical parameters of the maser spots can be estimated from maser models, which require gas density $_{H_2}$ $^7$ $^{-3}$, kinetic temperature 100 K, dust temperature 150 K, and OH abundance $^{-5}$ \citep*{gray95}." +. Such parameters can provide inversion of 1665 MlIz OII transition in a model with FIR line overlap and a velocity gradient of about 0.025 ΑΙ. (CravanclField 1995).., Such parameters can provide inversion of 1665 MHz OH transition in a model with FIR line overlap and a velocity gradient of about 0.025 $^{-1}$ /A.U. \citep*{gray95}. . + With the magnetic field strength of 10 miligauss the model of GravandField(1995) provides 100 per cent elliptically polarized c components. wilh 7 components suppressed. in agreement wilh results of this paper for W75N. The size of maser spots LO A.U. and molecular hydrogen density 10*em. ? correspond to the mass of maser spots of 2x10. ‘AL.. which is less than the mass of the Earth.," With the magnetic field strength of 10 milligauss the model of \citet*{gray95} provides 100 per cent elliptically polarized $\sigma$ –components, with $\pi$ –components suppressed, in agreement with results of this paper for W75N. The size of maser spots 10 A.U. and molecular hydrogen density $^7$ $^{-3}$ correspond to the mass of maser spots of $\times10^{-7}$ $_{\odot}$, which is less than the mass of the Earth." + If the maser spots are discrete physical objects dense cold gas condensations surrounded a low density medium — thev should be confined by the external pressure., If the maser spots are discrete physical objects – dense cold gas condensations surrounded a low density medium – they should be confined by the external pressure. + A gas condensation with the density L0'em* and temperature LOO IX. can be in pressure equilibrium with the gas of density 10?em.* and temperature 107 IX. Llowever. the magnetic pressure in the maser spots. with the magnetic field strength of 10 milligauss. is an order of magnitude higher. ancl can be compensated by (πριΙου or ram pressure of the hot medium (see discussion in a paper by Reidetal. (1987))).," A gas condensation with the density $^{7}$ $^{-3}$ and temperature 100 K can be in pressure equilibrium with the gas of density $^{5}$ $^{-3}$ and temperature $^4$ K. However, the magnetic pressure in the maser spots, with the magnetic field strength of 10 milligauss, is an order of magnitude higher, and can be compensated by turbulent or ram pressure of the hot medium (see discussion in a paper by \citet{reid87}) )." + Another model of maser spots proposed for Class II methanol masers (Slvshetal.1999). assumed (hat the maser spots are extended gaseous envelopes of solid icv planets orbiting around O. B-stars. outside their HII regions.," Another model of maser spots proposed for Class II methanol masers \citep{slysh99} assumed that the maser spots are extended gaseous envelopes of solid icy planets orbiting around O, B-stars, outside their HII regions." + OL molecules as well as methanol molecules are continuosly. supplied to the envelope by evaporation of ice from the surface of the planets., OH molecules as well as methanol molecules are continuosly supplied to the envelope by evaporation of ice from the surface of the planets. + In W75N the ultracompact III region VLAI (Fig., In W75N the ultracompact HII region VLA1 (Fig. + 5) marks the position of the central star with luminosity 14x 10°L. (Mooreetal.1991). which corresponds to the main sequence O9.star with mass 20M..., 5) marks the position of the central star with luminosity $\times10^{5}$ $_{\odot}$ \citep{moore91} which corresponds to the main sequence O9–star with mass $_{\odot}$. + The largest distance from VLAÀI to a maser spot is about 1000 mas. or 2000 astronomical units.," The largest distance from VLA1 to a maser spot is about 1000 mas, or 2000 astronomical units." + Atthis distance from a 20M. star the orbital velocity is 3 | which is consistent with the observed. velocity range of maser, Atthis distance from a $_{\odot}$ star the orbital velocity is 3 $^{-1}$ which is consistent with the observed velocity range of maser +cannot be excluded.,cannot be excluded. + The above described observations and further follow-up observations will be used to derive a coherent timing solution for PSR J1952+2630., The above described observations and further follow-up observations will be used to derive a coherent timing solution for PSR J1952+2630. + This will provide a more precisely measured sky position. orbital parameters. and values for the orbital eccentricity and the intrinsic spin-down of the pulsar.," This will provide a more precisely measured sky position, orbital parameters, and values for the orbital eccentricity and the intrinsic spin-down of the pulsar." + This should enable a detailed description of this binary system and constrain its possible formation., This should enable a detailed description of this binary system and constrain its possible formation. + A precise position would also enable searches for counterparts in X-ray. infrared. and optical wavelengths. although the large distance makes detections challenging.," A precise position would also enable searches for counterparts in X-ray, infrared, and optical wavelengths, although the large distance makes detections challenging." + Furthermore. detection of Shapiro delay could be possible with further timing observations for high orbital inclinations.," Furthermore, detection of Shapiro delay could be possible with further timing observations for high orbital inclinations." + Given the already high minimum companion mass derived in this Letter. even a non-detection of the Shapiro delay could provide interesting. more stringent limits on the companion mass and its nature.," Given the already high minimum companion mass derived in this Letter, even a non-detection of the Shapiro delay could provide interesting, more stringent limits on the companion mass and its nature." + This pulsar is the second pulsar discovered by the global distributed volunteer computing project Einstein?Home (?).., This pulsar is the second pulsar discovered by the global distributed volunteer computing project EinsteinHome \citep{2010Sci...329.1305K}. + This further demonstrates the value of volunteer computing for discoveries 1n astronomy and other data-driven science., This further demonstrates the value of volunteer computing for discoveries in astronomy and other data-driven science. + We thank the Einstein@Home volunteers. who made this discovery possible.," We thank the EinsteinHome volunteers, who made this discovery possible." + The Einstein?Home users whose computers detected the pulsar with the highest significance are VVitaliy. Shiryaev (Moscow. Russia) and Stacey Eastham (Darwen. UK).," The EinsteinHome users whose computers detected the pulsar with the highest significance are Vitaliy Shiryaev (Moscow, Russia) and Stacey Eastham (Darwen, UK)." + This work was supported by CFI. CIFAR. FORNT. MPG. NAIC. NRAO. NSERC. NSF. NWO. and STFC.," This work was supported by CFI, CIFAR, FQRNT, MPG, NAIC, NRAO, NSERC, NSF, NWO, and STFC." + Arecibo is operated by the National Astronomy and lonosphere Center under a cooperative agreement with the NSF., Arecibo is operated by the National Astronomy and Ionosphere Center under a cooperative agreement with the NSF. + This work was supported by NSF grant AST 0807151 to Cornell University., This work was supported by NSF grant AST 0807151 to Cornell University. + Pulsar research at UBC ts supported by an NSERC Discovery Grant and by the CFI., Pulsar research at UBC is supported by an NSERC Discovery Grant and by the CFI. + UWM and U. C. Berkeley acknowledge support by NSF grant 0555655., UWM and U. C. Berkeley acknowledge support by NSF grant 0555655. + ggratefully acknowledges the support of the Max Planck Society., gratefully acknowledges the support of the Max Planck Society. + acknowledges support from NSF grant AST-0806942., acknowledges support from NSF grant AST-0806942. +(see Dhattacharva&vandenHeuvel 1991 [or a review).,(see \citeauthor{bha91} 1991 for a review). + The mechanism for this remains unclear. wilh suggestions including decay of crustal fields due to heating (Blonclin&Freese 1986).. burial of the field (Disnovatvi-Ikogan&Ixomberg1974:Romani1990.1993). and decay of core fields due to flux tube expulsion from the superfhiud interior (Srinivasanetal. 1990))).," The mechanism for this remains unclear, with suggestions including decay of crustal fields due to heating \citep{blo86}, burial of the field \citep{bis74,rom90,rom93} and decay of core fields due to flux tube expulsion from the superfluid interior \citep{sri90}) )." + Ikonar&Bhattacharva(1997). suggested that rapid ohmic decay in the accretion heated crust occurs., \cite{kon97} suggested that rapid ohmic decay in the accretion heated crust occurs. + On the one hand. the heating reduces the electrical conductivity ancl consequently the ohimic decay (me-scale induces a faster decay of the field.," On the one hand, the heating reduces the electrical conductivity and consequently the ohmic decay time-scale induces a faster decay of the field." + Ou the other hand. the deposition of matter on top of the crust pushes the original current carrving lavers into deeper aud denser regions where (he higher conductivity slows down the decay (Ixonar&Bhattacharva1997).," On the other hand, the deposition of matter on top of the crust pushes the original current carrying layers into deeper and denser regions where the higher conductivity slows down the decay \citep{kon97}." +. In a class of reeveling models in which the magnetic field decrease is a finction only of the amount aecreted onto the neutron star. it was shown that no model of this class is consistent wilh all available data (Wijers1997).," In a class of recycling models in which the magnetic field decrease is a function only of the amount accreted onto the neutron star, it was shown that no model of this class is consistent with all available data \citep{wij97}." +. The detection of coherent X-ray pulsations with a millisecond period in a handful of LMXBDs (Lamb&Yu2005). is often used in support of the idea of accretion-induced [field decay (Wijnands&vanderIxlis1993)., The detection of coherent X-ray pulsations with a millisecond period in a handful of LMXBs \citep{lam05} is often used in support of the idea of accretion-induced field decay \citep{wij98}. +. However. whether this is evidence simply [or field submersion and spin-up during the accretion disk phase. or for field decay ancl spin-up. remains {ο be established (Ferrario&Wickramasinghe2007).," However, whether this is evidence simply for field submersion and spin-up during the accretion disk phase, or for field decay and spin-up, remains to be established \citep{fer07}." +. We conclude Irom the above. that it is not clear if low field ~105 G field MSPs can be produced in LMXDs.," We conclude from the above, that it is not clear if low field $\sim 10^{8}$ G field MSPs can be produced in LMXBs." + We pointed out that the field could simply be submerged by (he accreted matter and would then re-emeree later on when accretion stops., We pointed out that the field could simply be submerged by the accreted matter and would then re-emerge later on when accretion stops. + Zhangetal.(2009) show that there is no evidence for field restructuring and/or decay in accreting magnetic white dwarls., \cite{zha09} show that there is no evidence for field restructuring and/or decay in accreting magnetic white dwarfs. + This fact was already. known for the isolated magnetic white cwarls., This fact was already known for the isolated magnetic white dwarfs. + As far as we know. this could apply also to neutron stars.," As far as we know, this could apply also to neutron stars." +ionizing background.,ionizing background. + In $3 and $4. we present the PDFs and power spectra of various UVBs. respectively.," In \ref{sec:PDF} and \ref{sec:ps} we present the PDFs and power spectra of various UVBs, respectively." + In $5.. we study the impact of a spatially varying UVB on the Lya forest.," In \ref{sec:forest}, we study the impact of a spatially varying UVB on the $\alpha$ forest." + Finally. in $6... we summarize our findings and offer conclusions.," Finally, in \ref{sec:conc}, we summarize our findings and offer conclusions." +" We quote all quantities in comoving units. with the exception of flux. and we denote proper units with a prefix ""p."," We quote all quantities in comoving units, with the exception of flux, and we denote proper units with a prefix 'p'." + We adopt the background cosmological parameters (OQ. O1. Qn. n. as. Ho = (0.72. 0.28. 0.046. 0.96. 0.82. 70 km + . matching the five-year results of the satellite (22).," We adopt the background cosmological parameters $\Omega_\Lambda$, $\Omega_{\rm M}$, $\Omega_b$, $n$, $\sigma_8$ , $H_0$ ) = (0.72, 0.28, 0.046, 0.96, 0.82, 70 km $^{-1}$ $^{-1}$ ), matching the five–year results of the satellite \citep{Dunkley08, Komatsu08}." + We generate our ionizing flux fields following the procedure described in ?.., We generate our ionizing flux fields following the procedure described in \citet{MD08}. + We briefly outline the procedure below., We briefly outline the procedure below. + We begin with halo fields at >=5 and 2=6 generated with the semi-numerical simulationDexM?*.. which has been shown to reproduce the correet number density and clustering properties of halos well into the quasi-linear and non-linear regimes (?:: Fig.," We begin with halo fields at $z=5$ and $z=6$ generated with the semi-numerical simulation, which has been shown to reproduce the correct number density and clustering properties of halos well into the quasi-linear and non-linear regimes \citealt{MF07}; Fig." + | in 2: Mesinger et al., 1 in \citealt{Dijkstra08}; Mesinger et al. + in preparation)., in preparation). + Our simulation boxes are 150Mpe on a side. with a 150/1800 Mpe halo grid cell size.," Our simulation boxes are 150Mpc on a side, with a 150/1800 Mpc halo grid cell size." + The velocity fields used to perturb the halo field were generated on a lower resolution 900% erid: thus our final halo field resolution is Ar= 150/900 = 0.17 Mpc., The velocity fields used to perturb the halo field were generated on a lower resolution $^3$ grid; thus our final halo field resolution is $\Delta x =$ 150/900 = 0.17 Mpc. + For each halo field. we create a corresponding UV flux field on a 150° erid (spatial resolution of | Mpc). by performing a halo mass/r7 weighted sum.," For each halo field, we create a corresponding UV flux field on a $^3$ grid (spatial resolution of 1 Mpc), by performing a halo $r^2$ weighted sum." + Specitically. we compute the flux of ionizing photons (in units of ionizing photons s.+ 7) with where x is the location of the cell of interest. AJ; is the total halo miss. xj is its location. and the factorof (1|z)? converts the factor [x xi[ from comoving into properunits.," Specifically, we compute the flux of ionizing photons (in units of ionizing photons $^{-1}$ $^{-2}$ ) with where ${\bf x}$ is the location of the cell of interest, $M_i$ is the total halo mass, ${\bf x_i}$ is its location, and the factor of $(1+z)^2$ converts the factor $|{\bf x} - {\bf x_i}|^2$ from comoving into properunits." + We also include a duty parameter through the random variable .[N;(D€). which has a value of | with likelihood DC or O with likelihood 1.DC.," We also include a duty parameter through the random variable $X_i(\DC)$, which has a value of 1 with likelihood $\DC$ or 0 with likelihood $1-\DC$." +" Finally. the factor ej, in eg. CL) "," Finally, the factor $\epsilon_{\rm ion}$ in eq. \ref{eq:sum}) )" +denotes the rate at which ionizing photons are released into the IGM by a dark matter halo per unit mass., denotes the rate at which ionizing photons are released into the IGM by a dark matter halo per unit mass. + Unless stated otherwise. we assume a fiducial value of Gaz)2A385107/DCEOulul|M.petias which provides a good fit to the observed luminosity functions of Lya emitting galaxies (LAEs) (22222)... and the .=6 Lyman Break galaxies (LBGs) (?)..," Unless stated otherwise, we assume a fiducial value of $\epsilon_{\rm ion}(z) = 3.8 \times 10^{58}/\DC \left[\frac{\Omega_b}{\Omega_{\rm M}} \frac{1}{t_H(z)}\right]\hs\frac{{\rm photons}}{M_{\odot}\hs {\rm s}}.$, which provides a good fit to the observed luminosity functions of $\alpha$ emitting galaxies (LAEs) \citep{Shimasaku06, Kashikawa06, DWH07, SLE07, McQuinn07LAE}, and the $z=6$ Lyman Break galaxies (LBGs) \citep{Bouwens06}." + However. as we are mostly concerned with the shape of the flux PDF. where applicable we present results in units of the mean flux or intensity. J/0./5.," However, as we are mostly concerned with the shape of the flux PDF, where applicable we present results in units of the mean flux or intensity, $J/\langle J\rangle$." + In constructing the UVB. we also assume a minimum halo mass able to host stars. A4. and explore mainly two different values for this parameter: 1.6.5107 and 1.4.10° AZ...," In constructing the UVB, we also assume a minimum halo mass able to host stars, $\Mmin$, and explore mainly two different values for this parameter: $1.6\times10^8$ and $1.4\times10^9$ $\Msun$." + The former value corresponds to a virial temperature of 10 K at these redshifts. and represents the regime of ineffective feedback on atomically cooled halos during reionization (22)..," The former value corresponds to a virial temperature of $^4$ K at these redshifts, and represents the regime of ineffective feedback on atomically cooled halos during reionization \citep{MD08, OGT08}." + The later value represents the regime of very inefficient star formation inside such small halos. perhaps due to strong radiative and/or mechanical feedback (e.g. 2??? ," The later value represents the regime of very inefficient star formation inside such small halos, perhaps due to strong radiative and/or mechanical feedback (e.g. \citealt{Yepes97, Scannapieco06, PS08}) )." +"The exact value of the higher Mi, was also motivated by the fact that the number density of halos with mass greater than 14.10° AZ. is roughly ten times smaller than the number density of halos with masses greater than 1.6«107 AZ. at 2=5. thus allowing us to compare results at fixed source number density with values of DC= 1.0 and 0.1 in the two models. respectively."," The exact value of the higher $\Mmin$ was also motivated by the fact that the number density of halos with mass greater than $1.4\times10^9$ $\Msun$ is roughly ten times smaller than the number density of halos with masses greater than $1.6\times10^8$ $\Msun$ at $z\approx5$, thus allowing us to compare results at fixed source number density with values of $\DC=$ 1.0 and 0.1 in the two models, respectively." + Additionally. we generate a flux Ποιά corresponding to the >=5.71 source field from the cosmological hydrodynamical simulation presented in?) (their +=6 reionization model).," Additionally, we generate a flux field corresponding to the $z=5.71$ source field from the cosmological hydrodynamical simulation presented in \citet{TCL08} (their $z=6$ reionization model)." + This simulation is fixed-grid. 143 Mpe on a side. and includes wescriptions for modeling dark matter. baryons and ionizing shotons (for details see ? and 2).," This simulation is fixed-grid, 143 Mpc on a side, and includes prescriptions for modeling dark matter, baryons and ionizing photons (for details see \citealt{TC07} and \citealt{TCL08}) )." + The density field was calculated on grid of 0.19 Mpe cells. which resolves the Jeans length in he mean density. ionized intergalactic medium (IGM) by a factor of few. and then smoothed to a cell size of 0.74 Mpe.," The density field was calculated on grid of 0.19 Mpc cells, which resolves the Jeans length in the mean density, ionized intergalactic medium (IGM) by a factor of few, and then smoothed to a cell size of 0.74 Mpc." + Each wlo’s instantaneous star-formation rate (SFR) is proportional to the instantaneous gas accretion rate. and enters our eq. CL) ," Each halo's instantaneous star-formation rate (SFR) is proportional to the instantaneous gas accretion rate, and enters our eq. \ref{eq:sum}) )" +in place of ye halo's mass. AZ;. with the normalization adjusted accordingly so as to match the mean value of the UVB.," in place of the halo's mass, $M_i$, with the normalization adjusted accordingly so as to match the mean value of the UVB." + We make use of this flux field. combined with the +=5.71 gas density fields from 18 hydro-simulation. to generate more accurate mean Lya forest flux decrement statistics in S5...," We make use of this flux field, combined with the $z=5.71$ gas density fields from the hydro-simulation, to generate more accurate mean $\alpha$ forest flux decrement statistics in \ref{sec:forest}." + At these redshifts and scales. our semi-numerically generated density fields somewhat over-predict ye rare voids which dominate the this statistic (Mesinger et al..," At these redshifts and scales, our semi-numerically generated density fields somewhat over-predict the rare voids which dominate the this statistic (Mesinger et al.," + in preparation)., in preparation). + Furthermore. the ray-tracing algorithm from the numerical simulation over-predicts the fluctuations in the flux field. due to an insufficient number of ray splittings (Trac 2008. private communication).," Furthermore, the ray-tracing algorithm from the numerical simulation over-predicts the fluctuations in the flux field, due to an insufficient number of ray splittings (Trac 2008, private communication)." + This problem only becomes severe following reionization. but since this is the epoch westudy here. we use this aybrid preseription in some of the results below (i.e. we do not use he radiative transfer field from the simulation).," This problem only becomes severe following reionization, but since this is the epoch westudy here, we use this hybrid prescription in some of the results below (i.e. we do not use the radiative transfer field from the simulation)." + In Fig. l..," In Fig. \ref{fig:pics}," + we present a 0.74 Mpe thick slice through the density and flux fields based on this 2=5.71 simulation output rom ?.., we present a 0.74 Mpc thick slice through the density and flux fields based on this $z=5.71$ simulation output from \citet{TCL08}. + The flux fields were calculated assuming Ayu)=30 Mpe. and DC=|.," The flux fields were calculated assuming $\lmfp=30$ Mpc, and $\DC=1$." + Even for such a moderately high choice of Aj. we can qualitatively see that there is significant inhomogeneity in the flux fields.," Even for such a moderately high choice of $\lmfp$, we can qualitatively see that there is significant inhomogeneity in the flux fields." + Furthermore. it is evident that the flux and density fields are highly correlated. an issue we will return to in S5..," Furthermore, it is evident that the flux and density fields are highly correlated, an issue we will return to in \ref{sec:forest}." + We complement these numerical techniques with a relatively simple analytic model., We complement these numerical techniques with a relatively simple analytic model. + While this approach cannot incorporate all of the physics provided by the semi-numeric and numeric models. we will find it to be helpfulin elucidating the physies of the background radiation field.," While this approach cannot incorporate all of the physics provided by the semi-numeric and numeric models, we will find it to be helpfulin elucidating the physics of the background radiation field." + As in the remainder of this paper. we will focus on computing two statistical descriptions of the flux field: the PDF and the power spectrum.," As in the remainder of this paper, we will focus on computing two statistical descriptions of the flux field: the PDF and the power spectrum." + The PDF of the radiation background ./. normalized to its mean value. 0/5. can be computed exactly for randomly. distributed sources. provided that we assume a constant attenuation. length," The PDF of the radiation background $J$ , normalized to its mean value $\langle J\rangle$ , can be computed exactly for randomly distributed sources, provided that we assume a constant attenuation length" +remain eravitationally bouud to the low mass star.,remain gravitationally bound to the low mass star. + The conditions for photou-pressure blow-out of erains iu the disk around the low mass star can be derived as follows., The conditions for photon-pressure blow-out of grains in the disk around the low mass star can be derived as follows. + Let 3 be the ratio of photon to eravitational force on a grain in the vicinity of the O star by itself., Let $\beta$ be the ratio of photon to gravitational force on a grain in the vicinity of the O star by itself. + Photon-pressure-driven blow-out occurs for jJ > 0.5., Photon-pressure-driven blow-out occurs for $\beta$ $>$ 0.5. + The equivalent ratio of forces for à grain near the low mass star must include its gravity. resulting in a reduction of J approximately iu proportion to the ratio of eravitational forces from the two stars at the position of the erain.," The equivalent ratio of forces for a grain near the low mass star must include its gravity, resulting in a reduction of $\beta$ approximately in proportion to the ratio of gravitational forces from the two stars at the position of the grain." + It is casily shown that the modified ratio has a value of 0.5 at a distance frou the low mass (mass Af ) star given by where dis its distance from the lieh mass star (mass My)., It is easily shown that the modified ratio has a value of 0.5 at a distance from the low mass (mass $M_2$ ) star given by where $d$ is its distance from the high mass star (mass $M_1$ ). + The term + is of order 1 aud depends on where the erain is du its orbit., The term $\gamma$ is of order 1 and depends on where the grain is in its orbit. + Lamy&Perrin(1997) have determined values of JJ for eras of various compositions and sizes around a uiuuber of stars., \citet{Lamy97} have determined values of $\beta$ for grains of various compositions and sizes around a number of stars. + The values are roughly similar for a given grain size: erain composition enters as a secondary parameter., The values are roughly similar for a given grain size; grain composition enters as a secondary parameter. + We will use typical values in the following discussion., We will use typical values in the following discussion. + Taking the values for the 09.5 V star ¢ Oph. grains of radius between 0.01 aud 1/22 have ye 1000 - 10000.," Taking the values for the O9.5 V star $\zeta$ Oph, grains of radius between 0.01 and 1 $\mu$ m have $\beta \approx$ 1000 - 10000." + We take a typical distance between our high aud low mass stars to be d = 0.2 pe. aud also asstune LO M for the high mass star aud 0.6ML.. for he low mass one.," We take a typical distance between our high and low mass stars to be $d$ = 0.2 pc, and also assume 40 ${\rm M_{\sun}}$ for the high mass star and ${\rm M_{\sun}}$ for the low mass one." + We then find that the O-star photon xessure on such s1nall eras becomes dominant at a distance of z 110 AU from the low mass star., We then find that the O-star photon pressure on such small grains becomes dominant at a distance of $\approx$ 110 AU from the low mass star. + Simall eyaius well inside this radius will be held iu orbit bv he gravitational field of the low-mass star., Small grains well inside this radius will be held in orbit by the gravitational field of the low-mass star. + For larger eras. ο drops rapidly: typically it is < 50 for 10 μπι radius erains.," For larger grains, $\beta$ drops rapidly; typically it is $<$ 50 for 10 $\mu$ m radius grains." +" The corresponding distauce for them where ohoton pressure from the O star overcomes the gravity of the low-mass one is z 500 AU. that is. outside the youndary of a typical protoplanetary disk ίοιο,,Andrews&Willizuuus 2005)."," The corresponding distance for them where photon pressure from the O star overcomes the gravity of the low-mass one is $\approx$ 500 AU, that is, outside the boundary of a typical protoplanetary disk \citep[e.g.,][]{Andr05}." +. Therefore. the larger erains are likely ο remain bound to the low nass star throughout the disk. where they will coutiuue to be ground. down by collisions.," Therefore, the larger grains are likely to remain bound to the low mass star throughout the disk, where they will continue to be ground down by collisions." +" That is. the erains making up the ""conet tail” probably originate frou collisional cascades in the outer reeious of the circumstellar disk."," That is, the grains making up the “comet tail” probably originate from collisional cascades in the outer regions of the circumstellar disk." + These regious lave previously been cleared of gas by photoevaporation aud the remaining solid particles are settling toward the disk mud-plain aud starting to assemble iuto larger bodies (see Throop&Bally(2005) for details). leacling to ecucration of these eraims idu a vigorous episode of collisional cascades.," These regions have previously been cleared of gas by photoevaporation and the remaining solid particles are settling toward the disk mid-plain and starting to assemble into larger bodies (see \citet{Thro05} for details), leading to generation of these grains in a vigorous episode of collisional cascades." + IHTowever. eiveu typical sizes of protoplanctary disks. this process is likev to be effective only up to a WAN erain size of al)out a nuücron radius.," However, given typical sizes of protoplanetary disks, this process is likely to be effective only up to a maximum grain size of about a micron radius." + The tails are conrposed. primarily ¢of erains of & O.OL gan to z 1 jaa du radius (where the ower limit is set by the model fits to their surface brighttess profiles: Balog ct al., The tails are composed primarily of grains of $\approx$ 0.01 $\mu$ m to $\approx$ 1 $\mu$ m in radius (where the lower limit is set by the model fits to their surface brightness profiles; Balog et al. + 2006)., 2006). + We have modified the upper mass limits derived by Balogotal.(2006) to reflect the approximate eraiu size Iunit of l yan. This approximate nuit results from the teudeney of larecr grains to remai1 eravitationally bound to the low-luass star., We have modified the upper mass limits derived by \citet{Balo06} to reflect the approximate grain size limit of 1 $\mu$ m. This approximate limit results from the tendency of larger grains to remain gravitationally bound to the low-mass star. + From the mass loss rates and typical disk masses iu Section Ld. we can estimate an approximate timescale of 10—109 vrs for which this phenomenon is visible.," From the mass loss rates and typical disk masses in Section 4.1, we can estimate an approximate timescale of $10^5 - 10^6$ yrs for which this phenomenon is visible." + Therefore. the phenomenon might be quite common. however we see ouly three cases in our GTO survey of about 20 O stars (there are additional cases around three O-stars in the Wh region. Koenig et al.," Therefore, the phenomenon might be quite common, however we see only three cases in our GTO survey of about 20 O stars (there are additional cases around three O-stars in the W5 region, Koenig et al." + in preparation) sugecsting that this is probably a short lived rather rare phenomenon (oulv about L/L of the observed O-stars have cometary structures in their ucighborhood)., in preparation) suggesting that this is probably a short lived rather rare phenomenon (only about 1/4 of the observed O-stars have cometary structures in their neighborhood). + We present IIST/NICMIOS Pao images and IRS spectra of cometary structures detected in Spitzer/MIPS 2| yan images., We present HST/NICMOS $\alpha$ images and IRS spectra of cometary structures detected in /MIPS 24 $\mu$ m images. + We estimate an upper lint to the amount of gas iu the comets’ disk and tail and find that the eas-to-dust mass ratio is much lower than the value observed iu the ISAL: the tails are esseutially eas free., We estimate an upper limit to the amount of gas in the comets' disk and tail and find that the gas-to-dust mass ratio is much lower than the value observed in the ISM: the tails are essentially gas free. + Using this new observation we are able to coustrain the flow velocity aud thus the mass loss rate., Using this new observation we are able to constrain the flow velocity and thus the mass loss rate. + The new iiass oss rates allow us to estimate the timescale ou which the shenomenon occurs (10106 vr)., The new mass loss rates allow us to estimate the timescale on which the phenomenon occurs $10^5 - 10^6$ yr). + The short timescale avors photocvaporation models predicting quick removal of gas from the outer parts of the disk., The short timescale favors photoevaporation models predicting quick removal of gas from the outer parts of the disk. + The “comet tails” are produced. from the outer regions of the disks. where areor erains collide at au elevated rate generating second eeneration dust.," The “comet tails” are produced from the outer regions of the disks, where larger grains collide at an elevated rate generating second generation dust." + These suall erains are then ejected due o photon pressure from the nearby O-star., These small grains are then ejected due to photon pressure from the nearby O-star. + The SED of the sources shows excess cussion between 3 aud 5 ju. in agreement with the IRS low resolution spectra.," The SED of the sources shows excess emission between 3 and 8 $\mu$ m, in agreement with the IRS low resolution spectra." + This cussion mdicates that there is an iuncr disk that survives the plotoevaporation process for longer thu LO? years. as predicted by the photoevaporation models.," This emission indicates that there is an inner disk that survives the photoevaporation process for longer than $10^5$ years, as predicted by the photoevaporation models." + The authors thank the anouvinous referce for cohunents and sugeestious which improved the paper., The authors thank the anonymous referee for comments and suggestions which improved the paper. + We also thank Robert Iiug for providing the VLT data for the source iu NGC 2211., We also thank Robert King for providing the VLT data for the source in NGC 2244. + This work is based on, This work is based on +fiial gaaxy would be minimized if simall fragments/cdwarl galaxies were absett from tlie galaxys envlrornent.,final galaxy would be minimized if small fragments/dwarf galaxies were absent from the galaxy's environment. + Note. though. hat sucha situation is less likely for a ceutalcD galaxy.," Note, though, that such a situation is less likely for a central cD galaxy." + Late mergers a'e expected to p'ovide a significant population of metaI-poor globular clusters originating iu the »ogenior galaxies. predomiuautly meta—rich systenis «:'ould be explaiued if the progenitors were κ.OrLIC but οuster-poor (see also Gebjardt Ixissle-Patig 1999).," Late mergers are expected to provide a significant population of metal–poor globular clusters originating in the progenitor galaxies, predominantly metal–rich systems could be explained if the progenitors were gas–rich but cluster–poor (see also Gebhardt Kissler-Patig 1999)." + StrippitD>oO Call lesilt in the yrelerential re10val of metal-poor cluste‘s if the metal-j»oor population is more extended than the netal-‘ich one., Stripping can result in the preferential removal of metal–poor clusters if the metal–poor population is more extended than the metal–rich one. + siuce stripping will act 1lore efficiently ou the more exended population. it could 'esult i systels hat are biased towards veh metallicitses.," Since stripping will act more efficiently on the more extended population, it could result in systems that are biased towards high metallicities." + Iu this context. it is interesting to note hat the halo lel oL IC 1051 appears trucated beyonc 30 kpc (Jorgeusenetal.1992).," In this context, it is interesting to note that the halo light of IC 4051 appears truncated beyond $\sim$ 30 kpc \citep{jor92}." +. Preferentlally metal-rich globular €Uster svstenuis can be accommodated by adjusting the existiug scena‘ios., Preferentially metal–rich globular cluster systems can be accommodated by adjusting the existing scenarios. +" An exclusively metal-rich elobular clister population. should oue be discovered. would. probabv be most easily accomxlated in a siiele collapse mocel — au ""in situ galaxy formation sceiario with rapid star—lormaion preceding cluster formation."," An exclusively metal–rich globular cluster population, should one be discovered, would probably be most easily accommodated in a single collapse model – an “in situ” galaxy formation scenario with rapid star–formation preceding cluster formation." + We have shown that the color distribution of globular clusters in NCC 3311 is normal [or bright elliptical galaxies., We have shown that the color distribution of globular clusters in NGC 3311 is normal for bright elliptical galaxies. + It. is bi-inodal with peaks at V—/~0.91 aud. 1.09. correspoudiug to metallicity peaks at around [Fe/H~—1.D nali —(0.75 (the precise values being dependent. on the choice of the conversio1 ‘elation between color aud metallicity).," It is bi–modal with peaks at $V-I\sim0.91$ and $1.09$, corresponding to metallicity peaks at around $\sim -1.5$ and $-0.75$ (the precise values being dependent on the choice of the conversion relation between color and metallicity)." + This range of metallicities is uormal for bright elliptical gaaxles. a result. whicἩ contradicts au earlier claim that NCC 3311 might host an extremely metal-ricl elobular cluster syseinn.," This range of metallicities is normal for bright elliptical galaxies, a result which contradicts an earlier claim that NGC 3311 might host an extremely metal–rich globular cluster system." + We suggest that i is Worth revisitiug the globular cluster system of NGC 3923 whose globular cluster system was reported to be very re lontje basis of observations made ou the same run which produced the NCC 331:| results., We suggest that it is worth revisiting the globular cluster system of NGC 3923 whose globular cluster system was reported to be very red on the basis of observations made on the same run which produced the NGC 3311 results. + Although the evidence orexclusively wetal-rich globular cluster systems has been weakenec. there are still cases of galaxies whose elobular cluster systems may lack a significant metal-poor component.," Although the evidence for metal–rich globular cluster systems has been weakened, there are still cases of galaxies whose globular cluster systems may lack a significant metal–poor component." + We have briely discussed the implications of such systems for our wucderstaucing of elobular cluster aud galaxy formation and have concluded that. with some adjustiueuts. they cau be explained uuder existitD>& sCeLaLlos.," We have briefly discussed the implications of such systems for our understanding of globular cluster and galaxy formation and have concluded that, with some adjustments, they can be explained under existing scenarios." + We thank Johu Huch‘a for lis help and useful suggestions aud Duucan Forbes. Carl Cuiulimair and Wen Freeman for their contributions.," We thank John Huchra for his help and useful suggestions and Duncan Forbes, Carl Grillmair and Ken Freeman for their contributions." + This work was supported by HST eraut. GO.0655 National Science Foundation grant number AST0000732 aud Faculty Research fuus from the University of Califoruia. Santa Cruz.," This work was supported by HST grant GO.06554.01-95A, National Science Foundation grant number AST9900732 and Faculty Research funds from the University of California, Santa Cruz." + The solution to this equation is (for more details see 1908) with the normalization N adjusted to give |T|?=1., The solution to this equation is (for more details see JS08) with the normalization $\cal N$ adjusted to give ${|T|}^2=1$. +" Apparently the thus constructed nulling weights depend on which (£4,£5,5) combination is considered and with respect to which cosmological parameter we optimize the information content."," Apparently the thus constructed nulling weights depend on which $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$ combination is considered and with respect to which cosmological parameter we optimize the information content." +" In this paper the default cosmological parameter to optimize is O4, and we choose for each (i,j) combination the (£4,£2,£3) combination which maximizes FG»."," In this paper the default cosmological parameter to optimize is $\Omega_{\rm m}$, and we choose for each $(i,j)$ combination the $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$ combination which maximizes $F_{\rm o}^{(ij)}$." +" However one needs to be aware that this serves only as a clear choice of a (δι,£5,€3) combination and is not necessarily the best in terms of information preservation considering all angular frequency bins and all cosmological parameters."," However one needs to be aware that this serves only as a clear choice of a $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$ combination and is not necessarily the best in terms of information preservation considering all angular frequency bins and all cosmological parameters." +" To show which triangle shapes and sizes contain more information, we plot F? against the (21,&,£5) triangle shape and size for four typical (i,j) combinations in 1."," To show which triangle shapes and sizes contain more information, we plot $F_{\rm o}^{(ij)}$ against the $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$ triangle shape and size for four typical $(i,j)$ combinations in $\,$." +" In the left panel, the nulled information FGD contained in different triangles with a common shortest side length £;=171 is plotted against o, which is the angle opposite to £j."," In the left panel, the nulled information $F_{\rm o}^{(ij)}$ contained in different triangles with a common shortest side length $\bar{\ell}_1=171$ is plotted against $\alpha$, which is the angle opposite to $\bar{\ell}_1$." +" Due to our logarithmic binning in angular frequency, only eight (61,£5,£5) combinations with £j,=171 can form triangles."," Due to our logarithmic binning in angular frequency, only eight $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$ combinations with $\bar{\ell}_1=171$ can form triangles." + One sees that the more elongated triangles (small α) contain much more Fisher information than the almost equilateral triangles (large a)., One sees that the more elongated triangles (small $\alpha$ ) contain much more Fisher information than the almost equilateral triangles (large $\alpha$ ). +" The small separation between the 3rd and the 4th points from the left is caused by the degeneracy of different triangle shapes with respect to o, e.g. two equal and very long side lengths can result in the same value of α as two shorter side lengths with a length difference close to the length of the shortest side length."," The small separation between the 3rd and the 4th points from the left is caused by the degeneracy of different triangle shapes with respect to $\alpha$, e.g. two equal and very long side lengths can result in the same value of $\alpha$ as two shorter side lengths with a length difference close to the length of the shortest side length." +" The right panel shows the distribution of the Fisher information contained in one (£i,£5,(4) bin over the triangle size."," The right panel shows the distribution of the Fisher information contained in one $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$ bin over the triangle size." +" When the redshift in consideration is higher, the peak of the information distribution moves to higher angular frequencies."," When the redshift in consideration is higher, the peak of the information distribution moves to higher angular frequencies." + The figure suggests that most information comes from high redshifts and small angular scales., The figure suggests that most information comes from high redshifts and small angular scales. +" To explore the sensitivity of nulling weights on the choice of the cosmological parameter, we construct seven sets of weight functions, each optimizing the information content in terms of one parameter."," To explore the sensitivity of nulling weights on the choice of the cosmological parameter, we construct seven sets of weight functions, each optimizing the information content in terms of one parameter." +" For all (i,7) combinations we find that the nulling weights are not very sensitive to the choice of parameter."," For all $(i,j)$ combinations we find that the nulling weights are not very sensitive to the choice of parameter." +" As an example, the weights for (i,j)=(1,2) are shown in 2."," As an example, the weights for $(i,j) = (1,2)$ are shown in $\,$." +" This result is rather surprising at first sight, since for different parameters the distribution of information (contained in the bispectrum) over redshift bins is quite different."," This result is rather surprising at first sight, since for different parameters the distribution of information (contained in the bispectrum) over redshift bins is quite different." +" However, such insensitivity suggests that the shapes of nulling weights are already strongly constrained under our construction scheme."," However, such insensitivity suggests that the shapes of nulling weights are already strongly constrained under our construction scheme." +" One constraint is, evidently, the nulling condition."," One constraint is, evidently, the nulling condition." +" Moreover, considering the fact that we optimize the nulling weights for each (i,j) combination with respect to the information content they preserve, we have already required the shapes of these first order nulling weights to be as smooth as possible."," Moreover, considering the fact that we optimize the nulling weights for each $(i,j)$ combination with respect to the information content they preserve, we have already required the shapes of these first order nulling weights to be as smooth as possible." +" The fact that these two conditions have already imposed strong constraints on the nulling weights also suggests that nulling weights can be robustly and efficiently constructed, i.e. it is not critical to construct the “best” nulling weights."," The fact that these two conditions have already imposed strong constraints on the nulling weights also suggests that nulling weights can be robustly and efficiently constructed, i.e. it is not critical to construct the “best” nulling weights." +" What the nulling technique “nulls” is the GGI signal Baar, so the GGI/GGG ratio is the most direct quantification of its performance."," What the nulling technique “nulls” is the GGI signal $B_{\rm GGI}$, so the GGI/GGG ratio is the most direct quantification of its performance." + We plot the modeled GGI and GGG bispectra before and after nulling in Fig.3.," We plot the modeled GGI and GGG bispectra before and after nulling in $\,$." + The original GGI signal is shown in the left panels by dashed lines., The original GGI signal is shown in the left panels by dashed lines. + For comparison the GGG signals are shown as solid curves., For comparison the GGG signals are shown as solid curves. + The results are shown for equilateral triangle configurations for the convenience of presenting., The results are shown for equilateral triangle configurations for the convenience of presenting. +" One sees that when the redshift bin number j and/or k increase, the changes in GGG and GGI signals are different, which shows the expected different redshift dependence."," One sees that when the redshift bin number $j$ and/or $k$ increase, the changes in GGG and GGI signals are different, which shows the expected different redshift dependence." + For all redshift bin combinations the GGI signal is modeled to be subdominant to the GGG signal., For all redshift bin combinations the GGI signal is modeled to be subdominant to the GGG signal. +" In the nulled measures shown in the right panels, the GGI/GGG ratio is suppressed by a factor of 10 over all angular scales, which reflects the success of the nulling technique."," In the nulled measures shown in the right panels, the GGI/GGG ratio is suppressed by a factor of 10 over all angular scales, which reflects the success of the nulling technique." +" We further evaluate the performance of the nulling technique by looking at the constraining power of cosmic shear bispectrum tomography on cosmological parameters, as well as the biases caused by the GGI systematics before and after nulling."," We further evaluate the performance of the nulling technique by looking at the constraining power of cosmic shear bispectrum tomography on cosmological parameters, as well as the biases caused by the GGI systematics before and after nulling." +White dwarfs are the final remnants of low- and intermediate-mass stars.,White dwarfs are the final remnants of low- and intermediate-mass stars. + About of main-sequence stars will end their evolutionary pathways as white dwarfs and. hence. the study of the white dwarf population provides details about the late stages of the life of the vast majority of stars.," About of main-sequence stars will end their evolutionary pathways as white dwarfs and, hence, the study of the white dwarf population provides details about the late stages of the life of the vast majority of stars." + Since white dwarfs are long-lived objects. they also constitute useful objects to study the structure and evolution of our Galaxy (Liebert et al.," Since white dwarfs are long-lived objects, they also constitute useful objects to study the structure and evolution of our Galaxy (Liebert et al." + 2005a: Isern et al., 2005a; Isern et al. + 2001)., 2001). + For instance. the initial- mass relationship (IFMR). which connects the properties of a white dwarf with those of its main-sequence progenitor. is of paramount importance for different aspects in. modern astrophysics.," For instance, the initial-final mass relationship (IFMR), which connects the properties of a white dwarf with those of its main-sequence progenitor, is of paramount importance for different aspects in modern astrophysics." + It 1s required as an input for determining. the ages of globular clusters and their distances. for studying the chemical evolution of galaxies. and also to understand the properties of the Galactic population of white dwarfs.," It is required as an input for determining the ages of globular clusters and their distances, for studying the chemical evolution of galaxies, and also to understand the properties of the Galactic population of white dwarfs." + Despite its relevance. this relationship is still poorly constrained. both from the theoretical and the observational points of view.," Despite its relevance, this relationship is still poorly constrained, both from the theoretical and the observational points of view." + The first attempt to empirically determine the initial-final mass relationship was undertaken by Weidemann(1977).. who also provides a recent review on this subject (Weidemann 2000).," The first attempt to empirically determine the initial-final mass relationship was undertaken by \cite{wei77}, who also provides a recent review on this subject (Weidemann 2000)." + It is still not clear how this function depends on the mass and metallicity of the progenitor. its angular momentum. or the presence of a strong magnetic field.," It is still not clear how this function depends on the mass and metallicity of the progenitor, its angular momentum, or the presence of a strong magnetic field." + The total age of a white dwarf can be expressed as the sum of its cooling time and the main-sequence lifetime of its progenitor., The total age of a white dwarf can be expressed as the sum of its cooling time and the main-sequence lifetime of its progenitor. + The latter depends on the metallicity of the progenitor of the white dwarf. but it cannot be determined from observations of single white dwarfs.," The latter depends on the metallicity of the progenitor of the white dwarf, but it cannot be determined from observations of single white dwarfs." + This is because white dwarfs have such strong surface gravities that gravitational settling operates very efficiently in their atmospheres. and any information about their progenitors (e.g. metallicity) is lost in the very early evolutionary stages of the cooling track.," This is because white dwarfs have such strong surface gravities that gravitational settling operates very efficiently in their atmospheres, and any information about their progenitors (e.g. metallicity) is lost in the very early evolutionary stages of the cooling track." + Moreover. the evolution during the AGB phase of the progenitors is essential in determining the size and composition of the atmospheres of the resulting white dwarfs. since the burning processes that take place in H and He shells determine their respective thicknesses and their detailed chemical compositions. which are crucial ingredients for determining the evolutionary cooling times.," Moreover, the evolution during the AGB phase of the progenitors is essential in determining the size and composition of the atmospheres of the resulting white dwarfs, since the burning processes that take place in H and He shells determine their respective thicknesses and their detailed chemical compositions, which are crucial ingredients for determining the evolutionary cooling times." + A promising approach to circumvent the problem. and also to directly test the initial-final mass relationship. is to study white dwarfs for which external constraints are available.," A promising approach to circumvent the problem, and also to directly test the initial-final mass relationship, is to study white dwarfs for which external constraints are available." + This is the case of white dwarfs in open and globular clusters (Ferrario et al., This is the case of white dwarfs in open and globular clusters (Ferrario et al. + 2005. Dobbie et al.," 2005, Dobbie et al." + 2006) or in non-interacting binaries. for Instance. common proper motion pairs (Wegner 1973. Oswalt et al.," 2006) or in non-interacting binaries, for instance, common proper motion pairs (Wegner 1973, Oswalt et al." + 1988)., 1988). + Focusing on the latter. it is sound to assume that the members of a common proper motion par were born simultaneously and with the same chemical composition.," Focusing on the latter, it is sound to assume that the members of a common proper motion pair were born simultaneously and with the same chemical composition." + Since the components are well separated (100 to 1000 AU). mass exchange between them ts unlikely and it can be considered that they have evolved as isolated stars.," Since the components are well separated (100 to 1000 AU), mass exchange between them is unlikely and it can be considered that they have evolved as isolated stars." + Thus. important information of the white dwarf. such as its total age or the metallicity of the progenitor. can be inferred from the study of the companion.," Thus, important information of the white dwarf, such as its total age or the metallicity of the progenitor, can be inferred from the study of the companion." + In particular. if the companion ts an EF. G or K type star the metallicity can be derived with high accuracy from detailed spectral analysis.," In particular, if the companion is an F, G or K type star the metallicity can be derived with high accuracy from detailed spectral analysis." + On the other hand. the age can be obtained using different methods.," On the other hand, the age can be obtained using different methods." + In particular. we will use stellar isochrones when the star is moderately evolved. or the X-ray luminosity if the star is very close to the ZAMS.," In particular, we will use stellar isochrones when the star is moderately evolved, or the X-ray luminosity if the star is very close to the ZAMS." + The purpose of this work is to present our spectroscopic analysis of both members of some common proper motion pars containing a white dwarf. and the semi-empirical intial-final mass relationship that we have derived from this study.," The purpose of this work is to present our spectroscopic analysis of both members of some common proper motion pairs containing a white dwarf, and the semi-empirical intial-final mass relationship that we have derived from this study." + The paper is organized as follows., The paper is organized as follows. + In $2 we present the observations done so far and describe the data reduction., In 2 we present the observations done so far and describe the data reduction. + Section 3 1s devoted to discuss the classification and the analysis of the observed white dwarfs. whereas in $4 we present the analysis of the companions.," Section 3 is devoted to discuss the classification and the analysis of the observed white dwarfs, whereas in 4 we present the analysis of the companions." + This is followed by $5 where we present our main results and finally in $6 we elaborate our conclusions., This is followed by 5 where we present our main results and finally in 6 we elaborate our conclusions. +radius. (hen we need to correct for only enclosing part of the cooling gas in the aperture.,"radius, then we need to correct for only enclosing part of the cooling gas in the aperture." + As described in BAIL. this is accomplished by multiplving the total My by the fraction of the X-ray luminosity projected into the aperture.," As described in BMI, this is accomplished by multiplying the total ${\dot{M}}_X$ by the fraction of the X-ray luminosity projected into the aperture." + Here we use the value of Mx for the distributed model (q=1). corrected to the size of the aperture.," Here we use the value of ${\dot{M}}_X$ for the distributed model ), corrected to the size of the aperture." + I we had used the model with no mass drop-out (y=). the median predicted value of Ma hardly changes. although for the most X-ray Iuminous galaxies in (he sample (often the largest). the predicted My could be a factor of two higher.," If we had used the model with no mass drop-out ), the median predicted value of ${\dot{M}}_X$ hardly changes, although for the most X-ray luminous galaxies in the sample (often the largest), the predicted ${\dot{M}}_X$ could be a factor of two higher." + The various values of AM and other relevant derived quantities. including the N-vav huninositw. £y. and the X-ray. temperature. Ly are eiven in Table 3.," The various values of ${\dot{M}}$ and other relevant derived quantities, including the X-ray luminosity, $L_X$, and the X-ray temperature, $T_X$ are given in Table 3." + There is a complete set of X-ray fluxes and luminosities for (his sample. so we beein bv comparing these to the OVI data.," There is a complete set of X-ray fluxes and luminosities for this sample, so we begin by comparing these to the OVI data." + The nominal prediction was that there would be a connection between M and the detection of OVI emission. but we examined other relationships as well.," The nominal prediction was that there would be a connection between ${\dot{M}}_X$ and the detection of OVI emission, but we examined other relationships as well." + Some of those relationships investigated were between OVI and Ly. Ly/Ty. and Tx. where no strong correlations were found and no strong relationships were predicted.," Some of those relationships investigated were between OVI and $L_X$, $L_X/T_X$, and $T_X$, where no strong correlations were found and no strong relationships were predicted." + However. there seems {ο be a correlation between the OVI and My. as seen in Fieure 25.," However, there seems to be a correlation between the OVI and ${\dot{M}}_X$, as seen in Figure 25." + We see that none of the six galaxies with the lowest values of Ma. have any OVI emission. vet (he significance of this correlation is difficult to quantilv.," We see that none of the six galaxies with the lowest values of ${\dot{M}}_X$ have any OVI emission, yet the significance of this correlation is difficult to quantify." + We would like to use the Ixaplan-Meier estimator lor the analysis of censored data Nelson 19386).. but an underlving assumption is that the data are censored randomly.," We would like to use the Kaplan-Meier estimator for the analysis of censored data \citep{isobe86}, but an underlying assumption is that the data are censored randomly." + Here. the upper limits (censored data) are not randomly. distributed. but preferentially occur at the lower values of M.," Here, the upper limits (censored data) are not randomly distributed, but preferentially occur at the lower values of ${\dot{M}}_X$." +" Also. we have introduced ""possible"" detections. which is difficult to incorporate in statistical schemes."," Also, we have introduced “possible” detections, which is difficult to incorporate in statistical schemes." + Given these challenges. we can divide the sample into three bins by Ma. using our scoring for detections. possible detections. and upper limits.," Given these challenges, we can divide the sample into three bins by ${\dot{M}}_X$, using our scoring for detections, possible detections, and upper limits." + We find that for galaxies with the lowest M. values. 1/8 have OVI. while 4.5/8 of the highest My objects have OVI (and 3.5/8 of the intermediate objects have OVI).," We find that for galaxies with the lowest ${\dot{M}}_X$ values, 1/8 have OVI, while 4.5/8 of the highest ${\dot{M}}_X$ objects have OVI (and 3.5/8 of the intermediate objects have OVI)." + Using Poisson statistics. the joint probability that of the lowest My objects. 1/8 (or lewer) have OVI while 4.5/8 (or more) of the highest Mx objects have OVI would oceur by chance of the time confidence level).," Using Poisson statistics, the joint probability that of the lowest ${\dot{M}}_X$ objects, 1/8 (or fewer) have OVI while 4.5/8 (or more) of the highest ${\dot{M}}_X$ objects have OVI would occur by chance of the time confidence level)." + The correlation is probably a bit stronger than this value since none of the lowest six My object have either an OVI detection or possible detection., The correlation is probably a bit stronger than this value since none of the lowest six ${\dot{M}}_X$ object have either an OVI detection or possible detection. + For a Ixendall's T lest or a Spearman's p test for the whole sample (treating upper limits and detections equally). the significance improves (ο confidence. with the higher significance if the very poor upper limit object. NGC 3585 is eliminated from the sample.," For a Kendall's $\tau$ test or a Spearman's $\rho$ test for the whole sample (treating upper limits and detections equally), the significance improves to confidence, with the higher significance if the very poor upper limit object, NGC 3585 is eliminated from the sample." + Conservatively. we conclude that the correlation exists at the confidence level when using the," Conservatively, we conclude that the correlation exists at the confidence level when using the" +Even on the long timescales probed by our time-averaged monitoring data. the flux-dependent behaviour of the broad iron line is complex.,"Even on the long timescales probed by our time-averaged monitoring data, the flux-dependent behaviour of the broad iron line is complex." + For these data. the line flux increases more-or-less proportionally with the continuum flux. resulting. in a roughly constant equivalent width over a decade range of flux.," For these data, the line flux increases more-or-less proportionally with the continuum flux, resulting in a roughly constant equivalent width over a decade range of flux." + The December 1996 long-look data also show line flux increasing with continuum flux. although the relation is not directly proportionate. so that the equivalent width decreases with flux.," The December 1996 long-look data also show line flux increasing with continuum flux, although the relation is not directly proportionate, so that the equivalent width decreases with flux." + In fact. the line fluxes measured in December 1996 are consistently larger than the corresponding fluxes measured from the long-term monitoring data.," In fact, the line fluxes measured in December 1996 are consistently larger than the corresponding fluxes measured from the long-term monitoring data." + The anti-correlation of line equivalent width and continuum flux in December 1996 timescales is also in contrast to the result of (Wangetal.1999).. who report a positive correlation during an observation in 1994.," The anti-correlation of line equivalent width and continuum flux in December 1996 timescales is also in contrast to the result of \cite {Wang}, who report a positive correlation during an observation in 1994." + The discrepancy between the iron line behaviour in the December 1996 and long-term monitoring data might be explained if there is additional short-term variability in the iron line which is not simply related to the continuum flux., The discrepancy between the iron line behaviour in the December 1996 and long-term monitoring data might be explained if there is additional short-term variability in the iron line which is not simply related to the continuum flux. + For example. Vaughan Edelson (2001) show that in the Seyfert | MCG-6-30-15. the broad iron line flux varies significantly but independently of short term continuum variations.," For example, Vaughan Edelson (2001) show that in the Seyfert 1 MCG-6-30-15, the broad iron line flux varies significantly but independently of short term continuum variations." + One possibility is that the iron line flux tracks the long-term variations in the continuum flux Qvhich are being probed to some extent with the long-term monitoring data). but responds only weakly to the short-term variations whieh are observed during the December 1996 long-look observation.," One possibility is that the iron line flux tracks the long-term variations in the continuum flux (which are being probed to some extent with the long-term monitoring data), but responds only weakly to the short-term variations which are observed during the December 1996 long-look observation." + A number of theoretical papers have been written to explain why the iron line flux may not vary linearly with the continuum flux (teg Mattetal.1993.. Nayakshin&Kazanas 2002.. Ballantyne&Ross 20023). often involving ionised discs but these models have so far been largely untroubled by data.," A number of theoretical papers have been written to explain why the iron line flux may not vary linearly with the continuum flux (eg \ncite{Matt}, \ncite{Nayakshin}, \ncite{Ballantyne}) ), often involving ionised discs but these models have so far been largely untroubled by data." + We are aquiring more long-term monitoring data. sampling a broader range of long-term flux. variations. to determine whether the iron line does follow the continuum on long timescales and to provide some constraints for theoretical models.," We are aquiring more long-term monitoring data, sampling a broader range of long-term flux variations, to determine whether the iron line does follow the continuum on long timescales and to provide some constraints for theoretical models." + Our observations of NGC 40531 do not support the correlation between the photon index and the reflected fraction. # in the model as reported from spectroscopy of a sample of Seyfert galaxies (Zdziarski.Lu, Our observations of NGC 4051 do not support the correlation between the photon index and the reflected fraction $R$ in the model as reported from spectroscopy of a sample of Seyfert galaxies \cite{Zdziarski} . +bifiski&Smith, From Fig. +1999)... From Fig. + itis obvious that the reflected fraction remains below /?=1 even for the softest states of the source., \ref{dec_cont} it is obvious that the reflected fraction remains below $R=1$ even for the softest states of the source. + There is also no evidence for this correlation in theAXE spectra of NGC 5506 (Lamer.Ut-tley&M'Hardy 2000)., There is also no evidence for this correlation in the spectra of NGC 5506 \cite{Lamer2000}. +.. We therefore suggest that the reported correlation does not apply to the variations of photon index and reflected fraction in a given object., We therefore suggest that the reported correlation does not apply to the variations of photon index and reflected fraction in a given object. + During our monitoring campaign the primary continuum 2-10 keV photon index. L'. varies strongly with photon flux from 1.60 at the lowest flux levels to 2.35 at the highest fluxes.," During our monitoring campaign the primary continuum 2-10 keV photon index, $\Gamma$, varies strongly with photon flux from 1.60 at the lowest flux levels to 2.35 at the highest fluxes." + The same correlation is also observed on the shorter time-scales of the December 1996 long look., The same correlation is also observed on the shorter time-scales of the December 1996 long look. + Flux-L correlations have been observed before in NGC 4051 (Matsuokaetal.1987). and other Seyfert galaxies teg NGC 4151. Perolaetal.19869) but. as in the present paper. it has only recently been possible to disentangle the effects of reflection and variations of the primary X-ray spectrum (teg Lamer.Uttley&M'Hardy2000.. Chiangetal.2000.. Leeetal.20001).," $\Gamma$ correlations have been observed before in NGC 4051 \cite{Matsuoka} and other Seyfert galaxies (eg NGC 4151, \ncite{Perola}) ) but, as in the present paper, it has only recently been possible to disentangle the effects of reflection and variations of the primary X-ray spectrum (eg \ncite{Lamer2000}, \ncite{Chiang}, \ncite{Lee2000}) )." + The slope-luminosity correlation is. often. explained by stronger cooling of the accretion disk corona during episodes of high thermal seed photon flux from the accretion disk itself (eg Pietrini&Krolik1995.. Malzac&Jourdain2000)).," The slope-luminosity correlation is often explained by stronger cooling of the accretion disk corona during episodes of high thermal seed photon flux from the accretion disk itself (eg \ncite{Pietrini}, \ncite{Malzac}) )." + Haardt.Maraschi&Ghisellini(1997) have calculated luminosity — spectral index relations in Compton cooled accretion disk coronae., \scite{Haardt} have calculated luminosity – spectral index relations in Compton cooled accretion disk coronae. + For a compact. pair dominated corona they predict spectral index variations of AL~0.3 for luminosity variations by more than a factor of 20.," For a compact, pair dominated corona they predict spectral index variations of $\Delta\Gamma\sim 0.3$ for luminosity variations by more than a factor of 20." + However the variations seen here exceed their predictions and imply. in their scenario. a non-pair dominated corona.," However the variations seen here exceed their predictions and imply, in their scenario, a non-pair dominated corona." + In certain regimes this model predicts a positve correlation of 2-10 keV flux and spectral hardness. which is not observed in NGC 4051.," In certain regimes this model predicts a positve correlation of 2-10 keV flux and spectral hardness, which is not observed in NGC 4051." +" Pietrint&Krolik(1995) point out that the spectral index depends almost solely on the ratio of seed photon compactness ἐς and hot plasma heating rate compactness ἐν with a=1L60./0,):17.", \scite{Pietrini} point out that the spectral index depends almost solely on the ratio of seed photon compactness $l_s$ and hot plasma heating rate compactness $l_h$ with $\alpha=1.6(l_s/l_h)^{1/4}$. + The observed spectral indices in NGC 4051 then correspond to ἐς{δε=0.02..0.4., The observed spectral indices in NGC 4051 then correspond to $l_s/l_h=0.02..0.4$. + Examination of fig 7 shows that the change of spectral index with flux is not linear., Examination of fig \ref{lineflux} shows that the change of spectral index with flux is not linear. + The rate of increase of spectral index with flux is very rapid at low fluxes but decreases at the highest fluxes where the spectral index approaches an asymptotic level., The rate of increase of spectral index with flux is very rapid at low fluxes but decreases at the highest fluxes where the spectral index approaches an asymptotic level. +" This saturation of the ""spectral index/flux relationship has been known for some time: eg the saturation was clearly visible in our early RXTE monitoring observations of MCG-6-30-15 and was reported by M'Hardy.Papadakis&Uttley(1998) where it was suggested that the relationship might derive from the combination of a constant spectrum hard component. and a steeper spectrum variable component."," This saturation of the `spectral index/flux' relationship has been known for some time; eg the saturation was clearly visible in our early RXTE monitoring observations of MCG-6-30-15 and was reported by \scite{mch98} where it was suggested that the relationship might derive from the combination of a constant spectrum hard component, and a steeper spectrum variable component." + Saturation of the spectral index/flux relationship was again reported in MCG-6-30-15 by Shihetal.(2002) from a long ASCA observation., Saturation of the spectral index/flux relationship was again reported in MCG-6-30-15 by \scite{Shih} from a long ASCA observation. + In MCG-6-30-15 both the long term RXTE monitoring and short term ASCA observations agree that the saturation level of the spectral index is ~2.1 (see fig 7 of MHardy.Uttley1998 and tig 8 of Shihetal. 2002))., In MCG-6-30-15 both the long term RXTE monitoring and short term ASCA observations agree that the saturation level of the spectral index is $\sim2.1$ (see fig 7 of \ncite{mch98} and fig 8 of \ncite{Shih}) ). + However the monitoring observations cover a wider flux and spectral range and show variation of the spectral index between 1.65 and 2.05 whereas the continuous ASCA observation only shows an index variation between 1.9 and 2.1., However the monitoring observations cover a wider flux and spectral range and show variation of the spectral index between 1.65 and 2.05 whereas the continuous ASCA observation only shows an index variation between 1.9 and 2.1. + Similarly in NGC 4051 (fig 7)) we see that the monitoring observations cover a wider flux and spectral range than the December 1996 long look and. as with MCG-6-30- the resultant time-averaged spectral index/flux relationship is smoother.," Similarly in NGC 4051 (fig \ref{lineflux}) ) we see that the monitoring observations cover a wider flux and spectral range than the December 1996 long look and, as with MCG-6-30-15, the resultant time-averaged spectral index/flux relationship is smoother." + We note. however. that although the lowest spectral index so far measured in the RATE monitoring observations is about the same in both NGC 4051 and MCG-6-30-15. the saturation level is ~ 2.4in NGC 4051 compared to ~2.1 in MCG-6-30-15.," We note, however, that although the lowest spectral index so far measured in the RXTE monitoring observations is about the same in both NGC 4051 and MCG-6-30-15, the saturation level is $\sim2.4$ in NGC 4051 compared to $\sim2.1$ in MCG-6-30-15." + In M'Hardy.Papadakis&Uttley(1998). we suggested that the torus might be the source of the possible hard. constant. component.," In \scite{mch98} we suggested that the torus might be the source of the possible hard, constant, component." + However the very hard spectral component found in the May 1998 very low state. which represents an upper limit to the torus contribution. was removed before producing the spectral index/flux. relationship (fig 7).," However the very hard spectral component found in the May 1998 very low state, which represents an upper limit to the torus contribution, was removed before producing the spectral index/flux relationship (fig \ref{lineflux}) )." + Thus. if we wish to retain the two-component spectral model. we require a different location for," Thus, if we wish to retain the two-component spectral model, we require a different location for" +ssysteni would have a combined mass at least. 18% larger than Mes. but might not be a SN In progenitor if the conrpanion turus out to be an ONe WD instead of a CO WD (Carcia-Derroetal.1997).,"system would have a combined mass at least $43\%$ larger than $M_{Ch}$, but might not be a SN Ia progenitor if the companion turns out to be an ONe WD instead of a CO WD \citep{garcia-berro97:stars}." +.. Considering all the evidence. the most likely possibility bv far is that the companion of bbe the stellar remnant of| a supernova explosion. either a NS or a DII.," Considering all the evidence, the most likely possibility by far is that the companion of be the stellar remnant of a supernova explosion, either a NS or a BH." + We note that our estimated. distance range places this object closer to the Solar System thu any other mown NS (Posseltetal.2007)., We note that our estimated distance range places this object closer to the Solar System than any other known NS \citep{posselt07:M7}. +. The puzzle of the uature of the companion of ccannot be solved with the observations that we preseut in this paper. and must be the subject of future work.," The puzzle of the nature of the companion of cannot be solved with the observations that we present in this paper, and must be the subject of future work." + It is. however. uterestiug to speculate about the possibilities.," It is, however, interesting to speculate about the possibilities." + For our best-fit value of A4 (0.92NL... Alp is below 1.86 (thelargestmasuredmassforaNS.seeLattimerM...&Prakash2007:Niceetal.2008) for PIT. which has a raudoia likelihood of 39%.," For our best-fit value of $M_{A}$ $0.92\,\mathrm{M_{\odot}}$ ), $M_{B}$ is below $1.86\,\mathrm{M_{\odot}}$ \citep[the largest +masured mass for a NS, see][]{lattimer07:NS_EOS,nice08:no_massive_NS} for $i \geq 67^{\circ}$, which has a random likelihood of $39\%$." + Iu this case. the mass of the WD and the circularity of the orbit would place the system in the class of interiiediate-nass WDINS binaries (secTable1inStairs2001).," In this case, the mass of the WD and the circularity of the orbit would place the system in the class of `intermediate-mass' WD+NS binaries \citep[see Table 1 in][]{stairs04:pulsars_binary_systems}." + Curent models for binary stellar evolution predict that hese svstenis undergo unstable mass transfer during a conimion-envelope phase (Stairs2001).. which results iu he NS becoming a nülkdv recvcled millisecond. pulsar (MSDP).," Current models for binary stellar evolution predict that these systems undergo unstable mass transfer during a common-envelope phase \citep{stairs04:pulsars_binary_systems}, which results in the NS becoming a mildly recycled millisecond pulsar (MSP)." + This scenario would explain the high inferred uass for the companion of 5128.. well above he average for a NS. as a byproduct of the mass trausfer yroeess (Lattimer&Prakash2007).," This scenario would explain the high inferred mass for the companion of , well above the average for a NS, as a byproduct of the mass transfer process \citep{lattimer07:NS_EOS}." +". Df the NS is iudecd an MSP. we expect the magnetic field to be low (~10? Cass). the pulsar lifetime to be large (1 Cor). aud the opening augle to be wide (possiblymanytensofdegrees,seePhinney&I&ulkarui 1991)..."," If the NS is indeed an MSP, we expect the magnetic field to be low $\sim10^{9}$ Gauss), the pulsar lifetime to be large $\sim1$ Gyr), and the opening angle to be wide \citep[possibly many tens of degrees, see][]{phinney94:binary_and_ms_pulsars}." + Under these couditious. the prospects for detecting such a nearby. AISP are good. although we note that the cooling time for the WD is also of the order of Cyr (see Section 3.3)). aud the MSP nuelt have lost a large part of its maenuetic field.," Under these conditions, the prospects for detecting such a nearby MSP are good, although we note that the cooling time for the WD is also of the order of Gyr (see Section \ref{subsec:spectrum}) ), and the MSP might have lost a large part of its magnetic field." +" For Af,=0.92M. and inclination angles below 67° (6114( rvaudom Likelihood). the companion would probably be a stellar mass DIT."," For $M_{A}=0.92\,\mathrm{M_{\odot}}$ and inclination angles below $67^{\circ}$ $61\%$ random likelihood), the companion would probably be a stellar mass BH." + In this case. we would not expect αν sind of direct emission frou it.," In this case, we would not expect any kind of direct emission from it." + No radio or N-rav source appears at this location iu any of the indexed. astronomical catalogs. but this does rot preclude the existence of a faint counterpart to the companion of5128.," No radio or X-ray source appears at this location in any of the indexed astronomical catalogs, but this does not preclude the existence of a faint counterpart to the companion of." +. This part of the sky iis onlv been shallowly surveved for MSPs in the racio., This part of the sky has only been shallowly surveyed for MSPs in the radio. + The most stringent lanits are probably from the Crecn Bank 110 ft 350 MIITIZ survey. which lad a nominal sensitivity of 12-15 ταν (Saveretal.1997)..," The most stringent limits are probably from the Green Bank 140 ft 350 MHz survey, which had a nominal sensitivity of 12-15 mJy \citep{sayer97:GBT_northern_sky_pulsar_survey}." +" In the ravs. this location has never been observed with orNewton, aud a faint nearby source could have casily escaped detection by the All-Sky Survey."," In the X-rays, this location has never been observed with or, and a faint nearby source could have easily escaped detection by the All-Sky Survey." + A systematic cross-correlation between stellar sources 1u SDSS (ποιος all the WDs from E06) aud the catalogues was performed by Agüerosetal.(2009).. who ound no counterpart to15128.," A systematic cross-correlation between stellar sources in SDSS (including all the WDs from E06) and the catalogues was performed by \citet{agueros09:ROSAT_SDSS_Stars}, who found no counterpart to." +. One interesting implication of the companion of ος a NS or DII is that the system should have received some kind of kick from the SN explosion., One interesting implication of the companion of being a NS or BH is that the system should have received some kind of kick from the SN explosion. + Iu xinciple. the spatial velocity of cca be determuned by the temporal average of the jon-eravitational Doppler shifts iu the spectra. which eives the radial component. and the proper motion iieasured by SDSS (jp=04491228vr.1). which gives the colponcut on the plane of the sky.," In principle, the spatial velocity of can be determined by the temporal average of the non-gravitational Doppler shifts in the spectrum, which gives the radial component, and the proper motion measured by SDSS $\mu=0.049\,\mathrm{mas\,yr^{-1}}$ ), which gives the component on the plane of the sky." + Taking our distance estimate. the proper motion translates iuto a transverse velocity of 11aus1," Taking our distance estimate, the proper motion translates into a transverse velocity of $11^{+2}_{-4}\,\mathrm{km\,s^{-1}}$." + The radial coniponent is more difficult to estimate. because the coustaut conponent to the RV curve (24.=289+L6knis| in our fit. soe Section 3.2)) is the combination of the true radial velocity and the eravitational redshift of the WD.," The radial component is more difficult to estimate, because the constant component to the RV curve $\gamma_{A}=-28.9\pm4.6\,\mathrm{km\,s^{-1}}$ in our fit, see Section \ref{subsec:orbit}) ) is the combination of the true radial velocity and the gravitational redshift of the WD." + The value of the eravitational redshift depends on the WD amass. which we cannot measure with accuracy (see Section 3.3)). and the WD radius. which is also model depeudenut.," The value of the gravitational redshift depends on the WD mass, which we cannot measure with accuracy (see Section \ref{subsec:spectrum}) ), and the WD radius, which is also model dependent." + A detailed estimate of the eravitational redshitt for lis outside the scope of this work. but for a massive ~LAL. WD. we expect it to be of the order of οας+ (Weener&Reid1991).. which would require a radial velocity avound 120kus|.," A detailed estimate of the gravitational redshift for is outside the scope of this work, but for a massive $\sim1\,\mathrm{M_{\odot}}$ WD, we expect it to be of the order of $90\,\mathrm{km\,s^{-1}}$ \citep{wegner91:gravitational_redshift_WDs}, which would require a radial velocity around $-120\,\mathrm{km\,s^{-1}}$." + The total spatial velocity would then be ~120128.1. mostly in the radial direction. which is comparable to the measured kicks for pulsars im binary svstems (Waneetal.2006)..," The total spatial velocity would then be $\sim120\,\mathrm{km\,s^{-1}}$, mostly in the radial direction, which is comparable to the measured kicks for pulsars in binary systems \citep{wang06:NS_kicks}." + Regardless of what the nature of the companion to tturus out to be. the svsteii is clearly very interesting from απ astroplivsica ut oof view. and new observations should vield exciting results in the near future.," Regardless of what the nature of the companion to turns out to be, the system is clearly very interesting from an astrophysical point of view, and new observations should yield exciting results in the near future." +" From the measured orbital parameters. the separation of thecomponents must be small. with values of the semimajor axis lareer than 0.02 AU only for Ax17"" (0.0003 AU at ;/=607)."," From the measured orbital parameters, the separation of thecomponents must be small, with values of the semimajor axis larger than $0.02$ AU only for $i \leq 17^\circ$ $0.0093$ AU at $i = 60^\circ$ )." + Tf pulsations from a NS companion were detected. this could allow for a sjenificaut measurement of the Shapiro delay. as in PSR (715 (vauStratenetal. 2001)..," If pulsations from a NS companion were detected, this could allow for a significant measurement of the Shapiro delay, as in PSR $-$ 4715 \citep{vanstraten01:Shapiro_delay}. ." + The mereine time Paterge of the ssvsteni due to GW radiation is <511!M Aber with the uncertainty im this upper hut arising frou the uneertainty in the cetermination of A4.," The merging time $t_{Merge}$ of the system due to GW radiation is $\leq +511^{+342}_{-141}$ Myr, with the uncertainty in this upper limit arising from the uncertainty in the determination of $M_{A}$." + For the canonical inclination angle ¢=GOP. fij44; bocones 267|e Ab.," For the canonical inclination angle $i = 60^\circ$, $t_{Merge}$ becomes $267^{+165}_{-70}$ Myr." + We note that only three WD|NS binaries with fanggef;., We assume that the spectrum of radiation in the merger phase is confined to the frequency regime $f >f_i$. + As we discuss below. we cleline the end of the merger phase (ο occur when the waveform can be described by the /=m2 quasi-normal mode signal of a Ixerr black hole.," As we discuss below, we define the end of the merger phase to occur when the waveform can be described by the $l=m=2$ quasi-normal mode signal of a Kerr black hole." +" The quasi-normal ringing frequency f, gives an approximate upper-bound [ον the frequencies carrving substantial power during the merger (Flanagan llughes 1998).", The quasi-normal ringing frequency $f_q$ gives an approximate upper-bound for the frequencies carrying substantial power during the merger (Flanagan Hughes 1998). + where F(a)=120.63(1—a)! and a is the dimensionless spin parameter of the black hole (Echeverria 1989)., where $F(a)=1-0.63 (1-a)^{3/10}$ and $a$ is the dimensionless spin parameter of the black hole (Echeverria 1989). + Though (he energy spectrum could have some features related to the dvnamical instabilities (Zluge οἱ al., Though the energy spectrum could have some features related to the dynamical instabilities (Zhuge et al. + 1994: Dimmelmeier et al., 1994; Dimmelmeier et al. +" 2002). we assume the simplest flat spectrum with the following amplitude. Using eq (2)) and an approximation/,—f;~ J. the characteristic gravitational wave amplitude is given bv Ilere the AZ. ji and e; ave those appropriate to the end of the merger phase."," 2002), we assume the simplest flat spectrum with the following amplitude, Using eq \ref{eq:hc}) ) and an approximation$f_q-f_i \sim f_q$ , the characteristic gravitational wave amplitude is given by Here the $M$, $\mu$ and $\epsilon_m$ are those appropriate to the end of the merger phase." + If dynamical instabiliües develop in the rotating core or in (he rotating massive disk during the merger phase. the deformed core/cdisk could radiate strong gravitational waves in a narrow frequency band.," If dynamical instabilities develop in the rotating core or in the rotating massive disk during the merger phase, the deformed core/disk could radiate strong gravitational waves in a narrow frequency band." + The deformation may be considered. in ils simplest form. as either two blobs or a bar.," The deformation may be considered, in its simplest form, as either two blobs or a bar." + Using in either case a formula appropriate for a rotating bar (e.g. Frver. llolz IIughes 2002). we can estimate the amplitude of the corresponding exavitational wave enussion.," Using in either case a formula appropriate for a rotating bar (e.g. Fryer, Holz Hughes 2002), we can estimate the amplitude of the corresponding gravitational wave emission." + Considering a bar of mass mm and length 2r which rotates with angular frequency aw. (hemean strain is given by," Considering a bar of mass $m$ and length $2r$ which rotates with angular frequency $\omega$ , themean strain is given by" +outer regions.,outer regions. + The resulting evolution leads to star formation that is systematically less racially extended as time goes on., The resulting evolution leads to star formation that is systematically less radially extended as time goes on. + We can verily that the age gradient. observed. in. our simulations is established at formation rather than through stellar migration., We can verify that the age gradient observed in our simulations is established at formation rather than through stellar migration. + Figures 7. and 8 show the radius where stars formed as a function of time., Figures \ref{fig:kmsrformtform} and \ref{fig:bfrformtform} show the radius where stars formed as a function of time. + Ehe overall shape of Figures 7 and S closely resembles Figures 5. and 6:: both sets of figures show shrinking of the radial envelope within which stars form., The overall shape of Figures \ref{fig:kmsrformtform} and \ref{fig:bfrformtform} closely resembles Figures \ref{fig:kmsrtform} and \ref{fig:bfrtform}; both sets of figures show shrinking of the radial envelope within which stars form. + Formation location is therefore à primary factor in determining the final age gradient. rather than the degree of stellar migration.," Formation location is therefore a primary factor in determining the final age gradient, rather than the degree of stellar migration." + One aspect of Figures 5. and 6 that dillers greatly from Figures 7. and S is that many stars finish the simulation bevond where they form., One aspect of Figures \ref{fig:kmsrtform} and \ref{fig:bfrtform} that differs greatly from Figures \ref{fig:kmsrformtform} and \ref{fig:bfrformtform} is that many stars finish the simulation beyond where they form. + This outward movement is investigated in more detail in the next section., This outward movement is investigated in more detail in the next section. + Each of the models shows two distinct spatial regions., Each of the models shows two distinct spatial regions. + At small radii the star formation is abundant and nearly continuous.," At small radii, the star formation is abundant and nearly continuous." + At large radii. there is less star formation and what there is is episodic.," At large radii, there is less star formation and what there is is episodic." + During these episodes of elevated: star. formation. gas temporarily reaches star forming densities in the outer region of the disk. typically in spiral patterns.," During these episodes of elevated star formation, gas temporarily reaches star forming densities in the outer region of the disk, typically in spiral patterns." + Once the stars have formed. the supernova feedback disperses the dense gas and shuts down star formation.," Once the stars have formed, the supernova feedback disperses the dense gas and shuts down star formation." + 1n models with lower stellar mass. the cpisocic bursts are scattered. at regular. time intervals spacecl 300. Myr apart.," In models with lower stellar mass, the episodic bursts are scattered at regular time intervals spaced 300 Myr apart." + This timescale is similar to the star formation interval reported in ?.. and is related to the free fall time at the center ob halos.," This timescale is similar to the star formation interval reported in \citet{Stinson07}, and is related to the free fall time at the center of halos." + Higher mass galaxies also show similar episocic star formation. but only outside the inner stable star forming disk.," Higher mass galaxies also show similar episodic star formation, but only outside the inner stable star forming disk." + At large radii. the episodic star formation has a longer timescale of ~1 Gyr due to the lower characteristic densities associated with longer free fall times.," At large radii, the episodic star formation has a longer timescale of $\sim 1$ Gyr due to the lower characteristic densities associated with longer free fall times." + This episodie star formation can be explained with a delay cilferential equation as shown hy ?.., This episodic star formation can be explained with a delay differential equation as shown by \citet{Quillen2008}. + lor a More direct οςmparisc211 with observations. Figure 9 plots model CMDs showing the expected stellar populations in several radial bins.," For a more direct comparison with observations, Figure \ref{fig:cmds} plots model CMDs showing the expected stellar populations in several radial bins." + To create the CAIDs. we used StarISLE version 1.1 (?) to populate a set of isochrones (?) based on a user-supplied star-formation history. (SELL) set by the mass. age. metallicity (-2.3 « pefl] «-1 after 13.5 Gyr). and. position of the simulated star particles.," To create the CMDs, we used StarFISH version 1.1 \citep{harris01} to populate a set of isochrones \citep{Girardi02} based on a user-supplied star-formation history (SFH) set by the mass, age, metallicity (-2.3 $<$ [Fe/H] $<$ -1 after 13.5 Gyr), and position of the simulated star particles." + To mimic observing conditions. we adopted artificial star tests from the ACS Nearby Galaxy Survey (7). assuming that the simulated. galaxy is located at a distance of 500 kpe.," To mimic observing conditions, we adopted artificial star tests from the ACS Nearby Galaxy Survey \citep{Dalcanton2008} assuming that the simulated galaxy is located at a distance of 500 kpc." + The CALDs of the simulations show a prominent voung main sequence in the central 2 kpe that disappears at large radii., The CMDs of the simulations show a prominent young main sequence in the central 2 kpc that disappears at large radii. + The absence of the voung main sequence outside 2 kpe agrees with the age gradient shown in Figure 4.., The absence of the young main sequence outside 2 kpc agrees with the age gradient shown in Figure \ref{fig:ageprofile}. + Figure 9 also shows that any main sequence stars in the halo are more than 1 magnitude fainter than the red clump and horizontal branch. such that only the deepest. photometry in the nearest galaxies would. show evidence of this intermediate age population.," Figure \ref{fig:cmds} also shows that any main sequence stars in the halo are more than 1 magnitude fainter than the red clump and horizontal branch, such that only the deepest photometry in the nearest galaxies would show evidence of this intermediate age population." + The age gradient apparent in Figure 9. is consistent with the deep CALDs presented in Figure 2 of ? suggesting that isolated models can produce realistic stellar structure., The age gradient apparent in Figure \ref{fig:cmds} is consistent with the deep CMDs presented in Figure 2 of \citet{hidalgo03} suggesting that isolated models can produce realistic stellar structure. + While the location of star formation largely determines the age eracient and stellar structure of the galaxies. there are some features that are due to the motion of stars after they form.," While the location of star formation largely determines the age gradient and stellar structure of the galaxies, there are some features that are due to the motion of stars after they form." + Figures 10 and 11 highlight these cdillerences hy showing how far the stars have migrated. racially., Figures \ref{fig:kmsmigration} and \ref{fig:bfmigration} highlight these differences by showing how far the stars have migrated radially. +" The mean migration (dashed. line) in the constan f, 0.1 models shown in Figure 10. shows little deviation from zero (solid line). although many individual particles move a large distance."," The mean migration (dashed line) in the constant $f_b$ =0.1 models shown in Figure \ref{fig:kmsmigration} shows little deviation from zero (solid line), although many individual particles move a large distance." + For the lowest mass halos. most of this movement is in the outward direction and is concurren with star formation episodes.," For the lowest mass halos, most of this movement is in the outward direction and is concurrent with star formation episodes." + To explore this behavior. Figure 12. shows the stellar apocenters as a function of their velocity at the time of formation.," To explore this behavior, Figure \ref{fig:velsf} shows the stellar apocenters as a function of their velocity at the time of formation." + Compared to the vertical line at zero velocity. stars to the right formed from gas that was moving outwarels. while stars to the left formed as the gas was collapsing.," Compared to the vertical line at zero velocity, stars to the right formed from gas that was moving outwards, while stars to the left formed as the gas was collapsing." + There is a noticeable trend for stars with larger apocenters to. form with larger outward. velocities. particularly for the lowest mass 15 kms + halo.," There is a noticeable trend for stars with larger apocenters to form with larger outward velocities, particularly for the lowest mass 15 km $^{-1}$ halo." +— Physically. 1ese halo stars formed [rom outward [owing gas that was vecelerated: by supernovae. blastwaves and. shocks against infalling gas.," Physically, these halo stars formed from outward flowing gas that was accelerated by supernovae blastwaves and shocks against infalling gas." + Phe shock produces high densities and triggers μαar formation., The shock produces high densities and triggers star formation. + These stars are thus launched. on racial bits that create an extended stellar halo and a positively 4sewed velocity distribution., These stars are thus launched on radial orbits that create an extended stellar halo and a positively skewed velocity distribution. + Conversely. few stars. form uring the infall phase curing which shocks are weaker or ibsent.," Conversely, few stars form during the infall phase during which shocks are weaker or absent." + No stars are observed to be ereateck with sullicient nergv to become unbound from the chvarl galaxy., No stars are observed to be created with sufficient energy to become unbound from the dwarf galaxy. + Once the warf interacts with other satellites. some of these stars may become unbound.," Once the dwarf interacts with other satellites, some of these stars may become unbound." + Figure 12. suggests that shocks and instabilities in the SN-driven wind may be necessary for the formation of the most extended halo stars seen in dwarls., Figure \ref{fig:velsf} suggests that shocks and instabilities in the SN-driven wind may be necessary for the formation of the most extended halo stars seen in dwarfs. + To verily that the large radius. high initial velocity stars are indeed due to feedback. we have rerun the 15 km simulation. with feedback turned. oll.," To verify that the large radius, high initial velocity stars are indeed due to feedback, we have rerun the 15 km $^{-1}$ simulation with feedback turned off." + In. this simulation. no extended: halo forms.," In this simulation, no extended halo forms." + Instead. the distribution of apocenters is centered at zero radial velocity. consisting of disk stars formed from gas moving in stable circular orbits.," Instead, the distribution of apocenters is centered at zero radial velocity, consisting of disk stars formed from gas moving in stable circular orbits." + The signature of halo formation due to. supernova feedback is much reduced in higher mass galaxies. which form long-lived stable stelar disks.," The signature of halo formation due to supernova feedback is much reduced in higher mass galaxies, which form long-lived stable stellar disks." + In these cases. disk stars form on circular orbits anc appear near the zero initial racial velocity line in Figure 12..," In these cases, disk stars form on circular orbits and appear near the zero initial radial velocity line in Figure \ref{fig:velsf}." + ‘These stars may migrate outwards through disk instabilities (?).. but are unlikely to swell into a 3-dimensional halo.," These stars may migrate outwards through disk instabilities \citep{Roskar2008}, but are unlikely to swell into a 3-dimensional halo." + ligure 12 also sugecs sthat in the lowest mass galaxies. one expects a kinematic sienature where the outermost halo stars are all preferentially on radial orbits.," Figure \ref{fig:velsf} also suggests that in the lowest mass galaxies, one expects a kinematic signature where the outermost halo stars are all preferentially on radial orbits." + However. these stars can be strongly inlueneecl by tidal ellects. possibly making this signature cillicult to detect observationallv.," However, these stars can be strongly influenced by tidal effects, possibly making this signature difficult to detect observationally." +" Unlike in the f, nxxdels. the low f, models show an ollset between the mean initial and final radii as shown in Figure 11.."," Unlike in the $f_b$ models, the low $f_b$ models show an offset between the mean initial and final radii as shown in Figure \ref{fig:bfmigration}." + This olfset develops because while the halo potential well is deep enoteh that eas cools onto a disk. the gas is pressure supported and not dense enough to form stars outside the central region.," This offset develops because while the halo potential well is deep enough that gas cools onto a disk, the gas is pressure supported and not dense enough to form stars outside the central region." + ‘Thus. in these low fi models. the eas disk is significantly more massive than the stellar clisk ancl dominates the disk dynamics. as shown in Figure J DE ," Thus, in these low $f_b$ models, the gas disk is significantly more massive than the stellar disk and dominates the disk dynamics, as shown in Figure \ref{fig:gasstarmass}. ." +The stellar disk then meanders in response to the dominant influence of the gas., The stellar disk then meanders in response to the dominant influence of the gas. + As the stellar disk. meanders. Figure 1l shows that it scatters stars into the halo.," As the stellar disk meanders, Figure \ref{fig:bfmigration} shows that it scatters stars into the halo." + Stars that, Stars that +The spectruui of V132. Aur at primary uiuima is due ouly to the secoudary star. anc subtracting it from the spectrum at secondary eclipse would provide the spectrum of the primary component.,"The spectrum of V432 Aur at primary minimum is due only to the secondary star, and subtracting it from the spectrum at secondary eclipse would provide the spectrum of the primary component." + Unfortunately. during the scheduled spectroscopic observiug rus at the telescope. V132 Aur never passed through the primary eclipse. and therefore it has not been possible to obtain the isolated spectra of the individual components.," Unfortunately, during the scheduled spectroscopic observing runs at the telescope, V432 Aur never passed through the primary eclipse, and therefore it has not been possible to obtain the isolated spectra of the individual components." + To the aiu of performing an atmospheric analysis of the two components of V132 Aur we have therefore focused on the spectra of the highest S/N around phases 0.25 and 0.75 (cf., To the aim of performing an atmospheric analysis of the two components of V432 Aur we have therefore focused on the spectra of the highest S/N around phases 0.25 and 0.75 (cf. + Table 2). where the velocity separation of the components is asian aud the same lines from the two components are unbleded.," Table 2), where the velocity separation of the components is maximum and the same lines from the two components are unbleded." + Working siuultauncously at phase 0.25 and 0.75 allows also to eet rid of line superposition aud stronely reimforces the robustuess of the overall ft., Working simultaneously at phase 0.25 and 0.75 allows also to get rid of line superposition and strongly reinforces the robustness of the overall fit. + To derive the basic stellar parameters (τω. logg.o ‘Z| and Voor) we have performed a u best match analvsis of the high S/N observed spectra around phases 0.25 and 0.75 (spectrum 392323. 39239. 39605. 39291 and 39607 in Table 1) against the extensive erid of svuthetie Iuruczs spectra computed by Muni et al. (," To derive the basic stellar parameters $T_{\rm eff}$ , $\log g$, $_\odot$ ] and $V_{\rm rot}$ ) we have performed a $\chi^2$ best match analysis of the high S/N observed spectra around phases 0.25 and 0.75 (spectrum 39233, 39239, 39605, 39294 and 39607 in Table 1) against the extensive grid of synthetic Kurucz's spectra computed by Munari et al. (" +2003) for the same resolution of the Asiago Echelle spectrograph (R=20 0000) over the 5500 iranee (thus fully covering the wavelength rauge recorded or VI32 Aur),2003) for the same resolution of the Asiago Echelle spectrograph $R$ 000) over the $-$ 500 range (thus fully covering the wavelength range recorded for V432 Aur). + The Muuar et al. (, The Munari et al. ( +"2003) svuthetic atlas covers the range 355002Tigx 5500. 0loggyx:5.0. 5x |Z/Z.] € (with solar relative abundances or metals) and Ooo, then clearly Our proposed form of the gravitational (1.c., Hubble) radius in Equation (8) leads to the equality Αμ)= ομ."," If we now put $t_e\rightarrow 0$ and $z(t_e)\rightarrow \infty$, then clearly Our proposed form of the gravitational (i.e., Hubble) radius in Equation (8) leads to the equality $R_{\rm h}(t_0)=ct_0$ ." + Therefore; any cosmological model consistent withthe Weyl Postulate and the," Therefore, any cosmological model consistent withthe Weyl Postulate and the" +Period doubling. a phenomenon often observed in dynamical systems. was also found in stellar models and actual »ulsating variables in the last decades.,"Period doubling, a phenomenon often observed in dynamical systems, was also found in stellar models and actual pulsating variables in the last decades." + Period doubling (PD) means that the observed. quantity of the svstem alternates rclween a high. and low amplitude: evele., Period doubling (PD) means that the observed quantity of the system alternates between a high and low amplitude cycle. + Dynamical systenis as the simple Rosssler oscillator are usually capable of period doubling bifurcation. and through a series. of rifurcations called the can evolve to chaotic behaviour.," Dynamical systems as the simple Rösssler oscillator are usually capable of period doubling bifurcation, and through a series of bifurcations called the can evolve to chaotic behaviour." + The very definition of RY Tauri variables was originally the alternation of deep and shallow minima. a clear sign of PD Prestonetal. 1963)).," The very definition of RV Tauri variables was originally the alternation of deep and shallow minima, a clear sign of PD \citealt{preston63}) )." + “Phe phenomenon was reproduced by Fokin(1994). in radiative stellar models for RV Tauri stars as well as by Saitou.Takeuti&Tanaka(1989) in one-zone stellar models., The phenomenon was reproduced by \citet{fokin94} in radiative stellar models for RV Tauri stars as well as by \citet*{saitou89} in one-zone stellar models. + Models of Wo Vir variables (Buehler&IxovácsLOST) are also capable of bifurcation cascade towards chaos. and chaotic pulsations wereindeed identified in semiregular stars (Buehleretal.1996.. Ixolláth 1998... Buehler.Ixolláth.&Caclmus 2004)).," Models of W Vir variables \citep{bk87} are also capable of bifurcation cascade towards chaos, and chaotic pulsations wereindeed identified in semiregular stars \citealt{bksm96}, \citealt{kbsm98}, \citealt*{bkc04}) )." +. Period doubling was reported by Wiss&Szatmáry(2002). in the Mira star It Cvg., Period doubling was reported by \citet{kiss02} in the Mira star R Cyg. + Models of classical pulsators also showed oonmisng results., Models of classical pulsators also showed promising results. + Moskalik.&Buehler(1990) searched or half-integer resonances both in Cepheicl ancl RR Lyrac models and. indeed found PD in the former case (sec also Duchler&Aloskalik 1990))., \citet{mb90} searched for half-integer resonances both in Cepheid and RR Lyrae models and indeed found PD in the former case (see also \citealt{bm90}) ). + Α 2:3. resonance between the 'uncdamental mode and the first overtone was also iclentified as a root cause., A 2:3 resonance between the fundamental mode and the first overtone was also identified as a root cause. + But neither period. doubling nor suitable resonances were found in Rit Lyrae stars between the tundamental or first overtone and any higher modes up to he fourth overtone., But neither period doubling nor suitable resonances were found in RR Lyrae stars between the fundamental or first overtone and any higher modes up to the fourth overtone. + Aikawa(2001) also reported PD in very ong-period. radiative Cepheid mocdels but. did not identify any underlying resonance.," \citet{aikawa01} also reported PD in very long-period, radiative Cepheid models but did not identify any underlying resonance." + The signs of possible PD are the hall-integer frequencies (MILES) in the Fourier spectrum. in the form of (27|1)/2fy with respect to the fy main periodicity. sometimes. called as subharmonics.," The signs of possible PD are the half-integer frequencies (HIFs) in the Fourier spectrum, in the form of $ (2n+1)/2\, f_0 $ with respect to the $f_0$ main periodicity, sometimes called as subharmonics." + Similar peaks were found in some variable white dwarfs as well. suggesting PD in 11251|489 (Cioupiletal.1988). and even signs of four-period. behaviour in €G191-16 (Vauclairetal. 1989)..," Similar peaks were found in some variable white dwarfs as well, suggesting PD in PG1351+489 \citep{goupil88} and even signs of four-period behaviour in G191-16 \citep{vauc89}. ." + But because exact values usually differ slightlv from hall-inte@er values. they could," But because exact values usually differ slightly from half-integer values, they could" +origin is distinctly clouded.,origin is distinctly clouded. + In the solar svstem. copper owes ~30% of its abundance to the s-process weak (uassive star) and main (low mass star) components combined 1993).. with the remainder likely a product of some combination of SNe Type Ia and Type II.," In the solar system, copper owes $\sim$ of its abundance to the s-process weak (massive star) and main (low mass star) components combined \citep{Matteucci1993}, with the remainder likely a product of some combination of SNe Type Ia and Type II." +" Both the weak and main s-process are “secondary processes in (he sense that a ""secondary"" element requires a Fe (or Fe-peak) seed nucleus to build upon.", Both the weak and main s-process are “secondary” processes in the sense that a “secondary” element requires a Fe (or Fe-peak) seed nucleus to build upon. + Such an element is expected to decrease in abundance (relative to Fe) as the stars overall iron content decreases (because the production of the element depends upon the availability of seed Fe nuclei)., Such an element is expected to decrease in abundance (relative to Fe) as the star's overall iron content decreases (because the production of the element depends upon the availability of seed Fe nuclei). + In contrast. a “primary” process does not require a Fe seed nucleus. aud so the abundance of a primary element (relative to iron) should be constant wilh overall metallicity.," In contrast, a “primary” process does not require a Fe seed nucleus, and so the abundance of a primary element (relative to iron) should be constant with overall metallicity." + While [Cu/Fe] does decrease with metallicity in the manner of a secondary element. (he s-process contribution to copper is sharply restricted.," While [Cu/Fe] does decrease with metallicity in the manner of a secondary element, the s-process contribution to copper is sharply restricted." + Increasing the s-process component of copper in s-process nucleosvnthesis models overproduces other light s-process elements (like Sr). and models of chemical evolution [ail to reflect the observed. solar composition (Matteuccietal.1993:Daraffe&Takahashi1993).," Increasing the s-process component of copper in s-process nucleosynthesis models overproduces other light s-process elements (like Sr), and models of chemical evolution fail to reflect the observed solar composition \citep{Matteucci1993,Baraffe1993}." +. The massive star (weak s-process) contribution appears to be an order of magnitude too small to reproduce the Cu content of either the Sun or metal-poor stars. and it must be augmented by explosive nucleosvithesis.," The massive star (weak s-process) contribution appears to be an order of magnitude too small to reproduce the Cu content of either the Sun or metal-poor stars, and it must be augmented by explosive nucleosynthesis." + It is unclear whether the additional copper in field stars is produced mainly bv Type Ia supernovae (Matteuccietal.1993:Baralle&Takahashi1993) or bv Type 11 supernovae (Iimnmesetal.1995).," It is unclear whether the additional copper in field stars is produced mainly by Type Ia supernovae \citep{Matteucci1993, Baraffe1993} or by Type II supernovae \citep{Timmes1995}." +. Cohen(1978.1979. 1980)s early observations of copper abundances in giant stars of several globular clusters of varving metallicity (—2.4X [Fe/H] < —0.4) vielded somewhat ambiguous resulls.," \citet{Cohen1978, Cohen1979, Cohen1980}' 's early observations of copper abundances in giant stars of several globular clusters of varying metallicity $-2.4 \leq$ [Fe/H] $\leq -0.4$ ) yielded somewhat ambiguous results." + Cohen found evidence that copper is deficient. wilh respect to iron and that this deficiency may become larger at lower metallicities., Cohen found evidence that copper is deficient with respect to iron and that this deficiency may become larger at lower metallicities. + ILowever. uncertainties in the derived abundances related to hyperfine broadening in the Cu line made a clearer delineation of any such trend impossible (Cohen1980).," However, uncertainties in the derived abundances related to hyperfine broadening in the Cu line made a clearer delineation of any such trend impossible \citep{Cohen1980}." +. Early studies such as these showed no real abundance trends in globular cluster iron-peak elements. copper included (e.e..," Early studies such as these showed no real abundance trends in globular cluster iron-peak elements, copper included (e.g.," +much as a factor~2 in planet-star radius for an Earth mass moon with ες=0.01) from the parent star than (hie classical. stellar insolation. zone alone.,"much as a factor$\sim 2$ in planet-star radius for an Earth mass moon with $e_s=0.01$ ) from the parent star than the classical, stellar insolation, zone alone." +" llowever. in addition to the major caveat that the ""energv balance"" represented. by Equation 5 is extremely. approximate. it should be noted that the actual levels of tidal heating required in these zones can be as high as ~10° erg ! ? - which is a [actor ~10* larger than the surface heat flow estimated for Io."," However, in addition to the major caveat that the “energy balance” represented by Equation 5 is extremely approximate, it should be noted that the actual levels of tidal heating required in these zones can be as high as $\sim 10^6$ erg $^{-1}$ $^{-2}$ - which is a factor $\sim 10^3$ larger than the surface heat flow estimated for Io." + It is an interesting question whether or not this would create such an unstable surface environment that habitability would be compronmised., It is an interesting question whether or not this would create such an unstable surface environment that habitability would be compromised. + More modest heating levels are required {ο boost temperatures which are already close to temperate., More modest heating levels are required to boost temperatures which are already close to temperate. + The outer stable orbit (Equation 1) provides a natural scaling for a moon svstem architecture., The outer stable orbit (Equation 1) provides a natural scaling for a moon system architecture. +" A given hypothetical moon must have a semi-major axis of 3aeelop (assuming small eccentricities). where 3<1 and sae’>q""""*,"," A given hypothetical moon must have a semi-major axis of $\beta a_s^{outer}$ (assuming small eccentricities), where $\beta \leq 1$ and $\beta a_s^{outer}\geq a_s^{inner}$." +" We can also write this in terms of tidal heat flow: Thus. for a given exoplanet in (he sample used here we can estimate the (ime-averaged ITj vequired to attain a given 774, (Equation 5). and for an assumed set of moon properties. such as mass. orbital eccentricity. density. rigidity. dissipation. aud atmosphliere we can then evaluate the requirecl orbital radius of the moon aoulcrE"," We can also write this in terms of tidal heat flow: Thus, for a given exoplanet in the sample used here we can estimate the time-averaged $H_T$ required to attain a given $T_{eq}$ (Equation 5), and for an assumed set of moon properties, such as mass, orbital eccentricity, density, rigidity, dissipation, and atmosphere we can then evaluate the required orbital radius of the moon $\beta a_s^{outer}$." + We have applied (his calculation to the subset of known exoplanets considered above., We have applied this calculation to the subset of known exoplanets considered above. + Figure T summarizes the results for the example of a 0.1 moon (the minim mass moon likely capable of retaining a terrestrial-tvpe atmosphere) with an orbital eccentricity ol ος=0.01. density p;= 3g oE. and albedo. rigidity and dissipation commensurate wilh (hat estimated for Europa.," Figure 7 summarizes the results for the example of a $0.1$ $_{\oplus}$ moon (the minimum mass moon likely capable of retaining a terrestrial-type atmosphere) with an orbital eccentricity of $e_s=0.01$, density $\rho_s=3$ g $^{-3}$, and albedo, rigidity and dissipation commensurate with that estimated for Europa." + We have assumed an atmosphere with e=0.62., We have assumed an atmosphere with $\epsilon=0.62$. +" To attain a moon surface temperature 7;,=272A then (as described above) 46 of the exoplanets would require a moon to have My>0 to boost the stellar insolation. lor Ti,=3134Y. then 10 of the exoplanets would require a moon to have fy>0."," To attain a moon surface temperature $T_{eq}=273 K$ then (as described above) 46 of the exoplanets would require a moon to have $H_T>0$ to boost the stellar insolation, for $T_{eq}=373 K$ then 70 of the exoplanets would require a moon to have $H_T>0$." + In Figure 7 we plot the distribution of both the absolute orbital semianajor axis required [for such moons aud (he ratio of this orbital axis to the inner (a) stable orbital semi-major axis., In Figure 7 we plot the distribution of both the absolute orbital semi-major axis required for such moons and the ratio of this orbital axis to the $a_s^{inner}$ ) stable orbital semi-major axis. + The latter plot confirms that such moons would reside comfortably outside of the inner Roche limit., The latter plot confirms that such moons would reside comfortably outside of the inner Roche limit. +19343--2026. is a high mass protostellar object candidate located al a kinematic distance (measured using NIL; line velocities) of 4.2 kpe. with a FIR luninosity of 2.7x10! L. (Molinarietal.1996).,"19343+2026, is a high mass protostellar object candidate located at a kinematic distance (measured using $_3$ line velocities) of 4.2 kpc, with a FIR luminosity of $\times$ $^4$ $_{\odot}$ \citep{mol96}." +. This cluster is detected in the GLIMIPSE survey (cluster 24 of Mercer 2005))., This cluster is detected in the GLIMPSE survey (cluster 24 of \citealt*{mcm05}) ). + Section 2 describes (he detailed observations., Section 2 describes the detailed observations. + The photometric. spectroscopic and SED modelling results are also presented im (his section.," The photometric, spectroscopic and SED modelling results are also presented in this section." + The implications of the results are discussed in Section 3., The implications of the results are discussed in Section 3. + We then summarize our conclusions in Section 4., We then summarize our conclusions in Section 4. + NIB. photometric imaging observations were made al (he 3.8 m United Kingdom luilrarecl Telescope (UAIRT) with the [αοαν imager UFTI (Rocheetal.2002)., NIR photometric imaging observations were made at the 3.8 m United Kingdom Infrared Telescope (UKIRT) with the facility imager UFTI \citep{roche02}. +. UFTI houses a ILAWAII-I 1024 x 1024 pixel array., UFTI houses a HAWAII-1 1024 $\times$ 1024 pixel array. +" The UFTI plate scale of 0.091"" &ives an available field of view (FOV) of ~90"".", The UFTI plate scale of $\arcsec$ gives an available field of view (FOV) of $\sim 90\arcsec$. +" Photometric observations through J (A=1.25pam... AA=0.16 jn). IH (À=1.64yon.. XA=0.29 jam) and WA=2.20jam.. AA=0.34 jm) broad-band filters were obtained for the IRAS source during the night of 26"" June 2002."," Photometric observations through $J$ $\lambda=1.25$, $\Delta\lambda=0.16$ ), $H$ $\lambda=1.64$, $\Delta\lambda=0.29$ ) and $K$ $\lambda=2.20$, $\Delta\lambda=0.34$ ) broad-band filters were obtained for the IRAS source during the night of $^{th}$ June 2002." + An integration time of GO sec was used in each of the J. ££ and A band filters: averaging Ποιοί exposures vielded a total exposure Gime of 540 seconds in each band.," An integration time of 60 sec was used in each of the $J$, $H$ and $K$ band filters; averaging jittered exposures yielded a total exposure time of 540 seconds in each band." +" The mean seeing measured was 0.6"" in the A-band images.", The mean seeing measured was $\arcsec$ in the $K$ -band images. +" A nine point (2x3) jittered observing sequence was executed to obtain data that provided final mosaics with a total FOV of —115""x115"".", A nine point $\times$ 3) jittered observing sequence was executed to obtain data that provided final mosaics with a total FOV of $\sim$ $\arcsec\times$ $\arcsec$. + We note that the signal-to-noise ratio at the edges of these mosaics is lower than within the central area., We note that the signal-to-noise ratio at the edges of these mosaics is lower than within the central area. + Standard data reduction techniques involving dark subtraction aud mecdian-sky-fLTat-fielding ol the jittered object Iraaes were applied., Standard data reduction techniques involving dark subtraction and median-sky-flat-fielding of the jittered object frames were applied. + The A-band image of IRAS 193434-2026 is shown in Fig., The $K$ -band image of IRAS 19343+2026 is shown in Fig. + 1l. with an overlay ofSpitzer MIPS 24 jm contours.," 1, with an overlay of MIPS 24 $\mu$ m contours." + Subsequent (ο our observations. (his region was recently covered by (he UAIRT Infrared Deep Sky Survey (UIXIDS5: Lawrenceοἱal. 2007)) Galactic Plane Survey (GPS).," Subsequent to our observations, this region was recently covered by the UKIRT Infrared Deep Sky Survey (UKIDSS; \citealt*[]{lawrence07}) ) Galactic Plane Survey (GPS)." + The GPS is an ambitioussurvey of the Northern Galactic plane (Lucasetal.2003)., The GPS is an ambitioussurvey of the Northern Galactic plane \citep{lucas08}. +. The aim of the survey is (o map 1800 square degrees of the plane (|b| « 5 deg) in J. H/. and K to a depth ol J ~ 20.0. HI. — 19.1. ἐν 19.0 at sub-arcsecond resolution.," The aim of the survey is to map 1800 square degrees of the plane $|$ $|$ $<$ 5 deg) in $J$, $H$, and $K$ to a depth of $J$ $\sim$ 20.0, $H$ $\sim$ 19.1, $K$ $\sim$ 19.0 at sub-arcsecond resolution." + UIXKIDSS emplovs the Wide Field Camera (WFECAXM: Casalietal. 2007)) at UIXIRE., UKIDSS employs the Wide Field Camera (WFCAM; \citealt*[]{cas07}) ) at UKIRT. + WECAM contains four Rockwell Hawaii-II (11οςΤο 2048x2048 pixel) arravs spaced by in the focal plane., WFCAM contains four Rockwell Hawaii-II (HgCdTe 2048x2048 pixel) arrays spaced by in the focal plane. + With a pixel scale of the field. of view of each array is 13., With a pixel scale of the field of view of each array is . +7... All UIXIDSS. survey data are reduced. by the, All UKIDSS survey data are reduced by the +principle no natural mechanism in the setup that might break spherical symmetry.,principle no natural mechanism in the setup that might break spherical symmetry. +" So, what was the point in considering different-from-spherical enhangoon shells?"," So, what was the point in considering different-from-spherical enhançoon shells?" + Consider the case of two monopoles., Consider the case of two monopoles. + The first brane is placed at the origin so it is one monopole., The first brane is placed at the origin so it is one monopole. +" Now try to bring another brane to wrap on it, another brane on the same footing not a probe."," Now try to bring another brane to wrap on it, another brane on the same footing not a probe." + The six dimensional supergravity ansatz for the metric of this brane setup is clearly axially symmetric., The six dimensional supergravity ansatz for the metric of this brane setup is clearly axially symmetric. +" So, what is the point in considering that the branes finally melt out in a spherical enhancoon shell?"," So, what is the point in considering that the branes finally melt out in a spherical enhançoon shell?" + The above argument suggests that there is in principle no especial preference for spherical shells., The above argument suggests that there is in principle no especial preference for spherical shells. +" Moreover, that a non spherical geometry for the enhangoon locus is naturally favoured."," Moreover, that a non spherical geometry for the enhançoon locus is naturally favoured." +" However, although suggesting, the argument is inconclusive."," However, although suggesting, the argument is inconclusive." + Sphericalness may seem capricious but still within the brane picture whereas it is in a two or higher charge configuration from the field theory point of view., Sphericalness may seem capricious but still within the brane picture whereas it is in a two or higher charge configuration from the field theory point of view. + A satisfactory dynamical mechanism should rule out spherical enhangoon shells., A satisfactory dynamical mechanism should rule out spherical enhançoon shells. +" Fortunately, there is an elegant way out the spherically symmetric puzzle which involves phenomena beyond SUGRA."," Fortunately, there is an elegant way out the spherically symmetric puzzle which involves phenomena beyond SUGRA." + Recall that the enhancoon locus is the place where the probe brane (and also the gravitating one as seen by the probe) becomes tensionless., Recall that the enhançoon locus is the place where the probe brane (and also the gravitating one as seen by the probe) becomes tensionless. + At large distance from r=0 the probe was pointlike in the six noncompact dimensions., At large distance from $r=0$ the probe was pointlike in the six noncompact dimensions. +" However as the distance to the center approaches r,. the brane seems to ""emerge"" and smear on a four dimensional sphere over the noncompact dimensions.", However as the distance to the center approaches $r_e$ the brane seems to “emerge” and smear on a four dimensional sphere over the noncompact dimensions. +" Some lines above, it was explained that the geometry of the enhancoon need not to be spherical but a large family of shapes are both available an consistent with the enhancoon mechanism [14,26].."," Some lines above, it was explained that the geometry of the enhançoon need not to be spherical but a large family of shapes are both available an consistent with the enhançoon mechanism \cite{AM, DJJ}." + This was a comforting way out of the necessity of spherical symmetry but left us with an uneasy family of arbitrary shapes which are all on equal footing with the sphere., This was a comforting way out of the necessity of spherical symmetry but left us with an uneasy family of arbitrary shapes which are all on equal footing with the sphere. + Why are all valid?, Why are all valid? + Is there any mechanism that rules out any of them?, Is there any mechanism that rules out any of them? + It seems a little naive though to think of such geometries at a region where the branes are blown in new (noncompact) dimensions and spacetime seem not to behave ordinarily., It seems a little naive though to think of such geometries at a region where the branes are blown in new (noncompact) dimensions and spacetime seem not to behave ordinarily. +" Indeed, it is believed that the correct description of the geometry near the enhangcoon locus is a fuzzy sphere [27].."," Indeed, it is believed that the correct description of the geometry near the enhançoon locus is a fuzzy sphere \cite{M}." +" Fuzzy spheres and more generally, non-commutative geometries break unavoidably spherical symmetry."," Fuzzy spheres and more generally, non-commutative geometries break unavoidably spherical symmetry." +" Moreover, Riemannian geometry and the concept of manifold are no longer valid in this context."," Moreover, Riemannian geometry and the concept of manifold are no longer valid in this context." +" It is remarkable, besides, that the fuzzy geometry appears for .N>1 and so the charge-1 monopole does not get affected and recovers spherical symmetry as expected."," It is remarkable, besides, that the fuzzy geometry appears for $N>1$ and so the charge-1 monopole does not get affected and recovers spherical symmetry as expected." +" We will indicate within the next sections the relation between the brane setup, the monopoles and the fuzzy geometry."," We will indicate within the next sections the relation between the brane setup, the monopoles and the fuzzy geometry." +"In Figure 3. we compare the relation between Y ray luminosity and massweighted. temperature. Z5,4. for the WR and LR runs with gravitational heating (GIL) only.","In Figure \ref{fi:lt_res} we compare the relation between $X$ –ray luminosity and mass–weighted temperature, $T_{mw}$, for the HR and LR runs with gravitational heating (GH) only." + Increasing the resolution has a nonnegligible elect on the estimated Vo ray. luminosity. while. as expected. has only a marginal effect on the massweighted temperature.," Increasing the resolution has a non–negligible effect on the estimated $X$ –ray luminosity, while, as expected, has only a marginal effect on the mass–weighted temperature." + The £x value for the Εν run of the Virgo cluster is ~25% higher han for the LI run. the dilference increasing to 50% for he Fornax group and to 10054 for the Lickson group.," The $L_X$ value for the HR run of the Virgo cluster is $\sim 25\%$ higher than for the LR run, the difference increasing to $\sim 50\%$ for the Fornax group and to $\sim 100\%$ for the Hickson group." + We also verified that decreasing the softening by a factor two or the Fornax and Hickson runs. while keeping the mass resolution fixed. increases Ly by aboutπι Lus showing hat the adopted spatial resolution is adequate to resolve all he structures which are responsible for the No ray emission.," We also verified that decreasing the softening by a factor two for the Fornax and Hickson runs, while keeping the mass resolution fixed, increases $L_X$ by about, thus showing that the adopted spatial resolution is adequate to resolve all the structures which are responsible for the $X$ –ray emission." + In fact. at the highest resolution of our runs. the number of massive subhalos (ic. with circular velocity larger than enth of that of the main halo) is likely to have converged (Ghigna et al.," In fact, at the highest resolution of our runs, the number of massive subhalos (i.e., with circular velocity larger than one--tenth of that of the main halo) is likely to have converged (Ghigna et al." + 2000)., 2000). + We expect spatial resolution to be even loss of an issue when considering simulations with extra wating (see below)., We expect spatial resolution to be even less of an issue when considering simulations with extra heating (see below). + Indeed. in this case the σας is put on a ügher adiabat and. therefore. does not follow the smallscale potential wells which are characterized by a virial emperature of a few tens of keV. We stress that the ΕΙ runs predict a Ly 1) relation which agrees well. both in slope and normalization. with the prediction of the sealing model of eq.(2)) for a pure bremsstrahlung cooling function.," Indeed, in this case the gas is put on a higher adiabat and, therefore, does not follow the small--scale potential wells which are characterized by a virial temperature of a few tens of keV. We stress that the HR runs predict a $L_X$ $T$ relation which agrees well, both in slope and normalization, with the prediction of the scaling model of \ref{eq:lth}) ) for a pure bremsstrahlung cooling function." + We consider this agreement as a convincing indication that the Lt runs provide a correct description of the gas distribution. which requires using at least c5«103 particles within the virial racius.," We consider this agreement as a convincing indication that the HR runs provide a correct description of the gas distribution, which requires using at least $\simeq 5\times 10^4$ particles within the virial radius." + This result is in agreement with that from resolution studies involving the collisionless component only (e.g. Moore et al., This result is in agreement with that from resolution studies involving the collisionless component only (e.g. Moore et al. + 1998). which established the minimum number of particles required to correctly model the central profile of dark matter halos.," 1998), which established the minimum number of particles required to correctly model the central profile of dark matter halos." + Fig., Fig. + 3. also highlights a common problem of simulations of large cosmological volumes atresolution: as resolution becomes worse for smaller. masses. Lx becomes underestimated.," \ref{fi:lt_res} also highlights a common problem of simulations of large cosmological volumes at: as resolution becomes worse for smaller masses, $L_X$ becomes underestimated." + For instance. taking the same mass and spatial resolution for the Virgo. Fornax and Lickson runs would produce spurious steepening of the relation.," For instance, taking the same mass and spatial resolution for the Virgo, Fornax and Hickson runs would produce spurious steepening of the relation." + Finally. while a pure bremsstrahlung emissivity is à σου approximation at Z22 keV. the effect. of line emission is shown to become important for smaller/cooler systems.," Finally, while a pure bremsstrahlung emissivity is a good approximation at $T\magcir 2$ keV, the effect of line emission is shown to become important for smaller/cooler systems." + Lhe net effect of properly accounting for them is that of Hlattening the relation. thus further increasing the ciserepaney with respect to observations at the scale of poor clusters and. groups.," The net effect of properly accounting for them is that of flattening the relation, thus further increasing the discrepancy with respect to observations at the scale of poor clusters and groups." +This is illustrated iu the iuset pancl in Fie.,This is illustrated in the inset panel in Fig. + H4. (owervieht).," \ref{maxdisk} + (lower-right)." + Using the aremuents m Zwaanctal.(1995) we fud that Sy(Y)? needs to be coustaut for galaxies to obev a TF relation independent of surface brightucss., Using the arguments in \citet{zwaan_tf95} we find that $\Sigma_0(\Upsilon)^2$ needs to be constant for galaxies to obey a TF relation independent of surface brightness. + If all galaxies were truly maxiuun disk Gu the seuse that Vuax(disk) 2Vinax (observed). oue could replace this by the requirement that ου(ΓιHas needs to be constant.," If all galaxies were truly maximum disk (in the sense that $V_{\rm max}$ (disk) $\simeq V_{\rm max}$ (observed), one could replace this by the requirement that $\Sigma_0(\Upsilon_\star)_{\rm max}^2$ needs to be constant." + The lower-right pancl shows that this is not the case: at fixed Vas there is a substantial scatter which would translate in D mag scatter in TF., The lower-right panel shows that this is not the case: at fixed $V_{\rm max}$ there is a substantial scatter which would translate in $\sim 5$ mag scatter in TF. + Clearly the observed scatter is ος snidler. and this shows the clear need for au additional mass component to make TE work.," Clearly the observed scatter is much smaller, and this shows the clear need for an additional mass component to make TF work." + Iu other words. naxiuun disk for ealaxies aud TF are incompatible.," In other words, maximum disk for galaxies and TF are incompatible." + The imost mnuportaut conclusion frou this work is that the huge majority of the ligh-resolution rotation curves presented here prefer the pseudo-isothermal core-donünated halo model., The most important conclusion from this work is that the large majority of the high-resolution rotation curves presented here prefer the pseudo-isothermal core-dominated halo model. + For a small nuuber of galaxies neither the pseudo-isothermal nor the NFW models are an adequate description of the data., For a small number of galaxies neither the pseudo-isothermal nor the NFW models are an adequate description of the data. + This should not come as a surprise as the true DAL distribution is likely to be more complex than the models presented here., This should not come as a surprise as the true DM distribution is likely to be more complex than the models presented here. + Nevertheless. the general trend is that for alinost all galaxies discussed here the relative quality of the fits using the pseudo-isothermal model is better than those for the NFW 1nocdel.," Nevertheless, the general trend is that for almost all galaxies discussed here the relative quality of the fits using the pseudo-isothermal model is better than those for the NFW model." + For a siuiall umuer of galaxies the NEW model provides a eood fit. but geucrally the couceutrations derived from the observed rotation curves are lower than predicted by the simulations.," For a small numer of galaxies the NFW model provides a good fit, but generally the concentrations derived from the observed rotation curves are lower than predicted by the simulations." + This is hard to fix: the most likely effect which iav alter the initial cosmological NEW halo is adiabatic contraction. but this has the effect of making the fal (observed) halo couceutrated. so one would have to start off with (cosimologically relevant) halos that are even concentrated.," This is hard to fix: the most likely effect which may alter the initial cosmological NFW halo is adiabatic contraction, but this has the effect of making the final (observed) halo concentrated, so one would have to start off with (cosmologically relevant) halos that are even concentrated." +" It is worrving that for one or two extreme cases he difference between ""CDAML does work” or ""CDM doesu't work” depends on subtle differences in data. data iudlius. or analysis."," It is worrying that for one or two extreme cases the difference between “CDM does work” or “CDM doesn't work” depends on subtle differences in data, data handling, or analysis." + Figure 7 illustrates that opposite clainis can sometimes be made from the same data., Figure \ref{nfwswaters} illustrates that opposite claims can sometimes be made from the same data. + Heuce we re-iterate the need for the highest quality data of a aree saniple. in order to ΙΙχο these effects.," Hence we re-iterate the need for the highest quality data of a large sample, in order to minimize these effects." + We refer to deBloketal.(2001) where it is shown hat data prescuted here are consistent with a core-douninated model: the good NEW fits that are fouud for a number of LSB ealaxics can be attributed to resolution effects., We refer to \citet{paper3} where it is shown that data presented here are consistent with a core-dominated model; the good NFW fits that are found for a number of LSB galaxies can be attributed to resolution effects. + We stmunarize our results as follows., We summarize our results as follows. + We thank Roclof Bottema aud Rob Swaters for their helpful comments on carly drafts of this paper., We thank Roelof Bottema and Rob Swaters for their helpful comments on early drafts of this paper. + We thas the anonvinous referee for a thorough examination of the data., We thank the anonymous referee for a thorough examination of the data. + The work of SSM is supported iu part by NSF eraut. AST9901663., The work of SSM is supported in part by NSF grant AST9901663. + This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Tustitute of Techuologv. uncer contract with the National Acronauties and Space Adiinistration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." + This rescarch has made use of NASA's Astrophysics Data System Abstract Service., This research has made use of NASA's Astrophysics Data System Abstract Service. +has led to the notion of the condensation rank of topological spaces. see [11]. and also cf.,"has led to the notion of the condensation rank of topological spaces, see \cite{mg} and also c.f." + [ο for the classical rank due to Cantor-Dendixson., \cite{CP} for the classical rank due to Cantor-Bendixson. + The measure-preserving property of the condensation derivative ancl its iteration up to the condensation rank of the space provides a sufficient tool to prove a modified version of the Aleksandrov's theorem: a set with finite and positive measure in any regular non-atomic Borel measure space contains a perlect sel whose measure is positive., The measure-preserving property of the condensation derivative and its iteration up to the condensation rank of the space provides a sufficient tool to prove a modified version of the Aleksandrov's theorem: a set with finite and positive measure in any regular non-atomic Borel measure space contains a perfect set whose measure is positive. +" It is also shown that lor any ordinal number. sav a. there exists an appropriate totallv imperlect IHauscdorff topological space whose condensation rank is a. In the case of non-limit ordinal numbers. the space can be a totally imperfect ""compact space. see [L1].."," It is also shown that for any ordinal number, say $\alpha,$ there exists an appropriate totally imperfect Hausdorff topological space whose condensation rank is $\alpha.$ In the case of non-limit ordinal numbers, the space can be a totally imperfect “compact"" space, see \cite{mg}." + Some relevant discussions and applications in locally compact groups are also presented in |12].., Some relevant discussions and applications in locally compact groups are also presented in \cite{mgph}. + However. there has not been any discussion on or result of the condensation rank of Danach spaces.," However, there has not been any discussion on or result of the condensation rank of Banach spaces." + In the next section we define (he condensation derivative and the condensation rank., In the next section we define the condensation derivative and the condensation rank. + We also provide some necessary preliminary results from |LI.12]..," We also provide some necessary preliminary results from \cite{mg, mgph}." + In section ??.. we present our main result. that is. (he condensation rank of any infinite dimensional injective Banach space is equal to or greater than the first uncountable ordinal number.," In section \ref{inject}, we present our main result, that is, the condensation rank of any infinite dimensional injective Banach space is equal to or greater than the first uncountable ordinal number." + Let X be a Hausdorff topological space., Let $X$ be a Hausdorff topological space. + A Borel derivative on 25 is a Borel map which is monotone on the closed subsets of X. i.e.D(N)&NK for any closed set Iv.," A Borel derivative on $2^X$ is a Borel map $D:2^X\rightarrow 2^X$ which is monotone on the closed subsets of $X$, i.e.,$D(K)\subseteq K$ for any closed set $K$." +" For a Borel derivative D:22—25 and an ordinal number o. the a-th iterated derivative D:25—25 is defined inductively as follows: D'(N)=N. D(NK)=DID""(K)) and D(N)=f),.,,DUx). For limit ordinal number a."," For a Borel derivative $D:2^X\rightarrow 2^X$ and an ordinal number $\alpha$ , the $\alpha$ -th iterated derivative $D^\alpha: 2^X\rightarrow 2^X$ is defined inductively as follows: $D^0(K)=K$, $D^{\alpha+1}(K)=D(D^\alpha(K))$ and $D^\alpha(K)=\bigcap_{\beta\prec\alpha} D^\beta(K)$, for limit ordinal number $\alpha$." + Each D is à Borel map. c.f [5].. where ihe Borel complexity of the iterations is investigated.," Each $D^\alpha$ is a Borel map, c.f \cite{CM83}, where the Borel complexity of the iterations is investigated." + An illuminating presentation of Borel derivatives is given by IXechris [13].., An illuminating presentation of Borel derivatives is given by Kechris \cite{Ke94}. + A point p€X is called a condensation point of ACNX if any neighborhood of p contains an uncountable number of points Irom sl., A point $p\in X$ is called a condensation point of $A\subseteq X$ if any neighborhood of $p$ contains an uncountable number of points from $A$. + We reler to the set of all condensation points of 4 as the condensation derived set (CDS) of A and denote CD for the condensation derivative. (hat is à set valued funcüon. which maps any set (o its CDs.," We refer to the set of all condensation points of $A$ as the condensation derived set $\rm CDS$ ) of $A$ and denote $\rm CD$ for the condensation derivative, that is a set valued function, which maps any set to its $\rm CDS$." + Note that the maximal perfect subset of the closure of a set is called its perfect. kernel., Note that the maximal perfect subset of the closure of a set is called its perfect kernel. + Denote ayB as the least ordinal number among5 those which satisfy Lemma 2.1.., Denote $\alpha_A$ as the least ordinal number among those which satisfy Lemma \ref{ordinal}. . + Then. ↽↽ bU ⋅ ↕∫≼↽⊲↻∪⋖↜⇀∣↥∏⊳∩≜↓↕⋟∖⊽≀↧↪∖⊽⊔⋅↕≺∢⊔⋡∖⇁≼⇂≼↲⋟∖⊽≺∢≼↲∐≼∐∐≸≟≺∢↥⋯↴↕∐⋅⋅⋅," Then, $\{{\rm CD}^\alpha(A)\}^{\alpha_A}_{\alpha=1}$ is a strictly descendingchain." + The idea of the CR defined here is similar. but not identical idea. to the idea of classical rank due Cantor-Dendixson. cL. [6]..," The idea of the ${\rm CR}$ defined here is similar, but not identical idea, to the idea of classical rank due Cantor-Bendixson, c.f. \cite{CP}. ." +is luminous closer to than to of the time.,is luminous closer to than to of the time. + For the duty evele to fully reach a track with either a large (25% or more) radiative efficiency or a steep decline (towards £L) appears to be required.," For the duty cycle to fully reach, a track with either a large $\sim 25\%$ or more) radiative efficiency or a steep decline (towards $t^{-10}$ ) appears to be required." +" The implication is that SAIBLE evolution might not involve ""Hickering"". i.e. interspersed periods of luminous accretion and. quiescence on à LO’ vear timescale (?).. Ó]n"," The implication is that SMBH evolution might not involve “flickering”, i.e., interspersed periods of luminous accretion and quiescence on a $\sim 10^7$ year timescale \citep{Hatziminaoglou2001}." +nstead. a simpler picture suggests itself: (1) the SALDLIL is seeded: (2) the SMDII grows until it enters the SDSS catalog at the low-mass end and at the Iddington uminositv: (3) the SMBLIID accretes as a Type 1 quasar for 12 Gyr while the Eddington ratio declines sharply: and (4) the SIBLE permanently ceases its rapid. unobscured. unminous accretion. with various possible post-turnolf states including dquiescence. Sevferts. ancl Type 2 quasars.," Instead, a simpler picture suggests itself: (1) the SMBH is seeded; (2) the SMBH grows until it enters the SDSS catalog at the low-mass end and at the Eddington luminosity; (3) the SMBH accretes as a Type 1 quasar for $1-2$ Gyr while the Eddington ratio declines sharply; and (4) the SMBH permanently ceases its rapid, unobscured, luminous accretion, with various possible post-turnoff states including quiescence, Seyferts, and Type 2 quasars." + “Phis λογο also requires a low value of 5. corresponding to decline proportional to f° or sleeper.," This picture also requires a low value of $\kappa$ , corresponding to decline proportional to $t^{-6}$ or steeper." + The possibility ofa short. 1.2 €ivr quasar lifetime is xurticularlv intriguing in light of two additional results from he AJ.L plane.," The possibility of a short, $1-2$ Gyr quasar lifetime is particularly intriguing in light of two additional results from the $M-L$ plane." + The characteristic luminosity for quasar acecretion at fixed mass and redshift requires that accretion rates be svnchronizec to within 1.2 Gwe (7)..., The characteristic luminosity for quasar accretion at fixed mass and redshift requires that accretion rates be synchronized to within $1-2$ Gyr \citep{Steinhardt2010b}. + Also. quasar urnoll is svnchronized. depending upon the mass. to within 1753 Gor for Aledf10AJ. (2).," Also, quasar turnoff is synchronized, depending upon the mass, to within $0.75-3$ Gyr for $M_BH > 10^9 M_\odot$ \citep{Steinhardt2010b}." + Perhaps the similarity of these three synchronization timescales could be explaine » à svnchronization in the times with which quasars turn ancl follow a common track in the ALL plane combine with short lifetimes., Perhaps the similarity of these three synchronization timescales could be explained by a synchronization in the times with which quasars turn and follow a common track in the $M-L$ plane combined with short lifetimes. + Ashort-lived Pype 1 quasar phase might seem to violate the Soltan argument because the SMDII spends most. of its time in another state., A short-lived Type 1 quasar phase might seem to violate the Soltan argument because the SMBH spends most of its time in another state. + The Soltan argument shows tha most of the total quasar mass in the universe was accretec Iuminously in Twpe 1 quasar states., The Soltan argument shows that most of the total quasar mass in the universe was accreted luminously in Type 1 quasar states. + However. the Soltan argument only places a limit on the last 2-32 e-foldings of mass growth. during which most of the mass is added.," However, the Soltan argument only places a limit on the last 2-3 e-foldings of mass growth, during which most of the mass is added." + Prior to these last e-foldings. we do not know how much of the erowth takes place through luminous accretion.," Prior to these last e-foldings, we do not know how much of the growth takes place through luminous accretion." + Even these short tracks with decline between //U and £I grow the SALDII by 1-1.4 dex. i.e. 2-3 e-foldings. so such solutions are allowed.," Even these short tracks with decline between $t^{-6}$ and $t^{-10}$ grow the SMBH by 1-1.4 dex, i.e., 2-3 e-foldings, so such solutions are allowed." + As shown in Figures Figures 11.12.. 15.. ancl 16.. it is possible that one scaling law for feedback. with universal parameters might be able to describe the evolution of all quasars at all initial masses and times.," As shown in Figures Figures \ref{fig:allpl4panel}, \ref{fig:allexp4panel}, \ref{fig:allbothMgoverlap}, and \ref{fig:allintbothMgoverlap}, it is possible that one scaling law for feedback with universal parameters might be able to describe the evolution of all quasars at all initial masses and times." + The existence of a characteristic luminosity at. each combination of mass and redshift’ is insullicient to require such a uniformity among the evolution of individual quasars., The existence of a characteristic luminosity at each combination of mass and redshift is insufficient to require such a uniformity among the evolution of individual quasars. + However. (1) the synchronization between quasars at fixed mass. (2) the narrow Luminosity range at fixed mass and redshift. and (3) the sharp peak in number density at a single. characteristic luminosity at fixecl mass and redshift (ef 2))," However, (1) the synchronization between quasars at fixed mass, (2) the narrow luminosity range at fixed mass and redshift, and (3) the sharp peak in number density at a single, characteristic luminosity at fixed mass and redshift (cf. \citet{Steinhardt2010b}) )" + make such a moclel intriguing., make such a model intriguing. + In this paper. we have investigated tracks for SMDII accretion histories and have shown that the quasar mass-liuminosity plane constrains these mocdels remarkably precisely.," In this paper, we have investigated tracks for SMBH accretion histories and have shown that the quasar mass-luminosity plane constrains these models remarkably precisely." + The most intriguing result is Chat we can rule out models in which the SMDILI aceretion rate is proportional to the matter number clensity » in the universe., The most intriguing result is that we can rule out models in which the SMBH accretion rate is proportional to the matter number density $n$ in the universe. + Even models in which the accretion rate is proportional to n7 are not allowed without a combination of higher-than-expected racliative cllicteney and a SALBLL that spends most of its time quiescent. rather than in a quasar state.," Even models in which the accretion rate is proportional to $n^2$ are not allowed without a combination of higher-than-expected radiative efficiency and a SMBH that spends most of its time quiescent, rather than in a quasar state." + This paper is an intermediate. phenomenological step hat has produced. constraints that seem to be required of heoretical models for SAIBLL growth., This paper is an intermediate phenomenological step that has produced constraints that seem to be required of theoretical models for SMBH growth. + The next step is to oduce a physical model of fuelling ancl feedback. leading ο quasar tracks satisving these constraints., The next step is to produce a physical model of fuelling and feedback leading to quasar tracks satisfying these constraints. + The authors would like to thank Lars Hernaquist. and orm Murrav for valuable comments., The authors would like to thank Lars Hernquist and Norm Murray for valuable comments. + This work was supported in part by Chandra:grant number C07-8136A. This work was supported by World. Premier International tesearch Center Initiative (WPL Initiative). MIZNXT. Japan.," This work was supported in part by Chandragrant number G07-8136A. This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan." +interact with material within 2 scale heights from their orbit (2)..,interact with material within 2 scale heights from their orbit \citep{bate03}. + This is the maximum distance that is considered in. the inset of Fig. 3.., This is the maximum distance that is considered in the inset of Fig. \ref{fig3}. + For a Keplerian disc. à gap forms with a half width that is approximately 2H. and in the inset of Fig.," For a Keplerian disc, a gap forms with a half width that is approximately $2H$, and in the inset of Fig." + 5. all three curves fall below 0.1 for f=1., \ref{fig3} all three curves fall below $0.1$ for $f=1$. + For f=0.8. there is still a density depression around the orbit of the planet. but for lower values of f there is no clear gap near r=ry. it has shifted inwards enough so that the planet is basically embedded in the dise again.," For $f=0.8$, there is still a density depression around the orbit of the planet, but for lower values of $f$ there is no clear gap near $r=\rp$, it has shifted inwards enough so that the planet is basically embedded in the disc again." + However. since for the lowest values of f there are no more resonances located close to the planet. the Type I torque will not be fully restored.," However, since for the lowest values of $f$ there are no more resonances located close to the planet, the Type I torque will not be fully restored." + We find that typically Mf=0.6/I(£1)2 for gap-opening planets., We find that typically $\Gamma(f=0.6)/\Gamma(f=1)\approx 2$ for gap-opening planets. + The influence of the head wind (see Eq. 1)), The influence of the head wind (see Eq. \ref{eqhead}) ) + will be strong. however. since it does not rely on resonances.," will be strong, however, since it does not rely on resonances." + We comment that a opening planet is still tidally locked to the gap. just as in the Keplerian Type II migration case.," We comment that a gap-opening planet is still tidally locked to the gap, just as in the Keplerian Type II migration case." + The possibility of a high-mass planet fully embedded in the disc may have some important consequences for gas accretion., The possibility of a high-mass planet fully embedded in the disc may have some important consequences for gas accretion. + In a Keplerian disc. accretion drops by an order of magnitude when a gap is formed (?)..," In a Keplerian disc, accretion drops by an order of magnitude when a gap is formed \citep{dangelo3D}." + In a subkeplerian disc. there a significant amount of mass remains near the orbit of the planet. making accretion potentially very efficient.," In a subkeplerian disc, there a significant amount of mass remains near the orbit of the planet, making accretion potentially very efficient." + It is not clear. however. if the planet is able to accept material that has such a high relative velocity.," It is not clear, however, if the planet is able to accept material that has such a high relative velocity." + The results for a more massive planet of g=0.001 (1 My around a | Μι star) are very similar to those presented in Fig. 3.., The results for a more massive planet of $q=0.001$ (1 $\mj$ around a 1 $\msun$ star) are very similar to those presented in Fig. \ref{fig3}. + The gap shifts inward. and for f<0.7 the planet is located on the outer edge of its own density depression.," The gap shifts inward, and for $f<0.7$ the planet is located on the outer edge of its own density depression." + For smaller planets. which only open up a shallow density depression for f=1. remain fully embedded for f£«1. as shown in Fig. 4..," For smaller planets, which only open up a shallow density depression for $f=1$, remain fully embedded for $f<1$, as shown in Fig. \ref{fig4}." + While for f=Ll. aq=107+ planet decreases the surface density around its orbit by a factor 0.7. for f«0.7 there is no more evidence for any density depression.," While for $f=1$, a $q=10^{-4}$ planet decreases the surface density around its orbit by a factor $0.7$, for $f<0.7$ there is no more evidence for any density depression." + For this lower planet mass. the important resonances become too weak to affect the surface density in strongly subkeplerian dises.," For this lower planet mass, the important resonances become too weak to affect the surface density in strongly subkeplerian discs." + We have presented hydrodynamical simulations. of. planets embedded in subkeplerian dises., We have presented hydrodynamical simulations of planets embedded in subkeplerian discs. + They represent the first step towards modelling fully 3D magnetised dises., They represent the first step towards modelling fully 3D magnetised discs. + It is known for Keplerian disces that magnetic fields can have a strong impact on planet migration: regular fields introduce magnetic resonances (?).. while magnetic turbulence introduces stochastic migration (?2)..," It is known for Keplerian discs that magnetic fields can have a strong impact on planet migration: regular fields introduce magnetic resonances \citep{terquem03}, while magnetic turbulence introduces stochastic migration \citep{nelson04,adamsbloch09}." + It remains to be seen what impact a magnetic field configuration that gives rise to subkeplerian dises can have on the simple hydrodynamic picture presented here., It remains to be seen what impact a magnetic field configuration that gives rise to subkeplerian discs can have on the simple hydrodynamic picture presented here. + We have worked in the isothermal limit. but. since corotation torques only play à minor role in strongly subkeplerian dises. results for more realistic dises should be similar.," We have worked in the isothermal limit, but since corotation torques only play a minor role in strongly subkeplerian discs, results for more realistic discs should be similar." + The two-dimensional approximation. in combination with a gravitational softening parameter of order /. gives similar results to fully three-dimensional simulations. again at least as far as the Lindblad torque is concerned (?)..," The two-dimensional approximation, in combination with a gravitational softening parameter of order $h$, gives similar results to fully three-dimensional simulations, again at least as far as the Lindblad torque is concerned \citep{drag}." + We have found that the results do not depend strongly on the initial surface density profile., We have found that the results do not depend strongly on the initial surface density profile. + We have considered migration of low-mass planets (the Type I regime). finding that there is a strong dependence on f.," We have considered migration of low-mass planets (the Type I regime), finding that there is a strong dependence on $f$." + For |-fs/. the planet feels almost the full one-sided Lindblad torque. which ts a factor 1// stronger than the classical Type I torque.," For $1-f \approx h$, the planet feels almost the full one-sided Lindblad torque, which is a factor $1/h$ stronger than the classical Type I torque." + Such a dise would be very hazardous to low-mass planets. since inward migration is sped up by more than an order of magnitude compared to Keplerian dises.," Such a disc would be very hazardous to low-mass planets, since inward migration is sped up by more than an order of magnitude compared to Keplerian discs." + For |—-f>hr. the torque decreases because the resonances the planet interacts with become weaker.," For $1-f >h$, the torque decreases because the resonances the planet interacts with become weaker." + The dependence of the torque on /r and f is quite complicated. and it is not easy to say for a disc of given. f and /r whether the Type I torque will be stronger of weaker than the head-wind torque.," The dependence of the torque on $h$ and $f$ is quite complicated, and it is not easy to say for a disc of given $f$ and $h$ whether the Type I torque will be stronger of weaker than the head-wind torque." + Gap formation proceeds similar to that in. Keplerian discs., Gap formation proceeds similar to that in Keplerian discs. + However. because of the inward shift of the important resonances. the gap will be located inside the planet’s orbit.," However, because of the inward shift of the important resonances, the gap will be located inside the planet's orbit." + This then leaves the planet on the outside of its ow gap., This then leaves the planet on the outside of its own gap. + For strongly subkeplerian dises. a gap-opening planet can become fully embedded again.," For strongly subkeplerian discs, a gap-opening planet can become fully embedded again." + Since the torque-generating resonances are located far away. this does not restore the full Type I torque.," Since the torque-generating resonances are located far away, this does not restore the full Type I torque." + Accretion time scales could be very short. 1f the planet is able to accept the available matter.," Accretion time scales could be very short, if the planet is able to accept the available matter." +of candidate YSOs in the IC1396N. elobule.,of candidate YSOs in the IC1396W globule. + We distinguish ive eroups of objects., We distinguish five groups of objects. + For all five groups we acdcditionallv require the objects to be point. sources and to be spatially ocated. within the area of the globule (<9 distance fron Ηλ 21246|5748): 1n Table 1 we list the coordinates and photometry for the candidates. selected xwed on these four criteria: their positions are overplotted in Fig. 1.., For all five groups we additionally require the objects to be point sources and to be spatially located within the area of the globule $<9'$ distance from IRAS 21246+5743): In Table \ref{t2} we list the coordinates and photometry for the candidates selected based on these four criteria; their positions are overplotted in Fig. \ref{f100}. + In total. 15 candidates are identified from colour. variability. ancl spatial position.," In total, 15 candidates are identified from colour, variability, and spatial position." + ALL require spectroscopic confirmation. in particular the eroups (iii)-(v).," All require spectroscopic confirmation, in particular the groups (iii)-(v)." + Five of them do not show colour excess and could. thus be WETS in 1C1396W. In addition. the elobule is known to harbour the likely Class 0 source LRAS 21246|57435 (?)..," Five of them do not show colour excess and could thus be WTTS in IC1396W. In addition, the globule is known to harbour the likely Class 0 source IRAS 21246+5743 \citep{2003MNRAS.346..163F}." + This can be contrasted with the 31 red objects identified in the shallow survey by 2.., This can be contrasted with the 31 red objects identified in the shallow survey by \citet{2003A&A...407..207F}. + A pure colour selection. as used by 2.. clearly overestimates he number of YSOs in the cloud.," A pure colour selection, as used by \citet{2003A&A...407..207F}, clearly overestimates the number of YSOs in the cloud." + The depth and completeness. of our. sample is not trivial to determine. because we used a variety of cilferent indicators.," The depth and completeness of our sample is not trivial to determine, because we used a variety of different indicators." + Our photometry database requires the objects to have uncertainties <0.2 mmage in Ix- and J-band. which elfectively limits the survey ο.)«19 mmag (Sect. 3.1)).," Our photometry database requires the objects to have uncertainties $<0.2$ mag in K- and J-band, which effectively limits the survey to $J<19$ mag (Sect. \ref{ccd}) )." +" Assuming a maximum extinction of shy= 10mmage and a distance of ppc. this corresponds to AL,~ 7."," Assuming a maximum extinction of $A_V=10$ mag and a distance of pc, this corresponds to $M_J \sim 7$ ." + With the MMsyr track by ? this vields a mass limit 0.05AZ... which is applicable to categories. (i). (it) and (ui) above.," With the Myr track by \citet{1998A&A...337..403B} this yields a mass limit $\sim 0.05\,M_{\odot}$, which is applicable to categories (i), (ii) and (iii) above." + Since all objects identified in category (iv) have amplitudes < O.lmmag. the depth for this sample is likely to be mmaeg lower. corresponding to ~0.2AZ..," Since all objects identified in category (iv) have amplitudes $<0.1$ mag, the depth for this sample is likely to be mag lower, corresponding to $\sim 0.2\,M_{\odot}$." + Thus. the survey covers the regime around the peak in the EME.," Thus, the survey covers the regime around the peak in the IMF." + The sample of candidate. YSOs in the categories. (iii)- may contain à substantial [fraction of contaminating background objects., The sample of candidate YSOs in the categories (iii)-(v) may contain a substantial fraction of contaminating background objects. + On the other hand our method will miss certain tvpes of sources (see discussion in 3))., On the other hand our method will miss certain types of sources (see discussion in \ref{ident}) ). + Lt is sensitive to CTTS and variable WETS. which are the major fractions of objects in regions at MMwyr.," It is sensitive to CTTS and variable WTTS, which are the major fractions of objects in regions at Myr." + Fherefore we do not expect that the incompleteness alfects our most relevant result: The number of candidate YSOs in this globule is found to be low. probably less than 10.," Therefore we do not expect that the incompleteness affects our most relevant result: The number of candidate YSOs in this globule is found to be low, probably less than 10." + ICL39GW is one of the largest anc most. massive cloucls in the 1€1396 region., IC1396W is one of the largest and most massive clouds in the IC1396 region. + ? determined. a e@lobule mass of 400-550AZ. [rom near-infrared extinction. maps. assuming a distance of ppc.," \citet{2005A&A...432..575F} + determined a globule mass of $\,M_{\odot}$ from near-infrared extinction maps, assuming a distance of pc." + Combined: with the low number of YSOs this indicates low star formation elliciencv., Combined with the low number of YSOs this indicates low star formation efficiency. + Before we can quantify this more accurately. however. we re-assess the distance of 11396W. A standard: way of probing distances to dense clouds is by separating foreground ancl background objects using the near-infrared colour and comparing the number of foreground objects with predictions from stellar population models.," Before we can quantify this more accurately, however, we re-assess the distance of IC1396W. A standard way of probing distances to dense clouds is by separating foreground and background objects using the near-infrared colour and comparing the number of foreground objects with predictions from stellar population models." + In 1€1396NV this procedure is only applicable to the innermost part of the cloud. where the extinction is strong enough to block the background objects.," In IC1396W this procedure is only applicable to the innermost part of the cloud, where the extinction is strong enough to block the background objects." + Within 1.5. from the LRAS source there are 8S objects with unredcdened colours of JÁINo1.0. which agrees well with the typical colours of objects outside the cloud.," Within 1.5' from the IRAS source there are 8 objects with unreddened colours of $J-K \sim 1.0$, which agrees well with the typical colours of objects outside the cloud." + The other 14 objects in this area are clearly reddened with J9A>1.5., The other 14 objects in this area are clearly reddened with $J-K>1.5$. + We used the Galaxy model from the Besancon to simulate a catalogue of objects over an area of ssedeg in the direction of LCL396\W matching the dynamic range of our catalogue (9.82.8 pixels; otherwise, ffails to converge to a unique shape refnativeconvergence))."," If is to be used for shape analysis, the sampling rate must be such that the PSF minor-axis FWHM is sampled by $\ge2.8$ pixels; otherwise, fails to converge to a unique shape \\ref{nativeconvergence}) )." +" Similarly, the PSF-smeared objects which produce useful shapes must have a minimum resolution that depends on the significance (or vice-versa) in order to converge to a measurement of the pre-seeing galaxy shape."," Similarly, the PSF-smeared objects which produce useful shapes must have a minimum resolution that depends on the significance (or vice-versa) in order to converge to a measurement of the pre-seeing galaxy shape." +" If we require shape measurements of all values of e to be successful, then rp>1.8 is required at v=20, or ry>1.2 at v>40 refdeconvconvergence))."," If we require shape measurements of all values of $e$ to be successful, then $r_b\geq1.8$ is required at $\nu=20$, or $r_b\geq1.2$ at $\nu\geq40$ \\ref{deconvconvergence}) )." +" This implies that improvements in WL statistical accuracy are rapidly limited by the resolution of the galaxies: although going deep in the exposure increases the S/N of the detected objects and reduces the scatter and systematic in the shear estimate, the required S/N grows very rapidly for poorly resolved images, and it becomes difficult to produce additional useful WL data for poorly resolved galaxies."," This implies that improvements in WL statistical accuracy are rapidly limited by the resolution of the galaxies: although going deep in the exposure increases the $S/N$ of the detected objects and reduces the scatter and systematic in the shear estimate, the required $S/N$ grows very rapidly for poorly resolved images, and it becomes difficult to produce additional useful WL data for poorly resolved galaxies." +" We have also found that larger, well resolved galaxies (rp25) exhibit a problem with the deconvolution method when the PSF is an Airy function, due to the poor approximation of the Airy-functions wings by the GL expansion."," We have also found that larger, well resolved galaxies $r_b\simgeq\,5$ ) exhibit a problem with the deconvolution method when the PSF is an Airy function, due to the poor approximation of the Airy-functions wings by the GL expansion." + A simple remedy is available: smooth the PSF and galaxy images before measuring both., A simple remedy is available: smooth the PSF and galaxy images before measuring both. +" Another solution is to choose an alternative to Gauss-Laguerre as the PSF decomposition basis functions, one that is better suited to describe an Airy function."," Another solution is to choose an alternative to Gauss-Laguerre as the PSF decomposition basis functions, one that is better suited to describe an Airy function." +" However, a non-GL decomposition will make the deconvolution process excessively complex; another solution is to apodize the telescope to suppress the Airy wings."," However, a non-GL decomposition will make the deconvolution process excessively complex; another solution is to apodize the telescope to suppress the Airy wings." +" Kuijken(2006) offers an excellent description of the difference between various WL techniques; we refer the reader to this paper for the difference between, for example, the KSB method and Kuijken's method, which is applicable to the difference bewteen KSB method and the EGL method."," \citet{Kuijken} offers an excellent description of the difference between various WL techniques; we refer the reader to this paper for the difference between, for example, the KSB method and Kuijken's method, which is applicable to the difference bewteen KSB method and the EGL method." + Our EGL method is similar to Kuijken's polar shapelet method (Kuijken2006)., Our EGL method is similar to Kuijken's polar shapelet method \citep{Kuijken}. +". What the methods have in common are: the deconvolution of the PSF, which in principle allows for any PSF effects to be removed; forward fitting, which allows error propagation, and hence an error estimate to the measured shape; and the definition of shape as shear, which has a well-defined shear transformation."," What the methods have in common are: the deconvolution of the PSF, which in principle allows for any PSF effects to be removed; forward fitting, which allows error propagation, and hence an error estimate to the measured shape; and the definition of shape as shear, which has a well-defined shear transformation." + All of these features contribute to a better shear accuracy., All of these features contribute to a better shear accuracy. + The differences between EGL and Kuijken's methods are subtle., The differences between EGL and Kuijken's methods are subtle. + The first difference is that Kuijen method works the deconvolution and shearing in shapelet-coefficient space., The first difference is that Kuijken method works the deconvolution and shearing in shapelet-coefficient space. + Our EGL method determines the shape-as-shear by iteratively fitting within the pixel space., Our EGL method determines the shape-as-shear by iteratively fitting within the pixel space. +" Secondly, Kuijken's method obtains the shape using a shear transformation valid to first-order in e, which can be off by up to at e~0.9 (g= 0.6)."," Secondly, Kuijken's method obtains the shape using a shear transformation valid to first-order in $e$, which can be off by up to at $e\simeq0.9$ $g=0.6$ )." +" Our method uses basis functions that are elliptical, the shear transformation is valid to all orders, which allows for the shape to be measured accurately for any e."," Our method uses basis functions that are elliptical, the shear transformation is valid to all orders, which allows for the shape to be measured accurately for any $e$." +" 'The third difference is that, in Kuijken's method, only the m—0 terms are used to describe the galaxy."," The third difference is that, in Kuijken's method, only the $m=0$ terms are used to describe the galaxy." +" This allows for less coefficients needed, and hence is efficient."," This allows for less coefficients needed, and hence is efficient." +" In comparison, our methodobtains the full set of coefficients to the specified"," In comparison, our methodobtains the full set of coefficients to the specified" +(Ptak et al. 2006..,"(Ptak et al. \citeyear{ptak06}," + Zakamska et al. 20045)., Zakamska et al. \citeyear{zak04}) ). + They show a wide range of X-ray luminosities and obscuring column densities., They show a wide range of X-ray luminosities and obscuring column densities. + About 40 objects in their sample were detected with IRAS and have infrared luminosities among the most luminous quasars at similar redshift., About 40 objects in their sample were detected with IRAS and have infrared luminosities among the most luminous quasars at similar redshift. + The host galaxies are ellipticals. although with irregular morphologies. and the nuclear optical emission is highly polarized (Zakamska et al. 2006)).," The host galaxies are ellipticals, although with irregular morphologies, and the nuclear optical emission is highly polarized (Zakamska et al. \citeyear{zak06}) )." + The detection rate in radio (~10%.. Zakamska et al. 2004::," The detection rate in radio $\sim$ , Zakamska et al. \citeyear{zak04};" + Vir Lal Ho 2007)) is consistent with that of other AGN types., Vir Lal Ho \citeyear{vir07}) ) is consistent with that of other AGN types. + Spectroscopic studies of type 2 quasars have focused so far on identifying emission lines. measuring some basic parameters (line luminosities. redshift. line widths) and searching for correlations among them and with other observables (equivalent widths. color magnitudes. radio luminosities. ete).," Spectroscopic studies of type 2 quasars have focused so far on identifying emission lines, measuring some basic parameters (line luminosities, redshift, line widths) and searching for correlations among them and with other observables (equivalent widths, color magnitudes, radio luminosities, etc)." + All this is critical to classify the objects. to investigate the nature of the powering mechanism. the obscuring structure and. ultimately. test the validity of the unification models (e.g. Reyes et al. 2008)).," All this is critical to classify the objects, to investigate the nature of the powering mechanism, the obscuring structure and, ultimately, test the validity of the unification models (e.g. Reyes et al. \citeyear{rey08}) )." + However. little work has been done to characterize the gaseous and ionization properties of type 2 quasars.," However, little work has been done to characterize the gaseous and ionization properties of type 2 quasars." + Given this lack of knowledge. the primary goal of the work presented here is to use the emission line information to study the excitation mechanism. the physical conditions and ionization properties of the gas.," Given this lack of knowledge, the primary goal of the work presented here is to use the emission line information to study the excitation mechanism, the physical conditions and ionization properties of the gas." + Detailed spectroscopic studies of other active galaxy types. such as narrow line radio galaxies (NLRGs. e.g. Robinson et al. 1987))," Detailed spectroscopic studies of other active galaxy types, such as narrow line radio galaxies (NLRGs, e.g. Robinson et al. \citeyear{rob87}) )" + have allowed during the last few decades the characterization of the chemical abundances of the gas. the ionization mechanism. the physical and kinematic properties. etc.," have allowed during the last few decades the characterization of the chemical abundances of the gas, the ionization mechanism, the physical and kinematic properties, etc." + Similar work must be done for type 2 quasars., Similar work must be done for type 2 quasars. + These studies will ultimately provide valuable information about the formation process ofthe host galaxy. the star forming and chemical enrichment histories and the origin of the nuclear activity (e.g. Tadhunter. Fosbury Quinn 1989.. n et al. 2005..," These studies will ultimately provide valuable information about the formation process of the host galaxy, the star forming and chemical enrichment histories and the origin of the nuclear activity (e.g. Tadhunter, Fosbury Quinn \citeyear{tadh89}, n et al. \citeyear{vm05}," + Humphrey et al. 2008))., Humphrey et al. \citeyear{hum08}) ). + An important disadvantage of NLRG over type 2 quasar studies is that the radio activity. via jet-gas interactions. imprints important distortions on the properties of the ionized gas making it difficult to investigate the intrinsic properties of the host galaxy and environment. as well as the chemical abundances and the nature of the excitation mechanism (e.g. Tadhunter 20023).," An important disadvantage of NLRG over type 2 quasar studies is that the radio activity, via jet-gas interactions, imprints important distortions on the properties of the ionized gas making it difficult to investigate the intrinsic properties of the host galaxy and environment, as well as the chemical abundances and the nature of the excitation mechanism (e.g. Tadhunter \citeyear{tadh02}) )." + The study of radio-quiet type 2 quasars should not suffer from such effects., The study of radio-quiet type 2 quasars should not suffer from such effects. +" Throughout this paper we assume O4= 0.73. ©,,, = 0.27 and ily =7i kms ! Μρο|l"," Throughout this paper we assume $\Omega_{\Lambda} =$ 0.73, $\Omega_{m}$ = 0.27 and $H_{0}$ = 71 km $^{-1}$ $^{-1}$." + The objects studied in this paper are a sub-sample of candidate type 2 quasars from the Sloan Digital Sky Survey (SDSS) selected by Zakamskaetal.(2003) in the redshift range 0.37-2 550.8 (~ 145 objects).," The objects studied in this paper are a sub-sample of candidate type 2 quasars from the Sloan Digital Sky Survey (SDSS) selected by \cite{zak03} + in the redshift range $\la z \la$ 0.8 $\sim$ 145 objects)." + The selection criteria applied by Zakamskaetal.(2003) are listed below (notice that not necessarily all criteria apply to all objects., The selection criteria applied by \cite{zak03} are listed below (notice that not necessarily all criteria apply to all objects. + See Zakamska et al., See Zakamska et al. + 2003. for more detailed The sub-sample studied here contains 50 type 2 quasars. which have been selected to span the full z range and the full [ΟΠΗ luminosity range (223. 107 L. ) of the original type 2 quasar sample.," \citeyear{zak03} for more detailed The sub-sample studied here contains 50 type 2 quasars, which have been selected to span the full $z$ range and the full [OIII] luminosity range $\ge$ $\times$ $^8$ $_ {\odot}$ ) of the original type 2 quasar sample." + We did not set constraints on the line equivalent widths. although the selection criteria on the original sample do contain an EW criterion. as stated above.," We did not set constraints on the line equivalent widths, although the selection criteria on the original sample do contain an EW criterion, as stated above." + The spectra were corrected for Galactic extinction., The spectra were corrected for Galactic extinction. + A galaxy template spectrum was subtracted for objects with low line EWs. to correct for possible underlying stellar and interstellar absorption (Zhang. Dultzin-Hacyan Wang 2007).," A galaxy template spectrum was subtracted for objects with low line EWs, to correct for possible underlying stellar and interstellar absorption (Zhang, Dultzin-Hacyan Wang \citeyear{zh07}) )." + This procedure was necessary for a small fraction of objects (~ only)., This procedure was necessary for a small fraction of objects $\sim$ only). + The spectra were not corrected for internal dust reddening because such correction was not possible for all objects., The spectra were not corrected for internal dust reddening because such correction was not possible for all objects. + Tt should not affect our conclusions since we will compare our results with previous works on other AGN types (Seyfert 2s. radio galaxies). in which no internal extinction correction was applied either.," It should not affect our conclusions since we will compare our results with previous works on other AGN types (Seyfert 2s, radio galaxies), in which no internal extinction correction was applied either." +" We investigate in this section the dominant ionizing mechanism of the optical line emitting gas in the type 2 quasar sub-sample: AGN vs. stellar photoionization,", We investigate in this section the dominant ionizing mechanism of the optical line emitting gas in the type 2 quasar sub-sample: AGN vs. stellar photoionization. + We will ignore shocks in ourdiscussion as an alternative ionization mechanism (e.g. Dopita Sutherland 906)., We will ignore shocks in ourdiscussion as an alternative ionization mechanism (e.g. Dopita Sutherland \citeyear{dop96}) ). + In our sub-sample. 44 out of the 47 objects for which radio information is available are radio quiet (Le. Liaw. «107 ere 1 3 Land therefore. shocks induced by the radio structures are not expected to play a significant role in the ionization of the gas (e.g. Clark et al. 1998..," In our sub-sample, 44 out of the 47 objects for which radio information is available are radio quiet (i.e. $L_{1.4 GHz}<$ $^{31}$ erg $^{-1}$ $^{-1}$ $^{-1}$ ) and therefore, shocks induced by the radio structures are not expected to play a significant role in the ionization of the gas (e.g. Clark et al. \citeyear{clark98}," + n et al. 1999))., n et al. \citeyear{vm99}) ). + In the vast majority of the type 2 quasars in the sample considered here. the bulk of the line profiles is characterized by rather quiescent kinematies. rather than perturbed. as one would expect if shocks were present.," In the vast majority of the type 2 quasars in the sample considered here, the bulk of the line profiles is characterized by rather quiescent kinematics, rather than perturbed, as one would expect if shocks were present." + We show in Fig., We show in Fig. + | several diagnostic diagrams involving optica emission lines in which we plot the location of the SDSS type 2 quasar sub-sample (green. solid circles and blue solid triangles).," 1 several diagnostic diagrams involving optical emission lines in which we plot the location of the SDSS type 2 quasar sub-sample (green, solid circles and blue solid triangles)." + For comparison. we plot in the same diagrams the locus of HIT galaxies from the catalogue of Terlevichetal.(1991). (magenta small symbols).," For comparison, we plot in the same diagrams the locus of HII galaxies from the catalogue of \cite{ter91} (magenta small symbols)." + These are absent in diagrams involving the Hell and [NeV] because such lines are rarely detected in this objec class., These are absent in diagrams involving the HeII and [NeV] because such lines are rarely detected in this object class. + The solid lines represent the standard “Usequenceof photoionization models. buillwiththemallipurposccodeAl APL ," The solid lines represent the standard $U$ sequence of photoionization models, built with the multipurpose code MAPPINGS Ic (Binette, Dopita Tuohy \citeyear{bin85}; Ferruit et al. \citeyear{fer97}) )" +G5xv UY ," that reproduces some of the main properties of the emission line spectra of narrow line radio galaxies at different redshifts (e.g. Robinson et al. \citeyear{rob87}, ," +, Humphrey et al. \citeyear{hum08}) ). +with a eut off energy of 50 keV. The clouds are," The ionizing continuum isa power law of index $\alpha$ =1.5 $F_{\nu} \propto \nu^{-\alpha}$ ), with a cut off energy of 50 keV. The clouds are" +ereater than that of the narrow component.,greater than that of the narrow component. + No strong trends can be seen with either date of observation or orbital phase. with the exception of the equivalent width of the narrow component. which has been generally decreasing since 1976 (except for the extremely low value in April 1978).," No strong trends can be seen with either date of observation or orbital phase, with the exception of the equivalent width of the narrow component, which has been generally decreasing since 1976 (except for the extremely low value in April 1978)." + Infrared. spectra were obtained one orbit after the optical spectra., Infrared spectra were obtained one orbit after the optical spectra. + The mean spectrum is shown in Fig. 3.., The mean spectrum is shown in Fig. \ref{fig:IRspectrum}. + Bright emission lines of Br aand A2.058 wavere visible in the spectrum., Bright emission lines of Br $\gamma$ and $\lambda$ were visible in the spectrum. + TFhese two lines are generally observed in the Ix-band. spectra of low- and high-mass X-rav binaries 1999))) and may arise in accretion disces or larger emitting regions. such as dense winds fron the mass donors and/or ejecta from the binaries.," These two lines are generally observed in the K-band spectra of low- and high-mass X-ray binaries ) and may arise in accretion discs or larger emitting regions, such as dense winds from the mass donors and/or ejecta from the binaries." + Phere also seems to be a hint of asymmetry in the blue wing of the infrared lines. so we again fit. gaussians to the line profile.," There also seems to be a hint of asymmetry in the blue wing of the infrared lines, so we again fit gaussians to the line profile." + We modelled cach emission line as the sum of two gaussians. constraining the widths anc velocities of the blue anc red components to be the same for both lines.," We modelled each emission line as the sum of two gaussians, constraining the widths and velocities of the blue and red components to be the same for both lines." + Phe results are shown in Table 3.., The results are shown in Table \ref{tab:IRspec}. + Both lines are well fit bv one gaussian at |450lans.P. a velocity. very similar to the narrow red-shifted: optical component. plus a bluc-shifted component at a velocity of —2000kms+.," Both lines are well fit by one gaussian at $+450\kms$, a velocity very similar to the narrow red-shifted optical component, plus a blue-shifted component at a velocity of $\sim -2000\kms$." + Initially. it was suggested that Cir X-1 is a high mass binary Consisting of a compact star (cither a neutron star or black hole) and an OB supergiant companion star 1980))).," Initially, it was suggested that Cir X-1 is a high mass binary consisting of a compact star (either a neutron star or black hole) and an OB supergiant companion star )." + Its X-ray properties imply a very eccentric binary orbit., Its X-ray properties imply a very eccentric binary orbit. + Phe 16.6-clay modulation in the X-ray luminosity is due to orbital variations in the mass accretion of the compact star., The 16.6-day modulation in the X-ray luminosity is due to orbital variations in the mass accretion of the compact star. + Phe X-ray. ancl radio bursts occur when the compact star encounters the dense stellar wind from the supereiant1980).. or when tidal mass transfer is induced. during the periastron passage1987).," The X-ray and radio bursts occur when the compact star encounters the dense stellar wind from the supergiant, or when tidal mass transfer is induced during the periastron passage." +. The Type E X-ray bursts that were discovered in a brief epoch in the mid-1980s indicated that the compact star is a neutron star., The Type I X-ray bursts that were discovered in a brief epoch in the mid-1980s indicated that the compact star is a neutron star. + Recent observations citesnp91.gla94)). indicate that the companion star is unlikely to be a massive supergiant star., Recent observations ) indicate that the companion star is unlikely to be a massive supergiant star. + No Ένρο I bursts have vet been reported in ΗΝΕΣ observations., No Type I bursts have yet been reported in RXTE observations. + Llere. we propose a low-mass binary model. where the system consists of a neutron star orbiting around a subeiant companion star of about 3 to ((Figs. 4: ," Here, we propose a low-mass binary model, where the system consists of a neutron star orbiting around a subgiant companion star of about 3 to (Fig. \ref{fig:model}; ;" +see also Tennant Wu ‘Phe orbital eccentricity is 0.7 0.9., see also Tennant Wu The orbital eccentricity is $\sim 0.7$ –0.9. + During the periastron passage. the companion star overfills its Roche-lobe. causing a transfer of mass at à super-IExldington rate onto the neutron star.," During the periastron passage, the companion star overfills its Roche-lobe, causing a transfer of mass at a super-Eddington rate onto the neutron star." + As Cir N-1 is a X-ray. burster. the magnetic field. of the neutron star is relatively weak. and so the aceretion [low is probably quasi-spherical during the periastron passage.," As Cir X-1 is a X-ray burster, the magnetic field of the neutron star is relatively weak, and so the accretion flow is probably quasi-spherical during the periastron passage." + Because of the Large radiative pressure of emission. [rom the neutron star. there must also be a strong (anisotropic) matter outflow.," Because of the large radiative pressure of emission from the neutron star, there must also be a strong (anisotropic) matter outflow." + The inllow/outllow geometry may be related to the larger scale jets observed. from. the system. with symmetrical collimated outllows along some preferred axis.," The inflow/outflow geometry may be related to the larger scale jets observed from the system, with symmetrical collimated outflows along some preferred axis." + After the periastron passage. the companion star is detached. from itscritical Roche-surlace. and mass transfer," After the periastron passage, the companion star is detached from itscritical Roche-surface, and mass transfer" +line region.,line region. + If we assume that the stellar light from the host galaxy is well subtracted by the PSF+host decomposition. the spectrum of the unresolved source in the near-IR wavelengths is expected to be composed of essentially two components: (1) the thermal emission from hot dust grains in the innermost torus. nearly at the sublimation temperature: (11) the central engine emission. Le. the near-IR tail of the so-called big blue bump emission from the putative aceretion disk. (," If we assume that the stellar light from the host galaxy is well subtracted by the PSF+host decomposition, the spectrum of the unresolved source in the near-IR wavelengths is expected to be composed of essentially two components: (i) the thermal emission from hot dust grains in the innermost torus, nearly at the sublimation temperature; (ii) the central engine emission, i.e. the near-IR tail of the so-called big blue bump emission from the putative accretion disk. (" +We will discuss other possible components below.),We will discuss other possible components below.) + If we simply assume the near-IR spectrum of dust grains to be of a blackbody with a single temperature 7. and that of an aceretion disk to be of a power-law form f.«7!3 which ts a long wavelength limit of simple multi-temperature blackbody disks (Shakura Sunyaev 1973). then the spectral shape in the rest frame ts fixed for a given T and a given fraction of the accretion disk contribution at a certain wavelength.," If we simply assume the near-IR spectrum of dust grains to be of a blackbody with a single temperature $T$, and that of an accretion disk to be of a power-law form $f_{\nu} \propto \nu^{+1/3}$ which is a long wavelength limit of simple multi-temperature blackbody disks (Shakura Sunyaev 1973), then the spectral shape in the rest frame is fixed for a given $T$ and a given fraction of the accretion disk contribution at a certain wavelength." + We parameterize the latter as the disk fraction at the rest wavelength of 2.2 jm and denote it as fap., We parameterize the latter as the disk fraction at the rest wavelength of 2.2 $\mu$ m and denote it as $\fAD$. + These 7 and fap can be calculated from the observed set of aand ccolors and redshift z for each object., These $T$ and $\fAD$ can be calculated from the observed set of and colors and redshift $z$ for each object. + Equivalently. we can produce a grid of T and fap on the aand ccolor plane for z=0. and plot the aand ccolors of each object with K-corrections assuming this two-component spectrum.," Equivalently, we can produce a grid of $T$ and $\fAD$ on the and color plane for $z=0$, and plot the and colors of each object with K-corrections assuming this two-component spectrum." + Such a color-color diagram is shown in Fig.3 for the Tvpe 1 objects., Such a color-color diagram is shown in \ref{jh-hk-kcor} for the Type 1 objects. + Note that such K-corrections are noticeable essentially only for two objects in the plot., Note that such K-corrections are noticeable essentially only for two objects in the plot. + Fig.3 shows that the observed colors follow a relatively well-defined trend: they are along a locus of a roughly similar temperature 1200~ 1500K for the hot dust component. with a small range in fap of 5~25%..," \ref{jh-hk-kcor} shows that the observed colors follow a relatively well-defined trend: they are along a locus of a roughly similar temperature $\sim$ 1500K for the hot dust component, with a small range in $\fAD$ of $\sim$." + The corresponding accretion disk fractions at H and J are much higher. ~0.5 and 0.4~0.9. respectively.," The corresponding accretion disk fractions at $H$ and $J$ are much higher, $\sim$ 0.5 and $\sim$ 0.9, respectively." + To estimate the extent of the difference from simple black-body spectra. we have simulated the near-IR colors of more realistic AGN tort using our clumpy torus model (Hónnig et al.," To estimate the extent of the difference from simple black-body spectra, we have simulated the near-IR colors of more realistic AGN tori using our clumpy torus model (Hönnig et al." + 2006: Beckert Duschl 2004)., 2006; Beckert Duschl 2004). + We concentrate on Type | cases where inclinations 7 are smaller than the half opening angle of the torus and thus our line of sight toward the central engine is free of any model cloud., We concentrate on Type 1 cases where inclinations $i$ are smaller than the half opening angle of the torus and thus our line of sight toward the central engine is free of any model cloud. + We calculated spectra with à dust sublimation temperature Ts of 1200-1500K and a radial distribution of the number of clouds η)«7/7 where 8=—1.1~-2.0., We calculated spectra with a dust sublimation temperature $\Tsub$ of $-$ 1500K and a radial distribution of the number of clouds $\eta_r(r) \propto r^{\beta}$ where $\beta=-1.1 \sim -2.0$. + For each set of model parameters. we calculated 10 random arrangements of cloud placements with a fixed opening angle. or more precisely. a fixed ratio of scale height to radius corresponding to an average half opening angle of ~40° ((see Hónnig et al.," For each set of model parameters, we calculated 10 random arrangements of cloud placements with a fixed opening angle, or more precisely, a fixed ratio of scale height to radius corresponding to an average half opening angle of $\sim$ (see Hönnig et al." + 2006 for more details)., 2006 for more details). + We measured colors for the inclination angles free of clouds along the line of sight., We measured colors for the inclination angles free of clouds along the line of sight. + These colors are plotted in small gray squares in Fig.3.., These colors are plotted in small gray squares in \ref{jh-hk-kcor}. + Overlayed on these gray square points is a small grid of (T.i)=(1200—1500K. 0—40 nritliBz—1.5. which shows the averaged colors of the 10 random arrangements for each set.," Overlayed on these gray square points is a small grid of $(T,i)=(1200$$-$$1500$ K, $0$$-$$40$ $)$ with $\beta$ $-1.5$, which shows the averaged colors of the 10 random arrangements for each set." + The comparison of this single-radial-index grid with the gray square points (which include the indices from —1.1 to —2.0) shows that the radial-index generally has a smaller effect on colors for this half-opening angle case with Type | inclinations., The comparison of this single-radial-index grid with the gray square points (which include the indices from $-1.1$ to $-2.0$ ) shows that the radial-index generally has a smaller effect on colors for this half-opening angle case with Type 1 inclinations. + As the inclination increases from tto407.. the colors become slightly bluer since the fractional contribution from the hotter side of the innermost clouds becomes more significant.," As the inclination increases from to, the colors become slightly bluer since the fractional contribution from the hotter side of the innermost clouds becomes more significant." + This trend holds until the inclination becomes close to the half opening angle of the torus. when the colors start to become much redder.," This trend holds until the inclination becomes close to the half opening angle of the torus, when the colors start to become much redder." + For comparison we also have plotted the model colors of Type 2 or intermediate-type inclinations (/2 40°)) for which one or more clouds are along the line of sight. as small gray crosses.," For comparison we also have plotted the model colors of Type 2 or intermediate-type inclinations $i \ga 40$ ) for which one or more clouds are along the line of sight, as small gray crosses." + They generally show much redder colors and much larger scatters than those of Type | cases., They generally show much redder colors and much larger scatters than those of Type 1 cases. + We also have calculated the colors of optically-thin emission from dust grains with various sizes (radit a from 0.001 to 10 μπι) for two temperatures. 1200 and 1500K. using absorption efficiencies caleulated by Drame Lee (1984) and Laor Draine (1993).," We also have calculated the colors of optically-thin emission from dust grains with various sizes (radii $a$ from 0.001 to 10 $\mu$ m) for two temperatures, 1200 and 1500K, using absorption efficiencies calculated by Draine Lee (1984) and Laor Draine (1993)." + The color tracks for graphite grains are plotted in Fig.3 in gray/blue curves. where colors for «20.01. 0.1. 0.3 pm are marked as plus signs.," The color tracks for graphite grains are plotted in \ref{jh-hk-kcor} + in gray/blue curves, where colors for $a$ =0.01, 0.1, 0.3 $\mu$ m are marked as plus signs." + The colors of silicate grains are shown only for 721500K and «20.01. 0.1. 0.3. I. and 10 um cases in triangles for clarity. and they are connected with gray/purple dashed lines.," The colors of silicate grains are shown only for $T$ =1500K and $a$ =0.01, 0.1, 0.3, 1, and 10 $\mu$ m cases in triangles for clarity, and they are connected with gray/purple dashed lines." + As expected. the colors approach the blackbody colors of the same temperature as the grain size becomes larger.," As expected, the colors approach the blackbody colors of the same temperature as the grain size becomes larger." + The curves for graphite grains, The curves for graphite grains +the spectrum than for our data. and it is also rather insensitive to wavelengths >20A.. where the effect is expected to be the largest.,"the spectrum than for our data, and it is also rather insensitive to wavelengths $>$, where the effect is expected to be the largest." + We therefore re-investigate here the issue using the combined RGS spectrum. which has a better signal-to-noise ratio and extends beyond20Α.," We therefore re-investigate here the issue using the combined RGS spectrum, which has a better signal-to-noise ratio and extends beyond." +. The left panel of Fig., The left panel of Fig. + 3 shows the observed Lyman « lines. in velocity space.," \ref{veloc} shows the observed Lyman $\alpha$ lines, in velocity space." + For the figure. the lines were approximately continuum-subtracted and normalized to have a peak amplitude unity. to highlight their differences.," For the figure, the lines were approximately continuum-subtracted and normalized to have a peak amplitude unity, to highlight their differences." + Neighbouring lines can be seen for some of these Lyman « lines as bumps in the blue or red wings., Neighbouring lines can be seen for some of these Lyman $\alpha$ lines as bumps in the blue or red wings. + Note that we do not show the Ένα line as it is blended with a line., Note that we do not show the $\alpha$ line as it is blended with a line. + The variations with wavelength are obvious. as the peak velocity clearly appears less blueshifted for the short-wavelength lines.," The variations with wavelength are obvious, as the peak velocity clearly appears less blueshifted for the short-wavelength lines." + The comparison of width and skewness is more difficult by eye. as the RGS resolution broadens the short-wavelength lines in velocity space. blurring the trends.," The comparison of width and skewness is more difficult by eye, as the RGS resolution broadens the short-wavelength lines in velocity space, blurring the trends." + To quantify the wavelength variations. we fit the lines with the same as Cohenetal.(2010).. to ensure homogeneity.," To quantify the wavelength variations, we fit the lines with the same as \citet{coh10}, to ensure homogeneity." + Results are provided in Table 4: the first two columns identify the considered line. the next three columns define the line shape (characteristic continuum optical depth r.. radius R. for the onset of the X-ray emission. and the strength of the line). and the last two column provides details of the line ratios in the He-like fir triplets.," Results are provided in Table \ref{windprof}: the first two columns identify the considered line, the next three columns define the line shape (characteristic continuum optical depth $\tau_*$, radius $R_*$ for the onset of the X-ray emission, and the strength of the line), and the last two column provides details of the line ratios in the He-like fir triplets." + Several things must be noted., Several things must be noted. + First. in two cases (the He- triplets of N and O). resonance scattering was needed to achieve a good fit.," First, in two cases (the He-like triplets of N and O), resonance scattering was needed to achieve a good fit." + Second. the Lymana line of nitrogen is blended with a line fromNv.," Second, the $\alpha$ line of nitrogen is blended with a line from." +" We fit these two lines together. assuming that the line profile parameters are identical: keeping them independent yields unrealistic results (7,~ 0) for the weak line. and the lines are so blended that little independent information is available. explaining the apparently strange results for the weakest line."," We fit these two lines together, assuming that the line profile parameters are identical: keeping them independent yields unrealistic results $\tau_*\sim0$ ) for the weak line, and the lines are so blended that little independent information is available, explaining the apparently strange results for the weakest line." + The achieved fit of the nitrogen blend is far from perfect. however (y.~ 2).," The achieved fit of the nitrogen blend is far from perfect, however $\chi^2\sim2$ )." + Third. the iron line at iis not very well fitted (y~ 2). despite our efforts.," Third, the iron line at is not very well fitted $\chi^2\sim2$ ), despite our efforts." + [t seems that line blends (there are numerous lines in the neighbourhood) affect the profile: though these lines are weak. the very low noise of our data reveals their impact. which was not obvious in the data.," It seems that line blends (there are numerous lines in the neighbourhood) affect the profile: though these lines are weak, the very low noise of our data reveals their impact, which was not obvious in the data." + Finally. the fitting was done using a single terminal velocity for the winds7!.. Pulsetal. 2006)). a B=1 exponent for the velocity law. and a power law of zero slope to represent the continuum.," Finally, the fitting was done using a single terminal velocity for the wind, \citealt{pul06}) ), a $\beta$ =1 exponent for the velocity law, and a power law of zero slope to represent the continuum." +energv distributions show us that the disks are gas-rich throughout: ifthey were not. the disks would be flat. not flared with essentially pressure-supported scale heights ,"energy distributions show us that the disks are gas-rich throughout; if they were not, the disks would be flat, not flared with essentially pressure-supported scale heights ." +The presence of accretion shocks aud jets tell us that the disks are actively accreting requiring he eas to be sufficiently viscious to allow aneular nolenti transport (7)., The presence of accretion shocks and jets tell us that the disks are actively accreting requiring the gas to be sufficiently viscious to allow angular momentum transport . + Liudted disk lifetimes of about 6 Myr have been interred. albeit with siguificaut variation. demonstrating the need for efficient dispersal nechanisuis (?).," Limited disk lifetimes of about 6 Myr have been inferred, albeit with significant variation, demonstrating the need for efficient dispersal mechanisms ." +. Disks do not extend all the wav inward o the stellar surface. but exhibit a complex structure due o the sublimationoc of dust at high teniperatures leading o rapid opacity eradicuts (2).. anda coupling of the disk o the stellar 1naguoetic field facilitates both accretion aud nass loss (272).," Disks do not extend all the way inward to the stellar surface, but exhibit a complex structure due to the sublimation of dust at high temperatures leading to rapid opacity gradients , and a coupling of the disk to the stellar magnetic field facilitates both accretion and mass loss ." +. Some disks appear to have large excavated inner reeious of low dust opacity (7).. compared to the outer isk. but it appears that not all disks eo through such a y.tage (?2).. and it is still an open question whether this is irectlv related to the formation of plauctesimals or even eiut plaucts. or whether another dispersal mechanism is ut play (2).," Some disks appear to have large excavated inner regions of low dust opacity , compared to the outer disk, but it appears that not all disks go through such a stage , and it is still an open question whether this is directly related to the formation of planetesimals or even giant planets, or whether another dispersal mechanism is at play ." +.. Clearly. observing what the eas actually docs ni the inner disk impacts our understanding of all these isk properties aud enables us to estimate their relative oeuportance for the evolution of the disk.," Clearly, observing what the gas actually does in the inner disk impacts our understanding of all these disk properties and enables us to estimate their relative importance for the evolution of the disk." + Ultimately. the motion of the inner disk gas mav reveal the presence of accretiug protoplancts (7).," Ultimately, the motion of the inner disk gas may reveal the presence of accreting protoplanets ." + We present a spectro-astrometric nuaenig survey of molecular gas in the PEZs of disks around a sample of solar type stars using CRIRES on the European Very Large Telescope (?)., We present a spectro-astrometric imaging survey of molecular gas in the PFZs of disks around a sample of solar type stars using CRIRES on the European Very Large Telescope . +. The primary goal is to directly deteriuue the basic distribution and kinematics of the eas and to relate this to the process of plauct formation and inner disk evolution., The primary goal is to directly determine the basic distribution and kinematics of the gas and to relate this to the process of planet formation and inner disk evolution. + For iustauce. iu a purely passive. non-acercting. disk it may be expected that the eas orbits at csscutially I&epleriau speeds. dictated oulv bv the mass of the ceutral star. ucelecting minor correctious for the mass of the disk itself (V/V10 31 aud for the radial pressure eradient iu the disk293.," For instance, in a purely passive, non-accreting, disk it may be expected that the gas orbits at essentially Keplerian speeds, dictated only by the mass of the central star, neglecting minor corrections for the mass of the disk itself $dV/V_{\rm Kepler}\lesssim 10^{-2}$ ) and for the radial pressure gradient in the disk." + Phepresenecofdoubl peakedeimísHl]uz sionlincprofilesfromprotoplancturgydiskscanindeos, The presence of double-peaked emission line profiles from protoplanetary disks can indeed be explained by gas in Keplerian orbits. +tiecatubui ety) vobxdpededor di in (277).. Do mid-infraved molecular lines in fact — trace material strictly im Ieplerian ietion. or are there sienificant non-Weplerian coupoucuts present. and. if so. are they dominated bv iufall or outflow motions’?," However, disks are in general not passive as they accrete and eventually dissipate, so departures from pure Keplerian motion are expected at some level, and is indicated in FU Ori stars for the CO bandhead at $\mu$ m. Do mid-infrared molecular lines – in fact – trace material strictly in Keplerian motion, or are there significant non-Keplerian components present, and, if so, are they dominated by infall or outflow motions?" + What disk radi are traced dy rovibrational CO lines: the inner edge of the disk at AAT. the terrestrial plauct region at AAU or the eiaut planct region at AAU?," What disk radii are traced by rovibrational CO lines; the inner edge of the disk at AU, the terrestrial planet region at AU or the giant planet region at AU?" + What is the origin of the absorption compoucuts seen in CO rovibrational spectra absorption from edge-on disks. forceround clouds. remnant envelopes or disk winds?," What is the origin of the absorption components seen in CO rovibrational spectra – absorption from edge-on disks, foreground clouds, remnant envelopes or disk winds?" + Qur spectro-astronietrie survey was primarily focuse ou what is probably the best tracer of iiolecular eas im the immer disk. or at least the most casily observable the fundamental rovibrational band of CO ceutere at yan. These CO lunes are traditionally. thought to trace warn eas in disks at ~LAU. based on typica lue widths aud excitation temperatures).. and are invariably bright iu uearly all classical TO Tami aac llerbig Ac stars.," Our spectro-astrometric survey was primarily focused on what is probably the best tracer of molecular gas in the inner disk, or at least the most easily observable – the fundamental rovibrational band of CO centered at $\mu$ m. These CO lines are traditionally thought to trace warm gas in disks at $\sim$$1\,$ AU, based on typical line widths and excitation temperatures, and are invariably bright in nearly all classical T Tauri and Herbig Ae stars." + One of the most basic outcomes of this survev is the direct measurements of the size of the CÓ liue emitting regions., One of the most basic outcomes of this survey is the direct measurements of the size of the CO line emitting regions. + We demonstrate that astrometric signals in C'O were detected for all sources on AU-scales. but with varving alplitude and with an intriguing range of structure: The CO spectra are divided iuto three rough phenomenological classes. based on the line shape iu conibination with the shape of astrometric spectra: Keplerian disks characterized ly double-peaked liue-profiles. single-peaked line sources with broad wings. aud selt-absorbed sources.," We demonstrate that astrometric signals in CO were detected for all sources on AU-scales, but with varying amplitude and with an intriguing range of structure: The CO spectra are divided into three rough phenomenological classes, based on the line shape in combination with the shape of astrometric spectra: Keplerian disks characterized by double-peaked line-profiles, single-peaked line sources with broad wings, and self-absorbed sources." + This paper is arranged as follows: In refobservations the survey and data reduction are described. ducliding a detailed discussion of the capabilities of the spectro-astrometric mode of CRIRES for super-resolition maging.," This paper is arranged as follows: In \\ref{observations} the survey and data reduction are described, including a detailed discussion of the capabilities of the spectro-astrometric mode of CRIRES for super-resolution imaging." + Iu rofl&eplerzourecs)). wediscusstheresultsof fittingsiinple," In \\ref{Kepler_sources}) ), we discuss the results of fitting simple Keplerian disk models to the data." +lcplerian , The central issue is that many CO line and astrometric spectra be explained by Keplerian velocity fields. +RKeplevianclassofcimissionlinesints FNongeplecandecplainwhgapurelgIeplerianmodelfails., We introduce a non-Keplerian class of emission lines in \\ref{Non_Kepler} and explain why a purely Keplerian model fails. +"Ins refiind,,odel,. wedevelopa2 dimensionalnodelthataddsadishwindtoarcqularleplerian, Fla"," In \\ref{wind_model}, we develop a 2-dimensional model that adds a disk wind to a regular Keplerian, flared disk, and demonstrate that this provides a framework for matching all CO line and astrometric spectra from classical T Tauri stars under specific circumstances, namely if the wind is slow and uncollimated." +"red dominatedlines, possiblyscalinguwiththeniass faceretionrates"," We suggest that there is a smooth transition from lines dominated by Keplerian motions to wind-dominated lines, possibly scaling with the mass-loss/accretion rates." + LN refdiscussiontheinplications forourunderstandi ngofdiskdisperse , In \\ref{discussion} the implications for our understanding of disk dispersal and the nature of the warm molecular disk surface layer are discussed. +Spectro-astrometric observations were obtained as part of a laree CRIRES survey of infrared) molecular cluission from protoplanetary disks aud voung stellar objects within the framework of the European Southern Observatory (ESO) Large Program 179.C-0151(7)., Spectro-astrometric observations were obtained as part of a large CRIRES survey of infrared molecular emission from protoplanetary disks and young stellar objects within the framework of the European Southern Observatory (ESO) Large Program 179.C-0151. +" Spectro-astrometry is a highly seusitive method that allows a sinele telescope to obtain both spatial aud kinematic information on eas-plase lines on very small scales, «o Luumilliaresecoud. aud at very high spectral resolution. A/AA~100000."," Spectro-astrometry is a highly sensitive method that allows a single telescope to obtain both spatial and kinematic information on gas-phase lines on very small scales, $<1$ milliarcsecond, and at very high spectral resolution, $\lambda/\Delta \lambda \sim 100\,000$." + The final accuracy of a spectro-astrometric measurement depends linearly ou both the signal-to-noise and the width of the spatial PSF., The final accuracy of a spectro-astrometric measurement depends linearly on both the signal-to-noise and the width of the spatial PSF. + Basically. the method measures the spatial ceutroid offset of the spectrmm as a function of wavelength across a line or other spectral feature. relative to the contiuuua.," Basically, the method measures the spatial centroid offset of the spectrum as a function of wavelength across a line or other spectral feature, relative to the continuum." + This approach can reveal spatial structure on scales mich s:mdler than the formal diffraction limit of the ΓΙ, This approach can reveal spatial structure on scales much smaller than the formal diffraction limit of the observation. + det ve chromatic tuagine and μεςspectroscopy for the detection of stellar binaries m the visible rauge using specialized instrumentation (777)., Spectro-astrometry was first developed for chromatic imaging and spectroscopy for the detection of stellar binaries in the visible range using specialized instrumentation . +. The modern form. using au echelle spectrograph. was first presented bv7.. and is reviewed by?.," The modern form, using an echelle spectrograph, was first presented by, and is reviewed by." +". Infrared (A2 1) spectro-astromoetry of molecular lines with CRIRES was introduced by?.. who presented CO data from three transitional disks. TW να, ΠΟ 135311B aud SR 21."," Infrared $\lambda\gtrsim 1\,\mu$ m) spectro-astrometry of molecular lines with CRIRES was introduced by, who presented CO data from three transitional disks, TW Hya, HD 135344B and SR 21." + They. showed that sub-uilliarcsecoud precisions could routinely be achieved and that the basic geometrics of the line cutting regions sizes. inclinations aud position. angles could be deteriuued with a high deeree of confidence.," They showed that sub-milliarcsecond precisions could routinely be achieved and that the basic geometries of the line emitting regions – sizes, inclinations and position angles – could be determined with a high degree of confidence." + Tere we extend this sample to a auch wider range of disks im ternis of stellar type aud evolutionary stage., Here we extend this sample to a much wider range of disks in terms of stellar type and evolutionary stage. + Targets were selected for spectro-astrometric observations according— to.— overall— brightness and liuc-to-coutinuuni contrast. as well as to cover as wide a range as possible in known disk aud stellar," Targets were selected for spectro-astrometric observations according to overall brightness and line-to-continuum contrast, as well as to cover as wide a range as possible in known disk and stellar" +host-free AGN luminosities may significantly reduce the scatter of the μι—L relationship.,host-free AGN luminosities may significantly reduce the scatter of the $R_{\rm BLR} - L$ relationship. + Certainly. a true scatter may remain. simply because AGN are complicated objects and the Rez» determination depends on the continuum variability pattern and the geometry of the BLR which produces the line echo.," Certainly, a true scatter may remain, simply because AGN are complicated objects and the $R_{BLR}$ determination depends on the continuum variability pattern and the geometry of the BLR which produces the line echo." + Future data will show how far the scatter can be reduced., Future data will show how far the scatter can be reduced. + While spectroscopic reverberation mapping is the only way to explore the details of the innermost AGN structure and the geometry of the BLR (e.g. Kollatschny 2003a. 20020: Kollatschny Zetzl 2010). the advantage of photometric reverberation mapping with suitable filters is to efficiently measure BLR sizes and host-subtracted luminosities for large AGN and quasar samples — even with small telescopes.," While spectroscopic reverberation mapping is the only way to explore the details of the innermost AGN structure and the geometry of the BLR (e.g. Kollatschny 2003a, 2003b; Kollatschny Zetzl 2010), the advantage of photometric reverberation mapping with suitable filters is to efficiently measure BLR sizes and host-subtracted luminosities for large AGN and quasar samples – even with small telescopes." + Photometric broad- and narrow-band monitoring of a sample of 100 quasars (CV.<18 mag) can be performed with 1-m telescopes in an equivalent of 3 years observing time.," Photometric broad- and narrow-band monitoring of a sample of 100 quasars $V < +18~mag$ ) can be performed with 1-m telescopes in an equivalent of 3 years observing time." + In the case of Ark120 the Hf line contributes to only of the flux in the narrow-bandpass we used., In the case of Ark120 the $\beta$ line contributes to only of the flux in the narrow-bandpass we used. + This suggests that photometric reverberation mapping of emission line lags works even for broader bands. as long as the line contributes at least to the bandpass.," This suggests that photometric reverberation mapping of emission line lags works even for broader bands, as long as the line contributes at least to the bandpass." + Also. it is worthwhile to test the method even for weaker emission lines contributing less than to the bandpass.," Also, it is worthwhile to test the method even for weaker emission lines contributing less than to the bandpass." + The upeoming Large Synoptic Survey Telescope (LSST) is equipped with six broad band filters and will discover thousands of variable AGN., The upcoming Large Synoptic Survey Telescope (LSST) is equipped with six broad band filters and will discover thousands of variable AGN. + The Ha line is shifted into the /’ and z/ bands at z«0.16 and z=0.38. respectively and may be strong enough. contributing about to these broad bands.," The $\alpha$ line is shifted into the $i'$ and $z'$ bands at $z \approx 0.16$ and $z \approx 0.38$, respectively and may be strong enough, contributing about to these broad bands." + While an approximate photometric redshift may be sufficient to determine the filter which contains the Ha line. it is desirable to take a spectrum of the AGN. in order to measure an accurate redshift. also for luminosity determination. and the line dispersion for black hole mass estimates.," While an approximate photometric redshift may be sufficient to determine the filter which contains the $\alpha$ line, it is desirable to take a spectrum of the AGN, in order to measure an accurate redshift, also for luminosity determination, and the line dispersion for black hole mass estimates." + In order to determine the He line lag. the neighbouring filters. which are largely free of line emission. may be used to interpolate and remove the continuum variations underneath the Ha line. in analogy to what we did for Ark120.," In order to determine the $\alpha$ line lag, the neighbouring filters, which are largely free of line emission, may be used to interpolate and remove the continuum variations underneath the $\alpha$ line, in analogy to what we did for Ark120." + Recently. an interesting statistical alternative to our method has been proposed by Chelouche Daniel (2011). which ts specifically designed for large samples of AGN light curves expected to be obtained with the LSST.," Recently, an interesting statistical alternative to our method has been proposed by Chelouche Daniel (2011), which is specifically designed for large samples of AGN light curves expected to be obtained with the LSST." + Consider AGN light curves in two bandpasses. curve X (tracing the continuum largely free of emission lines) and curve Y (tracing the emission line with underlying continuum): While our approach aimed to remove the continuum contribution from curve Y by subtracting a scaled X curve. Chelouche Daniel propose to use the light curves X and Y unchanged. and to subtract the autocorrelation of X from the cross correlation of X and Y. in order to determine the line lag.," Consider AGN light curves in two bandpasses, curve X (tracing the continuum largely free of emission lines) and curve Y (tracing the emission line with underlying continuum): While our approach aimed to remove the continuum contribution from curve Y by subtracting a scaled X curve, Chelouche Daniel propose to use the light curves X and Y unchanged, and to subtract the autocorrelation of X from the cross correlation of X and Y, in order to determine the line lag." + Numerical simulations with synthetic AGN light curves and the treatment of four archival PG quasar light curves yield lags which are (in three of four cases) consistent with spectroscopic results., Numerical simulations with synthetic AGN light curves and the treatment of four archival PG quasar light curves yield lags which are (in three of four cases) consistent with spectroscopic results. + However. the reported lag uncertainties of individual AGN are large (~50%)) and only for averages of large ensembles of several hundred AGN the obtained lags appear satisfying.," However, the reported lag uncertainties of individual AGN are large $\sim$ ) and only for averages of large ensembles of several hundred AGN the obtained lags appear satisfying." + Future optimisations. combining our approach with that of Chelouche Daniel. would be intriguing.," Future optimisations, combining our approach with that of Chelouche Daniel, would be intriguing." + Finally we outline a modification of the proposals by Elvis Karovska (2002) and Horne et al. (, Finally we outline a modification of the proposals by Elvis Karovska (2002) and Horne et al. ( +2003) to determine quasar distances from reverberation data and thus to probedark energy.,2003) to determine quasar distances from reverberation data and thus to probedark energy. +" The luminosity difference between the open Einstein — de Sitter cosmology (Oy,=0.2.O40) and the concordance cosmology (Q4;=0.3.O40.7) ts at redshift O42 has been maintained from the formation time of the tenuous structure with density ofοπιὃ.,the IMF with $\gamma \geq 2$ has been maintained from the formation time of the tenuous structure with density of. +" In addition to the Orion cloud, a representative of massive star formation, the similarity between the CMF and the IMF was reported in low-mass star forming regions by Tachiharaetal.(2002)."," In addition to the Orion cloud, a representative of massive star formation, the similarity between the CMF and the IMF was reported in low-mass star forming regions by \citet{tac02}." +". The cores found in Taurus, Chamaeleon, Lupus, and other low-mass star forming regions show the CMF with = 2.6 above 56Mo. Krameretal.(1998),"," The cores found in Taurus, Chamaeleon, Lupus, and other low-mass star forming regions show the CMF with $\gamma$ = 2.6 above 56. \citet{kra98}," +", however,found a significantly smaller value of 1.7 for the S140 and M17SW regions by using the(J—2-1) line with a high critical density comparable to thatof(J—1-0)."," however,found a significantly smaller $\gamma$ value of 1.7 for the S140 and M17SW regions by using the line with a high critical density comparable to thatof." + Wongetal.(2008) also found y = 1.7 in the(J—1-0) CMF of RCW 106., \citet{won08} also found $\gamma$ = 1.7 in the CMF of RCW 106. +" In this study, we focus on $140 for the following reasons."," In this study, we focus on S140 for the following reasons." +" First, the distance to $140 of 910 pc (Crampton&Fisher1974) is the nearest one of them; the distances to M17SW and RCW 106 are 2.2 kpc (Chinietal.1980) and 3.6 kpc 1979),, respectively, and the two clouds are located in the Sagittarius arm."," First, the distance to S140 of 910 pc \citep{cra74} is the nearest one of them; the distances to M17SW and RCW 106 are 2.2 kpc \citep{chi80} and 3.6 kpc \citep{loc79}, respectively, and the two clouds are located in the Sagittarius arm." +" Since we discuss the power-law nature of the CMF on the basis of a comparison with that in OMC-1, it seems quite natural to first select the S140 region, located in the Local (Orion) Spur as the next step in our CMF study."," Since we discuss the power-law nature of the CMF on the basis of a comparison with that in OMC-1, it seems quite natural to first select the S140 region, located in the Local (Orion) Spur as the next step in our CMF study." +" Second, since the previous(J—2-1) observations of $140 (Johnen1992) covered only the brightest 4’x4' region around IRAS 22176+6303, we cannot exclude the possibility that their core identification was biased to high-mass cores, leading to the flatter CMF."," Second, since the previous observations of S140 \citep{joh92} covered only the brightest $4'\times4'$ region around IRAS 22176+6303, we cannot exclude the possibility that their core identification was biased to high-mass cores, leading to the flatter CMF." +" Third, the higher transition of with the transition energy of 15.8 K might prefer to pick up higher-mass protostellar cores, compared to the lowest transition ofJ=1-0."," Third, the higher transition of with the transition energy of 15.8 K might prefer to pick up higher-mass protostellar cores, compared to the lowest transition of." +" The aim of this paper is to re-estimate the power-law index of the CMF in the $140 region, also identified as Lynds 1204, and to examine whether the similarity between the CMF and the IMF holds in the region or not."," The aim of this paper is to re-estimate the power-law index of the CMF in the S140 region, also identified as Lynds 1204, and to examine whether the similarity between the CMF and the IMF holds in the region or not." +" Our observations were done to cover the cloud as widely as possible, in order to avoid the possible spatial bias."," Our observations were done to cover the cloud as widely as possible, in order to avoid the possible spatial bias." +" We employed the (J—1-0) line emission, which is the same tracer as Ikeda&Kitamura(2009) did,"," We employed the line emission, which is the same tracer as \citet{ike09b} did," +"the perturbation of the mass, pressure, sound speed squared (c?) and BV squared (N?) as a function of the perturbation of the density, gravity and adiabatic exponent.","the perturbation of the mass, pressure, sound speed squared $c^2$ ) and BV squared $N^2$ ) as a function of the perturbation of the density, gravity and adiabatic exponent." +" From these relations we derived an expression for the perturbation of the density as a function of the perturbations introduced for BV and the sound speed (60.N?,6c?)."," From these relations we derived an expression for the perturbation of the density as a function of the perturbations introduced for BV and the sound speed $\delta N^2, \delta c^2$ )." +" Finally, we wrote the perturbation of the dynamical variables of the model as a function of the already calculated perturbations (a complete description of the mathematical formulation is given in Appendix A)."," Finally, we wrote the perturbation of the dynamical variables of the model as a function of the already calculated perturbations (a complete description of the mathematical formulation is given in Appendix A)." + These new perturbed models underwent again the non-adiabatic analysis., These new perturbed models underwent again the non-adiabatic analysis. +" When we cancel out the He/H chemical transition region, we get a smooth kinetic energy for all the modes (Fig. 2,,"," When we cancel out the He/H chemical transition region, we get a smooth kinetic energy for all the modes (Fig. \ref{fig:allgkin}," + upper solid line)., upper solid line). +" Trapped modes vanish, revealing that the He/H transition is the main factor responsible for their occurrence."," Trapped modes vanish, revealing that the He/H transition is the main factor responsible for their occurrence." +" The plot of the weight function (Fig. 5,,"," The plot of the weight function (Fig. \ref{fig:grweif88}," +" right) reveals that the He/H region, once cancelled, no longer has any significant influence on mode formation."," right) reveals that the He/H region, once cancelled, no longer has any significant influence on mode formation." +" We also note that the growth rate no longer oscillates with frequency (Fig. 2,,"," We also note that the growth rate no longer oscillates with frequency (Fig. \ref{fig:allgkin}," +" lower solid line), as expected from the uniform kinetic energy; and we also get a uniform period separation (Fig. 3,,"," lower solid line), as expected from the uniform kinetic energy; and we also get a uniform period separation (Fig. \ref{fig:allgdeltap}," + solid line)., solid line). +" However, perturbed modes equivalent to trapped modes in the original model achieved higher values of the growth rate, while their kinetic energy was higher, which seems to be at odds with the growth rate dependence on the kinetic energy."," However, perturbed modes equivalent to trapped modes in the original model achieved higher values of the growth rate, while their kinetic energy was higher, which seems to be at odds with the growth rate dependence on the kinetic energy." +" The local minimum in the damping energy for model 8 at logg=—2.23 (Fig. 8,,"," The local minimum in the damping energy for model 8 at $\log q=-2.23$ (Fig. \ref{fig:dwzoom}," +" dotted line), which is absent in model pertHeH (Fig. 8,,"," dotted line), which is absent in model pertHeH (Fig. \ref{fig:dwzoom}," +" solid line), is responsible for the overall lower values of the growth rate in the original model."," solid line), is responsible for the overall lower values of the growth rate in the original model." +LAIC! Cepheids in the I band is more (han 80. the constructed light curve are expected to be well behaved and the Fourier amplitudes are assumed to [all within the appropriate ranges.,"LMC Cepheids in the I band is more than 80, the constructed light curve are expected to be well behaved and the Fourier amplitudes are assumed to fall within the appropriate ranges." + The plots of the Fourier amplitudes are shown in Figure 5.. with some suspected. outliers marked in (rianeles and labelled.," The plots of the Fourier amplitudes are shown in Figure \ref{fig:fig5}, with some suspected outliers marked in triangles and labelled." + We also plot out some of the Fourier light curves lor these outliers in Figure G.., We also plot out some of the Fourier light curves for these outliers in Figure \ref{fig:fig6}. + As seen [rom the figure. some of them have acceptable light. curves. with slightly laveer amplitudes when compared to the Fourier Leht curves from Cepheids with similar periods.," As seen from the figure, some of them have acceptable light curves, with slightly larger amplitudes when compared to the Fourier light curves from Cepheids with similar periods." + The exception is C686. which exhibits a tip around phase 0.1 from the original data.," The exception is $C686$, which exhibits a tip around phase 0.1 from the original data." + The simple 4 order Fourier expansion cannot reproduce this tip and hence the constructed Light curves do not show good agreement (o the data., The simple $4^{th}$ order Fourier expansion cannot reproduce this tip and hence the constructed light curves do not show good agreement to the data. + Nevertheless. the difference in amplitudes for the outliers and the majoritv of the data points are verv small. because the I band amplitudes for Cepheids are generally smaller (Freecdinan1983).," Nevertheless, the difference in amplitudes for the outliers and the majority of the data points are very small, because the I band amplitudes for Cepheids are generally smaller \citep{fre88}." +. From Figuree 3--5.. 1b Is clear that the Fourier amislitticles occupy certain rangese 11 the amplitude vs. log(P?) plots.," From Figure \ref{fig:fig3}- \ref{fig:fig5}, it is clear that the Fourier amplitudes occupy certain ranges in the amplitude vs. $\log(P)$ plots." + Therefore we can determine the appropriate ranges of Fourier amplitudes for a given period fom these figures., Therefore we can determine the appropriate ranges of Fourier amplitudes for a given period from these figures. + The adopted ranges for the Fourier amplitudes in V and LI band are presented in Table 1.., The adopted ranges for the Fourier amplitudes in V and I band are presented in Table \ref{tab1}. +" Due to the fact that the OGLE LMC data only contains Cepheids with periods less (han 32 davs (log(P?)< 1.5). the ranges for Cepheid with logt2)>1.5 are determined from the ""calibrating set. while (he ranges for shorter period Cepheids are determiied. [rom both OGLE LAIC and vcalibrating set” data."," Due to the fact that the OGLE LMC data only contains Cepheids with periods less than 32 days $\log(P)<1.5$ ), the ranges for Cepheid with $\log(P)>1.5$ are determined from the “calibrating set”, while the ranges for shorter period Cepheids are determined from both OGLE LMC and “calibrating set” data." + In addition. the ranges of the Fourjer «amplitudes are set lo be started rom zero (ο account Lor possible low amplitude Cepheids.," In addition, the ranges of the Fourier amplitudes are set to be started from zero to account for possible low amplitude Cepheids." + Note that the upper limit of the ranges given in Table 1. is an approximation. since |jere is no exact upper limit for a given period.," Note that the upper limit of the ranges given in Table \ref{tab1} is an approximation, since there is no exact upper limit for a given period." + Experience shows that sometimes a slightly arger range of the Fourier amplitudes than (he one given in Table can reconstruct the light curve better., Experience shows that sometimes a slightly larger range of the Fourier amplitudes than the one given in Table \ref{tab1} can reconstruct the light curve better. + An iterative process can be made. if necessary. to lind (he most suitable upper limits to reconstruct satisfactory light curves.," An iterative process can be made, if necessary, to find the most suitable upper limits to reconstruct satisfactory light curves." + The reduction in ranges can improve the quality of the Fourier fit. as some of the numerical bumps are removed in the reconstructed light curve. provided that the problem of bad phase coverage is nol too severe (see details in Section 2.3).," The reduction in ranges can improve the quality of the Fourier fit, as some of the numerical bumps are removed in the reconstructed light curve, provided that the problem of bad phase coverage is not too severe (see details in Section 2.3)." + The distributions of (he Fourier amplitudes for OGLE LMC Cepheids and| (he “calibrating sel” (or mostly Galactic) Cepheids appear to coincide. as seen in Figure 3--5«," The distributions of the Fourier amplitudes for OGLE LMC Cepheids and the “calibrating set” (or mostly Galactic) Cepheids appear to coincide, as seen in Figure \ref{fig:fig3}- \ref{fig:fig5}." + This may imply that (he ranges of the Fourier amplitucles depend weakly ou metallicity., This may imply that the ranges of the Fourier amplitudes depend weakly on metallicity. + However. this conclusion is only based on the analvsis of two galaxies. aud may not reflect the assumption that metallicity can affect the distribution of Fourier amplitudes.," However, this conclusion is only based on the analysis of two galaxies, and may not reflect the assumption that metallicity can affect the distribution of Fourier amplitudes." + vanGenceren(1973) showed that the upper limits of B band amplitudes are different lor Cepheids in Galaxy/M31.," \citet{van78} showed that the upper limits of B band amplitudes are different for Cepheids in Galaxy/M31," +of instrument noise contribution to P(k) measurement.,of instrument noise contribution to P(k) measurement. + The differences in Pyojse will translate into differing precisions in the reconstruction of the BAO peak positions and in the estimation of cosmological parameters., The differences in $P_{noise}$ will translate into differing precisions in the reconstruction of the BAO peak positions and in the estimation of cosmological parameters. +" In addition, we have seen (sec. 4.2))"," In addition, we have seen (sec. \ref{recsec}) )" +" that subtraction of continuum radio emissions, Galactic synchrotron and radio sources, has also an effect on the measured 21 cm power spectrum."," that subtraction of continuum radio emissions, Galactic synchrotron and radio sources, has also an effect on the measured 21 cm power spectrum." +" In this paragraph, we present our method and the results for the precisions on the estimation of Dark Energy parameters, through a radio survey of the redshifted 21 cm emission of LSS, with an instrumental setup similar to the (e) configuration (sec. 3.3)),"," In this paragraph, we present our method and the results for the precisions on the estimation of Dark Energy parameters, through a radio survey of the redshifted 21 cm emission of LSS, with an instrumental setup similar to the (e) configuration (sec. \ref{instrumnoise}) )," +" 400 five-meter diameter dishes, arrangedinto a filled 20x array."," 400 five-meter diameter dishes, arrangedinto a filled $20 \times 20$ array." +" In order to estimate the precision with which BAO peak positions can be measured, we used a method similar to the one established in (BlakeandGlazebrook(2003)) and (GlazebrookandBlake(2005))."," In order to estimate the precision with which BAO peak positions can be measured, we used a method similar to the one established in \citep{blake.03} and \citep{glazebrook.05}." +". To this end, we generated reconstructed power spectra P'**(K) for slices of Universe with a quarter-sky coverage and a redshift depth, Az=0.5 for 0.25«z2.75."," To this end, we generated reconstructed power spectra $P^{rec}(k)$ for slices of Universe with a quarter-sky coverage and a redshift depth, $\Delta z=0.5$ for $0.25 100$ MK are not observed preferentially to arise on a particular YSO class; a KS test on the set of temperatures results in a $98\%$ probability that the Class II and Class III temperature distributions originate in the same parent distribution. +" However. the two flares in our sample with n,>30xLOM em? occur on Class III. YSOs."," However, the two flares in our sample with $n_e > 30 \times 10^{10}$ $cm^{-3}$ occur on Class III YSOs." + These findings are consistent with Figure 4bb and. dec. which indicate that loop length is not a strong predictor of peak temperature but is rather anti-correlated wilh plasma density.," These findings are consistent with Figure \ref{BasicResults}b b and \ref{BasicResults}c c, which indicate that loop length is not a strong predictor of peak temperature but is rather anti-correlated with plasma density." + Even if lengthened flares are preferentially found on Class II YSOs. the hottest [lares will not necessarily be found on Class II YSOs as well.," Even if lengthened flares are preferentially found on Class II YSOs, the hottest flares will not necessarily be found on Class II YSOs as well." + As discussed in $2.1. our sample has a bias towards the brightest flares on voung stellar objects.," As discussed in $\S 2.1$, our sample has a bias towards the brightest flares on young stellar objects." + It is of interest to estimate the frequency. wilh which these intense flares occur., It is of interest to estimate the frequency with which these intense flares occur. + By multiplving the number of sources in each Chandra observation included in our sample by (he reported exposure time and sumnming over all observations. (his sample may be estimated (o contain approximately 2.9 million ks (i.e. 2.9x10? seconds) of von stai time.," By multiplying the number of sources in each Chandra observation included in our sample by the reported exposure time and summing over all observations, this sample may be estimated to contain approximately 2.9 million ks (i.e. $2.9 \times 10^{9}$ seconds) of “on star” time." + large flares were observed in this “on star” time. which translates to one large flare per 100.000 ks of observation time.," Twenty-nine large flares were observed in this “on star” time, which translates to one large flare per 100,000 ks of observation time." + Phrased differently. (he average YSO in our sample produces one of these intense flares. characterized by fast rise to a ten-fold increase in [hix over the characteristic level followed by a smooth quasi-exponential decay. about. once every. three vears.," Phrased differently, the average YSO in our sample produces one of these intense flares, characterized by fast rise to a ten-fold increase in flux over the characteristic level followed by a smooth quasi-exponential decay, about once every three years." +For a line width of 0.1 keV (o0) . the upper limit ou its equivalent width is 30 eV. This limit increases up to 80 eV when σ=0.5 keV (both values are eiven at the confidence level).,"For a line width of 0.1 keV $\sigma$ ), the upper limit on its equivalent width is $\sim 30$ eV. This limit increases up to $\sim 80$ eV when $\sigma=0.5$ keV (both values are given at the confidence level)." + Our observation coulirmued tle existence of a soft conmporeut in the X-ray spectruu of at a lumilosilv a‘ound 25.7 x1079 (Q310.0 keV. 7.7 Kyx).," Our observation confirmed the existence of a soft component in the X-ray spectrum of at a luminosity around 5.7 $\times 10^{36}$ (0.5-10.0 keV, 7.7 kpc)." + ΤΙe nou-detection of this soft COMpOLent in the ENOSAT atdà TIM data could be explained by a lack of seusitivity below 2 keV. Iftus soft comiponeut ]s à nuuti-colo| disk blacshocky. ten ΟΥ esimate of Vvcos? is consisten with the low valιο generally observed from neutroi stal systels. and auich sinaller tau he values derivec from black jole caxlidates.," The non-detection of this soft component in the EXOSAT and TTM data could be explained by a lack of sensitivity below 2 keV. If this soft component is a multi-color disk blackbody, then our estimate of $\sqrt{\cos\theta}$ is consistent with the low value generally observed from neutron star systems, and much smaller than the values derived from black hole candidates." + On he other hauc. hi sis not the case for whicl is much smaller ἰlan the 1.5 seV neτοι star vate. alid close to he black hee values (TanakaaudLewin.1995).," On the other hand, this is not the case for which is much smaller than the 1.5 keV neutron star value, and close to the black hole values \cite{tanaka95review}." +. As forHj. as »oiuted out by Cualazzl et al. (1998)..," As for, as pointed out by Guainazzi et al. \cite*{tz2:guainazzi98aa}," + in order or his radius to accom10date a neutron star radius. a arge iclination 0zτοῦ is required. iu contradiction with the fact that O sizable orbita moctilatious iive been observed from the source 1998)...," in order for this radius to accommodate a neutron star radius, a large inclination $\theta \ga +70^{0}$ is required, in contradiction with the fact that no sizable orbital modulations have been observed from the source \cite{tz2:olive98aa}." + For the Compli++BB inodel. the ratio of the luminosities 0.1-200 of the BB (Lpp)) component versus the One )) is ϱ.1.13-0.15.," For the +BB model, the ratio of the luminosities 0.1-200 of the BB ) component versus the one ) is 0.13-0.15." + The ratio of is 0.23-0.10 for t Comptt----DBB uiodel., The ratio of is 0.23-0.40 for the +DBB model. + The oriein of the x component is unclear., The origin of the soft component is unclear. + Obvioily it could cor from the neutron star surface isell or from an plically thick boundary laver near the neutron W.ar., Obviously it could come from the neutron star surface itself or from an optically thick boundary layer near the neutron star. + In this scenario. the Comj»Xtonized Component would be generated som.ewhere in a disk corona.," In this scenario, the Comptonized component would be generated somewhere in a disk corona." + The blackbodsy radius of ~10 an derived [rom ie. Compll++BB clearly argues in favor of this scenario., The blackbody radius of $\sim 10$ km derived from the +BB clearly argues in favor of this scenario. + Another possibility is that the soft component originates [ron the accretion disk. while ie harder X-rays are generated in the )oundary aver (Cuainazzietal.1998)..," Another possibility is that the soft component originates from the accretion disk, while the harder X-rays are generated in the boundary layer \cite{tz2:guainazzi98aa}." + Sunyaev aie ShakTa (1986) predicted that tre ralio between the «isk aud the boundary layer luminosities could be as ow as (215. if the disk euds at the marginally stable orbi (which is large‘than the netiron star ‘actius).," Sunyaev and Shakura \cite*{sunyaev86sal} + predicted that the ratio between the disk and the boundary layer luminosities could be as low as 0.45, if the disk ends at the marginally stable orbit (which is larger than the neutron star radius)." + As noticed. by CGlallazzi οἱ al. (1998)..," As noticed by Guainazzi et al. \cite*{tz2:guainazzi98aa}," + he properies of tle higl1 frequency quasi-periodic oscillatious receLtly discove“eC in LMXBs (VanderIxlis.1997) iXicates that 1lese svslenis cO LO ‘olate at their break-up periods. and further do no lave accretion cisks that extend bevoud the las uarginally stable ο‘bit.," the properties of the high frequency quasi-periodic oscillations recently discovered in LMXBs \cite{vdklis97review} indicates that these systems do not rotate at their break-up periods, and further do not have accretion disks that extend beyond the last marginally stable orbit." + In otler words. this means hat the predicted. ratio discussed. above could be even μιαοι than ~O.15.," In other words, this means that the predicted ratio discussed above could be even smaller than $\sim 0.45$." + Tjus the low ratio of he soft/hard fux {i.e. BB or DBB vs. Comptouize lux) woulc| favor tle pictire iu which the weak sol coniponenlt ¢omes from tle accretion disk. aud the C'omiptonizec conmpoteut originates from a hot ane optically thi1i boundary laver., Thus the low ratio of the soft/hard flux (i.e. BB or DBB vs. Comptonized flux) would favor the picture in which the weak soft component comes from the accretion disk and the Comptonized component originates from a hot and optically thin boundary layer. + This in ttn would support heoretical 11odes predictiig hard X-ray emnisslon roni such a boutdary layer (e.g. Ixluzniak and Wilson 1991: Waker 1992)., This in turn would support theoretical models predicting hard X-ray emission from such a boundary layer (e.g. Kluzniak and Wilson 1991; Walker 1992). + Our observation ILOVides the most accurate estinate obtained so far (see Fig. 2 )., Our observation provides the most accurate estimate obtained so far (see Fig. \ref{contours}) ). + Our values are consistent with the one derived by SAN (Cualnazzietal.1995).., Our values are consistent with the one derived by SAX \cite{tz2:guainazzi98aa}. + Following Predehl aud Schmitt (1995). the visual extinction is related to the X-ray absorbing coliuu density as Nyj=Ayx10?!RxECB—V)xJU 7.," Following Predehl and Schmitt \cite*{predehl95aa}, the visual extinction is related to the X-ray absorbing column density as $A_{\rm V} \times 10^{21}=R\times +E(B-V) \times 10^{21}$ ." + Taking E(B-VjJ=1.51 (Ortolanietal.1997).. we obtain Ny=O0.9¢ndL.0x107 for R=3.1 and 23.6 respectivels.," Taking E(B-V)=1.54 \cite{tz2:ortolani97aa}, we obtain $0.9$ and $1.0 \times 10^{22}$ for R=3.1 and 3.6 respectively." +" The ""optical value is remarkably close to 11e value derived with the Comptt----BB model (see Table 2).", The “optical” value is remarkably close to the value derived with the +BB model (see Table 2). + It is smaller by than the value derived Lor he Compl++DBB inodel, It is smaller by than the value derived for the +DBB model +"For the second case, we introduced an error in the slope of the wavelength calibration.","For the second case, we introduced an error in the slope of the wavelength calibration." +" Figure [2] illustrates the result of introducing an error of in the slope, in steps of0."," Figure \ref{figure:influence_slope} illustrates the result of introducing an error of in the slope, in steps of." +"05%.. In the case that we are considering here, it means varying the slope from 13.328 nm/pixel to 13.872 nm/pixel in steps of 68x107 nm/pixel."," In the case that we are considering here, it means varying the slope from 13.328 nm/pixel to 13.872 nm/pixel in steps of $68\times10^{-4}$ nm/pixel." + The results are similar to those for the systematic error., The results are similar to those for the systematic error. +" The effect is globally the same for all the models, although the two coldest models (600 K and 700 K) appear to be slightly less sensitive to a systematic error than the warmer models."," The effect is globally the same for all the models, although the two coldest models (600 K and 700 K) appear to be slightly less sensitive to a systematic error than the warmer models." +" The COND 600K model undergoes a loss for an error of 0.2 nm/pixel, while the SETTL 1700K model undergoes a loss for the same error."," The COND 600K model undergoes a loss for an error of 0.2 nm/pixel, while the SETTL 1700K model undergoes a loss for the same error." +" However, for errors of (34x10? nm/pixel) in the slope, the loss is smaller than for all models."," However, for errors of $34\times10^{-3}$ nm/pixel) in the slope, the loss is smaller than for all models." + After analyzing the influence of two possible sources of error in the wavelength calibration it appears that there is a clear necessity to achieve the smallest possible systematic error., After analyzing the influence of two possible sources of error in the wavelength calibration it appears that there is a clear necessity to achieve the smallest possible systematic error. +" An error of 10 nm (less than 1A) produces losses of several percent in the quality factor, even for bright companions."," An error of 10 nm (less than $1\Delta\lambda$ ) produces losses of several percent in the quality factor, even for bright companions." + Reaching an uncertainty level smaller than the spectral interval ΔΑ is then an absolute requirement for a proper characterization of planets with our method., Reaching an uncertainty level smaller than the spectral interval $\Delta\lambda$ is then an absolute requirement for a proper characterization of planets with our method. +" The influence of an error in the slope is also important, but the precision that can be achieved in the slope during the calibration procedure is small (0.25%))."," The influence of an error in the slope is also important, but the precision that can be achieved in the slope during the calibration procedure is small )." +" At this level of error, the loss in terms of quality factor is negligible."," At this level of error, the loss in terms of quality factor is negligible." +" We have implemented a promising method of characterizing planetary companions using long slit spectroscopy with coronagraphy, which has been considered for very high contrast imaging instruments, such as VLT-SPHERE."," We have implemented a promising method of characterizing planetary companions using long slit spectroscopy with coronagraphy, which has been considered for very high contrast imaging instruments, such as VLT-SPHERE." + The need to develop a specific method was mandatory to remove the scattered light residuals fully from the random speckles pattern in the spectra., The need to develop a specific method was mandatory to remove the scattered light residuals fully from the random speckles pattern in the spectra. +" Using the linear wavelength dependence of the speckle pattern, we were able to evaluate to high precision the precise contribution of the star to the spectrum, and remove this contribution before extracting a clean planetary companion spectrum."," Using the linear wavelength dependence of the speckle pattern, we were able to evaluate to high precision the precise contribution of the star to the spectrum, and remove this contribution before extracting a clean planetary companion spectrum." +" The simulations, performed using IDL, allowed us to test our method on realistic data for various cases of contrast in the case of low (R= 35) and medium (R= 400) resolution spectroscopy with extreme AO and Lyot coronagraphy."," The simulations, performed using IDL, allowed us to test our method on realistic data for various cases of contrast in the case of low $R = 35$ ) and medium $R = 400$ ) resolution spectroscopy with extreme AO and Lyot coronagraphy." +" The final gain of the method for a { hour exposure on MO and GO stars at 10 pc is of the order of 0.5 to 2 magnitudes in terms of contrast over the J, H and K bands, compared to the coronagraphic profile."," The final gain of the method for a 1 hour exposure on M0 and G0 stars at 10 pc is of the order of 0.5 to 2 magnitudes in terms of contrast over the J, H and K bands, compared to the coronagraphic profile." +" Although not very high in K band, the gain is substantial in J and H, allowing us to study companions with as low as 600 K. Following the evolutionary models of ?,, a 600 K companion in a 500 Myr system corresponds to amass of ~10 Mjup."," Although not very high in K band, the gain is substantial in J and H, allowing us to study companions with as low as 600 K. Following the evolutionary models of \citet{baraffe2003}, a 600 K companion in a 500 Myr system corresponds to a mass of $\sim$ 10 $M_{\mathrm{Jup}}$." +" To estimate the method efficiency, a quality factor has been introduced to measure the correlation between the input planetary spectrum in the simulation and the extracted spectra, as well as the discrepancy between the two."," To estimate the method efficiency, a quality factor has been introduced to measure the correlation between the input planetary spectrum in the simulation and the extracted spectra, as well as the discrepancy between the two." + This allowed us to be confident that our method will allow precise characterization at LRS and MRS of companions as cool as 600 K around, This allowed us to be confident that our method will allow precise characterization at LRS and MRS of companions as cool as 600 K around +"Of course, there are many other consequences of the AR,=cf constraint, e.9., with regard to baryogenesis, nucleosynthesis, and structure formation, all of which would have been affected in terms of when they could have occurred, if not the physical conditions prevalent at those times.","Of course, there are many other consequences of the $R_{\rm h}=ct$ constraint, e.g., with regard to baryogenesis, nucleosynthesis, and structure formation, all of which would have been affected in terms of when they could have occurred, if not the physical conditions prevalent at those times." +" Although it is beyond the scope of the present work to fully explore all of these processes, a detailed account is necessary before the viability of our proposal can be fully assessed."," Although it is beyond the scope of the present work to fully explore all of these processes, a detailed account is necessary before the viability of our proposal can be fully assessed." + This extended analysis is necessary because the current situation with the standard model is far trom adequate., This extended analysis is necessary because the current situation with the standard model is far from adequate. + For example. ACDM does not provide a compelling explanation for the galaxy correlation function.," For example, $\Lambda$ CDM does not provide a compelling explanation for the galaxy correlation function." +" Over the past four decades, the successively larger galaxy redshift surveys have mapped the distribution of galaxies with ever increasing precision, confirming correlation functions consistent with a single power law on all scales (c... Marzke et al."," Over the past four decades, the successively larger galaxy redshift surveys have mapped the distribution of galaxies with ever increasing precision, confirming correlation functions consistent with a single power law on all scales (e.g., Marzke et al." + 1995; Zehavi et al., 1995; Zehavi et al. +" 2002). fromlarge regions (>10 Mpo) exhibiting slight density fluctuations, to collapsed, virialized galaxy groups and clusters (7<1 Mpc)."," 2002), fromlarge regions $r>10$ Mpc) exhibiting slight density fluctuations, to collapsed, virialized galaxy groups and clusters $r< 1$ Mpc)." +" The lack of any observational feature signaling the transition from one physical domain to the next is surprising when viewed within context of the standard model (see, e.2.. Li White 2009), because the matter correlation function in the concordance model differs significantly from a power law."," The lack of any observational feature signaling the transition from one physical domain to the next is surprising when viewed within context of the standard model (see, e.g., Li White 2009), because the matter correlation function in the concordance model differs significantly from a power law." +" The most recent attempts at accounting for the unexpected galaxy correlation function have relied on several new, fine-tuning additions in order to get the correct profile (see, e.9.. Watson et al."," The most recent attempts at accounting for the unexpected galaxy correlation function have relied on several new, fine-tuning additions in order to get the correct profile (see, e.g., Watson et al." + 2011)., 2011). +" But the various contributing effects are intertwined and no simple, universal rule exists for which a power-law correlation function emerges."," But the various contributing effects are intertwined and no simple, universal rule exists for which a power-law correlation function emerges." +"The evolving competition between aceretion and destruction rates of subhalos over time isrequired to have struck just the right balance at z=0, leading Watson et al. (","The evolving competition between accretion and destruction rates of subhalos over time is to have struck just the right balance at $z\approx 0$, leading Watson et al. (" +2011) to conclude that the power-law galaxy correlation function is a cosmic coincidence.,2011) to conclude that the power-law galaxy correlation function is a cosmic coincidence. +" Part of the difficulty with this type of analysis is that, besides gravity and pressure, other physical processes can play an important role in the formation of structure, and these are not easy to handle."," Part of the difficulty with this type of analysis is that, besides gravity and pressure, other physical processes can play an important role in the formation of structure, and these are not easy to handle." +" For example. in baryonic models, the most important physical phenomenon is the interaction between baryons and photons during the pre-recombination era, and the consequent dissipation due to viscosity and heat conduction."," For example, in baryonic models, the most important physical phenomenon is the interaction between baryons and photons during the pre-recombination era, and the consequent dissipation due to viscosity and heat conduction." +" Insofar as the Rk),=cf universe is concerned, we can leave these elements aside for the moment. and at least suggest how the fundamental equation describing the dynamical growth of density fluctuations would appear in this cosmology."," Insofar as the $R_{\rm h}=ct$ universe is concerned, we can leave these elements aside for the moment, and at least suggest how the fundamental equation describing the dynamical growth of density fluctuations would appear in this cosmology." +" Defining the density contrast 6=ὁρ/ρ in terms of the density fluctuation óp and unperturbed density p, we can form the wavelike decomposition"," Defining the density contrast $\delta\equiv \delta\rho/\rho$ in terms of the density fluctuation $\delta \rho$ and unperturbed density $\rho$ , we can form the wavelike decomposition" + , +Perturbations to normally circular orbits in. nearly-Keplerian potentials are of fundamental interest for a variety of topics in astrophysics.,Perturbations to normally circular orbits in nearly-Keplerian potentials are of fundamental interest for a variety of topics in astrophysics. + For example. questions related to the fueling of super-massive black holes (BHs). their accretion disks. and the dynamics of nearby systems. the formation and fueling of protostars. and the behavior of protoplanetary disks and planets around. stars or rings and moons around planets.," For example, questions related to the fueling of super-massive black holes (BHs), their accretion disks, and the dynamics of nearby systems, the formation and fueling of protostars, and the behavior of protoplanetary disks and planets around stars or rings and moons around planets." + Particularly interesting are perturbations with azimuthal wavenumber a7=| (amplitude xcos ó). which can manifest as eccentric orbits or disks. lopsided or sloshing modes. or one-armed spirals.," Particularly interesting are perturbations with azimuthal wavenumber $m=1$ (amplitude $\propto \cos{\phi}$ ), which can manifest as eccentric orbits or disks, lopsided or sloshing modes, or one-armed spirals." +" It is easy to see why: the response of a nearly circular orbit to a weak perturbation. to leading order. scales with |[ποΟμ 7] where © is the orbital frequency. & is the epicyclic frequency. and ©, is the characteristic frequency (precession rate) ofthe perturbation."," It is easy to see why: the response of a nearly circular orbit to a weak perturbation, to leading order, scales with $1/[\kappa^{2}-m\,(\Omega-\Omega_{p})^{2}]$ , where $\Omega$ is the orbital frequency, $\kappa$ is the epicyclic frequency, and $\Omega_{p}$ is the characteristic frequency (precession rate) ofthe perturbation." +" In a Keplerian potential. &=Q747. so (since ©,i is finite) for any continuous system this scales at small radii as L/ClΗμὩς"," In a Keplerian potential, $\kappa=\Omega \propto r^{-3/2}$, so (since $\Omega_{p}$ is finite) for any continuous system this scales at small radii as $\sim1/(1-m)\,\Omega^{2}$." + For general zr. this vanishes. but for i—| the leading terms cancel and there is a strong resonant response.," For general $m$, this vanishes, but for $m=1$ the leading terms cancel and there is a strong resonant response." + Physically. this 1:1 resonance between radial and azimuthal frequencies is related to the fact that elliptical orbits in a Keplerian potential are closed and do not precess.," Physically, this 1:1 resonance between radial and azimuthal frequencies is related to the fact that elliptical orbits in a Keplerian potential are closed and do not precess." + As a consequence. the eccentricity distribution and mode behavior in such a disk can be determined by collective effects in the disk. even where these collective effects are very weak compared to the gravity of the central object.," As a consequence, the eccentricity distribution and mode behavior in such a disk can be determined by collective effects in the disk, even where these collective effects are very weak compared to the gravity of the central object." + Recently. for example. 3 have shown that the formation of lopsided. eccentric disks within the BH radius of influence is a ubiquitous feature in hydrodynamic simulations of massive gas inflows in galaxies. and that such disks can efficiently drive gas angular momentum loss and power BH accretion rates of up to ~LOA.yr.," Recently, for example, \citet{hopkins:zoom.sims} have shown that the formation of lopsided, eccentric disks within the BH radius of influence is a ubiquitous feature in hydrodynamic simulations of massive gas inflows in galaxies, and that such disks can efficiently drive gas angular momentum loss and power BH accretion rates of up to $\sim10\,\msun\,{\rm yr^{-1}}$." + The co-existence of gas and stars is critical for the large inflow rates seen: the torques on the gas are dominated by the mode in the collisionless portion of the disk., The co-existence of gas and stars is critical for the large inflow rates seen; the torques on the gas are dominated by the mode in the collisionless portion of the disk. + And the stellar relies of these disks bear a remarkable similarity to nuclear disks observed on Ope scales around nearby supermassive BHs. particularly the well-studied case at the center ofM31 (2).. whose origin has been mysterious.," And the stellar relics of these disks bear a remarkable similarity to nuclear disks observed on $\lesssim10\,$ pc scales around nearby supermassive BHs, particularly the well-studied case at the center ofM31 \citep{lauer93}, , whose origin has been mysterious." + The inflow and outflow regulated by, The inflow and outflow regulated by +"The present size of CoRoT-2b can thus be explained by the combination of a young age of between 30 and 40 MMa, and additional opacity sources (gases/clouds) in the atmosphere.","The present size of CoRoT-2b can thus be explained by the combination of a young age of between $30$ and $40$ Ma, and additional opacity sources (gases/clouds) in the atmosphere." + We note that ? also proposed an increase in atmospheric opacities to explain the large sizes of exoplanets., We note that \citet{BHBH07} also proposed an increase in atmospheric opacities to explain the large sizes of exoplanets. +" Our solution is similar, but we emphasize that this increase should concern more particularly the opacities at infrared wavelengths."," Our solution is similar, but we emphasize that this increase should concern more particularly the opacities at infrared wavelengths." + Alternative models invoked to explain the large sizes of other exoplanets are unlikely to work., Alternative models invoked to explain the large sizes of other exoplanets are unlikely to work. +" As shown in Fig. 13,,"," As shown in Fig. \ref{fig:compare_ctediff}," + the kinetic-energy dissipation model proposed by (?) and used successfully for most known transiting planets (??) fails for CoRoT-2.," the kinetic-energy dissipation model proposed by \citep{GS02} and used successfully for most known transiting planets \citep{Guillot+06,Guillot08} fails for CoRoT-2." + This is also the case of a considerable -30 fold- increase in interior opacities that would also explainthe sizes of most transiting planets (?).., This is also the case of a considerable -30 fold- increase in interior opacities that would also explainthe sizes of most transiting planets \citep{Guillot08}. +" In fact, as already noted (??),, the energy dissipation deep inside the planet required to explain the present-day radius is enormous, on the order of 10??ergs!."," In fact, as already noted \citep{Alonso+08,Gillon+10}, the energy dissipation deep inside the planet required to explain the present-day radius is enormous, on the order of $10^{29}\,\rm erg\,s^{-1}$." + This is about 30000 times the present intrinsic luminosity of Jupiter., This is about 30000 times the present intrinsic luminosity of Jupiter. + It is also about 1/4th of the power that the planet receives from its parent star., It is also about 1/4th of the power that the planet receives from its parent star. +" After that provided by stellar radiation, the most important potential source of energy is that taken from the planetary orbit."," After that provided by stellar radiation, the most important potential source of energy is that taken from the planetary orbit." +" When moving CoRoT-2b from infinity to its present orbit, AE=GM.My/2a310* erg have to be dissipated."," When moving CoRoT-2b from infinity to its present orbit, $\Delta E=GM_* M_{\rm p}/2a \approx 10^{45}\,$ erg have to be dissipated." +" If this energy dissipation were to occur entirely in the planet, the maximum amount of time one would be able to maintain a 10?ergs-! dissipation rate is ~300 MMa."," If this energy dissipation were to occur entirely in the planet, the maximum amount of time one would be able to maintain a $10^{29}\,\rm erg\,s^{-1}$ dissipation rate is $\sim 300$ Ma." +" As originally proposed by ? and ? and later studied by many authors (e.g.???),, stellar tides provide a way to transfer gravitational energy from the planetary orbit into the planet and either slow its contraction, or even produce a size inflation."," As originally proposed by \citet{BLM01} and \citet{GLB03} and later studied by many authors \citep[e.g.][]{JGB08a,IB09,MFJ09}, stellar tides provide a way to transfer gravitational energy from the planetary orbit into the planet and either slow its contraction, or even produce a size inflation." +" Models coupling the equations governing the dynamical evolution of the star+planet system with the physical planetary evolution rely however on a crucial assumption: that dissipation occurs at a sufficient depth in the planet interior, i.e. roughly within the planet's convective zone, deeper than a few 100 bars or so (see?,foradiscussion).."," Models coupling the equations governing the dynamical evolution of the star+planet system with the physical planetary evolution rely however on a crucial assumption: that dissipation occurs at a sufficient depth in the planet interior, i.e. roughly within the planet's convective zone, deeper than a few 100 bars or so \citep[see][for a discussion]{GS02}." +" The mechanisms responsible for the dissipation are yet unknown, and may occur either high up in the atmosphere (?) or throughout the planetary interior (?).."," The mechanisms responsible for the dissipation are yet unknown, and may occur either high up in the atmosphere \citep{LTL97} or throughout the planetary interior \citep{OL04}." +" Following ?,, we present models of the dynamical and physical evolution of the CoRoT-2 system caused by the action of stellar and planetary tides."," Following \citet{Gillon+10}, we present models of the dynamical and physical evolution of the CoRoT-2 system caused by the action of stellar and planetary tides." + We maximize the efficiency of the heat dissipation by assuming that it is entirely deposited at the center of the planet., We maximize the efficiency of the heat dissipation by assuming that it is entirely deposited at the center of the planet. + We use the dynamical evolution equations derived by ? and include high order terms in eccentricity and equations for the evolution of the stellar and planetary spin (see Appendix)., We use the dynamical evolution equations derived by \citet{BO09} and include high order terms in eccentricity and equations for the evolution of the stellar and planetary spin (see Appendix). +" On the basis of the calculations by ?,, we explore values of the tidal factor Ορ between 10? and 10°, and of Q. of 10? and higher."," On the basis of the calculations by \citet{JGB08a}, we explore values of the tidal factor $Q_{\rm p}$ between $10^{5}$ and $10^6$, and of $Q_*$ of $10^5$ and higher." + We analyze in Fig., We analyze in Fig. + 14 how the tidal heating rates and the orbital timescales depend on the eccentricity of the system using all known parameters of the system., \ref{fig:heating-vs-e} how the tidal heating rates and the orbital timescales depend on the eccentricity of the system using all known parameters of the system. +" We first note that for values of the eccentricity e>0.3, these become extremely stiff functions of e."," We first note that for values of the eccentricity $e>0.3$, these become extremely stiff functions of $e$ ." + This implies that any initially high eccentricity value causes a rapid evolution of the system which is hardly predicted by models developed only to second order in eccentricity (????)..," This implies that any initially high eccentricity value causes a rapid evolution of the system which is hardly predicted by models developed only to second order in eccentricity \citep{JGB08a,IB09,MFJ09,Gillon+10}." +" We find that a 10% asynchronous planet would dissipate the required luminosity, but the corresponding synchronization timescale is extremely short, about 10,000 yyears."," We find that a $10\%$ asynchronous planet would dissipate the required luminosity, but the corresponding synchronization timescale is extremely short, about $10,000$ years." +" At low eccentricities, an inward migration with a timescale ~1Ga(Q,/10°) results from tides raised by the planet onto the star."," At low eccentricities, an inward migration with a timescale $\sim 1\,{\rm Ga}\,(Q_*/10^6)$ results from tides raised by the planet onto the star." +"At high eccentricities and for our choice of Q factors, tides raised by the star onto the planet begin to dominate and cause a decrease in the semi-major axis that is concomitant to the circularization of stellar tides on the planet.","At high eccentricities and for our choice of Q factors, tides raised by the star onto the planet begin to dominate and cause a decrease in the semi-major axis that is concomitant to the circularization of stellar tides on the planet." +" The orbit circularization is mostly caused by the planet, unless Q,> 10Q.."," The orbit circularization is mostly caused by the planet, unless $Q_{\rm p}> 10Q_*$ ." +" While the planet is synchronized efficiently, the star is found to be spun up by the planet relatively slowly ~1 Ga for eccentricities e«0.2."," While the planet is synchronized efficiently, the star is found to be spun up by the planet relatively slowly $\sim 1\,$ Ga for eccentricities $e<0.2$." +" Given its inferred eccentricity, the present size of CoRoT- may be explained by tides only within two scenarios: (i) By a very low Ορ value and a forced eccentricity due to the presence of another planet. ("," Given its inferred eccentricity, the present size of CoRoT-2b may be explained by tides only within two scenarios: (i) By a very low $Q_{\rm p}$ value and a forced eccentricity due to the presence of another planet. (" +ii) By an initial stage of high-dissipation followed by a rapid circularization and contraction.,ii) By an initial stage of high-dissipation followed by a rapid circularization and contraction. + The former case is unlikely (seealso?).., The former case is unlikely \citep[see also][]{Gillon+10}. + The last possibility requires that the circularization proceeds faster than the planet's contraction., The last possibility requires that the circularization proceeds faster than the planet's contraction. + In Fig., In Fig. + 15 we explore the constraints that can be derived on Ορ., \ref{fig:heating-qpvalues} we explore the constraints that can be derived on $Q_{\rm p}$ . +" Using the equations in the Appendix, we calculate the minimum eccentricityrequired for tides to dissipate"," Using the equations in the Appendix, we calculate the minimum eccentricityrequired for tides to dissipate" +obtained a new LLR (Eq.(1)) but also discovered an even tiehter relation between duration aud Inuuinositv Coupling this to Eq.(3) then provides a very simple wav to ect the LLR.,obtained a new LLR (Eq.(1)) but also discovered an even tighter relation between duration and luminosity Coupling this to Eq.(3) then provides a very simple way to get the LLR. +" An important cifercuce with paper lis that we do uot necessarily asstlue the validity of the ~Amati-like relatioÜ to (Eq.(7)}lik , to η.", An important difference with paper I is that we do not necessarily assume the validity of the “Amati-like relation” (Eq.(7)) to link $E_{\rm p}$ to the luminosity. +" Even if Ej, aud £ are essentially dpendent quautities a LLR can still ]x4 6tained with the same value of the peak enerev at all ΠΠ", Even if $E_{\rm p}$ and $L$ are essentially independent quantities a LLR can still be obtained with the same value of the peak energy at all luminosities. +" In Fie.3 and [owe preseut the results for bot ithe Afia - f, xeajon and the LLR.", In Fig.3 and 4 we present the results for both the $\Delta t_{13}$ - $t_{\rm p}$ relation and the LLR. +" The full heavy. liu Cl1 each. diaerali corresponds to our reference case whic Lassuimies the validitv of the Amati-like relation aux σος fhe following values of the parameters: 0—1. 42.235. (; 0.5,4—bOd and |C|=10."," The full heavy line in each diagram corresponds to our reference case which assumes the validity of the Amati-like relation and uses the following values of the parameters: $\alpha=-1$, $\beta=-2.25$, ${\dot e}_{\rm p}= -0.5$, $\dot a=\dot b=0.1$ and $|C_1|=10$." +" Iu addition we plo iMith hin lines a few other cases: (1) Ἑ {οher paraneters unchaugeLy (2) ὃν025: (3) d=,=-0 (οheHY paraneters uuchanged): (CL) 4bh= 03: (5). (6) axd (7) 10 Amati relation but constant =250. 400 an d]O00 keV: (8) aud (9) sinular to 1) but with Cy,=3 alc| 30."," In addition we plot with thin lines a few other cases: (1) ${\dot e}_{\rm p} =-1$ (other parameters unchanged); (2) ${\dot e}_{\rm p} =-0.25$; (3) $\dot a=\dot b=0$ (other parameters unchanged); (4) $\dot a=\dot b=0.2$ ; (5), (6) and (7) no Amati relation but constant $E_{\rm p}=250$, 500 and 1000 keV; (8) and (9) similar to 1) but with $|C_1|=3$ and $30$." + All these lines define a narrow strip slhowine that O lireations remain fairly robust even when the γατατοῖςUS are varied by laree factors., All these lines define a narrow strip showing that both relations remain fairly robust even when the parameters are varied by large factors. + We have also ]aloted in Fie.3Oo and L the data points for the pulses beloreine to the sample studied by ITaxkila et al. (, We have also plotted in Fig.3 and 4 the data points for the pulses belonging to the sample studied by Hakkila et al. ( +2008).,2008). + It can be seen that the aerecment with our theoretical results is satisfactory., It can be seen that the agreement with our theoretical results is satisfactory. + The results preseied dn the last section rely on the validity of the αιrafion-Iuuinositv relation (DLR) for muses., The results presented in the last section rely on the validity of the duration-luminosity relation (DLR) for pulses. + Tf confirux«1. the DLR would also offer a new nethod to estimae GRB distances. simpler aud easier o use than the LER (IIakkila. Fragile Cablin. 2009).," If confirmed, the DLR would also offer a new method to estimate GRB distances, simpler and easier to use than the LLR (Hakkila, Fragile Giblin, 2009)." + Bursts with severa] pulses give the possibility of iuultiple neasures of the recshift. increasing the resulting accuracy.," Bursts with several pulses give the possibility of multiple measures of the redshift, increasing the resulting accuracy." + Conversely the ideutical redshift for all pulses in a given must alows to test the DLR., Conversely the identical redshift for all pulses in a given burst allows to test the DLR. + Assundug a power-lav of he form Lxf? Iakkia. Fragile Cablin (2009) fiud S—OSSEO.LE for a sample of 53 uulti-pulsed. CRBs. which is consistent with the result obtaimed from bursts with shown recshift.," Assuming a power-law of the form $L\propto t_{\rm p}^{-s}$ Hakkila, Fragile Giblin (2009) find $s=0.8 \pm 0.4$ for a sample of 53 multi-pulsed GRBs, which is consistent with the result obtained from bursts with known redshift." + We have performed an alternative aud indepeucdent est of the DLRusing a svuthetic population of CRB mulses for which we predict the resulting observational curation peal οποίοι flux (eon P) diagraia which is hen compared to real data., We have performed an alternative and independent test of the DLRusing a synthetic population of GRB pulses for which we predict the resulting observational duration – peak photon flux $t_{\rm p}^{\rm obs}$ – $P$ ) diagram which is then compared to real data. + The svuthetic population is eenerated followire a Monte-Carlo method simular to the one described in Daigue. Rossi \lochkovitch (2006): for cach pulse we draw a redshift + and a peak hDuunmositv L.," The synthetic population is generated following a Monte-Carlo method similar to the one described in Daigne, Rossi Mochkovitch (2006): for each pulse we draw a redshift $z$ and a peak luminosity $L$." +" We then either link E, aud f, to the huuinositv with Eq.(7) aud {8) or adopt log-normal distributions independent of £.", We then either link $E_{\rm p}$ and $t_{\rm p}$ to the luminosity with Eq.(7) and (8) or adopt log-normal distributions independent of $L$ . + We want to see if the predicted fon , We want to see if the predicted $t_{\rm p}^{\rm obs}$ +the upper-limit for the flux density at 5 Gllz).,the upper-limit for the flux density at 5 GHz). + We therefore tentatively classify this object as a CD., We therefore tentatively classify this object as a CD. +" Lt was not possible to reliably overlay the two maps at 1.6 and 5 Cillz. but the most likely mateh is shown in figure δν,"," It was not possible to reliably overlay the two maps at 1.6 and 5 GHz, but the most likely match is shown in figure \ref{fig2}." + Due to this uncertainty. it was not possible to reliably Classifv this source.," Due to this uncertainty, it was not possible to reliably classify this source." + The two components have similar spectra. with a possible jet leading to the northern component.," The two components have similar spectra, with a possible jet leading to the northern component." + This object is tentatively classified as a CLD., This object is tentatively classified as a CD. + Only the southern component is detected at 5 Cllz., Only the southern component is detected at 5 GHz. + Llowever its steep spectral index. and the upper-limit to the spectral index of the northern component makes us tentatively classify this source as a CD.," However its steep spectral index, and the upper-limit to the spectral index of the northern component makes us tentatively classify this source as a CD." + Only the western component is detected at 5 11»., Only the western component is detected at 5 GHz. + Llowever its steep spectral index. and the upper-limit to the spectral index of the eastern component. makes us classify this source as a CD.," However its steep spectral index, and the upper-limit to the spectral index of the eastern component makes us classify this source as a CD." + Two dominant components are visible in this source at 1.6. 5. and 15 Cillz with comparable spectra.," Two dominant components are visible in this source at 1.6, 5, and 15 GHz with comparable spectra." + A faint compact component is visible in between in the 5 CGllz map., A faint compact component is visible in between in the 5 GHz map. + This object is therefore classified as a CSO., This object is therefore classified as a CSO. + This object shows faint extended structure to the south- in its 1.6 and 5 Cllz images., This object shows faint extended structure to the south-west in its 1.6 and 5 GHz images. + Vhe bright northern component appears to have a [latter spectrum than the faint extended emission., The bright northern component appears to have a flatter spectrum than the faint extended emission. + We tentatively classify this object as a core-jet., We tentatively classify this object as a core-jet. + This source is the archetype compact symmetric object (CSO). and has been discussed. in detail by Taylor. and Vermeulen (1997).," This source is the archetype compact symmetric object (CSO), and has been discussed in detail by Taylor and Vermeulen (1997)." + The core is only visible at 15 CGllz., The core is only visible at 15 GHz. + Only the Lat spectrum compact component in the south is detected at 15 Gllz., Only the flat spectrum compact component in the south is detected at 15 GHz. + The limit to the spectral index of the northern component makes us tentatively classify this source as a core-Jet., The limit to the spectral index of the northern component makes us tentatively classify this source as a core-jet. +We refer (he reader to Druenn Mezzacappa (1997) [ον more detailed expressions for the cross section.,We refer the reader to Bruenn Mezzacappa (1997) for more detailed expressions for the cross section. + For the uncorrelated ions with $(/)=I. we have the angle-integrated cross section Therefore. we can express the ion-ion correlation effect 5(/)41 bv writing 50 lar we have considered only oue nuclear species (Z.A).," For the uncorrelated ions with $S(k)=1$, we have the angle-integrated cross section Therefore, we can express the ion-ion correlation effect $S(k) \neq 1$ by writing So far we have considered only one nuclear species $(Z,A)$." + Lowever. in the real supernova explosion more than one nuclear species exist in supernova cores (Liebendórrfer οἱ al.," However, in the real supernova explosion more than one nuclear species exist in supernova cores (Liebendörrfer et al." + 2003)., 2003). +" llere we give a prescription (o calculate the neutrino mean free path (due to the scattering including protons: where n; is the number density. of ions of j-th species and <σι,> is the scattering cross section by j-th species ions (nuclei).", Here we give a prescription to calculate the neutrino mean free path $\ell$ due to the neutrino-nucleus scattering including protons: where $n_{j}$ is the number density of ions of $j$ -th species and $< \sigma_{j} >$ is the neutrino-nucleus scattering cross section by $j$ -th species ions (nuclei). +" In calculating lor the neutrino-nucleus scattering by j-th nuclear species (Z;..1;). one uses the mass number <4, and (he angle-averaged ion-ion correlation [actor in equation (14) corresponding to ihe T-value (Itoh et al."," In calculating $< \sigma_{j} >$ for the neutrino-nucleus scattering by $j$ -th nuclear species $(Z_{j},A_{j})$, one uses the mass number $A_{j}$ and the angle-averaged ion-ion correlation factor $$ in equation (14) corresponding to the $\Gamma$ -value (Itoh et al." +" 1979) where A; is the mass traction of the /-th nuclear species (Z;.24;) and a, is the raclius"," 1979) where $X_{i}$ is the mass fraction of the $i$ -th nuclear species $(Z_{i},A_{i})$ and $a_{e}$ is the electron-sphere radius" +can vary locally due to the presence of filaments and flocculent spiral arms.,can vary locally due to the presence of filaments and flocculent spiral arms. + For each source the turbulent pressure ts (1.16accountsforHelium.seealso.?.p.37).," For each source the turbulent pressure is \citep[1.16 accounts for Helium, see also][p.37]{1978ppim.book.....S}." + The gas volume density ts then: We shall use Wmthe s)smallest linewidth measured in the 1-0 or 2-] line. which gives the highest volume density.," The gas volume density is then: We shall use the smallest linewidth measured in the 1-0 or 2-1 line, which gives the highest volume density." + We compute the maximum cloud size by equating the virial mass to the mass in pressure equilibrium which reads: This relation naturally explains the size-linewidth relation W«xVD., We compute the maximum cloud size by equating the virial mass to the mass in pressure equilibrium which reads: This relation naturally explains the size-linewidth relation $W\propto \sqrt{D}$. + In fact we find that the 2-1 linewidth (which is mostly used in this relation) correlates with the source size. with the right slope (see Figure 3. rp=0.94 slopez2.020.2).," In fact we find that the 2-1 linewidth (which is mostly used in this relation) correlates with the source size, with the right slope (see Figure 3, $r_P=0.94$ $\pm 0.2$ )." + A similar relation exists for the 1-0. but with a larger scatter (rp= 0.81).," A similar relation exists for the 1-0, but with a larger scatter $r_P=0.81$ )." + The size-linewidth relation implies another important feature often mentioned about molecular clouds. namely their rather constant column densities.," The size-linewidth relation implies another important feature often mentioned about molecular clouds, namely their rather constant column densities." + For this model in fact the gas column density reads: Values of the local ISM pressure in M33 do not vary much and this implies almost constant column densities. as can be seen in Table 5.," For this model in fact the gas column density reads: Values of the local ISM pressure in M33 do not vary much and this implies almost constant column densities, as can be seen in Table 5." + We can also infer the maximum value of Xco from the virial mass to the CO-Iuminosity mass ratio using the maximum size D: Where Mothe values of /.O.W refer to the line which has been used (smaller linewidth).," We can also infer the maximum value of $X_{CO}$ from the virial mass to the CO-luminosity mass ratio using the maximum size D: Where the values of $I,\Theta, W$ refer to the line which has been used (smaller linewidth)." + The correlation between cloud mass and the CO-to-H> conversion factor is shown in Figure 3 (rp= 0.95)., The correlation between cloud mass and the $_2$ conversion factor is shown in Figure 3 $r_P=0.95$ ). +" From the maximum size we can infer the maximum intrinsic line ratio. A"", given in Table 5 for isolated sources. at the beam center."," From the maximum size we can infer the maximum intrinsic line ratio, $R^{max}$, given in Table 5 for isolated sources, at the beam center." + With this method cloud sizes and masses are less dependent on the assumption of the cloud being centered with respect to the millimeter telescope beam., With this method cloud sizes and masses are less dependent on the assumption of the cloud being centered with respect to the millimeter telescope beam. + Unfortunately we are able only to derive upper limits to M. and. D., Unfortunately we are able only to derive upper limits to $M$ and $D$. + In Section 3.4 we use the observed size-linewidth relation to infer the size of self-gravitating cloud cores., In Section 3.4 we use the observed size-linewidth relation to infer the size of self-gravitating cloud cores. + We notice that there are 3 sources with Χαρ<1.5., We notice that there are 3 sources with $X_{CO}^{max} \le 1.5$. + Those are sources with sizes smaller than 25 pe and small masses («107 M.)., Those are sources with sizes smaller than 25 pc and small masses $< 10^4$ $_\odot$ ). + Since M33 has a lower metal abundance than the Milky Way we do not expect an overabundance of CO., Since M33 has a lower metal abundance than the Milky Way we do not expect an overabundance of CO. + Hence. these sources are probably overluminous in CO or they are not in virial equilibrium (?)..," Hence, these sources are probably overluminous in CO or they are not in virial equilibrium \citep{1990ApJ...348L...9M}." + The molecular gas might be so warm that the J21-0 luminosity 15 no longer proportional to the H» column density., The molecular gas might be so warm that the J=1-0 luminosity is no longer proportional to the $_2$ column density. + For example for a gas at 40 K the J=1-0 line intensity i$ more than twice as bright as a gas at 20 K (e.g.?).., For example for a gas at 40 K the J=1-0 line intensity is more than twice as bright as a gas at 20 K \citep[e.g.][]{1994ApJ...425..641S}. + Recent high resolution observations in the M33 outer disk have discovered clouds with high CO luminosity (2). in the proximity of sources hosting massive stars., Recent high resolution observations in the M33 outer disk have discovered clouds with high CO luminosity \citep{2010arXiv1010.2751B} in the proximity of sources hosting massive stars. + The very small values of R which we recover for some sources might be indicative of an offcenter molecular cloud due to the presence of massive stars., The very small values of R which we recover for some sources might be indicative of an offcenter molecular cloud due to the presence of massive stars. + This likely holds for sI5 where we detect two components. and for $20 where the CO observations have been centered on the optical HII region in the absence of a 24 ccounterpart.," This likely holds for s15 where we detect two components, and for s20 where the CO observations have been centered on the optical HII region in the absence of a 24 counterpart." + In Table 6 we derive the cloud properties for a radially varying Xco factor., In Table 6 we derive the cloud properties for a radially varying $X_{CO}$ factor. + The radial scaling used takes into account the weak Xco metallicity dependence estimated by ?:: where the average metallicity gradient O/H used is given by and the galactocentric distance r is in kpe.," The radial scaling used takes into account the weak $X_{CO}$ metallicity dependence estimated by \citet{2008ApJ...686..948B}: : where the average metallicity gradient O/H used is given by \citet{2010A&A...512A..63M} + and the galactocentric distance $r$ is in kpc." + The value of the constant a is such that Xco is 2.8 1079 em K7! at the center of M33., The value of the constant $a$ is such that $X_{CO}$ is 2.8 $^{20}$ $^{-2}$ $^{-1}$ at the center of M33. + The metallicity dependence of the Χου factor has not yet been firmly established., The metallicity dependence of the $X_{CO}$ factor has not yet been firmly established. + We prefer to consider a shallow radial dependence because in M33 the radial decrease of the average radiation field. which dissociates the CO molecule. might balance the already shallow radial metallicity gradient and keep Xco almost constant.," We prefer to consider a shallow radial dependence because in M33 the radial decrease of the average radiation field, which dissociates the CO molecule, might balance the already shallow radial metallicity gradient and keep $X_{CO}$ almost constant." + We derive the source size by equating the virial to the molecular mass given by the CO line luminosity: From the size we infer the volume density., We derive the source size by equating the virial to the molecular mass given by the CO line luminosity: From the size we infer the volume density. + We then use the source size and the observed CO line ratio to infer the intrinsic line ratio., We then use the source size and the observed CO line ratio to infer the intrinsic line ratio. + We take the CO line with the largest linewidth because it gives the highest gas density (see Eq.(6))., We take the CO line with the largest linewidth because it gives the highest gas density (see Eq.(6)). + For isolated clouds. centered in the beam. the intrinsic line ratio R expected for that size is also shown in Figure 3 and decreases moving radially outwards.," For isolated clouds, centered in the beam, the intrinsic line ratio $R$ expected for that size is also shown in Figure 3 and decreases moving radially outwards." + Limits to the validity of this method come from the faet that the weak metallicity dependence used here for Xco 1s based on CO interferometric measurements which might underestimate cloud sizes and hence invalidate the sealing law used (?).., Limits to the validity of this method come from the fact that the weak metallicity dependence used here for $X_{CO}$ is based on CO interferometric measurements which might underestimate cloud sizes and hence invalidate the scaling law used \citep{2001A&A...371..433I}. + Metallicity in M33 however. has a scatter at each radius larger than the overall observed radial gradient: a stronger metallicity dependence can be considered only if the metallicity at each source location is known.," Metallicity in M33 however, has a scatter at each radius larger than the overall observed radial gradient: a stronger metallicity dependence can be considered only if the metallicity at each source location is known." + This method has been based on the assumption that clouds are in. virial equilibrium., This method has been based on the assumption that clouds are in virial equilibrium. + In our galaxy data suggest that clouds with masses below 107 M. are strongly influenced by nongravitational forces and virial equilibrium overestimates their masses (?).., In our galaxy data suggest that clouds with masses below $^4$ $_\odot$ are strongly influenced by nongravitational forces and virial equilibrium overestimates their masses \citep{1990ApJ...348L...9M}. + Using only the CO observations presented in this paper it is hard to establish if the virial equilibrium assumption is correct for clouds in oursample., Using only the CO observations presented in this paper it is hard to establish if the virial equilibrium assumption is correct for clouds in oursample. + If not. clouds might be pressure confined (as considered in Section 3.2) or related to short-lived event (e.g. interstellar shocks).," If not, clouds might be pressure confined (as considered in Section 3.2) or related to short-lived event (e.g. interstellar shocks)." + over 3500 initial conditions were examined. in a erid of initial deusities. temperatures. aud initial carbon fraction.,"– over 3500 initial conditions were examined, in a grid of initial densities, temperatures, and initial carbon fraction." + The carbon (1uass) fractions were in the range 0.1xτοσο<1.0. with the remainder being oxvecu (Nisg= ος). temperatures of 0.5\pi\sqrt{\sigma}/3$, full dissipation is achieved." + However. this theory does not take account of the role of superluminal waves. allhough these waves are able to propagate in (he region in which reconnection is predicted. 7T..," However, this theory does not take account of the role of superluminal waves, although these waves are able to propagate in the region in which reconnection is predicted. \citet{sironispitkovsky11}," + on the other hand. performed 2D and 3D PIC simulations.," on the other hand, performed 2D and 3D PIC simulations." + They found Chat the shock (ήσσονος reconnection. leading to full dissipation of the magnetic field. over the entire parameter range investigated.," They found that the shock triggered reconnection, leading to full dissipation of the magnetic field, over the entire parameter range investigated." + In our notation. this range extends over 1/20$ ) might be expected to play a role at the upper end of this range. + However. the simulations do not appear lo reveal their presence.," However, the simulations do not appear to reveal their presence." +" The particle spectrum found in these simulations varies considerably, being closer to (that. observed in the Crab Nebula for lower values of FH."," The particle spectrum found in these simulations varies considerably, being closer to that observed in the Crab Nebula for lower values of $R$." + llowever. as we show in relresults.. (he termination shocks in (he nebulae around isolated voung pulsars are expected to lie much further from the pulsar than (the range covered by (these simulations. leaving us [ree to speculate that the physics controlling the structure and particle acceleration process might be substantially different in these objects.," However, as we show in \\ref{results}, the termination shocks in the nebulae around isolated young pulsars are expected to lie much further from the pulsar than the range covered by these simulations, leaving us free to speculate that the physics controlling the structure and particle acceleration process might be substantially different in these objects." + We have reexamined (he properties of (transverse superluminal waves in an plasma for parameters appropriate to pulsar winds., We have reexamined the properties of transverse superluminal waves in an electron-positron plasma for parameters appropriate to pulsar winds. +Our principal new results are:,Our principal new results are: +"has a larger contribution from shorter wavelengths than for star forming sources: they calculate log(Liaym/Lir)=—1.19+0.10 for star forming sources, but just —0.57+0.19 for AGN dominated systems.","has a larger contribution from shorter wavelengths than for star forming sources: they calculate $\log (\mathrm{L}_{14\mu m}/\mathrm{L}_{\mathrm{IR}}) = -1.19 \pm 0.10$ for star forming sources, but just $-0.57 \pm 0.19$ for AGN dominated systems." +" Being IR selected, Wu et al."," Being IR selected, Wu et al." +"'s sample has the advantage of having similar properties to our own, and therefore we expect that the AGN contribution, calculated as a function of IR luminosity, will be applicable to our data.","'s sample has the advantage of having similar properties to our own, and therefore we expect that the AGN contribution, calculated as a function of IR luminosity, will be applicable to our data." + The good agreement between the two IR LFs — our own and Wu et al., The good agreement between the two IR LFs – our own and Wu et al. +"’s — confirms this, and suggests that the AGN fraction derived from their sample is indeed applicable to our own.","'s – confirms this, and suggests that the AGN fraction derived from their sample is indeed applicable to our own." + We attribute the slight bright-end discrepancy between the functions to small number uncertainty at the upper end of their sample - Wu et al., We attribute the slight bright-end discrepancy between the functions to small number uncertainty at the upper end of their sample - Wu et al. +"'s complete sample consists of 330 galaxies, and will sample the rarer IR-bright galaxies poorly.","'s complete sample consists of 330 galaxies, and will sample the rarer IR-bright galaxies poorly." +" As a qualitative check, we compare the AGN contribution derived here to a previous result, the AGN luminosity function at 124m as calculated by ?.."," As a qualitative check, we compare the AGN contribution derived here to a previous result, the AGN luminosity function at $\mu m$ as calculated by \cite{1993ApJS...89....1R}." +" As discussed above, the AGN contribution to the star formation distribution only becomes significant at the bright end (>~10""? with the contribution from AGN being «1096 for non-LIRGs,Lo), with star formation rates below ~15Moyr-!."," As discussed above, the AGN contribution to the star formation distribution only becomes significant at the bright end $>\sim 10^{12} \mathrm{L}_{\sun}$ ), with the contribution from AGN being $<10\%$ for non-LIRGs, with star formation rates below $\sim 15 \; \mathrm{M}_{\sun}\; \mathrm{yr}^{-1}$." +" Both measures of AGN activity agree well, with a small (factor of — 2) discrepancy at the low Lo) end - the low value of 6(AGN) at these luminosities renders this difference relatively unimportant."," Both measures of AGN activity agree well, with a small (factor of $\sim 2$ ) discrepancy at the low $<10^{11} \mathrm{L}_{\sun}$ ) end - the low value of $\Phi$ (AGN) at these luminosities renders this difference relatively unimportant." +" We do note, however, that the 5MUSES sample has spectral AGN estimators which are more accurate than the photometric estimators of the older work, and it is to this that we attribute the difference."," We do note, however, that the 5MUSES sample has spectral AGN estimators which are more accurate than the photometric estimators of the older work, and it is to this that we attribute the difference." +" All luminosity functions, star formation distributions, and related values calculated hereafter have had the above AGN LF contribution subtracted as per the estimate from Wu et al.,"," All luminosity functions, star formation distributions, and related values calculated hereafter have had the above AGN LF contribution subtracted as per the estimate from Wu et al.," + and are therefore interpretable in terms of pure star formation., and are therefore interpretable in terms of pure star formation. +" All galaxies in our datasets have been observed with multiple bands in the IR: either with Spitzer (at 24m/70um/160um), or IRAS (12um/25um/60um/1004m)."," All galaxies in our datasets have been observed with multiple bands in the IR: either with Spitzer (at $\mu$ $\mu$ $\mu$ m), or IRAS $\mu$ $\mu$ $\mu$ $\mu$ m)." +" As such, very accurate estimates - to better than for most galaxies - of their bolometric IR flux (defined as the integrated flux from 8um-10004m) can be made, using the three-component prescriptions provided by ?.."," As such, very accurate estimates - to better than for most galaxies - of their bolometric IR flux (defined as the integrated flux from $\mu$ $\mu$ m) can be made, using the three-component prescriptions provided by \cite{2002ApJ...576..159D}." + Fig., Fig. + 2 shows the TIR luminosity function for both the large IR sample (red triangles) and the LVL data (green squares)., \ref{fig:tir_lf} shows the TIR luminosity function for both the large IR sample (red triangles) and the LVL data (green squares). +" As we are interested in measuring the true underlying distributions, rather than just the local density enhancement, the number densities for the LVL data in Fig."," As we are interested in measuring the true underlying distributions, rather than just the local density enhancement, the number densities for the LVL data in Fig." + 2 (and for all LVL volume densities hereafter) have been adjusted downwards by factor of 1.85 as discussed above., \ref{fig:tir_lf} (and for all LVL volume densities hereafter) have been adjusted downwards by a factor of 1.85 as discussed above. +" The data points were deriveda using the 1/Vmax method, and the black line is the best fitting Schechter function, obtained using standard least squares fitting."," The data points were derived using the $_{\mathrm{max}}$ method, and the black line is the best fitting Schechter function, obtained using standard least squares fitting." +" The blue fit to the data is the Schechter function obtained using maximum likelihood fitting, as discussed above."," The blue fit to the data is the Schechter function obtained using maximum likelihood fitting, as discussed above." +" The two methods agree on all counts, with the exception of a small discrepancy in the faint end slope (1.41+0.09 for the 1/Vmax method, 1.53+0.08 for maximum likelihood)."," The two methods agree on all counts, with the exception of a small discrepancy in the faint end slope $1.41 \pm 0.09$ for the $_{\mathrm{max}}$ method, $1.53 \pm 0.08$ for maximum likelihood)." +" Power law fits to the IR data, once the AGN component was removed, were generally poor - in all cases, a Schechter function was able to fit the data more closely."," Power law fits to the IR data, once the AGN component was removed, were generally poor - in all cases, a Schechter function was able to fit the data more closely." +" For comparison, the luminosity function for IRAS IR-selected galaxies from ? (corrected slightly for our cosmological parameters) has been overplotted as a dashed line."," For comparison, the luminosity function for IRAS IR-selected galaxies from \cite{2003ApJ...587L..89T} (corrected slightly for our cosmological parameters) has been overplotted as a dashed line." +" There is a discrepancy at the high end, caused by both AGN removal (c.f."," There is a discrepancy at the high end, caused by both AGN removal (c.f." + our original sample shown in Fig 1)) and the redshift cut (taking z«0.1 reduces the number, our original sample shown in Fig \ref{fig:agn_lf}) ) and the redshift cut (taking $z<0.1$ reduces the number +of the inner regions of BLR or a face-ou orieuation of a disk-like BLR as the explanation for the relatively narrow broac-liue profiles.,of the inner regions of BLR or a face-on orientation of a disk-like BLR as the explanation for the relatively narrow broad-line profiles. +" The connection between plysical properties of nuclear supermassive BHs aud their host galaxies. on which several works rave focused in the last vears. might turn out to be a powerl| tool to tude""saud the nature o“NLS! Ls and settle tje above citec C)itroversies."," The connection between physical properties of nuclear supermassive BHs and their host galaxies, on which several works have focused in the last years, might turn out to be a powerful tool to understand the nature of NLS1s and settle the above cited controversies." + first found out a correation betwee BH mass (Vp ) aud the absolute B inagnitude of the sjleroidal compoueti (AlB )., \citet{koric95} first found out a correlation between BH mass $\cal M_{\rm BH}$ ) and the absolute B magnitude of the spheroidal component $M_{B}$ ). +" Magorrianetal.(1998). «etermined Mpi values for a sample of 32 neaby galaxies and sugeeMODSed that Map), is proportional to the Viu such that oi average Mpu/νοv 0.005.", \citet{maget98} determined $\cal M_{\rm BH}$ values for a sample of 32 nearby galaxies and suggested that $\cal M_{\rm BH}$ is proportional to the $\cal M_{\rm bulge}$ such that on average $\cal M_{\rm BH}/\cal M_{\rm bulge}\sim$ 0.005. + Other authors estimated a similar 1lass ratio. ~ 0.002 (see δ.ο.. Ho 1999).," Other authors estimated a similar mass ratio, $\sim$ 0.002 (see e.g., Ho 1999)." + Recenty. studying a sample of jiearby galaxies Gebliardtetal.(2000a).. Ferrarese auc T‘elnaineetal.(2002) have shown that Mjjj is tightly correlated with the velocity cispersiou ol the 3ilge stellar component (σι). although they clisagreed about the value o‘the slope.," Recently, studying a sample of nearby galaxies \citet{gebet00a}, \citet{fermer00} and \citet{tre02} have shown that $\cal M_{\rm BH}$ is tightly correlated with the velocity dispersion of the bulge stellar component $\sigma_*$ ), although they disagreed about the value of the slope." + Iu ACUNs as well. BHs are also expected to correlate wihb their host bulges.," In AGNs as well, BHs are also expected to correlate with their host bulges." + This possibility was exjxored on a sample of PC quasars by Laor(1998) who found agreement with the relation of Magorriauetal.(1998)., This possibility was explored on a sample of PG quasars by \citet{lao98} who found agreement with the relation of \citet{maget98}. +". Later Waudel(1999) claimed that Seyfert galaxies show ou average a M"">1/Moiulge ratio systematically lower than that lor norual gaaxies aud quasars.", Later \citet{wan99} claimed that Seyfert galaxies show on average a $\cal M_{\rm BH}/\cal M_{\rm bulge}$ ratio systematically lower than that for normal galaxies and quasars. + Couversely Cieblardtetal.(2000b) included iu their work seven ACUNs or which the My were obtained by lueals of the reverberation mappiug techuique., Conversely \citet{gebet00b} included in their work seven AGNs for which the $\cal M_{\rm BH}$ were obtained by means of the reverberation mapping technique. +" They found hat tese objects were in agreement with their previously found M pico., correlation.", They found that these objects were in agreement with their previously found $\cal M_{\rm BH}$ $\sigma_*$ correlation. + Further stpport came [rom ).. aud frou Wu&Han(2001) who studied samples of quasars aid Seyfert galaxies. and cid not fiud any evidence that Seyfert. galaxies follow a cilferent Jp—Mouse relation from quasars or nearby Until now 1o agreement has been fouud about NLSIs.," Further support came from \citet{mcdun01}, and from \citet{Wuhan01} + who studied samples of quasars and Seyfert galaxies, and did not find any evidence that Seyfert galaxies follow a different $\cal M_{\rm BH}- +\cal M_{\rm bulge}$ relation from quasars or nearby Until now no agreement has been found about NLS1s." + Mathur.Ixuraszkiewicz&Czerny(2001) and very recently Bian&Zhao(2003a) aud Crupe&Mathur(2001) showed that the fpiνου ratio in NLS!Ls is significantly sinaller tha ithat for Sevlert galaxies., \citet*{matet01} and very recently \citet{bz03} and \citet{gm04} showed that the $\cal M_{\rm BH}/\cal M_{\rm bulge}$ ratio in NLS1s is significantly smaller than that for Seyfert galaxies. +" Couversely Wane&Lu(2001).. studyiug a sample of 50 NLSIs observe[1a W.yectroscopically by (2001).. fourd that there is nou clear cliference in the Mp )j-o, relation (where o, is represeutecd by the eemission lite witth) betwee NL51s. B‘Oa-Line AGNs and nearby galaxies."," Conversely \citet{walu01}, studying a sample of 59 NLS1s observed spectroscopically by \citet*{vvg01}, found that there is non clear difference in the $\cal M_{\rm BH}$ $\sigma_*$ relation (where $\sigma_*$ is represented by the emission line width) between NLS1s, Broad-Line AGNs and nearby galaxies." + Qur purJOSE in this wor‘k is to dunrest]eate the nature of NLSIs by exploring the physical properties of thei: bulges. nauelv the Ltmiiosity aud the nuclear stellar velocity dispersion.," Our purpose in this work is to investigate the nature of NLS1s by exploring the physical properties of their bulges, namely the luminosity and the nuclear stellar velocity dispersion." + Our approach maτος |ise of both jew observatioial data aud data [rom the literature., Our approach makes use of both new observational data and data from the literature. + The necessary Corrections aο αyplied to the latter in Orcer to obtain as homogeneous as possible a dataset., The necessary corrections are applied to the latter in order to obtain as homogeneous as possible a dataset. + Furthermore. as a main cliffe'eice with respec to several other works ou this topic. when cleterminine the bulge properties of the |lost galaxies we ake into account the iuflueuce of the AGN. which. as we show. cau be uou-neeligie aud affect the results considerably.," Furthermore, as a main difference with respect to several other works on this topic, when determining the bulge properties of the host galaxies we take into account the influence of the AGN, which, as we show, can be non-negligible and affect the results considerably." + The structure of the paper is as follows: in, The structure of the paper is as follows: in +be <300 AAU.,be $\lesssim$ AU. +" The total mass of the dust in the belt is 1.2x107! MMs, with grains ranging in size from um to mmm."," The total mass of the dust in the belt is $\times$ $^{-1}$ $_\earth$, with grains ranging in size from $\mu$ m to mm." +" The left panels of Figure 2 show an image-domain comparison between the SMA data and the SED-based model of ?,, calculated at the same wavelength as the data."," The left panels of Figure \ref{fig:hr8799} show an image-domain comparison between the SMA data and the SED-based model of \citet{su09}, calculated at the same wavelength as the data." +" The inset in the central panel shows the predicted spatial distribution of emission for the ? model observed with the same noise level as the SMA data; the 4c peak offset by 6"" from the star position and the partial arc of emission match well the observed morphology.", The inset in the central panel shows the predicted spatial distribution of emission for the \citet{su09} model observed with the same noise level as the SMA data; the $\sigma$ peak offset by 6” from the star position and the partial arc of emission match well the observed morphology. +" 'The residuals subtract fairly cleanly, with only a slight negative 3c peak."," The residuals subtract fairly cleanly, with only a slight negative $\sigma$ peak." +" While such a large residual could potentially point to an azimuthal asymmetry in the dust distribution due to the gravitational influence of the planet HR 8799b, which is located at a similar azimuth to the negative peak, the signal-to-noise ratio is too low to permit a firm conclusion."," While such a large residual could potentially point to an azimuthal asymmetry in the dust distribution due to the gravitational influence of the planet HR 8799b, which is located at a similar azimuth to the negative peak, the signal-to-noise ratio is too low to permit a firm conclusion." +" The separation between the star and emission peak in the central panel inset is comparable to that in the data, certainly within the astrometric uncertainty of the observation."," The separation between the star and emission peak in the central panel inset is comparable to that in the data, certainly within the astrometric uncertainty of the observation." +" The right panel of Figure 2 makes the same comparison in the visibility domain, where the visibilities have been azimuthally averaged to enhance the signal-to-noise ratio in each bin."," The right panel of Figure \ref{fig:hr8799} makes the same comparison in the visibility domain, where the visibilities have been azimuthally averaged to enhance the signal-to-noise ratio in each bin." +" Within the uncertainties, the ? model predicts well the spatially resolved data."," Within the uncertainties, the \citet{su09} model predicts well the spatially resolved data." + We also perform an exploration of the SMA visibilities and SED using a modified version of the method described in Section 4.1 aimed at determining whether the data can distinguish between a narrow or broad dust ring., We also perform an exploration of the SMA visibilities and SED using a modified version of the method described in Section \ref{sec:hd_analysis} aimed at determining whether the data can distinguish between a narrow or broad dust ring. +" To do so, we fix a to lum, 8 to 0.5, and p to 0, implying a ring of constant surface density."," To do so, we fix $a$ to $\mu$ m, $\beta$ to 0.5, and $p$ to 0, implying a ring of constant surface density." +" We explore the narrow ring scenario by assuming that the width of the ring is AAU, and allowing only ri, to vary."," We explore the narrow ring scenario by assuming that the width of the ring is AU, and allowing only $r_\mathrm{in}$ to vary." +" The SED is assembled from the literature, including 2MASS,IRAS, andHipparcos fluxes"," The SED is assembled from the literature, including 2MASS, and fluxes \citep{mos89,moo06, +wil06,su09}." +" To reproduce the SED, we allow Maia, to vary, and (????)..add a KK belt of variable mass Myer, as in ?,, to reproduce the observed mid-IR flux."," To reproduce the SED, we allow $M_\mathrm{disk}$ to vary, and add a K belt of variable mass $M_\mathrm{belt}$ , as in \citet{su09}, to reproduce the observed mid-IR flux." +" We use a Kurucz-Lejune model photosphere for a star of luminosity 4.92LLo, radius RRo, effective(?) temperature KK, and metallicity [Fe/H]—-0.5 (??).."," We use a Kurucz-Lejune model photosphere \citep{lej97} for a star of luminosity $_\sun$ , radius $_\sun$ , effective temperature K, and metallicity [Fe/H]=-0.5 \citep{sad06, +mar08}." +" The x? minimization results in a best-fit model with a ring radius of AAU, with Mais, and Mbeit equal to 5.5x1074 and 4.0x1079 MMa, respectively."," The $\chi^2$ minimization results in a best-fit model with a ring radius of AU, with $M_\mathrm{disk}$ and $M_\mathrm{belt}$ equal to $5.5\times10^{-4}$ and $4.0\times10^{-6}$ $_\earth$, respectively." + The combination of SED and visibilities can help to distinguish between a narrow ring and a broad belt., The combination of SED and visibilities can help to distinguish between a narrow ring and a broad belt. +" The null in the visibility function of the SMA data occurs at roughly 12kkA; using Equation A11 from 7,, if the underlying flux distribution were a thin ring, it would have a radius of about AAU."," The null in the visibility function of the SMA data occurs at roughly $\lambda$ ; using Equation A11 from \citet{hug07}, if the underlying flux distribution were a thin ring, it would have a radius of about AU." +" On the other hand, if it were a broad ring like the ? model predicts, then using Equation A9 of ? the kkA null implies a band with a smaller inner radius by up to a factor of 3, depending on how quickly the flux decreases with distance from the star."," On the other hand, if it were a broad ring like the \citet{su09} model predicts, then using Equation A9 of \citet{hug07} the $\lambda$ null implies a band with a smaller inner radius by up to a factor of 3, depending on how quickly the flux decreases with distance from the star." +" The AAU result for the ring obtained in our SED--visibility analysis is odd in this context, since it is roughly 2/3 the radius implied by the visibility null and the location of the emission peak."," The AU result for the ring obtained in our $+$ visibility analysis is odd in this context, since it is roughly 2/3 the radius implied by the visibility null and the location of the emission peak." + The mismatch is due to the SED fit: the ~45 KK temperature implied by the SED (?) is warmer than would be predicted for a AAU ring given the assumed dust properties., The mismatch is due to the SED fit: the $\sim$ K temperature implied by the SED \citep{su09} is warmer than would be predicted for a AU ring given the assumed dust properties. + The AAU result also depends strongly on the choice of à lym dust grain size., The AU result also depends strongly on the choice of a $\mu$ m dust grain size. +" If the grain size is allowed to vary, even smaller grain sizes are preferred, since raising the temperature of the dust grains results in a better match between the SED and visibilities."," If the grain size is allowed to vary, even smaller grain sizes are preferred, since raising the temperature of the dust grains results in a better match between the SED and visibilities." + It is therefore difficult to reconcile the large radius of a thin ring implied by the visibility data with the relatively warm dust implied by the SED for a narrow ring configuration., It is therefore difficult to reconcile the large radius of a thin ring implied by the visibility data with the relatively warm dust implied by the SED for a narrow ring configuration. +" Yet we have already shown that the observed flux distribution is also consistent with that predicted for a broad band of emission with an inner radius of ~150 AAU, as in the ? model, which contains warmer dust than a narrow ring far from the star."," Yet we have already shown that the observed flux distribution is also consistent with that predicted for a broad band of emission with an inner radius of $\sim$ AU, as in the \citet{su09} model, which contains warmer dust than a narrow ring far from the star." + This is consistent with the location of the visibility null for a broad ring configuration., This is consistent with the location of the visibility null for a broad ring configuration. +" Put another way, the spatially resolved SMA dataalone are unable to discriminate between a narrow ring located 7-200 AAU from the star and a broad disk with an inner radius of ~150 AAU, but the of visibilities and SED favors the latter scenario."," Put another way, the spatially resolved SMA data are unable to discriminate between a narrow ring located $\sim$ AU from the star and a broad disk with an inner radius of $\sim$ AU, but the of visibilities and SED favors the latter scenario." +" Spatially resolved data with a higher signal-to-noise ratio are requiredto place more stringentconstraints on thedust morphology, although the spatially extended ? model is capable of reproducing both the detailed SED properties and the SMAdata."," Spatially resolved data with a higher signal-to-noise ratio are requiredto place more stringentconstraints on thedust morphology, although the spatially extended \citet{su09} model is capable of reproducing both the detailed SED properties and the SMAdata." + 'The emerging theoretical framework for understanding, The emerging theoretical framework for understanding +The eutropy lost (for ο)223/2) or gained (for J<3/2) by the material as it moves toward smaller radius causes a niuor variation of the conductive luminosity: where the strong inequality applies far outside the absorbing boundary. i.c. for k>>FR. Bah,"The entropy lost (for $\beta>3/2$ ) or gained (for $\beta<3/2$ ) by the material as it moves toward smaller radius causes a minor variation of the conductive luminosity: where the strong inequality applies far outside the absorbing boundary, i.e., for $r \gg R$." +call&Wolf(1976). solved the important case of eravitational interactions i connection with the accretion of stars by a black hole., \cite{BaW76} solved the important case of gravitational interactions in connection with the accretion of stars by a black hole. +" Because the cross section for strong scatterings is proportional toe. 1.22 2,"," Because the cross section for strong scatterings is proportional to $c^{-4}$, $\beta=2$." + Thus pxκ(4., Thus $\rho\propto r^{-7/4}$. + Ax earlier attempt by Peebles(1972) vielded the incorrect result poxrc7 and herein lies an interesting lesson.," An earlier attempt by \cite{Peebles72} yielded the incorrect result $\rho\propto r^{-9/4}$ , and herein lies an interesting lesson." + Peebles”. assumed AL—D rrpe. whereas the correct result follows from setting £L—rrpe? (Shapiro1985).," Peebles' assumed ${\dot M}\sim +\tau r^2\rho c$ , whereas the correct result follows from setting $L\sim \tau r^2\rho c^3$ \citep{Shapiro85}." +. Tu steady-state accretion. both 3T aud L inst be independent of r.," In steady-state accretion, both ${\dot M}$ and $L$ must be independent of $r$." + ILowever. as shown above. the conduction of energy occurs at the iiaxuuun rate permitted bv relaxation whereas lass ds transported more slowly.," However, as shown above, the conduction of energy occurs at the maximum rate permitted by relaxation whereas mass is transported more slowly." +" Collisions of uubound particles tuside ry occur at relative velocities of order ος(rypr),", Collisions of unbound particles inside $r_g$ occur at relative velocities of order $c_\infty(r_g/r)^{1/2}$. + Provided they dissipate a sjenificaut fraction of the ceuter of mass kinetic energx. hey produce bound particles.," Provided they dissipate a significant fraction of the center of mass kinetic energy, they produce bound particles." + Comparable vields of bound articles come frou collisions between two uubounud outicles and from collisious between au uubouud aud a bound particle., Comparable yields of bound particles come from collisions between two unbound particles and from collisions between an unbound and a bound particle. + Iu either case. the addition of bouud articles comes αλαλα] from collisions that occur near rye Subsequent collisious cause the bound particles to acerete.," In either case, the addition of bound particles comes mainly from collisions that occur near $r_g$ Subsequent collisions cause the bound particles to accrete." +" The total accretion rate is bounced by the sum of he collisional aud collisionless accretion rates For τιyoKir, collisions douiuate the accretiou rate aud Next we turn our attention to the density profile in semu-collisional atinospheres."," The total accretion rate is bounded by the sum of the collisional and collisionless accretion rates For $\tau_g> R/r_g$, collisions dominate the accretion rate and Next we turn our attention to the density profile in semi-collisional atmospheres." + Collisions involving iu mabe particle serve as a source for bound particles at a rate ATARTON: lu ," Collisions involving an unbound particle serve as a source for bound particles at a rate $\dot M\sim 2\pi\tau_g r_g^2 +\rho_\infty c_{\infty}$." +steady state the deusitv of bou particles around ry is of the same order of magnitude as px., In steady state the density of bound particles around $r_g$ is of the same order of magnitude as $\rho_\infty$. + dti set by a balance between the rate at which bom particles are produced and the rate at which their ματια collisions cause them to dift sva., It is set by a balance between the rate at which bound particles are produced and the rate at which their mutual collisions cause them to drift inward. + The mass acerction rate is independent of radius for reorg.," The mass accretion rate is independent of radius for $r \ll +r_g$." + Together with knowledge of the average radia velocity. c. this allows us to determine the density profile for constaut #.," Together with knowledge of the average radial velocity, $v$, this allows us to determine the density profile for constant $\kappa$." + Where τοπρSL. ος~Typr). but οος~(rgpr)? where 7zl.," Where $\tau\sim \kappa\rho r \lesssim 1$, $v/c_\infty \sim +\tau (r_g/r)^{1/2}$, but $v/c_\infty\sim (r_g/r)^{1/2}$ where $\tau\gtrsim 1$." + Thus ifr =Land ir 2., Thus if $\tau\lesssim 1$ and if $\tau\gtrsim 1$. + For Réry15 kpe but [alls short of the observational poiuls in the rauge 6—12 kpe.,curve of the Galaxy only for $r \geq 15$ kpc but falls short of the observational points in the range $6-12$ kpc. + Wea lso show here how tie model precliction varies with the strengtl ol the magnetic field (dotted aud dash-doted curves i Fige.1)., We also show here how the model prediction varies with the strength of the magnetic field (dotted and dash-doted curves in Fig.1). + As expected. increase (by 5 %)) in the magietic field vields commensurate increase in the 'otatioual velocity. while decrease (by 5 in the uagnetic field vields decrease in the rotational velocity.," As expected, increase (by 5 ) in the magnetic field yields commensurate increase in the rotational velocity, while decrease (by 5 ) in the magnetic field yields decrease in the rotational velocity." + The case of no magnetic field By—() recovers the Newtonian rotatiOla curve (thick soid line) which is well below of the observational data poiuts for all r., The case of no magnetic field $B_0=0$ recovers the Newtonian rotational curve (thick solid line) which is well below of the observational data points for all $r$. + In Fig.2 we stucy depeudence of the rotationa velocity ou variation in the pitch aigle., In Fig.2 we study dependence of the rotational velocity on variation in the pitch angle. + We eather hat au increase (by )) in he magnetic field pitch angle p results in au increase of the rotational velocitv for large r., We gather that an increase (by ) in the magnetic field pitch angle $p$ results in an increase of the rotational velocity for large $r$. + While decrease in p srocluces a lower velocity beyoud r=15 kpe., While decrease in $p$ produces a lower velocity beyond $r=15$ kpc. + This co‘lusiou is similar to that of Nelson (LOSS) (also see cliscussion below)., This conclusion is similar to that of Nelson (1988) (also see discussion below). + Iu Fi2.oOκ)+) we Investigate how variation in the leleth seale of the magnetic field ry allects the LOlatiol1 curve., In Fig.3 we investigate how variation in the length scale of the magnetic field $r_0$ affects the rotational curve. + We eather from this grap rthat aui icrease in ry vields an increase in tle rotational velocitv. while decrease in ry produces smaller velociies.," We gather from this graph that an increase in $r_0$ yields an increase in the rotational velocity, while decrease in $r_0$ produces smaller velocities." + Again. this result seem reasonable because ro essentially quautifies the extent of the magnetic field.," Again, this result seem reasonable because $r_0$ essentially quantifies the extent of the magnetic field." + Hence. as ry decreases. the effect of jxB orce is weakeued :uid rotation velocity sharply falls cow.," Hence, as $r_0$ decreases, the effect of $\vec j \times \vec B$ force is weakened and rotation velocity sharply falls down." + I1 Fig.Ll we stuly whether a better fi than in Figs.(1)-(3) is possible., In Fig.4 we study whether a better fit than in Figs.(1)–(3) is possible. + We thus try to vary By N Lac‘tor of two οἱher way. Le. Byx 2aud 50/2.," We thus try to vary $B_0$ by factor of two either way, i.e. $B_0 \times 2$ and $B_0 /2$." + We gather from Fig.l that the simall values (e.g. By/2 of By cauno provide a reasonable fit., We gather from Fig.4 that the small values (e.g. $B_0 /2$ ) of $B_0$ cannot provide a reasonable fit. + However. the large values (Byx 2) provide au excellent it.," However, the large values $B_0 \times 2$ ) provide an excellent fit." + O “COULSE. SUL‘h large values should be discouuted ou the grounds that such maguetic fields are 101 οserved.," Of course, such large values should be discounted on the grounds that such magnetic fields are not observed." + However. we remark that sarting from about By=11 ji(C a good fit is possible for all r.," However, we remark that starting from about $B_0=11 $ $\mu$ G a good fit is possible for all $r$." + This leaves us with a conclusion the in the Galaxy. whilst ouly being important for large r (r>15 kpe). jxB force may be imporaut for the gas aud. plasma dvuamics for other galaxies with stronger ma[n]0retic Ποια».," This leaves us with a conclusion that in the Galaxy, whilst only being important for large $r$ $r \geq 15$ kpc), $\vec j \times \vec B$ force may be important for the gas and plasma dynamics for other galaxies with stronger magnetic fields." + Earlier work ol Nelson (1985) coujecurec about importance of tle dynamical effect of magnetic stress on the tenlous Outer gaseous disces of galaxies., Earlier work of Nelson (1988) conjectured about importance of the dynamical effect of magnetic stress on the tenuous outer gaseous discs of galaxies. + One of tlie coiclusions of Nelson (1988) was hat an increase i ithe pitch angle of the niaguetic field yields üehlerrotational velocities (this result is also corroborated in our inodel — see our Fig.2)., One of the conclusions of Nelson (1988) was that an increase in the pitch angle of the magnetic field yields higher rotational velocities (this result is also corroborated in our model – see our Fig.2). + The mode presened here is au innprovement on elsou (1988) wo ‘kin that we used a more realistic magnetic ield moclel of Hau Qiao (1991). and we perform an acual fit to the Milky Way rotatioual curve.," The model presented here is an improvement on Nelson (1988) work in that we used a more realistic magnetic field model of Han Qiao (1994), and we perform an actual fit to the Milky Way rotational curve." + Tje latte js possible because our model is süunpler aud presents an analytical expression lor the rotational ν‘elocity Eq.(10) as opposed to he ueed for solviug an ordinary differenial equation (Eq.(7 from Nelsou (1958))., The latter is possible because our model is simpler and presents an analytical expression for the rotational velocity Eq.(10) as opposed to the need for solving an ordinary differential equation (Eq.(7) from Nelson (1988)). + Other previous developments inelude (Ixatz 1991: Battauer et al., Other previous developments include (Katz 1994; Battaner et al. + 1992: Bataner Florido 2000: Battaner et al., 1992; Battaner Florido 2000; Battaner et al. + 2002: Battaner Florido 2007: Sauchez-Salcedo Reyes-Rtiz 2001J., 2002; Battaner Florido 2007; Sanchez-Salcedo Reyes-Ruiz 2004). + Iu the present study we investigate the effect of jxB force on the cyuamics of gas aud plasma., In the present study we investigate the effect of $\vec j \times \vec B$ force on the dynamics of gas and plasma. +iu turn leading to where the hininosities are in | aud 140) is expressed as v£(v).,"in turn leading to where the luminosities are in $^{-1}$ and $\mu$ m) is expressed as $\nu\, L(\nu)$." +" The unit of X(IIo),4, and “(2|ya) iseresbom7."," The unit of $\Sigma(\rm H\alpha)_{obs}$ and $\Sigma(24\,\mu{\rm m})$ is $\rm erg\, s^{-1}\, cm^{-2}$." + We use the IIo. nuage of M32 as given bv ToopesWalterbos (2000)., We use the $\alpha$ image of M33 as given by \citet{hoopes00}. +. It was obtained using the 0.6- Dwazell-Schuidt telescope at the Kitt Peak National Observatory., It was obtained using the 0.6-m Burrell-Schmidt telescope at the Kitt Peak National Observatory. + The dimensions of the CCD are 2018« with a pixel size of 27.03 and the total feld of view is approximately τος«70%," The dimensions of the CCD are $2048 \times 2048$ with a pixel size of $2''.03$ and the total field of view is approximately $70'\times +70'$." + The seusitivity is 0.8«&10MorestemZaresee? (Πουροςetal.2001).," The sensitivity is $0.8 \times 10^{-17}\, \rm erg\, s^{-1}\, +cm^{-2}\, arcsec^{-2}$ \citep{hoopes01}." +. We retrieved the Multibaud huagiug Photometer (AUPS:Riekeetal.2001) datasets CAORs 3617711. 3618256. 3618512. 3618768) of the basic calibrated data (BCD) created bv. the Spitzer Science. Center (SSC) pipeline from the Spitzer Space Telescope (Werneretal.2001) data archive.," We retrieved the Multiband Imaging Photometer \citep[MIPS:][]{rieke04} datasets (AORs 3647744, 3648256, 3648512, 3648768) of the basic calibrated data (BCD) created by the Spitzer Science Center (SSC) pipeline from the Spitzer Space Telescope \citep{werner04} data archive." + The mosaics were assenibled by eatherimg all the BCDs except the frst data frames of each observation because they have shorter integration times., The mosaics were assembled by gathering all the BCDs except the first data frames of each observation because they have shorter integration times. + The individual calibrated ralnes were processed using MOPLENX (Makovoz&whan2005) for cosmic-ray rejection and backerownd natching was applied to overlapping fields of view., The individual calibrated frames were processed using MOPEX \citep{makovoz05} for cosmic-ray rejection and background matching was applied to overlapping fields of view. +" The fual dimension of the each mosaic was 21’&80""."," The final dimension of the each mosaic was $21' +\times 89'$." + After we removed the zodiacal light. aud the noisy pixels near he edges by trimming. the four nuages were aligned with their coordinates aud combined.," After we removed the zodiacal light, and the noisy pixels near the edges by trimming, the four images were aligned with their coordinates and combined." +" The PWOAL of yoint spread fuuctiou is 5"".7.", The FWHM of point spread function is $5''.7$. + The Πα aud images were convolved iuto the sale augular resolution as the CO(J==110) data (197.3). veeridded to τς per pixel aud trimmucd to match the CO(/==110) map.," The $\alpha$ and images were convolved into the same angular resolution as the 1–0) data $19''.3$ ), regridded to $7''.5$ per pixel, and trimmed to match the 1–0) map." + The rims noise is 5«10Sorestem? iu the Πα imap. aud 3ον10Peresten7 in the map.," The rms noise is $5\times\rm 10^{-7}\,erg\,s^{-1}\,cm^{-2}$ in the $\alpha$ map, and $3\times\rm 10^{-5}\,erg\,s^{-1}\,cm^{-2}$ in the map." + The resultant SFR inge is shown in Fie., The resultant SFR image is shown in Fig. + 2 with the overlaid 110) contours., 2 with the overlaid 1--0) contours. +" The riis noises in the Πα and maps result in a Mere, error aud a seusitivitv limit of 5νLOMALνιtpe 7."," The rms noises in the $\alpha$ and maps result in a $\Sigma_{\rm SFR}$ error and a sensitivity limit of $5\times 10^{-11}{\it \mo}\,\rm \,yr^{-1}\,pc^{-2}$ ." + Fig., Fig. + 2 reveals a striking variety of star formation properties., 2 reveals a striking variety of star formation properties. + In regions where CO enmüssionu is detected. there is a large dispersion in the values of Xugg of over four orders of magnitude.," In regions where CO emission is detected, there is a large dispersion in the values of $\Sigma_{\rm SFR}$ of over four orders of magnitude." +" For example. the most mmassive GAIC at (a. 8) = (18933995.6,|30°ο τή) lias little star formation activity despite the large amount of molecular gas it contaius."," For example, the most massive GMC at $\alpha$, $\delta$ ) = $\rm 1^h33^m9^s.6, +30^\circ49'7''.3$ ) has little star formation activity despite the large amount of molecular gas it contains." + Iu the three major star-forming reeious 5595. and 1133). there is a considerable difference66014. in the amount of molecular gas associated with these star-forming regions.," In the three major star-forming regions 604, 595, and 133), there is a considerable difference in the amount of molecular gas associated with these star-forming regions." + 660L has its associated GMCs at the same position. 5595 has the ones offset from it. and moreover. none of the CAICs are associated with 1133.," 604 has its associated GMCs at the same position, 595 has the ones offset from it, and moreover, none of the GMCs are associated with 133." + Fig., Fig. +" 3 presents the relationship between the SER aud molecular hydrogen surface densities for four aneular resolutions: 197.3 ονNO pc). GO"" (~210 pe). 1207 (~500 pc). and 2107 (~1 kpce)"," 3 presents the relationship between the SFR and molecular hydrogen surface densities for four angular resolutions: $19''.3$ $\sim\!80\pc$ ), $60''$ $\sim\!240\pc$ ), $120''$ $\sim\!500\pc$ ), and $240''$ $\sim\!1\kpc$ )." + The panel of ~δpc resolutiou is the K-S law plot with the highest spatial resolution for an extra-galaxy to date., The panel of $\sim\!80\pc$ resolution is the K-S law plot with the highest spatial resolution for an extra-galaxy to date. + Fig., Fig. +" 2 shows that apparent correlations exist between Xj, aud Xupgg at the ]kpe resolution. as already found in the disk-averaged data of M33 (Ποναetal.200D.."," 3 shows that apparent correlations exist between $\Sigma_{\rm H_2}$ and $\Sigma_{\rm SFR}$ at the $\sim\!1\kpc$ resolution, as already found in the disk-averaged data of M33 \citep{heyer04}." +" The best least-squares Bt for the —1kpe resolution data with Nyy,>20 is We have fitted the power law only to the data at the 1- resolution. because the data at the other resolutions lave a significant sclection bias due to the ouission of data points having Xp,<26."," The best least-squares fit for the $\sim\!1\kpc$ resolution data with $\Sigma_{\rm H_2}>2\sigma$ is We have fitted the power law only to the data at the 1-kpc resolution, because the data at the other resolutions have a significant selection bias due to the omission of data points having $\rm \Sigma_{H_2}<2\sigma$." + The selection bias makes he correlation slopes appear steeper than real., The selection bias makes the correlation slopes appear steeper than real. + Fig., Fig. + 3 also shows that the correlation becomes looser with higher resolution. and it is hardly visible in the dot for ~SOpe resolution.," 3 also shows that the correlation becomes looser with higher resolution, and it is hardly visible in the plot for $\sim\!80\pc$ resolution." +" Although most “yp, values je within 10.10AL.pe? where Nib26. Xapg values exhibit a wide range of over four orders of magnitude. Yom <101"" to 2109Movrtpe2. indicating that he I&-S law becomes mvalid at this resolution."," Although most $\Sigma_{\rm H_2}$ values lie within $10\textendash40\mo\pc^{-2}$ where $\rm \Sigma_{H_2}>2\sigma$, $\Sigma_{\rm SFR}$ values exhibit a wide range of over four orders of magnitude, from $\lesssim\!10^{-10}$ to $\sim\!10^{-6}\mo\yr^{-1}\pc^{-2}$, indicating that the K-S law becomes invalid at this resolution." + That is. he I&-S law is valid ouly for averaging SER aud gas mass in large scales of several πιάνο pirsecs.," That is, the K-S law is valid only for averaging SFR and gas mass in large scales of several hundred parsecs." + Our resolution. NÜpe is smaller than these scales.," Our resolution, $\sim\!80\pc$ is smaller than these scales." + We have exinuned the effects of stochasticifv on the estimation of SFR due to small samplue at high spatial resolutions., We have examined the effects of stochasticity on the estimatiion of SFR due to small sampling at high spatial resolutions. + The initial mass function isnot fully populated when simaller regions that coutain only a few stars du clusters are sampled., The initial mass function isnot fully populated when smaller regions that contain only a few stars in clusters are sampled. + Thus. in regions witli weaker extinctiou-corrected Πα emission. this effect may lead to significant scatter in the estimated Nope.," Thus, in regions with weaker extinction-corrected $\alpha$ emission, this effect may lead to significant scatter in the estimated $\Sigma_{\rm SFR}$." + We have estimated the significance of this effect oun the 80-pc resolution data., We have estimated the significance of this effect on the 80-pc resolution data. + For instance. Xapgg;—10.9Moye!pec2? corresponds to the total flux of extiuction-corrected Ila emission having £(IInνι=6.6|QUere «Επ the S0-pe beau.," For instance, $\Sigma_{\rm SFR}=10^{-9}\mo\yr^{-1}\pc^{-2}$ corresponds to the total flux of extinction-corrected $\alpha$ emission having $L(\rm H\alpha)_{corr}=6.6\times 10^{35} erg\, s^{-1}$ within the 80-pc beam." +" Asstunineg a eas temperature of LOTS and an electron density of θέσιν? in regions. the ionizing photon fins is given by QUIP)=7,3&7ΜΗ... (Ieunicutt1988:Brocklehurst1971)."," Assuming a gas temperature of $10^4\K$ and an electron density of $100\rm\, cm^{-3}$ in regions, the ionizing photon flux is given by $Q(\rm H^0)=7.3\times 10^{11} L(\rm H\alpha)_{corr}\,s^{-1}$ \citep{kennicutt88,brocklehurst71}." + Therefore. the correspoucdiue total ionizing plotou flux is QUI!)=LosLOS 1.," Therefore, the corresponding total ionizing photon flux is $Q(\rm H^0)=4.9\times10^{48} \rm s^{-1}$ ." + According to Fig., According to Fig. + 3 in Cervitoetal. (20051. QUIT) per unit mass varies with cluster age from LOY to ttstar.| ," 3 in \cite{cervino02}, , $Q(\rm H^0)$ per unit mass varies with cluster age from $10^{47}$ to $10^{44}\, {\rm s}^{-1} \mo ^{-1}$." +"The ratio of the error in QUI"") to the mean value. QUI)|/QUT), is ~LOALE? (the ratio cau vary wea factor ~2 depending ou the cluster age). where AL is the cluster mass."," The ratio of the error in $Q(\rm H^0)$ to the mean value, $\sigma [Q({\rm H^0})]/Q({\rm H^0})$, is $\sim 10 M^{-1/2}$ (the ratio can vary by a factor $\sim 2$ depending on the cluster age), where $M$ is the cluster mass." + Thus. the cluster mass required to xoduce the ionizing flux 1uieutioned above is estimated to je 50 to 5«101 which results in ο./QUIU)z1 o 0.01.," Thus, the cluster mass required to produce the ionizing flux mentioned above is estimated to be 50 to $5\times10^4 \mo$, which results in $\sigma[Q({\rm H^0})]/Q({\rm H^0})\approx 1$ to 0.04." + In sunununary. in the 80-pc scale. the error due to he effect of stochasticity at Sopp=lOPAvrtpe 23s ~OOLT110PALvepe7.," In summary, in the 80-pc scale, the error due to the effect of stochasticity at $\Sigma_{\rm SFR}=10^{-9}\mo\yr^{-1}\pc^{-2}$ is $\approx 0.04\textendash 1\times 10^{-9}\mo\yr^{-1}\pc^{-2}$." + The error decreases with arecr Mapp aud lower spatial! resolutions., The error decreases with larger $\Sigma_{\rm SFR}$ and lower spatial resolutions. +" For example. he mania o|QUI""j|QUI"") in the NÜ-pc scale is 1. Wt. and 0.1. aud in the 210-pc scale it is 0.5. 0.1. and L05 for Sopp=107.105. and 10*M.xrbpe7. respectively,"," For example, the maximam $\sigma [Q({\rm H^0})]/Q({\rm H^0})$ in the 80-pc scale is 1, 0.4, and 0.1, and in the 240-pc scale it is 0.5, 0.1, and 0.05 for $\Sigma_{\rm SFR}=10^{-9}, 10^{-8}$, and $10^{-7} \mo\yr^{-1}\pc^{-2}$, respectively." + Althoueh the error is significant at smaller Mere at the SQ-pe resolution. it cannot explain the scatter of over four orders of magnitude in Msp.," Although the error is significant at smaller $\Sigma_{\rm SFR}$ at the 80-pc resolution, it cannot explain the scatter of over four orders of magnitude in $\Sigma_{\rm SFR}$." + Now. we consider the possible causes for the breakdown of the I&-S law at high spatial resolutions.," Now, we consider the possible causes for the breakdown of the K-S law at high spatial resolutions." + Ii eraud desigu spiral galaxies. we often see a systematic offset between the molecular gas arius and the star foriuing arms as a result of the deusity wave aud the time delay between the acciunulatiou of eas and its ionization by uewborn stars (e.g...Egusaetal. 2009)..," In grand design spiral galaxies, we often see a systematic offset between the molecular gas arms and the star forming arms as a result of the density wave and the time delay between the accumulation of gas and its ionization by newborn stars \citep[e.g.,][]{egusa09}. ." + If such an offset exists in M32. it mav result in the breakdownof the [νο law when we observe the galaxy with a spatial resolution comparable to the offset.," If such an offset exists in M33, it may result in the breakdownof the K-S law when we observe the galaxy with a spatial resolution comparable to the offset." + IHTowever. there is no such systematic offset between the CO aud the star-forming arm in MO. as," However, there is no such systematic offset between the CO and the star-forming arm in M33, as" +lists were found.,lists were found. + A complete list of these problems will be reported elsewhere., A complete list of these problems will be reported elsewhere. + The photometric calibration of the patch was carried out by first bringing all frames to a common zero-poiut as determined from the relative magnitudes of objects im overlap regions. within a pre-selected maguitude rauge.," The photometric calibration of the patch was carried out by first bringing all frames to a common zero-point as determined from the relative magnitudes of objects in overlap regions, within a pre-selected magnitude range." + This was doue by a global least-square fit to all the relative zero-poiuts. constraining thei simu to be equal to zero.," This was done by a global least-square fit to all the relative zero-points, constraining their sum to be equal to zero." + The internal accuracy of the derived photometric solutiou is <0.005 mag (Paper I)., The internal accuracy of the derived photometric solution is $\lsim 0.005$ mag (Paper I). + Secoud. absolute zero-poiuts are found for frames observed iu photometric conditions.," Second, absolute zero-points are found for frames observed in photometric conditions." + The zoro-poiuts for these frames were determined using a total of 36 frames of 7 fields contaimime standard stars taken from. Laudolt (1992 a.)). observed over 5 nights.," The zero-points for these frames were determined using a total of 36 frames of 7 fields containing standard stars taken from Landolt (1992 a,b), observed over 5 nights." + These funes were also reduced through the pipeline. which identified the stauclare stars and measured magnitudes through Landolt apertures automatically (sce paper I).," These frames were also reduced through the pipeline, which identified the standard stars and measured magnitudes through Landolt apertures automatically (see paper I)." + Altosether 118 independent measurements of standards were used in the calibration., Altogether 148 independent measurements of standards were used in the calibration. + Two solutions are then determined: one which colmputes a single zero-point offset. based on the weighted average of the zero-poiuts of the calibrated frames. aud the other using a first-order polvnonual in both right asceusiou and declination.," Two solutions are then determined: one which computes a single zero-point offset, based on the weighted average of the zero-points of the calibrated frames, and the other using a first-order polynomial in both right ascension and declination." + Comparison with external data suggests that a zero-point offset provides an adequate plotometric calibration for the entire patch., Comparison with external data suggests that a zero-point offset provides an adequate photometric calibration for the entire patch. + External photometric data come from the Dutch 0.914 telescope at La Silla aud frou overlaps with DENIS data aud with frames taken by Lidman Peterson (1996)., External photometric data come from the Dutch 0.9m telescope at La Silla and from overlaps with DENIS data and with frames taken by Lidman Peterson (1996). + The regions of overlap of these data are shown in Figure 6.., The regions of overlap of these data are shown in Figure \ref{fig:overlaps}. + Iu the fgure the regious observed uncer photometric conditions are also indicated., In the figure the regions observed under photometric conditions are also indicated. + Comparison of this figure with its counterpart in paper 1. demonstrates that the data," Comparison of this figure with its counterpart in paper I, demonstrates that the data" +PSR 70205-6449 in supernova remnant (SNR) 3C58 is a recently discovered X-ray and radio pulsar (Camiloetal.2002:al.2002) with a period of 65 ms.,"PSR J0205+6449 in supernova remnant (SNR) 3C58 is a recently discovered X-ray and radio pulsar \citep{ca02,mu02} with a period of 65 ms." + 3C 58 was thought to be young due to a possible association with SN 1181 (vandenBergh1975)., 3C 58 was thought to be young due to a possible association with SN 1181 \citep{vb78}. + Consequently it should share many of the characteristics of the Crab nebula. including the presence of a young pulsar.," Consequently it should share many of the characteristics of the Crab nebula, including the presence of a young pulsar." + However an embedded pulsar defied detection for over twenty years., However an embedded pulsar defied detection for over twenty years. + PSR 1020560349 has a considerably weaker flux than the Crab pulsar., PSR J0205+6449 has a considerably weaker flux than the Crab pulsar. + Its X-ray emission is 1000 times lower than the Crab and its radio emission 120 times lower., Its X-ray emission is 1000 times lower than the Crab and its radio emission 120 times lower. + Some of this discrepancy can be attributed to the mounting evidence that the characteristic age of the pulsar (P/2P = 5400 years) is near to its true age and hence it is not associated with SN 1181 (Gotthelf.Helfand.&Newburgh 2007)., Some of this discrepancy can be attributed to the mounting evidence that the characteristic age of the pulsar $P / 2\dot{P} $ $\approx$ 5400 years) is near to its true age and hence it is not associated with SN 1181 \citep{go07}. +. VLA observations at 1.4GHz show a nebula expansion rate of 0.014%+0.003 | (Bietenholz2006)... inconsistent with S LIS] unless substantial deceleration of the remnant has occurred.," VLA observations at 1.4GHz show a nebula expansion rate of $0.014\% \pm 0.003$ $^{-1}$ \citep{bi06}, inconsistent with SN 1181 unless substantial deceleration of the remnant has occurred." + A comprehensive optical study of 3C 58 showed no evidence of an optical pulsar at mj z22.5 (Fesenetal.2008)., A comprehensive optical study of 3C 58 showed no evidence of an optical pulsar at $_R \approx $ 22.5 \citep{Fesen08}. +. Furthermore based upon the relatively low proper motion of knots within 3C 58 these authors also cast doubt on the association between 3C 58 and S 1ISI., Furthermore based upon the relatively low proper motion of knots within 3C 58 these authors also cast doubt on the association between 3C 58 and SN 1181. + Deeper optical observations of 3C 58 show evidence of an optical nebulosity at the same location as the X-ray counterpart to PSR J020546449 (Shibanovetal.2008)., Deeper optical observations of 3C 58 show evidence of an optical nebulosity at the same location as the X-ray counterpart to PSR J0205+6449 \citep{Shibanov08}. +. These authors interpre this nebulosity as a pulsar wind nebula (PWN)., These authors interpret this nebulosity as a pulsar wind nebula (PWN). + PSR JO205+6449 has the third highest spin down energy flux [Efdx2.61079 ergs/s/kpc] after the Crab and Vela pulsars., PSR J0205+6449 has the third highest spin down energy flux $\dot{E}/d^2 \approx 2.6~10^{36}$ $^2$ ] after the Crab and Vela pulsars. + The X-ray determined hydrogen column density [Ny=4.1I0?!eai 7]. (Gotthelf.Helfand.&Newburgh2007) and optical extinction. E(B-V) ~ 0.68 (Fesenetal.2008). are similar to the Crab pulsar.," The X-ray determined hydrogen column density $N_H\approx 4.1~10^{21} cm^{-2}$ ], \citep{go07} and optical extinction, E(B-V) $\sim$ 0.68 \citep{Fesen08}, are similar to the Crab pulsar." + From observations a Kinematic distance of 3C 58 has been established at 3.2 kpe (Robertsetal.1993)... consistent with its Dispersion Measure (Camiloetal.2002).," From observations a kinematic distance of 3C 58 has been established at 3.2 kpc \citep{ro93}, consistent with its Dispersion Measure \citep{ca02}." +. These combine to make PSR J020546449 a likely candidate for optical emission studies., These combine to make PSR J0205+6449 a likely candidate for optical emission studies. +" If we assume that the optical luminosity scales with light cylinder magnetic field. L,,;«i (Shearer&Golden2001). then we estimate that the pulsar should have a visual magnitude in the range 23-25. depending on interstellar absorption and ettects of beaming geometry (Shearer2008).."," If we assume that the optical luminosity scales with light cylinder magnetic field, $L_{opt} \propto B_{lc}^{1.6}$ \citep{sg02}, then we estimate that the pulsar should have a visual magnitude in the range 23–25, depending on interstellar absorption and effects of beaming geometry \citep{sh08b}." +. This paper reports on : William Herschel telescope (WHT) service time observation of PSR J0205+6449 to look for evidence of an optical pulsar and iu possible PWN., This paper reports on a William Herschel telescope (WHT) service time observation of PSR J0205+6449 to look for evidence of an optical pulsar and its possible PWN. + Photometric observations of the field surrounding 3C 58 were performed on the night of September 10. 2007 using the 4.2-m WHT at the Isaac Newton Group of Telescopes. La Palma.," Photometric observations of the field surrounding 3C 58 were performed on the night of September 10, 2007 using the 4.2-m WHT at the Isaac Newton Group of Telescopes, La Palma." + The observations were taken in Service mode with the Auxiliary Port Imaging Camera (AUX). using the Harris set of the broadband BYR filters.," The observations were taken in Service mode with the Auxiliary Port Imaging Camera (AUX), using the Harris set of the broadband BVR filters." + It is thought that when the filter response curves are convolved with a typical CCD response. these glass filters provide," It is thought that when the filter response curves are convolved with a typical CCD response, these glass filters provide" +"shows that the motion of this satellite is not close to a keplerian one, as it is the case for the planets of the Solar system.","shows that the motion of this satellite is not close to a keplerian one, as it is the case for the planets of the Solar system." +" The effects of the attraction of the Sun, Jupiter and the other satellites of Saturn on Phoebe ’s orbit entail an important departure from the keplerian motion."," The effects of the attraction of the Sun, Jupiter and the other satellites of Saturn on Phoebe 's orbit entail an important departure from the keplerian motion." + The individual study of the other orbital elements confirms this result., The individual study of the other orbital elements confirms this result. +" In the following, the formula for the mean elements of Phoebe keplerian motion e,M and Lg are given, where M,L, are respectively the mean anomaly and mean longitude with respect to the ""departure point” γι."," In the following, the formula for the mean elements of Phoebe keplerian motion $e, M$ and $L_{S}$ are given, where $M,L_{s}$ are respectively the mean anomaly and mean longitude with respect to the ""departure point"" $\gamma_{t}$." +" They were obtained by fitting the curves of the temporal variations of these elements given by Emelyanov (2007) with a polynomial expression at order 6 as it has been done for the planets of the Solar system (Simon et al, 1994)."," They were obtained by fitting the curves of the temporal variations of these elements given by Emelyanov (2007) with a polynomial expression at order 6 as it has been done for the planets of the Solar system (Simon et al, 1994)." +" Considering the limits of the ephemerides, truncating the polynomial functions at the order 6 looks as a sufficient approximation."," Considering the limits of the ephemerides, truncating the polynomial functions at the order 6 looks as a sufficient approximation." +" Thus: where ¢ is counted in julian days,M and L, being expressed in degrees."," Thus: where $t$ is counted in julian days,$M$ and $L_{s}$ being expressed in degrees." + Fig.3 shows the variations of the eccentricity of Phoebe for a 9000 days time span., \ref{fig18} shows the variations of the eccentricity of Phoebe for a 9000 days time span. + An important feature of Phoebe orbit is the large eccentricity as well as its very large relative variations (of the order of 1096)., An important feature of Phoebe orbit is the large eccentricity as well as its very large relative variations (of the order of $10 \%$ ). + As we will see in section ?? this will be very important in our study because of the large corresponding variations of (2)? that it causes for the orbit., As we will see in section \ref{6} this will be very important in our study because of the large corresponding variations of $(\frac{a}{r})^3$ that it causes for the orbit. +" Figures 4, 5 and 6 represent respectively the residuals after substraction of the polynomial functions given by (19)), (20)) and (21))from the eccentricity, the mean anomaly and the mean longitude of Phoebe."," Figures \ref{fig20}, \ref{fig14} and \ref{fig17} represent respectively the residuals after substraction of the polynomial functions given by \ref{e}) ), \ref{mp}) ) and \ref{ls2}) )from the eccentricity, the mean anomaly and the mean longitude of Phoebe." +" As already observed for the semi-major axis, the residuals have periodic components which reach an amplitude of 4? for the mean anomaly."," As already observed for the semi-major axis, the residuals have periodic components which reach an amplitude of $4^{\circ}$ for the mean anomaly." +" Thanks to a FFT analysis the leading ampitudesand the periods of the sinusoids characterizing the signals in Figs.4, 5 and 6 are determined and given in Table 2.."," Thanks to a FFT analysis the leading ampitudesand the periods of the sinusoids characterizing the signals in \ref{fig20}, \ref{fig14} and \ref{fig17} are determined and given in Table \ref{tab2new}. ." +The combined EA/—T diagram for solar and stellar flares (Fig.,The combined $EM-T$ diagram for solar and stellar flares (Fig. + 3) shows some similarities but also intriguing differences in the scaling behavior., 3) shows some similarities but also intriguing differences in the scaling behavior. +" Solar flares have been observed mostly in the temperature range of Tj,227—30 MEIN (or T,z1—30 MEIN if we include the EUV nanoflares). while stellar flares have been detected within the temperature range of MIN."," Solar flares have been observed mostly in the temperature range of $T_p \approx 7-30$ MK (or $T_p \approx 1-30$ MK if we include the EUV nanoflares), while stellar flares have been detected within the temperature range of $T_p \approx 10-150$ MK." +" The lack of observations of cooler stellar flares 7,Ppne=10 MIN is likely to be due to the sensitivity limit. which is about at EM,210°! ? for stellar flares."," The lack of observations of cooler stellar flares $T_p \lapprox 10$ MK is likely to be due to the sensitivity limit, which is about at $EM_p \gapprox 10^{51}$ $^{-3}$ for stellar flares." +" The sensitivity limit also svstematically increases with higher flare temperatures. up to zz10 for the hottest stellar flares with T,2100 MI. which is likely a consequence of the decreasing sensitivity of current soft. X-ray detectors at higher temperature lines."," The sensitivity limit also systematically increases with higher flare temperatures, up to $\approx 10^{53}$ $^{-3}$ for the hottest stellar flares with $T_p \gapprox 100$ MK, which is likely a consequence of the decreasing sensitivity of current soft X-ray detectors at higher temperature lines." +" What is similar for both solar and stellar flares is the overall slope of the EAM,—T, relationship. which was found to have a powerlaw slope of a=4.7z0.1 for solar flares (excluding the RILESSI data that have a hieh-temperature bias). ancl a slope of slope of forstellar flares (Fig."," What is similar for both solar and stellar flares is the overall slope of the $EM_p-T_p$ relationship, which was found to have a powerlaw slope of $\alpha=4.7\pm0.1$ for solar flares (excluding the RHESSI data that have a high-temperature bias), and a slope of slope of $\alpha=4.5\pm0.4$ forstellar flares (Fig." + 3)., 3). + Both powerlaw slopes are consistent with the theoretically expected sealing of a224.3 (Eq., Both powerlaw slopes are consistent with the theoretically expected scaling of $\alpha \approx 4.3$ (Eq. + 33). which is based on the RIV scaling law (Eq.," 33), which is based on the RTV scaling law (Eq." + 23). the fractal volume scaling (Eq.," 23), the fractal volume scaling (Eq." +" 29). and the observed spatial scaling L(1,)zzT5 in solar flares (Eq."," 29), and the observed spatial scaling $L(T_p)\approx T_p^{0.9}$ in solar flares (Eq." + 18)., 18). + This agreement supports the assumption of the fractal volume scaling., This agreement supports the assumption of the fractal volume scaling. +" If we were lo assume a monolithic single-loop model with constant cross-section Chat scales with VGL)xL. the vesulling scaling law would be EM,xTS. or a monolithie cubic model with V(L)xL would vield EM,xT. whieh are both less consistent with the observations."," If we were to assume a monolithic single-loop model with constant cross-section that scales with $V(L) \propto L$, the resulting scaling law would be $EM_p \propto T_p^{3.9}$, or a monolithic cubic model with $V(L) \propto L^3$ would yield $EM_p \propto T_p^{5.9}$, which are both less consistent with the observations." + What is different. between solar and stellar flares is the emission measure in the same temperature range., What is different between solar and stellar flares is the emission measure in the same temperature range. +" In the overlapping temperature range of T,210—30 MIN we find that the total emission measure of stellar flares is larger by an average [actor οἱ comparing the [actors (Eqs.", In the overlapping temperature range of $T_p \approx 10-30$ MK we find that the total emission measure of stellar flares is larger by an average factor of comparing the factors (Eqs. + 15. 16) of the two linear regression fits in Fie.," 15, 16) of the two linear regression fits in Fig." + 3., 3. + II. we compare the theoretical model of the RTV law and the fractal volume scaling (Eq., If we compare the theoretical model of the RTV law and the fractal volume scaling (Eq. + 31) for the same temperature range (Eq., 31) for the same temperature range (Eq. +" 33). we see that the total volume-integrated emission measure ratio of stellar to solar [Iare depends on (he volume filling factor qv. length scale £L. and volume fractal dimension D,:."," 33), we see that the total volume-integrated emission measure ratio of stellar to solar flare depends on the volume filling factor $q_V$, length scale $L$, and volume fractal dimension $D_V$." + Since the sensitivity limit of stellar soft X-ray cletectors represents a bias for larger emission measures. we think that the observed stellar flares have a bias for both higher volume filling factors gy ancl flare sizes L.," Since the sensitivity limit of stellar soft X-ray detectors represents a bias for larger emission measures, we think that the observed stellar flares have a bias for both higher volume filling factors $q_V$ and flare sizes $L$ ." + For solar flares we found spatial filling factors in the range of οι=0.03—0.08 (Aschwanden Aschwanden 200Gb).," For solar flares we found spatial filling factors in the range of $q_V=0.03-0.08$ (Aschwanden Aschwanden 2006b)," +GRS 1915]105. is a luminous ancl spectacularly variable source of radiation from radio through to hare X-ray regimes.,GRS 1915+105 is a luminous and spectacularly variable source of radiation from radio through to hard X-ray regimes. + lis behaviour in both hard and soft X-rays is unique (e.g. Foster et al., Its behaviour in both hard and soft X-rays is unique (e.g. Foster et al. + 1996: Morgan. Iemillard Creiner 1997: Belloni et al.," 1996; Morgan, Remillard Greiner 1997; Belloni et al." + 2000). and it is a celebrated source of relativistic jets (Mirabel guez 1994: Fender ct al.," 2000), and it is a celebrated source of relativistic jets (Mirabel guez 1994; Fender et al." + 1999: guez Mirabel 1999: Dhawan. Mirabel σος 2000. Ciovannini ct al.," 1999; guez Mirabel 1999; Dhawan, Mirabel guez 2000, Giovannini et al." + 2001)., 2001). + X-ray [lux variations on a variety of timescales have been interpreted. as the repeated draining and. refilling of the inner aceretion disc. possibly due to extremely rapid transitions between ‘canonical’ black hole accretion states (e.g. Belloni ct al.," X-ray flux variations on a variety of timescales have been interpreted as the repeated draining and refilling of the inner accretion disc, possibly due to extremely rapid transitions between `canonical' black hole accretion states (e.g. Belloni et al." + L997a.b: Feroci et al.," 1997a,b; Feroci et al." + 1999: 3elloni ct al., 1999; Belloni et al. + 2000): however the physical meaning of these apparent changes in inner disc radius is not entirely certain (Merloni. Fabian Ross 2000).," 2000); however the physical meaning of these apparent changes in inner disc radius is not entirely certain (Merloni, Fabian Ross 2000)." + Quasi-sinusoidal oscillations with similar periods. almost certainly the signature of synchrotron emission. from repeated. ejection events. have been observed at racio. millimetre and infrared wavelengths (Pooley Fender 1997: Fender et al.," Quasi-sinusoidal oscillations with similar periods, almost certainly the signature of synchrotron emission from repeated ejection events, have been observed at radio, millimetre and infrared wavelengths (Pooley Fender 1997; Fender et al." + 1997: Eikenberry ct al., 1997; Eikenberry et al. + 1998. 2000: Mirabel et al.," 1998, 2000; Mirabel et al." + 1998: Fender Pooley 1998. 2000).," 1998; Fender Pooley 1998, 2000)." + These oscillations appear to have a direct connection to the X-ray clips (Pooley Fender 1997: Eikenberry et al., These oscillations appear to have a direct connection to the X-ray dips (Pooley Fender 1997; Eikenberry et al. + 1905. Mirabel et al.," 1998, Mirabel et al." + 1905. IxIein-Wolt. et al.," 1998, Klein-Wolt et al." +" 2001). although there is some debate as to whether they are associated with 'soft (c.g. Naik Rao 2000) or ""hard? (e.g. IxIcin-Wolt et al."," 2001), although there is some debate as to whether they are associated with `soft' (e.g. Naik Rao 2000) or `hard' (e.g. Klein-Wolt et al." + 2001) X-ray states., 2001) X-ray states. + Delays. between different racio bands (Pooley Fender 1997: Mirabel οἱ al., Delays between different radio bands (Pooley Fender 1997; Mirabel et al. + 1998) and. between the infrared ancl racio bands (Mirabel et al., 1998) and between the infrared and radio bands (Mirabel et al. + 1998: Fender Pooley 1998). clearly indicate that optical depth ellects play an important role in the observed emission from these ejections., 1998; Fender Pooley 1998) clearly indicate that optical depth effects play an important role in the observed emission from these ejections. + Details such as the magnitude, Details such as the magnitude +to be 0.05 6c.,to be 0.05 $\AERR$. + Because tjere are only small diTerences between PSPL. PSFL. FSPL. and FSFL. we ony show the case of PSPL in Fig. 1H1..," Because there are only small differences between PSPL, PSFL, FSPL, and FSFL, we only show the case of PSPL in Fig. \ref{fig.Max_thetaC}." + To see how muc1 the FL trayectory deviates from that of PL and the influence fron1 FS. we furher caleulate the maximum difference between the P.SPL. PSFL. and FSFL trajectories at a given time.," To see how much the FL trajectory deviates from that of PL and the influence from FS, we further calculate the maximum difference between the PSPL, PSFL, and FSFL trajectories at a given time." + The result is s10wn in Fig., The result is shown in Fig. +" {1 foralens with Am,.. 2. 0. -2 and a dark lens."," \ref{fig.Max_thetaC} for a lens with $\Delta m_{_{\mathrm{LS}}}$ = 2, 0, -2 and a dark lens." + The FSFL ony shows small difference to that of PSFL and PSPL., The FSFL only shows small difference to that of PSFL and PSPL. + The difference is less tjan. 10 µας for the case of Galactie bulge. and even smaler than | µας for the more distant source in the SMC and ΜΟΙ.," The difference is less than 10 $\mu$ as for the case of Galactic bulge, and even smaller than 1 $\mu$ as for the more distant source in the SMC and M31." + This is because the FL effect is important only when the lens is extremely close to the observer or the source and the major difference between FSFL and PSPL or PSFL comes from the finiteness of the source., This is because the FL effect is important only when the lens is extremely close to the observer or the source and the major difference between FSFL and PSPL or PSFL comes from the finiteness of the source. + Since my is larger than p. for most of the time. the FS effect only slightly changes the astrometric trajectory.," Since $u_0$ is larger than $\RS$ for most of the time, the FS effect only slightly changes the astrometric trajectory." + Even when the lens is extremely close to the source (see Fig. 11). ," Even when the lens is extremely close to the source (see Fig. \ref{fig.Max_thetaC}) )," +the already reduced 6p makes the difference so small that it is hardly observable., the already reduced $\AERR$ makes the difference so small that it is hardly observable. + In order to test if the astrometric signal is observable towards SMC. we simulate the astrometric trajectory of MACHO-97-SMC-| (Alcocketal.1997a)..," In order to test if the astrometric signal is observable towards SMC, we simulate the astrometric trajectory of MACHO-97-SMC-1 \citep{1997ApJ...491L..11A}." + This event has baseline magnitude = 17.7. so it will take ~ 3 hours to reach ὀθ-μας accuracy (Goullioudetal.2008)..," This event has baseline magnitude = 17.7, so it will take $\sim$ 3 hours to reach $\mu$ as accuracy \citep{2008SPIE.7013E.151G}." + We thus simulate observations by assuming the measurement errors to be Gaussian distribution with a = 30 yrs., We thus simulate observations by assuming the measurement errors to be Gaussian distribution with $\sigma$ = 30 $\mu$ as. + We pu the lens at a distance of 15 kKpe and 64 Κρο corresponding to the halo and sel-lensing scenario towards SMC., We put the lens at a distance of 15 kpc and 64 kpc corresponding to the halo and self-lensing scenario towards SMC. + We then assign a puative finite size of 1.5. and 10 10. to the lens and the source.," We then assign a putative finite size of 1, 5, and 10 $R_{\odot}$ to the lens and the source." + The mass of the lens is set tobe | A/.., The mass of the lens is set to be 1 $M_{\odot}$. + From Fig., From Fig. + We can see that if Ye lens is in he Galactic halo. we are able to detect the astrometric signal because of the very large 6c.," \ref{fig.SMC} we can see that if the lens is in the Galactic halo, we are able to detect the astrometric signal because of the very large $\AERR$." + However. the finite size of the source and tje lens is not revealed in such a close lens.," However, the finite size of the source and the lens is not revealed in such a close lens." + On the oyer hand. the FS and FL effects are prominent in the self-lensing regime due to he small Gc.," On the other hand, the FS and FL effects are prominent in the self-lensing regime due to the small $\AERR$." + But the astrometric trajectory is too sma| to be constrained by current instruments. not to mention to disenangle between the PSPL and FSPL or PSFL.," But the astrometric trajectory is too small to be constrained by current instruments, not to mention to disentangle between the PSPL and FSPL or PSFL." + Nevertheless. it is sill possible to use the (non-jdetection of the astrometric ellipse to infer if the lens is in the Galactic halo or it is a self-lensing event owards SMC," Nevertheless, it is still possible to use the (non-)detection of the astrometric ellipse to infer if the lens is in the Galactic halo or it is a self-lensing event towards SMC." + We also considered the possibility to detect the astrometric trajectory. from. ground-based instruments such as for VLTI., We also considered the possibility to detect the astrometric trajectory from ground-based instruments such as for VLTI. + can determine the astrometry to [θ-μας level in 30 minutes provided a reference star within 10 arcsec and a 200-m baseline (ATs mode)., can determine the astrometry to $\mu$ as level in 30 minutes provided a reference star within 10 arcsec and a 200-m baseline (ATs mode). + The goal of is to perform astrometric measurement for a target as faint as 18 (15) mag with UTs (ATs) provided a 13 (10) mag reference star in, The goal of is to perform astrometric measurement for a target as faint as 18 (15) mag with UTs (ATs) provided a 13 (10) mag reference star in +to 10.5 min. with ~40% of the features living less than 100 s. The area distribution has a peak al 0.1 arcsec?. with ~12% of the features being smaller than that.,"to $10.5$ min, with $\sim$ of the features living less than $100$ s. The area distribution has a peak at 0.1 $^2$, with $\sim$ of the features being smaller than that." + Around 97% of the features. are smaller (han 1 aresec.> which- was givenB as (he mean IHE size. in. previous- studies (Ishikawa&Tsuneta2009:Jinetal.2009).," Around $97$ of the features are smaller than $\sim1$ $^2$, which was given as the mean HIF size in previous studies \citep{Ishikawa:Tsuneta:2009,Jin:etal:2009}." +. Figures 2cc and d show scatter plots of maximum area and maximum linear polarization signal versus feature lifetime., Figures \ref{fig:basics}c c and d show scatter plots of maximum area and maximum linear polarization signal versus feature lifetime. + Figure 2dd has a cutoff at 0.1596... which is the lowest threshold value taken for MLT segmentation.," Figure \ref{fig:basics}d d has a cutoff at $0.15$, which is the lowest threshold value taken for MLT segmentation." + The curves connect binned values for 189 points each., The curves connect binned values for $189$ points each. + The plots indicate that longer-lasting features tend to be larger. and to display a higher mean linear polarization signal.," The plots indicate that longer-lasting features tend to be larger, and to display a higher mean linear polarization signal." + The largest feature has a lifetime of 9.4 min ancl occupies up (o ~2.3 arcsec? in the course of its evolution., The largest feature has a lifetime of $9.4$ min and occupies up to $\sim2.3$ $^2$ in the course of its evolution. + Its mean linear polarization signal reaches , Its mean linear polarization signal reaches $0.5$. +In order to study whether the features are located in prelerred locations with respect to the granular pattern. we Iollow the method of Litesetal.(2008).," In order to study whether the features are located in preferred locations with respect to the granular pattern, we follow the method of \citet{Lites:etal:2008}." +". Unsharp-anasked continuum images are obtained bv subtracting. from the originals. the images smoothed with a 59 pixel wide (3.2"") boxear funetion."," Unsharp-masked continuum images are obtained by subtracting, from the originals, the images smoothed with a 59 pixel wide $^{\prime\prime}$ ) boxcar function." + In this wav. intensity. variations on scales larger than eranulation (due to. e.g.. p-mode oscillations) are suppressed.," In this way, intensity variations on scales larger than granulation (due to, e.g., p-mode oscillations) are suppressed." + The pixels are then sorted into 250 equally populated intensity bins. ranging from dark intergranuar lanes to bright granular centers.," The pixels are then sorted into 250 equally populated intensity bins, ranging from dark intergranuar lanes to bright granular centers." + The fractional area occupied by the LIF is calculated for each bin., The fractional area occupied by the HIF is calculated for each bin. + The results are shown in Fig., The results are shown in Fig. + 2ee. The solid line represents uusharp-maskecl continuum values (see v-axis on (he left)., \ref{fig:basics}e e. The solid line represents unsharp-masked continuum values (see y-axis on the left). + The right v-axis shows (he range of Iractional areas occupied bv the HIF in each bin., The right y-axis shows the range of fractional areas occupied by the HIF in each bin. + The distribution is similar to the resulis shown by 9).., The distribution is similar to the results shown by \citet[][Fig. 9]{Lites:etal:2008}. + It has a peak of at positive values of the unsharp-maskecl intensity distribution., It has a peak of at positive values of the unsharp-masked intensity distribution. + This suggests. as Litesetal.(2008) noticed. that HIF tend to be located at intermediate intensities. presumably at the periphery of granules.," This suggests, as \citet{Lites:etal:2008} noticed, that HIF tend to be located at intermediate intensities, presumably at the periphery of granules." +Observation of gravitational waves (GWs) by extragalactic sources is going to open a new window for astronomy.,Observation of gravitational waves (GWs) by extragalactic sources is going to open a new window for astronomy. + The space-based Laser Interferometer Space Antenna (Danzmann&etal.1996.LISA) is expected to observe up to several hundreds of events per year (Sesanaetal.2005.2007.2010).," The space-based Laser Interferometer Space Antenna \citep[ LISA]{dan+al96} is expected to observe up to several hundreds of events per year \citep{s05,ses+al07,ses+al10}." +.. The loudest signals at LISA frequencies. fmllz. should originate from coalescing massive black hole binaries (MBHBs) with total masses in the range 10°- 10°AL. out to z~ 10-15 (Hughes2002:Kleinetal.2009).," The loudest signals at LISA frequencies, $f\sim \mathrm{mHz}$, should originate from coalescing massive black hole binaries (MBHBs) with total masses in the range $10^3$ $10^7~M_\odot$ out to $z\sim 10$ $15$ \citep{hug02,kle+al09}." +. Whenever a new experimental set-up to observe the universe starts working. new possibilities open out.," Whenever a new experimental set-up to observe the universe starts working, new possibilities open out." + In a previous paper. we discussed a potential new channel for LISA science: multiple imaging of GW sources by intervening strong lensing galaxies (Serenoetal.2010).," In a previous paper, we discussed a potential new channel for LISA science: multiple imaging of GW sources by intervening strong lensing galaxies \citep{ser+al10}." + Lensing of distant sources has been long considered as a test for cosmological theoriestherein)., Lensing of distant sources has been long considered as a test for cosmological theories. + GW sources might allow for a variation of these classical tests., GW sources might allow for a variation of these classical tests. + The main novelty of making cosmography with LISA relies on the property of MBHBs of being standard sirens (Schutz 1986)., The main novelty of making cosmography with LISA relies on the property of MBHBs of being standard sirens \citep{sch86}. +. The luminosity distance to the inspiral GWs can. be determined with good accuracy and several methods have already been proposed to exploit this property (Holz&Hughes 2010».," The luminosity distance to the inspiral GWs can be determined with good accuracy and several methods have already been proposed to exploit this property \citep{ho+hu05,bro+al10,sha+al10,hil+al10}." + The main idea on the table is to build-up the Hubble diagram., The main idea on the table is to build-up the Hubble diagram. + The relation between distance and redshift changes for different cosmological theories or different cosmological parameters., The relation between distance and redshift changes for different cosmological theories or different cosmological parameters. + However. the redshift cannot be measured from the analysis of gravitational waves alone.," However, the redshift cannot be measured from the analysis of gravitational waves alone." + The use of MBHBs as cosmological probes should rely on the identification of the electromagnetic counterpart in order to measure the redshift of the source., The use of MBHBs as cosmological probes should rely on the identification of the electromagnetic counterpart in order to measure the redshift of the source. + Lensing offers an alternative tool., Lensing offers an alternative tool. + In the classical Hubble, In the classical Hubble +around a spectroscopic binary (Torres ct al.,around a spectroscopic binary (Torres et al. + 2001). aud the first around a star with evidence or a disk (Javawardlana et al.," 2001), and the first around a star with evidence for a disk (Jayawardhana et al." + 1999)., 1999). + While the first four wow dwarfs confirmed as companions all orbit A-type stars. au nU star also Uu have a brown dwarf companion (c.g. IIR.n 7329 with PAetral type A0).," While the first four brown dwarfs confirmed as companions all orbit M-type stars, an A-type star also can have a brown dwarf companion (e.g. HR 7329 with spectral type A0)." + Therefore. both ΠΟ 199] (Fs) and TID 358623 (IX7-MO) are promising targets for the direct Huaeine search for sub-stellar companious.," Therefore, both HD 199143 (F8) and HD 358623 (K7-M0) are promising targets for the direct imaging search for sub-stellar companions." + The probability for the two companion candidates detected by JBOL to be unrelated backerounu objects happen to lie iu he line-of-sight jext to the primary stars ix very μαμα (BOL)., The probability for the two companion candidates detected by JB01 to be unrelated background objects happen to lie in the line-of-sight next to the primary stars is very small (JB01). + However. oue should no rely on such probabilities. even when observing only a small sample.," However, one should not rely on such probabilities, even when observing only a small sample." +" Some previous very fait sub-stellar companion candidates (e.g, Terebey et al.", Some previous very faint sub-stellar companion candidates (e.g. Terebey et al. + 1998. Neuhauuscr ot al.," 1998, Neuhäuuser et al." + 2000a) with very low background probability were fouud to be backeround stars by follow-up spectroscopy (Terchbey et al., 2000a) with very low background probability were found to be background stars by follow-up spectroscopy (Terebey et al. + 2000. Neubauuser et al.," 2000, Neuhäuuser et al." + 2001)., 2001). + This shows how important it is to take multi-epoch images aud spectra., This shows how important it is to take multi-epoch images and spectra. + We present our inagiug observations m Sect., We present our imaging observations in Sect. + 2 and the resulting photometry for the two stars and their companion candidates in Sect., 2 and the resulting photometry for the two stars and their companion candidates in Sect. + 3., 3. + Astrometry is presented in Sect., Astrometry is presented in Sect. + to check whether the companion candidates are co-moving with their putative primary stars., 4 to check whether the companion candidates are co-moving with their putative primary stars. + Then. in Sect.," Then, in Sect." + 5. we present an ILEbaud spectiuui of oue of the two companion candidates.," 5, we present an H-band spectrum of one of the two companion candidates." + We conclude in Sect., We conclude in Sect. + 6, 6. + We observed TD 199115 aud ΠΟ 358623 several times with the Son of Isaac 1] at the 3.11 New Technology Telescope (NTT) of the European Southern Observatory (ESO) on La Silla. Chile.," We observed HD 199143 and HD 358623 several times with the Son of Isaac ) at the 3.5m New Technology Telescope (NTT) of the European Southern Observatory (ESO) on La Silla, Chile." + The SofI detector is an Hawai UeCdTe 1021« array with 18.5712 pixel sizes., The SofI detector is an Hawaii HgCdTe $1024 \times 1024$ array with $18.5 \mu$ m pixel sizes. + We used the μια. Sofl field. with its best pixel scale for better angular resolution aud determined the pixel scale bv comparing the separations jetween several stars on other images taken in the same nieht with 2\LASS images of the same fields tobe 0.150+0.002” or pixel., We used the small SofI field with its best pixel scale for better angular resolution and determined the pixel scale by comparing the separations between several stars on other images taken in the same night with 2MASS images of the same fields to be $0.150 \pm 0.002^{\prime \prime}$ per pixel. + Darks. flats. and standards were observed in the same nights with the same setup and data reduction was done with versjon 38. a C-based software bikebrary.," Darks, flats, and standards were observed in the same nights with the same set-up and data reduction was done with version 3.8, a C-based software library." + While is made for VLT data reduction. e.g. the Infrared Thnaging Aud Array Camera ISAAC). and not enaranteed to work for Sofl data. it also docs work for Sofl imagine data reduction (dark. flat. shift|ada): after all. Sof is the Sou of Isaac.," While is made for VLT data reduction, like e.g. the Infrared Imaging And Array Camera (ISAAC), and not guaranteed to work for SofI data, it also does work for SofI imaging data reduction (dark, flat, shift+add); after all, SofI is the Son of Isaac." + See Table 1 for the observations log., See Table 1 for the observations log. + Then. we observed ΠΟ 199113 and WD 2358625 at the end of the nights of 1 2 July 2001. respectively. usine SIIARP-I (System for μοι Aneular Resolution Pictures. Hofuigun ct al.," Then, we observed HD 199143 and HD 358623 at the end of the nights of 1 2 July 2001, respectively, using SHARP-I (System for High Angular Resolution Pictures, Hofmann et al." + 1992) at the NTT., 1992) at the NTT. + The targets were placed outo the two lower. ie. western. SITARDP-I quadrants. because they have better pixel aud flat field characteristics.," The targets were placed onto the two lower, i.e. western SHARP-I quadrants, because they have better pixel and flat field characteristics." +" The data were corrected for bad pixels followed by a sky mage subtraction aud the application of a ΠατΠοια,", The data were corrected for bad pixels followed by a sky image subtraction and the application of a flat-field. + For each baud we then co-added the256« pixel frauues using the brightest pixel as shift-aud-add reference (Cliistou 1991)., For each band we then co-added the $256 \times 256$ pixel frames using the brightest pixel as shift-and-add reference (Christou 1991). +" Exposure times aud. EWIIMiu the final co-added images (using the SITARP. pixel scale of 0.0191"". see also Neuhliiuuscer et al."," Exposure times and FWHM in the final co-added images (using the SHARP pixel scale of $0.0491^{\prime \prime}$, see also Neuhäuuser et al." + 2000a) are eiven du Table 1, 2000a) are given in Table 1. + The companion candidates detected in J EK bv JBOL in their May 2001 ADONIS images are also detected iu our II-lxud Soff images in Dec. 2000 and Dec. 2001 and as well in JIS in our July 2001 SITARP-I images., The companion candidates detected in J K by JB01 in their May 2001 ADONIS images are also detected in our H-band SofI images in Dec. 2000 and Dec. 2001 and as well in JHK in our July 2001 SHARP-I images. + We, We +Done (2004) suggested that the πο excess is actually a fake continuum component due to a broad absorption trough at ~2 5 keV. arising in partially ionized gas along the line of sight subject to high. velocity smearing.,"Done (2004) suggested that the soft excess is actually a fake continuum component due to a broad absorption trough at $\sim$ 2–5 keV, arising in partially ionized gas along the line of sight subject to high velocity smearing." + The latest. simulations. however. prove that 1ο properties of any realistic accretion disc wind are not able to reproduce the observed smoothness of the soft excess (Sehurch Done 2007: Schurch. Done Proga 2009).," The latest simulations, however, prove that the properties of any realistic accretion disc wind are not able to reproduce the observed smoothness of the soft excess (Schurch Done 2007; Schurch, Done Proga 2009)." + Another viable explanation is that of rellection. from. the photoionized surface lavers of the aceretion disc itself. where the relativistic motion of the infalling matter. provides the blurring of the narrow atomic features (Fabian ct al.," Another viable explanation is that of reflection from the photoionized surface layers of the accretion disc itself, where the relativistic motion of the infalling matter provides the blurring of the narrow atomic features (Fabian et al." + 2002: Crummy ct al., 2002; Crummy et al. + 2006)., 2006). + This moclel occasionally implies a strong suppression of the intrinsic power law in order to account for a prominent soft excess. as justified in the context of strong gravitational light bending (Miniutti Fabian 2004).," This model occasionally implies a strong suppression of the intrinsic power law in order to account for a prominent soft excess, as justified in the context of strong gravitational light bending (Miniutti Fabian 2004)." + On sheer statistical grounds all the interpretations outlined so far vielcL acceptable results (Sobolewska Done 2007)., On sheer statistical grounds all the interpretations outlined so far yield acceptable results (Sobolewska Done 2007). + To pursue further this Kind. of study. access is needed to energies beyond. 10 keV. where the physica models make dillerent. predictions.," To pursue further this kind of study, access is needed to energies beyond $\sim$ 10 keV, where the physical models make different predictions." + The advent. of (Mitsucla et al., The advent of (Mitsuda et al. + 2007) and its hard. N-rav. detector. (LIND: Takahashi et al., 2007) and its hard X-ray detector (HXD; Takahashi et al. + 2007) has made it possible to put. solic spectral constraints up to 0 keV. opening a new era of AGN observations.," 2007) has made it possible to put solid spectral constraints up to $\sim$ 70 keV, opening a new era of AGN observations." + Concerning the soft. excess. it. shoulc also be noticed that the possible presence of complex are variable absorption can mask the intrinsic appearance of this critical component.," Concerning the soft excess, it should also be noticed that the possible presence of complex and variable absorption can mask the intrinsic appearance of this critical component." + Indeed. warm absorbers are very common among type 1 XGN (Crenshaw. Ixraemer George 2003: Blustin et al.," Indeed, warm absorbers are very common among type 1 AGN (Crenshaw, Kraemer George 2003; Blustin et al." + 2005)., 2005). + Lt is therefore desirable to selec a target with the cleanest view of the nuclear regions., It is therefore desirable to select a target with the cleanest view of the nuclear regions. + Arakelian 120 (2= 0.0327) is a rare case of a ‘hare’ Sevlert galaxy. hence it represents the optimal candidate to test whether the soft. excess is a signature of blurrec reflection from the inner accretion disc.," Arakelian 120 $z=0.0327$ ) is a rare case of a `bare' Seyfert galaxy, hence it represents the optimal candidate to test whether the soft excess is a signature of blurred reflection from the inner accretion disc." + No evidence for redcdening is found in the infrared (Mrd et al., No evidence for reddening is found in the infrared (Ward et al. + LOST). anc ultraviolet observations establish that Ark 120 is devoic of intrinsic absorption (Crenshaw ct al.," 1987), and ultraviolet observations establish that Ark 120 is devoid of intrinsic absorption (Crenshaw et al." + 1999)., 1999). + In the soft X-rav band the source has been shown to have a steep spectrum by both Cl'urner Pounds 1989) ane (Brandt et al., In the soft X-ray band the source has been shown to have a steep spectrum by both (Turner Pounds 1989) and (Brandt et al. + 1993). while the ltellection Grating Spectrometer data allow stringent upper limits (~12 orders of magnitude lower than those of usua σον[ος 13) to be placed on the ionic column densities of any possible warm. absorber (Vaughan ct al.," 1993), while the Reflection Grating Spectrometer data allow stringent upper limits $\sim$ 1–2 orders of magnitude lower than those of usual Seyfert 1s) to be placed on the ionic column densities of any possible warm absorber (Vaughan et al." + 2004)., 2004). + Lt is worth emphasizing that Ark 120 is a broad-line Sevfert 1 (BLS) ealaxy. whereas the soft excess has been long associate with narrow-line sources only.," It is worth emphasizing that Ark 120 is a broad-line Seyfert 1 (BLS1) galaxy, whereas the soft excess has been long associated with narrow-line sources only." + NLSIs are rather eccentric objects. known for their very steep X-ray. spectrum (Boller. Brandt Fink 1996). high aceretion rate (Cirupe 2004. anc references therein). largc-aniplituce X-ray. variability on short timescales (Callo et al.," NLS1s are rather eccentric objects, known for their very steep X-ray spectrum (Boller, Brandt Fink 1996), high accretion rate (Grupe 2004, and references therein), large-amplitude X-ray variability on short timescales (Gallo et al." + 2004). metal overabundance (Shemmer Netzer 2002: Fabian et al.," 2004), metal overabundance (Shemmer Netzer 2002; Fabian et al." + 2009) and enhance star formation (Sani et al., 2009) and enhanced star formation (Sani et al. + 2010)., 2010). + Ark 120 is an outstanding counter example of a normal DLSI with a prominent soft excess. ensuring as such a completely unbiased. exploration of this component.," Ark 120 is an outstanding counter example of a normal BLS1 with a prominent soft excess, ensuring as such a completely unbiased exploration of this component." + ‘This work is organized as follows: Section 2 concerns the observation ancl data reduction: our results are presented ancl Lully discussed. in Section 3. while in Section + we summarize our conclusion and outline the future research.," This work is organized as follows: Section 2 concerns the observation and data reduction; our results are presented and fully discussed in Section 3, while in Section 4 we summarize our conclusion and outline the future research." + Ark 120 was observed by on 2007 April 1.3 in the LIND nominal position. with a resulting net exposure of ~101 ks for the X-ray imaging spectrometer. (NIS: lxovama oet al.," Ark 120 was observed by on 2007 April 1–3 in the HXD nominal position, with a resulting net exposure of $\sim$ 101 ks for the X-ray imaging spectrometer (XIS; Koyama et al." + 2007) and ~S9 ks for the LIND/PIN detector., 2007) and $\sim$ 89 ks for the HXD/PIN detector. + Events were collected. by the three operational XIS CCDs in both 3x3 and 5x5 editing modes (71 and 30 ks exposures. respectively).," Events were collected by the three operational XIS CCDs in both 3x3 and 5x5 editing modes (71 and 30 ks exposures, respectively)." + Following the standard. procedure illastrated in the Data Reduction we used the 6.8 package to obtain a new set of clean event Liles for each detector. editing. mode and telemetry by reprocessing the unfiltered: events with the latest calibrations.," Following the standard procedure illustrated in the Data Reduction we used the 6.8 package to obtain a new set of clean event files for each detector, editing mode and telemetry by reprocessing the unfiltered events with the latest calibrations." + The source spectra and light curves were extracted from circular regions with racius of ~3.5 arcmin (200 pixels) centred. on the target. while the background was evaluated on the same chip from adjacent regions devoid of significant contamination.," The source spectra and light curves were extracted from circular regions with radius of $\sim$ 3.5 arcmin (200 pixels) centred on the target, while the background was evaluated on the same chip from adjacent regions devoid of significant contamination." +" Finally. the source ancl background: spectra. from the two front-illuminated detectors (XISO ancl NIS3). as well as the response files generated through the ""xisresp! script. were merged. and rebinned by a factor of 4."," Finally, the source and background spectra from the two front-illuminated detectors (XIS0 and XIS3), as well as the response files generated through the `xisresp' script, were merged and rebinned by a factor of 4." +" Concerning the HILIND/PIN data reduction. we again reprocessed the unfiltered event files using the standard tools and got the output spectrum by running the ""hxdpinxbpi script. which takes into account the contribution of both the non X-ray and the cosmic X-ray. background. ancl applies the dead time correction."," Concerning the HXD/PIN data reduction, we again reprocessed the unfiltered event files using the standard tools and got the output spectrum by running the `hxdpinxbpi' script, which takes into account the contribution of both the non X-ray and the cosmic X-ray background and applies the dead time correction." + This returned a source count rate of (12.10:3)107 lo corresponding to 18.3 per cent of the PIN total counts.," This returned a source count rate of $(12.1 \pm 0.3) \times 10^{-2}$ $^{-1}$, corresponding to 18.7 per cent of the PIN total counts." + The spectral analysis has been performed. using the v12.6 fitting package. ancl involves only the 0.5 keV enerev range of the two Lront-illuminated XLS detectors: indeed. the 1.72.0 keV interval appears to be stronely alfected by systematic calibration uncertainties around the instrumental silicon Ix-edge. hence it has been excluded.," The spectral analysis has been performed using the v12.6 fitting package, and involves only the 0.5--12 keV energy range of the two front-illuminated XIS detectors; indeed, the 1.7–2.0 keV interval appears to be strongly affected by systematic calibration uncertainties around the instrumental silicon K-edge, hence it has been excluded." + Phe NISI. back-illuminatecl spectrum has been emploved throughout as an independent. check., The XIS1 back-illuminated spectrum has been employed throughout as an independent check. + Ehe source is confidentIy detected at high energy up to ~4050 keV: we have therefore considered the conservative 1240 keV range of the HXD/PIN spectrum., The source is confidently detected at high energy up to $\sim$ 40–50 keV; we have therefore considered the conservative 12–40 keV range of the HXD/PIN spectrum. + In order to allow the use of 4? minimization during the spectral fitting. the NIS data were grouped so that each energy channel contains no less than 20 counts. while a minimum of 50 counts per bin was adopted for the IND/PIN spectrum.," In order to allow the use of $\chi^2$ minimization during the spectral fitting, the XIS data were grouped so that each energy channel contains no less than 20 counts, while a minimum of 50 counts per bin was adopted for the HXD/PIN spectrum." + The uncertainties reported in this work correspond to the 90 per cent confidence intervals ο.= 271) lor the single. parameter of interest., The uncertainties reported in this work correspond to the 90 per cent confidence intervals $\Delta \chi^2 = 2.71$ ) for the single parameter of interest. + Fluxes and count rates are given at the le level., Fluxes and count rates are given at the $\sigma$ level. + In Fig., In Fig. + I. we show the data/mocdel ratio plot obtained by, \ref{rp} we show the data/model ratio plot obtained by +are inseusitive to the ratio of the energy densities in the magnetic field aud electron population.,are insensitive to the ratio of the energy densities in the magnetic field and electron population. +citemoswO04)) showed that these stars are indeed both hotter and more helium-rich than the canonical EHB stars.,) showed that these stars are indeed both hotter and more helium-rich than the canonical EHB stars. + However. the blue hook stus still show. considerable amounts of hydrogen.," However, the blue hook stars still show considerable amounts of hydrogen." + Unfortunately due to limited resolution and signal-to-notse (S/N) we could not derive good abundances for C and N. Instead we could only state that the most helium-rich stars appear to show some evidence for C/N enrichment., Unfortunately due to limited resolution and signal-to-noise ) we could not derive good abundances for C and N. Instead we could only state that the most helium-rich stars appear to show some evidence for C/N enrichment. + Therefore we started a project to obtain higher resolution spectra of EHB and blue hook stars mw Cen., Therefore we started a project to obtain higher resolution spectra of EHB and blue hook stars in $\omega$ Cen. + We selected stars along the blue HB in w Cen from the multi-band (U.B.V. /) photometry of Castellani et al. (2007)).," We selected stars along the blue HB in $\omega$ Cen from the multi-band $U,B,V,I$ ) photometry of Castellani et al. \cite{cast07}) )." + These data were collected with the mosaic CCD camera Wide Field Imager available at the 2.2m ESO/MPI telescope., These data were collected with the mosaic CCD camera Wide Field Imager available at the 2.2m ESO/MPI telescope. + The field of view covered by the entire mosaic 1s 42x48’ across the center of the cluster., The field of view covered by the entire mosaic is $42'\times 48'$ across the center of the cluster. + These data together with multiband data from the Advanced Camera for Surveys on board the Hubble Space Telescope provided the largest sample of HB stars (53.200) ever collected in a globular cluster.," These data together with multiband data from the Advanced Camera for Surveys on board the Hubble Space Telescope provided the largest sample of HB stars $\approx$ 3,200) ever collected in a globular cluster." +" Among them we concentrated on the stars at the faint end of the HB. which are the most likely ""blue hook"" candidates as shown by Moehler et al. (2002.. 2004))."," Among them we concentrated on the stars at the faint end of the HB, which are the most likely “blue hook” candidates as shown by Moehler et al. \cite{mosw02}, \cite{mosw04}) )." + In order to avoid crowding problems. we only selected isolated EHB stars.," In order to avoid crowding problems, we only selected isolated EHB stars." + The astrometry was performed using the UCAC? catalog (Zacharias et al. 2004)).," The astrometry was performed using the UCAC2 catalog (Zacharias et al. \cite{zacharias2004}) )," + which does not cover the central crowded regions., which does not cover the central crowded regions. + However. thanks to the large field covered by current dataset the astrometric solution is based on «3.000 objects with an rms error of 0006.," However, thanks to the large field covered by current dataset the astrometric solution is based on $\approx$ 3,000 objects with an rms error of 06." + The spectroscopic data were obtained in 2005 (4 observations) and in 2006 (5 observations) in. Service Mode using the MEDUSA mode of the multi-object fibre spectrograph FLAMES+GIRAFFE on the UT2 Telescope of the VLT., The spectroscopic data were obtained in 2005 (4 observations) and in 2006 (5 observations) in Service Mode using the MEDUSA mode of the multi-object fibre spectrograph $+$ GIRAFFE on the UT2 Telescope of the VLT. + We used the low spectroscopic resolution mode with the spectral range — ((LR2. R = 6400) and observed spectra for a total of 101 blue hook and canonical blue HB/EHB star candidates and 17 empty positions for sky background.," We used the low spectroscopic resolution mode with the spectral range – (LR2, R = 6400) and observed spectra for a total of 101 blue hook and canonical blue HB/EHB star candidates and 17 empty positions for sky background." + For our analysis we used the pipeline reduced data., For our analysis we used the pipeline reduced data. + For each exposure we subtracted the median of the spectra from the sky fibres from the extracted spectra., For each exposure we subtracted the median of the spectra from the sky fibres from the extracted spectra. + We corrected all spectra for barycentric motions., We corrected all spectra for barycentric motions. + The individual spectra of each target star have been eross-correlated with appropriate template spectra. in order to search for radial velocity variations.," The individual spectra of each target star have been cross-correlated with appropriate template spectra, in order to search for radial velocity variations." + Since the few spectra per object did not permit a sophisticated period search. we determined the standard deviation. of the radial velocity measurements for each star and compared it with the S/N ratio of the spectra.," Since the few spectra per object did not permit a sophisticated period search, we determined the standard deviation of the radial velocity measurements for each star and compared it with the S/N ratio of the spectra." + As expected. the standard deviation of the radial velocity measurements decreases with increasing S/N ratio.," As expected, the standard deviation of the radial velocity measurements decreases with increasing S/N ratio." + None of our target stars deviates significantly from this correlation. which would be the case for close binaries.," None of our target stars deviates significantly from this correlation, which would be the case for close binaries." + Therefore none of our target stars appears to be in à close binary system., Therefore none of our target stars appears to be in a close binary system. + After verifying that there were no radial velocity variations we co-added all spectra for each star., After verifying that there were no radial velocity variations we co-added all spectra for each star. +" The co-added and velocity-corrected spectra were fitted with various model atmospheres: metal-free helium-rich non-LTE (Werner Dreizler 1999)), metal-free helium-poor non-LTE (Napiwotzki 1997)). and metal-rich heltum-poor LTE (Moehler et al. 2000))"," The co-added and velocity-corrected spectra were fitted with various model atmospheres: metal-free helium-rich non-LTE (Werner Dreizler \cite{wedr99}) ), metal-free helium-poor non-LTE (Napiwotzki \cite{napi97}) ), and metal-rich helium-poor LTE (Moehler et al. \cite{mosw00}) )" + as described in Moehler et al. (2004))., as described in Moehler et al. \cite{mosw04}) ). + This procedure yielded the effective temperatures. surface gravities. and helium abundances shown in Figs.," This procedure yielded the effective temperatures, surface gravities, and helium abundances shown in Figs." + | and 2., 1 and 2. + In this paper we concentrate only on the hottest HB stars with 20.000 K. The helium-poor stars in Fig.," In this paper we concentrate only on the hottest HB stars with $>$ 20,000 K. The helium-poor stars in Fig." + | basically agree with the predictions of canonical evolutionary theory in that they populate the HB up to its hot end and then also contribute some evolved stars at higher effective temperatures and lower surface gravities.," \ref{Fig:Teff_logg} + basically agree with the predictions of canonical evolutionary theory in that they populate the HB up to its hot end and then also contribute some evolved stars at higher effective temperatures and lower surface gravities." + As we move to hotter stars 330.000 KK). we find a clump of stars populating the range in effective temperature and surface gravity between a fully mixed late hot flasher and the hot edge of the canonical HB.," As we move to hotter stars $\gtrsim$ K), we find a clump of stars populating the range in effective temperature and surface gravity between a fully mixed late hot flasher and the hot edge of the canonical HB." + These stars show roughly solar helium abundance (cf., These stars show roughly solar helium abundance (cf. + Fig. 2))., Fig. \ref{Fig:Teff_loghe}) ). + The hottest stars lying along the evolutionary track of a fully mixed late hot flasher show the highest helium abundances.," The hottest stars lying along the evolutionary track of a fully mixed late hot flasher show the highest helium abundances," +The first assumption is justified by the small distance οποσα the two stars (—10 AU).,The first assumption is justified by the small distance between the two stars $\sim10$ AU). + The seco asstuuptiou is less strouely justified and one can imagine a low colui eusitv component without detectable nietal Lue. ot with a still significant absorption atα," The second assumption is less strongly justified and one can imagine a low column density component without detectable metal line, but with a still significant absorption at." +"ν, The uost we can argue is that it is possible to ft the ""pure oeierstelbu ine only with the BC aud the LIC as found with the uectal lines aud the no extra coniponent is required by jo data.", The most we can argue is that it is possible to fit the “pure interstellar” line only with the BC and the LIC as found with the metal lines and that no extra component is required by the data. + We did uo fud anv width or velocity structure unexplaimed by our simple iuterstellar model oonlv two components). as Linsky Wood (1996)) did oon the sightline of a Con.," We did not find any width or velocity structure unexplained by our simple interstellar model only two components), as Linsky Wood \cite{linsky96}) ) did on the sightline of $\alpha$ Cen." + This led them to the detection of an extra component they called the “lvdrogen wall”, This led them to the detection of an extra component they called the “hydrogen wall”. + We aro however unable to formally exclude the presence of additional ow column density clouds., We are however unable to formally exclude the presence of additional low column density clouds. + The third assumption is justified again bv the oxoxinitv between the two targets whereas their absorptions are very different., The third assumption is justified again by the proximity between the two targets whereas their absorptions are very different. + This favours processes inked to the stars as causes of the extra aabsorptious., This favours processes linked to the stars as causes of the extra absorptions. + Finally these suspected processes. the wind roni Sirius A and the Sirius D photospleric line shape. are unable to disturb the other wing of the line.," Finally these suspected processes, the wind from Sirius A and the Sirius B photospheric line shape, are unable to disturb the other wing of the line." + The reliability of our result is linked to the robustuess of these hvpotheses aud to the possible inaccuracy in the netal cobluun densities. as described in the 5.1..," The reliability of our result is linked to the robustness of these hypotheses and to the possible inaccuracy in the metal column densities, as described in the \ref{abundances_and_depletions}." + We can note however that the are column densities. suspected to be too high. do not seriously coustrain the fait.," We can note however that the and column densities, suspected to be too high, do not seriously constrain the fit." + Iudeed. the radial velocity shift of 5.9 bbetween BC aud LIC applied to the line Is essentially οςistrained by theFeu. and lines which oulv show clearly the DC aud LIC componcuts.," Indeed, the radial velocity shift of 5.9 between BC and LIC applied to the line is essentially constrained by the, and lines which only show clearly the BC and LIC components." + Moreover. we used1 aud not Olas tracer ofITI. in order to areue that the column deusitv ratio between LIC aud DC should be probably ranging between 0.5 aud 1.," Moreover, we used and not as tracer of, in order to argue that the column density ratio between LIC and BC should be probably ranging between 0.5 and 4." + We thus concluded that possible inaccuracies iu the and cohunn deusities do uot affect our eevaluation., We thus concluded that possible inaccuracies in the and column densities do not affect our evaluation. + Although the value of οσο] be between 0 and 1.6«10D the best result is obtained with a low value.," Although the value of could be between 0 and $1.6\times10^{-5}$, the best result is obtained with a low value." + We found thus à abundance which secs to be low in oue of the two compoucuts (BC) toward Sirius without being able to fined an artifact able to explain that result., We found thus a abundance which seems to be low in one of the two components (BC) toward Sirius without being able to find an artifact able to explain that result. + O aud N are not overabuudant in this component., O and N are not overabundant in this component. + It is thus difficult to see DC as a cloud polluted by D ree material eyected bv the auetarv nebula preceeding he formation of the white dwarf Sinus D since furthermore its radial velocity shoud ο Dlne-shifted. whereas the DC one is redshifted.," It is thus difficult to see BC as a cloud polluted by D free material ejected by the planetary nebula preceeding the formation of the white dwarf Sirius B since furthermore its radial velocity shoud be blue-shifted, whereas the BC one is redshifted." + This act does not aeree with the simple idea of DC being an expanding shell of material ejected by the planetary webula related to the white dwarf Sinus D. After G191-B2B (Vidal-Madjar et al. 10051) , This fact does not agree with the simple idea of BC being an expanding shell of material ejected by the planetary nebula related to the white dwarf Sirius B. After G191-B2B (Vidal-Madjar et al. \cite{avm98}) ) +and ó Ori (Jenkins et al. 1999)), and $\delta$ Ori (Jenkins et al. \cite{jenkins99}) ) + on the line of sight of which low wwere measured. Sirius secuis to be a good candidate for finding another low interstellar deuterum abundance.," on the line of sight of which low were measured, Sirius seems to be a good candidate for finding another low interstellar deuterium abundance." + The cause of these variatious has to be understood iu order to know what is the actua value of the(D/ID;sa;. if any.," The cause of these variations has to be understood in order to know what is the actual value of the, if any." + It is diffüeult to see interstellar deuterium as the siuuple tracer of the galactic chemical evolution., It is difficult to see interstellar deuterium as the simple tracer of the galactic chemical evolution. + The study ofits possible variation as a fiction of the radial distance to the galactic center max help us in that matter., The study of its possible variation as a function of the radial distance to the galactic center may help us in that matter. + Moreover. if irafio actually prescuts dispersion. oue can argue that the other deuterimu abundance evaluations. pproto-solar and primordial abundances. can also present dispersion.," Moreover, if ratio actually presents dispersion, one can argue that the other deuterium abundance evaluations, proto-solar and primordial abundances, can also present dispersion." + Indeed. variatious of iuterstellar abundiuce of deuterium was detected thanks to the huge nunber of sigehtliues available (several tens). whereas proto-solar and primordial abundances are deteriined ouly frou few targets.," Indeed, variations of interstellar abundance of deuterium was detected thanks to the large number of sightlines available (several tens), whereas proto-solar and primordial abundances are determined only from few targets." + Talking iuto consideration this problem. obscrving deuteriun in the interstellar imuediun toward a large uunuber of sighitlines is a good wax to proceed.," Taking into consideration this problem, observing deuterium in the interstellar medium toward a large number of sightlines is a good way to proceed." + We have presented new spectroscopic observations of Siius A and Sirius B performed usiug IIST-CIIRS., We have presented new spectroscopic observations of Sirius A and Sirius B performed using HST-GHRS. + 11 iuterstellar lines were detected at hieh and/or media spectral resolutiou., 14 interstellar lines were detected at high and/or medium spectral resolution. + The sightline. which is asuned to xeseut the same structure toward the two stars. ds coniposed bv two clouds: the Blue Component (BC) aud he Local Iuterstellar Cloud (LIC). in aereciment with the xevious HST-CGIIRS observations of Sirius A reported by Lallement et al. (199 1)).," The sightline, which is assumed to present the same structure toward the two stars, is composed by two clouds: the Blue Component (BC) and the Local Interstellar Cloud (LIC), in agreement with the previous HST-GHRS observations of Sirius A reported by Lallement et al. \cite{lalle}) )." + The three main results of our observations are the ollowiug:, The three main results of our observations are the following: +As such. we have fixed logg=L12zx0.015 as inferred from the best-fit of the Nepler photometiv.,"As such, we have fixed $\logg=\koicurSMElogg$ as inferred from the best-fit of the Kepler photometry." + The analysis vields =56304100 A.[V/7I] —0.340.1. esin;=ΕΤΕ1 5.," The analysis yields $\koicurSMEteff$ K, $\koicurSMEfeh$, $\vsini=\koicurSMEvsin$ ." + When corrected for the orbital motion of aand the TRES zero point offset. determined by loue-term monitoring of the LAU RV standard ΠΟ 159155. we find the absolute mean svstemic velocity of Πο be 23.82+0.10i.," When corrected for the orbital motion of and the TRES zero point offset, determined by long-term monitoring of the IAU RV standard HD 182488, we find the absolute mean systemic velocity of to be $-23.82\pm0.10$." +" Note that this docs not mcelude anv uncertainty in the absolute velocity of IID 152188, which we take to be -21.508i. as observed by Nideveretal.(2002)."," Note that this does not include any uncertainty in the absolute velocity of HD 182488, which we take to be -21.508, as observed by \cite{nidever02}." +. We also obtained Ixeck HIRES spectra aud estimated the line strengths of Squ.=0.322+0.01 aaud L6lforlvepler (assumingDB|V—0.52)., We also obtained Keck HIRES spectra and estimated the line strengths of $0.322\pm0.01$ and $-4.61$ for (assuming B-V=0.82). + TheCa Hinestrengthsarcaqoodindicatorofthestelaracti city 20dsureiients, The line strengths are a good indicator of the stellar activity \citep{isaacson10}. + The astrometry derived from theWepler images themselves. when combined with high-resolution mages of the target neighborhood. provides a very powerful tool for identifving background eclipsing binaries bleuded with aud contaminating the target images (Datallia 2010).," The astrometry derived from the images themselves, when combined with high-resolution images of the target neighborhood, provides a very powerful tool for identifying background eclipsing binaries blended with and contaminating the target images \citep{batalha10}." +. The astrometry of iudicated uo significant offset during transifs du iu quarter. and computed offsets are well within the formal Jesenia radius of confusion.," The astrometry of indicated no significant offset during transits in any quarter, and computed offsets are well within the formal 3-sigma radius of confusion." + Therefore lis considered to be the source for the trausits observed iu the ]liehteurves., Therefore is considered to be the source for the transits observed in the lightcurves. + We obtained an Ebaud image at the Lick Observatory laueter. Nickel telescope with the Direct huagiug Camera (see Figure 3)).," We obtained an I-band image at the Lick Observatory 1-meter, Nickel telescope with the Direct Imaging Camera (see Figure \ref{fig:image}) )." +" The L.0° arc-second secing revealed no companions frou 27 to 5 from the star's center, down to a lait of 19th maenitude."," The 1.0"" arc-second seeing revealed no companions from 2"" to 5"" from the star's center, down to a limit of 19th magnitude." + Similar conchision were reached using UKIRT J-baud tages (Figure 3))., Similar conclusion were reached using UKIRT J-band images (Figure \ref{fig:image}) ). + We obtained precise radial velocity (RV) follow-up observations of wwith the IIET (Ramsey et al., We obtained precise radial velocity (RV) follow-up observations of with the HET (Ramsey et al. + 1998) aud its TRS spectrograph (Tull1998). at. McDonald. Observatory., 1998) and its HRS spectrograph \citep{tull98} at McDonald Observatory. + wowas observed ten times iu the 2010 observiug season. from 2010. August 22 until 2010 November 22.," was observed ten times in the 2010 observing season, from 2010 August 22 until 2010 November 22." + The iustrumnental setup aud observing mode are described iu more detail in Eudletal.(2011)., The instrumental setup and observing mode are described in more detail in \cite{endl11}. +. Hs the second planet coufiiied with WET after Ἱνωρία--15b (Endletal.2011)., is the second planet confirmed with HET after Kepler-15b \citep{endl11}. +. We eunploved a ‘snap shot? strategy. using relatively short exposures of 1200 seconds. that vield a SNR sufficient to detect the racial-velocity sienal of a hot-Jupiter.," We employed a “snap shot” strategy, using relatively short exposures of 1200 seconds, that yield a SNR sufficient to detect the radial-velocity signal of a hot-Jupiter." + Thirteen spectra were taken with the L-cell iu the light path to compute precise ciffereutial RVs., Thirteen spectra were taken with the $_2$ -cell in the light path to compute precise differential RVs. + These spectra have a typical S/N-ratio of 32 per resolution clement., These spectra have a typical S/N-ratio of $32$ per resolution element. + The radial velocity data are listed in Table 1.. We use, The radial velocity data are listed in Table \ref{tab:RVs}. +Gaonssfit. the generalized least-squares software of Jeffervsctal.(1988) to fit a Nepleran orbit to the HRS radial velocity data.," We use, the generalized least-squares software of \citet{jefferys88} to fit a Keplerian orbit to the HRS radial velocity data." + Oulv the velocity zero-point and the radial velocity semiesuuplitude A are included as free parouneters in the fitting process., Only the velocity zero-point and the radial velocity semi-amplitude $K$ are included as free parameters in the fitting process. + We first fitted the radial-velocity data alouc. requiring the orbit to be circular (ο=0) aud adopting the ephemeris derived from the pphotometiv.," We first fitted the radial-velocity data alone, requiring the orbit to be circular $e=0$ ) and adopting the ephemeris derived from the photometry." + The best-fit orbit has a A of 15nuuuss à \2 of 0.9 and a residual ruis scatter around the fit of 52 nuuss|.," The best-fit orbit has a $K$ of $420\pm15$ $^{-1}$, a $\chi^{2}_{\rm red}$ of $0.9$ and a residual rms scatter around the fit of 52 $^{-1}$." + The radial velocity data and the orbital solution are shown in Figure 1., The radial velocity data and the orbital solution are shown in Figure \ref{fig:RVs}. + We determined the spectral line. bisectors. which are a neasure of Hue asvuuuetry. frou the HET spectra to test if the radial velocity variatious could be caused bv distortions in the spectral line profiles due to contamination from a nearby unresolved eclipsing binary.," We determined the spectral line bisectors, which are a measure of line asymmetry, from the HET spectra to test if the radial velocity variations could be caused by distortions in the spectral line profiles due to contamination from a nearby unresolved eclipsing binary." + We can only use a sinall fraction of the available spectral range that is not contaminated by the iodine absorption cell (50006100 Anestrom) and thus the uncertainties in the bisector velocity span (DVS) are quite large with an average uncertainty of 99 t., We can only use a small fraction of the available spectral range that is not contaminated by the iodine absorption cell (5000–6400 Angstrom) and thus the uncertainties in the bisector velocity span (BVS) are quite large with an average uncertainty of 99 $^{-1}$. + The RMS of πας Bisedtor is 146 +., The RMS of the bisector measurements is 146 $^{-1}$. + There is no evidence of a correlation between the velocities aud the bisectors. which supports the interpretation that the velocity variations are due to a planetary companion (e.g. Quelozetal.2001)) We derive the mass. racius. aud age of the host star using the method deseribed by Torresetal.(2008).," There is no evidence of a correlation between the velocities and the bisectors, which supports the interpretation that the velocity variations are due to a planetary companion (e.g. \citealt{queloz01}) ) We derive the mass, radius, and age of the host star using the method described by \cite{torres08}." +. We first created a set of stellar evolution models frou the Yousei-Yale (Y?) series by Yietal.(2001)... with corrections from Deniqueetal.(2001).," We first created a set of stellar evolution models from the Yonsei-Yale $^{2}$ ) series by \cite{yi01}, with corrections from \cite{demarque04}." +".. We employed their interpolation software which accepts as inputs the age of the star. the iron abundance. and the abundance of a-clements (relative to solu) for which we assume the solar value. and outputs a erid of stellar isochrones corresponding to a range of masses,"," We employed their interpolation software which accepts as inputs the age of the star, the iron abundance, and the abundance of $\alpha$ -elements (relative to solar) for which we assume the solar value, and outputs a grid of stellar isochrones corresponding to a range of masses." + We evaluated a set of isochrones at ages from 0.1 to Ll Gyr (at intervals of 0.1 Car) and stellar inetallicities spanning a range of 30 (at intervals of 0.01 dex) from the best-fit metallicity derived from spectra of /TMJ=0.36 0.1., We evaluated a set of isochrones at ages from 0.1 to 14 Gyr (at intervals of 0.1 Gyr) and stellar metallicities spanning a range of $3\sigma$ (at intervals of 0.01 dex) from the best-fit metallicity derived from spectra of $\koicurSMEfeh$ . + ethenperformedasplineinterpolationofcachoutputtableatare ," We then performed a spline interpolation of each output table at a resolution of 0.005 in effective temperature, the log of the surface gravity $(g)$, and the stellar luminosity $L_{\star}$." +"We evaluated the plivsical radius corresponding to cach stellar model via logtg) aud the massof the star. thoug[um it is also possible to convert to physical radius using the model stellar huninosity aud effective teniperature (assunime L,=ln R2eT!): in practice these conversions eive identical results."," We evaluated the physical radius corresponding to each stellar model via $(g)$ and the massof the star, though it is also possible to convert to physical radius using the model stellar luminosity and effective temperature (assuming $L_{\star}=4\pi R_{\star}^{2}\sigma T^{4}$ ); in practice these conversions give identical results." + We fitted for the stellar mass and radius using Neowtous version of Neplers third law in the mamnereniploved. by. Seager&Mallén-Ornelas(2003).. Sozzettietal.(2007) and Torresetal.(2008).," We fitted for the stellar mass and radius using Newton's version of Kepler's third law in the manneremployed by \cite{seager03}, \cite{sozzetti07} and \cite{torres08}." +. We asstuuect that the planetary mass is negligible when compared to the mass of the host star., We assumed that the planetary mass is negligible when compared to the mass of the host star. +" Using the Markov Chain Moute Carlo sequence of a/R,. and generating a series of Gaussian raudom realizations of ann uuxme the values and error bars derived from spectroscopy of =56304100 Nand| -0.:3-0.1. respectively, we located the best isochroneFe fit at cach realization using the 47 eooduess-of-fit eiven in Equation 1.."," Using the Markov Chain Monte Carlo sequence of $a/R_{\star}$, and generating a series of Gaussian random realizations of and using the values and error bars derived from spectroscopy of $\koicurSMEteff$ K and $\koicurSMEfeh$ , respectively, we located the best isochrone fit at each realization using the $\chi^{2}$ goodness-of-fit given in Equation \ref{eq:chisquared}. ." +" Usine the output of the MCMXC chain of e/IR, cusures that any correlations between paraiueters, which are"," Using the output of the MCMC chain of $a/R_{\star}$ ensures that any correlations between parameters, which are" +similar evolutionary scenario for dust settling in which dust is acquired externally. form laree scale dust lanes that gracually evolve to dusty disks with associated star-ormation. and then finally collapse to nuclear dusty disks associated with stellar disks.,"similar evolutionary scenario for dust settling in which dust is acquired externally, form large scale dust lanes that gradually evolve to dusty disks with associated star-formation, and then finally collapse to nuclear dusty disks associated with stellar disks." + As star formation ceases and their colors become similar to the host galaxy. the disks then become more difficult to observe.," As star formation ceases and their colors become similar to the host galaxy, the disks then become more difficult to observe." + Additional support for the evolutionary scenario above is the kinematic evidence for inflow along nuclear spirals in at least one case: 11097., Additional support for the evolutionary scenario above is the kinematic evidence for inflow along nuclear spirals in at least one case: 1097. + Its nuclear dusty. spiral has been revealed by near-IR. observations (Prietoetal.2005) and by structure maps in (2006)., Its nuclear dusty spiral has been revealed by near-IR observations \citep{prieto05} and by structure maps in \citet{fathi06}. +. Using the Integral-Eield Unit of the Gemini Multi-Object Spectrograph. the latter authors have found streaming motions along (he nuclear spiral arms with inwarcl velocities of up to | in the Io emitting gas throughout the nuclear region.," Using the Integral-Field Unit of the Gemini Multi-Object Spectrograph, the latter authors have found streaming motions along the nuclear spiral arms with inward velocities of up to $^{-1}$ in the $\alpha$ emitting gas throughout the nuclear region." + Another relevant finding on this galaxy is the voung obscurecl starburst discovered by very close to the nucleus (within 10 ppc). in agreement with the suggestion that inllowing gas and dust gives birth to stars in the nuclear dusty spiral or disk.," Another relevant finding on this galaxy is the young obscured starburst discovered by \citet{sb05} very close to the nucleus (within $\sim$ pc), in agreement with the suggestion that inflowing gas and dust gives birth to stars in the nuclear dusty spiral or disk." + A kev point in testing this evolutionary scenario is the evaluation of the life eveles of the dusty and stellar disks., A key point in testing this evolutionary scenario is the evaluation of the life cycles of the dusty and stellar disks. + In the case of 11097. the velocity observed for the streaming motions along the nuclear spiral allows an estimate of a few Myr for the gas to flow from a few hundred parsecs to the nucleus.," In the case of 1097, the velocity observed for the streaming motions along the nuclear spiral allows an estimate of a few Myr for the gas to flow from a few hundred parsecs to the nucleus." +" This is also consistent with the above estimates that the clust may survive for on order several clvnamical timescales,", This is also consistent with the above estimates that the dust may survive for on order several dynamical timescales. + If substantial star formation does add to stellar nuclear disks each activity evele. then there should be some stars associated with the disks vounger than the characteristic or episodic timescale of the dust replenishment and AGN lifetime. or vounger than 105 vears.," If substantial star formation does add to stellar nuclear disks each activity cycle, then there should be some stars associated with the disks younger than the characteristic or episodic timescale of the dust replenishment and AGN lifetime, or younger than $10^8$ years." + While we do not have color information for our sample. a number of stellar disks are indeed found to be blue (Ixrajnovié&Jaffe2004).. although many authors also argue Chat the colors are (he same as those of (he bulge (Erwin&Sparke2002).," While we do not have color information for our sample, a number of stellar disks are indeed found to be blue \citep{krajnovic04}, although many authors also argue that the colors are the same as those of the bulge \citep{erwin02}." +. Relatively old ages — from 6 to 15 Gyr. have been reported from studies using broad-band colors aud spectral indices (IXrajnovió&Jaffe2004:Morellietal.2004).," Relatively old ages – from 6 to 15 Gyr – have been reported from studies using broad-band colors and spectral indices \citep{krajnovic04,morelli04}." +.. Nevertheless. a close look at these studies reveals (hat the methods used to date the disk stellar population are not verv sensitive to the presence of a small young component in the middle of a luminous old bulge.," Nevertheless, a close look at these studies reveals that the methods used to date the disk stellar population are not very sensitive to the presence of a small young component in the middle of a luminous old bulge." + In particular. the spectral indices are measured in a restricted interval (5000 1., The higher CMB temperature at high redshift has a clear effect on the line profile shapes and the suppression of the line strengths could potentially lead to extra difficulties in the detection of molecular clouds at redshifts $z>1$. + lt has been argued that the intensity. anc shape of submillimetre molecular. line profiles as modelled by radiative transfer codes of prestellar anc protostellar cores are sensitive to the lone-waveleneth ambient raciation field illuminatine the exterior of the cloud., It has been argued that the intensity and shape of submillimetre molecular line profiles as modelled by radiative transfer codes of prestellar and protostellar cores are sensitive to the long-wavelength ambient radiation field illuminating the exterior of the cloud. + Some caution is therefore suggested in the modelling of observational results - the ambient. environment must somehow be constrained before fitting profiles and making conclusions about the ονπαλος and chemical composition of the system., Some caution is therefore suggested in the modelling of observational results - the ambient environment must somehow be constrained before fitting profiles and making conclusions about the dynamics and chemical composition of the system. + Lt should. be noted. that the οσοι described here is not unknown to workers in computational radiative transfer (it was discussed at the benchmarking exercise that led to the paper by Van Zadelholl et al 2002). in. preparation).," It should be noted that the effect described here is not unknown to workers in computational radiative transfer (it was discussed at the benchmarking exercise that led to the paper by Van Zadelhoff et al 2002), in preparation)." + l]lowever. this is the first time that the astrophysical consequences of this elect have been explored in any detail.," However, this is the first time that the astrophysical consequences of this effect have been explored in any detail." + In future papers on star-formation. we will - following the preliminary study of Ward-Fhompson&Buckley.2001)) - address the issue of how the velocity structure in general. and the microturbulent velocity in particular. allects the line profiles.," In future papers on star-formation, we will - following the preliminary study of \citealt{ward-thompson&buckley01}) ) - address the issue of how the velocity structure in general, and the microturbulent velocity in particular, affects the line profiles." + It is important to realise that it is essential to characterise correctly the microphysics of potential infall sources., It is important to realise that it is essential to characterise correctly the microphysics of potential infall sources. + This will eventually allow more robust inferences to be mace from line profile data than is currently possible., This will eventually allow more robust inferences to be made from line profile data than is currently possible. + ΑΗ and DAW were supported by PPARC ancl the Leverhulme Trust respectively while this work was carried out., MPR and DAW were supported by PPARC and the Leverhulme Trust respectively while this work was carried out. + Some of the calculations described. here were carried out on the Miracle Supercomputer. at. the. HiPerSPACIE computing Centre. UCL. which is funded by the Ul Particle Physics and Astronomy Research Council.," Some of the calculations described here were carried out on the Miracle Supercomputer, at the HiPerSPACE computing Centre, UCL, which is funded by the UK Particle Physics and Astronomy Research Council." +where HoGr)=3(sin:r—;irσος)fr? is the Fourier trausform of a real-space tophat window fuuction.,where $W(x)= 3(\sin x - x \cos x)/x^3 $ is the Fourier transform of a real-space tophat window function. + The mass M is related to / by AL=πρὸ., The mass $M$ is related to $R$ by $M=4\pi\bar\rho R^3/3$. +" For scale free models with a power law initial power spectrum Px&"". this iso =(M/M,)8."," For scale free models with a power law initial power spectrum $P\propto k^n$, this is $\sigma = +(M/M_*)^{-(3+n)/6}$." +" The parameter AL, characterizes the mass scale at the onset of nonlinearity. 6(M,)= 1. and is related to the noulinear wavenuumber μι (defined as Tael?PUOy*= 1) by where (defined for —3xn< 1)."," The parameter $M_*$ characterizes the mass scale at the onset of nonlinearity, $\sigma(M_*)=1$ , and is related to the nonlinear wavenumber $k_\nl$ (defined as $\int_0^{k_\nl} 4\pi k^2 dk +\, P(k) / (2\pi)^3 =1$ ) by where (defined for $-3\le n < 1$ )." + Various modificatious to the Press-Schechter mass function have been suggestedMOD (e.g.. Sheth Tormen 1999: Lee Shanucarin 1999: Jenkius et al.," Various modifications to the Press-Schechter mass function have been suggested (e.g., Sheth Tormen 1999; Lee Shandarin 1999; Jenkins et al." + 2000) to improve the accuracy of the original formula., 2000) to improve the accuracy of the original formula. + Dark matter halos do not cluster in the same way as the mass deusity [ield., Dark matter halos do not cluster in the same way as the mass density field. + On large scales. a bias parameter b is typically used to quantify this difference.," On large scales, a bias parameter $b$ is typically used to quantify this difference." +" Let £pGr:M.AL) be the two-point correlation function of halos with masses AZ and AL’. £g,(r) be the linear correlation function for the mass deusity field. auc Paap, aud Pj, be the corresponding power spectra."," Let $\xi_\halo(r;M,M')$ be the two-point correlation function of halos with masses $M$ and $M'$, $\xi_\lin(r)$ be the linear correlation function for the mass density field, and $P_\halo$ and $P_\lin$ be the corresponding power spectra." + Ou large length scales. we asstume a linear bias aud write Based ou the peak and the Press-Schechter formalism. Mo White (1996) developed a model for the linear bias 6(AL). which is later modified by Jing (1998) to be The original formula for 6(374) by Mo White includes only the first factor above: tlie second factor. dependent ou the primordial spectral index η. is obtained empirically [or an improved Lit to simulation results at thelower mass end (Jing 1998).," On large length scales, we assume a linear bias and write Based on the peak and the Press-Schechter formalism, Mo White (1996) developed a model for the linear bias $b(M)$, which is later modified by Jing (1998) to be The original formula for $b(M)$ by Mo White includes only the first factor above; the second factor, dependent on the primordial spectral index $n$, is obtained empirically for an improved fit to simulation results at thelower mass end (Jing 1998)." + In this bias model. bCAL) is below unity," In this bias model, $b(M)$ is below unity" +studies in Section 6..,studies in Section \ref{Comparison}. + The limitations of our approach are discussed in Section 7.., The limitations of our approach are discussed in Section \ref{Limitation}. + We consider a planetary system consisting of a star surrounded by a planet and a debris disk., We consider a planetary system consisting of a star surrounded by a planet and a debris disk. +" We address the case of large particles, which are insensitive to pressure forces (radiation, stellar wind or gas pressure)."," We address the case of large particles, which are insensitive to pressure forces (radiation, stellar wind or gas pressure)." + The simulated disk is thus rather a planetesimal disk than a debris disk and we only consider gravitational forces., The simulated disk is thus rather a planetesimal disk than a debris disk and we only consider gravitational forces. +" Importantly, we also do not take into account the gravitational interactions between planetesimals as they are negligible, nor mutual collisions."," Importantly, we also do not take into account the gravitational interactions between planetesimals as they are negligible, nor mutual collisions." +" Dynamically speaking, the planetesimals are thus considered as test particles."," Dynamically speaking, the planetesimals are thus considered as test particles." + A typical configuration for the simulations is a Vega-like central star (2.5 Mo) and a planet orbit with a 40 AU pericenter at the starting time., A typical configuration for the simulations is a Vega-like central star $2.5$ $_\odot$ ) and a planet orbit with a $40$ AU pericenter at the starting time. +" The initial planetesimal disk consists of 50000 planetesimals distributed between 40 and 75 AU on circular orbits, with a surface density distribution proportional to r!."," The initial planetesimal disk consists of $50\,000$ planetesimals distributed between $40$ and $75$ AU on circular orbits, with a surface density distribution proportional to $r^{-1}$." +" The disk midplane coincides with the orbital plane of the planet, and the inclinations of the planetesimals are randomly distributed within +3°."," The disk midplane coincides with the orbital plane of the planet, and the inclinations of the planetesimals are randomly distributed within $\pm 3^\circ$." +" In this model, the planet keeps a Keplerian orbit around the star, or migrates at a constant rate without modification of its eccentricity."," In this model, the planet keeps a Keplerian orbit around the star, or migrates at a constant rate without modification of its eccentricity." +" This basic model is easy to implement and to analyze, and corresponds to the case described by ?.."," This basic model is easy to implement and to analyze, and corresponds to the case described by \citet{2003ApJ...598.1321W}." + The goal of this paper is to extend this initial work to a wider range of planet eccentricities by a numerical study., The goal of this paper is to extend this initial work to a wider range of planet eccentricities by a numerical study. +" We start by studying planets on low-eccentricity orbits (e«0.1), and then extend our work to larger eccentricities."," We start by studying planets on low-eccentricity orbits $e<0.1$ ), and then extend our work to larger eccentricities." +" To perform our simulations we have used the symplectic package SWIFT (??), to which we have added planetary migration."," To perform our simulations we have used the symplectic package SWIFT \citep{1991AJ....102.1528W,1994Icar..108...18L}, to which we have added planetary migration." +" To do this, we plugged in the ? prescription."," To do this, we plugged in the \citet{2003ApJ...598.1321W} prescription." +" This method consists of adding an acceleration in the direction of the orbital motion of the planet, with an intensity equal to: v,=05d,GM./a}, where G is the gravitational constant, M. the stellar mass and αρ the variation rate of the planet semi-major axis ay."," This method consists of adding an acceleration in the direction of the orbital motion of the planet, with an intensity equal to: $\dot{v_p}=0.5\dot{a_p}\sqrt{GM_{\ast}/a_p^3}$, where $G$ is the gravitational constant, $M_{\ast}$ the stellar mass and $\dot{a_p}$ the variation rate of the planet semi-major axis $a_p$." + This causes a change in the planet semi- axis without modifying its eccentricity (for a planet on a low-eccentricity orbit; for a planet on a higher eccentricity orbit the change is not significant) or its inclination., This causes a change in the planet semi-major axis without modifying its eccentricity (for a planet on a low-eccentricity orbit; for a planet on a higher eccentricity orbit the change is not significant) or its inclination. + We do not discuss here the origin of the migration., We do not discuss here the origin of the migration. +" It can be due either to the migration of a large internal planet, or to the gravitational influence of the planetesimals themselves."," It can be due either to the migration of a large internal planet, or to the gravitational influence of the planetesimals themselves." +" The most important here is that we keep αρ constant during each simulation, generally at 0.5 AU Myr-!, to match the ? model for the Vega disk."," The most important here is that we keep $\dot{a_p}$ constant during each simulation, generally at $0.5$ AU $^{-1}$, to match the \citet{2003ApJ...598.1321W} model for the Vega disk." +" We have used the RMVS3 version of the SWIFT integrator, in order to have a better modeling of the close encounters between the planet and the planetesimals."," We have used the RMVS3 version of the SWIFT integrator, in order to have a better modeling of the close encounters between the planet and the planetesimals." +" In all the simulations, the system evolution is followed for 40 Myr."," In all the simulations, the system evolution is followed for $40$ Myr." +" The scenario of a planet on a low-eccentricity orbit is the most studied case (see Table 1)), for several reasons."," The scenario of a planet on a low-eccentricity orbit is the most studied case (see Table \ref{previousWorks}) ), for several reasons." +" First, planets were originally expected to be on almost circular orbits because, during the protoplanetary phase, circumstellar gas forces the planets to remain on very low eccentricity orbits."," First, planets were originally expected to be on almost circular orbits because, during the protoplanetary phase, circumstellar gas forces the planets to remain on very low eccentricity orbits." +" A planet on such an orbit therefore corresponds to the ""standard scenario"".", A planet on such an orbit therefore corresponds to the “standard scenario”. +" Also, a low or zero planetary eccentricity simplifies an analytical analysis (?).."," Also, a low or zero planetary eccentricity simplifies an analytical analysis \citep{2003ApJ...588.1110K}." +" Nevertheless, it must be noted that many of the extrasolar planets detected so far have highcentricities!,, and we will therefore extend our study to high eccentricities in Section 4.."," Nevertheless, it must be noted that many of the extrasolar planets detected so far have high, and we will therefore extend our study to high eccentricities in Section \ref{highEccOrb}." +" Although this standard scenario has already been well studied, all its aspects have not yet been investigated."," Although this standard scenario has already been well studied, all its aspects have not yet been investigated." +" ? studied the case of an outward migrating planet on a strictly circular orbit, while ? and ? studied the case of planets on fixed low- orbits, considering only inward dust migration due to P-R drag."," \citet{2003ApJ...598.1321W} + studied the case of an outward migrating planet on a strictly circular orbit, while \citet{2003ApJ...588.1110K} and \citet{2005ApJ...625..398D} + studied the case of planets on fixed low-eccentricity orbits, considering only inward dust migration due to P-R drag." + We propose in this section to numerically study a migrating planet on a circular or low-eccentricity orbit to search for possible differences with respect to previous studies., We propose in this section to numerically study a migrating planet on a circular or low-eccentricity orbit to search for possible differences with respect to previous studies. + Figures 2 to 5 show examples of results obtained with our numerical model., Figures \ref{figure_e0} to \ref{figure_e05_ae} show examples of results obtained with our numerical model. +" It appears that, with a planet on a low-eccentricity orbit, the planetesimals trapped in MMRs are numerous and dominate the shape of the disk."," It appears that, with a planet on a low-eccentricity orbit, the planetesimals trapped in MMRs are numerous and dominate the shape of the disk." + Four important factors must be taken into account to determine which resonances govern the aspect of the structures in the disk:, Four important factors must be taken into account to determine which resonances govern the aspect of the structures in the disk: +"Tustead of comparing the spectra. one can work directly with the telpcrature field to measure the preseuce of the ISW ασια],","Instead of comparing the spectra, one can work directly with the temperature field to measure the presence of the ISW signal." + The observable in this case is now the ISW temperature field (Raw). rather thaw the cross-correlation power spectra επί).," The observable in this case is now the ISW temperature field $\delta_{\mathrm{ISW}}$ ), rather than the cross-correlation power spectra $C_{gT}(\ell)$." +" The observed CAB temperature anisotropies óops can be described as: where dpsy is he ISW field aud A its amplitude (normally near 1). d¢ the munordial CAIB temperature Ποια. Author represents fluctuations due to secoudary auisotropies other thau the ISW effect aud AC represents noise,"," The observed CMB temperature anisotropies $\delta_{\rm OBS}$ can be described as: where $\delta_{\mathrm{ISW}}$ is the ISW field and $\lambda$ its amplitude (normally near 1), $\delta_T$ the primordial CMB temperature field, $\delta_{\rm other}$ represents fluctuations due to secondary anisotropies other than the ISW effect and $\mathcal{N}$ represents noise." + In the coutext of the ISW effect. which occurs oulv ou large (linear) scales where noise aud other secondary anisotropics are uceligible. we have: The iain difference between the fields and spectra approach is that the fields method requires au estimation of the ISW temperature field (yay).," In the context of the ISW effect, which occurs only on large (linear) scales where noise and other secondary anisotropies are negligible, we have: The main difference between the fields and spectra approach is that the fields method requires an estimation of the ISW temperature field $\delta_{\rm ISW}$ )." + There are several methods to calculate dpa fom a given matter overdcusity map., There are several methods to calculate $\delta_{\rm ISW}$ from a given matter overdensity map. + The most accurate way to reconstruct he ISW signal is fo use information roni the full 3-dimensional matter distribution. which iu theory requires overlapping galaxy and weak leusime maps on large scales. in order to 1ieasure he galaxy bias.," The most accurate way to reconstruct the ISW signal is to use information from the full 3-dimensional matter distribution, which in theory requires overlapping galaxy and weak lensing maps on large scales, in order to measure the galaxy bias." + This may be possible iu the future with surveys like Euclid(2)., This may be possible in the future with surveys like Euclid. + Assunuiug a simple bias relation. he matter field cau also be estimated directly from galaxy strversskv).," Assuming a simple bias relation, the matter field can also be estimated directly from galaxy surveys." +". Iu the case where oulv the general redshift distribution of he ealaxy survey is kuown. the ISW field dyyyy can be approximated directly frou the galaxy and temperature haps usine where gr, are the spherical haruouic coeffücieuts of the ealaxy map. and al the cocfficieuts of the. ISW temperature anisotropy nip."," In the case where only the general redshift distribution of the galaxy survey is known, the ISW field $\delta_{\rm ISW}$ can be approximated directly from the galaxy and temperature maps using: where $g_{\ell m}$ are the spherical harmonic coefficients of the galaxy map, and $a^{\rm ISW}_{\ell m}$ the coefficients of the ISW temperature anisotropy map." + Another approach is to reconstruct the ISW imap using Equation 1 where ® is estimated using the Poisson Equation(?)., Another approach is to reconstruct the ISW map using Equation \ref{sec:theory:eq:isw} where $\Phi'$ is estimated using the Poisson Equation. +. Tn general. it is assumed that ou non-linear scales. the ISW is called the Rees-Sciama effect. aud. will produce a negatively correlated signal due to non-linear growing modes of the matter distribution(27).," In general, it is assumed that on non-linear scales, the ISW is called the Rees-Sciama effect and will produce a negatively correlated signal due to non-linear growing modes of the matter distribution." +. However. some uon-linear modes could also be decaving for example duc to major mergers or tidal stripping. or due to alternative cosinologics as in7).," However, some non-linear modes could also be decaying for example due to major mergers or tidal stripping, or due to alternative cosmologies as in." +. Iu this case the signal could be positively correlated even on non-linear scales (frou equation 1)), In this case the signal could be positively correlated even on non-linear scales (from equation \ref{sec:theory:eq:isw}) ). + The total ISW sienal (i.c.. the signal which 1s positively correlated) would not necessarily be Cassia in this case.," The total ISW signal (i.e., the signal which is positively correlated) would not necessarily be Gaussian in this case." +" Tn our approach. we do net imodel possible contributions frou, non-linear (erowine or decaying) modes. but we allow quasilinear modes in the data or sinulatious to produce a positively correlated ISW signal as an approxination: we do this since it is in practice very difficult to separate linear aud quasi-linear modes."," In our approach, we do not model possible contributions from non-linear (growing or decaying) modes, but we allow quasi-linear modes in the data or simulations to produce a positively correlated ISW signal as an approximation; we do this since it is in practice very difficult to separate linear and quasi-linear modes." + As for the spectra approach. there are several statistical methods available to qualify detection: We have identified two main classes of imoethods: either using power spectra or fields to measure the ISW signal.," As for the spectra approach, there are several statistical methods available to qualify detection: We have identified two main classes of methods: either using power spectra or fields to measure the ISW signal." + For cach approach one can choose amongst several statistical tools to measure the significance of a correlation or validate simultaneously a correlation aud a model., For each approach one can choose amongst several statistical tools to measure the significance of a correlation or validate simultaneously a correlation and a model. + The advantages aud disadvantages of both approaches are stunarised below and in the top part of Table 2.., The advantages and disadvantages of both approaches are summarised below and in the top part of Table \ref{tab:prosandcons}. + One of the main advantages of using the field approach is that it assumes only that the primordial CAMB field cones from a Gaussian randoni process. which is largely believed to be true.," One of the main advantages of using the field approach is that it assumes only that the primordial CMB field comes from a Gaussian random process, which is largely believed to be true." + In the other approach. the spectra are asstuned to be Caussian. which is not the case.," In the other approach, the spectra are assumed to be Gaussian, which is not the case." + Several, Several +In addition. we find a gradient of ~4 dn the same direction. which we interpret as being procuced by an outflow(s)-cloud interaction.,"In addition, we find a gradient of$\sim$ 4 in the same direction, which we interpret as being produced by an outflow(s)-cloud interaction." +The need for turbulent. (transport. to account for the rather short. accretion/ejection time-scales of Young Stellar Objects (YSOs) and binary svstems (CV. X-ray binaries). or,"The need for turbulent transport to account for the rather short accretion/ejection time-scales of Young Stellar Objects (YSOs) and binary systems (CV, X-ray binaries), or" +The number of points that can be fitted by the SED online tool is limited.,The number of points that can be fitted by the SED online tool is limited. +" Therefore, from the ISO spectrum about one flux point per one micron was used."," Therefore, from the ISO spectrum about one flux point per one micron was used." +" From the MIDI spectrum, about two flux points per micron were chosen as the shape of the spectrum changes much more in this wavelength regime because of the silicate absorption feature."," From the MIDI spectrum, about two flux points per micron were chosen as the shape of the spectrum changes much more in this wavelength regime because of the silicate absorption feature." +" When comparing the model visibilities and fluxes to the observed data, it is important to consider the very different (effective) beam-sizes of the different observations."," When comparing the model visibilities and fluxes to the observed data, it is important to consider the very different (effective) beam-sizes of the different observations." +" The MIDI instrument has an effective field-of-view of 0.5"" (slit width), corresponding to ~450 AU at the distance of our target."," The MIDI instrument has an effective field-of-view of $0.5''$ (slit width), corresponding to $\approx 450$ AU at the distance of our target." +" The beam sizes for all other data points beyond near-infrared wavelengths are much larger: the beam size from which the ISO spectrum was extracted («13000x18 AU) is already =1100 times larger, and the beam sizes for all far-infrared data points are at least ~3000 times larger than the MIDI field-of-view."," The beam sizes for all other data points beyond near-infrared wavelengths are much larger: the beam size from which the ISO spectrum was extracted $\approx 13\,000 \times 18\,000$ AU) is already $\approx 1100$ times larger, and the beam sizes for all far-infrared data points are at least $\sim 3000$ times larger than the MIDI field-of-view." +" The ISO and far-infrared fluxes do therefore not only trace the emission from the central YSO and its immediate circumstellar material (on spatial scales of up to ~500 AU), but also contain contributions from the surrounding extended molecular cloud, on spatial scales of 220000 AU (=20.1 pc)."," The ISO and far-infrared fluxes do therefore not only trace the emission from the central YSO and its immediate circumstellar material (on spatial scales of up to $\sim 500$ AU), but also contain contributions from the surrounding extended molecular cloud, on spatial scales of $\ga 20\,000$ AU $\cor \ga 0.1$ pc)." +" Therefore, as a first approach we include all SED points with 2> l13j4m only as upper limits."," Therefore, as a first approach we include all SED points with $\lambda > 13\,\mu$ m only as upper limits." +" To compute the visibilities, we used the HO-CHUNK code from ? to calculate images for the model."," To compute the visibilities, we used the HO-CHUNK code from \citet{Whitney} to calculate images for the model." +" Doing so, the ten best-fit models consist of circumstellar disks only (see Sect. 3.3.1))."," Doing so, the ten best-fit models consist of circumstellar disks only (see Sect. \ref{DiskRobi}) )." +" As a second approach, none of the data points was used as an upper limit, but they all were given with their errors."," As a second approach, none of the data points was used as an upper limit, but they all were given with their errors." +" Here, rather different best-fit models are found by the fitting tool."," Here, rather different best-fit models are found by the fitting tool." +" They all consist of a large circumstellar envelope and either have no additional disk, or just a small ring-like structure with radii from 0.5 to 8 AU (see Sect. 3.3.2))."," They all consist of a large circumstellar envelope and either have no additional disk, or just a small ring-like structure with radii from 0.5 to 8 AU (see Sect. \ref{EnvelopeRobi}) )." +" For similar applications of this fitting tool and its advantages and limitations in this respect, we refer to for instance ?,, ?,, and ?.."," For similar applications of this fitting tool and its advantages and limitations in this respect, we refer to for instance \citet{Linz}, \citet{deWit2}, and \citet{Follert}." + We note that the parameter space is not covered uniformly., We note that the parameter space is not covered uniformly. +" In particular, the spacing of the grid parameters is much finer in the case of low-mass YSOs than for MYSOs."," In particular, the spacing of the grid parameters is much finer in the case of low-mass YSOs than for MYSOs." + The SED and visibilities of the best-fit Robitaille disk models are shown in Fig. 4.., The SED and visibilities of the best-fit Robitaille disk models are shown in Fig. \ref{SpektrumRobitaille}. + This model is able to reproduce the flux in the near- and mid-infrared., This model is able to reproduce the flux in the near- and mid-infrared. +" To reproduce the flux in the FIR, one would have to add for example some blackbody components as shown later for the RADMC model (see Sect.3.4))."," To reproduce the flux in the FIR, one would have to add for example some blackbody components as shown later for the RADMC model (see \ref{RADMC}) )." +" The model can reproduce the level of the 90 m baseline visibility, and also the 40 m baseline visibility is reproduced within the errorbars."," The model can reproduce the level of the 90 m baseline visibility, and also the 40 m baseline visibility is reproduced within the errorbars." +" The parameters of this fit model are (model ID 3004478): Here, ‘our is the outer disk radius and Aq; would be the height of the disk when extending it to a radius of 100 AU."," The parameters of this best-fit model are (model ID 3004478): Here, $r_{\rm out}$ is the outer disk radius and $h_{\rm disk}$ would be the height of the disk when extending it to a radius of 100 AU." + The Robitaille envelope model with the smallest y? is shown in Fig. 5.., The Robitaille envelope model with the smallest $\chi^2$ is shown in Fig. \ref{SpektrumHuelle}. + It fails to model especially the shape of the 40 m baseline visibility curve., It fails to model especially the shape of the 40 m baseline visibility curve. +" The flux in the mid-IR can be reproduced, but the model cannot reproduce the flux in"," The flux in the mid-IR can be reproduced, but the model cannot reproduce the flux in" +despite being more massive and having higher photospheric temperatures. Αίας coronal X-ray properties are very similar to those of similarly active stars of later spectral type.,"despite being more massive and having higher photospheric temperatures, Altair's coronal X-ray properties are very similar to those of similarly active stars of later spectral type." + We find that equatorial regions or low to intermediate latitudes are the most X-ray active areas of Altair’s surface. Le. the same regions that exhibit the lowest surface temperatures (?)..," We find that equatorial regions or low to intermediate latitudes are the most X-ray active areas of Altair's surface, i.e. the same regions that exhibit the lowest surface temperatures \citep{mon07}." + This is in contrast to fast rotating. but less massive stars like the K2 dwarf BO Mic. where magnetically active regions are predominantly found at high latitudes and polar regions (?)..," This is in contrast to fast rotating, but less massive stars like the K2 dwarf BO Mic, where magnetically active regions are predominantly found at high latitudes and polar regions \citep{wol08}." + Magnetic activity. that is mainly located at low latitude regions is independently suggested by a modulation of the X-ray light curve with the rotation period. as well as from the study of possible plasma locations derived from emission line ratios.," Magnetic activity, that is mainly located at low latitude regions is independently suggested by a modulation of the X-ray light curve with the rotation period, as well as from the study of possible plasma locations derived from emission line ratios." + The analysis of the size of the coronal structures supports this finding and indicates. that Altair's corona consists of rather small coronal loops and has an overall small filling factor.," The analysis of the size of the coronal structures supports this finding and indicates, that Altair's corona consists of rather small coronal loops and has an overall small filling factor." + In this scenario. the X-ray emission is related to magnetic activity. that is predominantly generated in the equatorial bulge and neighboring regions.," In this scenario, the X-ray emission is related to magnetic activity, that is predominantly generated in the equatorial bulge and neighboring regions." + The equatorial regions of Altair's surface have photospheric temperatures of an early F-type star. and such stars are known to exhibit X-ray emission.," The equatorial regions of Altair's surface have photospheric temperatures of an early F-type star, and such stars are known to exhibit X-ray emission." + Very thin plasma residing in very large coronal structures. that contributes to the observed X-ray emission. is in principle not contradicting our data. but its confinement and the stability of such structures is questionable given Altair's fast rotation and absence/weakness of large scale magnetic fields (?)..," Very thin plasma residing in very large coronal structures, that contributes to the observed X-ray emission, is in principle not contradicting our data, but its confinement and the stability of such structures is questionable given Altair's fast rotation and absence/weakness of large scale magnetic fields \citep{lan82}." + A compact emission region located close to the surface of Altair is also supported by emission lines originating in the chromosphere and transition region., A compact emission region located close to the surface of Altair is also supported by emission lines originating in the chromosphere and transition region. + The lines at and.. tracing plasma roughly at 3x10° K that is located in the transition region. Le. from the atmospheric layer below the corona. are also apparently formed close to the stellar surface.," The lines at and, tracing plasma roughly at $3\times 10^{5}$ K that is located in the transition region, i.e. from the atmospheric layer below the corona, are also apparently formed close to the stellar surface." + Their broad. double-horned profile is well fitted by optically thin emission originating on a star with Vsig?=210 km/s. that exhibits either strong limb. brightening or emitting regions preferentially located towards the equator (2).," Their broad, double-horned profile is well fitted by optically thin emission originating on a star with $Vsini=210$ km/s, that exhibits either strong limb brightening or emitting regions preferentially located towards the equator \citep{red02}." +. A chromosphere covering mainly equatorial regions was also suggested as a possible scenario by ?.. deduced from the modelling of the « line profiles.," A chromosphere covering mainly equatorial regions was also suggested as a possible scenario by \cite{fer95}, deduced from the modelling of the $\alpha$ line profiles." + While not much is known about the interior structure of Altair. the star is clearly oblate and its surface is highly distorted.," While not much is known about the interior structure of Altair, the star is clearly oblate and its surface is highly distorted." + Therefore. most possibly also the outer part of the interior is not uniform and it seems reasonable to associate the development of convective cells with the more cooler surface areas near the equator.," Therefore, most possibly also the outer part of the interior is not uniform and it seems reasonable to associate the development of convective cells with the more cooler surface areas near the equator." + In this scenario. localized. dynamo processes significantly contribute to the observed magnetic activity.," In this scenario, localized dynamo processes significantly contribute to the observed magnetic activity." + This would naturally explain low latitude emission and. since only a fraction of Altair’s surface is magnetically active. could be a main cause for its very low activity level.," This would naturally explain low latitude emission and, since only a fraction of Altair's surface is magnetically active, could be a main cause for its very low activity level." + Additionally. the locally operating dynamo appears to be less efficient in generating X-ray flux per surface area. when compared the global. solar-Itke dynamo for the same effective temperature and rotation period.," Additionally, the locally operating dynamo appears to be less efficient in generating X-ray flux per surface area, when compared the global, solar-like dynamo for the same effective temperature and rotation period." + However. surprisingly low activity levels also seem to be present in other weakly active stars of later spectral type.," However, surprisingly low activity levels also seem to be present in other weakly active stars of later spectral type." + Altogether. the cause for the diminished stellar activity levels remains uncertain and quite possible it differs for stars with shallow convection zones and those with slow rotation.," Altogether, the cause for the diminished stellar activity levels remains uncertain and quite possible it differs for stars with shallow convection zones and those with slow rotation." + On the other hand. the weak X-ray activity level of Altair seems to be also the highest possible activity level. since a significant spin-up would disrupt the star.," On the other hand, the weak X-ray activity level of Altair seems to be also the highest possible activity level, since a significant spin-up would disrupt the star." + Consequently. the fast rotator Altair is likely already around the saturation limit for magnetic X-ray activity when considering its dynamo efficiency. or rotation period.," Consequently, the fast rotator Altair is likely already around the saturation limit for magnetic X-ray activity when considering its dynamo efficiency or rotation period." + This implies. that the X-ray saturation level in stars with very shallow convection zones around spectral type A7 is about four orders of magnitude below the saturation level for later-type stars.," This implies, that the X-ray saturation level in stars with very shallow convection zones around spectral type A7 is about four orders of magnitude below the saturation level for later-type stars." + No matter what are the details of the generating mechanism that is underlying Altairs magnetic activity. its corona appears to be fairly stable on timescales from days to decades.," No matter what are the details of the generating mechanism that is underlying Altair's magnetic activity, its corona appears to be fairly stable on timescales from days to decades." + It is highly desirable to study of other. ideally also more slowly rotating mid to late A-type stars. to derive a more complete picture of magnetic and X-ray activity related phenomena at the onset of the development of outer convection zones.," It is highly desirable to study of other, ideally also more slowly rotating mid to late A-type stars, to derive a more complete picture of magnetic and X-ray activity related phenomena at the onset of the development of outer convection zones." + The here presented X-ray observation of the A7 star Altair leads. together with chromospheric and transition region measurements. to an overall comprehensive and consistent picture of the magnetic activity for this fast rotating. distorted star.," The here presented X-ray observation of the A7 star Altair leads, together with chromospheric and transition region measurements, to an overall comprehensive and consistent picture of the magnetic activity for this fast rotating, distorted star." +correlation of size with Lbuuinositv. aud a null withdistaucc?.,"correlation of size with luminosity, and a mild with." +. We next consider the proposition that GCs or UCDs around a ealaxy are tidally limited. ic.. they fll their tidal radiusγ," We next consider the proposition that GCs or UCDs around a galaxy are tidally limited, i.e., they fill their tidal radius." +ι We assume that they have fairly homologous huninosity profiles. so that the value of ry/ is roughly the same for every CC/UCD.," We assume that they have fairly homologous luminosity profiles, so that the value of $r_{\rm h}/r_{\rm t}$ is roughly the same for every GC/UCD." + The latter proposition has some support from theory (Ixüppoerctal.2008:Tinley&Alackey2010). anc from observations of extended clusters (ECs) im the AMilsv Way halo (Daunugardtetal.2010)..," The latter proposition has some support from theory \citep{2008MNRAS.389..889K,2010MNRAS.408.2353H} and from observations of extended clusters (ECs) in the Milky Way halo \citep{2010MNRAS.401.1832B}." + Following Batueardtetal.(2010)... the predictedà5.. or Jacobi radius (which is not necessarily the same as the tidal radius from a Wine modol fit). is: where es ds the circular velocity of the host galaxy and AM is the total mass of the satellite object.," Following \citet{2010MNRAS.401.1832B}, the predicted, or Jacobi radius (which is not necessarily the same as the tidal radius from a King model fit), is: where $v_{\rm c}$ is the circular velocity of the host galaxy and $M$ is the total mass of the satellite object." + We have substituted the projected distance A as a rough proxy for the 3-D distance. after multiplying by 2/73 to account for a median viewing angele of 607.," We have substituted the projected distance $R$ as a rough proxy for the 3-D distance, after multiplying by $2/\sqrt{3}$ to account for a median viewing angle of $60^\circ$." + If e; is nearly coustaut with distance (as suggested by the dynamical analvsis of S|11). aud AZ scales closely with £. then the tidal limitation scenario predicts the size scaling expoucuts a~0.3 and i~ 0.7.," If $v_{\rm c}$ is nearly constant with distance (as suggested by the dynamical analysis of S+11), and $M$ scales closely with $L$, then the tidal limitation scenario predicts the size scaling exponents $\alpha \sim 0.3$ and $\beta \sim 0.7$ ." + This tidal model may explain the observed size-distance relation of Ailky Way halo clusters. with je 0.10.5 (wandenBerehetal.1991:MeLbaugliliu2000:Bammeardtetal. 2010:: cf Giclesetal. 20113).," This tidal model may explain the observed size-distance relation of Milky Way halo clusters, with $\beta$ $\sim$ 0.4–0.5 \citealt{1991ApJ...375..594V,2000ApJ...539..618M,2003ApJ...593..340L,2005MNRAS.360..631M,2010MNRAS.401.1832B}; cf \citealt{2011MNRAS.413.2509G}) )." + Tlowever. he overall GCs and UCDs around AIST are inconsisteut with this Milkv Wav finding. with the fits sugeestiug ittle or uo distance dependence.," However, the overall GCs and UCDs around M87 are inconsistent with this Milky Way finding, with the fits suggesting little or no distance dependence." + This implies that the AIS? objects” sizes are in generalnot stronglv influenced w, This implies that the M87 objects' sizes are in general strongly influenced by. + Examiuing the huninosity trends in more detail. there nay be an interesting pattern οσοιο for the lower-unminostv objects (with M; between ~ s.land = 11.3).," Examining the luminosity trends in more detail, there may be an interesting pattern emerging for the lower-luminosity objects (with $M_i$ between $\sim -8.4$ and $-11.3$ )." + Iu the loft panel of Figure L.. some of the GCs and UCDs appear to coincide ou a narrow diagonal track extending youn rg~ Lope at Roe 2.5 kpe to rj~ 25 pe at Ro 30 kpc.," In the left panel of Figure \ref{fig:dist}, some of the GCs and UCDs appear to coincide on a narrow diagonal track extending from $r_{\rm h}\sim$ 4 pc at $R\sim$ 2.5 kpc to $r_{\rm h}\sim$ 25 pc at $R\sim$ 30 kpc." + This track is mainly driven by the ACS photometric sauple of GCs. which should be complete and unbiased.," This track is mainly driven by the ACS photometric sample of GCs, which should be complete and unbiased." + The slope of Jj~0.7 is remarkably similar o the tidal-linitation prediction., The slope of $\beta\sim0.7$ is remarkably similar to the tidal-limitation prediction. +" Attempting to model lis track using Equation 2.. sve adopt e= 5001. atypical mass of AL=LOCAL... aud then adjust the tidal o half-light radius ratio to match the data: à/ry,=9."," Attempting to model this track using Equation \ref{eqn:rt}, we adopt $v_{\rm c}=$ 500, a typical mass of $M=10^6 M_\odot$, and then adjust the tidal to half-light radius ratio to match the data: $r_{\rm t}/r_{\rm h}\simeq9$." + The statistical robustuess of this finding is uuclear (c.g... we have somewhat arbitrarily chosen the uaenitude Bits). but we meution it to motivate future investigation and to provide a tentative clic that some of the fainter UCDs may be related. to more compact GC's.," The statistical robustness of this finding is unclear (e.g., we have somewhat arbitrarily chosen the magnitude limits), but we mention it to motivate future investigation and to provide a tentative clue that some of the fainter UCDs may be related to more compact GCs." + As we discuss below. the existence of such a subpopulation would be cousisteut with the notion of a distinct mode of diffuse star cluster formation. producing objects whose sizes are tidally limited.," As we discuss below, the existence of such a subpopulation would be consistent with the notion of a distinct mode of diffuse star cluster formation, producing objects whose sizes are tidally limited." +" No such velatiouship would be interred from consideration of the bright UCDs alone. although a tew of these could be roughly consistent with the ""tidal trend” of the faint UCDs. after rescaling for mass (see right panel of Figure 1)."," No such relationship would be inferred from consideration of the bright UCDs alone, although a few of these could be roughly consistent with the “tidal trend” of the faint UCDs, after rescaling for mass (see right panel of Figure \ref{fig:dist}) )." + We also provide estimated rjr; values for all of the UCDs individually in Table 1.. using Equation (2)) as before. with au assumed. mass-to-lishlit ratio of A//L;=1.5 in solar units.," We also provide estimated $r_{\rm h}/r_{\rm t}$ values for all of the UCDs individually in Table \ref{tab:data}, using Equation \ref{eqn:rt}) ) as before, with an assumed mass-to-light ratio of $M/L_i=1.5$ in solar units." + Note that projectiou effects will scatter objects around a eeuuine tidal trend. mt there nav beaeny faint UCDs scattered cftwards.," Note that projection effects will scatter objects around a genuine tidal trend, but there may be faint UCDs scattered leftwards." +" Some of these (e.g... ILL1905 and Ssoos with mfr,~0.1) would be worth more detailed follow-up to ook for indications of dark matter or oueoiuejon."," Some of these (e.g., H44905 and S8005 with $r_{\rm h}/r_{\rm t} \sim 0.4$ ) would be worth more detailed follow-up to look for indications of dark matter or ongoing." + Af very small distauces (1— 13 kpc). there are1ο conpact objects larger thin my~ 8 pe. sugeestiug lat any exteuded objects iu these ceutral regions are lisrupted very quickly.," At very small distances $R \sim$ 1–3 kpc), there are compact objects larger than $r_{\rm h} \sim$ 8 pc, suggesting that any extended objects in these central regions are disrupted very quickly." +" Overall. there mav be a population of UCDs following je scaling relations recently sugeested for ECs. namely quocOL, Uhuley&Mackey2010.afteraccountingoradifferencebetween2-Daud3-D radii)."," Overall, there may be a population of UCDs following the scaling relations recently suggested for ECs, namely $r_{\rm h} \sim 0.1 \, r_{\rm t}$ \citep[after accounting for a difference between 2-D and 3-D radii]{2010MNRAS.408.2353H}." + Ultimately. rough. most of the UCDs (at all Iuuinosities) have sizes ~ [times sinmaller than this. while still beiug much larger lan compact GCs.," Ultimately, though, most of the UCDs (at all luminosities) have sizes $\sim$ 4 times smaller than this, while still being much larger than compact GCs." + This would apparently areuc against a diffuse. tidally-lauited mode of star cluster formation as the origin of these UCDs.," This would apparently argue against a diffuse, tidally-limited mode of star cluster formation as the origin of these UCDs." + There is. potentially. also a woblem for the stripped nuclei scenario. since these are x definition tidally-limited objects.," There is, potentially, also a problem for the stripped nuclei scenario, since these are by definition tidally-limited objects." + However. the Ην scaling relations discussed above may not apply to these objects because of their iuitial two-compoucut structures (nucleus plus envelope).," However, the $r_{\rm h}/r_{\rm t}$ scaling relations discussed above may not apply to these objects because of their initial two-component structures (nucleus plus envelope)." + Tn addition to direct size-related analyses of the AIS? UCDs. we may survev their other properties for conumaionalitfies with star clusters aud galaxy nuclei that could reveal shared heredity or physical influcuces.," In addition to direct size-related analyses of the M87 UCDs, we may survey their other properties for commonalities with star clusters and galaxy nuclei that could reveal shared heredity or physical influences." + These properties include color. age. aud metallicity information: and kinematics (in the next Section).," These properties include color, age, and metallicity information; and kinematics (in the next Section)." + Tn Figure 5 2we present the color-magnitude diagrams (CAID) of AIST GCs and UCDs (those with spectroscopy and measured sizes)., In Figure \ref{fig:cmd} we present the color-magnitude diagram (CMD) of M87 GCs and UCDs (those with spectroscopy and measured sizes). + For magnitudes fainter than M;~ 12.5. the UCDs have a remarkably narrow rauge of colors. compared to the overall GC population. or even to the blue GC subpopulation.," For magnitudes fainter than $M_i \sim -12.5$ , the UCDs have a remarkably narrow range of colors, compared to the overall GC population, or even to the blue GC subpopulation." +" The faint UCD colors are slightly bluer than the blue CC peak. and follow a ""blue tilt” of redder colors with increasingIuninosities."," The faint UCD colors are slightly bluer than the blue GC peak, and follow a “blue tilt” of redder colors with increasingluminosities." +" Among GCs, the blue tilt has been interpreted in terms of sclfeurichinent (e.g.. Iurisetal.2006:Straderct 20001)."," Among GCs, the blue tilt has been interpreted in terms of self-enrichment (e.g., \citealt{2006ApJ...636...90H,2006AJ....132.2333S,2006ApJ...653..193M,2008AJ....136.1828S,2009ApJ...695.1082B}) )." + At the brightest magnitudes. a few UCDs scatter to the red and it is initially teiiptiug to associate these with a different UCD formation chauncl.," At the brightest magnitudes, a few UCDs scatter to the red and it is initially tempting to associate these with a different UCD formation channel." +that svstematic errors in SN Ia photometry will improve sullicienUy for further refinement of cosmological tests to succeed: they must acheive a high level of photometric precision ancl insensilivily (o svstematic error in order (ο measure higher-order parameters characterizing dark energy. (see Linder IHuterer 2003. Tonry 2004).,"that systematic errors in SN Ia photometry will improve sufficiently for further refinement of cosmological tests to succeed; they must acheive a high level of photometric precision and insensitivity to systematic error in order to measure higher-order parameters characterizing dark energy (see Linder Huterer 2003, Tonry 2004)." + While several techiicues incorporate extinction corrections to predict (he Iuminosity of oNe Ia. dust in the interstellar and. circiunstellar medium (ISAT and CSM) can have other ellects.," While several techniques incorporate extinction corrections to predict the luminosity of SNe Ia, dust in the interstellar and circumstellar medium (ISM and CSM) can have other effects." + For instance. Patat (2005) shows that light echoes from dust can introduce several percent changes into the luminosity £L. particularly on the decrease from maximum light. and reducing L while increasing maximum lighteurve width Any; in a stochastic manner depending on seemingly random placement of surrounding material.," For instance, Patat (2005) shows that light echoes from dust can introduce several percent changes into the luminosity $L$, particularly on the decrease from maximum light, and reducing $L$ while increasing maximum lightcurve width $\Delta m_{15}$ in a stochastic manner depending on seemingly random placement of surrounding material." + There are many wavs in whieh SN Ia luminosity might relate to environment., There are many ways in which SN Ia luminosity might relate to environment. + Hanniy οἱ ((2000) explore how SN Ia brightness is related to galaxian integrated colors and speculate that Chis connection proceeds via metallicity., Hamuy et (2000) explore how SN Ia brightness is related to galaxian integrated colors and speculate that this connection proceeds via metallicity. + Umeda et ((1999) suggest that metallicity impacts the carbon fraction in C+O white dwarf stus (WD)., Umeda et (1999) suggest that metallicity impacts the carbon fraction in $+$ O white dwarf stars (WD). +" Recent evidence points to a relation of Aimy; to galaxy morphology (Altavilla et 22004. Della Valle et 22005) and there appears to be bimodality in progenitor age (1 Gv aa few Gv: Moanucd et 22006). w""Iich is reflected in Any; (Hoanuy et 11996. van den Bergh et 22005)."," Recent evidence points to a relation of $\Delta m_{15}$ to galaxy morphology (Altavilla et 2004, Della Valle et 2005) and there appears to be bimodality in progenitor age $\approx 1$ Gy a few Gy: Mannucci et 2006), which is reflected in $\Delta m_{15}$ (Hamuy et 1996, van den Bergh et 2005)." + These ellects are sulliciently well known to SN observers but become much more difficult to treat ab higher redshift where host galaxies are more ellusive e.g.. Folev et ((2007).," These effects are sufficiently well known to SN observers but become much more difficult to treat at higher redshift where host galaxies are more ellusive e.g., Foley et (2007)." +" There are several wavs to determine if substantial cireumstellar effects er 5Ne Ia e.g.. high-velocitv and spectroscopic MON (Gerardy οet ...22004. Mazzali et 22005. Wang et 22003. MMQuimby et ""22006) that might be elv (Quimby et -22006) as structure internal to explosion (Mazzali οἱ GN22005)."," There are several ways to determine if substantial circumstellar effects influence SNe Ia e.g., high-velocity and time-variable spectroscopic components (Gerardy et 2004, Mazzali et 2005, Wang et 2003, Quimby et 2006) that might be explained alternatively (Quimby et 2006) as structure internal to the explosion (Mazzali et 2005)." + In many Or ost Cases efforts fail to establish a circumstellar component e.g.. 2000ex atn et 220072). ancl when detected sometimes involves peculiar SNe Ia (PMEN --et 22006) or questionable (Denetti οἱ 22006) SNe Ia (see also Lanny et 22003. el 22006. Prieto et 22007).," In many or most cases such efforts fail to establish a circumstellar component e.g., SN 2000cx (Patat et 2007a), and when detected sometimes involves peculiar SNe Ia (Panagia et 2006) or questionable (Benetti et 2006) SNe Ia (see also Hamuy et 2003, Aldering et 2006, Prieto et 2007)." + Tammy et (2003) suggest a new class of CSM-dominated Type la (for example SNe 19976. LODOE and 2000210). bul these would compose fewer than of all SNe Ia. In general only upper limits are placed on the mass-loss rate by optical (Mattila et 22005). radio (Panagia et 22006) and UV/X observations (lamer et 22006).," Hamuy et (2003) suggest a new class of CSM-dominated Type Ia (for example SNe 1997cy, 1999E and 2002ic), but these would compose fewer than of all SNe Ia. In general only upper limits are placed on the mass-loss rate by optical (Mattila et 2005), radio (Panagia et 2006) and UV/X observations (Immler et 2006)." + Likewise. theory is a poor guide. in part because SN la progenitors are a small and not well-isolated subcomponent of accreGne WDs: SN Ia progenitors compose probably about. of binaries in the appropriate initial mass range (38 AL.) and almost certainly of these (Maoz 2007).," Likewise, theory is a poor guide, in part because SN Ia progenitors are a small and not well-isolated subcomponent of accreting WDs: SN Ia progenitors compose probably about of binaries in the appropriate initial mass range (3–8 $M_\odot$ ) and almost certainly of these (Maoz 2007)." + Since the last known Galactic SN In was in the vear 1604 (and last in the Local Group probably in 1885). detailed ground-based study of SN Ia remnants or the small fraction of la progenitors among the larger population of WD accreting binaries," Since the last known Galactic SN Ia was in the year 1604 (and last in the Local Group probably in 1885), detailed ground-based study of SN Ia remnants or the small fraction of Ia progenitors among the larger population of WD accreting binaries" +where ης is the deusity for s=0. aud mmass-size slopes Both velatious apply oulv if À<3.,"where $n_{\rm c}$ is the density for $s = 0$, and mass-size slopes Both relations apply only if $k < 3$." + As the equations show. the intercept contains information on the ceutral density. aud the mass-size slope depends on the slope of the density law. &.," As the equations show, the intercept contains information on the central density, and the mass-size slope depends on the slope of the density law, $k$." + Both does. of course. only hold. at intermediate radi. sy«rB.," Both does, of course, only hold at intermediate radii, $s_0 \ll r \ll R$." +" For reference. we note that the column density obeys Nxr4.F, "," For reference, we note that the column density obeys $N \propto r^{1 - k}$." +A eeneralized version of power-law spheres are tri- cllipsoids., A generalized version of power-law spheres are tri-axial ellipsoids. + Appendix A.3 cousiders the case iu which n(s)x(s/sy) along any main axis. but with sj depending ou the direction chosen reteq-app:deusity-law-cllipsoidal)).," Appendix \ref{sec-app:density-triaxial} considers the case in which $n(s) \propto (s / s_0)^{-k}$ along any main axis, but with $s_0$ depending on the direction chosen \\ref{eq-app:density-law-ellipsoidal}) )." + —Detailed analvsis shows that such cllipsoids follow the same iass-size relations as spheres. when r=(4z)bO.," Detailed analysis shows that such ellipsoids follow the same mass-size relations as spheres, when $r = (A / \pi)^{1/2}$." + Thus the laws listed above apply.," Thus, the laws listed above apply." + Iu a nest step. one nav wish to consider models of cevlndzrical clouds of leugth (.," In a next step, one may wish to consider models of cylindrical clouds of length $\ell$ ." + Tere. we adopt deusitv drops nfs)xsP perpendicular to the cylinder axis for intermediate values of s.," Here, we adopt density drops $n(s) \propto s^{-k}$ perpendicular to the cylinder axis for intermediate values of $s$." + At interiuediate radi R. such clouds obey if their major axis is perpendicular to the line of sight. aud if the axes are aligned. (," At intermediate radii $s_0 \ll r \ll R$ , such clouds obey if their major axis is perpendicular to the line of sight, and if the axes are aligned. (" +Iuteriiediate angles are not considered here.),Intermediate angles are not considered here.) + Meauingful relations are ouly obtained for k<2., Meaningful relations are only obtained for $k < 2$. + Iu both relations. the radius is defined as r—(ax).," In both relations, the radius is defined as $r = (A / \pi)^{1/2}$." + Thus. just as one may naivolv expect. the mass-s1ze slope gauges the slope of the density profile.," Thus, just as one may naively expect, the mass-size slope gauges the slope of the density profile." + Further. the intercepts of miass-size relations coustrain the absolute density of cloud fragments.," Further, the intercepts of mass-size relations constrain the absolute density of cloud fragments." + There is. however. onc less obvious fact that calls for attention: the exact relations between imass-size slopes. intercepts. and deusitv law depends on the cloud model aud viewing angele.," There is, however, one less obvious fact that calls for attention: the exact relations between mass-size slopes, intercepts, and density law depends on the cloud model and viewing angle." + It is therefore not possible to derive the true density profile without further information ou the cloud geometry., It is therefore not possible to derive the true density profile without further information on the cloud geometry. + Such information maw. eg. be derived bv studving the elongation of cloud fragments.," Such information may, e.g., be derived by studying the elongation of cloud fragments." + Also. the above power-law relations do oulv apply at intermediate radi sy< pF.," Also, the above power-law relations do only apply at intermediate radii, $s_0 \ll r \ll R$ ." + This domain night not exist in actual observed clouds., This domain might not exist in actual observed clouds. + Then. the central density plateau aud the fuite size have to be cousidered.," Then, the central density plateau and the finite size have to be considered." + These eive The density slopes theiiselves depend on the processes shaping the model cloud., These give The density slopes themselves depend on the processes shaping the model cloud. + As a first example. here we consider static equilibria models in which pressure eradieuts are in balance with sclferavity.," As a first example, here we consider static equilibrium models in which pressure gradients are in balance with self-gravity." + We assume a polvtrophic equation of state. Px»5n. in which pressure and density are related by the polytrophic exponent. 7p.," We assume a polytrophic equation of state, $P \propto n^{\gamma_P}$, in which pressure and density are related by the polytrophic exponent, $\gamma_P$." + Iu Appendix D. ve show that for polvtropic equilibrimm spheres (Gf sp<< 1/23) aud evliuders Gf +p< 1)., In Appendix \ref{sec-app:polytropes} we show that for polytropic equilibrium spheres (if $\gamma_P < 4/3$ ) and cylinders (if $\gamma_P < 1$ ). + The deusitv aud. miass-size slopes are. thus. related to the polvtrophic exponent.," The density and mass-size slopes are, thus, related to the polytrophic exponent." + Tsothermal pressure. for which +p=1. προς &=2 in spheres. for example.," Isothermal pressure, for which $\gamma_P = 1$, implies $k = 2$ in spheres, for example." + Then. dlug)/dlute)=1 iu spherical model clouds: laws too complex to be considered here apply to evliuders.," Then, ${\rm d} \, \ln(m) / {\rm d} \, \ln(r) = 1$ in spherical model clouds; laws too complex to be considered here apply to cylinders." +" As seen in reffie:elobal-slopes,fendb.. suchaimodcleauceplaiusoime .butnotinos "," As seen in \\ref{fig:global-slopes_sf} and \ref{fig:slope-comparison}, such a model can explain some, but not most slope measurements." +Polvtropic exponeuts sp=1/2 are sometimes suggested to describe “turbulent” pressure within clouds. as aarising from Alfvóun waves (7).," Polytropic exponents $\gamma_P = 1/2$ are sometimes suggested to describe “turbulent” pressure within clouds, as arising from Alfvénn waves \citep{mckee1995:alfven_waves}." + In this case. k3. and so dluda)/dlade) assumes values of 5/3z1.67 (spheres aud ellipsoids). L/3221.33 (perpenudicularly viewed οΗστ). aud 2/33z0.67 fenc-ou ονΠιο). for he different models.," In this case, $k = 4/3$, and so ${\rm d} \, \ln(m) / {\rm d} \, \ln(r)$ assumes values of $5/3 \approx 1.67$ (spheres and ellipsoids), $4/3 \approx 1.33$ (perpendicularly viewed cylinder), and $2/3 \approx 0.67$ (end-on cylinder) for the different models." + Amoue these. spheres. ellipsoids. and cylinders viewed from the side provide au acceptable natch to the observed mass-size slopes 521.," Among these, spheres, ellipsoids, and cylinders viewed from the side provide an acceptable match to the observed mass-size slopes $b > 1$." + Cylinders viewed along their major axis vield too shallow niass-size aws (and such a viewing direction is hiehly unlikely)., Cylinders viewed along their major axis yield too shallow mass-size laws (and such a viewing direction is highly unlikely). + For a given physical model. the intercept cau be used ο gauge a clouds stability against collapse. rexpectively Sugeest the level of supporting pressure.," For a given physical model, the intercept can be used to gauge a cloud's stability against collapse, respectively suggest the level of supporting pressure." + Here. we μπιτ ourselves to the isothermal case. 5p=1.," Here, we limit ourselves to the isothermal case, $\gamma_P = 1$." + Stability considerations (ce... of Dounor-Ebert-tvpe: ?.. 2)) iuplyv for the total mass. where e(c) is the characteristic one-dimensional velocity dispersion refeq-appianass-limut-spheres and D5)).," Stability considerations (e.g., of Bonnor-Ebert-type; \citealt{ebert1955:be-spheres}, , \citealt{bonnor1956:be-spheres}) ) imply for the total mass, where $\sigma(v)$ is the characteristic one-dimensional velocity dispersion \\ref{eq-app:mass-limit-spheres} and \ref{eq-app:mass-limit-cylinders}) )." + For spheres. A> is the radius. while Ro»¢€ in cxliuders.," For spheres, $R$ is the radius, while $R \to \ell$ in cylinders." + If ofe) is known (eg. for thermal pressure). AfoM4 nuplies collapse of the object considered.," If $\sigma(v)$ is known (e.g., for thermal pressure), $M > M_{\rm cr}$ implies collapse of the object considered." + Conversely. depending ou the situation. a(¢) can be interred by requiring tha AM=AL.," Conversely, depending on the situation, $\sigma(v)$ can be inferred by requiring that $M = M_{\rm cr}$." + Required values of o(¢) significantly in excess of the thermal velocity dispersion of the mean fee particle nueht. e.g.. sugeest the presence of significa nou-thermal pressure.," Required values of $\sigma(v)$ significantly in excess of the thermal velocity dispersion of the mean free particle might, e.g., suggest the presence of significant non-thermal pressure." +" If we oulv require that pressur¢ balances gravity, aud drop the constraint that the objec is to be stable against perturbations. the above law yield:4. ((8))."," If we only require that pressure balances gravity, and drop the constraint that the object is to be stable against perturbations, the above law yields \ref{eq:mass-size-sis}) )." + As particular example. consider BGs.," As particular example, consider B68." + It is thought tha this dense core has a structure very similar to à Dounor-Ebert sphere (?).., It is thought that this dense core has a structure very similar to a Bonnor-Ebert sphere \citep{alves2001:b68}. + Thus. one would expect the mass aud size of BOS to obey ((8)). when considering larec enough radii.," Thus, one would expect the mass and size of B68 to obey \ref{eq:mass-size-sis}) ), when considering large enough radii." + This is indeed the case. as seen in veffiie:cloud-samiple..," This is indeed the case, as seen in \\ref{fig:cloud-sample}." + For intuitivecomuuication. it may be helpful to report svnoptic density slopes. tthe density slope a sphere of the same mass-size slope would have when observed at intermeciate radi.," For intuitivecommunication, it may be helpful to report synoptic density slopes, the density slope a sphere of the same mass-size slope would have when observed at intermediate radii." + The synoptic slopes give a good first idea of the true density slopes., The synoptic slopes give a good first idea of the true density slopes. + First. recall that the modelmass-size laws do not scusitively depend ou the assuuption of exact spheres: the same relation holds for ellipsoids.," First, recall that the modelmass-size laws do not sensitively depend on the assumption of exact spheres; the same relation holds for ellipsoids." + Also. in the observed range1ZdπαςInter)« 2. spheres (or ellipsoids) aud perpendicularly viewed cvlucders (the end-on view is statistically insignificant) nuplv similar slopes: for these geometries. the svnoptic slopes exceed the true ones by less than 0.5. assunüug intermeciate," Also, in the observed range$1 \lesssim {\rm d} \, \ln(m) / {\rm d} \, \ln(r) < 2$ , spheres (or ellipsoids) and perpendicularly viewed cylinders (the end-on view is statistically insignificant) imply similar slopes; for these geometries, the synoptic slopes exceed the true ones by less than 0.5, assuming intermediate" +frequency in the power spectral density distribution or a turnover (rollover) time scale in the structure function (Meyer et al.,frequency in the power spectral density distribution or a turnover (rollover) time scale in the structure function (Meyer et al. + 2009)., 2009). + This technique is widely used in the study of AGN light curves in X-rays (Kataoka et al., This technique is widely used in the study of AGN light curves in X-rays (Kataoka et al. + 2001)., 2001). +" However, a recent study by Emmanoulopoulos et al. ("," However, a recent study by Emmanoulopoulos et al. (" +2010) concludes that any break timescales derived from SFs are doubtful as they depend very much on the length and underlying power spectral density of the data sets used.,2010) concludes that any break timescales derived from SFs are doubtful as they depend very much on the length and underlying power spectral density of the data sets used. +" Thus, this paper does not investigate the nature of breaks in the structure function and uses different analysis techniques to confirm the behavior of the calculated structure functions at short time scales."," Thus, this paper does not investigate the nature of breaks in the structure function and uses different analysis techniques to confirm the behavior of the calculated structure functions at short time scales." +" To address the time variability of Ser ΑΧ. we use three different methods of analysis, namely, structure function, power spectra and autocorrelation function."," To address the time variability of Sgr A*, we use three different methods of analysis, namely, structure function, power spectra and autocorrelation function." + Two different types of power spectrum are also calculated., Two different types of power spectrum are also calculated. +" One type of power spectrum is subjected to the CLEAN deconvolution algorithm and the power spectra are calculated using the procedure documented in Appendices B and C of Roberts, Lehar Dreher (1987)."," One type of power spectrum is subjected to the CLEAN deconvolution algorithm and the power spectra are calculated using the procedure documented in Appendices B and C of Roberts, Lehar Dreher (1987)." +" The CLEAN power spectrum is shown in equally-spaced bins in log space, with 30 bins covering the range between v=10°? min-1 and 10 min!."," The CLEAN power spectrum is shown in equally-spaced bins in log space, with 30 bins covering the range between $\nu = 10^{-2}$ $^{-1}$ and 10 $^{-1}$." + Another type of power spectrum follows the prescription given by Uttley et al. (, Another type of power spectrum follows the prescription given by Uttley et al. ( +2002).,2002). +" This derivation, which does not include any CLEAN deconvolution, computes the power spectrum from Vpn (1/T when T is the length of the light curve in the time domain) up to the Nyquist frequency and normalizes it such that the integration from 1, to νο gives the contribution to the fractional rms squared variability on time scales v4! to VQ'"," This derivation, which does not include any CLEAN deconvolution, computes the power spectrum from $\nu_{min}$ (1/T when T is the length of the light curve in the time domain) up to the Nyquist frequency and normalizes it such that the integration from $\nu_1$ to $\nu_2$ gives the contribution to the fractional rms squared variability on time scales $\nu_2^{-1}$ to $\nu_1^{-1}$." + Both power spectra are binned and power law slopes are fitted into the entire spectrum., Both power spectra are binned and power law slopes are fitted into the entire spectrum. +" In addition, we present autocorrelation function which can potentially provide information on the nature of the physical process causing any observed variability."," In addition, we present autocorrelation function which can potentially provide information on the nature of the physical process causing any observed variability." + The auto-correlation analysis uses the Z-transformed discrete correlation function (ZDCF) algorithm (Alexander 1997)., The auto-correlation analysis uses the Z-transformed discrete correlation function (ZDCF) algorithm (Alexander 1997). + A maximum in the likelihood value is identified at a zero time lag., A maximum in the likelihood value is identified at a zero time lag. + The ZDC function is an improved solution to the problem of investigating correlation in unevenly sampled light curves., The ZDC function is an improved solution to the problem of investigating correlation in unevenly sampled light curves. +" The standard solutions are interpolation of the existing light curve, which is considered to be unreliable when power exists on smaller timescales than the gaps and binning the data using discrete correlation functions (e.g., Edelson Krolik 1988)."," The standard solutions are interpolation of the existing light curve, which is considered to be unreliable when power exists on smaller timescales than the gaps and binning the data using discrete correlation functions (e.g., Edelson Krolik 1988)." +" Here, we first investigate the nature of time variability of Sgr A* in radio wavelengths using these three different statistical analysis."," Here, we first investigate the nature of time variability of Sgr A* in radio wavelengths using these three different statistical analysis." +" We then compare structure function and CLEAN power spectrum of IR, X-ray and radio data taken simultaneously on 2007, April 4."," We then compare structure function and CLEAN power spectrum of IR, X-ray and radio data taken simultaneously on 2007, April 4." +The challenge with using the far-IR bump as a redshift indicator is that the average dust teiiperature and the redshift are degenerate (e.g.displacement Blain 1999: Blain. Daruaxd Chapman 2003).,"The challenge with using the far-IR bump as a redshift indicator is that the average dust temperature and the redshift are degenerate (e.g. Blain 1999; Blain, Barnard Chapman 2003)." + Wieus law tells us that the waveleusth of the peak of a blackbody scales with the dust temperature., Wien's displacement law tells us that the wavelength of the peak of a blackbody scales with the dust temperature. + Coupling this with the displacement of the peak due to redshift we fud that the observed wavelength of the far-IR peak depends linearly ou both the redshift and the inverse of the dust temperature:ARESX(1d2Taner:, Coupling this with the displacement of the peak due to redshift we find that the observed wavelength of the far-IR peak depends linearly on both the redshift and the inverse of the dust temperature:$\lambda_{\rm{obs}}^{\rm{max}}\propto(1+z)/\rm{T}_{\rm{dust}}$. + The most bhpuuimous galaxies in the local Universe show fu-infrared color temperatures that peak at ~ lols althoueh there is a ο“ scatter in lhuninositv-teiiperature parameter space (e.g.uiperatures Dunne et al.," The most luminous galaxies in the local Universe show far-infrared color temperatures that peak at $\sim$ $\,$ K although there is a significant scatter in luminosity-temperature parameter space (e.g. Dunne et al." + 2000)., 2000). + For a reasonable range of dust te for ULIRGs. sources that peak at 500442 can be found auvwhere between :~23 6.," For a reasonable range of dust temperatures for ULIRGs, sources that peak at $\,\mu$ m can be found anywhere between $z\sim3$ –6." + This is a verv huge range in redshift and without prior information about the dust teiiperature it is difficult to further constrain the redshitt with the SPIRE data alone., This is a very large range in redshift and without prior information about the dust temperature it is difficult to further constrain the redshift with the SPIRE data alone. + Iu order to test this technique on observations we use the data from the BLAST survev of ECDFS (Devlin et al., In order to test this technique on observations we use the data from the BLAST survey of ECDFS (Devlin et al. + 2009)., 2009). + BLAST has the same three detectors as Terschel/SPIRE but with beam sizes that are twice as bie: 36. 12. GO aresecs FWIIM. at 250. 350 and 500/24 respectively (Marsden ot al.," BLAST has the same three detectors as /SPIRE but with beam sizes that are twice as big; 36, 42, 60 arcsecs FWHM at 250, 350 and $\,\mu$ m respectively (Marsden et al." + 2009)., 2009). + We use the publicly released BLAST aud the matched filter catalogs (Chapin et al., We use the publicly released BLAST and the matched filter catalogs (Chapin et al. + 2010)., 2010). + These matched filter catalogs o a nmch better job at de-bleudiug adjacent sources and result in higher signal-to-noise ratios thin previous BLAST catalogs (see Chapin et al., These matched filter catalogs do a much better job at de-blending adjacent sources and result in higher signal-to-noise ratios than previous BLAST catalogs (see Chapin et al. + 2010 for further etails)., 2010 for further details). +" We restrict our analysis to the ceutral dee? of the BLAST image where og,< 101iJy. at ju. We have couservatively added the confusion noise im quadrature with the instrament noise (στcouiust2 O24) for all analysis iu this paper."," We restrict our analysis to the central $\,$ $^{2}$ of the BLAST image where $\sigma_{\rm{inst}}<10\,$ mJy at $\,\mu$ m. We have conservatively added the confusion noise in quadrature with the instrument noise $\sigma_{\rm{conf}}^{2}+\sigma_{\rm{inst}}^{2}=\sigma_{\rm{tot}}^{2}$ ) for all analysis in this paper." + We only cousider detections if they 59g (C 3054)., We only consider detections if they are $>5\sigma_{\rm{inst}}$ $>3\sigma_{\rm{tot}}$ ). + Iu this central region there are23 andy.anegalaxies robustly detected at 500 pau with $399> ," In this central region there are 23 galaxies robustly detected at $500\,\mu$ m with $S_{500}>45\,$ mJy." +"We iatch the gau-sclected ealaxies to the matched filter catalogs at 25000. and 350,00: we consider auv >Soi, detection within a radius of G0 arcsecs to be the counterpart to the sau cCluission."," We match the $\,\mu$ m-selected galaxies to the matched filter catalogs at $\,\mu$ m and $\,\mu$ m; we consider any $>5\sigma_{\rm{inst}}$ detection within a radius of 60 arcsecs to be the counterpart to the $\,\mu$ m emission." + For sources which are at these other wavelengths we set upper limits ou nideteetedlimitthe350 aud 250424 fluxes from the coiipleteness of the survev (Chapin et al.," For sources which are undetected at these other wavelengths we set upper limits on the 350 and $\,\mu$ m fluxes from the completeness limits of the survey (Chapin et al." +" 2010) which is equivalent to 361,4.", 2010) which is equivalent to $3\sigma_{\rm{tot}}$ . + Of these 23 500 pau-sclected galaxies 8 have 9399>Sa35sg indicating that the dust SED peaks at or near gan we refer to these galaxies as san speakers’ (although their peak may be at even lonecr wavelengths).," Of these 23 $\,\mu$ m-selected galaxies, 8 have $S_{500}>S_{350}$ indicating that the dust SED peaks at or near $\,\mu$ m – we refer to these galaxies as $\,\mu$ m `peakers' (although their peak may be at even longer wavelengths)." +" Tuterestingly. none of these jan peakers (detected at > Foire) are detected above 5og, at 250 and pan. We inspected all of these candidates by haud in the BLAST images to make sure they are not obviously blended."," Interestingly, none of these $\,\mu$ m peakers (detected at $>5\sigma_{\rm{inst}}$ ) are detected above $5\sigma_{\rm{inst}}$ at 250 and $\,\mu$ m. We inspected all of these candidates by hand in the BLAST images to make sure they are not obviously blended." + We have not attempted to correct for flux boosting(c.g. hotCoppin ct al., We have not attempted to correct for flux boosting (e.g. Coppin et al. + 2006) in this analysis but. suce We are iuterested iu the absolute fluxes aud ouly the relative colors. this is less of a concern.," 2006) in this analysis but, since we are not interested in the absolute fluxes and only the relative colors, this is less of a concern." + Iu additiou by considering only higher signal-to-noise ratio sources we eusure that this effect is minimal., In addition by considering only higher signal-to-noise ratio sources we ensure that this effect is minimal. +" In order to assess how photometric uncertainties (from both confusion aud iustrunient noise) affect the απνο of jan peakers identified. we ran a Moute Carlo simulation to randomly xuuple the fluxes of each of the 223 sources frou a Gaussian distribution 90,4."," In order to assess how photometric uncertainties (from both confusion and instrument noise) affect the number of $\,\mu$ m peakers identified, we ran a Monte Carlo simulation to randomly sample the fluxes of each of the 23 sources from a Gaussian distribution $S\pm\sigma_{\rm{tot}}$." + We find that photometric uncertainties can vary the wmmber of sources with 5399 by 2., We find that photometric uncertainties can vary the number of sources with $S_{500}>S_{350}$ by 2. + Thus our final number of pau peakers is 52.," Thus our final number of $\,\mu$ m peakers is $8\pm2$ ." + These 8 high redshift candidates are listed in Table 1 along with their fluxes aud Fie., These 8 high redshift candidates are listed in Table 1 along with their fluxes and Fig. + 1 shows an example SED for oue source., \ref{fig:sed} shows an example SED for one source. + Five of these san peakers are within the ECDFS field and one is within the smaller CGOODS- region (sce Table 1).," Five of these $\,\mu$ m peakers are within the ECDFS field and one is within the smaller GOODS-S region (see Table 1)." + The source within GOODS-S is associated (6 aresecs away) frou an AzTEC nuu cleteeted source (GSII. Scott etal.," The source within GOODS-S is associated (6 arcsecs away) from an AzTEC $\,$ mm detected source (GS11, Scott etal." + 2010): however. flux boosting in the BLAST bands prohibit a detailed conarison.," 2010); however, flux boosting in the BLAST bands prohibit a detailed comparison." + Knowing that à source peaks at (or near) jun does not provide a definitive redshift due to the degeueracy between redshift and temperature (e.g. Fie. 2)).," Knowing that a source peaks at (or near) $\,\mu$ m does not provide a definitive redshift due to the degeneracy between redshift and temperature (e.g. Fig. \ref{fig:Tdust}) )." + If we conservatively assume that all jaa peakers are atity 2> can obtain au upper lait ou the uuuber cer of ;>| galaxies predicted inMersehel SPIRE surveys.," If we conservatively assume that all $\,\mu$ m peakers are at $z>4$ we can obtain an upper limit on the number density of $z>4$ galaxies predicted in SPIRE surveys." + Based ou our analysis of the BLAST data. the mmuber density of galaxies (wwith Ssoy2Mandy) which peal a µια is 17+[deg 7.," Based on our analysis of the BLAST data, the number density of galaxies (with $_{500}>45\,$ mJy) which peak at $\,\mu$ m is $17\pm4\,$ $^{-2}$." + We expect that some of the μι peakers will be at 2<S_{350}$ but be at $z<4$." + To get an estimate of the contamination of low redshift. cooler galaxies in the 500444 peaker saiuple we nius assune a redshift and dust temperature distribution.," To get an estimate of the contamination of low redshift, cooler galaxies in the $\,\mu$ m peaker sample we must assume a redshift and dust temperature distribution." + Asstuuing a flat redshift and a dust color temperature distribution of 35+που7IN'.. we estimate tha 15% of 500;mu peakers will be :«L4 (eft panel of Fie. 21).," Assuming a flat redshift and a dust color temperature distribution of $35\pm7\,$, we estimate that $15\,$ of $\,\mu$ m peakers will be $z<4$ (left panel of Fig. \ref{fig:Tdust}) )." + In addition. we must also account for the contribution from wariuer sources at 2o>[ but which peak at lower waveleusths (συ 5339).," In addition, we must also account for the contribution from warmer sources at $z>4$ but which peak at lower wavelengths $S_{500}[ again followiug a dust distribution of 354 71k. we find that oulv 104 have tenrperatureS309aud4$ again following a dust temperature distribution of $35\pm7\,$ K, we find that only $10\,$ have $S_{500}4$ sources (with$_{500}>45\,$ mJy) of $<17\,$ $^{-2}$." + The above lint on the number deusitv of :> SAICs ambitiously assumes a flat redshift distribution., The above limit on the number density of $z>4$ SMGs ambitiously assumes a flat redshift distribution. + If instead we asstune the observed redshift distribution of SACs (2.24 0.8. Chapman et al.," If instead we assume the observed redshift distribution of SMGs $2.2\pm0.8$ , Chapman et al." + 2005: Pope et al., 2005; Pope et al. + 2006). we find only of the 500444 peakers at + (xieght panel of Fig. 2))," 2006), we find only of the $\,\mu$ m peakers at $z>4$ (right panel of Fig. \ref{fig:Tdust}))" + which brings the wuuber density estimate down to 2deg 7.," which brings the number density estimate down to $2\,$ $^{-2}$ ." + Based ou our analvsis of the BLAST data. we conclude that the umber density of στ> Lundy sources at 2> Lis <Ἱτάσο 7 and couk be as low as 2dee 7.," Based on our analysis of the BLAST data, we conclude that the number density of $_{500}>45\,$ mJy sources at $z>4$ is $<17\,$ $^{-2}$ and could be as low as $2\,$ $^{-2}$ ." + With some assumptions about the dust teniperature distribution. we have shown that the swhinilimetercolor selection. Ssyy2S359 is a plausible wav to ideutity," With some assumptions about the dust temperature distribution, we have shown that the submillimetercolor selection, $S_{500}>S_{350}$ is a plausible way to identify" +third bodies around eclipsing binaries because the amplitude of the time delay due to the LTT effect is proportional to 5 while the spectroscopic semi-amplitude is proportional to P7.,third bodies around eclipsing binaries because the amplitude of the time delay due to the LTT effect is proportional to $P_{12}^{2/3}$ while the spectroscopic semi-amplitude is proportional to $P_{12}^{-1/3}$. + When the samples of spectroscopic and LTT systems are sufficiently large. we will have a complete picture of the distribution of bodies in a stellar system and a realistic test of planet formation theories will be possible.," When the samples of spectroscopic and LTT systems are sufficiently large, we will have a complete picture of the distribution of bodies in a stellar system and a realistic test of planet formation theories will be possible." + Finally. the LTT analysis method does not have to be necessarily applied to eclipsing binaries.," Finally, the LTT analysis method does not have to be necessarily applied to eclipsing binaries." + In essence. the method is based upon having a “beacon in orbit”. which. in the case of eclipsing binaries. are the mid-eclipse times.," In essence, the method is based upon having a “beacon in orbit”, which, in the case of eclipsing binaries, are the mid-eclipse times." + However. any strictly periodic event that can be predicted with good accuracy could be potentially useful to detect stellar or sub-stellar companions.," However, any strictly periodic event that can be predicted with good accuracy could be potentially useful to detect stellar or sub-stellar companions." + This includes. for example. pulsating stars.," This includes, for example, pulsating stars." + More interestingly. transiting planets are also prime candidates for LTT studies.," More interestingly, transiting planets are also prime candidates for LTT studies." + In this case. not only further orbiting planets could be discovered. but also good chances for detecting moons around the transiting planet exist.," In this case, not only further orbiting planets could be discovered, but also good chances for detecting moons around the transiting planet exist." + Dr. S. E. Urban (US Naval Observatory). who provided the older epoch astrometric data of R CMa ts warmly thanked.," Dr. S. E. Urban (US Naval Observatory), who provided the older epoch astrometric data of R CMa is warmly thanked." + The APT observations were acquired and reduced using programs developed by Dr. G. P. MeCook. who is gratefully acknowledged.," The APT observations were acquired and reduced using programs developed by Dr. G. P. McCook, who is gratefully acknowledged." + Also. we thank astronomy students J. J. Bochanski and D. Stack for help with data preparation for this work.," Also, we thank astronomy students J. J. Bochanski and D. Stack for help with data preparation for this work." + The anonymous referee is thanked for a number of important comments and suggestions that led to the improvement of the paper., The anonymous referee is thanked for a number of important comments and suggestions that led to the improvement of the paper. + [. R. thanks the Catalan Regional Government (CIRIT) for financial support through a Fulbright fellowship., I. R. thanks the Catalan Regional Government (CIRIT) for financial support through a Fulbright fellowship. + This research was supported by NSE/RUI grants AST 93-15365. AST 95-285006. and AST 00-71260.," This research was supported by NSF/RUI grants AST 93-15365, AST 95-28506, and AST 00-71260." +Absorption Line (BAL) quasar.,Absorption Line (BAL) quasar. +" We thus refit the Ly-a-N Si I, fixing the Ly-o peak using the O redshift."," We thus refit the $\alpha$ -N }-Si , fixing the $\alpha$ peak using the O redshift." +" We present both the ""free"" (non-BAL) and ""fixed"" (BAL) results."," We present both the ""free"" (non-BAL) and ""fixed"" (BAL) results." +" For the remainder of this paper, we use values consistent with the BAL assumption."," For the remainder of this paper, we use values consistent with the BAL assumption." +" We estimate the redshift to be 5.7321 + 0.0065 the O line in Fig. 6,"," We estimate the redshift to be 5.7321 $\pm$ 0.0065 using the O line in Fig. \ref{fig:fit}," + which is our most statistically usingrobust emission line., which is our most statistically robust emission line. +" Using the ""fixed"" fit, the lines have a measured redshift scatter of 0.02 (see Table 3)), which represents the astrophysical systematic uncertainty."," Using the ""fixed"" fit, the lines have a measured redshift scatter of 0.02 (see Table \ref{tab:fits}) ), which represents the astrophysical systematic uncertainty." +" If we refit our peaks with the (SDSS average) ΑΙ power law continuum, the redshifts only shift by 0.004, so our dominant source of uncertainty appears to be astrophysical."," If we refit our peaks with the (SDSS average) $\lambda^{-1.3}$ power law continuum, the redshifts only shift by 0.004, so our dominant source of uncertainty appears to be astrophysical." + Ourfinal redshift estimate is 5.73 + 0.02., Ourfinal redshift estimate is 5.73 $\pm$ 0.02. +cosmological hyvdrodynamic simulations.,cosmological hydrodynamic simulations. + In Section 3.. we construct the composite CSME by combining the samples of galaxies from simulations with different resolution and volumes.," In Section \ref{sec:MF}, we construct the composite GSMF by combining the samples of galaxies from simulations with different resolution and volumes." + We study the cosmic SER and p; evolution in Section 4.., We study the cosmic SFR and $\rhostar$ evolution in Section \ref{sec:SF}. + We summarise and discuss our [findings in Section 5.., We summarise and discuss our findings in Section \ref{sec:summary}. + We use the modified. version of the. tree-particle-mesh smoothed particle hyelrodvnamics (SPII) code CLADGIZI-3 (originallydescribedinSpringel2005)., We use the modified version of the tree-particle-mesh smoothed particle hydrodynamics (SPH) code GADGET-3 \citep[originally described in][]{Springel:05}. +. Our conventional code includes radiative cooling by LL. Ho. and metals (Choi&Nagamine 2009).. heating by a uniform UV background of a moclified Llaarcdt&Macau(1996). spectrum: (Ixatzetal.1996:Davé 1999).. star formation. its feedback. a phenomenological model for galactic winds. and a resolution model of multiphase LSAL (Springel& LHoern- 2003a).," Our conventional code includes radiative cooling by H, He, and metals \citep{Choi.Nagamine:09}, heating by a uniform UV background of a modified \citet{Haardt.Madau:96} spectrum \citep{Katz.etal:96,Dave.etal:99}, star formation, its feedback, a phenomenological model for galactic winds, and a sub-resolution model of multiphase ISM \citep{Springel.Hernquist:03}." +. For the star formation model. we use the “Pressure model” whieh reduces the high-: SERD (Schave&DallaVecchia2008:ChoiNagamine2010). relative to the previous model by Springel&Iernquist.(2003a).," For the star formation model, we use the “Pressure model” which reduces the $z$ SFRD \citep{Schaye.DallaVecchia:08,Choi.Nagamine:10} relative to the previous model by \citet{Springel.Hernquist:03}." +. For the galactic outflow model. we use the Multicomponent VariableVelocity. wind. model developed. by Choi.&Nagamine (2011)..," For the galactic outflow model, we use the Multicomponent VariableVelocity wind model developed by \citet{Choi.Nagamine:11}. ." +" We adopt the following cosmological parameters that are consistent with the WALADP best-fit values (xomatsuetal.2011): O,,= 0.26. O4=0.74. QO,=0.044. h=0.72. n,=0.96. and ax=0.50."," We adopt the following cosmological parameters that are consistent with the WMAP best-fit values \citep{Komatsu.etal:11}: $\Omega_m = 0.26$ , $\Omega_{\Lambda} = 0.74$, $\Omega_b = 0.044$, $h=0.72$, $n_{s}=0.96$, and $\sigma_{8}=0.80$." + To identify galaxies in simulations. we use simplified variant of the SUBFIND algorithm (Springelctal.2001:Choi&σαπο 2009).," To identify galaxies in simulations, we use simplified variant of the SUBFIND algorithm \citep{Springel.etal:01,Choi.Nagamine:09}." +. Although cosmological simulations have been widely used. to study galaxy formation. there are inevitable imitations due to resolution and box size.," Although cosmological simulations have been widely used to study galaxy formation, there are inevitable limitations due to resolution and box size." + One critical imitation is that the low-mass galaxies are not captured in a ow-resolution simulation with a large box size. and the high mass galaxies are missed in a small box size simulation cue o limited box size.," One critical limitation is that the low-mass galaxies are not captured in a low-resolution simulation with a large box size, and the high mass galaxies are missed in a small box size simulation due to limited box size." + To alleviate this problem. we construct composite CGISMES in a wide range of galaxy stellar mass using a few simulations with dillerent resolution and volumes (sce Table 1)).," To alleviate this problem, we construct composite GSMFs in a wide range of galaxy stellar mass using a few simulations with different resolution and volumes (see Table \ref{table:sim}) )." + An important point to note is that the SERD is one of the most. direct. output. of our ab. initio cosmological simulations: our simulation follows the gas and dark matter dvnamics within the framework of ACDAL mocdel. and converts part of the gas into star particles when the SE threshold. density is satisfied at every time step.," An important point to note is that the SFRD is one of the most direct output of our ab initio cosmological simulations; our simulation follows the gas and dark matter dynamics within the framework of $\Lambda$ CDM model, and converts part of the gas into star particles when the SF threshold density is satisfied at every time step." + Therefore the ΕΙ) is the most cürect outcome of gas cynamics. and no uncertain conversion is necessary to obtain SEBRD from our simulations.," Therefore the SFRD is the most direct outcome of gas dynamics, and no uncertain conversion is necessary to obtain SFRD from our simulations." + Εις is why our simulations are helpful to resolve this problem between SEIUD and pe., This is why our simulations are helpful to resolve this problem between SFRD and $\rhostar$. + Figure 1: shows the composite GSMES for cillerent recdshifts., Figure \ref{fig:MF} shows the composite GSMFs for different redshifts. +" Three simulations with cilferent resolutions ancl volumes (N216LI0. N400L34. and NGOOLLOO runs) are used to construct the composite CSMESs. which cover the galaxy stellar mass range of LO'htAL.1045.ΤΑ.," The simulated GSMF shows a reasonable agreement with observations (yellow and blue shade) at $2\lesssim z \lesssim 4$, although the simulated GSMF is slightly lower than the observations at the very massive end of $\Mstar > 10^{11} \himsun$." + The number density of these high-mass galaxies is so low wt there are only about 1...10 galaxies in a volume of 100/)*\Ipey?. therefore this discrepancy. could be clue to 16 cosmic variance.," The number density of these high-mass galaxies is so low that there are only about $1-10$ galaxies in a volume of $(100 h^{-1}{\rm Mpc})^3$, therefore this discrepancy could be due to the cosmic variance." + Another possible reason is that the lower mass galaxies are scattered up into the more massive bins due to observational errors. causing it to be higher than 1e intrinsic simulated CSME.," Another possible reason is that the lower mass galaxies are scattered up into the more massive bins due to observational errors, causing it to be higher than the intrinsic simulated GSMF." + AX marked feature in the simulated ΟΛΗ is the very steep. slope at. the. low-massend., A marked feature in the simulated GSMF is the very steep slope at the low-massend. +" When fitted with a Schechter function. the simulated: composite CSAIL has a faint-end slope of a~2 at ς=3 for the mass range of 105b.AL.0$ ) rather than the radial field is available to make a higher accretion-rate than $\delta<0$ cases. + The location of ire}=0 has a weal: dependence ou 6., The location of $\hat\eta(r_{\rm F})=0$ has a weak dependence on $\delta$. + The location of the muddle fast 1iagnetosonic point aso has a weak dependence on à. aud the slow magnetosonic point remains at a fixed location except for suialler jj cases," The location of the middle fast magnetosonic point also has a weak dependence on $\delta$, and the slow magnetosonic point remains at a fixed location except for smaller $\hat\eta$ cases." + Tere. we will preseut accretion solutions.," Here, we will present accretion solutions." + To plot an SAF-solution. we uced to deermine the five coustaut quantities: Op. Loy. E. hüàj.," To plot an -solution, we need to determine the five field-aligned constant quantities: $\Omega_F$, $L$, $\eta$, $E$, $h_{\rm inj}$." + Although these coustauts should be given as boundary conditions at the plasima source (inj). mathematically we can choose the locations cMorp. rp. ry aud the sound velocity Cp as free paralcters to fix the conserved quantities if oue restricts heir interest to ideal AMID solutions.," Although these constants should be given as boundary conditions at the plasma source ), mathematically we can choose the locations of $r_{\rm F}$, $r_{\rm L}$, $r_{\rm A}$ and the sound velocity $\zeta_{\rm F}$ as free parameters to fix the conserved quantities if one restricts their interest to ideal MHD solutions." + First. for the plasiua sources to exist in a black hole maguetosplrere. We require flat QνιOrOui then. two leht surfaces +ENE(Qpia.V) and r—1TGpia.) are determined.," First, for the plasma sources to exist in a black hole magnetosphere, we require that $\Omega_{\rm min}<\Omega_F<\Omega_{\rm max}$; then, two light surfaces $r=r_{\rm L}^{in}(\Omega_F; a,\Psi)$ and $r=r_{\rm L}^{out}(\Omega_F; a,\Psi)$ are determined." + Second. from equation (163). £ is deeruuned by the Alfvéun radius rà. which is locaed between two lieht surfaces ieutioued above.," Second, from equation \ref{eq:AP}) ), $\tilde L$ is determined by the Alfvénn radius $r_{\rm A}$ , which is located between two light surfaces mentioned above." + Third. as we have seen in the previous section. by specifving rg aud Gp. 5 iux E are calculated from equations (30)) aid (15)).," Third, as we have seen in the previous section, by specifying $r_{\rm F}$ and $\zeta_{\rm F}$, $\eta$ and $E$ are calculated from equations \ref{eq:eta}) ) and \ref{eq:fobid}) )." + Similuly. when rg and ος are set. jj and £ are also calculated.," Similarly, when $r_{\rm S}$ and $\zeta_{\rm S}$ are set, $\eta$ and $E$ are also calculated." + Of course. we should require that +=re.cr)μις) for the SAF-solution.," Of course, we should require that $\eta=\eta(r_{\rm F}, \zeta_{\rm F})=\eta(r_{\rm S}, \zeta_{\rm S})$ for the -solution." +"Finally. we cau plo a contour map of £i, on the raul pane.","Finally, we can plot a contour map of $E/\mu_{\rm c}$ on the $r$ $u^r$ plane." + The SAF-solution is obtained as the curve with E=EgFX. where E44—Era. Cop) ," The -solution is obtained as the curve with $E=E_{\rm F}=E_{\rm S}$, where $E_{\rm cr}\equiv E(r_{\rm cr}, \zeta_{\rm cr})$ ." +When the forbidden region is tvx» TA (or TTA). where both inner and outer Alfvéóun points appear ou the ral plane. there are two regimes of SAF-MIID accretion solutions (see Takahashi (2000))): The accreting matter for case 1) would be injected near the separation poiut.," When the forbidden region is type IA (or IIIA), where both inner and outer Alfvénn points appear on the $r$ $u^r$ plane, there are two regimes of -MHD accretion solutions (see \cite{Takahashi00}) ): The accreting matter for case (i) would be injected near the separation point." + Iu Figure lbh. we see that heejiergy Py/pig is vestricted within a very uarrow rango.," In Figure \ref{fig:eta}b b, we see that the energy $E_{\rm S}/\mu_{\rm c}$ is restricted within a very narrow range." +" ""Though he sound velocity is not constant along he flflow. which means ονσὲCr. the possible location of the! juncr-fast niaenetosonic point which must give Lg=Es would be also restricted to a narrow ranuec."," Though the sound velocity is not constant along the flow, which means $\zeta_{\rm S}\neq\zeta_{\rm F}$, the possible location of the inner-fast magnetosonic point which must give $E_{\rm F}=E_{\rm S}$ would be also restricted to a narrow range." + Note that if t1ο accreting plasma is iutceuscly heated up. tiere nav be no solution of case (4): for example. iu Figure db » the flow of cs=0.1 and dg=0.2 is orbidden. because such plasina heating causesa conflict situation of EE>Lu.," Note that if the accreting plasma is intensely heated up, there may be no solution of case (i); for example, in Figure \ref{fig:eta}b b, the flow of $\zeta_{\rm S}=0.1$ and $\zeta_{\rm F}=0.2$ is forbidden, because such plasma heating causesa conflict situation of $E_{\rm F} > E_{\rm S}$." + The aecretiug matter for case (ii) would be injected inward from an area between the outer Alven radius aud the ouer light surface., The accreting matter for case (ii) would be injected inward from an area between the outer Alfvénn radius and the outer light surface. + If the separation point is located outside the outer Alfvén1 poiut. 1 is possible that the case (11) accreting uatter is injected from near the separation point.," If the separation point is located outside the outer Alfvénn point, it is possible that the case (ii) accreting matter is injected from near the separation point." + Figures 10 and 11 show typical examples of case (1) aud case (1). which satisfy the requirement that jjζω and Vik.," Under the assumption that the fields and currents have the standard plane-wave spacetime dependence, we can make the replacements $\pderiv{}{t} \rightarrow -i\omega$ and $\nabla \rightarrow i {\bf + k}$." + We can then write a second expression for σα57.," We can then write a second expression for $\pderiv{{\bf + J}}{t}$." + where we have used the nonrelativistic approximation. which is appropriate for small waves.," Setting equations \ref{eqn:dJdt1}) ) and \ref{eqn:dJdt2}) ) equal, we get where we have used the nonrelativistic approximation, which is appropriate for small waves." + We will now specialize toa background magnetic field pointing in the z-direction., We will now specialize to a background magnetic field pointing in the $\bhat{z}$ -direction. +" We can then write this background. field in terms of the cyclotron frequency⋅ o,=52. eBoc", We can then write this background field in terms of the cyclotron frequency $\omega_c = \frac{eB}{m}$. +"pPhe density. ο determines. the plasma [requeney.⋅ or,2Eni—.", The density $n$ determines the plasma frequency $\omega_p^2 =n \frac{e^2}{m}$. +" E‘Phen. we can write. equation. (21)) as We can solve this for J, by writing a matrix equation Finally. we would like to use equation (30)) to write the right hand side of equation (1) in the small wave limit in à manner we can interpret as a dielectric tensor."," Then, we can write equation \ref{eqn:ainJ}) ) as We can solve this for $\Jp$ by writing a matrix equation inverting the matrix gives Finally, we would like to use equation \ref{eqn:Jmatrix}) ) to write the right hand side of equation \ref{eqn:Maxwell1}) ) in the small wave limit in a manner we can interpret as a dielectric tensor." + lenoring (for now) the contributions from the vacuum. and assuming an approximately homogeneous. plasma density. equation (1)) simplifies to If our macroscopic field is to obey VEDD—.we can insert equation (30)) into (31)) to obtain the following expression for the dielectric tensor due to plasma effects: This expression is in agreement with the cold plasma dielectric tensor given in. 2..," Ignoring (for now) the contributions from the vacuum, and assuming an approximately homogeneous plasma density, equation \ref{eqn:Maxwell1}) ) simplifies to If our macroscopic field is to obey $\laplace {\bf D} - \ddt{{\bf D}}=0$, we can insert equation \ref{eqn:Jmatrix}) ) into \ref{eqn:RHSMax1}) ) to obtain the following expression for the dielectric tensor due to plasma effects: This expression is in agreement with the cold plasma dielectric tensor given in \citet{meszarosbook}." + Xs noted above. our analysis neglects the olf-ciagonal (Llall) terms. as is appropriate for pair plasmas or waves with frequencies much less than the evelotron Frequency.," As noted above, our analysis neglects the off-diagonal (Hall) terms, as is appropriate for pair plasmas or waves with frequencies much less than the cyclotron frequency." + Because the vacuum cllects are added explicitly in the form of dielectric and magnetic permeability tensors. we only need to confirm that the weak field limits of our expressions agree with the standard results.," Because the vacuum effects are added explicitly in the form of dielectric and magnetic permeability tensors, we only need to confirm that the weak field limits of our expressions agree with the standard results." + This confirmation is done explicitly in ?.., This confirmation is done explicitly in \citet{1997JPhA...30.6485H}. + 1n the weak field limit. the Censors given by equations (11)) and (12)) are In the case of a weak background magnetic field pointing in the z-direction. these become wwith," In the weak field limit, the tensors given by equations \ref{eqn:epsilon}) ) and \ref{eqn:mu}) ) are In the case of a weak background magnetic field pointing in the $\bhat{z}$ -direction, these become with" +the PLEC fit: gives Euto[f Ss.3t1.7 GeV. A total of 10 photons with E>10 GeV (out of 12 detected during the eutire 5-day flare) were collected in that 1.5-day time lapse (secoucl pauel of Figure 2)).,the PLEC fit gives $E_\textit{cutoff}\;$ $\pm$ $\:$ GeV. A total of 10 photons with $E>10\:$ GeV (out of 12 detected during the entire 5-day flare) were collected in that 1.5-day time lapse (second panel of Figure \ref{fig:light_curve_2}) ). +" The variation of Ep, aud Euf with [lux are displayed in the inset of Figure L..", The variation of $E_\textit{break}$ and $E_\textit{cutoff}$ with flux are displayed in the inset of Figure \ref{fig:SED}. + As already found curing the 2009 December αμα 2010 April Hares.no strong evolution of either Εν: OF Euto]fi is found.," As already found during the 2009 December and 2010 April flares,no strong evolution of either $E_\textit{break}$ or $E_\textit{cutoff}$ is found." + Eppap remains constant within a factor of z2 while the flux varies by a factor of =10., $E_\textit{break}$ remains constant within a factor of $\approx2$ while the flux varies by a factor of $\approx40$. + During its five-day outburst from 2010 November 17 to 21 (flare interval in Figure 1)). 3C151.3 was the brightest GeV 5-ray source in the sky. with a flux Figg=6642 on 2010 November 15-19.," During its five-day outburst from 2010 November 17 to 21 (flare interval in Figure \ref{fig:light_curve_1}) ), 3C454.3 was the brightest GeV $\gamma$ -ray source in the sky, with a flux $F_{100}=66\pm2$ on 2010 November 18–19." + Prior to the Haring phase. the Fern-LAT light curve displays a 13-day loug flux plateau preceding he major outburst.," Prior to the flaring phase, the -LAT light curve displays a 13-day long flux plateau preceding the major outburst." + The onset of the plateau is marked by a rapid (<1) day flux increase by a actor of zz2., The onset of the plateau is marked by a rapid $<1$ ) day flux increase by a factor of $\approx 2$. + This feature appears to be a characteristic behavior iudicatiug that 3C[51.3 is about o flare. as noted in Ackermannetal.(2010)..," This feature appears to be a characteristic behavior indicating that 3C454.3 is about to flare, as noted in \cite{2010ApJ...721.1383A}." + In the December 2009 flare. the plateau Lastecd lor 6 days at a level of Foozz10 before flaring to a daily Dux of 22. while for the April 2010 outburst. it lasted for days at a level of Figg)zz7 before reaching a peak flux of z16.," In the December 2009 flare, the plateau lasted for 6 days at a level of $F_{100}\approx10$ before flaring to a daily flux of $\approx22$ , while for the April 2010 outburst, it lasted for $\:$ days at a level of $F_{100}\approx7$ before reaching a peak flux of $\approx16$." + The spectrum arcdeus slightly [rom the pre-flare to the plateau prececling the giant flare., The spectrum hardens slightly from the pre-flare to the plateau preceding the giant flare. + Spectral liardeuiug aud clustering of photous with E> 10GeV is also seen in tlie decayiug stage of the gamma-ray outburst at MJD55520.0-55521.5. which could point to the preseuce of racdiatiug[n] hadrous or 55-absorptiou effects.," Spectral hardening and clustering of photons with $E>10\:$ GeV is also seen in the decaying stage of the gamma-ray outburst at MJD55520.0-55521.5, which could point to the presence of radiating hadrons or $\gamma\gamma$ -absorption effects." + In the former case. protons require additional time to accelerate aud cool while the <1GeV Παν. if due to rapidly cooling electrous. would decline more rapidly.," In the former case, protons require additional time to accelerate and cool while the $<1\:$ GeV flux, if due to rapidly cooling electrons, would decline more rapidly." + In the latter case. the emergence ol the hard component could occur if the racdiatiug plasma becomes optically thin to 55-absorptiou. either due to a larger bulk Lorentz factor or increased size of the racliating plasma.," In the latter case, the emergence of the hard component could occur if the radiating plasma becomes optically thin to $\gamma\gamma$ -absorption, either due to a larger bulk Lorentz factor or increased size of the radiating plasma." + The features of the giaut. flare can be compared to those of the two earlier. fainter [lares (December 2000 aud April 2010) that have been carefully investigated iu the LAT energy band (the different observation mode used during most of the July 2008 [Iare 2'ovided poorer-quality data).," The features of the giant flare can be compared to those of the two earlier, fainter flares (December 2009 and April 2010) that have been carefully investigated in the LAT energy band (the different observation mode used during most of the July 2008 flare provided poorer-quality data)." + The overall lisht curves slow similarities (preseuce of a preflare plateau. main flare lastiug a lew days. several week-loug [adiug period).," The overall light curves show similarities (presence of a preflare plateau, main flare lasting a few days, several week-long fading period)." + The rise time 7; of the November 2010 flare is about half that of the December 2009 flare hr vs hr)., The rise time $T_r$ of the November 2010 flare is about half that of the December 2009 flare $\:$ hr vs $\:$ hr). +" Whereas the lattershowed iudication of ""lickeriug activity on timescales as short as hours above MeV. this ellect is not clearly present here. as demonstrated by similar 3-lu aud 6-hr light curves in Figure L.."," Whereas the lattershowed indication of “flickering” activity on timescales as short as $\:$ hours above $\:$ MeV, this effect is not clearly present here, as demonstrated by similar 3-hr and 6-hr light curves in Figure \ref{fig:light_curve_1}." + For the first time. a siguificant temporary hardening of the spectrum leacing to P 22.1 has been observed for 3C15L3.," For the first time, a significant temporary hardening of the spectrum leading to $\Gamma\simeq$ 2.1 has been observed for 3C454.3." + Note that in the first LAT ACN catalog (Abdoetal.2010a).. less than of FSRQs are found with Ll-mouth averaged D «2.1.," Note that in the first LAT AGN catalog \citep{1LAC}, less than of FSRQs are found with 11-month averaged $\Gamma<\-$ 2.1." + The moderately hard spectrum curing the large luminosity [lare deviates from the treud seeu iu the blazar divide (Ghisellinietal.2009).. where the most 5-ray huninous blazars generally have DZ 2.5.," The moderately hard spectrum during the large luminosity flare deviates from the trend seen in the blazar divide \citep{Ghi09}, where the most $\gamma$ -ray luminous blazars generally have $\Gamma\gtrsim2.5$ ." + Despite the overall spectral variation. the energy. cutoff remains essentially uuchaugedas observed in earlier [lares (Figure 1)).," Despite the overall spectral variation, the energy cutoff remains essentially unchangedas observed in earlier flares (Figure \ref{fig:SED}) )." + luterestiugly. several-day long spectral variations are also observed period (beyond MJD55521 in Figure," Interestingly, several-day long spectral variations are also observed (beyond MJD55524 in Figure" +Because a one-dimensional spline is also a simple cubic polvnomial. aud therefore only has four free coefficients. it is sufficient to know the function values and second-order derivatives at all evid corners to uniquelv specify every coefficient.,"Because a one-dimensional spline is also a simple cubic polynomial, and therefore only has four free coefficients, it is sufficient to know the function values and second-order derivatives at all grid corners to uniquely specify every coefficient." +" As a consequence of this. tle first-order derivative aloug the .-direction at grid poiut. ήν) is uniquely eiven by (Press2002) IHeye h,Sarpyyey is the w-direction grid cell size for the current cell."," As a consequence of this, the first-order derivative along the $x$ -direction at grid point $(x_i, y_j)$ is uniquely given by \citep{press:2002} + Here $h_x = x_{i+1}-x_i$ is the $x$ -direction grid cell size for the current cell." + Au equivalent expression obviously holds for the y-direction derivatives., An equivalent expression obviously holds for the $y$ -direction derivatives. + Finally. to estimate the second-order cross-derivatives. fy.(0.y). the above process is repeated such that y-derivatives are computed from f(r.gy) splines for all y-direction coordinate lines.," Finally, to estimate the second-order cross-derivatives, $f_{xy}(x,y)$, the above process is repeated such that $y$ -derivatives are computed from $f_x(x,y)$ splines for all $y$ -direction coordinate lines." + Thus. all required derivatives nay be obtained by performing i|209 one-dimensional spline computations. where ais the umber of exid cells iu «-direction. aud η is the umber of erid cells in y-direction.," Thus, all required derivatives may be obtained by performing $m ++ 2n$ one-dimensional spline computations, where $m$ is the number of grid cells in $x$ -direction, and $n$ is the number of grid cells in $y$ -direction." +"and c, is the dispersion of the density distribution.",and $\sigma_{\rho}$ is the dispersion of the density distribution. + This is related to the Mach. number Af of the turbulence wo 057In(l|ar). where > is à constant of order unity (77)..," This is related to the Mach number $\mathcal{M}$ of the turbulence by $\sigma_{\rho}^2 \approx \ln (1 + \gamma \mathcal{M}^2)$, where $\gamma$ is a constant of order unity \citep{padoan02, federrath08a}." +" For a,=2.53. the range of values expected for the Mach numbers found in giant. clumps. he quantity A(cp)ffy(p) varies bv only a factor of a jw over a range of densities p/pz104+107."," For $\sigma_{\rho} = 2.5 - 3$, the range of values expected for the Mach numbers found in giant clumps, the quantity $M(>\rho)/t_{\rm ff}(\rho)$ varies by only a factor of a few over a range of densities $\rho/\bar{\rho} \approx 10^{-1} - 10^5$." + Thus even if most of the mass is at a density vastly. larger han the mean density we have used. as long as the mass distribution follows the lognormal form expected or supersonic turbulence. the star formation rate will not be modified significantlv [rom our estimate using he volume-averaged density.," Thus even if most of the mass is at a density vastly larger than the mean density we have used, as long as the mass distribution follows the lognormal form expected for supersonic turbulence, the star formation rate will not be modified significantly from our estimate using the volume-averaged density." + Our finding that the fraction of gas ejected from giant clumps depends. critically on their dimoensionless star-formation rate elliciencv ej; naturally [σας to the question of how this quantity is set. and. whether the physical processes responsible for setting qr21 in the local universe might. determine a cdillerent value in high-redshift clumps.," Our finding that the fraction of gas ejected from giant clumps depends critically on their dimensionless star-formation rate efficiency $\epsff$ naturally leads to the question of how this quantity is set, and whether the physical processes responsible for setting $\epsfftwo \sim 1$ in the local universe might determine a different value in high-redshift clumps." + ? show that. as long as the gas in à molecular cloud. is supersonically turbulent with a velocity dispersion. comparable to the cloucl’s virial velocity. as is observed to be the case in all molecular clouds in the Local universe. ο2~ Lis the inevitable consequence.," \citet{krumholz05c} show that, as long as the gas in a molecular cloud is supersonically turbulent with a velocity dispersion comparable to the cloud's virial velocity, as is observed to be the case in all molecular clouds in the local universe, $\epsfftwo \sim 1$ is the inevitable consequence." +" La contrast. in the absence of supersonic turbulence. simulations find that clouds undergo a rapid global collapse in which they convert all their mass into stars in roughly a dynamical time. Le. cp,27100 (c.g. "," In contrast, in the absence of supersonic turbulence, simulations find that clouds undergo a rapid global collapse in which they convert all their mass into stars in roughly a dynamical time, i.e. $\epsfftwo \sim 100$ \citep[e.g.][]{nakamura07, wang09a}." +Thus. a value of ei;2~1 may be expected. in high-z ogiant clumps only if they maintain the level of turbulence required to avoid rapid. elobal collapse.," Thus, a value of $\epsfftwo \sim 1$ may be expected in $z$ giant clumps only if they maintain the level of turbulence required to avoid rapid, global collapse." + Whether the turbulence can actually be maintained is somewhat less clear., Whether the turbulence can actually be maintained is somewhat less clear. + Simulations show that supersonic turbulence decays in roughly one. cloud-crossing time (c.g.PPP). so global collapse can be avoided: only if this energy. is replaced on a comparable timescale.," Simulations show that supersonic turbulence decays in roughly one cloud-crossing time \citep[e.g.][]{stone98, maclow98, maclow99}, so global collapse can be avoided only if this energy is replaced on a comparable timescale." + In local. low-mass star-forming clouds (Ss10 ALL). observations (?).. simulations (??).. and analytic theory (?) all suggest that protostellar outfTows can supply the necessary energv.," In local, low-mass star-forming clouds $\la 10^4$ $\msun$ ), observations \citep{quillen05}, simulations \citep{nakamura07, wang09a}, and analytic theory \citep{matzner07} all suggest that protostellar outflows can supply the necessary energy." + In local giant. molecular clouds with masses of ~107Lo? AZ.. rregions driven by the pressure of photoionized eas are likely to be able to supply the necessary energy. (22)..," In local giant molecular clouds with masses of $\sim 10^4 - 10^6$ $\msun$, regions driven by the pressure of photoionized gas are likely to be able to supply the necessary energy \citep{matzner02, krumholz06d}." +" llowever. neither of these mechanisms are ellective for clumps with Ao~I and X.4,~I. because they do not provide enough momentum input and because they are overwhelmed by radiation pressure (see Figure 2 of ?))."," However, neither of these mechanisms are effective for clumps with $M_9\sim 1$ and $\Sigma_{-1}\sim 1$, because they do not provide enough momentum input and because they are overwhelmed by radiation pressure (see Figure 2 of \citealt{fall10a}) )." + Supernova feedback (7) does not appear to be a likely candidate to crive the turbulence either., Supernova feedback \citep{dekel86a} does not appear to be a likely candidate to drive the turbulence either. + Supernovac do not provide enough power to drive the observed. level o£. turbulence (2)... and. analytic calculations (2?).. numerical simulations of isolated clisk ealaxies (??).. and numerical simulations of galaxies in cosmological context (2?) all indicate that supernova-heated gas is likely to escape through low-clensity holes in the molecular gas without driving much turbulence.," Supernovae do not provide enough power to drive the observed level of turbulence \citep{dekel09b}, and analytic calculations \citep{harper-clark09a, krumholz09d}, numerical simulations of isolated disk galaxies \citep{tasker08a, joung09a}, and numerical simulations of galaxies in cosmological context \citep{ceverino09a} all indicate that supernova-heated gas is likely to escape through low-density holes in the molecular gas without driving much turbulence." + Contrary to this conclusion. ? use the observed correlation between Ho surface brightness and linewidth in 2 galaxies to argue that supernova feedback. is responsible for driving the turbulence. based. in. part on simulations by 2.. who obtain a scaling relation between velocity. dispersion. ancl supernova rate in numerical simulations.," Contrary to this conclusion, \citet{lehnert09a} use the observed correlation between $\alpha$ surface brightness and linewidth in $z\sim 2$ galaxies to argue that supernova feedback is responsible for driving the turbulence, based in part on simulations by \citet{dib06a}, who obtain a scaling relation between velocity dispersion and supernova rate in numerical simulations." + Llowever. the elliciencv with which supernova energy is coupled to the ISM is à free parameter in both 27s analysis and in οος simulations. and their results are consistent with the data only if itis ~254. whereas in the dense environments found in high redshift galaxiesit is expected to be far lower (?)..," However, the efficiency with which supernova energy is coupled to the ISM is a free parameter in both \citeauthor{lehnert09a}' 's analysis and in \citeauthor{dib06a}' 's simulations, and their results are consistent with the data only if it is $\sim 25\%$, whereas in the dense environments found in high redshift galaxiesit is expected to be far lower \citep{thompson05}." + This conclusion is confirmed by the more recent simulations. which do not need to assume an elliciency because they have sullicient resolution to resolve the multiphase structure of the ISM.," This conclusion is confirmed by the more recent simulations, which do not need to assume an efficiency because they have sufficient resolution to resolve the multiphase structure of the ISM." + Finally. we note that the correlation between Ho surface. brightness and linewidth observed by ? has a more prosaic explanation: in à mareinally stable galactic disk of constant circular velocity. the velocity. dispersion is proportional to the gas surface densitv. since Q=so/(x6GYM)1.," Finally, we note that the correlation between $\alpha$ surface brightness and linewidth observed by \citeauthor{lehnert09a} has a more prosaic explanation: in a marginally stable galactic disk of constant circular velocity, the velocity dispersion is proportional to the gas surface density, since $Q=\kappa\sigma/(\pi G \Sigma) = 1$." + Thus higher velocity. dispersions correspond to higher surface densities. which in turn produce higher star formation rates in accordance with the standard ? relation.," Thus higher velocity dispersions correspond to higher surface densities, which in turn produce higher star formation rates in accordance with the standard \citet{kennicutt98a} relation." + This naturally explains the observed. correlation., This naturally explains the observed correlation. + ltadiation pressure is) another mechanism to consider., Radiation pressure is another mechanism to consider. + 1f radiation pressure is not able to drive mass out of the clump. as found above for 0.01. this suggests that it might. not be able to drive turbulence to the required. virial level either. since the virial and escape velocities only dilfer hy a [actor of VD.," If radiation pressure is not able to drive mass out of the clump, as found above for $\epsff \sim 0.01$ , this suggests that it might not be able to drive turbulence to the required virial level either, since the virial and escape velocities only differ by a factor of $\sqrt{2}$." + However. it is unclear whether this conclusion is warranted.," However, it is unclear whether this conclusion is warranted." + Racliation pressure cannot drive material out ol a clump not because stars do not accelerate material enough. but because they evolve olf the main sequence before they are actually able to cject matter.," Radiation pressure cannot drive material out of a clump not because stars do not accelerate material enough, but because they evolve off the main sequence before they are actually able to eject matter." + As a result. they produce expanding shells whose velocities ereatly exceed the escape velocity.," As a result, they produce expanding shells whose velocities greatly exceed the escape velocity." + They. simply. fail to drive mass out because the clump because the driving sources turn. olf before the shells actually escape from the cluster., They simply fail to drive mass out because the clump because the driving sources turn off before the shells actually escape from the cluster. + Lt is unclear if the expanding shells might provide enough energy to maintain the turbulence: this problem will require further modeling., It is unclear if the expanding shells might provide enough energy to maintain the turbulence; this problem will require further modeling. + We are left with the possibility that the turbulence is driven by gravity., We are left with the possibility that the turbulence is driven by gravity. + The driving source cannol be the collapse of the clump itself although such a collapse does produce. turbulence. it does so at the price of reducing the crossing time. raising the rate of energy," The driving source be the collapse of the clump itself; although such a collapse does produce turbulence, it does so at the price of reducing the crossing time, raising the rate of energy" +"even inercase, along the jet.","even increase, along the jet." + Tn the N-vay jets of FRI galaxies. such as 3C 66D (Ularcdeastle.Birkinshaw.&Worrall2001) and some kuots in ALS?s jet (Wilson&Yaug2002:Magshalletal. 2002).. the N-rayvopticalradio spectra are consistent with a single or smootily steepening power-law spectrum. which is reacilv explained by a sinele-componcut svuchrotrou ΕΕ," In the X-ray jets of FR1 galaxies, such as 3C 66B \citep{hbw01} and some knots in M87's jet \citep{wy02,mar02}, the X-ray–optical–radio spectra are consistent with a single or smoothly steepening power-law spectrum, which is readily explained by a single-component synchrotron spectrum." + It is a common pattern that the pezuss of the cussion of the knots aud hot spots iu he radio. optical. aud X-ray domains of quasar jots are well correlated aud often comcide. such as in the jet of 3€ 273 (Sambrunaeal.2001:\Larshalletal. 2001).," It is a common pattern that the peaks of the emission of the knots and hot spots in the radio, optical, and X-ray domains of quasar jets are well correlated and often coincide, such as in the jet of 3C 273 \citep{sam01,mar01}." +. When the profiles do not coincide. as iu the FRI galaxy M87 (Wilson&Yang.2002) or the CPS quasar PINS 1127-115 (Siciniginowskaetal. 2002).. the peak emdssiou of the N-ray. profile is closer to the core than the radio profile.," When the profiles do not coincide, as in the FR1 galaxy M87 \citep{wy02} or the GPS quasar PKS 1127-145 \citep{siem02}, the peak emission of the X-ray profile is closer to the core than the radio profile." + This behavior suggestsCoco a common svuclrotron origin for the radiation du all bands. where nouthermal clectrous accelerated at a shock lose enerev5 through adiabatic aud radiative processes as thev flow cownstream from the shock.," This behavior suggests a common synchrotron origin for the radiation in all bands, where nonthermal electrons accelerated at a shock lose energy through adiabatic and radiative processes as they flow downstream from the shock." + The svuchrotron optical aud N-rav emissious from the highest enerev clectrons have roughly coincideut profiles. but the radio cussion is far more extended due to the longer cooling timescale. and can even be offset as a consequence of a low-energv cutoff iu the electron injection Iu apparent conflüct with a svuclirotrou model are the SEDs of many quasar knots aud hot spots hat show a general behavior whereby the optical spectra are steeper than both the radio aud the A-rav spectra. and the X-rav fluxes are above he extrapolation from the optical baud.," The synchrotron optical and X-ray emissions from the highest energy electrons have roughly coincident profiles, but the radio emission is far more extended due to the longer cooling timescale, and can even be offset as a consequence of a low-energy cutoff in the electron injection In apparent conflict with a synchrotron model are the SEDs of many quasar knots and hot spots that show a general behavior whereby the optical spectra are steeper than both the radio and the X-ray spectra, and the X-ray fluxes are above the extrapolation from the optical band." + This ychavior cannot be lnunediately oxplaimed bw a “standard” svuchrotron model with a siuele vower-law electron component., This behavior cannot be immediately explained by a “standard” synchrotron model with a single power-law electron component. + It appareutlv requires a second clectron compouceut a very high energies z10 TeV with a sharp cutoff at lower energies., It apparently requires a second electron component at very high energies $\gtrsim 10$ TeV with a sharp cutoff at lower energies. + However. the origin of such electrons iu the kuot was not easy to muderstand aud obviousv needs an explanation.," However, the origin of such electrons in the knot was not easy to understand and obviously needs an explanation." +" Iu our model (DAO2). we have shown that iu WALLY Cases even a silele population of electrons with a power-law injection spectrum Q;,;05/).Xal/νιSumas Could explain the observed spectral peculiarities if the clectrous aro accelerated to sutiicicntly high cncreicww]swith afHIAXpOCmax!|6072mσα105."," In our model (DA02), we have shown that in many cases even a single population of electrons with a power-law injection spectrum $Q_{inj}(\gamma^\prime) \propto \gamma^{\prime -p} +e^{-\gamma\prime/\gamma^\prime_{\rm max}}$ could explain the observed spectral peculiarities if the electrons are accelerated to sufficiently high energies with $\gamma^\prime_{\rm max} = +E^\prime_{\rm max} /m_e c^2 \gtrsim 10^8$ ." + Whe CABR cooling iu he Thomson regiae exceeds svuchrotron cooling. oe. when the maenetic and radiatiou field οσον deusities relate as ul.—UCALROL2HCPP/3)mus=(BY?fs. a hardemime in he electrou spectra js formed at comoving clectrou energies 5!popO=LOΤΙ| :). where IXN effects ii Comptou losses become miportant.," When CMBR cooling in the Thomson regime exceeds synchrotron cooling, e., when the magnetic and radiation field energy densities relate as $u_o^{\prime} = +\hat u_{CMB} (1+z)^4 \,(4\Gamma^2/3) \gtrsim u^{\prime}_{B}=(B^\prime)^2 +/8\pi$ , a hardening in the electron spectrum is formed at comoving electron energies $\gamma^\prime \gtrsim 10^8/\Gamma (1+z)$ , where KN effects in Compton losses become important." + The specruni steepons again at hieher cποο]ος when SVC.wotron losses take over., The spectrum steepens again at higher energies when synchrotron losses take over. + For B’ up to few tens of pC. this condition js satisfied for jets with Dz10.," For $B^\prime$ up to few tens of $\mu \rm G$, this condition is satisfied for jets with $\Gamma \gtrsim 10$." + Such au effect produces a hardening in the sv1Tuotron spectruni between optical aud X-ray frecjuencles., Such an effect produces a hardening in the synchrotron spectrum between optical and X-ray frequencies. + Iu 1l we show fits to t1e multivaveleuetli SEDs of krots Al aud Bl of the jet of 3€ 273. with deprojected length =>10tepe. caleulated iu the framework of a siugle-conryonent svuchrotron model (DA2).," In 1 we show fits to the multiwavelength SEDs of knots A1 and B1 of the jet of 3C 273, with deprojected length $> 100 \,\rm kpc$, calculated in the framework of a single-component synchrotron model (DA02)." + For all knots. B=15pC Gueluding the knot D/IIJ3). and practicaly all other moclel paranieters are also the same.," For all knots, $B = 15\,\rm \mu G$ (including the knot D/H3), and practically all other model parameters are also the same." + The single parameter which is «ifferent for the 3 curves is the time frou the start of electron imjection. which call also be interpreted as the different escape times of clectrous from the knots.," The single parameter which is different for the 3 curves is the time from the start of electron injection, which can also be interpreted as the different escape times of electrons from the knots." + These times are elven i he Seure caption., These times are given in the figure caption. +" The curves are are normalized to the observed ταν fluxes at 1 keV. The otal electron cucreics in knots Al aud Bl are WeyAl=!BSLPPorg and WApy=16.10"" ore. and the required electron injection powers are Loy=:we10cre fsaud L/py=13105erg/s."," The curves are are normalized to the observed X-ray fluxes at 1 keV. The total electron energies in knots A1 and B1 are $W_{e.A1}^\prime =1.3\times +10^{56} \,\rm erg$ and $W_{e.B1}^\prime =1.6\times 10^{57} \,\rm erg$ , and the required electron injection powers are $L_{e.A1}^\prime +=2\times 10^{45} \,\rm erg/s$ and $L_{e.B1}^\prime =1.3\times 10^{45} +\,\rm erg/s$." + Note that the specra in Fie., Note that the spectra in Fig. + l are fitted for the jet inclination angle 0=17 in 3C 273., 1 are fitted for the jet inclination angle $\theta = 17^\circ$ in 3C 273. +" For the assuned Lorentz factor D—15. this anele is much larger than fie effective. beaming angle of the iuuer jet cussion b,=ONTUIT. aud results in ézol.5D."," For the assumed Lorentz factor $\Gamma= 15$, this angle is much larger than the effective beaming angle of the inner jet emission $\theta_{beam}\cong 57^\circ/\Gamma$, and results in $\delta \approx 1.5 \ll \Gamma$." +" Even for this stronely debeamed case; the siuple ""one-zone and sinele- svuclirotix 1i0odoel provides good fits to the observed fluxes of the knots Al aud Bl with still acceptable otal energv requirements."," Even for this strongly debeamed case, the simple “one-zone and single-component'' synchrotron model provides good fits to the observed fluxes of the knots A1 and B1 with still acceptable total energy requirements." +Functional forms for. V.D. and P can be found in Jertschinecr (1985) for different values of the adiabatic exponent 5.,"Functional forms for V,D, and P can be found in Bertschinger (1985) for different values of the adiabatic exponent $\gamma$." +" We have set up an initial perturbation with 2;=0.1 and ο,—0.1 at a given time.", We have set up an initial perturbation with $R_i=0.1$ and $\delta_i=0.1$ at a given time. + The simulation has been done using four refinement levels and a coarse grid with GL? cells., The simulation has been done using four refinement levels and a coarse grid with $64^3$ cells. + ‘This is an extremely stringent test for our code. because a strong shock moves outwards and the self-similarity has to be kept numerically.," This is an extremely stringent test for our code, because a strong shock moves outwards and the self-similarity has to be kept numerically." + Moreover. it is à spherical problem described with a Cartesian code.," Moreover, it is a spherical problem described with a Cartesian code." + Lt should be stressed tha this test also checks the multilevel Poisson solver describe above., It should be stressed that this test also checks the multilevel Poisson solver described above. + The refinement. criteria is. based on a Lagrangian approach which tries to keep same mass within anv cel of the simulations regardless of the level of refinement., The refinement criteria is based on a Lagrangian approach which tries to keep same mass within any cell of the simulations regardless of the level of refinement. +" In order to do that. a cell in the coarse grid. is labelled as when its density is higher than the backerounc density (pj,= 28""): therefore. the initial perturbation is completely refined."," In order to do that, a cell in the coarse grid is labelled as when its density is higher than the background density $\rho_{_{B}}=\frac{3H^2}{8\pi G}$ ); therefore, the initial perturbation is completely refined." +" Ehe cells at. first levels are labelled as when their density exceeds the initial mean density at the coarse level by a factor of eight. that is when the local density is larger than Sp,,."," The cells at first levels are labelled as when their density exceeds the initial mean density at the coarse level by a factor of eight, that is when the local density is larger than $8\rho_{_{B}}$." +" The process is similar for higher evels. thus for example. for the second level the condition or à cell to be refineable is a local density higher than 64p,,."," The process is similar for higher levels, thus for example, for the second level the condition for a cell to be refineable is a local density higher than $64\rho_{_{B}}$." + Figure 3.λ shows the results (triangles) compared. with he analvtical solution [from Bertschinger (1985) after four housand time steps., Figure \ref{bert} shows the results (triangles) compared with the analytical solution from Bertschinger (1985) after four thousand time steps. + The numerical solution exhibits a good agreement with the analyticalone., The numerical solution exhibits a good agreement with the analytical one. + H must be noticedthat in he pressure plo. numerical limitations force a low. non-zero numerical value for the pressure although with irrelevant physical consequences — as the code can not cope with a zero value.," It must be noticed that in the pressure plot, numerical limitations force a low, non-zero numerical value for the pressure – although with irrelevant physical consequences – as the code can not cope with a zero value." + Selt-similaritv is well maintained for as long as we have kept this test running (more than six thousand time steps)., Self-similarity is well maintained for as long as we have kept this test running (more than six thousand time steps). + To illustrate the convergence properties. we display the results (squares) when only two refinement. levels are allowecl.," To illustrate the convergence properties, we display the results (squares) when only two refinement levels are allowed." + Force accuracy is crucial to describe correctly the dynamics of both the dark matter ancl gaseous components., Force accuracy is crucial to describe correctly the dynamics of both the dark matter and gaseous components. + In order to test the properties of our gravity solver. we present a simple test comparing the acceleration when a single point. mass is considered.," In order to test the properties of our gravity solver, we present a simple test comparing the acceleration when a single point mass is considered." + We have placed a single point mass (~LOMAZ. ) at the centre of the computational box., We have placed a single point mass $\sim 10^{15} M_{\odot}$ ) at the centre of the computational box. + The numerical acceleration is computed. for several thousand test. points. randomly placed within the computational domain., The numerical acceleration is computed for several thousand test points randomly placed within the computational domain. + The basic grid has 64 cells., The basic grid has $64^3$ cells. + This procedure is repeated with two. four. and six nested refinements.," This procedure is repeated with two, four, and six nested refinements." + In each of these cases. the massive particle is always located at the finest refinement.," In each of these cases, the massive particle is always located at the finest refinement." + In the upper panel of Figure 4.. we plot the relative errors of the computed aecelerations when compared with the theoretical ones given by Vo=τι às à function of the radial distance normalized to the distance from the box centre to the edge of the computational box.," In the upper panel of Figure \ref{gravity}, we plot the relative errors of the computed accelerations when compared with the theoretical ones given by $\nabla\phi=Gm/r^2$, as a function of the radial distance normalized to the distance from the box centre to the edge of the computational box." + Due to the PM-like scheme we are using. the forces are obtained by cillerencing," Due to the PM-like scheme we are using, the forces are obtained by differencing" +UGC9796 (Fig. 2)).,"UGC9796 (Fig. \ref{9796}) )," + also known as ILZw 73. is at a distance of about 72 Mpe based on Hy=75kins!Mpc! and heliocentric radial velocity of V=5406kms!. which implies that | aresec = 0.35 kpe.," also known as IIZw 73, is at a distance of about 72 Mpc based on $H_{0} = 75 \ km \ s^{-1} \ Mpc^{-1}$ and heliocentric radial velocity of $V = 5406\ km \ s^{-1}$, which implies that 1 arcsec = 0.35 kpc." + It has one of the most non-polar PRG., It has one of the most non-polar PRG. + Its apparent major axis in fact is only 65° from the major axis of the central SO rotationally supported galaxy and this implies a rapid rate of differential precession., Its apparent major axis in fact is only $65^{\circ}$ from the major axis of the central S0 rotationally supported galaxy and this implies a rapid rate of differential precession. + The polar structure is less symmetric than in UGC7576 and the distribution of the colors is also asymmetric. with the NE side considerably redder than the SW side.," The polar structure is less symmetric than in UGC7576 and the distribution of the colors is also asymmetric, with the NE side considerably redder than the SW side." + The color asymmetry coincides with the asymmetry of the HI density distribution., The color asymmetry coincides with the asymmetry of the HI density distribution. +" The HI gas is all associated with the polar structure. which thus contains as many baryons as the host galaxy (Schechteretal..1984). and shows a central hole at about 25""."," The HI gas is all associated with the polar structure, which thus contains as many baryons as the host galaxy \citep{Sch84}, and shows a central hole at about $25''$ ." +" The huge mass-to-light ratio of My,,/L,=50 in solar units. lead Coxetal.(2006) to conclude that most of the mass in this system is dark."," The huge mass-to-light ratio of $M_{dyn}/L_{B} \simeq 50$ in solar units, lead \cite{Cox06} to conclude that most of the mass in this system is dark." +" As in the case of UGC7576. the H, rotation curve (Reshetnikov&Combes.1994) is in good agreement with the HI rotation curve (Schechteretal..1984)."," As in the case of UGC7576, the $H_{\alpha}$ rotation curve \citep{Res94} is in good agreement with the HI rotation curve \citep{Sch84}." +. The shape of the rotation curve indicates that this component is actually a differentially rotating disk. rather than à ring. very similar to the polar disk in NGC4650A. In Tab.," The shape of the rotation curve indicates that this component is actually a differentially rotating disk, rather than a ring, very similar to the polar disk in NGC4650A. In Tab." + | we summarize the photometric and HI observed quantities for UGC7576 and UGC9796 and we add those of NGC4O6S0A for reference in the same table., \ref{global} we summarize the photometric and HI observed quantities for UGC7576 and UGC9796 and we add those of NGC4650A for reference in the same table. + The spectra analyzed in this work were obtained with DOLORES@TNG (Device Optimized for the LOw RESolution). in. visitor mode during the observing run A21TAC-54 (on May 2010).," The spectra analyzed in this work were obtained with DOLORESTNG (Device Optimized for the LOw RESolution), in visitor mode during the observing run A21TAC-54 (on May 2010)." + DOLORES is installed at the Nasmyth B focus of the TNG and is equipped with the E2V 4240 CCD with an angular resolution of 0.252pix!., DOLORES is installed at the Nasmyth B focus of the TNG and is equipped with the E2V 4240 CCD with an angular resolution of $0''.252\ pix^{-1}$. + TThe adopted slit was 2” wide and it was aligned along both the North and South side of the polar structures of the two galaxies UGC7576 and UGC9796. at PA.=53° and PA.=16° respectively (see Fig. 3)).," The adopted slit was $2''$ wide and it was aligned along both the North and South side of the polar structures of the two galaxies UGC7576 and UGC9796, at $P.A. = 53^{\circ}$ and $P.A. = 16^{\circ}$ respectively (see Fig. \ref{slit}) )," + in order to include the most luminous HII regions in the polar structures., in order to include the most luminous HII regions in the polar structures. +" The total integration time for each object is 4 hrs. with an average seeing of 1.2, "," The total integration time for each object is 4 hrs, with an average seeing of $1''.2$ ." +"At the systemic velocities of UGC7576 and UGC9796. to cover the red-shifted emission lines of [ΟΠΗ121321. HyQ4340). [OTT44363. |OHE11959.5007. ApCl4861) and H,C06563). the grism LR-B was used in the 3600—6800A wwavelength range. with a dispersion of 2.52 A//pix."," At the systemic velocities of UGC7576 and UGC9796, to cover the red-shifted emission lines of $[OII]\lambda3727$, $H_{\gamma}(\lambda4340)$, $[OIII]\lambda4363$, $[OIII]\lambda\lambda4959,5007$, $H_{\beta}(\lambda4861)$ and $H_{\alpha}(\lambda6563)$, the grism LR-B was used in the $3600-6800$ wavelength range, with a dispersion of 2.52 /pix." + The data reduction was carried out using the package in the Facility) environment., The data reduction was carried out using the package in the ) environment. +" The main strategy adopted for each data-set included darksubtraction"".. flat-fielding correction. sky subtraction and rejection of bad pixels."," The main strategy adopted for each data-set included dark, flat-fielding correction, sky subtraction and rejection of bad pixels." + Wavelength calibration was achieved by means of comparison spectra of Hg-Ne lamps acquired for each observing night. using the IRAF TWODSPEC.LONGSLIT package.," Wavelength calibration was achieved by means of comparison spectra of Hg+Ne lamps acquired for each observing night, using the IRAF TWODSPEC.LONGSLIT package." + The sky spectrum was extracted at the outer edges of the slit. for r.>30 aresec from the galaxy center. where the surface brightness is fainter than 24mag/aresec*. and subtracted off each row of the two dimensional spectra by using the IRAF task BACKGROUND in the TWODSPEC.LONGSLIT package.," The sky spectrum was extracted at the outer edges of the slit, for $r \ge +30$ arcsec from the galaxy center, where the surface brightness is fainter than $24 mag/arcsec^2$, and subtracted off each row of the two dimensional spectra by using the IRAF task BACKGROUND in the TWODSPEC.LONGSLIT package." + On average. a sky subtraction better than 1% was achieved.," On average, a sky subtraction better than $1\%$ was achieved." + The sky-subtracted frames Were co-added to a final median averaged 2D spectrum., The sky-subtracted frames were co-added to a final median averaged 2D spectrum. + The final step of the data-processing Is the fluxcalibration. of each 2D spectra. by using observations. ofthe standard star Feige66 and the standard tasks in IRAF (STANDARD. SENSFUNC and CALIBRATE).," The final step of the data-processing is the fluxcalibration of each 2D spectra, by using observations ofthe standard star Feige66 and the standard tasks in IRAF (STANDARD, SENSFUNC and CALIBRATE)." + To perform, To perform +subtract the images of the quasars.,subtract the images of the quasars. + Phere are three possible methods for psf subtraction., There are three possible methods for psf subtraction. + We could. use the software to create artificial psfs. or we could use images of bright stars in the archive. or we could. use the 15 quasar images themselves.," We could use the software to create artificial psfs, or we could use images of bright stars in the archive, or we could use the 15 quasar images themselves." + The advantages of psfs over real psfs are that the psfs are noiseless. and can be ereated at the requiredy location on the array (the psf varies withry location). and at the precise sub-pixel position (which is desirable as the psf is slightly: uncdersampled).," The advantages of psfs over real psfs are that the psfs are noiseless, and can be created at the required location on the array (the psf varies with location), and at the precise sub-pixel position (which is desirable as the psf is slightly undersampled)." + Lowever because the accuracy of the psfs is limited by the detail in the models. real psfs are preferred if suitably placed highin] S/N imagesIn] are available.," However because the accuracy of the psfs is limited by the detail in the models, real psfs are preferred if suitably placed high $S/N$ images are available." + The main advantage of using images of bright stars is the high. S/N. with the proviso that any non-linear behaviour of the detector. must be accurately characterised.," The main advantage of using images of bright stars is the high $S/N$, with the proviso that any non-linear behaviour of the detector must be accurately characterised." + Phe undersampling of the psf nevertheless sets a fundamental limit to the accuracy achievable if a single star is used., The undersampling of the psf nevertheless sets a fundamental limit to the accuracy achievable if a single star is used. + Systematic residuals are unavoicable unless the star was positioned. at exactly. the same sub-pixel position as the target., Systematic residuals are unavoidable unless the star was positioned at exactly the same sub-pixel position as the target. + Other disadvantages. include »ossible. poor colour match. and mismatch. of the psf in erms ofy location.," Other disadvantages include possible poor colour match, and mismatch of the psf in terms of location." + Primarily to deal with the problem of undersampling we chose to use the 15 quasar images hemselves to subtract the psfs., Primarily to deal with the problem of undersampling we chose to use the 15 quasar images themselves to subtract the psfs. + Because we have 15 targets we can use dithering to recover full sampling of the psf. without seriously compromising the SYN of the composite os.," Because we have 15 targets we can use dithering to recover full sampling of the psf, without seriously compromising the $S/N$ of the composite psf." + Additional advantages of using the quasars are that 10 colours are perfectly matched (assuming the range in ‘colour is small). aad that the initial location and step xutern is the same for all the quasars.," Additional advantages of using the quasars are that the colours are perfectly matched (assuming the range in colour is small), and that the initial location and step pattern is the same for all the quasars." + In. addition. all 10 observations were completed over a few months. so the 'ondition of the telescope and camera was similar for each arget.," In addition all the observations were completed over a few months, so the condition of the telescope and camera was similar for each target." + A drawback to this approach is that it. diminishes 1e possibility of detecting the quasar host galaxies. since we will subtract the average host-galaxy profile from eac= inage.," A drawback to this approach is that it diminishes the possibility of detecting the quasar host galaxies, since we will subtract the average host-galaxy profile from each image." + The procedure followed for each. quasar was to create a subtraction psf by averaging the images of the other 14 quasars., The procedure followed for each quasar was to create a subtraction psf by averaging the images of the other 14 quasars. + Taking the relevant 14 images. the first step was to scale the images to the same count level. ancl to register them to the nearest. half. pixel.," Taking the relevant 14 images, the first step was to scale the images to the same count level, and to register them to the nearest half pixel." + “Phen. using the package. the data were interlaced into pixels of side half the originalsize.," Then, using the package, the data were interlaced into pixels of side half the original." +. Εις sub-pixelised psf was then scaled. and registered to the quasar image by minimising X7. computing the flux at the location of a pixel by interpolation.," This sub-pixelised psf was then scaled and registered to the quasar image by minimising $\chi^2$, computing the flux at the location of a pixel by interpolation." +" In computing the X7. pixels within 0.3""0f the quasar centroid were exeluded from the sum."," In computing the $\chi^2$, pixels within of the quasar centroid were excluded from the sum." + Having subtracted the images of all 15 quasars. mask frames were created. by adding to he mask anv galaxies found. close to the quasar. as well as any remaining bad pixels visible.," Having subtracted the images of all 15 quasars, mask frames were created by adding to the mask any galaxies found close to the quasar, as well as any remaining bad pixels visible." + Phe whole procedure was hen iterated. using the masks to exclude these pixels in creating the psfs. and in making the fits.," The whole procedure was then iterated, using the masks to exclude these pixels in creating the psfs, and in making the fits." + In this second stage he quasar 11222 was excluding from the averaging in creating subtraction psfs because of excess emission clearly visible., In this second stage the quasar 1222 was excluding from the averaging in creating subtraction psfs because of excess emission clearly visible. + Phis excess emission is centred on the quasar and is ikelv to be from the host galaxy of the quasar., This excess emission is centred on the quasar and is likely to be from the host galaxy of the quasar. + Sub-pixclisation of the psf has two effects., Sub-pixelisation of the psf has two effects. + First. it improves the sampling and so reduces systematic errors in subtraction near the centre of the psf, First it improves the sampling and so reduces systematic errors in subtraction near the centre of the psf. + However the resulting os is noisier., However the resulting psf is noisier. + Because of the limited number of quasars used he psf subtraction aclels noise to the frames., Because of the limited number of quasars used the psf subtraction adds noise to the frames. + TFhis is more noticeable for the brightest. quasars. since the subtraction E is formed by. sealing up the images of fainter quasars.," This is more noticeable for the brightest quasars, since the subtraction psf is formed by scaling up the images of fainter quasars." + The procedure could be improved. therefore. by using a sub-jxixelised. psf for subtraction near the centre of the quasar image. but using full-sized pixels away from the centre where he issue of sampling is less important.," The procedure could be improved, therefore, by using a sub-pixelised psf for subtraction near the centre of the quasar image, but using full-sized pixels away from the centre where the issue of sampling is less important." + The approach Ixulkarni et al. (, The approach Kulkarni et al. ( +2000) followed: was to use single bright stars for psf subtraction.,2000) followed was to use single bright stars for psf subtraction. + They. provide an extensive and detailed analysis of the sources of uncertainty using this approach., They provide an extensive and detailed analysis of the sources of uncertainty using this approach. + In section 3.2.3. we compare the accuracy of our psf subtraction with that of Ixulkarni et al., In section 3.2.3 we compare the accuracy of our psf subtraction with that of Kulkarni et al. + The final stage before searching for candidates was to compute revised le error frames for cach quasar., The final stage before searching for candidates was to compute revised $1\sigma$ error frames for each quasar. + The purpose ofthis is to be able to measure the significance of candidate detections., The purpose of this is to be able to measure the significance of candidate detections. + Ehe revised error frames must include the contribution of random and svstematic errors associated with the psf subtraction., The revised error frames must include the contribution of random and systematic errors associated with the psf subtraction. + We first computed: S/N. frames by dividing the subtracted frames. by the current error frames., We first computed $S/N$ frames by dividing the subtracted frames by the current error frames. + σαν. if the subtraction psf were both noiseless. ancl perfectly accurate. then the distribution of counts in the S/N frames. outside remaining objects. would. be Gaussian with standard deviation σον=1.0.," Ideally, if the subtraction psf were both noiseless, and perfectly accurate, then the distribution of counts in the $S/N$ frames, outside remaining objects, would be Gaussian with standard deviation $\sigma_{S/N}=1.0$." + Because the subtraction psf is not noiseless. to account for the added noise we scaled theerror frame by the measured σον in the skv. and then created. new S/N frames.," Because the subtraction psf is not noiseless, to account for the added noise we scaled theerror frame by the measured $\sigma_{S/N}$ in the sky, and then created new $S/N$ frames." + Even then os... although now unity in the sky. increased. towards the centre of the (subtractect) quasar.," Even then $\sigma_{S/N}$, although now unity in the sky, increased towards the centre of the (subtracted) quasar." + The increase was greater for the xiehter quasars., The increase was greater for the brighter quasars. + “Phe reason for this can be understood as follows., The reason for this can be understood as follows. + For bright objects. such as the quasars in. this programme. the errors. are. dominated. by object photon noise Le. YN. where AN. is the number of detected photons.," For bright objects, such as the quasars in this programme, the errors are dominated by object photon noise i.e. $\sqrt N$, where $N$ is the number of detected photons." + Suppose that the psf has a fractional accuracy f ic. the vpical residual for any pixel after psf subtraction is fin’., Suppose that the psf has a fractional accuracy $f$ i.e. the typical residual for any pixel after psf subtraction is $fN$. + Then in the S/N frame the resicuals will be visible as deviations of S/N= fVN. ie. larger where the counts are arecr. and larger for brighter quasars.," Then in the $S/N$ frame the residuals will be visible as deviations of $S/N=f\sqrt N$ , i.e. larger where the counts are larger, and larger for brighter quasars." +In these equations all equilibrium quantities are calculated at x=0.,In these equations all equilibrium quantities are calculated at $x=0$. +" Using these equations we can express all dependent variables in terms of ul ha"" and p It follows from Eq. (71))"," Using these equations we can express all dependent variables in terms of $u_1^{(1)}$ , $v_{\perp1}^{(1)}$ and $P_1^{(1)}$, It follows from Eq. \ref{eq:epsilonapprox2}) )" + that Finally. we obtain the relation between ul and VlI: Note that Eqs. (79))-(85))," that Finally, we obtain the relation between $u_1^{(1)}$ and $v_{\perp1}^{(1)}$, Note that Eqs. \ref{eq:Fdone}) \ref{eq:reluvperp}) )" + are formally identical to Eqs. (43))-(49)), are formally identical to Eqs. \ref{eq:pressuretheta}) \ref{eq:relationuvperp}) ) + for the linear approximation in Section HI., for the linear approximation in Section III. +" This is not surprising as both methods are designed to replicate linear theory in the first order approximation,", This is not surprising as both methods are designed to replicate linear theory in the first order approximation. + Once the first order terms are known we can proceed to derive the second and third order approximations with respect to € (i.e. terms from the expansion of Eqs. (57))-(65)), Once the first order terms are known we can proceed to derive the second and third order approximations with respect to $\epsilon$ (i.e. terms from the expansion of Eqs. \ref{eq:massconservation1}) \ref{eq:totalpressurenew}) ) + that are proportional to € and €. respectively).," that are proportional to $\epsilon^2$ and $\epsilon^3$, respectively)." + First. we write out the secod order approximations and substitute for all first order terms (1.8. terms of the form f umsing Eqs. (79))-(85)).," First, we write out the second order approximations and substitute for all first order terms (i.e. terms of the form $f_1^{(1)}$ ) using Eqs. \ref{eq:Fdone}) \ref{eq:reluvperp}) )." + Secondly. we find (by solving the Inhomogeneous system) the expansions of second order terms (terms with 727)," Secondly, we find (by solving the inhomogeneous system) the expansions of second order terms (terms with $2$ ')." + Thirdly. we derive the second order relations between all variables. similar to the ones obtained in the first order approximation.," Thirdly, we derive the second order relations between all variables, similar to the ones obtained in the first order approximation." + The equations representing the second order approximation with respect to ε (with variables in the first order substituted) are It is clear that nonlinear terms appear from this order of approximation and they are expressed in terms of variables obtained in the first order., The equations representing the second order approximation with respect to $\epsilon$ (with variables in the first order substituted) are It is clear that nonlinear terms appear from this order of approximation and they are expressed in terms of variables obtained in the first order. + The analysis of the system of Eqs. (86))-(94)), The analysis of the system of Eqs. \ref{eq:epsilon2ndapprox1}) \ref{eq:epsilon2ndapprox9}) ) + revealsthat the expansions with respect to 6 has to be written in the form for us. bs. vs. b5 and P» and," revealsthat the expansions with respect to $\delta$ has to be written in the form for $u_2$, $b_{x2}$, $v_{\perp2}$, $b_{\perp2}$ and $P_2$ and" +aud Il» are always mich less than the Ibubble time at cach epoch. so that our equilibrium calculations here indicate real changes to the primordial freeze-in abundance of IL».,"and $_2$ are always much less than the Hubble time at each epoch, so that our equilibrium calculations here indicate real changes to the primordial freeze-in abundance of $_2$." +" To illustrate the relative roles plaved by aun NRB and he associated radiation fields below 13.6 eV. we display in Table 1 the equilibrimm abundances of and UT, calculated by successively incliding radiation from two vackerounds. defined as follows."," To illustrate the relative roles played by an XRB and the associated radiation fields below 13.6 eV, we display in Table 1 the equilibrium abundances of $^{-}$ and $_2$ calculated by successively including radiation from two backgrounds, defined as follows." + The FUV includes the oXiotous relevant for IT» photocissociation iu the Lymanu-Werner bands (11.213.6 eV)., The FUV includes the photons relevant for $_2$ photodissociation in the Lyman-Werner bands (11.2–13.6 eV). + The is) dissociatect * photous haviug energies of 0.75513.6 eV. in the yalmework of this paper.," The $^{-}$ is dissociated by photons having energies of 0.755–13.6 eV, in the framework of this paper." + For the purposes of Table l. however. the IR/O (iutrared/optical) teria refers to he inclusion of all sub-13.6 eV photons except those in the ΤΑΝ bands.," For the purposes of Table 1, however, the IR/O (infrared/optical) term refers to the inclusion of all sub-13.6 eV photons except those in the LW bands." + Although this euerev range (0.75511.2 eV) corresponds to some UV photons as well. most of the photodissociation occurs at near IR aud optical wavelengths. eiveu the nature of the cross section aud our adopted power-law formi for the background inteusitv at these energies.," Although this energy range (0.755--11.2 eV) corresponds to some UV photons as well, most of the photodissociation occurs at near IR and optical wavelengths, given the nature of the $^{-}$ cross section and our adopted power-law form for the background intensity at these energies." + We see that the minia IB/O aud FUV backgrounds associated with any putative ARB from bigh-: quasars nore than compensate for any positive feedback frou he XRD in the form of au increased electron fraction in the ICM. (see. however. Ricottietal.(2001) on he positive feedback for II formation in the vicinity of individual ionization fronts ecuerated by lard stellar spectra).," We see that the minimum IR/O and FUV backgrounds associated with any putative XRB from $z$ quasars more than compensate for any positive feedback from the XRB in the form of an increased electron fraction in the IGM (see, however, \citet{rgshull01} on the positive feedback for $_2$ formation in the vicinity of individual ionization fronts generated by hard stellar spectra)." + The negative feedback from FUV. radiation jus already been noted im several works: we point out iere the additional feedback from IR/O photons., The negative feedback from FUV radiation has already been noted in several works; we point out here the additional feedback from IR/O photons. + The importance of the IR/O photons in this paper relative o the results of previous works. e.g. Iianuanotal. (2000).. can be traced to at least two factors.," The importance of the IR/O photons in this paper relative to the results of previous works, e.g., \citet{har}, can be traced to at least two factors." +" Firstly. our equilibrium calculation is performed for the relatively ow-density conditions iu the ICAL at 2=ο, rather than within highly overdeuse collapsed halos. so that some variance can be attributed to the differing densities of he studied euvironmeuts."," Firstly, our equilibrium calculation is performed for the relatively low-density conditions in the IGM at $z = 9$, rather than within highly overdense collapsed halos, so that some variance can be attributed to the differing densities of the studied environments." + Secoudly. Table 1 represcuts he effects of the strongest NRB cousicdered here. which was a correspondingly hieh IR/O associated background.," Secondly, Table 1 represents the effects of the strongest XRB considered here, which has a correspondingly high IR/O associated background." + Au NRB that was extrapolated from the observed EUV specific intensity at 2=3. such as case S du this work. would have a related IR/O backeround that has a neslieible müpact on the not and hence IL. abuudances.," An XRB that was extrapolated from the observed EUV specific intensity at $z =3$, such as case S in this work, would have a related IR/O background that has a negligible impact on the net $^{-}$, and hence $_2$, abundances." + Note also that a combination of these two actors. IGAL density and vacation intensity at the shotocdissociation threshold. iuiplies that only a relatively nodest IR/O background is required at +<12 to destroy IT.," Note also that a combination of these two factors, IGM density and radiation intensity at the $^{-}$ photodissociation threshold, implies that only a relatively modest IR/O background is required at $z < 12$ to destroy $^{-}$." + Avacdiation field of fay greater energy density is needed. o accomplish this in the early universe: this leads to the wellknown result that the CAIB photons are believed. to iive photodissociated at 2100.," A radiation field of far greater energy density is needed to accomplish this in the early universe; this leads to the well-known result that the CMB photons are believed to have photodissociated $^{-}$ at $z +\ga 100$." + Our estimate of the FUV backeround is not necessarily he munimal value. due to the opacity of the IGAL in the Lyian-Werner binds which we have not accounted for rere.," Our estimate of the FUV background is not necessarily the minimal value, due to the opacity of the IGM in the Lyman-Werner bands which we have not accounted for here." + The table shows. however. that even au order of uaenitude reduction in the FUV backeround aloue will rot increase the fractional abundance of Πο above 9.," The table shows, however, that even an order of magnitude reduction in the FUV background alone will not increase the fractional abundance of $_2$ above $^{-6}$." + As we have neglected contributions from stellar radiation. we have in fact underestimated the effects of IR/O and FUV photons at the epochs we cousicer.," As we have neglected contributions from stellar radiation, we have in fact underestimated the effects of IR/O and FUV photons at the epochs we consider." + Iu ΠΑΝ. we find that an NRB does not produce significant amouuts of new II» in the ICM. uuless the associated FUV and IRο backerounds were somehow strongly attenuated.," In summary, we find that an XRB does not produce significant amounts of new $_2$ in the IGM, unless the associated FUV and IR/O backgrounds were somehow strongly attenuated." + Finally. it may be possible for a heated IGAL with sufficient pressure to inhibit outflows from star-forming protogalaxies.," Finally, it may be possible for a heated IGM with sufficient pressure to inhibit outflows from star-forming protogalaxies." +" Mass loss from carly objects through ealactic winds or evaporation is often invoked to explain the ubiquitous presence of metals in the Lye forest clouds at 2~3: a pre-heated IGAL could. however. hinder such outflows of metal-enriehed gas frou, host galaxies at sufficiently high redshifts (priorto reionization)."," Mass loss from early objects through galactic winds or evaporation is often invoked to explain the ubiquitous presence of metals in the $\alpha$ forest clouds at $z +\sim 3$; a pre-heated IGM could, however, hinder such outflows of metal-enriched gas from host galaxies at sufficiently high redshifts (priorto reionization)." + An estimate of the effect of a saxi IGM in inhibiting ealactic winds may be made as follows., An estimate of the effect of a warm IGM in inhibiting galactic winds may be made as follows. +" Setting the ram pressure of the wind pyc2. equal to Paar = (ndone done) ATiear. and using AL,=πιuec Where AL acl ora are respectively the mass outflow rate of the wind aud the wind stalling radius iu the ICAL where pressure equilibriun is reached. we have: for the IGM deusity at 2= 9."," Setting the ram pressure of the wind $\rho_{\rm w} v_{\rm w}^2$, equal to $P_{\rm IGM}$ = $n_{\rm H} + +n_{\rm He} + n_{\rm e}$ ) $k T_{\rm IGM}$, and using $\dot{M_{\rm w}} = 4 +\pi r_{\rm st}^2 \, \rho_{\rm w} v_{\rm w}$, where $\dot{M_{\rm w}}$ and $r_{\rm st}$ are respectively the mass outflow rate of the wind and the wind stalling radius in the IGM where pressure equilibrium is reached, we have: for the IGM density at $z = 9$ ." + Note that if the ΤΝΤ had cooled adiabatically frou 2~ 150. then Zi would be," Note that if the IGM had cooled adiabatically from $z \sim 150$ , then $T_{\rm IGM}$ would be" +system at the same instant is 6.5x10? Mo.,system at the same instant is $6.5 \times 10^9$ $_\sun$. + The simulated tail exhibits a density peak about 150 kpc away from the parent galaxy center., The simulated tail exhibits a density peak about 150 kpc away from the parent galaxy center. +" As explained in Section 5.1,, the formation in tidal tails of sub-structures that may even be gravitationally bound is not uncommun."," As explained in Section \ref{fakedark}, the formation in tidal tails of sub-structures that may even be gravitationally bound is not uncommun." + The denser region gathers a gas mass of 5x10: Mo over 20 kpc., The denser region gathers a gas mass of $5 \times 10^7$ $_\sun$ over 20 kpc. +" These values are comparable to that observed for the object known as VirgoHI21: M07 give an HI mass of 3x10"" Mo over 14 kpc.", These values are comparable to that observed for the object known as VirgoHI21: M07 give an HI mass of $3 \times 10^7$ $_\sun$ over 14 kpc. + The fact that the tidal structure extends in our model further out beyond the HI condensation is also consistent with the detection of HI North of VirgoHI21 recently reported by, The fact that the tidal structure extends in our model further out beyond the HI condensation is also consistent with the detection of HI North of VirgoHI21 recently reported by +where tps is last scattering. c; is the sound syeecl. α is the scale [actor. & is its time derivative. aud D4 is the augular size distance.,"where $z_{LS}$ is last scattering, $c_s$ is the sound speed, $a$ is the scale factor, $\dot{a}$ is its time derivative, and $D_A$ is the angular size distance." +" The stretch parameter 2 las a different normalization and approximates he denominator⋅ as Xx(Qj,1/2 which⋅⋅ is not a good approximation⋅ when the dark energy is siguilicaut at cps."," The stretch parameter $R$ has a different normalization and approximates the denominator as $\propto \Omega_M^{-1/2}$, which is not a good approximation when the dark energy is significant at $z_{LS}$." + fy is very well determined by the CMB data. with (4=303.1141.01 in the nou-flat ACDM chain.," $\ell_a$ is very well determined by the CMB data, with $\ell_a = 303.14 +\pm 1.04$ in the non-flat $\Lambda$ CDM chain." + There are correlate| deviations iu wy. was. Qa aud Qy that produce correlated deviations in the utumerator and denornator ol Eq(2.6)) which cancel out in the ratio.," There are correlated deviations in $\omega_B$, $\omega_M$, $\Omega_\Lambda$ and $\Omega_k$ that produce correlated deviations in the numerator and denominator of \ref{eq:ella}) ) which cancel out in the ratio." + Iu this paper he full fit to the CMB cata is no perforued. but the aLVO1 aud CDA densities are fixed at tlelr Wea1 values.," In this paper the full fit to the CMB data is not performed, but the baryon and CDM densities are fixed at their mean values." + With this simplification. the determination of the acoustic scale ooselis {ο (4=302.97+Lll because the deviations in te numerator are still preseut.," With this simplification, the determination of the acoustic scale loosens to $\ell_a = 302.97 \pm +4.14$ because the deviations in the numerator are still present." + The relative accuracy of(4 with [ixecd wy anc| ca is the same as tlie relative accuracy of £2., The relative accuracy of$\ell_a$ with fixed $\omega_B$ and $\omega_M$ is the same as the relative accuracy of $R$. +" The main reason O use f, Instead o 4?2 is that dt is clear how (4 is modified when the dark euergy is important. at ast scattering.", The main reason to use $\ell_a$ instead of $R$ is that it is clear how $\ell_a$ is modified when the dark energy is important at last scattering. + Figre { shows 1hat £4( shifts à egreat deal when the dark euerey density is egreater han the radiation xus matter deusity at recoruibinatio. While the change iid i2 is sinaller aud in he wrong direction.," Figure \ref{fig:R-ell_a} shows that $\ell_a$ shifts a great deal when the dark energy density is greater than the radiation plus matter density at recombination, while the change in $R$ is smaller and in the wrong direction." + The CMB also ooviles the matter deusity way used as par ol the large scale structure analysis., The CMB also provides the matter density $\omega_M$ used as part of the large scale structure analysis. + For models far fro1 the geomeric degeneracy line. a [ull fit to the CMB power spectrum will compeusate for au incorrect. distauce to the surface of last scattering by changiug way aud wy to eive a different. valte of the sotud horizou at last scattering. but this ellect has not been been iucluded here.," For models far from the geometric degeneracy line, a full fit to the CMB power spectrum will compensate for an incorrect distance to the surface of last scattering by changing $\omega_M$ and $\omega_B$ to give a different value of the sound horizon at last scattering, but this effect has not been been included here." + Ultiiately a full it to all the data σοι] be performed. aud the CMB is both the inost informative ald the most €omputationally intensive of all the datasets.," Ultimately a full fit to all the data should be performed, and the CMB is both the most informative and the most computationally intensive of all the datasets." + Spergel ((2007) has some limits on «e. bit not on the 0.40 plane. and does not include either the Riess ((2007) aud Wood-Vasey ((2007) increments to the supernova data or the GBB cata.," Spergel (2007) has some limits on $w$, but not on the $w,w'$ plane, and does not include either the Riess (2007) and Wood-Vasey (2007) increments to the supernova data or the GRB data." + The second tajor input involving acoustic oscillations comes Crom the baryou acoustic oscillatious detected by Eiseustein (2005)., The second major input involving acoustic oscillations comes from the baryon acoustic oscillations detected by Eisenstein (2005). + Iu this paper we use the ratio of the clistance Dy(0.35) at 2=0.35 to the tangential distance at last scattering. = This ratio is easily computed even when the dark energy is significant a last scattering.," In this paper we use the ratio of the distance $D_V(0.35)$ at $z=0.35$ to the tangential distance at last scattering, = This ratio is easily computed even when the dark energy is significant at last scattering." + The ratio is also slightly more precise than the A parameter since the scatter induced by the uncertainty in og; μα αλ cancels out in the ratio., The ratio is also slightly more precise than the $A$ parameter since the scatter induced by the uncertainty in $\omega_B$ and $\omega_M$ cancels out in the ratio. +" The 4A parameter also uses the appronitjation that the soui| travel distauce is x0,13 which fails when dark energy dominates early.", The $A$ parameter also uses the approximation that the sound travel distance is $\propto \Omega_M^{-1/2}$ which fails when dark energy dominates early. + Finally. AZFR is exactly proportional to Dy(0.35)/[C4tes)Dates)).," Finally, $A/R$ is exactly proportional to $D_V(0.35)/[(1+z_{LS})D_A(z_{LS})]$." + Using both A and the distaice ralio amounts ) double counting the barvon acoustic oscillations., Using both $A$ and the distance ratio amounts to double counting the baryon acoustic oscillations. + The redshift of last scattering. σεις. is essentially independent of both tLe baryou deusity aud ihe expausiou rate because the electron density is n4xH(z)/a(1) while the optical depth is," The redshift of last scattering, $z_{LS}$ , is essentially independent of both the baryon density and the expansion rate because the electron density is $n_e \propto H(z)/\alpha(T)$ while the optical depth is" +"more. and so on until the value of 2 The clusters were set up using a Plummer density distribution with a ratio of hall-mass radius to Jacobi radiusof HifI0;=0.2. Le. à ratio of projected. half-mass radius o Jacobi radius of Rp,fy=0.15.","more, and so on until the value of $R_J$ The clusters were set up using a Plummer density distribution with a ratio of half-mass radius to Jacobi radiusof $R_h/R_J = 0.2$, i.e. a ratio of projected half-mass radius to Jacobi radius of $R_{hp}/R_J = +0.15$." + This choice resembles he extended. globular clusters of the Alilky Way. which are ess concentrated. anc stand. in contrast to the compact clusters. which are deeply embedded: within their Jacobi raciius and for which tidal inlluences are rather negligible (Daumgardtctal.2010).," This choice resembles the extended globular clusters of the Milky Way, which are less concentrated, and stand in contrast to the compact clusters, which are deeply embedded within their Jacobi radius and for which tidal influences are rather negligible \citep{Baumgardt10}." +. All clusters had initially 65536 stars which were crawn rom the canonical (Ixroupa2001) ranging from VIAL. to L2M.. resulting in a total initial mass of about 20000M...," All clusters had initially 65536 stars which were drawn from the canonical \citep{Kroupa01} ranging from $0.1\msun$ to $1.2 \msun$, resulting in a total initial mass of about $20\,000 \msun$." + ALL clusters were modelled without stellar evolution and without primordial binaries., All clusters were modelled without stellar evolution and without primordial binaries. + “Pheyv were computed for a time span of 4 Gr. if they did not dissolve before reaching this age.," They were computed for a time span of 4 Gyr, if they did not dissolve before reaching this age." + An overview of all clusters in our sample is ogiven in Ta Jd., An overview of all clusters in our sample is given in Tab. \ref{table1}. + For all clusters we produced two-climensional snapshots of the stars projected onto the orbital plane every 10 Myr: thus. as each of the 20 clusters is modelled over 4 Cyr. we have about 20.400~107 representations of star clusters.," For all clusters we produced two-dimensional snapshots of the stars projected onto the orbital plane every 10 Myr; thus, as each of the 20 clusters is modelled over 4 Gyr, we have about $20\times 400 \sim +10^4$ representations of star clusters." + In each snapshot we determine the centre of the cluster stars within the Jacobi radius following Casertano&Lut and bin the stars around this centre in 50 annuli of equal logarithmic width between 1.0 pe and 500 pe to produce the velocity dispersion and surface density profiles., In each snapshot we determine the centre of the cluster stars within the Jacobi radius following \citet{Casertano85} and bin the stars around this centre in 50 annuli of equal logarithmic width between 1.0 pc and 500 pc to produce the velocity dispersion and surface density profiles. + By going out to 500 pc we are able to show not only the region close to the Jacobi radius but also a considerable. part of. the tidal tails. which have not been investigated in this respect vet. but show an interesting. variable behaviour. depending on the cluster orbit. whieh can even influence the velocity dispersion and surface density within the Jacobi radius (see Ixüpperetal. 20102).," By going out to 500 pc we are able to show not only the region close to the Jacobi radius but also a considerable part of the tidal tails, which have not been investigated in this respect yet, but show an interesting, variable behaviour, depending on the cluster orbit, which can even influence the velocity dispersion and surface density within the Jacobi radius (see \citealt{Kuepper09}) )." + For most of the investigation. however. we concentrate on the inner LOO pc.," For most of the investigation, however, we concentrate on the inner 100 pc." + In each annulus the velocity dispersion alongthe line-of-sight (los). o. is determined using where ο) is the velocity of the 7th star along the 7 is the mean los velocity of the I stars in the annulus. and 07 ds their mean squared. los velocity.," In each annulus the velocity dispersion alongthe line-of-sight (los), $\sigma$ , is determined using where $v_i$ is the velocity of the $i$ -th star along the line-of-sight, $\overline{v}$ is the mean los velocity of the $N$ stars in the annulus, and $\overline{v^2}$ is their mean squared los velocity." + In. addition. we estimate an uncertainty for cach velocity. clispersion. which originates from a Taylor expansion of the standard deviation of the velocity The velocity. dispersion is first. measured. by. taking into account all stars in the snapshot. independent of their projected. distance from the cluster centre. which is what an ideal observer would see.," In addition, we estimate an uncertainty for each velocity dispersion, which originates from a Taylor expansion of the standard deviation of the velocity The velocity dispersion is first measured by taking into account all stars in the snapshot, independent of their projected distance from the cluster centre, which is what an ideal observer would see." + Then it is measured. for only the stars within the Jacobi radius. Le. r65% probability that the"," Indeed, in of our resamples, there is a $>65\%$ probability that the" +Stellar winds from hot massive stars. OB and Wolf-Rayet (WR) type stars. emit free-free thermal emission detectable at radio frequencies.,"Stellar winds from hot massive stars, OB and Wolf-Rayet (WR) type stars, emit free-free thermal emission detectable at radio frequencies." +" Stars with spherically symmetric. isothermal. and stationary outflows are predicted to produce radio spectra with a characteristic frequency dependence of S$,o""9 (see. Panagia Felli. 1975; Wright Barlow 1975)."," Stars with spherically symmetric, isothermal, and stationary outflows are predicted to produce radio spectra with a characteristic frequency dependence of $S_{\nu} \propto +\nu^{0.6}$ (see, Panagia Felli, 1975; Wright Barlow 1975)." + The spectral index a=0.6 results from the radial dependence of the electron density. 2e77.," The spectral index $\alpha = 0.6$ results from the radial dependence of the electron density, $n \propto r^{-2}$." + These authors also show that variations in this electron density behavior results in free-free spectra with a frequency dependence different from the 0.6 value., These authors also show that variations in this electron density behavior results in free-free spectra with a frequency dependence different from the 0.6 value. + Likewise. Leitherer & Robert (1991) discuss several mechanisms that may cause a deviation from a 0.6 spectral index focusing on changes in the ionization structure and velocity gradients in the wind.," Likewise, Leitherer $\&$ Robert (1991) discuss several mechanisms that may cause a deviation from a 0.6 spectral index focusing on changes in the ionization structure and velocity gradients in the wind." + Such effects may be present and produce small variations in the observed slope of the radio spectrum (0.61.5$ the softening length in the $\Lambda$ CDM simulation is larger than in the SCDM simulation and, as a result, non-physical effects due to softening may be expected to be more pronounced at early times in the $\Lambda$ CDM simulation." + Although a variety of prescriptions have been tried in attempts to model supernovae feedback in SPL simulations. usually by converting cold gas into “star particles” which hen inject thermal and kinetic energy into the surrounding eas (e.g. Navarro&White1993:SteinmetzMüller.1995:katz.Weinberg&IHlernquist| 1996)). this process remains xoorlv understood.," Although a variety of prescriptions have been tried in attempts to model supernovae feedback in SPH simulations, usually by converting cold gas into “star particles” which then inject thermal and kinetic energy into the surrounding gas (e.g. \pcite{nw93,SM95,katz96}) ), this process remains poorly understood." + Ln cosmological SPILL simulations. gas can only begin to cool clicienth in. objects well above he minimum resolved halo mass. around several times 10tip7hM. in. our case.," In cosmological SPH simulations, gas can only begin to cool efficiently in objects well above the minimum resolved halo mass, around several times $10^{11}h^{-1}{\rm +M}_\odot$ in our case." + sPhus. resolution. ellects.. prevent all the gas from cooling in small halos at high redshift. a oocess that. in reality. is probably due to feedback. from. supernovae or other energetic sources.," Thus, resolution effects prevent all the gas from cooling in small halos at high redshift, a process that, in reality, is probably due to feedback from supernovae or other energetic sources." + The resolution of our simulation was. in fact. chosen to ensure that the fraction of barvons that cools by the present in the SCDAL mocel is comparable to the observed fraction of cold gas ancl stars in galaxies today.," The resolution of our simulation was, in fact, chosen to ensure that the fraction of baryons that cools by the present in the SCDM model is comparable to the observed fraction of cold gas and stars in galaxies today." + This was achieved by carrying out several test simulations with varving resolution until the clesireel cold gas fraction was obtained (yayetal.2000)., This was achieved by carrying out several test simulations with varying resolution until the desired cold gas fraction was obtained \cite{kay99}. +. In semi-analvtic models. some of the processes. involved in galaxv formation (e.g. the growth of dark matter halos by mergers of smaller halos) are followed using analytic solutions and Monte-Carlo techniques.," In semi-analytic models, some of the processes involved in galaxy formation (e.g. the growth of dark matter halos by mergers of smaller halos) are followed using analytic solutions and Monte-Carlo techniques." + Other. more uncertain processes. such as feedback. from supernovae are mocelled. by means of simple. physically motivated rules.," Other, more uncertain processes, such as feedback from supernovae are modelled by means of simple, physically motivated rules." + Typically. each such rule contains one or two free parameters which are constrained. using observations of galaxies in the ocal Universe (e.g. Coleetal. 2000)).," Typically, each such rule contains one or two free parameters which are constrained using observations of galaxies in the local Universe (e.g. \pcite{coleetal99}) )." + In semi-analvtic models. the cvnanmies of the eas are strongly coupled to the evolution of dark matter halos and o the processes of star formation and feedback.," In semi-analytic models, the dynamics of the gas are strongly coupled to the evolution of dark matter halos and to the processes of star formation and feedback." + Phe starting xot. for our own mocelling is the set of dark matter halos at 2=O0 drawn from the Press-Schechter mass function., The starting point for our own modelling is the set of dark matter halos at $z=0$ drawn from the Press-Schechter mass function. + A merging history for cach halo is then constructed using he extended. Press-Schechter. formalism., A merging history for each halo is then constructed using the extended Press-Schechter formalism. + Beginning with he earliest. progenitor halo. our model assumes that gas (initially assumed to have zero metallicity) is shock-heated o the virial temperature of the halo. after which it begins to cool according to à specified cooling function.," Beginning with the earliest progenitor halo, our model assumes that gas (initially assumed to have zero metallicity) is shock-heated to the virial temperature of the halo, after which it begins to cool according to a specified cooling function." + Any σας that does cool forms a galaxy at the centre of the halo within which stars begin to form at a specified rate. producing xh metals and supernovae.," Any gas that does cool forms a galaxy at the centre of the halo within which stars begin to form at a specified rate, producing both metals and supernovae." + Supernovac reheat some of the eas in the galaxy. ejecting it back out into the surrounding ido. (," Supernovae reheat some of the gas in the galaxy, ejecting it back out into the surrounding halo. (" +Lhis gas is not allowed to cool again until the halo ws merged to form part of a larger halo.),This gas is not allowed to cool again until the halo has merged to form part of a larger halo.) + These processes continue until the halo mass has increased. by a factor of wo or more. either by merging with a lareer halo. or bv numerous accretions of smaller halos.," These processes continue until the halo mass has increased by a factor of two or more, either by merging with a larger halo, or by numerous accretions of smaller halos." + Any leftover hot gas »conies. part of the new halo. and the largest galaxy of the newly formed halo becomes the central galaxy. onto which urther gas can cool.," Any leftover hot gas becomes part of the new halo, and the largest galaxy of the newly formed halo becomes the central galaxy, onto which further gas can cool." + Any. other galaxies become satellites in the new halo. and may eventually merge with the central ealaxy due to energy. loss by dynamical friction.," Any other galaxies become satellites in the new halo, and may eventually merge with the central galaxy due to energy loss by dynamical friction." + The full model includes other processes such as stellar. population synthesis and morphological evolution which are not directly relevant to the present work., The full model includes other processes such as stellar population synthesis and morphological evolution which are not directly relevant to the present work. +" As well as this “fall” semi-analvtic (ES.)) model. for the purposes of this work we have constructed a. ""stripped-down"" semi-analvtic (SDSA)) model which is designed to be directly comparable to the SPL simulations (in a statistical sense)."," As well as this “full” semi-analytic ) model, for the purposes of this work we have constructed a ``stripped-down'' semi-analytic ) model which is designed to be directly comparable to the SPH simulations (in a statistical sense)." + In the mmocdel. we switch olf star formation ancl the associated supernovae feedback. and chemical enrichment. since these xwocesses are not included in the SPL caleulation.," In the model, we switch off star formation and the associated supernovae feedback and chemical enrichment, since these processes are not included in the SPH calculation." + Instead. we assume a fixed metallicity of 0.3 times the Solar value. just as in the simulations.," Instead, we assume a fixed metallicity of 0.3 times the Solar value, just as in the simulations." +" We also mimic the SPLE resolution w truncating. halo merger trees at INE,Ju times. the clark matter particle mass in the simulation. ancl by switching olf⋅ gas cooling. when the hot. gas mass is. less than Nepy, imes: the gas particle: mass."," We also mimic the SPH resolution by truncating halo merger trees at $N'_{\rm SPH}$ times the dark matter particle mass in the simulation, and by switching off gas cooling when the hot gas mass is less than $N'_{\rm SPH}$ times the gas particle mass." + sPhe parameter NiaHu Is: set to 2.Nupg=64. ie. twice the number of particles in the SPLE smoothing kernel.," The parameter $N'_{\rm +SPH}$ is set to $2\times N_{\rm SPH}=64$, i.e. twice the number of particles in the SPH smoothing kernel." + This value was chosen since it allows the numodel to mateh the position of the peak in the galaxy mass function in the SPIT simulations (as will be shown in re[fsecimassfunc.. see Fig.," This value was chosen since it allows the model to match the position of the peak in the galaxy mass function in the SPH simulations (as will be shown in \\ref{sec:massfunc}, see Fig." + 7)., 7). + Phe munidel has no such truncation of merger trees and. has ellectively unlimited. resolution (in practice. we resolve progenitor halos down to masses several hundred: times smaller than in the SPII and mimocels).," The model has no such truncation of merger trees and has effectively unlimited resolution (in practice, we resolve progenitor halos down to masses several hundred times smaller than in the SPH and models)." + To further emulate conditions in the SPLIT simulations in the nminiodel. we replace the Press-Schechter formula for the mass Function of dark matter halos (which is commonly used in semi-analvtic models. includingour numodel) with the formula proposed. by Sheth.Mo&Tor-men(1999) which provides a better match to the results of large N-body simulations (Jenkinsetal.2000).," To further emulate conditions in the SPH simulations in the model, we replace the Press-Schechter formula for the mass function of dark matter halos (which is commonly used in semi-analytic models, includingour model) with the formula proposed by \scite{smt} which provides a better match to the results of large N-body simulations \cite{arj00}." +.. Although this ensures that the abundance of halos at z=0 in the mmociel is similar to that in the SPIT simulations. it cloes not guarantee that the distribution of progenitor halo masses will also be the same.," Although this ensures that the abundance of halos at $z=0$ in the model is similar to that in the SPH simulations, it does not guarantee that the distribution of progenitor halo masses will also be the same." + In [act. as has been shown hy Somervilleetal. (2000)... we find that at high redshifts the merger trees in our," In fact, as has been shown by \scite{rsetal98}, , we find that at high redshifts the merger trees in our" +in the legend.,in the legend. + The same integration limits as in this study were used in most of the works considered., The same integration limits as in this study were used in most of the works considered. +" The only exceptions are the Mortlocketal.(2011) points (M.> 107Mo), the etal.(2010) ones (M.>10? M5), and those from Dickinsonetal.(2003) and Pérez-Gonzálezetal.(2008), who adopted redshift-dependent mass limits (we refer to these works for more details)."," The only exceptions are the \cite{mortlock11} points $M_*>10^7 M_\odot$ ), the \cite{ilbert10} ones $M_*>10^5 M_\odot$ ), and those from \cite{dickinson03} and \cite{perezgonzalez08}, who adopted redshift-dependent mass limits (we refer to these works for more details)." +" Our results show good agreement with those computed by previous authors at 0.6€zx2, although we recall once again that our mass densities in the redshift intervals around z~1.6 and z~2.2—2.3 might be systematically too high owing to a few known overdensities."," Our results show good agreement with those computed by previous authors at $0.6 \lesssim z \lesssim 2$, although we recall once again that our mass densities in the redshift intervals around $z\sim 1.6$ and $z\sim 2.2-2.3$ might be systematically too high owing to a few known overdensities." + The steepness in the faint-end of the GSMF computed by this work is responsible for the large values of the SMD inferred at z>2., The steepness in the faint-end of the GSMF computed by this work is responsible for the large values of the SMD inferred at $z>2$. +" Our estimates are higher than those reported by previous authors, with the exception of the Mortlocketal.(2011) results."," Our estimates are higher than those reported by previous authors, with the exception of the \cite{mortlock11} results." +" However, the latter results originate from a different shape of the GSMF: Mortlocketal.(2011) indeed found flatter faint-end slopes than we do, and the large SMD is a consequence of a higher density of high mass galaxies (see Fig. 3))."," However, the latter results originate from a different shape of the GSMF: \cite{mortlock11} indeed found flatter faint-end slopes than we do, and the large SMD is a consequence of a higher density of high mass galaxies (see Fig. \ref{fig:mf_obs}) )." + We note that the SMD is affected by uncertainties caused by systematic effects., We note that the SMD is affected by uncertainties caused by systematic effects. +" In Fig. 9,,"," In Fig. \ref{fig:mdens}," +" the grey shaded region indicates the dispersion in the SMD when including the outputs obtained by integrating the fit to our 1/V,,4, points plus those collected from the literature with both a Schechter function and a double power-law shape (see Sect. 4)).", the grey shaded region indicates the dispersion in the SMD when including the outputs obtained by integrating the fit to our $1/V_{max}$ points plus those collected from the literature with both a Schechter function and a double power-law shape (see Sect. \ref{sec:faintend}) ). +" This region represents the systematic errors caused by the choice of the stellar library and the functional shape of the GSMF, as well as the simultaneous use of the ERS observations as a probe of the low-mass end of the GSMF and the results of large surveys to constrain the bright-end."," This region represents the systematic errors caused by the choice of the stellar library and the functional shape of the GSMF, as well as the simultaneous use of the ERS observations as a probe of the low-mass end of the GSMF and the results of large surveys to constrain the bright-end." +" The dispersion increases significantly at z3, reflecting the large scatter among existing surveys."," The dispersion increases significantly at $z\gtrsim 3$, reflecting the large scatter among existing surveys." +" Moreover, the lack of overlap with most previous results at these redshifts is a sign of the impossibility to assemble a single, self-consistent GSMF from the highest to the lowest masses."," Moreover, the lack of overlap with most previous results at these redshifts is a sign of the impossibility to assemble a single, self-consistent GSMF from the highest to the lowest masses." +" This is due to the inhomogeneity of the samples, to the variance between different fields and also to the intrinsic uncertainties at high redshift in both the stellar masses and GSMF."," This is due to the inhomogeneity of the samples, to the variance between different fields and also to the intrinsic uncertainties at high redshift in both the stellar masses and GSMF." + We compared the SMD with the integrated star formation rate density., We compared the SMD with the integrated star formation rate density. +" For this purpose, we first considered the best-fit to the compilation of SFRD measurements made by Hopkins&Beacom (2006)."," For this purpose, we first considered the best-fit to the compilation of SFRD measurements made by \cite{hopkins06}." +". Following Wilkinsetal.(2008),, we rescaled it to a Salpeter IMF and integrated it as a function of time, after accounting for the gas recycle fraction."," Following \cite{wilkins08}, we rescaled it to a Salpeter IMF and integrated it as a function of time, after accounting for the gas recycle fraction." +" The latter is the fraction of stellar mass returned to the interstellar medium as a function of time, and was computed using the Bruzual&Charlot model."," The latter is the fraction of stellar mass returned to the interstellar medium as a function of time, and was computed using the \cite{bc03} model." + The result of this calculation is shown in Fig., The result of this calculation is shown in Fig. + 9 by the blue dashed line., \ref{fig:mdens} by the blue dashed line. + We then performed the same calculation by using the best-fit parametric shape for the star formation history, We then performed the same calculation by using the best-fit parametric shape for the star formation history +equivalent widths with L47«z2.3.,equivalent widths with $1.47 < z < 2.3$. + Figures 11. and 12. show the number of observations of each line binned by redshift and dereddened /* apparent magnitude.," Figures \ref{fig:zhist} + and \ref{fig:imaghist} show the number of observations of each line binned by redshift and dereddened $\iband$ apparent magnitude." + There are several important. considerations (hat apply to the choice of quasar sample or (his test., There are several important considerations that apply to the choice of quasar sample for this test. +" One central assumption in the development of (he equivalent width moclel distribution is that the sample is continuum. flux-limited. in order (hat amplification bias nav be (treated correctly,"," One central assumption in the development of the equivalent width model distribution is that the sample is continuum flux-limited, in order that amplification bias may be treated correctly." + Optically selected samples such as the SDSS Quasar Catalog will 100 be exactly limited by contimuun flux due to contributions from line emission., Optically selected samples such as the SDSS Quasar Catalog will not be exactly limited by continuum flux due to contributions from line emission. + Because (he sample is limited by 7 magnitude. the line will contribute to the measured filter [lux for quasars with redshifts 1.4«z<1.9 (2): the and llines not appear in / over the redshifts studied. although other lines such as acid some of (he Dalmer series do move into (he / filler at low redshilt.," Because the sample is limited by $\iband$ magnitude, the line will contribute to the measured filter flux for quasars with redshifts $1.4 < z < 1.9$ \citep{sdss:photo-filter}; ; the and lines not appear in $i$ over the redshifts studied, although other lines such as and some of the Balmer series do move into the $i$ filter at low redshift." + ILowever. the width of the filter is about wwhile the tvpical observed emission line equivalent width is less than of this. so the (vpical magnitude in Chis situation will be less than 0.1 brighter than the continuum-only value.," However, the width of the filter is about while the typical observed emission line equivalent width is less than of this, so the typical magnitude in this situation will be less than $0.1$ brighter than the continuum-only value." + It is also important [ον the sample to be as complete as possible., It is also important for the sample to be as complete as possible. + The SDSS quasar targeting algorithm (?) has been shown to be at least complete lor 2<2.5 and P<19.1 (19.0 lor the EDR)., The SDSS quasar targeting algorithm \citep{sdss:qso-target} has been shown to be at least complete for $z < 2.5$ and $\iband < 19.1$ (19.0 for the EDR). + Since the luninosity finetion is only determined for 2<2.3 (?).. completeness in redshift is not a concern.," Since the luminosity function is only determined for $z < +2.3$ \citep{twodf:lf}, , completeness in redshift is not a concern." + The Quasar Catalog absolute magnitude limit ol Afj=—23 does not in practice affect the sample either., The Quasar Catalog absolute magnitude limit of $M_\iband = -23$ does not in practice affect the sample either. + As shown in Figure 3 of ?.. this resiriction removes onlv observalions near /=19.0 with 2« 0.42. a neeligiblv small population that is hiehlv unlikely to exhibit microlensing.," As shown in Figure 3 of \citet{sdss:edr-qsocat}, this restriction removes only observations near $\iband = 19.0$ with $z < 0.42$ a negligibly small population that is highly unlikely to exhibit microlensing." + The Quasar Catalog requirement (hat EWIIM km ! for at least one emission line is more worrisome. since this mav exclude small equivalent width observations.," The Quasar Catalog requirement that FWHM $> 1000$ km $^{-1}$ for at least one emission line is more worrisome, since this may exclude small equivalent width observations." + On the other hand. (this criterion was chosen specifically to eliminate narrow-lned quasars. which don't belong in a study. of the broad. emission line region.," On the other hand, this criterion was chosen specifically to eliminate narrow-lined quasars, which don't belong in a study of the broad emission line region." + Moreover. only 10 quasars were droppedfrom the catalog based solely onthis criterion.," Moreover, only 10 quasars were droppedfrom the catalog based solely onthis criterion." + Finally.the bright-limit discrepancy. 6*=15.0 versus /*= 16.5) in different EDR," Finally,the bright-limit discrepancy $\iband = 15.0$ versus $\iband = 16.5$ ) in different EDR" +is sullicient (ο determine the neutrino mass matrix wilh two texture zeros. will be able to overrule various neutrino mass moclels with (wo texture zeros if (he model parameters are known and to constrain the model parameters if thev are unknown.,"is sufficient to determine the neutrino mass matrix with two texture zeros, will be able to overrule various neutrino mass models with two texture zeros if the model parameters are known and to constrain the model parameters if they are unknown." +" In the class of GUT models under consideration. the mass matrices M,,, lor the Dirac neutrinos which gives rise to neutrino masses via see-saw mechanism can be taken identical to AL, except for the accompanying CG coefficients which depend upon the representations of the coupling Higgs field [8.9].."," In the class of GUT models under consideration, the mass matrices $M_{\nu_ D}$ for the Dirac neutrinos which gives rise to neutrino masses via see-saw mechanism can be taken identical to $M_{u}$ except for the accompanying CG coefficients which depend upon the representations of the coupling Higgs field \cite{Bando and Obara +1, Bando and Obara 2}." + Therefore. these mass models predict the neutrino mass matrix al GUT scale.," Therefore, these mass models predict the neutrino mass matrix at GUT scale." + This theoretical mass matrix should be consistent with the phenomenological mass matrix at weak scale calculated. [or the texture scheme consistent with the mocel., This theoretical mass matrix should be consistent with the phenomenological mass matrix at weak scale calculated for the texture scheme consistent with the model. + llowever. (he neutrino mass matrix calculated at GUT scale has to be run down to the weak scale before comparing it wilh the neutrino mass matrix calculated phenomenologically from its texture scheme from the neutrino data at the weak scale.," However, the neutrino mass matrix calculated at GUT scale has to be run down to the weak scale before comparing it with the neutrino mass matrix calculated phenomenologically from its texture scheme from the neutrino data at the weak scale." + The effect of renormalization eroup (RG) running will be small for the neutrino mass matrices with normal hierarchy., The effect of renormalization group (RG) running will be small for the neutrino mass matrices with normal hierarchy. + llowever. il can be sienilicantlv large for the mass matrices wilh inverted or quasi-degenerale hierarchy.," However, it can be significantly large for the mass matrices with inverted or quasi-degenerate hierarchy." + In (he present work. we first derive (he phenomenological neutrino mass matrix for a particular texture scheme proposed by Frampton. Glashow and Marfatia |I] and confront it with a class of (wo-zero symmetric texture GUT models based upon minimal supersvinuetric SO(10) iS.9]..," In the present work, we first derive the phenomenological neutrino mass matrix for a particular texture scheme proposed by Frampton, Glashow and Marfatia \cite{FGM paper} and confront it with a class of two-zero symmetric texture GUT models based upon minimal supersymmetric SO(10) \cite{Bando and Obara 1, Bando and Obara 2}." + We take the neutrino mass matrix to be the real symmetric matrix with (wo texture zeros: where since we are interested in obtaining only the relative magnitudes of the neutrino mass matrix elements without phases or signs., We take the neutrino mass matrix to be the real symmetric matrix with two texture zeros: where since we are interested in obtaining only the relative magnitudes of the neutrino mass matrix elements without phases or signs. + This is the texture A» of Frampton. Glashow and Meurfatia νι ," This is the texture $\mathcal{A}_2$ of Frampton, Glashow and Marfatia \cite{FGM paper}. ." +"The eigenvalues of M, are nma. Πο and ma."," The eigenvalues of $M_{\nu}$ are $m_1$, $-m_2$ and $m_3$ ." + The real orthogonal matrix O which diagonalizes (he neutrino massmatrix AMaccording to the relation, The real orthogonal matrix $O$ which diagonalizes the neutrino massmatrix $M$according to the relation +a planar surface. is ~170 m. Assuming a depth-to-diameter ratio of 0.2 (Melosh 1989)). the corresponding crater depth is ~34 mThhis number cannot be interpreted as a precise measure of the thickness of the original mantle of P/Read (could have been thinner at the impact point). but is only useful to give an idea of the orders of magnitude involved.,"a planar surface, is $\sim 170$ m. Assuming a depth-to-diameter ratio of 0.2 (Melosh \cite{melosh}) ), the corresponding crater depth is $\sim 34$ mṪhhis number cannot be interpreted as a precise measure of the thickness of the original mantle of P/Read (could have been thinner at the impact point), but is only useful to give an idea of the orders of magnitude involved." + This rough computation is performed for a crater close to the subsolar point: in case of an impact at a higher latitude. all the numbers should be scaled The crater size estimate given above is a lower limit.," This rough computation is performed for a crater close to the subsolar point: in case of an impact at a higher latitude, all the numbers should be scaled The crater size estimate given above is a lower limit." + It would apply only for inert mantle thickness much lower that the estimated crater depth., It would apply only for inert mantle thickness much lower that the estimated crater depth. + However. we expect that MBCs have mantles thickness of the order of tens of meters because thinner mantles would have not have been able to prevent the complete sublimation of volatiles for MBC-sized objects.," However, we expect that MBCs have mantles thickness of the order of tens of meters because thinner mantles would have not have been able to prevent the complete sublimation of volatiles for MBC-sized objects." + For instance. in the case that a thickness of half of excavated depth consist of inert mantle. the same active area is obtained for a crater diameter about (2) times Looking to the plots in figures l.. 2.. 5 and 6.. the hypothesis of an impact leaving a mantled bottom appears much less compatible with observation. unless we consider a surviving dust layer much thinner that in the Cases 2. 3. 4 and 5: the activity level is so faint that 1t would be hardly detected from ground.," For instance, in the case that a thickness of half of excavated depth consist of inert mantle, the same active area is obtained for a crater diameter about $\sqrt(2)$ times Looking to the plots in figures \ref{fig1}, \ref{fig2}, \ref{fig5} and \ref{fig6}, the hypothesis of an impact leaving a mantled bottom appears much less compatible with observation, unless we consider a surviving dust layer much thinner that in the Cases 2, 3, 4 and 5: the activity level is so faint that it would be hardly detected from ground." + In order to address if cratering events are a viable process to explain the observed activity and number of MBCs. it is important to estimate not only the size of the crater required to sustain the observed activity. but also the frequency of its The estimate of the projectile size needed to form a crater of 170 m has been performed considering two scaling laws. namely for porous material and cohesive soils (Holsapple anc Housen 2007))," In order to address if cratering events are a viable process to explain the observed activity and number of MBCs, it is important to estimate not only the size of the crater required to sustain the observed activity, but also the frequency of its The estimate of the projectile size needed to form a crater of 170 m has been performed considering two scaling laws, namely for porous material and cohesive soils (Holsapple and Housen \cite{holsapple}) )." +" The material strength has been set to 2x10"" and 10 dyne/em*.", The material strength has been set to $2x10^4$ and $10^7~$ $^2$ . + We assumed a target and projectile density of 1000 kg/m? and 2600 kg/m? respectively., We assumed a target and projectile density of 1000 $^3$ and 2600 $^3$ respectively. + Moreover. the computed P/Read intrinsic average impact probability withir the Main Belt is about 10/5 km? yr1 and the average impact velocity is about 3.7 km s7!.," Moreover, the computed P/Read intrinsic average impact probability within the Main Belt is about $^{18}$ $^{2}$ ${^-1}$ and the average impact velocity is about 3.7 km $^{-1}$." + These values are computec according to the Bottke et al. (2005)), These values are computed according to the Bottke et al. \cite{bottke}) ) + Main Belt population. and following the procedure described in the work of Marchi et al. (2010)).," Main Belt population, and following the procedure described in the work of Marchi et al. \cite{marchi}) )." + The derived projectile sizes are ~8.18.5 m for porous and cohesive material. The computed time for having a collision with a projectile »8monabody with the size of P/Read (0.6 km) is 107 yr.," The derived projectile sizes are $\sim 8, 18.5$ m for porous and cohesive material, The computed time for having a collision with a projectile $\ge 8$ m on a body with the size of P/Read (0.6 km) is $^7$ yr." + The estimated total number of objects larger than 0.6 km is 2.9105. therefore such a collision is expected to occur on average every ~17 yr everywhere in the Main Belt.," The estimated total number of objects larger than 0.6 km is $2.9x10^6$ , therefore such a collision is expected to occur on average every $\sim17$ yr everywhere in the Main Belt." + This time become ~147 yr for projectiles > 18.5 Of course these numbers have to be taken as a rough indication. given the uncertainties in the Main Belt size distribution at such small size and in the target material parameters.," This time become $\sim 147$ yr for projectiles $\ge$ 18.5 Of course these numbers have to be taken as a rough indication, given the uncertainties in the Main Belt size distribution at such small size and in the target material parameters." + Note that the timescales above also depend on the target size., Note that the timescales above also depend on the target size. + For a body having the size of Elst-Pizarro (5 km). it is estimated that the same impacts occur every ~10 and ~100 yr. respectively for projectiles of 8 and 18.5 m. When running a simulation. it would be impossible to test all the possible combination of input parameters.," For a body having the size of Elst-Pizarro (5 km), it is estimated that the same impacts occur every $\sim 10$ and $\sim 100$ yr, respectively for projectiles of 8 and 18.5 m. When running a simulation, it would be impossible to test all the possible combination of input parameters." + What is usually done is. once found a meaningful combination. to keep fixed values for most of the parameters and vary only one or two at a time. in order to test the influence of the changes on the results.," What is usually done is, once found a meaningful combination, to keep fixed values for most of the parameters and vary only one or two at a time, in order to test the influence of the changes on the results." + The variable parameters are the ones considered to be most influential on the properties or phenomena that are the object of the simulation., The variable parameters are the ones considered to be most influential on the properties or phenomena that are the object of the simulation. + In this paper. an initial composition for P/2005 U1 (Read) has been assumed. and we have varied. to build the 5 Cases that have been studied. the parameters defining the thickness and composition of the dust mantle.," In this paper, an initial composition for P/2005 U1 (Read) has been assumed, and we have varied, to build the 5 Cases that have been studied, the parameters defining the thickness and composition of the dust mantle." + As for the possible effects of changing the value attributed to the remaining initial parameters. it is here discussed on the basis of our A lower value of dust/ice. (for example. a value of I. usually attributed to classical comets) would give as a result a lower dust flux. and consequently a slower erosion of the surface.," As for the possible effects of changing the value attributed to the remaining initial parameters, it is here discussed on the basis of our A lower value of dust/ice, (for example, a value of 1, usually attributed to classical comets) would give as a result a lower dust flux, and consequently a slower erosion of the surface." + Changing the thermal conductivity. porosity. density. pore radius would have the effect of slowing or quickening the evolution of the model body.," Changing the thermal conductivity, porosity, density, pore radius would have the effect of slowing or quickening the evolution of the model body." + The thickness of the surviving mantle in the Cases 2. 3. 4 and 5 has been chosen in a quite arbitrary way.," The thickness of the surviving mantle in the Cases 2, 3, 4 and 5 has been chosen in a quite arbitrary way." + It is clear. anyway. that a larger thickness would tend to completely quench any possible activity.," It is clear, anyway, that a larger thickness would tend to completely quench any possible activity." + The mantle thickness necessary to completely block the underneath sublimation strongly depends on the average porosity. thermal conductivity and the other physical properties of the dust The issue of the initial temperature attributed to the model body deserves some more discussion.," The mantle thickness necessary to completely block the underneath sublimation strongly depends on the average porosity, thermal conductivity and the other physical properties of the dust The issue of the initial temperature attributed to the model body deserves some more discussion." + Surface temperature Is mainly determined by the solar input. and is spanning. along the orbit followed by the model body. the range 147 - 190 K (subsolar point. fast rotator approximation).," Surface temperature is mainly determined by the solar input, and is spanning, along the orbit followed by the model body, the range 147 - 190 K (subsolar point, fast rotator approximation)." + Obviously. nobody knows what really is the average internal temperature (below diurnal and seasonal skin depth) of such a body. but the assumption has been made that it should be around 130 K. a value at which water ice can survive.," Obviously, nobody knows what really is the average internal temperature (below diurnal and seasonal skin depth) of such a body, but the assumption has been made that it should be around 130 K, a value at which water ice can survive." + When the insulating mantle is disrupted. the internal temperature ts steadily rising tll an equilibrium value is reached.," When the insulating mantle is disrupted, the internal temperature is steadily rising till an equilibrium value is reached." + A different value of the initial temperature would result in a slowing or quickening of this process., A different value of the initial temperature would result in a slowing or quickening of this process. + In this paper the possible effect of a single impact has been simulated., In this paper the possible effect of a single impact has been simulated. + During the long time spent orbiting around the Sun.many small impactors hit the surface of bodies in the MainBelt.," During the long time spent orbiting around the Sun,many small impactors hit the surface of bodies in the MainBelt." + Even if these impacts are not able to disrupt, Even if these impacts are not able to disrupt +DL models.,BL models. + The best one-ring model is lor a DL temperature of 175.000). This model has a relatively low AZ and agrees well with the distance.," The best one-ring model is for a BL temperature of 175,000K. This model has a relatively low $\chi^2_{\nu}$ and agrees well with the distance." + For the two-ring BL models. there is little difference (in terms of \2) between a temperature of LOO.QO00I. 125.000IN. and 150.0001 (or any combination of those) as they produce 4221 with dz500+50pc.," For the two-ring BL models, there is little difference (in terms of $\chi^2_{\nu}$ ) between a temperature of 100,000K, 125,000K and 150,000K (or any combination of those) as they produce $\chi^2_{\nu} \approx 1$ with $d\approx 500 \pm 50$ pc." + A 150.0001 extended (2 rings) DL model with disk and WD is shown in Figure 2.," A 150,000K extended (2 rings) BL model with disk and WD is shown in Figure 2." + This model fits the [κ in the shorter wavelength range very well (A<970A.. ignoring the broad absorptions of vi)) but produces too much Εαν around.," This model fits the flux in the shorter wavelength range very well $\lambda < 970$, ignoring the broad absorptions of ) but produces too much flux around." + Extended DL models with a lower temperature (e.g. LOO.Q00K) do not fit the shorter wavelengths as well. but on the other side thev better fit the region and. consequently. (hey have the same X7.," Extended BL models with a lower temperature (e.g. 100,000K) do not fit the shorter wavelengths as well, but on the other side they better fit the region and, consequently, they have the same $\chi^2_{\nu}$." + In a last effort to improve the modeling. ihe temperature of the WD is increased to see how it affects the results.," In a last effort to improve the modeling, the temperature of the WD is increased to see how it affects the results." + As the WD temperature increases the hotter DL models deteriorate slightly while the cooler BL models improve slightly., As the WD temperature increases the hotter BL models deteriorate slightly while the cooler BL models improve slightly. + These models are listed in the lower part of Table 2 A fit with a 50.0001Ix WD. an extended 100.000«&« BL and a 2x10.9M. /vr accretion disk model is shown in Figure eB," These models are listed in the lower part of Table 2 A fit with a 50,000K WD, an extended 100,000K BL and a $2 \times 10^{-9}M_{\odot}$ /yr accretion disk model is shown in Figure 3." +i Overall. (he best fit to theFUSE spectrum of MV. Lyr in its high state consists of a composite WD + disk + DL model with a mass accretion rate M=2x10. /vr.," Overall, the best fit to the spectrum of MV Lyr in its high state consists of a composite WD + disk + BL model with a mass accretion rate $\dot{M} = 2 \times 10^{-9}M_{\odot}$ /yr." + There are (wo equally acceptable DL solutions. either a broad extended ((wo-ring) BL with a rather low temperature (in (he range 100.000Ix-150.000IX). or a thin (one-aring) BL with a higher temperature (175.000).," There are two equally acceptable BL solutions, either a broad extended (two-ring) BL with a rather low temperature (in the range 100,000K-150,000K), or a thin (one-ring) BL with a higher temperature (175,000K)." + The WD temperature is probably higher than the 44.0001Kk found in the low state. due to ongoing accretion but it affects only slightly the quality of the fitting of the models. we discuss this further at the end of this section.," The WD temperature is probably higher than the 44,000K found in the low state, due to ongoing accretion but it affects only slightly the quality of the fitting of the models, we discuss this further at the end of this section." + since the modeling of theFUSE spectrum generates more (han one solution over a finile spectral range. one must consider the bolometric huminositv of each component [or comparison with equations (2) (6).," Since the modeling of the spectrum generates more than one solution over a finite spectral range, one must consider the bolometric luminosity of each component for comparison with equations (2) (6)." + For each model. the total luminosity of the BL is computed assuming it racdiates as a black body.," For each model, the total luminosity of the BL is computed assuming it radiates as a black body." + This is a reasonable assumption. as in this reeime (he DL is most probably optically Chick (Godonetal. 1995).," This is a reasonable assumption, as in this regime the BL is most probably optically thick \citep{god95,pop95}." +". The two components of temperature Ty T5 (given in Table 2). ancl with radii r=1.054, and re=1.24, ave added."," The two components of temperature $T_1$ $T_2$ (given in Table 2), and with radii $r_1=1.05R_*$ and $r_2=1.2R_*$ are added." + One then simply uses the Stefan-Doltzmann law aud area of each ring to find the total BL Iuminosity., One then simply uses the Stefan-Boltzmann law and area of each ring to find the total BL luminosity. + The bolometric luminosity obtained is then compared with the theoretical expectation in eq.(6) using eq.(2)., The bolometric luminosity obtained is then compared with the theoretical expectation in eq.(6) using eq.(2). + For almost all the disk+BL, For almost all the disk+BL +of the components always dominates the flux of the other oue bv a factor larger than 2.,of the components always dominates the flux of the other one by a factor larger than 2. + This factor is even better --i the north-east since the north-eastern component is stronecr., This factor is even better in the north-east since the north-eastern component is stronger. + We have added the spectra of Ll and 12 leuslets at a distance lareer than 172 from the maxinuuu (taking oeito account the leuslet size) aud inside a radius of (78 in the north-east and south-west directions respectively., We have added the spectra of 14 and 12 lenslets at a distance larger than $\farcs$ 2 from the maximum (taking into account the lenslet size) and inside a radius of $\farcs$ 8 in the north-east and south-west directions respectively. + To avoid possible systematic errors due ο the discrete 2D-spectroscopy. we have perform the same extraction on the standard star that was observed just after the science exposure.," To avoid possible systematic errors due to the discrete 2D-spectroscopy, we have performed the same extraction on the standard star that was observed just after the science exposure." + The ratio of the nortl-castern to the southwestern spectra corrected from the standard star is shown in Fie. 2.., The ratio of the north-eastern to the south-western spectra corrected from the standard star is shown in Fig. \ref{apmspe}. + In the red. σ = 0.1. aud it is apparent that there is no significant difference in the emission Ime rauge except at 6112 ((0σ deviation).," In the red, $\sigma$ = 0.1, and it is apparent that there is no significant difference in the emission line range except at 6112 $\sigma$ deviation)." +" Iuterestiug cuough. this is the wavelength of the 11A2803 absorption line at z41, = 1.18 sugeestiug that the doublet ratio ix weaker (mud so is the columu deusitv) iu front of the northern image. indicative of sall-scale spatial variations of the cohuun densitics in this strong system."," Interesting enough, this is the wavelength of the $\lambda$ 2803 absorption line at $z_{\rm abs}$ = 1.18 suggesting that the doublet ratio is weaker (and so is the column density) in front of the northern image, indicative of small-scale spatial variations of the column densities in this strong system." + In the Lya forest. σ = 0.25.," In the $\alpha$ forest, $\sigma$ = 0.25." + However. it is appareut that there is no difference in the strong broad absorptions just blueward the Lye cussion liue.," However, it is apparent that there is no difference in the strong broad absorptions just blueward the $\alpha$ emission line." + This altogether is a eood indication that the quasar is leused., This altogether is a good indication that the quasar is lensed. + Tudeed. if the two quasars were different. we would expect to sce strong differeuces in the BAL as it is the case for TS 1216|5032A4.B (?)..," Indeed, if the two quasars were different, we would expect to see strong differences in the BAL as it is the case for HS 1216+5032A,B \citep{1996A&A...308L..25H}." + BALs are expected to arise in gas ejectedby the quasar with rapid spatial variations (?).., BALs are expected to arise in gas ejectedby the quasar with rapid spatial variations \citep{1998ApJ...496..177M}. + There is an apparently strong deviation at λςδΟ but this is due to the presence of the verv strong skv ciission ine., There is an apparently strong deviation at $\lambda$ 5885 but this is due to the presence of the very strong sky emission line. + There may be a significaut difference at ASST Ll aud AhT66 but it must be noticed that the uncertiüntv at hese wavelenetls is very large since these two wavelenetls correspoud to minima in the spectrum., There may be a significant difference at $\lambda$ 5874 and $\lambda$ 5766 but it must be noticed that the uncertainty at these wavelengths is very large since these two wavelengths correspond to minima in the spectrum. + Usine the flas-calibrated object datacube. narrow-van Tages of the field can be reconstructed at amy wavelength within the observed range to search for line-cutting objects.," Using the flux-calibrated object datacube, narrow-band images of the field can be reconstructed at any wavelength within the observed range to search for line-emitting objects." + Without any quasar subtraction. we fud no such object to a limi of ος 1 erg ? +.," Without any quasar subtraction, we find no such object to a limit of $\times$ $^{-17}$ erg $^{-2}$ $^{-1}$." +" The redshift range probed by our observations js 1503-0.661 for [OUJA3T27 aud. 3.609-1.103. for Ίνα,", The redshift range probed by our observations is 0.503-0.664 for $\lambda$ 3727 and 3.609-4.103 for $\alpha$. + Uufortuuatelv. the current observations do not cover the redshifts of either the candidate danmipec Svsteni at tan. = 3.07 (2?) or the strong system at tap. = 1.15.," Unfortunately, the current observations do not cover the redshifts of either the candidate damped system at $z_{\rm abs}$ = 3.07 \citep{1998ApJ...505..529I} or the strong system at $z_{\rm +abs}$ = 1.18." + The quasar. although attenuated by a large factor in the Lva forest. is still bright in most of the nuages however.," The quasar, although attenuated by a large factor in the $\alpha$ forest, is still bright in most of the images however." + Iu order to detect objects Wing in projection close to the quasar. we have performed a subtraction of tle residual helt usingo the nuageo of the quasar| iuteeratedoO over the whole wavelength interval and then scaled to the residual intensity in the narrow-band filter.," In order to detect objects lying in projection close to the quasar, we have performed a subtraction of the residual light using the image of the quasar integrated over the whole wavelength interval and then scaled to the residual intensity in the narrow-band filter." + This procedure takes iuto account the exact shape of the double image aud. because ofthe scaling operation. subtracts very few of an hypothetical fat-spectrum or lne-ciitting object except at wavelengths where the quasar is at its niaxinnun.," This procedure takes into account the exact shape of the double image and, because of the scaling operation, subtracts very few of an hypothetical flat-spectrum or line-emitting object except at wavelengths where the quasar is at its maximum." + This prevents however to detect sources with the same spectrum as the quasar., This prevents however to detect sources with the same spectrum as the quasar. + No prominent line-cnutting object is detected but. when performing the QSO subtraction. residual iuteusity is seen din a region 175 away from the quasar to the north-," No prominent line-emitting object is detected but, when performing the QSO subtraction, residual intensity is seen in a region $\farcs$ 5 away from the quasar to the north-east." + To check whether this residual is au artifact of the QSO subtraction or not. we can take advantage ofthe fact that the Lvo liue at 5766.1 lis nearly blackto coustruct an image where the quasar is at its nüninnuul.," To check whether this residual is an artifact of the QSO subtraction or not, we can take advantage of the fact that the $\alpha$ line at 5766.4 is nearly blackto construct an image where the quasar is at its ." +. The image in a narrow spectral band centered at 5766.1 aand of width 5.7 A. corresponding to the spectral resolution clement (EWIIMD. is shown in Fie.," The image in a narrow spectral band centered at 5766.4 and of width 5.7 , corresponding to the spectral resolution element (FWHM), is shown in Fig." + 5. (left, \ref{pixblack} (left +an inherent property of polarization. because Stokes Q and U are not subject to change under a rotation of the plane of polarization by1503.,"an inherent property of polarization, because Stokes $Q$ and $U$ are not subject to change under a rotation of the plane of polarization by." + In the case of eccentric orbits we need to distinguish two additional parameters that affect the polarization curves in a different manner. namely the eccentricity e and the periastron longitude c.," In the case of eccentric orbits we need to distinguish two additional parameters that affect the polarization curves in a different manner, namely the eccentricity $e$ and the periastron longitude $\omega$." + For eccentric orbits we choose the periastron. passage as zero fo. because the polarization peaks shift towards the periastron. and the radial velocity method well constrains the periastron epoch for elliptic orbits.," For eccentric orbits we choose the periastron passage as zero $t_0$, because the polarization peaks shift towards the periastron, and the radial velocity method well constrains the periastron epoch for elliptic orbits." +" To allow a comparison with circular orbits we selected ωΞ90"" im Fig.", To allow a comparison with circular orbits we selected $\omega\!=\!90$ in Fig. + 5 so that the periastron epoch coincides with fy used in Sects., \ref{fig:ecc} so that the periastron epoch coincides with $t_0$ used in Sects. + ?? and ??.. where it was defined by the largest phase angle.," \ref{subsec:inclination} and \ref{subsec:OMEGA}, where it was defined by the largest phase angle." + The eccentricity ¢ influences the polarization curves in two ways when the semi-major axis is kept fixed: it shifts and scales the extrema of the light curves (Fig. 5))., The eccentricity $e$ influences the polarization curves in two ways when the semi-major axis is kept fixed: it shifts and scales the extrema of the light curves (Fig. \ref{fig:ecc}) ). + The shift of the extrema results from the varying orbital velocity of the planet., The shift of the extrema results from the varying orbital velocity of the planet. + With increasing eccentricity the extrema group closer to the periastron passage. although maximum polarization is generally not reached exactly at the periastron.," With increasing eccentricity the extrema group closer to the periastron passage, although maximum polarization is generally not reached exactly at the periastron." + At the same time most extrema become stronger. in the case shown in Fig.," At the same time most extrema become stronger, in the case shown in Fig." + 5 even all extrema. because the planet approaches the star much closer at periastron for eccentric orbits (with fixed semi-major axis).," \ref{fig:ecc} even all extrema, because the planet approaches the star much closer at periastron for eccentric orbits (with fixed semi-major axis)." + Recall that the incident flux on the planet and thus the scattering. polarization scale with the inverse square of the distance D between the star and the planet., Recall that the incident flux on the planet and thus the scattering polarization scale with the inverse square of the distance $D$ between the star and the planet. + Initially it. might sound surprising that all. extrema strengthen for elliptic orbits in. Fig. 5..," Initially it might sound surprising that all extrema strengthen for elliptic orbits in Fig. \ref{fig:ecc}," +" since for circular orbits the maximum polarization always occurs at phase angles smaller than90°.. which occur when the planet moves through the part of the orbit around the apastron for our specific choice of w=90""."," since for circular orbits the maximum polarization always occurs at phase angles smaller than, which occur when the planet moves through the part of the orbit around the apastron for our specific choice of $\omega\!=\!90$." + However. for very eccentric orbits the phase angle decreases quickly after the periastron passage. and the phase function exceeds the value of 0.5 already when the planet moves through the descending node.," However, for very eccentric orbits the phase angle decreases quickly after the periastron passage, and the phase function exceeds the value of 0.5 already when the planet moves through the descending node." + This happens when D is still much smaller than the semi-major axis and long before the maximum elongation., This happens when $D$ is still much smaller than the semi-major axis and long before the maximum elongation. + Moreover the phase angles at which the extrema occur move closer to the periastron due to the strong dependenee of polarization on the distance D., Moreover the phase angles at which the extrema occur move closer to the periastron due to the strong dependence of polarization on the distance $D$. + The distance dependenee of the polarization also explains why the extrema in Fig., The distance dependence of the polarization also explains why the extrema in Fig. + 5 are strongly scaled up near the periastron passage., \ref{fig:ecc} are strongly scaled up near the periastron passage. + By comparine the circular orbit (solid) with the most eccentric case, By comparing the circular orbit (solid) with the most eccentric case +"declinations the dwell time of a source in the FOV increases as 1/cosd with the telescopes scanning at diurnal rate, reaching a full day of integration at the pole itself.","declinations the dwell time of a source in the FOV increases as $\delta$ with the telescopes scanning at diurnal rate, reaching a full day of integration at the pole itself." +" We therefore devised a program for the first two months of performance verification when we would carefully calibrate TAUVEX as to sensitivity, stray light, etc.,"," We therefore devised a program for the first two months of performance verification when we would carefully calibrate TAUVEX as to sensitivity, stray light, etc.," + essentially performing an acceptance test using calibrated celestial sources., essentially performing an acceptance test using calibrated celestial sources. +" Following this period, if the throughput would be found as low as during the ground tests, we planned to spend most of the time on the North and South celestial polar caps (|ó|>80°), performing a survey of these areas to the depth of the GALEX MIS with the suspected reduced sensitivity, or to the level of the GALEX DIS if the original sensitivity would be confirmed in-orbit."," Following this period, if the throughput would be found as low as during the ground tests, we planned to spend most of the time on the North and South celestial polar caps $|\delta|\geq80^{\circ}$ ), performing a survey of these areas to the depth of the GALEX MIS with the suspected reduced sensitivity, or to the level of the GALEX DIS if the original sensitivity would be confirmed in-orbit." + Various delays at ISRO moved the first integration exercise of TAUVEX to the end of 2008., Various delays at ISRO moved the first integration exercise of TAUVEX to the end of 2008. + The integration took place at the ISRO clean room facilities in Bangalore with the different TAUVEX flight units on a table and the satellite units mounted in the satellite but connected to TAUVEX via cables that simulated the on-board telemetry., The integration took place at the ISRO clean room facilities in Bangalore with the different TAUVEX flight units on a table and the satellite units mounted in the satellite but connected to TAUVEX via cables that simulated the on-board telemetry. + This allowed a first testing of the command and scientific telemetry and of the electrical connections to the spacecraft., This allowed a first testing of the command and scientific telemetry and of the electrical connections to the spacecraft. + For this test the spacecraft power was supplied from UPS devices; at the second integration the supply was from solar panel simulators and undesired TAUVEX behaviour was detected as will be described below., For this test the spacecraft power was supplied from UPS devices; at the second integration the supply was from solar panel simulators and undesired TAUVEX behaviour was detected as will be described below. + TAUVEX was first tested alone against the test equipment (EGSE) brought with it from Israel., TAUVEX was first tested alone against the test equipment (EGSE) brought with it from Israel. + It was then connected to the satellite subsystems with the satellite open and long cables connecting TAUVEX to the beacon modulator (for downlink scientific telemetry at 1 Mbps) and to the various other connectors for uplink command and downlink slow (technical) telemetry., It was then connected to the satellite subsystems with the satellite open and long cables connecting TAUVEX to the beacon modulator (for downlink scientific telemetry at 1 Mbps) and to the various other connectors for uplink command and downlink slow (technical) telemetry. +" In general, this exercise showed that the design was correct and that most of the systems operated as planned; those that did not could be reworked promptly to do so for the subsequent integrationj stage."," In general, this exercise showed that the design was correct and that most of the systems operated as planned; those that did not could be reworked promptly to do so for the subsequent integration stage." +" 'The second and final pre-flight integration, originally expected to take place in early-2009 for a launch before summer 2009, was delayed to November 2009."," The second and final pre-flight integration, originally expected to take place in early-2009 for a launch before summer 2009, was delayed to November 2009." +" This integration was with the complete satellite, although some units not related to TAUVEX were still to be mounted."," This integration was with the complete satellite, although some units not related to TAUVEX were still to be mounted." + The procedure required less than four days and could be completed in such a short time due to the dedication of the El-Op team and the extensive and, The procedure required less than four days and could be completed in such a short time due to the dedication of the El-Op team and the extensive and +not mean that the eas gains angular momentum in this region.,not mean that the gas gains angular momentum in this region. + The viscous torques compensate by transporting the angular momentum out of this region so that the overall torque is negative., The viscous torques compensate by transporting the angular momentum out of this region so that the overall torque is negative. + “Phe negative cumulative gravitational dise torque is achieved somewhat outside the orbit crossing radius., The negative cumulative gravitational disc torque is achieved somewhat outside the orbit crossing radius. + A small amount of disc mass. less than1054... that is located outside that radius provides the net negative torque on the disc.," A small amount of disc mass, less than, that is located outside that radius provides the net negative torque on the disc." + In that region of space. rQ.41rg. the spiral armis are very prominent in ligure 9 and gas response is highly nonlinear.," In that region of space, $r \ga 0.41 r_{\rm H}$, the spiral arms are very prominent in Figure \ref{final} and gas response is highly nonlinear." + A similar spiral structure was found in the case of a warm disc with ///r=0.1 within a binary star svstem by Savonijeetal.(1994). that we have argued should be similar to the cireumplanetary disc case (sce Section 4))., A similar spiral structure was found in the case of a warm disc with $H/r=0.1$ within a binary star system by \cite{savonije94} that we have argued should be similar to the circumplanetary disc case (see Section \ref{eqs}) ). + The SPLL code is less accurate in these outer low density regions because the interparticle pressure force caleulation is more approximate., The SPH code is less accurate in these outer low density regions because the interparticle pressure force calculation is more approximate. + Also. we have simplified the inflow on to the disc to be occurring within an annulus in the disc.," Also, we have simplified the inflow on to the disc to be occurring within an annulus in the disc." + But. we expect that the general properties of gravitational torque to generally hold.," But, we expect that the general properties of gravitational torque to generally hold." + That is. the gravitational torque involves a relatively small amount of gas in the outer parts of disc.," That is, the gravitational torque involves a relatively small amount of gas in the outer parts of disc." +A more accurate constraint of the properties of the stellar populations in the northernmost region may help us to untangle the origin of the stellar feature around M33.,A more accurate constraint of the properties of the stellar populations in the northernmost region may help us to untangle the origin of the stellar feature around M33. +" Therefore, we applied the method of synthetic CMD fitting to the diagram of NW7 to derive the best-fit SFH of the stellar populations in this region."," Therefore, we applied the method of synthetic CMD fitting to the diagram of NW7 to derive the best-fit SFH of the stellar populations in this region." +" We used the StarFISH package (?),, which determines the best-fit CMD according to a maximum likelihood statistic."," We used the StarFISH package \citep{2001ApJS..136...25H}, which determines the best-fit CMD according to a maximum likelihood statistic." +" To build the model CMDs, we selected four sets of isochrones with metallicities [M/H]—--1.7, -1.3, -1.0, -0.7, and ages between 1 and 10 Gyr (with a time binning step of log(age) = 0.2), as derived from the analysis of the RGB and RC features in Sect."," To build the model CMDs, we selected four sets of isochrones with metallicities -1.7, -1.3, -1.0, -0.7, and ages between 1 and 10 Gyr (with a time binning step of log(age) = 0.2), as derived from the analysis of the RGB and RC features in Sect." + 5., 5. +" The code populates the set of stellar isochrones (2?) assuming a given initial mass function (?),, shifting the magnitudes according to the distance modulus, and applying photometric scatters derived from the artificial star tests (see Sect."," The code populates the set of stellar isochrones \citep{2008A&A...482..883M} assuming a given initial mass function \citep{1955ApJ...121..161S}, shifting the magnitudes according to the distance modulus, and applying photometric scatters derived from the artificial star tests (see Sect." + 2.2 for details)., 2.2 for details). + Each synthetic CMD with a given range of ages and a fixed metallicity can be linearly combined to construct a model diagram for any arbitrary SFH., Each synthetic CMD with a given range of ages and a fixed metallicity can be linearly combined to construct a model diagram for any arbitrary SFH. + The code then determines the best-fit SFH performing y? minimization of the differences in the number of stars between the model and observed CMD., The code then determines the best-fit SFH performing $\chi^2$ minimization of the differences in the number of stars between the model and observed CMD. + We tried fitting several combinations of the four sets of isochrones and found the best-fit solution for a metallicity [M/H]=--1.3., We tried fitting several combinations of the four sets of isochrones and found the best-fit solution for a metallicity -1.3. +" The corresponding SFH and model CMD are displayed in theupper and lower-left panel of Fig. 9,,"," The corresponding SFH and model CMD are displayed in the and panel of Fig. \ref{sfh}," + respectively., respectively. + The error bars reflect the 1c confidence interval on the star formation rate averaged over an age bin., The error bars reflect the $\sigma$ confidence interval on the star formation rate averaged over an age bin. +" According to the recovered history of star formation, the stellar population in NW7 is metal-poor and older than 4 Gyr ago, and most of the stars formed around 6*1$ Gyr ago."," According to the recovered history of star formation, the stellar population in NW7 is metal-poor and older than 4 Gyr ago, and most of the stars formed around $^{+1.6}_{-1.3}$ Gyr ago." + This agrees with our qualitative analysis in Sect., This agrees with our qualitative analysis in Sect. + 5., 5. + The derived star formation rate corresponds to a total stellar mass of ~2x10°Mo., The derived star formation rate corresponds to a total stellar mass of $\sim 2 \times 10^6$. +. A comparison to the observed data(lower-right panel) shows a reasonably good match., A comparison to the observed data panel) shows a reasonably good match. + An isochrone at 6.3 Gyr (log(age) = 9.8) is overlaid on both diagrams to guide the reader's eye., An isochrone at 6.3 Gyr (log(age) = 9.8) is overlaid on both diagrams to guide the reader's eye. +" However, the match is not perfect since the colour of the simulated RGB appears roughly 0.1 mag redder than the observed one at /p>23.5, and ~0.05 mag bluer in the upper part of the RGB."," However, the match is not perfect since the colour of the simulated RGB appears roughly 0.1 mag redder than the observed one at $I_0 > 23.5$, and $\sim 0.05$ mag bluer in the upper part of the RGB." + Adding higher metallicity isochrones at [M/H]- -1 to the model diagram in order to match the upper part of the RGB did not help us to improve the fit but led to an overalltoo red CMD., Adding higher metallicity isochrones at = -1 to the model diagram in order to match the upper part of the RGB did not help us to improve the fit but led to an overalltoo red CMD. +the core's growth during the TP-AGB phase represents a direct lower bound on the fuel burned during this phase (Marigo&Girardi2001).,the core's growth during the TP-AGB phase represents a direct lower bound on the fuel burned during this phase \citep{Marigo01}. +". True, there are contributions to the light output from gravitational contraction of the core and neutrino loses."," True, there are contributions to the light output from gravitational contraction of the core and neutrino loses." +" However, these can be ignored in our analysis as they only represent corrections on the percent level (Marigo&Girardi2001)."," However, these can be ignored in our analysis as they only represent corrections on the percent level \citep{Marigo01}." +". In addition, significant observable light will come from nuclear burning reactions whose products (notably He) are expelled in stellar winds and do not end up in the remnant."," In addition, significant observable light will come from nuclear burning reactions whose products (notably He) are expelled in stellar winds and do not end up in the remnant." +" Hence, we define the growth of the core as a strict on the fuel consumed in the TP-AGB phase."," Hence, we define the growth of the core as a strict on the fuel consumed in the TP-AGB phase." +" Mathematically, we couple the consumed fuel to the energy released during the TP-AGB phase via (cf.eq.5fromMarigo&Girardi 2001):: The fuel, F(Mj). is expressed in solar masses and the integral is the sum of the energy released during the TP-AGB phase."," Mathematically, we couple the consumed fuel to the energy released during the TP-AGB phase via \citep[\cf\ eq. 5 from][]{Marigo01}: : The fuel, $F(M_i)$, is expressed in solar masses and the integral is the sum of the energy released during the TP-AGB phase." + The conversion trom energy to mass is represented by Αμ. the efficiency of H burning reactions.," The conversion from energy to mass is represented by $A_H$, the efficiency of $H$ burning reactions." +" Here. we adopt Aj=9.75x10!""L.vrM! following rardi (2001)."," Here, we adopt $A_H= 9.75 \times 10^{10}\ L_{\odot}\ yr\ M_{\odot}^{-1}$ following \citet{Marigo01}." +". Above, we note that nucleosynthesis is the dominant stellar energy source."," Above, we note that nucleosynthesis is the dominant stellar energy source." +" The fuel consumed in the TP-AGB phase is therefore: Xj» is the surface mass fraction of hydrogen after the second dredge-up event. Y' is defined as Y,»/(€Xq5-Yi2) where Y;» is the mass fraction of helium in the envelope after the second and M!67(He) and M'(CO) refer to the stellar yield of He and CO. respectively. during the TP-AGB phase."," The fuel consumed in the TP-AGB phase is therefore: $X_{1,2}$ is the surface mass fraction of hydrogen after the second dredge-up event, $Y'$ is defined as $Y_{1,2}/(X_{1,2}+ Y_{1,2})$ where $Y_{1,2}$ is the mass fraction of helium in the envelope after the second dredge-up, and $M_y^{TP-AGB}(He)$ and $M_y^P(CO)$ refer to the stellar yield of $He$ and $CO$, respectively, during the TP-AGB phase." +" We assume an initial H abundance (Xo) of 0.71 and map to Xj» using the tabulated surface compositions in Bertellietal.(2008,2009)."," We assume an initial H abundance $X_0$ ) of $0.71$ and map to $X_{1,2}$ using the tabulated surface compositions in \citet{Bertelli08, Bertelli09}." +. Irrespective of our lack of knowledge regarding the yields of He and CO we can construct our strict lower limit using only the observed growth of the core during the TP-AGB phase., Irrespective of our lack of knowledge regarding the yields of He and CO we can construct our strict lower limit using only the observed growth of the core during the TP-AGB phase. +" The bound on the fuel consumed during this phase, and hence the energy released, is obtained by setting the fuel in equation 2. equal to the first term on the right hand side and setting that equal to F(Mj) in equation |.."," The bound on the fuel consumed during this phase, and hence the energy released, is obtained by setting the fuel in equation \ref{eq:fueltp} equal to the first term on the right hand side and setting that equal to $F(\mi)$ in equation \ref{eq:fuel}." + Solving for ]Lu.COdt in equation 1.. we obtain the minimum energy release (Lyin)) necessary to increase the core mass byAM.," Solving for $\int L_{M_i}(t)dt$ in equation \ref{eq:fuel}, we obtain the minimum energy release ) necessary to increase the core mass by." +.. The uncertainty in iis propagated from σηων., The uncertainty in is propagated from $\sigma_{F_{TP-AGB}}$. + We list this value for each cluster in Table 2.., We list this value for each cluster in Table \ref{tab:fuel}. + We compare tto the predicted integrated luminosity of evolutionary tracks incorporating the TP-AGB phase (e.g.Pietrinfernietal.2004;Marigo&Girardi2007;Bertelli2005. 2009).," We compare to the predicted integrated luminosity of evolutionary tracks incorporating the TP-AGB phase \citep[\eg][]{Pietrinferni04, Marigo07, Bertelli08, Bertelli09}." +". Straightforwardly, we canintegrate [|Li(dt in the TP-AGB phase for any choice of model and find the predicted energy release."," Straightforwardly, we canintegrate $\int L_{M_i}(t)dt$ in the TP-AGB phase for any choice of model and find the predicted energy release." + As they incorporate up to date physics and produce tracks that span a wide range, As they incorporate up to date physics and produce tracks that span a wide range +The research described in this paper was in part carried out al the Jet Propulsion Laboratory. California Institute of Technology. under a contract with the National Aeronautics and Space Administration.,"The research described in this paper was in part carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration." + Grant support [rom the Eppley Foundation for Research. and Research Coundl of the University of Missouri-Columbia is greatly appreciated., Grant support from the Eppley Foundation for Research and Research Council of the University of Missouri-Columbia is greatly appreciated. +northwest. though is less obvious to the east.,"northwest, though is less obvious to the east." +" Phe connecting ""bridge", The connecting `bridge' +"function. fy. or £F, is not more sensitive to the detection rate than the other source parameters.","function, $f_A$, or $E_{\rm low}$ is not more sensitive to the detection rate than the other source parameters." +" Finally, we roughly estimate the detection. rate for the case of alerts from SVOAL/ECLAIRs. whose launch before the C""EX operation is being planned (Schanneetal.2010) and which will provide well-localized alerts (<107). of about SO vr+ (Pauletal.BOLL)..."," Finally, we roughly estimate the detection rate for the case of alerts from /ECLAIRs, whose launch before the CTA operation is being planned \citep{Schanne2010} and which will provide well-localized alerts $<10^\prime$ ) of about 80 $^{-1}$ \citep{Paul2011}." + Here. we assume tha 15 uration distribution is the same as the Durst. ler Telescope (BAT) onboard.Swiff because the two detectors. ECLAIRs (4250 keV) and BAT (15150keV:Sakamotoeal. 2007).. cover a similar energv range.," Here we assume that its duration distribution is the same as the Burst Alert Telescope (BAT) onboard because the two detectors, ECLAIRs (4–250 keV) and BAT \citep[15--150~keV:][]{Sakamoto2007}, cover a similar energy range." + The data on Tuy was taken from the web site (from CRB 041217 to GRB 110519A)., The data on $T_{\rm 90}$ was taken from the web site (from GRB 041217 to GRB 110519A). + 80 o£ ECLALIIS GRBs are expected a ><6 (Pauletal.2011). and ~90% of the BAT bursts are ong GRBs., 80 of ECLAIRs GRBs are expected at $z<6$ \citep{Paul2011} and $\sim 90$ of the BAT bursts are long GRBs. + Hence we assume that the fraction of all GRBs rigecrine ECLAIRS that have Jou2 sec and z<5 is TOM., Hence we assume that the fraction of all GRBs triggering ECLAIRS that have $T_{90}>2$ sec and $z<5$ is 70. + We set the delay time Ziqu o£ SO sec for all bursts or simplicity. while we assumed typically Loja.=LOO sec or GDM.," We set the delay time $T_{\rm delay}$ of $80$ sec for all bursts for simplicity, while we assumed typically $T_{\rm delay} = 100$ sec for GBM." + ‘This is because theSVOAL alerts are expected to »o faster than the CDM ones (L0. €1 min (Schanneοἱal. 201023).," This is because the alerts are expected to be faster than the GBM ones (i.e., $< 1$ min \citep{Schanne2010}) )." + With the above assumptions. we can estimate the raction of well localized events for which Zouων ds ~33% for long GRBs°.," With the above assumptions, we can estimate the fraction of well localized events for which $T_{90}>T_{\rm delay}$ is $\simeq33$ for long GRBs." +. Lt is qualitatively expected that he fraction of or to the bursts in the LST FOY ocalized by ECLAIRs is lower than that by CDM., It is qualitatively expected that the fraction of or to the bursts in the LST FOV localized by ECLAIRs is lower than that by GBM. + The reasons for this are as follows: (1) ECLALRs does not need veh Iluence for localization as much as €DM. which leads o à lot of burst samples with dim Εαν in the ςΕλ band. (," The reasons for this are as follows: (1) ECLAIRs does not need high fluence for localization as much as GBM, which leads to a lot of burst samples with dim flux in the CTA band. (" +2) ECLAIRs has better sensitivity for softer bursts rather han the hard ones. which again leads to the small number of events detectable with CTA.,"2) ECLAIRs has better sensitivity for softer bursts rather than the hard ones, which again leads to the small number of events detectable with CTA." + Also. the redshift distribution of bursts localized by οςAIIts shifts to higher redshift than hat by €BM. so that larger fraction of events are severely alloected by the EBL attenuation.," Also, the redshift distribution of bursts localized by ECLAIRs shifts to higher redshift than that by GBM, so that larger fraction of events are severely affected by the EBL attenuation." + In evaluating the fraction of or to the bursts in LST FOV quantitatively. we do not simulate in detail the follow-up observation of ECLAIRs bursts with CTA taking into account its performance. but we just assume that the eflicicney is the same as the case of BAT if BAT is assumed to be the burst trigger and its trigger threshold for peak photon flux is simply set to 0.4 phis. tem 7 in the 15150 keV band (about 90% of actually detected BAT bursts have their peal flux above this value). we obtain lower detection elliciency than the case of GBAL by a factor of 0.54 for the prompt emission and 0.34 for the afterglow in the case of e=3.5 Tqspae=80 sec for BAT. and. 100 sec for CDM.," In evaluating the fraction of or to the bursts in LST FOV quantitatively, we do not simulate in detail the follow-up observation of ECLAIRs bursts with CTA taking into account its performance, but we just assume that the efficiency is the same as the case of /BAT – if BAT is assumed to be the burst trigger and its trigger threshold for peak photon flux is simply set to 0.4 ph $^{-1}$ $^{-2}$ in the 15–150 keV band (about 90 of actually detected BAT bursts have their peak flux above this value), we obtain lower detection efficiency than the case of GBM by a factor of 0.54 for the prompt emission and 0.34 for the afterglow in the case of $\sigma_{\rm th} = 3.5^\circ$, $\tau_{\rm delay}=80$ sec for BAT, and 100 sec for GBM." + Actelitionally. we must consider that SVOXM operations feature a. bias of preferentially pointing toward the anti-solar direction. which increases the probability of follow-up. observations with ground-based. telescopes.," Additionally, we must consider that SVOM operations feature a bias of preferentially pointing toward the anti-solar direction, which increases the probability of follow-up observations with ground-based telescopes." + We set the increase of the etection rate by a factor of 1.4 referring to Gilmoreοἱal.2010)., We set the increase of the detection rate by a factor of 1.4 referring to \cite{Gilmore2010}. +. With the above assumptions we can estimate the CPA etection rate for alerts from ECLALRs as ~0.1 vr.+ for 116 prompt emission. while c0.37 ve+ for the afterglow (see Table 1)). which is about three times higher rate than GDM.," With the above assumptions we can estimate the CTA detection rate for alerts from ECLAIRs as $\simeq 0.1$ $^{-1}$ for the prompt emission, while $\simeq 0.37$ $^{-1}$ for the afterglow (see Table \ref{table:GRBrate_theory1}) ), which is about three times higher rate than GBM." + HenceSVOAL will probably. become better for the etection of GRBs with CPA thanf, Hence will probably become better for the detection of GRBs with CTA than. +ermi Note that the -—‘BAL localization accuracy is estimated: optiniistically for —10 prompt emission phase (see Section 3.1)). and also note iu. unless the SVOXM alerts are. transmitted. to enough erouncl stations. the delay time of SO sec for SVOM alerts turns out to be an optimistic assumption.," Note that the GBM localization accuracy is estimated optimistically for the prompt emission phase (see Section \ref{subsec:GBMlocalization}) ), and also note that, unless the SVOM alerts are transmitted to enough ground stations, the delay time of 80 sec for SVOM alerts turns out to be an optimistic assumption." + In this paper. we have presented the prospects for detection of GRBs with the LSTs of CPA. the most vital component for GIU observations with their [fast slewing capability and the best sensitivity at the lowest energies.," In this paper, we have presented the prospects for detection of GRBs with the LSTs of CTA, the most vital component for GRB observations with their fast slewing capability and the best sensitivity at the lowest energies." + We have modeled and simulated the follow-up observation of GRBs with ου2 sec and z«5 alerted bv. BM., We have modeled and simulated the follow-up observation of GRBs with $T_{90}>2$ sec and $z<5$ alerted by /GBM. + Our CRB population is mocelled according to a given luminosity function that is consistent. with Swift observations together with wellknown spectral correlations., Our GRB population is modelled according to a given luminosity function that is consistent with Swift observations together with well-known spectral correlations. + We note the following streneths of our model: (1) It reproduces the fluence and duration distributions of GDM bursts (Figure 1)). (," We note the following strengths of our model: (1) It reproduces the fluence and duration distributions of GBM bursts (Figure \ref{fig:S_vs_T90,S-pdf}) ). (" +2) The cilferential sensitivity of our model LSTs is consistent with he ollicial one given by the CPAConsortium(2010) in the energv range less than a few LOO GeV. (Figure 3)) (,"2) The differential sensitivity of our model LSTs is consistent with the official one given by the \citet{CTA10} in the energy range less than a few 100 GeV (Figure \ref{fig:toy_model,0.5h}) ). (" +3) The XE. detection rate is predicted. to be 12 + for he bursts satisfving both Zou>2 sec and z«5. which is roughly consistent with the actual rate of 78 1,"3) The /LAT detection rate is predicted to be 12 $^{-1}$ for the bursts satisfying both $T_{90}>2$ sec and $z<5$ , which is roughly consistent with the actual rate of 7–8 $^{-1}$." + Assuming fermndfGBAL alerts alone. our fiducial xwameter set. predicts the GARB detection rate with LSTs or one array site (ie. north or south) as 0.03 ve+ or the prompt emission. and 0.13. 7 for the afterglow emission (Table 1)).," Assuming /GBM alerts alone, our fiducial parameter set predicts the GRB detection rate with LSTs for one array site (i.e., north or south) as 0.03 $^{-1}$ for the prompt emission and 0.13 $^{-1}$ for the afterglow emission (Table \ref{table:GRBrate_theory1}) )." + The expected event rates become larger when two arrav sites of ϱΤΑ and. additional alerts. [rom SVOAL/ECLAIRs are taken into account if the array performance for the two sites are the same in the energy range less than a few 100 GeV. the detection rates go up to about 0.3 t+ and 1 yr.+ for the prompt and afterglow emissions. respectively. where we assume no overlap of FOVs of GBAL and ECLAIRs.," The expected event rates become larger when two array sites of CTA and additional alerts from /ECLAIRs are taken into account — if the array performance for the two sites are the same in the energy range less than a few 100 GeV, the detection rates go up to about 0.3 $^{-1}$ and 1 $^{-1}$ for the prompt and afterglow emissions, respectively, where we assume no overlap of FOVs of GBM and ECLAIRs." + Note that in the above estimates. we optimistically estimate the onboarcd-localization ability of GBAL in the prompt phase. expecting improvement. by 16 CPA cra (see Section 3.1)).," Note that in the above estimates, we optimistically estimate the onboard-localization ability of GBM in the prompt phase, expecting improvement by the CTA era (see Section \ref{subsec:GBMlocalization}) )." + For the afterglow emission. ur treatment of the GDM localization ability harelly alfects Ίο rate estimation.," For the afterglow emission, our treatment of the GBM localization ability hardly affects the rate estimation." + For our fiducial assumptions. once. CEA. succeeds. in electing the prompt. emissions for GBAL alerts. the total ohoton counts V~ are expected to be >107 for 60% of CTA etected events.," For our fiducial assumptions, once CTA succeeds in detecting the prompt emissions for GBM alerts, the total photon counts $N_\gamma$ are expected to be $> 10^2$ for 60 of CTA detected events." + Our simulation also shows that /N- is 10.100 ines larger than the number of GeV photons expected. by LAT for the same bursts., Our simulation also shows that $N_\gamma$ is 10–100 times larger than the number of GeV photons expected by LAT for the same bursts. + This suggests that CPA can obtain 1e time resolved light curve in the energy range greater than a Few tens of GeV with higher statistics than ever before., This suggests that CTA can obtain the time resolved light curve in the energy range greater than a few tens of GeV with higher statistics than ever before. + We expect 90 of the prompt burst detected by CTAto aave redshifts less than 3.5. and 90% of the afterglows to rave less than 2.9.," We expect 90 of the prompt burst detected by CTAto have redshifts less than 3.5, and 90 of the afterglows to have less than 2.9." + Because of the follow-up observation after, Because of the follow-up observation after +at around 0.7 keV (Fig.,at around 0.7 keV (Fig. + | lower left panel)., 1 lower left panel). + The inclusion of the Gaussian line with the parameters fixed to those found in the RGS data improves the fit to the MOS? data further with q7=1.13 for 282 d.o.f. (, The inclusion of the Gaussian line with the parameters fixed to those found in the RGS data improves the fit to the MOS2 data further with $\chi^2_{\nu}=1.13$ for 282 d.o.f. ( +Table |. Fig.,"Table 1, Fig." + |. lower right panel).," 1, lower right panel)." + Whereas the Gaussian line on-top of a power-law continuum describes the data. the model lacks a physical interpretation.," Whereas the Gaussian line on-top of a power-law continuum describes the data, the model lacks a physical interpretation." + A plausible interpretation of the emission feature is that of a relativistically broadened emission line., A plausible interpretation of the emission feature is that of a relativistically broadened emission line. + Therefore we fit the Laor profile (2) to the residuals present in the RGS data., Therefore we fit the Laor profile \citep{laor} to the residuals present in the RGS data. + Since the peak of the feature is very close to the energy of the O VIII Ίνα. we fix the wavelength of the line to 18.97 A.," Since the peak of the feature is very close to the energy of the O VIII $\alpha$, we fix the wavelength of the line to 18.97 $\AA$." + We fix the outer radius to GM/c., We fix the outer radius to $~GM/c^2$. + The fit reveals an unexpectedly high inclination of 88 deg (Table 3)., The fit reveals an unexpectedly high inclination of 88 deg (Table 3). + With such a high inclination. we expect to observe eclipses in the light curve. which are not present.," With such a high inclination, we expect to observe eclipses in the light curve, which are not present." + It could be the case that the inner part of the disc. where the photons are reflected. has a different inclination than the binary system.," It could be the case that the inner part of the disc, where the photons are reflected, has a different inclination than the binary system." + The inner part of the dise can be warped and twisted if it is strongly irradiated by the neutron star in a non-uniform way (?).., The inner part of the disc can be warped and twisted if it is strongly irradiated by the neutron star in a non-uniform way \citep{pringle}. + The fit gives an inner radius of ~14:Μο with qz=144 for 681 d.o.f£..," The fit gives an inner radius of $\sim14~GM/c^2$ with $\chi_{\nu}^2=1.44$ for 681 d.o.f.," +" however we tind also another solution r;,~3.5GM/c with y;=1.45. An additional mechanism broadening the line is Compton scattering.", however we find also another solution $r_{in}\sim3.5~GM/c^2$ with $\chi_{\nu}^2=1.45$ An additional mechanism broadening the line is Compton scattering. +" The Compton downseattering can be estimated using the formula, /E=Ετος, where σι is Half Width at Half Maximum of the Gaussian line and £ is the energy of the line in keV. The calculation gives τ=9. which seems unlikely. since it indicates an extremely optically-thick layer of material."," The Compton downscattering can be estimated using the formula $\sigma_{E}/E=E\tau^2/m_{e}c^2$, where $\sigma_{E}$ is Half Width at Half Maximum of the Gaussian line and $E$ is the energy of the line in keV. The calculation gives $\tau\approx9$, which seems unlikely, since it indicates an extremely optically-thick layer of material." + This makes it impossible that Compton downseattering alone is responsible for the line broadening., This makes it impossible that Compton downscattering alone is responsible for the line broadening. + Therefore. the plausible solution points towards broadening by the strong gravitational field and scattering off the ionized material of the disc.," Therefore, the plausible solution points towards broadening by the strong gravitational field and scattering off the ionized material of the disc." + We fit a relativistically broadened reflection model (2).. available in (2).. which takes into account etfects of Compton scattering in the ionized reflecting material.," We fit a relativistically broadened reflection model \citep{ross}, available in \citep{arnaud}, which takes into account effects of Compton scattering in the ionized reflecting material." + For the relativistic broadening we use the convolution modelkbBLCR (based on Laor model) and for the Galactic absorption we use the model (?.. in prep).," For the relativistic broadening we use the convolution model (based on Laor model) and for the Galactic absorption we use the model \citeauthor{wilms}, in prep)." + In order to fit the spectrum with the reflection model we need a signiticant overabundance of oxygen., In order to fit the spectrum with the reflection model we need a significant overabundance of oxygen. + In order to mimic the enhancement of oxygen. we decrease the abundance of iron by a factor of 5.," In order to mimic the enhancement of oxygen, we decrease the abundance of iron by a factor of 5." +" Using the described fit-function we tind that the 47 distribution around the (local) minimum for the inner radius does not allow for an error screening on the best-fit r;, values using the current data set.", Using the described fit-function we find that the $\chi^2$ distribution around the (local) minimum for the inner radius does not allow for an error screening on the best-fit $r_{in}$ values using the current data set. + Because of additional complexity of the reflection model. we fix the inner dise radius to that of the innermost stable circular orbit for a non-rotating neutron star (6 GAZ/c ).," Because of additional complexity of the reflection model, we fix the inner disc radius to that of the innermost stable circular orbit for a non-rotating neutron star (6 $GM/c^2$ )." + The outer disc radius is again fixed to 1000 GAZ/c., The outer disc radius is again fixed to 1000 $GM/c^2$. + In the fit we use RGS in the same energy range as before and MOS? in the range from 1.5 to 10 keV. in order to have good constraints on the power-law slope and the abundances of oxygen. iron and neon.," In the fit we use RGS in the same energy range as before and MOS2 in the range from 1.5 to 10 keV, in order to have good constraints on the power-law slope and the abundances of oxygen, iron and neon." + The best fit yields a vo28 for 1454 d.o.f., The best fit yields a $\chi_{\nu}^2=1.28$ for 1454 d.o.f. + The best-fit inclination is ~57 deg and the best-fit ionization parameter is ~222 erg em ! (Table 3). which indicates that indeed some Compton scattering is present as well as relativistic broadening etfects.," The best-fit inclination is $\sim57$ deg and the best-fit ionization parameter is $\sim222$ erg cm $^{-1}$ (Table 3), which indicates that indeed some Compton scattering is present as well as relativistic broadening effects." +On the other hand. the spectrum after correction. ο)no€.77/3MP?(1). has an inverse Fourier transform which is not a simple function. and does not aclmil such a suggestive interpretation.,"On the other hand, the spectrum after correction, $S(k)\simeq e^{-2kd}/M^2(k)$, has an inverse Fourier transform which is not a simple function, and does not admit such a suggestive interpretation." +Figure 13. shows the functions f/(r) for both the uncorrected (dashed) and MTE-corrected (solid) spectra [rom 23 11997.,Figure \ref{fig:shape} shows the functions $f(r)$ for both the uncorrected (dashed) and MTF-corrected (solid) spectra from 23 1997. + The integrated field (bottom) shows that lor each case half of all flux is confined to a similar ryc4 Mm circle., The integrated field (bottom) shows that for each case half of all flux is confined to a similar $r_0\simeq4$ Mm circle. + The variance of a photospheric field composed of random elements is 2m — der =," The variance of a photospheric field composed of random elements is _p^2 = d^2x = ," +Lawrence Livermore NationalLaboratory*.,Lawrence Livermore National. +. has a built-in stereo output., has a built-in stereo output. +" As a further example for the visualization of theoreticalfJ data benefiting from stereoscopy, Fig."," As a further example for the visualization of theoretical data benefiting from stereoscopy, Fig." + 7 shows a Stereo pair of fractal clouds., \ref{fig:clouds} shows a stereo pair of fractal clouds. + These were generated with the procedure outlined by LewisandAustin(2002)., These were generated with the procedure outlined by \cite{LA2002}. +. The procedure creates a spatially fractal distribution in cloud pixels that simultaneously obeys a single-point log-normal probability density function in cloud density., The procedure creates a spatially fractal distribution in cloud pixels that simultaneously obeys a single-point log-normal probability density function in cloud density. +" On certain scales, fractal structure and log-normal single point statistics are characteristic of atmospheric (Barkeretal.1996) and_ interstellar (Federrathetal.2009) clouds, and 3D data sets such as those depicted in Fig."," On certain scales, fractal structure and log-normal single point statistics are characteristic of atmospheric \citep{BWP1996} and interstellar \citep{FKS2009} clouds, and 3D data sets such as those depicted in Fig." + 7 may be used as initial conditions in hydrodynamical simulations (Saxtonetal.2005;SutherlandandBicknell 2007).," \ref{fig:clouds} may be used as initial conditions in hydrodynamical simulations \citep{SBSM2005,SB2007}." +. Such fractal structures usually prove difficult to visualize., Such fractal structures usually prove difficult to visualize. + The use of stereo pairs provides an enhanced depth perception and thereby a clearer view of the relative positions of the clouds., The use of stereo pairs provides an enhanced depth perception and thereby a clearer view of the relative positions of the clouds. +" The fractal outlines are more obvious, even interior to the clouds."," The fractal outlines are more obvious, even interior to the clouds." +" In the previous Sections, we have described how stereoscopy, in the form of stereo pairs, can be a powerful tool for publishing multi-dimensional data sets."," In the previous Sections, we have described how stereoscopy, in the form of stereo pairs, can be a powerful tool for publishing multi-dimensional data sets." +" As of today, stereoscopy is the (Sharifetal.2011),, whereas other methods, such as holography (e.g.Smith1975;AckermannandEichler 2007),, are considered very promising, but, as of now, harder to implement on a large scale."," As of today, stereoscopy is the \citep[][]{Sharif11}, whereas other methods, such as holography \citep[e.g.][]{Smith75,Ackermann07}, are considered very promising, but, as of now, harder to implement on a large scale." +" In that sense, we believe that stereo pairs can play a major role in the future of data visualization in Astrophysics (and any field of Science), by providing researchers today with a simple way to explore, discover, imagine, identify, and share new analysis methods of their data, methods that will then be ready for implementation in exquisite interactive, immersive, high-end visualization tools tomorrow."," In that sense, we believe that stereo pairs can play a major role in the future of data visualization in Astrophysics (and any field of Science), by providing researchers today with a simple way to explore, discover, imagine, identify, and share new analysis methods of their data, methods that will then be ready for implementation in exquisite interactive, immersive, high-end visualization tools tomorrow." +" Such immersive 3D visualization technologies, both for the scientific and non-scientific community, still appears rather cubersome to use and implement, and often require off-the-shelf, custom software and setup."," Such immersive 3D visualization technologies, both for the scientific and non-scientific community, still appears rather cubersome to use and implement, and often require off-the-shelf, custom software and setup." + But technology is moving at a fast pace., But technology is moving at a fast pace. +" For example, working with and sharing data sets in 3D on televisions and hand-held devices might become commonplace fairly soon, as such devices are already easily available on the market."," For example, working with and sharing data sets in 3D on televisions and hand-held devices might become commonplace fairly soon, as such devices are already easily available on the market." +" The idea of 3D television is rather old, with early experiments on stereo TV as early as 1920, and the first 3D TV broadcast occurring in 1980 (Onuraletal.2006)."," The idea of 3D television is rather old, with early experiments on stereo TV as early as 1920, and the first 3D TV broadcast occurring in 1980 \citep[][]{Onural06}." +". Yet, very recently, the rapid re-appearance of 3D televisions (and 3D hand-held devices) lead Shermanetal.(2010) to state that immersive 3D visualization technologies are now well in the so-called within the Hype's cycle (FennandRaskino2008) of new technologies, the last step before reaching a more productive phase."," Yet, very recently, the rapid re-appearance of 3D televisions (and 3D hand-held devices) lead \cite{Sherman10} to state that immersive 3D visualization technologies are now well in the so-called within the Hype's cycle \citep[][]{Fenn08} of new technologies, the last step before reaching a more productive phase." +" So far, one of the main issues slowing down the expansion of 3D television on the market is most probably the lack of 3D content to be displayed on those devices, a key factor for success (Sharifetal.2011)."," So far, one of the main issues slowing down the expansion of 3D television on the market is most probably the lack of 3D content to be displayed on those devices, a key factor for success \citep[][]{Sharif11}." +". This is also true for scientific applications of this technology, and a wider usage of stereo pairs may help scientists identify in what ways 3D TV could soon play a significant role in their research."," This is also true for scientific applications of this technology, and a wider usage of stereo pairs may help scientists identify in what ways 3D TV could soon play a significant role in their research." +" Once the need will have been clearly and widely identified, there is no doubt that the yet missing standardized application programming interface (API) and software links between scientific data sets and already existing hardware will be rapidly implemented."," Once the need will have been clearly and widely identified, there is no doubt that the yet missing standardized application programming interface (API) and software links between scientific data sets and already existing hardware will be rapidly implemented." +" In short, we believe that stereo pairs, an old and well documented tool (which can now be easily implemented), could help scientists keep an open mind, and potentially shape the future of multi-dimensional data visualization and analysis."," In short, we believe that stereo pairs, an old and well documented tool (which can now be easily implemented), could help scientists keep an open mind, and potentially shape the future of multi-dimensional data visualization and analysis." + We have discussed the concept of stereo pairs and highlighted their potential benefits for the Astrophysics community., We have discussed the concept of stereo pairs and highlighted their potential benefits for the Astrophysics community. +" First, we presented the free-viewing techniqueli and provided advice to easily visualize both parallel and cross-eyed stereo pairs for the first time."," First, we presented the free-viewing technique and provided advice to easily visualize both parallel and cross-eyed stereo pairs for the first time." + We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages ll software used nowadays withinnz: the AAstrophysics, We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages or software used nowadays within the Astrophysics + We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages ll software used nowadays withinnz: the AAstrophysicsh, We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages or software used nowadays within the Astrophysics + We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages ll software used nowadays withinnz: the AAstrophysicshv, We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages or software used nowadays within the Astrophysics + We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages ll software used nowadays withinnz: the AAstrophysicshvs, We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages or software used nowadays within the Astrophysics + We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages ll software used nowadays withinnz: the AAstrophysicshvsi, We then argued that stereo pairs can be easily produced and reproduced on a computer screen or on printed material with most of the usual programming languages or software used nowadays within the Astrophysics +Observations were carriedl out with the GBT. observing al a frequency of 2.0GIHz using SOOMlIIg of bandwidth. although persistent radio Irequency. interference (REI) reduced the usable bandwidth to ~600MlIz.,"Observations were carried out with the GBT, observing at a frequency of $2.0\; \GHz$ using $800\; \MHz$ of bandwidth, although persistent radio frequency interference (RFI) reduced the usable bandwidth to $\sim 600\; \MHz$." + This lrequencey. was chosen to overcome (he deleterious effects of dispersive smearing caused by [ree electrons in the ISA] and has been used successfully by our group before.," This frequency was chosen to overcome the deleterious effects of dispersive smearing caused by free electrons in the ISM, and has been used successfully by our group before." + Data were recorded in (le (?) format using the Green Bank Ultimate Pulsar Processor (GUPPI) (2) with a 64jis sampling Gime and 2048 frequency channels across the entire bandwidth., Data were recorded in the \citep{hvm04} format using the Green Bank Ultimate Pulsar Processor (GUPPI) \citep{drd+08} with a $64\; \us$ sampling time and 2048 frequency channels across the entire bandwidth. + We tvpically observed NGC 6544 for 30 minutes. and M62 and NGC 6624 for 4560 minutes each. although the exact integration times varied between observations.," We typically observed NGC 6544 for 30 minutes, and M62 and NGC 6624 for 45–60 minutes each, although the exact integration times varied between observations." + In general. data were relatively [ree ol REI. but when necessary. we used the REI excision tools in {he software suite to mask out. contaminated portions of the data.," In general, data were relatively free of RFI, but when necessary, we used the RFI excision tools in the software suite to mask out contaminated portions of the data." + We also used archival GBT data taken in 2004., We also used archival GBT data taken in 2004. + These data were collected using the GBT Pulsar Spigot (72). at either 820MlIz (vith 50MlIz of bandwidth) or at 2Giz (with the same bandwidth as above).," These data were collected using the GBT Pulsar Spigot \citep{kel+05} at either $820\; +\MHz$ (with $50\; \MHz$ of bandwidth) or at $2\; \GHz$ (with the same bandwidth as above)." + Most of these observations used 2048 Irequency channels aud 40.96ji sampling. although some used 1024 channels and 81.92yrs sampling.," Most of these observations used 2048 frequency channels and $40.96\; \us$ sampling, although some used 1024 channels and $81.92\; \us$ sampling." + All of these data were analvzed usingPRESTO., All of these data were analyzed using. +. The pulsars in NGC 6544 were observed again in 2011 as part of a campaign to measure Shapiro delav in PSR. —2500D (see 4.6))., The pulsars in NGC 6544 were observed again in 2011 as part of a campaign to measure Shapiro delay in PSR $-$ 2500B (see \ref{sec:NGC6544B}) ). + These data were collected using GUPPI in a coherent de-dispersion search mode (ie. a filterbank where each channel was coherently de-dispersed) αἱ 1.4GlIz using 800MlIIZz of bandwidth.," These data were collected using GUPPI in a coherent de-dispersion search mode (i.e. a filterbank where each channel was coherently de-dispersed) at $1.4\; \GHz$ using $800\; +\MHz$ of bandwidth." + For these observations we used 512 frequency channels and 10.24jes sampling., For these observations we used 512 frequency channels and $10.24\; \us$ sampling. + Data were processed using a combination of audnotehttp://psrchive., Data were processed using a combination of and. +sourceforge.net/.. All of the folded pulse profiles were and summed to create hieh signal-to-noise (5/N)) proliles., All of the folded pulse profiles were phase-aligned and summed to create high signal-to-noise ) profiles. + The profiles were fit with one or more Gaussians. [rom which standard pulse templates were made ancl used to obtain pulse times of arrival (TOAs) via eross-correlation in the Fourier domain.," The profiles were fit with one or more Gaussians, from which standard pulse templates were made and used to obtain pulse times of arrival (TOAs) via cross-correlation in the Fourier domain." + We typically obtained three to six TOAs per pulsar per observation depending on the oof that observation. though some pulsars (such as NGC 65414) were sullicientlv bright that," We typically obtained three to six TOAs per pulsar per observation depending on the of that observation, though some pulsars (such as NGC 6544A) were sufficiently bright that" +"To illustrate. consider (he ""best fit model with time-variable UV-efficieney described in the main text.","To illustrate, consider the “best fit” model with time-variable UV-efficiency described in the main text." +" Using a temperature of 101 IXelvin. Ομ=0.14. Oi?=0.024. the quenching fraction 1s In our “best fit” model. we fixed e,=0.03. while ei ranged [rom ~0.8xLO? at low redshift to 1.3x10. at high redshift."," Using a temperature of $10^4$ Kelvin, $\Omega_0h^2=0.14$, $\Omega_bh^2=0.024$, the quenching fraction is In our “best fit” model, we fixed $\epsilon_\ast = 0.03$ , while $\epsilon_{\rm UV}$ ranged from $\sim 0.8\times 10^{-5}$ at low redshift to $1.3\times 10^{-4}$ at high redshift." + At verv high redshift. we have This implies that at very. high redshift. when η>I. all the photons are absorbed locally so (hat the escape fraction is essentially 0.," At very high redshift, we have This implies that at very high redshift, when $\eta \geq 1$, all the photons are absorbed locally so that the escape fraction is essentially 0." + This is (o expected since densities are much higher at high redshift., This is to expected since densities are much higher at high redshift. +" At redshifts near transition ~ 15. when εν~6xLO?. we have implying an escape Traction e0.2. comparable {ο values used in other semianalvtic models,"," At redshifts near transition $\sim 15$ , when $\epsilon_{\rm UV} \sim 6\times 10^{-5}$, we have implying an escape fraction $\sim 0.2$, comparable to values used in other semianalytic models." + At z~6. we have inplving an escape Traction eq~0.03.," At $z\sim 6$, we have implying an escape fraction $\epsilon_{\rm esc} \sim 0.03$." + These values are all within the range used bv others in semi-analvtic models (e.8.. Cen 2003: Wivitheand Loeb 2002: Laima andILokder 2003).," These values are all within the range used by others in semi-analytic models (e.g., Cen 2003; Wiyitheand Loeb 2002; Haiman andHolder 2003)." +We have presented a mocel for the high-ionization state gas seen in DLA systems. based on a galaxy formation moclel set within the hierarchical structure formation paracignm.,"We have presented a model for the high-ionization state gas seen in DLA systems, based on a galaxy formation model set within the hierarchical structure formation paradigm." + The basis of this model is to associate hot halo or sub- gas with the highly ionized eas that gives rise to CIV. absorption., The basis of this model is to associate hot halo or sub-halo gas with the highly ionized gas that gives rise to CIV absorption. + Assuming a simple mocel for the hot gas distribution. we generate absorption systems with kinematic properties in reasonable agreement with observations of DLAS at z=3.," Assuming a simple model for the hot gas distribution, we generate absorption systems with kinematic properties in reasonable agreement with observations of DLAS at $z=3$." + We thus conclude that a CDÀM-based ealaxy formation mocel can also account for both the Low- and high-ionization state gas in observed: DLA absorption systems., We thus conclude that a CDM-based galaxy formation model can also account for both the low- and high-ionization state gas in observed DLA absorption systems. + Agreement with the data is not a strong function of any [ree parameter of the model and thus we conclude that the general concept of a spherical hotter component as the source of CIV absorption provides a viable explanation for the observed kinematic properties., Agreement with the data is not a strong function of any free parameter of the model and thus we conclude that the general concept of a spherical hotter component as the source of CIV absorption provides a viable explanation for the observed kinematic properties. + Associating some hot gas with subhalos and including a CIV component in co-rotation with the low ionization state gas improves the agreement. but models without these features cannot be categorically ruled out.," Associating some hot gas with subhalos and including a CIV component in co-rotation with the low ionization state gas improves the agreement, but models without these features cannot be categorically ruled out." + While the galaxy formation model provides the information about the of hot and cold gas present in a given halo. our model requires a number of additional assumptions about the easdishribulion.," While the galaxy formation model provides the information about the of hot and cold gas present in a given halo, our model requires a number of additional assumptions about the gas." +. Phe most striking is our requirement that the cold gas be in a rather extended configuration (paper ED)., The most striking is our requirement that the cold gas be in a rather extended configuration (paper I). + Also. in order for our model to work. we require that the gas termed. “hot” in the semi-analvtic model is in the form. of clouds in a two-phase medium (asin.2)..," Also, in order for our model to work, we require that the gas termed “hot” in the semi-analytic model is in the form of clouds in a two-phase medium \citep[as in ][]{mm:96}." + This is clearly bevond the level of detail tha semi-analvtic galaxy formation models or hvdrodynamic simulations currently attempt to address., This is clearly beyond the level of detail that semi-analytic galaxy formation models or hydrodynamic simulations currently attempt to address. +" Our model produces good agreement with the observe distribution of CIV column densities under the assumption that hot gas is distributed like the dark matter and tha the fraction in a state suitable for CIV. absorption feuy and the metallicity. Z,,. are uniform throughout the halo."," Our model produces good agreement with the observed distribution of CIV column densities under the assumption that hot gas is distributed like the dark matter and that the fraction in a state suitable for CIV absorption $\fciv$, and the metallicity, $Z_{hg}$, are uniform throughout the halo." + While this description has the advantage of simplicity. i is unlikely to be correct.," While this description has the advantage of simplicity, it is unlikely to be correct." +" The fact that the different hieh- species do not always trace one another implies jud fege and Zi, vary throughout the gas.", The fact that the different high-ionization species do not always trace one another implies that $\fciv$ and $Z_{hg}$ vary throughout the gas. +" We [our iu a model in which a larger fraction of the gas was issociated with sub-halos produced. better agreement with 10 observations. but an alternative scenario in which the subhalo gas possesses higher values of Zi, or fegy might provide a better explanation."," We found that a model in which a larger fraction of the gas was associated with sub-halos produced better agreement with the observations, but an alternative scenario in which the subhalo gas possesses higher values of $Z_{hg}$ or $\fciv$ might provide a better explanation." + The other high-ionization state metal lines may. be used. in future studies to. help constrain the distributions of eas censity. metallicity and ionization state in high redshift halos.," The other high-ionization state metal lines may be used in future studies to help constrain the distributions of gas density, metallicity and ionization state in high redshift halos." + We also explored 10 predictions of our mocel for the lower column censiE sub-DLA and LL systems., We also explored the predictions of our model for the lower column density sub-DLA and LL systems. + We suggest that the kinematics of sub-DLA systems may be a decisive test of the multiple component model, We suggest that the kinematics of sub-DLA systems may be a decisive test of the multiple component model. + Any multiple component model must have a large cross-section to single component intersections., Any multiple component model must have a large cross-section to single component intersections. + Most sub-DLA systems should be produced by lines of sight passing through a single disk and therefore they should have significantly dillerent. kinematies than the DLA systems., Most sub-DLA systems should be produced by lines of sight passing through a single disk and therefore they should have significantly different kinematics than the DLA systems. + This will also be true for CIV. systems if the hot σας is clumped into subhalos., This will also be true for CIV systems if the hot gas is clumped into subhalos. + Finally. we expect a large drop in the number of absorption svstems with column densities below the level where our gas disks are truncated. an additional test ofthe model.," Finally, we expect a large drop in the number of absorption systems with column densities below the level where our gas disks are truncated, an additional test of the model." + We find that in our model. only about a third of the observed population of LL systems are produced by hot gas in halos.," We find that in our model, only about a third of the observed population of LL systems are produced by hot gas in halos." + We furthermore find in agreement with ? that there is enough cold gas in mini-halos to produce all of the LL systems at 2=3 and that there is also a similar amount of hot gas in these halos., We furthermore find in agreement with \citet{am:98} that there is enough cold gas in mini-halos to produce all of the LL systems at $z=3$ and that there is also a similar amount of hot gas in these halos. + Llowever if we adopt a realistic mocel of the eas in mini-halos. we find that they produce an almost negligible contribution to the cross-section of LL svstenis.," However if we adopt a realistic model of the gas in mini-halos, we find that they produce an almost negligible contribution to the cross-section of LL systems." + This is because to cover a large area the gas must have a low column density and therefore will be photolonzied by the UV background., This is because to cover a large area the gas must have a low column density and therefore will be photoionzied by the UV background. + Having high enough column densities to be πο shielding implies the cross-section is small and therefore not a significant source of LL svstems., Having high enough column densities to be self shielding implies the cross-section is small and therefore not a significant source of LL systems. +" We therefore. propose that gas surrounding halos but outside the virial radius (e.g. in filaments) may give rise to LL systems. a view supported. by. the hydrodynamic simulations of ον,"," We therefore propose that gas surrounding halos but outside the virial radius (e.g. in filaments) may give rise to LL systems, a view supported by the hydrodynamic simulations of \citet{dhkw:99}." + Lf this gas is pre-enriched or enriched by metals ejected from the halo it may also produce metal lino systems., If this gas is pre-enriched or enriched by metals ejected from the halo it may also produce metal line systems. + Further investigations using hydrodynamical, Further investigations using hydrodynamical +As we increase the scale length to Ry>3 kpe. MOND produces less plausible looking rotation curves.,"As we increase the scale length to $\rd > 3$ kpc, MOND produces less plausible looking rotation curves." + In (hese cases. the bulge causes a prominent peak in the inner rotation curve.," In these cases, the bulge causes a prominent peak in the inner rotation curve." + such a morphology is sometimes seen in early (vpe spirals (Noordermeer 22007). but the sharp peak in Fie.," Such a morphology is sometimes seen in early type spirals (Noordermeer 2007), but the sharp peak in Fig." + 4 is rather unusual., \ref{MW_panelC} is rather unusual. + This aspect is sensitive to the bulge model. ancl more plausible results are possible 4.1)).," This aspect is sensitive to the bulge model, and more plausible results are possible \ref{bulgscal}) )." + Comparison with the observed terminal velocities (INXerr 11936: Malhorta 1995) also favors short scale lengths., Comparison with the observed terminal velocities (Kerr 1986; Malhorta 1995) also favors short scale lengths. + The agreement is particularly οσους for νι When Ry=2.3 kpc., The agreement is particularly good for $\hat \nu_1$ when $\rd = 2.3$ kpc. + The other interpolation functions are hard (o distinguish from one another. ancl seem (o prefer slightly longer scale leneths Ry2z2.5 kpe.," The other interpolation functions are hard to distinguish from one another, and seem to prefer slightly longer scale lengths $\rd \approx 2.5$ kpc." + This result is sensitive to small changes (of order £%)) in the terminal velocity data (85)).Hr so stronger statements seein unwarranted.," This result is sensitive to small changes (of order ) in the terminal velocity data \ref{MW_emp}) ), so stronger statements seem unwarranted." + The Galactic constants can be computed for each model., The Galactic constants can be computed for each model. + Table 2. gives the rotation velocity al the solar circle Oo and the Oort Constants A and D: The latter depend on the derivative of (he rotation curve. which in (hese models clepencs somewhat on the extent over which the derivative is measured.," Table \ref{Oort_tab} gives the rotation velocity at the solar circle $\Theta_0$ and the Oort Constants A and B: The latter depend on the derivative of the rotation curve, which in these models depends somewhat on the extent over which the derivative is measured." + That is. there are bumps and wigeles in the rotation curve as a result of the non-smooth gas distribution (Olling Merrifield 2001).," That is, there are bumps and wiggles in the rotation curve as a result of the non-smooth gas distribution (Olling Merrifield 2001)." + This causes the derivative to vary in a non-trivial fashion., This causes the derivative to vary in a non-trivial fashion. + For specificity. ] compute A and D over 40.5 kpe around Ay=3 kpe.," For specificity, I compute A and B over $\pm 0.5$ kpc around $R_0 = 8$ kpc." + One may wonder if this effect has plaved a role in (he various values of the Oort constants that have been derived historically., One may wonder if this effect has played a role in the various values of the Oort constants that have been derived historically. + The Galactic constants are shown eraphically in Fig. 5.., The Galactic constants are shown graphically in Fig. \ref{Oort_fig}. . + The measurement of Feast Whitelock (1997) is most consistent with 74 for Ry=2.1 kpe., The measurement of Feast Whitelock (1997) is most consistent with $\hat \nu_1$ for $\rd = 2.1$ kpc. + Other interpolation functions and scale lengths are possible. depending on how literally we take (he error bars.," Other interpolation functions and scale lengths are possible, depending on how literally we take the error bars." + The function v seems to perform best. with reasonable values of Oy. A. and B for fy<2.5 kpe.," The function $\hat \nu_1$ seems to perform best, with reasonable values of $\Theta_0$, A, and B for $\rd \le 2.5$ kpc." + This interpolation function is verv similar to (he simple [function found by Famaeyv Binney (2005) to work best in combination with the Basel moclel., This interpolation function is very similar to the simple function found by Famaey Binney (2005) to work best in combination with the Basel model. + The other interpolation functions perform less well. though again one must be cautious as alwavs about the interpretation of astronomical uncertainües.," The other interpolation functions perform less well, though again one must be cautious as always about the interpretation of astronomical uncertainties." +" For example. ry, gives reasonable Ομ up to Ry=3 kpe. but tends to give A < |D| in contradiction to most measurements,"," For example, $\tilde \nu_1$ gives reasonable $\Theta_0$ up to $\rd = 3$ kpc, but tends to give A $< |$ $|$ in contradiction to most measurements." +" Similarly. P, gives reasonable B values. but tends to run low inthe other Galactic constants except for the smallest scale lengths."," Similarly, $\bar \nu_1$ gives reasonable B values, but tends to run low inthe other Galactic constants except for the smallest scale lengths." + The standard Iunction traditionally, The standard function traditionally +SNe are possibly biased to large ἐς0.1pum) sizes because small grains tend to be destroyed in the shocked region SNe (Bianchi&SchneiderNozawaetal.,"SNe are possibly biased to large $\ga 0.1~\micron$ ) sizes because small grains tend to be destroyed in the shocked region SNe \citep{bianchi07,nozawa07}." + 2007).. Hirashitaetal.(2010). show that small grains are produced by shattering driven by interstellar turbulence if the dust abundance is as high as that expected from the solar metallicity.," \citet{hirashita10} + show that small grains are produced by shattering driven by interstellar turbulence if the dust abundance is as high as that expected from the solar metallicity." + Efficient production of small grains enhances the surface-to-volume ratio. activating the grain growth by the accretion of metals.," Efficient production of small grains enhances the surface-to-volume ratio, activating the grain growth by the accretion of metals." + Thus. we should consider various grain size distributions depending on galaxy age and metallicity. and the grain growth efficiency may vary with a variety of grain size distributions.," Thus, we should consider various grain size distributions depending on galaxy age and metallicity, and the grain growth efficiency may vary with a variety of grain size distributions." + The first aim of this paper is to formulate the grain growth in clouds by explicitly considering the dependence on grain size distribution., The first aim of this paper is to formulate the grain growth in clouds by explicitly considering the dependence on grain size distribution. + Therefore. the former part of this paper is devoted to the formulation of the grain growth in clouds under an arbitrary grain size distribution.," Therefore, the former part of this paper is devoted to the formulation of the grain growth in clouds under an arbitrary grain size distribution." + Then. by using this formulation. we point out the importance of grain size distribution for the grain growthaccretion.," Then, by using this formulation, we point out the importance of grain size distribution for the grain growth." + The tinal scope of this work is to examine if the grain size distribution has a significant influence on the dust enrichment in galaxies through the grain growth in clouds., The final scope of this work is to examine if the grain size distribution has a significant influence on the dust enrichment in galaxies through the grain growth in clouds. + Thus. in the latter part of this paper. we implement our formulation of the grain growth in clouds into a simple framework of dust enrichment in a galaxy. also taking into account the grain formation by stellar sources and the destruction by interstellar shocks driven by SN remnants.," Thus, in the latter part of this paper, we implement our formulation of the grain growth in clouds into a simple framework of dust enrichment in a galaxy, also taking into account the grain formation by stellar sources and the destruction by interstellar shocks driven by SN remnants." + Thereby. we will show that our formulation of dust growth is successfully incorporated into dust enrichment models. and we will address the importance of grain size distribution for the grain mass budget in galaxies.," Thereby, we will show that our formulation of dust growth is successfully incorporated into dust enrichment models, and we will address the importance of grain size distribution for the grain mass budget in galaxies." + This paper is organized as follows., This paper is organized as follows. + We explain the formulation in Section ??.. and describe some basic results on the evolution of grain size distribution through the grain growth in individual clouds in Section 3..," We explain the formulation in Section \ref{sec:formula}, and describe some basic results on the evolution of grain size distribution through the grain growth in individual clouds in Section \ref{sec:result}." + We implement the results for the grain growth in clouds into a simple evolution model of dust mass in an entire galactic system in Section 4.. where the model also treats the dust formation by stellar sources and the dust destruction by SN shocks.," We implement the results for the grain growth in clouds into a simple evolution model of dust mass in an entire galactic system in Section \ref{sec:timescale}, where the model also treats the dust formation by stellar sources and the dust destruction by SN shocks." + We discuss the results in more general contexts in Section ??.., We discuss the results in more general contexts in Section \ref{sec:discussion}. + Finally. Section ??. gives the conclusion.," Finally, Section \ref{sec:conclusion} gives the conclusion." + In this section. we formulate the evolution of grain size distribution by the accretion of metals (grain. growth) in a single interstellar cloud.," In this section, we formulate the evolution of grain size distribution by the accretion of metals (grain growth) in a single interstellar cloud." + Our procedures in this paper are divided into the following two steps: (4) we construct a formulation of the grain growth in clouds. which is conveniently incorporated in any dust evolution models in galaxies: and (11) we show that our formulation in this— section can be used generally to treat the grain growth in galaxies.," Our procedures in this paper are divided into the following two steps: (i) we construct a formulation of the grain growth in clouds, which is conveniently incorporated in any dust evolution models in galaxies; and (ii) we show that our formulation in this section can be used generally to treat the grain growth in galaxies." + This section is aimed at item (1)., This section is aimed at item (i). + In Section +.. we address item (i) by incorporating our formulation for the grain growth into simple dust enrichment models which also include dust formation by stellar sources and dust destruction in SN shocks.," In Section \ref{sec:timescale}, we address item (ii) by incorporating our formulation for the grain growth into simple dust enrichment models which also include dust formation by stellar sources and dust destruction in SN shocks." + Other mechanisms that modify the grain size distribution such as shattering and coagulation are treated in other papers (Jonesetal.etal. 2011).," Other mechanisms that modify the grain size distribution such as shattering and coagulation are treated in other papers \citep{jones94,jones96,yan04,hirashita09,yamasawa11}." +. These processes are to be included in future work for the comprehensive understanding of the evolution of grain size distribution., These processes are to be included in future work for the comprehensive understanding of the evolution of grain size distribution. + Throughout this paper. we call the elements composing grains ‘metals’.," Throughout this paper, we call the elements composing grains `metals'." + We only treat grains refractory enough to survive after the dispersal of the cloud. and do not consider volatile grains such as water ice.," We only treat grains refractory enough to survive after the dispersal of the cloud, and do not consider volatile grains such as water ice." + More specifically. we consider silicate and graphite as main dust components.," More specifically, we consider silicate and graphite as main dust components." + We also assume that the grains are spherical with a constant material density s. so that the grain mass m and the grain radius e are related as We define the grain size distribution such that υί��.0)de is the number density of grains whose radii are between e and e|cla at time /.," We also assume that the grains are spherical with a constant material density $s$, so that the grain mass $m$ and the grain radius $a$ are related as We define the grain size distribution such that $n(a,\, t)\,\mathrm{d}a$ is the number density of grains whose radii are between $a$ and $a+\mathrm{d}a$ at time $t$." + For simplicity. we assume that the gas density is constant and the evolution of grain size distribution occurs only through the accretion of metals on dust grains.," For simplicity, we assume that the gas density is constant and the evolution of grain size distribution occurs only through the accretion of metals on dust grains." + In this situation. the number density of grains is conserved.," In this situation, the number density of grains is conserved." + Thus. the following continuity equation in terms of n(a./) holds: where s—dedi is the growth rate of the grain radius and is given in the next subsection.," Thus, the following continuity equation in terms of $n(a,\, t)$ holds: where $u\equiv\mathrm{d}a/\mathrm{d}t$ is the growth rate of the grain radius and is given in the next subsection." + Coagulation and shattering. which do not conserve the number density of grains. are not treated to focus on the grain growth by accretion here.," Coagulation and shattering, which do not conserve the number density of grains, are not treated to focus on the grain growth by accretion here." + Note that these processes do not change the grainmass. while the grain growth by accretion increases it.," Note that these processes do not change the grain, while the grain growth by accretion increases it." + The evolution of grain size distribution by coagulation and shattering is treated in other papers (Jonesetal.1996:Hi-rashita&Yan2009:Ormeletal. 2009).," The evolution of grain size distribution by coagulation and shattering is treated in other papers \citep{jones96,hirashita09,ormel09}." +. We also neglect possible grain destruction mechanisms in molecular clouds by cosmic rays or shocks., We also neglect possible grain destruction mechanisms in molecular clouds by cosmic rays or shocks. + The grain growth rate is basically determined by the collision rate between a grain and particles of the relevant metal species., The grain growth rate is basically determined by the collision rate between a grain and particles of the relevant metal species. + We adopt silicate and graphite as dominant grain species (e.g.Draine&Lee 1984). and denote elements composing the grains as X (for example. X = C. Si. etc).," We adopt silicate and graphite as dominant grain species \citep[e.g.][]{draine84}, and denote elements composing the grains as X (for example, X = C, Si, etc.)." + We neglect the effect of Coulomb interaction on the cross section tthe cross section of a grain or accretion of metals is simply estimated by the geometric one) because the grains and the atoms are neutral in molecular clouds (Weingartner&Draine1999:Yanetal. 2004).," We neglect the effect of Coulomb interaction on the cross section the cross section of a grain for accretion of metals is simply estimated by the geometric one) because the grains and the atoms are neutral in molecular clouds \citep{weingartner99,yan04}. ." +. The rate at which atomsof element X strike the surface of a grain with radius @ is denoted as and is estimated as where nx is the number density of element X. & is the Boltzmann constant. {ως is the gas temperature. and (x is the atom mass of element X. In general. dust grains are not composed of a single species.," The rate at which atomsof element X strike the surface of a grain with radius $a$ is denoted as $\mathcal{R}$ and is estimated as \citep{evans94} + where $n_\mathrm{X}$ is the number density of element X, $k$ is the Boltzmann constant, $T_\mathrm{gas}$ is the gas temperature, and $m_\mathrm{X}$ is the atom mass of element X. In general, dust grains are not composed of a single species." + We adopt a key element. whose mass fraction in the grain material is. /x. and represent the grain growth by the accretion of element X. The conceptof key element is also adopted by Zhukovskaetal. (2008).," We adopt a key element, whose mass fraction in the grain material is $f_\mathrm{X}$, and represent the grain growth by the accretion of element X. The conceptof key element is also adopted by \citet{zhukovska08}. ." +heating and do not take iuto account tidally-induced heating via bar aud beuding instabilities.,heating and do not take into account tidally-induced heating via bar and bending instabilities. + The exact value of Όρωνέσ for our galaxies is thus somewhat uncertain as our σ may be regarded as lower luit., The exact value of $v_{\rm rot}/\sigma$ for our galaxies is thus somewhat uncertain as our $\sigma$ may be regarded as lower limit. + We experimented with several values for the classification threshold iu the range 11. where Rj, 1s the spatial resolution of the observations."," We consider `secure' those masses for which the black hole sphere of influence, $\RBH=G\MBH/\sigstar^2$ (column 7 of Table 1), has been clearly resolved, $N_{res}=2\RBH/R_{res}>1$, where $R_{res}$ is the spatial resolution of the observations." + Additional reasons for placing galaxies in Group 2 are given in Table I., Additional reasons for placing galaxies in Group 2 are given in Table 1. + We have constructed a homogeneous set of NIR images of the galaxies presented in Table | (except for the Milky Way and M31) by retrieving J. H. and K atlas images from the 2-Micron All Sky Survey (2MASS: http://www.tpac.caltech.edu/2mass)).," We have constructed a homogeneous set of NIR images of the galaxies presented in Table 1 (except for the Milky Way and M31) by retrieving J, H, and K atlas images from the 2-Micron All Sky Survey (2MASS; )." + When a single atlas image contained only a portion of the galaxy. we also retrieved adjacent tiles and mosaicked the images after subtracting the sky background and rescaling for the different zero points.," When a single atlas image contained only a portion of the galaxy, we also retrieved adjacent tiles and mosaicked the images after subtracting the sky background and rescaling for the different zero points." + The 2MASS images are photometrically calibrated with a typical accuracy of a few percent., The 2MASS images are photometrically calibrated with a typical accuracy of a few percent. + More details can be found in Hunt Marconi (2003; hereafter Paper ID)., More details can be found in Hunt Marconi (2003; hereafter Paper II). + We performed a 2D bulge/disk decomposition of the images using the program GALFIT (Pengetal.2002) which is made publicly available by the authors., We performed a 2D bulge/disk decomposition of the images using the program GALFIT \citep{peng} which is made publicly available by the authors. + This code allows the fitting of several components with different functional shapes (e.g.. generalized exponential (Sersic) and simple exponential laws): the best fit parameters are determined by minimizing V7.," This code allows the fitting of several components with different functional shapes (e.g., generalized exponential (Sersic) and simple exponential laws); the best fit parameters are determined by minimizing $\chi^2$." + More details on GALFIT can be found in Pengetal.(2002)., More details on GALFIT can be found in \cite{peng}. +. We fit separately the J. H and K images.," We fit separately the J, H and K images." + Each fit was started by fitting a single Sersic component and constant background., Each fit was started by fitting a single Sersic component and constant background. + Whei necessary ffor spiral galaxies). an additional component (usually ai exponential disk) was added.," When necessary for spiral galaxies), an additional component (usually an exponential disk) was added." + In many cases these initial fits left large residuals and we thus increased the number of components (see also Pengetal. 2002))., In many cases these initial fits left large residuals and we thus increased the number of components (see also \citealt{peng}) ). + The fits are described in detail in Paper II., The fits are described in detail in Paper II. +" In Table | we present the J. H and K bulge magnitudes. effective bulge radii R, in the J band. and their uncertainties."," In Table 1 we present the J, H and K bulge magnitudes, effective bulge radii $R_e$ in the J band, and their uncertainties." + The J. H and K magnitudes were corrected for Galactic extinction using the data by Schlegel.Finkbeiner.&Davis (1998).," The J, H and K magnitudes were corrected for Galactic extinction using the data by \cite{galabs}." +". We used the J band to determine R, because the images tend to be flatter. and thus the background is better determined."," We used the J band to determine $R_e$ because the images tend to be flatter, and thus the background is better determined." +" In reffig:corr we plot. from left to right. VVSbul** vvsMpy.. and the residuals of vvs R, (based on the fit from ΤΟ2)."," In \\ref{fig:corr} we plot, from left to right, vs, vs, and the residuals of vs $R_e$ (based on the fit from T02)." + Only Group | galaxies are shown., Only Group 1 galaxies are shown. +" iis the virial bulge mass given by £R,o7/G; if bulges behave asisothermal spheres. k=8/3."," is the virial bulge mass given by $k\,R_e\,\sigstar^2/G$; if bulges behave asisothermal spheres, $k=8/3$." +" However. comparing our virial estimates wwith thoseMyjy,.. obtained from dynamical modeling (Magorrianetal.1998:Gebhardt2003). shows that aand aare well correlated (r=0.88): setting &=34 (rather than 8/3) gives an average ratio of unity."," However, comparing our virial estimates with those, obtained from dynamical modeling \citep{magorrian,gebhardt03}, shows that and are well correlated $r=0.88$ ); setting $k=3$ (rather than $8/3$ ) gives an average ratio of unity." + Therefore. we have used k23 in the above formula.," Therefore, we have used $k=3$ in the above formula." + Considering the uncertainties of both mass estimates. the scatter of the ratio iis 0.21 dex.," Considering the uncertainties of both mass estimates, the scatter of the ratio is 0.21 dex." + We fit the data withMpu//Mayn the bisector linear regression from Akritas&Bershady(1996) which allows for uncertainties on both variables and intrinsic dispersion., We fit the data with the bisector linear regression from \cite{ab} which allows for uncertainties on both variables and intrinsic dispersion. + The FITEXY routine (Pressetal.1992) used by TO2 gives consistent results (see reffig:corr))., The FITEXY routine \citep{numrec} used by T02 gives consistent results (see \\ref{fig:corr}) ). + Fit results of vvs galaxy properties for Group ] and the combined samples are summarized in Table 2., Fit results of vs galaxy properties for Group 1 and the combined samples are summarized in Table 2. + The intrinsic dispersion of the residuals (755) has been estimated with a maximum likelihood method assuming normally-distributed values., The intrinsic dispersion of the residuals $rms$ ) has been estimated with a maximum likelihood method assuming normally-distributed values. + Inspection of reffig:corr and Table 2 show that aand ccorrelate well with the mmass., Inspection of \\ref{fig:corr} and Table 2 show that and correlate well with the mass. + The correlation between aand iis equivalent to that between the radius of the ssphere of influence (=GMyyu /07) and Κ.., The correlation between and is equivalent to that between the radius of the sphere of influence $=G\MBH/\sigstar^2$ ) and $R_e$. + To compare the scatter of ffor different wavebands. we have also analyzed the B-band bulge luminosities for our sample.," To compare the scatter of for different wavebands, we have also analyzed the B-band bulge luminosities for our sample." + The upper limit of the intrinsic dispersion of the ccorrelations goes from ~0.5 dex in logMgy when consideringall galaxies. to ~0.3 when considering only those of Group I.," The upper limit of the intrinsic dispersion of the correlations goes from $\sim 0.5$ dex in $\log\MBH$ when consideringall galaxies, to $\sim +0.3$ when considering only those of Group 1." +" Hence. for galaxies with reliable aandLyy.. the scatter of ccorrelations is ~0.3.JHK). comparable to that ofMgg-o,."," Hence, for galaxies with reliable and, the scatter of correlations is $\sim +0.3$, comparable to that of." +. This scatter would be smaller if measurement errors are underestimated., This scatter would be smaller if measurement errors are underestimated. + MeLure&Dunlop(2002) and Erwinetal.(2003) reached a similar conclusion using R-band bbut on smaller samples., \cite{mclure02} and \cite{erwin} reached a similar conclusion using R-band but on smaller samples. + The correlation between R-band bulge light concentration and hhas a comparable scatter (Grahametal.2001)., The correlation between R-band bulge light concentration and has a comparable scatter \citep{graham01}. +. Since aand hhave comparable dispersions. the rough bulge/disk decomposition refsec:intro)). the larger reddening and stellar population effects do not apparently compromise the correlation.," Since and have comparable dispersions, the rough bulge/disk decomposition \\ref{sec:intro}) ), the larger reddening and stellar population effects do not apparently compromise the correlation." + Most of the galaxies in the sample are early types. and thus may be less sensitive to the above effects.," Most of the galaxies in the sample are early types, and thus may be less sensitive to the above effects." + However. the scatter in the ccorrelations does not decrease significantly when considering only elliptical galaxies.," However, the scatter in the correlations does not decrease significantly when considering only elliptical galaxies." + The correlation between aand hhas a slightly lower dispersion (0.25 versus 0.3) than Ly., The correlation between and has a slightly lower dispersion (0.25 versus 0.3) than . + Hf the scatter of ((0.2] dex) is an indication of the additional uncertainties onourvirial estimates. then the intrinsic scatter of ddrops to ~0.15 dex.," If the scatter of (0.21 dex) is an indication of the additional uncertainties onourvirial estimates, then the intrinsic scatter of drops to $\sim 0.15$ dex." + Judging from the present data where only secure παπα are included. σο.. M," Judging from the present data where only secure and are included, , ," + Judging from the present data where only secure παπα are included. σο.. Mi," Judging from the present data where only secure and are included, , ," + Judging from the present data where only secure παπα are included. σο.. Miu," Judging from the present data where only secure and are included, , ," + Judging from the present data where only secure παπα are included. σο.. Miu.," Judging from the present data where only secure and are included, , ," +seeing conditions and only provide loose upper limits to the OT magnitudes.,seeing conditions and only provide loose upper limits to the OT magnitudes. + We evaluated the Galactic extinction in the optical and NIR bands in the direction of GRBO0O0911 using the Galactic dust infrared maps by Schlegel et al. (, We evaluated the Galactic extinction in the optical and NIR bands in the direction of GRB000911 using the Galactic dust infrared maps by Schlegel et al. ( +1998): from these data we obtained a color excess E(B—V) = 0.120.,1998); from these data we obtained a color excess $E(B-V)$ = 0.120. + By applying the relation of Cardelli et al. (, By applying the relation of Cardelli et al. ( +"1989). we derived Ap = 0.51. Ay = 0.38. Ay = 0.32. A, = 0.23. Ay = 0.13. Ay 2 0.07 and Ag. = 0.04.","1989), we derived $A_B$ = 0.51, $A_V$ = 0.38, $A_R$ = 0.32, $A_I$ = 0.23, $A_J$ = 0.13, $A_H$ = 0.07 and $A_{K_s}$ = 0.04." + The corrected magnitudes were then converted into flux densities following Fukugita et al. (, The corrected magnitudes were then converted into flux densities following Fukugita et al. ( +1995) for the optical filters and Bersanelli et al. (,1995) for the optical filters and Bersanelli et al. ( +1991) for the NIR ones.,1991) for the NIR ones. + We also added a error in quadrature to the uncertainties on the optical-NIR flux densities in order to account for differences in the instrumental responses of different telescopes in the same band., We also added a error in quadrature to the uncertainties on the optical-NIR flux densities in order to account for differences in the instrumental responses of different telescopes in the same band. + The optical and ΝΙΚ colors of the OT of GRBO000911 during the first 10 days after the high-energy event fall in the loci populated by GRB afterglows in the color-color diagrams as illustrated by Siimon et al. (, The optical and NIR colors of the OT of GRB000911 during the first 10 days after the high-energy event fall in the loci populated by GRB afterglows in the color-color diagrams as illustrated by Šiimon et al. ( +2001) and by Gorosabel et al. (,2001) and by Gorosabel et al. ( +2002).,2002). + The host galaxy of GRB000911 appears unresolved in all of our VLT frames. as the PSF of the galaxy image is always consistent with that of a pointlike object.," The host galaxy of GRB000911 appears unresolved in all of our VLT frames, as the PSF of the galaxy image is always consistent with that of a pointlike object." + This implies an upper limit of 3.3 kpe on the host galaxy half-light radius., This implies an upper limit of 3.3 kpc on the host galaxy half-light radius. + To estimate the flux of the GRBOOOOTI host. we considered the measurements or upper limits acquired since December 2000 as reported in Table |.," To estimate the flux of the GRB000911 host, we considered the measurements or upper limits acquired since December 2000 as reported in Table 1." + In case of detections. when more than one measurement was avallable in the same band. we considered their average value.," In case of detections, when more than one measurement was available in the same band, we considered their average value." + The fit to the GRB00091] host galaxy Spectral Flux Distribution (SFD) was carried out with the use of the version 1.1 of the code (Bolzonella et al., The fit to the GRB000911 host galaxy Spectral Flux Distribution (SFD) was carried out with the use of the version 1.1 of the code (Bolzonella et al. + 2000a)., 2000a). + This allows a y fit of the observed data with 8 different templates of synthetic galaxy spectra (starburst. elliptical. lenticular. four kinds of spirals. and irregular).," This allows a $\chi^2$ fit of the observed data with 8 different templates of synthetic galaxy spectra (starburst, elliptical, lenticular, four kinds of spirals, and irregular)." + In all cases. the evolution of the Star Formation Rate (SFR) in the galaxy templates is modeled using an exponential law.," In all cases, the evolution of the Star Formation Rate (SFR) in the galaxy templates is modeled using an exponential law." + The Initial Mass Function is modeled assuming the law by Miller Scalo (1979)., The Initial Mass Function is modeled assuming the law by Miller Scalo (1979). + In the fits a solar metallicity Z=Z.z0.02 (with Z the mass fraction of heavy elements) was assumed.," In the fits a solar metallicity $Z = Z_\odot +\simeq 0.02$ (with $Z$ the mass fraction of heavy elements) was assumed." + This code also allows an estimate of the photometric redshift of the studied galaxy. the age of its dominant stellar population. and the presence of further overall absorption local to the galaxy itself.," This code also allows an estimate of the photometric redshift of the studied galaxy, the age of its dominant stellar population, and the presence of further overall absorption local to the galaxy itself." + Four possible extinetion laws were considered. Le.. those by Seaton (1979). Fitzpatrick (1986). Prévvot et al. (," Four possible extinction laws were considered, i.e., those by Seaton (1979), Fitzpatrick (1986), Prévvot et al. (" +1984) and Calzetti et al. (,1984) and Calzetti et al. ( +2000) which are suitable to describe the extinetions within the Milky Way. the Large Magellanic Cloud (LMC). the Small Magellanie Cloud (SMC) and a generic starburst (Stb) galaxy. respectively.,"2000) which are suitable to describe the extinctions within the Milky Way, the Large Magellanic Cloud (LMC), the Small Magellanic Cloud (SMC) and a generic starburst (Stb) galaxy, respectively." + By considering the templates over a redshift range z 2 0-5 with a step Az = 0.001. and varying the V-band local extinction Αν in the range 0—2 with AAy = 0.01. we find that the template which best fits our VLT VR7H data points and BJ upper limits of the GRB000911 host is that of an irregular galaxy at ς = 0.904 with the presence of slight reddening due to either a LMC-. or à SMC-. or a Stb-like absorption law (see Table 2 and Fig.," By considering the templates over a redshift range $z$ = $0-5$ with a step $\Delta z$ = 0.001, and varying the $V$ -band local extinction $A_V$ in the range $0-2$ with $\Delta A_V$ = 0.01, we find that the template which best fits our VLT $VRIH$ data points and $BJ$ upper limits of the GRB000911 host is that of an irregular galaxy at $z$ = 0.904 with the presence of slight reddening due to either a LMC-, or a SMC-, or a Stb-like absorption law (see Table 2 and Fig." + 3)., 3). + The spectroscopically determined redshift ἐς = 1.058540.0001; Price et al., The spectroscopically determined redshift $z$ = $\pm$ 0.0001; Price et al. + 2002) is within the confidence level interval of that obtained from our photometry using theHyperz code (see Table 2)., 2002) is within the confidence level interval of that obtained from our photometry using the code (see Table 2). + The best-fit age of the host galaxy stellar population is 0.7 Gyr for à SMC-like template and 0.5 Gyr for LMC- and Stb-like templates., The best-fit age of the host galaxy stellar population is 0.7 Gyr for a SMC-like template and 0.5 Gyr for LMC- and Stb-like templates. + Extinction 1s moderate with Ay=0.3-0.5.," Extinction is moderate with $A_V\,=\,0.3-0.5$." + The assumption of an evolving metallicity. as remarked by several authors (e.g.. Bolzonella et al.," The assumption of an evolving metallicity, as remarked by several authors (e.g., Bolzonella et al." + 2000a.b: Gorosabel et al.," 2000a,b; Gorosabel et al." + 2003a.b: Christensen et al.," 2003a,b; Christensen et al." + 2004). can be considered as a second-order parameter of the fit; thus. this i$ not expected to significantly alter our results and conclusions.," 2004), can be considered as a second-order parameter of the fit; thus, this is not expected to significantly alter our results and conclusions." + The same applies to the choice of à LMC- or a SMC-like template. instead of a starburst. for the host galaxy.," The same applies to the choice of a LMC- or a SMC-like template, instead of a starburst, for the host galaxy." + Using the best-fit galaxy template we have computed the expected host flux in the B. J and Κι band. for which we only have either upper limits or no late-time observations.," Using the best-fit galaxy template we have computed the expected host flux in the $B$, $J$ and $K_s$ band, for which we only have either upper limits or no late-time observations." +" The nagnitudes. not corrected for Galactic extinction. are B= 26.1. J = 23.6 and K, = 21.9."," The magnitudes, not corrected for Galactic extinction, are $B$ = 26.1, $J$ = 23.6 and $K_s$ = 21.9." + For each of these three values an cIncertainty of 0.3 mag can be assumed., For each of these three values an uncertainty of 0.3 mag can be assumed. + In order to study the GRBO0OO911 optical/NIR afterglow light curves and to determine the presence of an underlying SN contribution. we took into aecount the host galaxy contamination as measured at late epochs with ΝΕΤ (VR7H ," In order to study the GRB000911 optical/NIR afterglow light curves and to determine the presence of an underlying SN contribution, we took into account the host galaxy contamination as measured at late epochs with VLT $VRIH$ " +I would like to thauk P. Madau. M. Magliocchetti aud II. Zhao for useful discussions aud comets.,"I would like to thank P. Madau, M. Magliocchetti and H. Zhao for useful discussions and comments." + Special thanks to D. Rusiu for bringing the case of D11521199 to mv attention aud providing the VLBI maps., Special thanks to D. Rusin for bringing the case of B1152+199 to my attention and providing the VLBI maps. +Among the possible ways of explaining our non-detection. we exclude calibration errors since we detect the central source. at the expected position and with the expected flux. which ts an excellent internal quality check.,"Among the possible ways of explaining our non-detection, we exclude calibration errors since we detect the central source, at the expected position and with the expected flux, which is an excellent internal quality check." + Given the above-mentioned flux calibration scaling with respect to the ? data. any supposed bias in the flux calibrationshould enhance the probability of detecting the blobs in our maps. since their intensity should also be higher by had rotated according to Keplerian motion. the displacement within the ~ 6 year interval would have been smaller than1.," Given the above-mentioned flux calibration scaling with respect to the \citet{Wilner_2002} data, any supposed bias in the flux calibrationshould enhance the probability of detecting the blobs in our maps, since their intensity should also be higher by had rotated according to Keplerian motion, the displacement within the $\sim$ 6 year interval would have been smaller than." +. Our PdBI observations are consistent with no detectable millimetrie emission from the outer dusty dise (or ring) surrounding Vega., Our PdBI observations are consistent with no detectable millimetric emission from the outer dusty disc (or ring) surrounding Vega. + We briefly discuss the impact of this new constraint on the dust properties in this system., We briefly discuss the impact of this new constraint on the dust properties in this system. + We have shown in section 2.3 that the clumps previously reported at 1.3mmm by ? and ? are not detected in our observations. which are deeper in sensitivity by a factor of two. and are probably low-significance artifacts.," We have shown in section \ref{sec:comp} that the clumps previously reported at mm by \citet{Koerner_2001} and \citet{Wilner_2002} + are not detected in our observations, which are deeper in sensitivity by a factor of two, and are probably low-significance artifacts." + A trivial implication of this finding is that no planet is required to trap dust in mean-motion resonance at these positions., A trivial implication of this finding is that no planet is required to trap dust in mean-motion resonance at these positions. + More generally. our results also shed new light on the clumpiness of the dust surrounding Vega.," More generally, our results also shed new light on the clumpiness of the dust surrounding Vega." + Observations at shorter wavelengths display very smooth images (??) and the asymmetry of the image ts only at the 2« level. hence also compatible with a smooth dust distribution (?)..," Observations at shorter wavelengths display very smooth images \citep{su05,sib10} and the asymmetry of the image is only at the $\sigma$ level, hence also compatible with a smooth dust distribution \citep{hol98}." + The only detection of a possible asymmetry comes from the SHARC II images at 350 and citepmar06 but is at the 2-4co and <10% of the ring brightness.," The only detection of a possible asymmetry comes from the SHARC II images at 350 and \\citep{mar06} + but is at the $\sigma$ and $<10$ of the ring brightness." + In. conclusion. all observations display or are compatible with a smooth dust distribution.," In conclusion, all observations display or are compatible with a smooth dust distribution." + Earlier sub-mm observations have convineingly established the existence of an extended emission around Vega. with a ring-like morphology atjum.. wwith CSO SHARC II (?).. and wwith Herschel/PACS (?)..," Earlier sub-mm observations have convincingly established the existence of an extended emission around Vega, with a ring-like morphology at, with CSO SHARC II \citep{mar06}, and with Herschel/PACS \citep{sib10}." + According to these studies. the peak intensity is located around 85—100 AAU (11— 15”).," According to these studies, the peak intensity is located around $85-100$ AU $11-13$ )." + To set an upper limit on the mmm emission of this ring. we fitted a thin. uniform. AAU radius ring into the data. carefully taking into account the different fields of the mosaic (for numerical reasons. this thin ring is represented by an adequately sampled series of point sources).," To set an upper limit on the mm emission of this ring, we fitted a thin, uniform, AU radius ring into the data, carefully taking into account the different fields of the mosaic (for numerical reasons, this thin ring is represented by an adequately sampled series of point sources)." + We find an integrated flux of 0.1]+ 2.0mmly. re. à 3 co upper limit of 6 mJy.," We find an integrated flux of $0.1\pm2.0$ mJy, i.e. a 3 $\sigma$ upper limit of 6 mJy." + The lack of clear detection at high angular resolution relative to the bolometer results. which are more sensitive to extended flux. suggests that a thin ring may not be the most appropriate distribution.," The lack of clear detection at high angular resolution relative to the bolometer results, which are more sensitive to extended flux, suggests that a thin ring may not be the most appropriate distribution." + If we instead assume a uniform annulus of inner radius AAU and outer radius AAU. we find an integrated flux of 25.342.4 mmly. 1.8.. a 3c upper limit of 7.2 mJy. which ts similar to the narrow ring value.," If we instead assume a uniform annulus of inner radius AU and outer radius AU, we find an integrated flux of $-5.3\pm2.4$ mJy, i.e., a $3 \sigma$ upper limit of 7.2 mJy, which is similar to the narrow ring value." +" Using the ? model. with an inner Gaussian and outer exponential decline in surface brightness (with à transition radius of 14"")). our results are compatible with a total flux <24 mJy (3 o) if the distribution is truncated at 200 AU. and «30mJy if it extends up to 300 AU."," Using the \citet{sib10} model, with an inner Gaussian and outer exponential decline in surface brightness (with a transition radius of ), our results are compatible with a total flux $< 24$ mJy (3 $\sigma$ ) if the distribution is truncated at 200 AU, and $ <30 $ mJy if it extends up to 300 AU." + This modelling also agrees with the 3c upper limit of mmJy for emission within 105 AU., This modelling also agrees with the $3\sigma$ upper limit of mJy for emission within 105 AU. + With this model. we are clearly unable to place strong constraints on the dust properties. since our data lack sensitivity to faint extended emission.," With this model, we are clearly unable to place strong constraints on the dust properties, since our data lack sensitivity to faint extended emission." + Assuming a dust temperature of (?)D) (2).. ? ? ? ?..," Assuming a dust temperature of \citep{Sheret_2004} \citep{Natta_2004}, \citet{sib10} \citet{muel10} \citet{sib10} \citet{hol98}," +Most of the UST data analvzed here (except [ον brief references to D.V. and U data) are archival data trom (he September 19097. WEPC?2 observations of Chabover (GO-6517).,"Most of the HST data analyzed here (except for brief references to $B, +V$, and $U$ data) are archival data from the September 1997 WFPC2 observations of Chaboyer (GO-6517)." + Under this program. an orbit of short (238) F555W ancl (208) FS14W. images were obtained al two different pointines. followed by an orbit of 12 long (160s) F555W images and an orbit of 12 long (160s) FSI4W images.," Under this program, an orbit of short (23s) F555W and (20s) F814W images were obtained at two different pointings, followed by an orbit of 12 long (160s) F555W images and an orbit of 12 long (160s) F814W images." + The second and third orbits were obtained at a fixed pointing with the center of NGC 6652 placed in the center of the PC., The second and third orbits were obtained at a fixed pointing with the center of NGC 6652 placed in the center of the PC. + The 12 deep F555W and ES14W images were cleaned of cosmic ravs and combined into single images., The 12 deep F555W and F814W images were cleaned of cosmic rays and combined into single images. + Aperture photometry and PSE-fitting were used (o derive instrumental mss; and ma; magnitudes. which were then converted into V and / using the prescripüon given in lloltzman et al. (," Aperture photometry and PSF-fitting were used to derive instrumental $_{555}$ and $_{814}$ magnitudes, which were then converted into $V$ and $I$ using the prescription given in Holtzman et al. (" +1995).,1995). + The precision of the PSF-litting photometry along (he main sequence was interior to that obtained for aperture photometry. but was much less affected by crowcling. especially near cluster center.," The precision of the PSF-fitting photometry along the main sequence was inferior to that obtained for aperture photometry, but was much less affected by crowding, especially near cluster center." + LIST positional information makes reference to the Guide Star Catalog vill. which has known absolute positional errors in the southern celestial hemisphere of to (Tall et 11990).," HST positional information makes reference to the Guide Star Catalog v.1.1, which has known absolute positional errors in the southern celestial hemisphere of to (Taff et 1990)." + Six sources were detected in the central radius circle using WAVDETECT., Six sources were detected in the central radius circle using WAVDETECT. + Two sources more than from the core are probably not associated with the cluster. as the cluster half-mass radius is.. ancl the core radius is (June 22. 1999 version of catalog described in Harris 1996).," Two sources more than from the core are probably not associated with the cluster, as the cluster half-mass radius is, and the core radius is (June 22, 1999 version of catalog described in Harris 1996)." + We were unable to find counterparts for these sources. ancl ignore them in this paper.," We were unable to find counterparts for these sources, and ignore them in this paper." + We detect. 4 sources within of the cluster center. including the bright LAINB X1832-330. hereafter source A (Figure D): the others we label D. C5 and D. All four sources are well-detected: A has 9140 counts. D has 75 counts. C and D have 15 and 16 respectively. with formal significances greater (han 6 o0 in each case.," We detect 4 sources within of the cluster center, including the bright LMXB X1832-330, hereafter source A (Figure 1); the others we label B, C, and D. All four sources are well-detected: A has 9140 counts, B has 75 counts, C and D have 15 and 16 respectively, with formal significances greater than 6 $\sigma$ in each case." + We consider all four of these sources to be associated with the cluster. since the probability that. any of 6 sources within a eircle would fall within of the cluster center is96.," We consider all four of these sources to be associated with the cluster, since the probability that any of 6 sources within a circle would fall within of the cluster center is." +.. We give sources A. D. C. and D the formal designations CNOGLD J183543.6-325926. CNOGLD J183544.5-325939. CXOGLD J133545.7-325923. and CNOGLB J133545.6-325926 respectively. but. use the letter designations for this paper.," We give sources A, B, C, and D the formal designations CXOGLB J183543.6-325926, CXOGLB J183544.5-325939, CXOGLB J183545.7-325923, and CXOGLB J183545.6-325926 respectively, but use the letter designations for this paper." + The second brightest source (Source D) is detected in the HIIRC-I data at a position from the position of star 49 (in the UIST Guide Star Catalog frame)., The second brightest source (Source B) is detected in the HRC-I data at a position from the position of star 49 (in the HST Guide Star Catalog frame). + Star 49 was sugeested by DALA9S as the counterpart for the LMXD. which we cleteet away.," Star 49 was suggested by DMA98 as the counterpart for the LMXB, which we detect away." + Star 49 has measured (U—D)2—0.9 (DAIA98). and shows variability of 1 magnitude. possibly with a 43.6 minute periodie modulation (Deutsch et al 2000).," Star 49 has measured $(U-B)=-0.9$ (DMA98), and shows variability of 1 magnitude, possibly with a 43.6 minute periodic modulation (Deutsch et al 2000)." + DALA9S searched a x LST WF/PCI field (not including source A: the GO-6517 data was not public then). for U-brighi stars.," DMA98 searched a $\times$ HST WF/PC1 field (not including source A; the GO-6517 data was not public then), for $U$ -bright stars." + Thev found only one object. star 49. with ©—£D color ancl magnitude similar to known LMXDs.," They found only one object, star 49, with $U-B$ color and magnitude similar to known LMXBs." + Adding the GSC (maximum) and IRC absolute positional errors, Adding the GSC (maximum) and HRC absolute positional errors +"Ilere ry is a characteristic length scale ancl p;=9,Pepi, 18 a characteristic density. which is equal to a density enhancement ὃς times the critical density [or closure p;=3417/32G.","Here $r_s$ is a characteristic length scale and $\rho_s = \delta_c \ \rho_{crit}$ is a characteristic density, which is equal to a density enhancement $\delta_c$ times the critical density for closure $\rho_{crit}=3H^2/8\pi G$." + The two [ree parameters 9. ancl r; can be determined [rom the halo concentration ea(M) and the virial mass Alyex(X2)hf/Akpe wherefT. righl)) = 118," The two free parameters $\delta_c$ and $r_s$ can be determined from the halo concentration $c_{\Delta}\left(M_{\Delta}\right)$ and the virial mass $M_{\Delta}$ where, ) = 178." + llere r4 is the virial radius. inside which the average overdensitv is A times the critical density for closure. and Ay is the mass within ry.," Here $r_{\Delta}$ is the virial radius, inside which the average overdensity is $\Delta$ times the critical density for closure, and $M_{\Delta}$ is the mass within $r_{\Delta}$." + For anv particular cosmology. the concentration ονCV) is a function of the virial mass which results from the fact Chat dark halo densities reflect the density of the universe at their formation epoch. and smaller mass halos collapse earlier in hierarchical structure formation.," For any particular cosmology, the concentration $c_{\Delta}\left(M_{\Delta}\right)$ is a function of the virial mass which results from the fact that dark halo densities reflect the density of the universe at their formation epoch, and smaller mass halos collapse earlier in hierarchical structure formation." + ence. for CDM power spectra. €CM) is a decreasing function of Ma.," Hence, for CDM power spectra, $c_{\Delta}\left(M_{\Delta}\right)$ is a decreasing function of $M_{\Delta}$." + ENS (2001) have carried out an extensive suite of simulations to characterize the dependence οἱ ονCM) on the cosmological parameters, ENS (2001) have carried out an extensive suite of N-body simulations to characterize the dependence of $c_{\Delta}\left(M_{\Delta}\right)$ on the cosmological parameters +SB. IB. GM and GCP acknowledge AST and MIUR (under grant COFIN--00-02-36) for financial support.,"SB, IB, GM and GCP acknowledge ASI and MIUR (under grant -00-02-36) for financial support." + We would like to thank Sergei Nayakshin for his helpful comments on the code. and the anonymous referee.," We would like to thank Sergei Nayakshin for his helpful comments on the code, and the anonymous referee." +The dynamical expansion of a bubble of wari. ionized eas produced by a vounug star or star ¢luster is one of the classical problems of the iuterstelar mediuu.,"The dynamical expansion of a bubble of warm, ionized gas produced by a young star or star cluster is one of the classical problems of the interstellar medium." +" reeion dvuamics are Hmuportaut iu par ec""wdlse they plav a dominant role iu regulatiie the formation o star clusters.", region dynamics are important in part because they play a dominant role in regulating the formation of star clusters. + 2 and 7 arene base on observations hat uo more than 10:4 of the mass ln a eunt niolecular cloud can ever be incorporated iuto stars. and ? and ? preseut GAIC models that explai1 this inefficiency cnautitatively in teris of the evaporation of CAIC mass by regions.," \citet{williams97} and \citet{carpenter00a} argue based on observations that no more than $\sim 10\%$ of the mass in a giant molecular cloud can ever be incorporated into stars, and \citet{matzner02} and \citet{krumholz06d} present GMC models that explain this inefficiency quantitatively in terms of the evaporation of GMC mass by regions." + Nearby star clusters provide direc evidence for this phenomenon., Nearby star clusters provide direct evidence for this phenomenon. +" For example in the Orkà Nebula Cluster. the radiation of 04 Ori C Ilzauuches au ionized wind frou the molecular cloud surface that caTies a nuass flux of ~10? AY, Vr l(Ty. sufficien to ablate a dass conrparable to he ONCs stellar mass in ~LO? vr."," For example in the Orion Nebula Cluster, the radiation of $\theta^1$ Ori C launches an ionized wind from the molecular cloud surface that carries a mass flux of $\sim 10^{-2}$ $\msun$ $^{-1}$ \citep{Odell01a}, sufficient to ablate a mass comparable to the ONC's stellar mass in $\sim 10^5$ yr." + Ànv nuderstanuding of star formation rates and efficiencies. and of molecular cloud lifetimes. nius therefore be based on an uuderstancding of regious.," Any understanding of star formation rates and efficiencies, and of molecular cloud lifetimes, must therefore be based on an understanding of regions." + Most work on this problem to «ate has focused. ou regionsOo where conditions are simular to those fouud in the Calaxy within several kpc ο| the Sun., Most work on this problem to date has focused on regions where conditions are similar to those found in the Galaxy within several kpc of the Sun. + The star clusters in this region are typically below LO! AJ. in mass (0.8.77).. and since a fully-sanypled IMIF at zero age produces S~10167 3oniziug pletous J| per M. of stars (?).. they have Iuuinosities ο at most 5[UU ioniziug photous |.," The star clusters in this region are typically below $10^4$ $\msun$ in mass \citep[e.g.][]{williams97, lada03}, and since a fully-sampled IMF at zero age produces $S \sim 10^{46.5}$ ionizing photons $^{-1}$ per $\msun$ of stars \citep{krumholz06d}, they have luminosities of at most $S\sim 10^{50}$ ionizing photons $^{-1}$." + For iouizing lhunünosities in this range. both nunuerical treatments aud analytic estimates show that radiation pressure is geucraIv simall compared ο gas pressure inside reogious (ec.TYTT)L.," For ionizing luminosities in this range, both numerical treatments and analytic estimates show that radiation pressure is generally small compared to gas pressure inside regions \citep[e.g.][]{mathews69a, gail79a, arthur04a, henney07a}." +" Thus while radiation ou dust eraius may plas ""an iuiportant role xoducimg σα] holes in region ceitets (e.g.27). the standard asstuuption has been that raciation pressure is tot significant for determining the cvusandes the region as a whole."," Thus while radiation on dust grains may play an important role producing small holes in region centers \citep[e.g.][]{mathews67a, inoue02a}, the standard assumption has been that radiation pressure is not significant for determining the dynamics the region as a whole." + Treatiieuts of regious under clyctunstances where radiation pressire ds slenificaut have eoncrally been Iuited to hvdrostatic inodels that do noti iclude any dyviuuules (0.2.5227) or πιοΊσα models of particular reeious (e.g.?2??)..," Treatments of regions under circumstances where radiation pressure is significant have generally been limited to hydrostatic models that do not include any dynamics \citep[e.g.][]{dopita02a, dopita03a, dopita06a} or numerical models of particular regions \citep[e.g.][]{pellegrini07a, pellegrini09a, harper-clark09a}." + The forner provide little infornation ou how radiation pressure affects gas motion. while the latter do not eaxilv lead to 2ereral couclusions abou when radiation pressure is portant aud how regioi αναος are altered when it is.," The former provide little information on how radiation pressure affects gas motion, while the latter do not easily lead to general conclusions about when radiation pressure is important and how region dynamics are altered when it is." +" AxCHassessnent of the role of radiatio1 pressure in regioji dvnsnudies is timev because observations of sta"" cluster formation are beeimuine to probe new regnmueS where earlier αποπλο mizing the role of radiation pressure no longer apply.", A re-assessment of the role of radiation pressure in region dynamics is timely because observations of star cluster formation are beginning to probe new regimes where earlier arguments minimizing the role of radiation pressure no longer apply. +τς The import:uice of radiatio1 pressure ries as the ioniziug luniuositv does. and i1 coutrast to the values o Cat oanost S~1079 + founl iu local regious. the Arches cluster near the Galactic centev has an ionizing huuünositv of 5zΓκΊο Peery. and some extragalactic custers have even larecr values.," The importance of radiation pressure rises as the ionizing luminosity does, and in contrast to the values of at most $S\sim 10^{50}$ $^{-1}$ found in local regions, the Arches cluster near the Galactic center has an ionizing luminosity of $S\approx 4\times 10^{52}$ $^{-1}$ \citep{figer02a}, and some extragalactic clusters have even larger values." + Moreover. regions with large ionizing luminosities also tend to have large virial aud escape velocities. aud in this case the conventional description of region expansion daiven by ionized eas pressure also breaks down.," Moreover, regions with large ionizing luminosities also tend to have large virial and escape velocities, and in this case the conventional description of region expansion driven by ionized gas pressure also breaks down." +" ? lueasure velocity dispersions of 10οί Flan | for the super star clusters in M82. and this probably represeuts a lower lint on the velocity dispersions and escape volocities iu the clusters"" pareut molecular clouds."," \citet{mccrady07a} measure velocity dispersions of $10-30$ km $^{-1}$ for the super star clusters in M82, and this probably represents a lower limit on the velocity dispersions and escape velocities in the clusters' parent molecular clouds." + Since the sotud speed iu ionized gas is only 1 Haas to an reglon driven by gas pressure could uot have expauded witli nor driven mass out of the the couds from which these star clusters formed.," Since the sound speed in ionized gas is only $10$ km $^{-1}$, an region driven by gas pressure could not have expanded within or driven mass out of the the clouds from which these star clusters formed." + We ave forces to conclude that either hese clusters must have formed with an efficiency of nearly or that some mechanisu other than lonizc (eas pressure is responsible for renoving lass aud Iunitiug the efficiency.," We are forced to conclude that either these clusters must have formed with an efficiency of nearly, or that some mechanism other than ionized gas pressure is responsible for removing mass and limiting the efficiency." + WIule we cannot directly rule out fιο hypothesis of star formation cficieney for the M82 clusters. we can rule it out for similar huge clusters im other ealaxies.," While we cannot directly rule out the hypothesis of star formation efficiency for the M82 clusters, we can rule it out for similar large clusters in other galaxies." + For example. the young star clusters observed im," For example, the young star clusters observed in" +"The agreeimoeut between the two different iiethods is. on average, always better than 0.1 dex.","The agreement between the two different methods is, on average, always better than 0.1 dex." + A similar comparisou between stellar masses obtained from spectral fitting aud ποια photometry. calculated using aperture maguitucdes instead of the total ones. shows an equally good agreemenut between the two methods.," A similar comparison between stellar masses obtained from spectral fitting and from photometry, calculated using aperture magnitudes instead of the total ones, shows an equally good agreement between the two methods." + The Bell&deJoug(2001) ass photometric values are also provided in our final catalogs., The \cite{bdj01} mass photometric values are also provided in our final catalogs. + As we describe in ΕΟΤ aud stumuarize iu Sect. ??..," As we describe in F07 and summarize in Sect. \ref{sec:ssp}," + our search for the best fit-model is performed using 12 SSPs of different ages. obtained. iu turi. by binning a auch higher age-resolutiou stellar age exid.," our search for the best fit-model is performed using 12 SSPs of different ages, obtained, in turn, by binning a much higher age-resolution stellar age grid." + Still. we verified that it is iot possible to recover the star formation as a function of stellar age with the relatively lieh temporal resolution xovided by the 12 SSPs.," Still, we verified that it is not possible to recover the star formation as a function of stellar age with the relatively high temporal resolution provided by the 12 SSPs." + After performing accurate tests ou template spectra that were built in order to match he spectral features of sspectra in terms of both spectral resolutiou. signal-to-noise ratio and wavelength coverage. we found that if is possible to properly recover he star formation history (hereafter. SEII) iu |1 aad stellar age bins.," After performing accurate tests on template spectra that were built in order to match the spectral features of spectra in terms of both spectral resolution, signal-to-noise ratio and wavelength coverage, we found that it is possible to properly recover the star formation history (hereafter, SFH) in 4 main stellar age bins." +" The details of the choice are explained iu F0?7: here we just recall their ranges that are. respectively: Γὃν ον1086 «105.610σον10? aud 5.6«10.τεςτοῦ) vears,"," The details of the choice are explained in F07; here we just recall their ranges that are, respectively: $0-2\times 10^7$, $2\times 10^7-6\times 10^8$, $6\times 10^8-5.6\times 10^9$ and $5.6\times 10^9-14\times +10^9$ years." + The SEIT is eiven in our catalogs in two differeut Onus: 1) percentage of the stellar mass aud 2) star formation rate (SER) iu the four bins., The SFH is given in our catalogs in two different forms: 1) percentage of the stellar mass and 2) star formation rate (SFR) in the four bins. +" The first is computed accordiug to the followiue: where Vp;,, is the ummber of SSPs contained iu a given age biu: C; is the normalisation constant of each SSP of that biu. ie. the stellar mass at cach age according to definition 1: M7? is the factor. which is a function of the stellar age. that couverts the SSP initial mass (cfinition 1.)"," The first is computed according to the following: where $N_{bin}$ is the number of SSPs contained in a given age bin; $C +_i$ is the normalisation constant of each SSP of that bin, i.e. the stellar mass at each age according to definition 1; $M^\star_i$ is the factor, which is a function of the stellar age, that converts the SSP initial mass (definition 1.)" + iuto either the mass locked iuto stars (1iass definition 2.), into either the mass locked into stars (mass definition 2.) + or mto mass of nuclear buruiung stars (definition 3.).," or into mass of nuclear burning stars (definition 3.)," + while the suni at the denominator is the total stellar mass (according to definitions 2 aud 3. respectively).," while the sum at the denominator is the total stellar mass (according to definitions 2 and 3, respectively)." + The star formation rate as a function ofthe stellar age 1s computed by dividiug the stellar mass of a given age biu by its duration., The star formation rate as a function of the stellar age is computed by dividing the stellar mass of a given age bin by its duration. + Definition 1 of the mass was applied iu this calculation (seealsoequation1iuLoughetti&Saracco. 20049)., Definition 1 of the mass was applied in this calculation \citep[see also equation 1 in][]{longhetti09}. +. The current SFR value. ic. the one calculated withiu the vouugest age biu. deserves a particular attention. since if is calculated bw fitting the equivalent width of cinission lines. namely Hydrogen (Πα and IL/) aud Oxygen at 3727 Aj).," The current SFR value, i.e. the one calculated within the youngest age bin, deserves a particular attention, since it is calculated by fitting the equivalent width of emission lines, namely Hydrogen $\alpha$ and $\beta$ ) and Oxygen at 3727 )." + The lines? hnuinosity is eutirely attributed to star formation processes neglecting other mechanisnis that can produce ionizing fiux., The lines' luminosity is entirely attributed to star formation processes neglecting other mechanisms that can produce ionizing flux. + Iu this wav we are overestimating the current SFR in both LINERS and AGNs., In this way we are overestimating the current SFR in both LINERS and AGNs. + In a forthcoming work. we will present au analysis of standard diagnostic diagrams such as those by Veilleux&Osterbrock(1987).. with the lines itensitices accurately imieasured by subtracting stellar templates from the observed spectrum (Alarziani ct al.," In a forthcoming work, we will present an analysis of standard diagnostic diagrams such as those by \cite{veilleux87}, with the lines' intensities accurately measured by subtracting stellar templates from the observed spectrum (Marziani et al.," + iu prep.)., in prep.). +" This work will enable the distinction between ""pure star fornunmeoU svsteiis aud those where other mechamisiis nuielto be co-responsible for line emission.", This work will enable the distinction between “pure” star forming systems and those where other mechanisms might be co-responsible for line emission. +" According to the ""selective extinction” lhivpotliesis (Calzettietal...1991).. which we fully cousicder du our modelling. cach SSP las its own value of the dust attenuation."," According to the “selective extinction” hypothesis \citep{calzetti94}, which we fully consider in our modelling, each SSP has its own value of the dust attenuation." +" Wecompute an age-averaged value of dust extinction. as it is derived by the model. by using Eq.6:: where L25 aud EM, are. respectively. the model spectitmun and the model nou-attenuated spectrum (d.e. the model with the same SEIT as £34, but with d=0 for cach stellar population)."," Wecompute an age-averaged value of dust extinction, as it is derived by the model, by using \ref{eqn:av}: where $L_{tot}^M$ and $L_{unext}^M$ are, respectively, the model spectrum and the model non-attenuated spectrum (i.e. the model with the same SFH as $L_{tot}^M$ but with $A_V=0$ for each stellar population)." + We calculate two distinct values: we first take iuto account oulv stellar populations that are vounecr than ~2«10. ie. those that are responsible for nebular eudssiou: this value is comparable with extinction that is computed from euission lines ratio.," We calculate two distinct values: we first take into account only stellar populations that are younger than $\sim 2\times 10^7$, i.e. those that are responsible for nebular emission; this value is comparable with extinction that is computed from emission lines ratio." + Secondly. we use all stellar populations providing. iu this wav. an extinction value which is averaged over SSP of all ages.," Secondly, we use all stellar populations providing, in this way, an extinction value which is averaged over SSP of all ages." +-- Exploiting the iuformiation derived by our analysis. we are able to provide au estimate of the average age of a ealaxy. weighted on the stellar populations that compose its spectimm.," Exploiting the information derived by our analysis, we are able to provide an estimate of the average age of a galaxy, weighted on the stellar populations that compose its spectrum." + Civenu that the mass-to-leht ratio changes as à function ofthe age. there are two different definitions hat can be eiven: the massaveighted aud the Iuninuositi-weighted age (seealsoFernandeseal..2003).," Given that the mass-to-light ratio changes as a function of the age, there are two different definitions that can be given: the mass-weighted and the luminosity-weighted age \citep[see also][]{fernandes03}." +. The latter is the uost conunonlv eiven. since it is directly derived roni the spectrum. beiug weighted im this wav towards he age of the stellar populations that dominate the helt. while the first definition requires the knowledge of the nass distribution as a function of stellar age. 1.0. the SEIT.," The latter is the most commonly given, since it is directly derived from the spectrum, being weighted in this way towards the age of the stellar populations that dominate the light, while the first definition requires the knowledge of the mass distribution as a function of stellar age, i.e. the SFH." + We can compute the logarithin of these two quantities as ollows: for the logarithun of the huninosity weighted age. where LAV) aud L44(V) ave the resttrame Iuuinosities of the SSP aud of the total spectrum. respectively. iu the," We can compute the logarithm of these two quantities as follows: for the logarithm of the luminosity weighted age, where $L_i(V)$ and $L_{tot}(V)$ are the restframe luminosities of the SSP and of the total spectrum, respectively, in the" +enhanced over (he standard post-bed mosaics used here.,enhanced over the standard post-bcd mosaics used here. + In the NGC 0523 paper we noted a discrepancy. between (he mid-inflrared distance moduli and the two near-infrared (J Ix} moduli from (Gieren et al., In the NGC 6822 paper we noted a discrepancy between the mid-infrared distance moduli and the two near-infrared (J K) moduli from (Gieren et al. + 2006)., 2006). + No such discrepancy is seen in a comparison of these IRAC observations and the nemr-inlrared (again J IX) moduli for IC 1613. this time published bv Pietrzvnski et al. (," No such discrepancy is seen in a comparison of these IRAC observations and the near-infrared (again J K) moduli for IC 1613, this time published by Pietrzynski et al. (" +2006).,2006). + As such we are still no closer to understanding the differences seen in the NGC! 6822 near-infrared data sets., As such we are still no closer to understanding the differences seen in the NGC 6822 near-infrared data sets. + Given the sensitivity of IRAC. especially for the shortest wavelength. bands. modest integration times (hours) could. in principle. allow one to press (he application of mid-inlrared period-Iuminositv relations in determining distances out (to several megaparsecs.," Given the sensitivity of IRAC, especially for the shortest wavelength bands, modest integration times (hours) could, in principle, allow one to press the application of mid-infrared period-luminosity relations in determining distances out to several megaparsecs." + Scaling from 1¢ data on IC 1613. similar Cepheids at a distance of 2 Alpe could be measured to the same V.ignal-to-noise in about three hours.," Scaling from the data on IC 1613, similar Cepheids at a distance of 2 Mpc could be measured to the same signal-to-noise in about three hours." + llowever. sensitivilv is not the limiting factor: erowding is.," However, sensitivity is not the limiting factor: crowding is." + The mid-inlrared studies of 1e stellar populations in WLM and IC 1613 by Jackson et al. (, The mid-infrared studies of the stellar populations in WLM and IC 1613 by Jackson et al. ( +2007a.b) have convincingly V.1i0wn (hat (he vast majority of stars resolved at the brightest magnitudes (i.e. above the ip of the red giant branch. M44 = -6.0 mag and brighter) are IR-AGB stars. a substantial component of which (40-4554)) are not detected in the optical.,"2007a,b) have convincingly shown that the vast majority of stars resolved at the brightest magnitudes (i.e., above the tip of the red giant branch, $_{3.6}$ = -6.0 mag and brighter) are IR-AGB stars, a substantial component of which ) are not detected in the optical." + From the data presented in Figure 5 of Jackson et al. (, From the data presented in Figure 5 of Jackson et al. ( +2007a) il is possible to estimate the areal density of these stus across the [ace of IC 1613.,2007a) it is possible to estimate the areal density of these stars across the face of IC 1613. + From that we deduce (hat the mean separation of stars brighter than -6 mag at 3.6//mm is 18 aresec., From that we deduce that the mean separation of stars brighter than -6 mag at $\mu$ m is 18 arcsec. + Translated into practical terms this means that for a ealaxy 10 times further than IC: 1613 (i.e. 7-8 Alpe) the average separation of bright sources would be less than 2 aresec. which is now comparable to the resolution of IRAC.," Translated into practical terms this means that for a galaxy 10 times further than IC 1613 (i.e. 7-8 Mpc) the average separation of bright sources would be less than 2 arcsec, which is now comparable to the resolution of IRAC." + Even ad the distance of IC 1612 itself we found that upwards of half of the known Cepheids in this galaxy were visibly contaminated., Even at the distance of IC 1613 itself we found that upwards of half of the known Cepheids in this galaxy were visibly contaminated. + Thus we estimate that care must be taken in using IRAC to measure. Cepheids in galaxies another [actor of two or three further in distance than IC. 1613., Thus we estimate that care must be taken in using IRAC to measure Cepheids in galaxies another factor of two or three further in distance than IC 1613. + More than half of the Cepheids will be crowded but lor a given pointing the total number of Cepheids Chat [it in the detector's [field of view will also go up so that the absolute vield of uncontaminated Cepheids might be maintained at this limit., More than half of the Cepheids will be crowded but for a given pointing the total number of Cepheids that fit in the detector's field of view will also go up so that the absolute yield of uncontaminated Cepheids might be maintained at this limit. + Pressing this method bevond 2 Alpe is best left for JWST: but evervthing inside of that sphere is plausibly within reach., Pressing this method beyond 2 Mpc is best left for JWST; but everything inside of that sphere is plausibly within reach. +incorporating a nanodiamond component.,incorporating a nanodiamond component. + This will enhance understanding of radiation induced transformations of carbonaceous matter in the ISM., This will enhance understanding of radiation induced transformations of carbonaceous matter in the ISM. +" The use of High Performance Computing and library facilities at IUCAAA, Pune is acknowledged."," The use of High Performance Computing and library facilities at IUCAA, Pune is acknowledged." + Valuable discussions with Dr. R. Gupta and Dr. D.D. Vaidya are greatly appreciated., Valuable discussions with Dr. R. Gupta and Dr. D.B. Vaidya are greatly appreciated. +"[X/Zu| (for X = Si. P. Cr. Fe. aud Ni) similar to those for group 10 toward SN 1987À. TheFUSE spectra also show strong absorption from IT». with ΑΠΟ) ον 101? 2. Ty, ~ GOK. and T4 ~ 800 K for J 2 35 (1p).","[X/Zn] (for X = Si, P, Cr, Fe, and Ni) similar to those for group 10 toward SN 1987A. The spectra also show strong absorption from $_2$, with $N$ $_2$ ) $\sim$ 3 $\times$ $^{19}$ $^{-2}$ , $T_{01}$ $\sim$ 60 K, and $T_{\rm ex}$ $\sim$ 800 K for $J$ = 3–5 \cite{fri00}) )." + STIS echelle spectra (FWHAL ~ 6.5 ian 13 have been obtained for DI 1388. located in the Magellanic Bridge. where the overall metallicity las been estimatei as about 1.1 dex below solar (qv.," STIS echelle spectra (FWHM $\sim$ 6.5 km $^{-1}$ ) have been obtained for DI 1388, located in the Magellanic Bridge, where the overall metallicity has been estimated as about 1.1 dex below solar \cite{lsd01}) )." + For two compoueuts with total ;V(IT) ~ 12 ον IUOU 7. the relative abuudauces [X/S] (for X = AL Si. Fe. and Ni) are similar to those found for Calactic halo clouds (Fig.," For two components with total $N$ (H) $\sim$ 1–2 $\times$ $^{20}$ $^{-2}$, the relative abundances [X/S] (for X = Al, Si, Fe, and Ni) are similar to those found for Galactic halo clouds (Fig." + 2)., 2). + The apparent uuderabundance of N Iin the weaker component max be due to partial ionization., The apparent underabundance of N Iin the weaker component may be due to partial ionization. +" Combining a (tentative) detection of C I with a limit on 5», (froin analysis of the € IL fine structure excitation) suggests either a relatively weak radiation field or a relatively low TZ for the stronger componcut.", Combining a (tentative) detection of C I with a limit on $n_e$ (from analysis of the C II fine structure excitation) suggests either a relatively weak radiation field or a relatively low $T$ for the stronger component. + GIIRS echelle spectra (FWHAL ~ L2 kin 1j reveal at least 16 SAIC componcuts between 89 and 210 km E (Fig., GHRS echelle spectra (FWHM $\sim$ 4.2 km $^{-1}$ ) reveal at least 16 SMC components between 89 and 210 km $^{-1}$ (Fig. + 3: [22]))., 3; \cite{wlb97}) ). + For all the SMC componcnts. the relative abundances [N/Zn]| (for X = Si. Cr. Mu. Fe. and Ni) are broadly similar to those in Galactic halo clouds. though Si max bo slightly hieh aud Ni slightly low (Fie.," For all the SMC components, the relative abundances [X/Zn] (for X = Si, Cr, Mn, Fe, and Ni) are broadly similar to those in Galactic halo clouds, though Si may be slightly high and Ni slightly low (Fig." + 5)., 5). + For ΑΠ) ~ 3.5 & 1078 cin2. the overall [Zu/TI| is consistent with a metallicity 0.6 dex below solar and a Zu depletion of 0.1 dex (as in the halo clouds).Analysis of lower resolution GIIRS C1GOA and FUSE spectra (FWIIM ~ 2025 kins 1) suggests that P. S. aud Ar are," For $N$ (H) $\sim$ 3.5 $\times$ $^{20}$ $^{-2}$, the overall [Zn/H] is consistent with a metallicity 0.6 dex below solar and a Zn depletion of 0.1 dex (as in the halo clouds).Analysis of lower resolution GHRS G160M and spectra (FWHM $\sim$ 20–25 km $^{-1}$ ) suggests that P, S, and Ar are" +the asstuuption that the atinosphere is homogenous im kc aud 0.,the assumption that the atmosphere is homogenous in $r$ and $\theta$. + Tn other words. the radiation field does not “see” pots at other values of r aud 0. only the variation in the + direction is accounted for (this is iuiplicit in )).," In other words, the radiation field does not `see' points at other values of $r$ and $\theta$, only the variation in the $z$ direction is accounted for (this is implicit in \\ref{eqint}) )." + A significant portion of the pluue mass was likely present in the form of silicate or other erains whose deposition is believed. to account for the post-impact debris patterus on the jovian disk., A significant portion of the plume mass was likely present in the form of silicate or other grains whose deposition is believed to account for the post-impact debris patterns on the jovian disk. + However.?..?.. aud Paper I calculate that the phuues were mostly cutraimed jovian air.," However, and Paper I calculate that the plumes were mostly entrained jovian air." + We assume that the overall lyvdrodvuamics of the splasliback was determined by the gaseous component. with erains advected by the flow aud heated by the shocks(2).," We assume that the overall hydrodynamics of the splashback was determined by the gaseous component, with grains advected by the flow and heated by the shocks." +. Nevertheless. we have incorporated an option in the code for following the motion of tracer eraius. bv explicit integration of the eraiu uonientuni equations.," Nevertheless, we have incorporated an option in the code for following the motion of tracer grains, by explicit integration of the grain momentum equations." + Ballistic studies have shown conclusively that coutinued radial transport after splasliback Is necessary to explain the disk debris patterus., Ballistic studies have shown conclusively that continued radial transport after splashback is necessary to explain the disk debris patterns. + We performed exploratory erain transport calculations. which indicated eood agreement with the observed radial extent of disk debris. but also couviuced us that the transport of erains does iof have a nmiajor effect on the phenomena discussed in this paper (e.g. light curves).," We performed exploratory grain transport calculations, which indicated good agreement with the observed radial extent of disk debris, but also convinced us that the transport of grains does not have a major effect on the phenomena discussed in this paper (e.g., light curves)." + The original version of ZEUS-3D applies to a sinele-compoucut fluid. having a siugle value for R aud 5.," The original version of ZEUS-3D applies to a single-component fluid, having a single value for $R$ and $\gamma$." + We adopt 5=12 from the Galileo observations of the C-imypact fireball(?)., We adopt $\gamma=1.2$ from the Galileo observations of the G-impact fireball. +. We also apply this value to the jovian atinosphiere. ackiug a direct deteriunation for shocked jovian air.," We also apply this value to the jovian atmosphere, lacking a direct determination for shocked jovian air." + However. we have modified ZEUS to use two values for the gas constant (2). consistent with different molecular weights (20) for the pluie material aud for joviau air.," However, we have modified ZEUS to use two values for the gas constant $R$ ), consistent with different molecular weights $\mu$ ) for the plume material and for jovian air." + We use jj=2.28 + for jovian air. which reflects the helium abundance from the Galileo Probe Helium Interferometer (?).," We use $\mu= 2.28$ $^{-1}$ for jovian air, which reflects the helium abundance from the Galileo Probe Helium Interferometer ." +. For the unie. we calculated gr assuniug that the impacting object was predominately water (jj—I8): the fraction of the plume naterial which was impactor was determined in the ballistic plume modeling. and was not a free paraicter iu ZEUS-3D. To explore the zero-th order’ effects of large versus small impacts. we vary the plume mass by a scale factor. keeping the sale proportions of inupactor and jovian air in the phuc.," For the plume, we calculated $\mu$ assuming that the impacting object was predominately water $\mu=18$ ); the fraction of the plume material which was impactor was determined in the ballistic plume modeling, and was not a free parameter in ZEUS-3D. To explore the `zero-th order' effects of large versus small impacts, we vary the plume mass by a scale factor, keeping the same proportions of impactor and jovian air in the plume." + ZEUS-3D uses a source step and a trausport step to integrate the fluid equations(?2)., ZEUS-3D uses a source step and a transport step to integrate the fluid equations. +. The source step accelerates the fluid using the pressure eracdient aud eravity terms ou the right of aud the radiation term ou the right of reteqenerey.., The source step accelerates the fluid using the pressure gradient and gravity terms on the right of \\ref{eqmom} and the radiation term on the right of \\ref{eqenergy}. + The transport step intcerates the spatial aud temporal eradicuts to advect the fluid variables across the Eulerian spatial erid. based ou the scheme.," The transport step integrates the spatial and temporal gradients to advect the fluid variables across the Eulerian spatial grid, based on the scheme." + Exploratory calculations indicated that there is little müxiug at the plhune/atinosphere interface iu the first hours after impact. so we used the following simplified treatineut.," Exploratory calculations indicated that there is little mixing at the plume/atmosphere interface in the first hours after impact, so we used the following simplified treatment." + We added an additional van Leer advection calculation to ZEUS-3D. tracking the total overlying colin density of plume material at cach r. thus determining the location of the phune/atimosphere boundary.," We added an additional van Leer advection calculation to ZEUS-3D, tracking the total overlying column density of plume material at each $r$, thus determining the location of the plume/atmosphere boundary." + This permits two values of HR. depending on whether the fluid in a given erid zone is plume. atinosphiere. or both.," This permits two values of $R$, depending on whether the fluid in a given grid zone is plume, atmosphere, or both." + The ZEUS livdrocode has itself beeu tested well against a suite of standard livdrodvuaimic test problems(2)., The ZEUS hydrocode has itself been tested well against a suite of standard hydrodynamic test problems. +. Since we have modified the code. we must establish the validity of our modifications aud also show that we have not inadverteutlv intertered with the existing code algorithms.," Since we have modified the code, we must establish the validity of our modifications and also show that we have not inadvertently interfered with the existing code algorithms." + We have performed uunerous tests for these purposes. inchiding direct clicks of some code algorithius against hand calculations.," We have performed numerous tests for these purposes, including direct checks of some code algorithms against hand calculations." + We also conducted five iiore-coniplex tests of the code. as described below.," We also conducted five more-complex tests of the code, as described below." + The shock tube is a one-dimensional test problem wherein a boundary separates two isotropic regions of differcut pressures and deusities., The shock tube is a one-dimensional test problem wherein a boundary separates two isotropic regions of different pressures and densities. + When the boundary is removed. a shock propagates iuto the lower pressure region. aud the code results can be compared to au analytic solution(?).," When the boundary is removed, a shock propagates into the lower pressure region, and the code results can be compared to an analytic solution." +. For these tests. we configured ZEUS-3D in a 1-D mode with 1000 zones and with the radiation terms turned off.," For these tests, we configured ZEUS-3D in a 1-D mode with 1000 zones and with the radiation terms turned off." + We first repeated the shock tube test described by?.. and verified that we can reproduce their 111.," We first repeated the shock tube test described by, and verified that we can reproduce their 11." + However. shocks in the SE9 problem will have larger compression ratios. e.g.. the jump iu pressure across the shock can be as large as 105.," However, shocks in the SL9 problem will have larger compression ratios, e.g., the jump in pressure across the shock can be as large as $10^{4}$." + Fieure 2) shows a successful test for this compression ratio., Figure \ref{figtest} shows a successful test for this compression ratio. + The second term on the right of refeqmoin represents Jupiters constant gravitational acceleration., The second term on the right of \\ref{eqmom} represents Jupiter's constant gravitational acceleration. + To test the addition of this teri we started with a 2-D voluue with initial coustant pressure but oscillatory temperature aud censity.," To test the addition of this term, we started with a 2-D volume with initial constant pressure but oscillatory temperature and density." + Since constant pressure is not a solution to (2). the code evolved this atumosphere.," Since constant pressure is not a solution to (2), the code evolved this atmosphere." + We used the radiative damping option. with the arbitrary coustraint that J=5$ for £=500 Ik. (This is equivalent to placing an optically-thin atimosphere in a blackbody cavity at this tempecratiure.)," We used the radiative damping option, with the arbitrary constraint that $J=S$ for $T=500$ K. (This is equivalent to placing an optically-thin atmosphere in a blackbody cavity at this temperature.)" + Att=s<109 sec. a near-equilibriun state with constant temperature aud gradients in pressure aud density prevailed.," At ${t=8\times +10^5}$ sec, a near-equilibrium state with constant temperature and gradients in pressure and density prevailed." + We verified that there were uo significant horizontal exadients. aud the pressure eracdicut tex balanced the gp term to within a fractional error <5«10.9.," We verified that there were no significant horizontal gradients, and the pressure gradient term balanced the $\mathbf{g}\rho$ term to within a fractional error $<{5 \times 10^{-6}}$." + The scale heielit agreed with the analvtie value to within, The scale height agreed with the analytic value to within. + The radiative damping tine of a tempcrature perturbation depends on its spatial scale as well as its temperature auaplitude., The radiative damping time of a temperature perturbation depends on its spatial scale as well as its temperature amplitude. + Perturbations of large spatial scale can extend over many optical depths. and these damp slowly because their optical thickuess hiuders photou transter.," Perturbations of large spatial scale can extend over many optical depths, and these damp slowly because their optical thickness hinders photon transfer." + derived au analytic expression for the damping time of smallamplitude teiiperature perturbations in au isothermal atinosphiere in LTE., derived an analytic expression for the damping time of smallamplitude temperature perturbations in an isothermal atmosphere in LTE. + We turned off the eravitational acceleration term in, We turned off the gravitational acceleration term in +HST optical imaging was used to analyze the morphology of the GPs (see Figure 7 in C09)., optical imaging was used to analyze the morphology of the GPs (see Figure 7 in C09). +" To be consistent, the oxygen and nitrogen abundances for the sample of LBAs were re-calculated using the line ratios measured from SDSS spectra (Overzieretal.2009), and the same empirical calibrations described above."," To be consistent, the oxygen and nitrogen abundances for the sample of LBAs were re-calculated using the line ratios measured from SDSS spectra \citep{Overzier09a}, and the same empirical calibrations described above." +" In Figure 1, we show histograms with our metallicity estimates for the GPs and those derived by C09 for comparison."," In Figure \ref{fig1}, we show histograms with our metallicity estimates for the GPs and those derived by C09 for comparison." +" The GPs show direct metallicities 7.7SS 12+log(O/H)< 8.4, witha mean value of 8.05 + 0.14, i.e., ~20% the solarvalue*,, whereas their measured C(H8)andHa/ mmeanvaluesare0.23and3.3, respectively."," The GPs show direct metallicities $7.7 \la$ $+$ $\la 8.4$, witha mean value of 8.05 $\pm$ 0.14, i.e., $\sim$ the solar, whereas their measured $($ $)$ and mean values are 0.23 and 3.3, respectively." +Ourdirectestimatesane 7 ewellin-0.05 dex., Our direct estimates and those derived using the N2 parameter agree well in $\sim$ 0.05 dex. +" While extinction values are in agreement with those obtained by C09, Figure 1 shows a clear offset of ~0.65 dex between their metallicity estimates (mean log(O/H) +12= 8.7) and ours."," While extinction values are in agreement with those obtained by C09, Figure \ref{fig1} shows a clear offset of $\sim$ 0.65 dex between their metallicity estimates (mean log(O/H) $+ 12 =$ 8.7) and ours." + The C09 values were obtained using the rratio to estimate log(O/H) 4- 12 via the theoretical calibration based on photoionization models by Kewley&Dopita(2002)., The C09 values were obtained using the ratio to estimate log(O/H) $+$ 12 via the theoretical calibration based on photoionization models by \citet{KD02}. +". Systematical discrepancies are usually found in the literature between metallicities derived from theoretical and empirical methods (Kewley&Ellison2008,andreferencestherein).", Systematical discrepancies are usually found in the literature between metallicities derived from theoretical and empirical methods \citep[][and references therein]{KE08}. + We have used the conversion constants provided by Kewley&Ellison(2008) to scale our N2-based oxygen abundance estimates to those expected from the theoretical calibration (their Table 3)., We have used the conversion constants provided by \citet{KE08} to scale our N2-based oxygen abundance estimates to those expected from the theoretical calibration (their Table 3). +" In doing so, we obtained a mean difference of 0.23 dex, which is not enough to explain the largest offset in O/H shown in Figure 1.."," In doing so, we obtained a mean difference of 0.23 dex, which is not enough to explain the largest offset in O/H shown in Figure \ref{fig1}." + We conclude that GPs are genuine metal-poor galaxies with low extinction values., We conclude that GPs are genuine metal-poor galaxies with low extinction values. + The nitrogen-to-oxygen ratio is a powerful evolutionary indicator in galaxies (Pilyuginetal.2004;Molláetal. 2006).," The nitrogen-to-oxygen ratio is a powerful evolutionary indicator in galaxies \citep{Pilyugin04,Molla06}." +". We have investigated the relation between the N/O ratio and the oxygen abundance for the sample of GPs, LBAs, and the SFGs taken from the SDSS in Figure 2.."," We have investigated the relation between the N/O ratio and the oxygen abundance for the sample of GPs, LBAs, and the SFGs taken from the SDSS in Figure \ref{fig2}." +" For the SFGs, we found a positive trend with an increasing scatter toward the metal-rich regime reflecting both primary and secondary production of nitrogen in the same metallicity range."," For the SFGs, we found a positive trend with an increasing scatter toward the metal-rich regime reflecting both primary and secondary production of nitrogen in the same metallicity range." +" At low metallicities the trend flattens out, possibly a consequence of nitrogen being of primary origin, coming mainly from massive stars."," At low metallicities the trend flattens out, possibly a consequence of nitrogen being of primary origin, coming mainly from massive stars." +" In the low-to-intermediate metallicity range, most GPs and some LBAs display systematically larger N/O ratios for a given metallicity compared to the SDSS SFGs."," In the low-to-intermediate metallicity range, most GPs and some LBAs display systematically larger N/O ratios for a given metallicity compared to the SDSS SFGs." +" Possible reasons for this include extra production of primary nitrogen, coming from low-metallicity intermediate-mass stars (Renzini&Voli1981;Gavilánetal.2006;Mollá 2006),, pollution by Wolf-Rayet stars (e.g.,Brinch-Monreal-Iberoetal. 2010), or hydrodynamical effects involving outflow and inflow of gas (vanZeeetal.1998;Kóppen&Hensler 2005).."," Possible reasons for this include extra production of primary nitrogen, coming from low-metallicity intermediate-mass stars \citep{Renzini81,Gavilan06,Molla06}, pollution by $-$ Rayet stars \citep[e.g.,][]{Brinchmann08,Angel10,AnaMon10}, or hydrodynamical effects involving outflow and inflow of gas \citep{Vanzee98,Koppen05}. ." + This systematically larger N/O ratios could explain the difference between our metallicity and the higher estimates obtained by C09 using the calibration by Kewley&Dopita (2002).., This systematically larger N/O ratios could explain the difference between our metallicity and the higher estimates obtained by C09 using the calibration by \cite{KD02}. . + The latter assumes that, The latter assumes that +Finding patterns in large astronomical databases ancl erouping the data into different Classes has become an important task in recent vears. one that must be done in an automated fashion given the massive amounts of skv survey data currently being collected and stored.,"Finding patterns in large astronomical databases and grouping the data into different classes has become an important task in recent years, one that must be done in an automated fashion given the massive amounts of sky survey data currently being collected and stored." + Traditional methods such as looking at large sky plates and idenlilving galaxies and clusters by eve are no longer feasible., Traditional methods such as looking at large sky plates and identifying galaxies and clusters by eye are no longer feasible. + Within statistical pattern recognition (here are (wo traditional approaches to data classification: supervised statistical classification and unsupervised learning (clustering)., Within statistical pattern recognition there are two traditional approaches to data classification: supervised statistical classification and unsupervised learning (clustering). + In (he supervised approach one is given a batch of training data containing labeled examples from each of the known classes of interest., In the supervised approach one is given a batch of training data containing labeled examples from each of the known classes of interest. + These examples are used to learn a decision function which partitions Che feature space into disjoint regions. each associated with one of the classes.," These examples are used to learn a decision function which partitions the feature space into disjoint regions, each associated with one of the classes." + Typical decision function structures used in practice are neural networks. decision trees. and prototvpe-based classifiers.," Typical decision function structures used in practice are neural networks, decision trees, and prototype-based classifiers." + Once (he decision function is leuned il can be used to automatically classify new examples., Once the decision function is learned it can be used to automatically classify new examples. + The supervised learning of the decision [function can be slow and generally requires off-lime (raining., The supervised learning of the decision function can be slow and generally requires off-line training. + Moreover. enough labeled exanples from each of the classes are required (o learn an accurate decision function that adequately separates data into the different classes.," Moreover, enough labeled examples from each of the classes are required to learn an accurate decision function that adequately separates data into the different classes." + However. extracting labeled examples from a large database is a (ime consuming and expensive process. generally requiring hand labeling bv human experts.," However, extracting labeled examples from a large database is a time consuming and expensive process, generally requiring hand labeling by human experts." + Alternativelv. unsupervised learning. or clustering. techniques assign data to groups without anv need for supervising examples.," Alternatively, unsupervised learning, or clustering, techniques assign data to groups without any need for supervising examples." +" In these approaches. (he grouping is chosen so that the data examples belonging to each cluster are ""as similar as possible” and so that examples rom clifferent clusters are “as dissimilar as possible”."," In these approaches, the grouping is chosen so that the data examples belonging to each cluster are “as similar as possible” and so that examples from different clusters are “as dissimilar as possible”." + This notion of similarity is quantified through a mathematical clustering objective function. one which relies on the choice of a distance measure defined on the feature space. e.g. the sum-ol-sequared-errors criterion.," This notion of similarity is quantified through a mathematical clustering objective function, one which relies on the choice of a distance measure defined on the feature space, e.g. the sum-of-squared-errors criterion." + Mixture models (Duda.Hart.&Stork2001:MelachlanPeel2000:Banfield&halteryv.1993). are one form of moclelbased clustering.," Mixture models \citep{Duda, Mclachlan, Raftery} are one form of model-based clustering." + They. produce. probabilistic. or soft. assignments of data points to each of the mixture components. or clusters.," They produce probabilistic, or soft, assignments of data points to each of the mixture components, or clusters." + The nature and equality of the learned groupings obtained via unsupervised clustering critically depends upon the choice of clustering distance measure and also on the number of clusters to be learned. which must be specified as part of the algorithun.," The nature and quality of the learned groupings obtained via unsupervised clustering critically depends upon the choice of clustering distance measure and also on the number of clusters to be learned, which must be specified as part of the algorithm." + There are currently no eenerallv agreed upon approaches lor choosing these parameters in unsupervised learning., There are currently no generally agreed upon approaches for choosing these parameters in unsupervised learning. + Furthermore. without supervising examples. there are no guarantees that (he chosen parameters are consistent wilh (he learning of clusters that correspond {ο the ground. truth classes in ihe data.," Furthermore, without supervising examples, there are no guarantees that the chosen parameters are consistent with the learning of clusters that correspond to the ground truth classes in the data." + In recent vears. seeking (o overcome the disadvantages of both supervised ancl unsupervised learning. techniques have been proposed. e.g.," In recent years, seeking to overcome the disadvantages of both supervised and unsupervised learning, techniques have been proposed, e.g." +ancalibrated instrumental Huxes.,uncalibrated instrumental fluxes. + This contrasts with most prior analyses of M3 RRL light curves which were plotted using standard apparent magnitudes., This contrasts with most prior analyses of M3 RRL light curves which were plotted using standard apparent magnitudes. + In. this section. we acldress the sell-consisteney of this method and compare the results to published photometry of RRLs.," In this section, we address the self-consistency of this method and compare the results to published photometry of RRLs." + To test the sensitivity of the period. searching method. to variations in the cata. two stars were selected at random. one with a very clean light curve and the other with a relatively noisy one.," To test the sensitivity of the period searching method to variations in the data, two stars were selected at random, one with a very clean light curve and the other with a relatively noisy one." + Five data points. equivalent to eight. per cent of the total data set. were then randomly. selected. for each star and removed from the set of observations.," Five data points, equivalent to eight per cent of the total data set, were then randomly selected for each star and removed from the set of observations." + The period searching algorithm was then run as previously cliscussect., The period searching algorithm was then run as previously discussed. + vYT was chosen as the star with the clean light curve., v77 was chosen as the star with the clean light curve. + Period analysis on both the full and reduced data sets gave he same period. 0.459419 d. The resulting light curve is slightly better than that produced using the published value rom CCOL. 0.459350 d. v214 was selected. for its more scattered. light curve.," Period analysis on both the full and reduced data sets gave the same period, 0.459419 d. The resulting light curve is slightly better than that produced using the published value from CC01, 0.459350 d. v214 was selected for its more scattered light curve." + In this case. the best fit period changed from. 0.539507 d ο 0.539492 d. These are both close to the most recent xublished: period. 0.539493 d. taken from CCOL," In this case, the best fit period changed from 0.539507 d to 0.539492 d. These are both close to the most recent published period, 0.539493 d, taken from CC01." + A visual inspection of the Light curves for our two derived. periods show no significant dillerences., A visual inspection of the light curves for our two derived periods show no significant differences. + These results imply that our method is fairly robust: a slight pertubation of the data set does not have a substantial impact on our derived. periods to four decimal places., These results imply that our method is fairly robust: a slight pertubation of the data set does not have a substantial impact on our derived periods to four decimal places. + Another test of the accuracy of our method is how well it reproduces periods and light curves for wellstuclied stars., Another test of the accuracy of our method is how well it reproduces periods and light curves for well-studied stars. + One dilliculty is that we are studying primarily the inner core of M3. where the scatter in the data is inherently higher.," One difficulty is that we are studying primarily the inner core of M3, where the scatter in the data is inherently higher." + Llowever. many stars with previously measured periods were included in our field of view.," However, many stars with previously measured periods were included in our field of view." + For example. many variable stars in the uncrowcded outer portions of M3 were studied here and by CCOI.," For example, many variable stars in the uncrowded outer portions of M3 were studied here and by CC01." + For each of these variable stars. the light curves associated with the repsective periods. were compared by PDALP analysis and by visual inspection.," For each of these variable stars, the light curves associated with the repsective periods were compared by PDMP analysis and by visual inspection." + In many cases the period. search algorithm was used on an interval that contained the ς01 period. and. exeluded: ours to ascertain whether the CCOL period was a secondary extremum in the PDMDP analysis of our data., In many cases the period search algorithm was used on an interval that contained the CC01 period and excluded ours to ascertain whether the CC01 period was a secondary extremum in the PDMP analysis of our data. + For each star studied by CCOL and included: in. our sample. we found that the period determined by our analysis eave a lit that matched or exceeded the fit obtained using the CCOL period.," For each star studied by CC01 and included in our sample, we found that the period determined by our analysis gave a fit that matched or exceeded the fit obtained using the CC01 period." + In the latter cases. though the CCOL period might have a larger number of decimal places. PDMP analysis and. visual inspection suggested that our periods were a better match than the CCOL periods to our data.," In the latter cases, though the CC01 period might have a larger number of decimal places, PDMP analysis and visual inspection suggested that our periods were a better match than the CC01 periods to our data." + In total. we found that 71 stars had. period dilferences of less than 0.001 d between our period and the CCOL period.," In total, we found that 71 stars had period differences of less than 0.001 d between our period and the CC01 period." + 'Pwenty-cight adcditiona stars had period differences of 0.001 d or more., Twenty-eight additional stars had period differences of 0.001 d or more. + Since M3 is an Oos erholE cluster. the expected period change rate )63) is relatively lowECCOL found that tvpically. /κdayMyr.+.," Since M3 is an Oosterhoff I cluster, the expected period change rate $\beta$ ) is relatively low–CC01 found that typically, $\beta < 1 \textrm{ day Myr}^{-1}$." + Thos. given that the CCOL periods were determined. using 1992-1997 data. it seems unlikely that more than a [ew of these dillerences could. be reasonably attributed to period changes.," Thus, given that the CC01 periods were determined using 1992-1997 data, it seems unlikely that more than a few of these differences could be reasonably attributed to period changes." + Lor seven of these 28 stars (v41. v148. v165. v170. v201. v209. «226) our periods agree with the COS or COL periods to within 0.001 d. Nine of the remaining 21 stars are listed as blends! by CCOL.," For seven of these 28 stars (v41, v148, v165, v170, v201, v209, v226) our periods agree with the C98 or C01 periods to within 0.001 d. Nine of the remaining 21 stars are listed as `blends' by CC01." + Their color index suggests the light of the variable star is mixed with that of a nearby non-variable star., Their color index suggests the light of the variable star is mixed with that of a nearby non-variable star. + Two additional stars merged. with other Πιν (v122 with v229. v241 with 262).," Two additional stars merged with other RRLs (v122 with v229, v241 with v262)." + This merging may have led to a somewhat higher uncertainty in the period., This merging may have led to a somewhat higher uncertainty in the period. + For these eleven stars. we could not make an unambiguous determination as o which period gave a superior fit.," For these eleven stars, we could not make an unambiguous determination as to which period gave a superior fit." + Seven of the remaining ten stars have noisy. published ight curves in CCOL, Seven of the remaining ten stars have noisy published light curves in CC01. + Two of these stars. (v193.. v235) iwl coverage too poor in our data set to make a definite determination between our period and the CCOL period.," Two of these stars (v193, v235) had coverage too poor in our data set to make a definite determination between our period and the CC01 period." + For each of the other five stars. we plotted the light curves for xh periods. ancl present them side by side for comparison in Figure 2.," For each of the other five stars, we plotted the light curves for both periods, and present them side by side for comparison in Figure 2." + Visual inspection of these light curves indicates hat our periods give superior results for each of these five stars., Visual inspection of these light curves indicates that our periods give superior results for each of these five stars. + Though three of these five stars (v161. v175. vist) jwe periods included in COL. neither our. periods nor those of CCOL agree with the COL periods to 0.001 d. Only three of the original 28 stars. with period discrepancies greater than 0.001 d have both clean published fight curves in CCOL anc clean light curves when phased with our periods.," Though three of these five stars (v161, v175, v184) have periods included in C01, neither our periods nor those of CC01 agree with the C01 periods to 0.001 d. Only three of the original 28 stars with period discrepancies greater than 0.001 d have both clean published light curves in CC01 and clean light curves when phased with our periods." + Further study of these variables. (v149. V208. v219) is needed to determine the correct. periods.," Further study of these variables (v149, v208, v219) is needed to determine the correct periods." + These consisteney. tests and the fact that the data spanned xetyveen. 200-400. cveles of most. variables Ied us to conclude hat our measured. periods were accurate to approximately 0001 d. In some cases our periods appear to be valid. to at least 0.00001 cd. and revised periods spanning many more eveles will be published in a future paper.," These consistency tests and the fact that the data spanned between 200-400 cycles of most variables led us to conclude that our measured periods were accurate to approximately 0.0001 d. In some cases our periods appear to be valid to at least 0.00001 d, and revised periods spanning many more cycles will be published in a future paper." + Therefore. all of he measured. period values in Tables 1: and 2 are rounded o four decimal places.," Therefore, all of the measured period values in Tables 1 and 2 are rounded to four decimal places." + Published values are rounded to four daces for comparison., Published values are rounded to four places for comparison. + Comments on some of the newly discovered. suspected. ancl previously known variable stars are given below.," Comments on some of the newly discovered, suspected, and previously known variable stars are given below." + Light curves for the newly cliscovered variables. labeled 81-811. are presented in Figure 3. unless no period could be determined.," Light curves for the newly discovered variables, labeled S1-S11, are presented in Figure 3, unless no period could be determined." + For five of these stars (S1. $2. 86. S9. 510). the quality of the photometry was too poor to ascertain with certainty that the stars were variable. and thus we label these suspected variable stars.," For five of these stars (S1, S2, S6, S9, S10), the quality of the photometry was too poor to ascertain with certainty that the stars were variable, and thus we label these suspected variable stars." + Additional study of these stars is needed to constrain our identifications ancl period determinations., Additional study of these stars is needed to constrain our identifications and period determinations. + RR Lyrac types are identified using the descriptive nomenclature of COL. based on pulsation modes.," RR Lyrae types are identified using the descriptive nomenclature of C01, based on pulsation modes." + In this system. RRO and RR denote fundamental ancl first overtone pulsators. respectively. ¢uxresponding to. Bailey tvpes RRab and Hc.," In this system, RR0 and RR1 denote fundamental and first overtone pulsators, respectively, corresponding to Bailey types RRab and RRc." + RROD refers to double-moce stars oulsating5 in both the fundamental ancl first) overtone frequencies. commonly called It stars.v29:," RR01 refers to double-mode stars pulsating in both the fundamental and first overtone frequencies, commonly called RRd stars.:" + ος01 misidentifies this star as v155. an error esent in aprevious paper (IEvstigneeva5ctal. 1994)..," CC01 misidentifies this star as v155, an error present in aprevious paper \citep{e94}. ." +The origin of the combination (p2)/(p—1) can be traced to equation CXI2)) in appendix A of this paper (2002))) actually absorb it into ce).,The origin of the combination $(p-2)/(p-1)$ can be traced to equation \ref{gamma_m_equation}) ) in appendix \ref{distro_section} of this paper \cite{Granot2002}) ) actually absorb it into $\epsilon_E$ ). + The term (17.44) is linked to the energy. Z5» and the two will always occur with the same power as can be seen from comparing tables Cl and 1.., The term $(17-4k)$ is linked to the energy $E_{52}$ and the two will always occur with the same power as can be seen from comparing tables \ref{coefficients_table} and \ref{scalings_table}. + Ht enters our calculations via equation (69) from (1976)., It enters our calculations via equation (69) from \cite{Blandford1976}. +. The term (4A) is likewise linked to the observer time ρα.," The term $(4-k)$ is likewise linked to the observer time $t_{obs,d}$." + Lhe extra term is a result from the transition from emission time in the erid lab [rame to observer time., The extra term is a result from the transition from emission time in the grid lab frame to observer time. + For the shock front the two are related via The final terms ave different for the dillerent. power law regimes., For the shock front the two are related via The final terms are different for the different power law regimes. + Γον are contributed by the leading order terms of the various approximations of Q., They are contributed by the leading order terms of the various approximations of $\mathcal{Q}$. + (Q is given by (see eqn. CXI6))):, $Q_+$ is given by (see eqn. \ref{Q_large_equation}) )): + For low uncooled frequencies we have as can be seen from equation CX15))., For low uncooled frequencies we have as can be seen from equation \ref{Q_small_equation}) ). + When cooling plavs a role we find that equation (D9)) provides us with Note that the elfect of ρω in Cr and Cp is to cancel out the first (p1) term -we only. kept both terms for clarity of presentation., When cooling plays a role we find that equation \ref{Q_cool_equation}) ) provides us with Note that the effect of $Q_{cool}$ in $C_E$ and $C_F$ is to cancel out the first $(p-1)$ term -we only kept both terms for clarity of presentation. +Looking bevond Jupiter and Saturn. we now have 200 extrasolar giant planets (EGDPs) that have been found to orbit other stars.,"Looking beyond Jupiter and Saturn, we now have 200 extrasolar giant planets (EGPs) that have been found to orbit other stars." + A subclass of these planets are the “hot Jupiters? that orbit (heir parent stars at around 0.05 AU., A subclass of these planets are the “hot Jupiters” that orbit their parent stars at around 0.05 AU. + To date. ten planets (with masses [from 0.36 to 1.5 Mj)) have been seen (ο transit their parents stars.," To date, ten planets (with masses from 0.36 to 1.5 ) have been seen to transit their parents stars." + All of these objects awe hot Jupiters. with orbital periods of onlv a lew davs (seeCharbonneauetal.2006).," All of these objects are hot Jupiters, with orbital periods of only a few days \citep[see][]{Charb06}." +. These transiting planets are important because we can measure (heir masses radi. thereby. allowing us access [o information on their interior structure (Guillot.2005).," These transiting planets are important because we can measure their masses radii, thereby allowing us access to information on their interior structure \citep{Guillot05}." +. While our understanding of the interiors of these planets will never be as detailed as (hat for Jupiter and Saturn. we will eventually have a very large sample of these transiting objects al various masses. compositions. and orbital distances. which will allow for an understanding of the massradius relation lor eiant planets under a variety of conditions.," While our understanding of the interiors of these planets will never be as detailed as that for Jupiter and Saturn, we will eventually have a very large sample of these transiting objects at various masses, compositions, and orbital distances, which will allow for an understanding of the mass–radius relation for giant planets under a variety of conditions." + By [ar the most important physical input into giant planet structural models is the equation of state (EOS) of hydrogen., By far the most important physical input into giant planet structural models is the equation of state (EOS) of hydrogen. + The decade of pressure (hat is most important. [or understanding the interiors of eiant planets is 1-10 Mbar (100-1000 Gpa) 2004)., The decade of pressure that is most important for understanding the interiors of giant planets is 1-10 Mbar (100-1000 Gpa) \citep{Saumon04}. +. In the past decade experiments have been able to probe into the lower end of this pressure range (Weiretal.1996:Collins1998:Ixnudson 2005).," In the past decade experiments have been able to probe into the lower end of this pressure range \citep{Weir96, Collins98, Knudson01, Boriskov05}." +. In this paper. instead. of focusing on equation of state physics we will focus on kev questions for understanding (he structure and composition of giant planets.," In this paper, instead of focusing on equation of state physics we will focus on key questions for understanding the structure and composition of giant planets." + As we discuss ejant planet interiors we will investigate how high pressure laboratory experiments have ancl will continue to allow us to better answer these questions., As we discuss giant planet interiors we will investigate how high pressure laboratory experiments have and will continue to allow us to better answer these questions. + This question is directly related to whether hydrogens molecular-(o-metallic transition is continuous or first-order., This question is directly related to whether hydrogen's molecular-to-metallic transition is continuous or first-order. + Whether or not hvdrogens transition to a metal in the {hud state is first order has always been an open issue., Whether or not hydrogen's transition to a metal in the fluid state is first order has always been an open issue. + The importance of this question to giant planets cannot be overstated., The importance of this question to giant planets cannot be overstated. +" If the transition is first order (a so-called. ""plasma phase transition."" or PPT) then there will be an impenetrable barrier to convection within the planet and (here must also be several discontinuities at this transition."," If the transition is first order (a so-called “plasma phase transition,” or PPT) then there will be an impenetrable barrier to convection within the planet and there must also be several discontinuities at this transition." + One is a discontinuity in entropy (Stevenson&Salpeter1977:SaumonChabrier1992).," One is a discontinuity in entropy \citep{SS77b, SC92}." +. In the 1970s. W. BD. IIubbad discussed. (hat. for a fully convective and adiabatic giant planet. a measurement of of the specific entropy in (he convective atmosphere would essentially allow us to understaixd the run of temperature vs. pressure for the entire planet. as all regions would share this specific entropy. (seeHubbard1973).," In the 1970s, W. B. Hubbard discussed that, for a fully convective and adiabatic giant planet, a measurement of of the specific entropy in the convective atmosphere would essentially allow us to understand the run of temperature vs. pressure for the entire planet, as all regions would share this specific entropy \citep[see][]{Hubbard73}." +. ILowever. if à PPT exists. this will not be true," However, if a PPT exists, this will not be true" +has a distinctly lower peak value.,has a distinctly lower peak value. + Early surface (rausport models (Devore.Boris&Sheeley1984:1989) were the first to use a latitudinal meridional (low profile peaking at low latitudes. in particular. 6 degrees. even before observations could tell us where (he flow peaks.," Early surface transport models \citep{dbs1984,wns1989} were the first to use a latitudinal meridional flow profile peaking at low latitudes, in particular, 6 degrees, even before observations could tell us where the flow peaks." + Such a peak eave the best fit of model-derived surface features wilh observations of surface magnetic fields., Such a low-latitude peak gave the best fit of model-derived surface features with observations of surface magnetic fields. + In future the much more extensive Doppler based observations of meridional flow can be used as input to both surface transport models and flux-tiranusport dvnamo models. capturing the low latitude peak now observed.," In future the much more extensive Doppler based observations of meridional flow can be used as input to both surface transport models and flux-transport dynamo models, capturing the low latitude peak now observed." + By contrast. the magnetic speed should be compared wilh the output of such models in order to estimate the surface magnetic diffusivity.," By contrast, the magnetic feature-tracking speed should be compared with the output of such models in order to estimate the surface magnetic diffusivity." + There is a tracking speed that might also be useful as input (o dvnamo and surface transport models., There is a tracking speed that might also be useful as input to dynamo and surface transport models. + That is (he tracking speed that comes [rom the Doppler signal of supereramiules (Svandaetal2008)., That is the tracking speed that comes from the Doppler signal of supergranules \citep{sksb2008}. +. It has been used to measure. differential rotation and. meridional circulation for solar cvele 23., It has been used to measure differential rotation and meridional circulation for solar cycle 23. + It will be useful to compare the details of flow profiles obtained bv this method with those obtained by more global surface Doppler as well as helioseisnic Measures., It will be useful to compare the details of flow profiles obtained by this method with those obtained by more global surface Doppler as well as helioseismic measures. + In most f[Iux-transport dynamo moclels. starting [rom Dikpati&Charbonneau(1999).. the poleward surface flow has generally been taken to be a maximum in midlatitude.," In most flux-transport dynamo models, starting from \citet{dc99}, the poleward surface flow has generally been taken to be a maximum in midlatitude." + So according to the qualitative reasoning eiven in Figure I. (he fields from the follower polarity separate out Irom the leader polarity at a faster rate (see Figure 1(0)) when the flow speed is increased.," So according to the qualitative reasoning given in Figure 1, the fields from the follower polarity separate out from the leader polarity at a faster rate (see Figure 1(c)) when the flow speed is increased." + Thus (here is less annihilation amone them: consequently the polar field increases., Thus there is less annihilation among them; consequently the polar field increases. + To test (his with flux-transport clvuamo simulations. we must take account of the fact that there are additional physical processes al work in (he model that will change the poloidal and toroidal fields in other parts of the clvnamo domain in response to a change in meridional flow.," To test this with flux-transport dynamo simulations, we must take account of the fact that there are additional physical processes at work in the model that will change the poloidal and toroidal fields in other parts of the dynamo domain in response to a change in meridional flow." + For example. if the flow Coward the poles at the top speeds up. the return flow near the bottom will also speed up.," For example, if the flow toward the poles at the top speeds up, the return flow near the bottom will also speed up." + This bottom flow then moves the poloidal field (here faster toward the equator. leaving less time to induce toroidal field at a particular latitude.," This bottom flow then moves the poloidal field there faster toward the equator, leaving less time to induce toroidal field at a particular latitude." + This reduction in bottom toroidal field in (urn leads to a reduced surface poloidal source., This reduction in bottom toroidal field in turn leads to a reduced surface poloidal source. + Which wins in determining whether (he polar fields increase or decrease?, Which wins in determining whether the polar fields increase or decrease? + In Figure 2a we show results from new sinmlations with our flux-transport dvnamo model using ingredients verv similar to, In Figure 2a we show results from new simulations with our flux-transport dynamo model using ingredients very similar to +"is sone ixultiple Jof the ISCO located at R,/e.",is some multiple $\beta$ of the ISCO located at $R_g/\epsilon$. + Within a dvuaimical time. the disk becomes viscous and — for lack of a better choice he viscosity can be approximated by the usual £oc (Shakira Suuvaev 1973).," Within a dynamical time, the disk becomes viscous and – for lack of a better choice – the viscosity can be approximated by the usual $\nu\sim \alpha c_s H$ (Shakura Sunyaev 1973)." +" The viscous time f, doeteriunes the characteristic duration of the event.", The viscous time $t_{\nu}$ determines the characteristic duration of the event. + Since the radiation cooling time is long in colparison to the viscous time. the flow is likely to be geometrically thick ie. the vertical scale height II~R with sound speed «2~GAL/R.," Since the radiation cooling time is long in comparison to the viscous time, the flow is likely to be geometrically thick i.e., the vertical scale height $H\sim R$ with sound speed $c^2_s\sim +GM_{\bullet}/R$." + Iu terms of these paraimoeters.the viscous time is given by — R," In terms of these parameters,the viscous time is given by = ." +"7————dea (11) Reasonable changes in € aud Jj lead to comparable values of f, for a variation of ~10 in A4.", Reasonable changes in $\epsilon$ and $\beta$ lead to comparable values of $t_{\nu}$ for a variation of $\sim 10$ in $M_{\bullet}$. +" Reported παπααν timescales of ~LOO s indicate that AM,~ LOCAL...", Reported variability timescales of $\sim 100$ s indicate that $M_{\bullet}\sim 10^7M_{\odot}$ . + The size of the host galaxy further supports tle Usnall black hole hypothesis., The size of the host galaxy further supports the “small” black hole hypothesis. +" If LAL. worth of material is swallowed with radiative cficicncey €~0.2. then the event can support a luminosity L-10/7 ore/s for 3«109 s. I£ AL,~LOCAL... then ὃς consistent with the high cud of Eddiustou ratios for L/L,,extra-galactic IINUXD«."," If $\sim 1\,M_{\odot}$ worth of material is swallowed with radiative efficiency $\epsilon\sim 0.2$, then the event can support a luminosity $L\sim 10^{47}$ erg/s for $3\times 10^6$ s. If $M_{\bullet}\sim 10^7M_{\odot}$, then $L/L_{_{\rm Edd}}$ is consistent with the high end of Eddington ratios for extra-galactic HMXBs." + Since LL4; hydrostatic balance is broken in the absence of other forces (e.g. magnetic fields anchored deep in the cold dense disk SDOG).," Since $L>L_{_{\rm Edd}}$, hydrostatic balance is broken in the absence of other forces (e.g., magnetic fields anchored deep in the cold dense disk SD06)." +" A Compton radiatiou-driven wind develops aud even for a suuiall black hole with M,~WAL... the total compactness (=eL/L,.,, is ouly LO."," A Compton radiation-driven wind develops and even for a small black hole with $M_{\bullet}\sim 10^7M_{\odot}$, the total compactness $\ell\equiv\epsilon L/L_{_{\rm Edd}}$ is only $\sim 10$." + Under these couditious. a Compton-diiven wind is inefficient at converting the input photon huninosity ito bulk wind power (Madau Thompson 2000).," Under these conditions, a Compton-driven wind is inefficient at converting the input photon luminosity into bulk wind power (Madau Thompson 2000)." + On energetic erounds. a heavily Comptonized medium is unable to cficicutly launch a powerful wind since. by coustruction. the clectrous are donating enerev to the photons as they attempt to they eain moment from them (Phinney 1982).," On energetic grounds, a heavily Comptonized medium is unable to efficiently launch a powerful wind since, by construction, the electrons are donating energy to the photons as they attempt to they gain momentum from them (Phinney 1982)." + Along with the low coronal optical depth z.. which nuples that adiabatic are uot catastrophic. it seenis reasonable that a losses105AL. black hole can accrete a stellar mass in ~LO s with hieh radiative efficieucy as long as a fraction f of the binding cucrev dissipated in the corona is z1.," Along with the low coronal optical depth $\tau_c$, which implies that adiabatic losses are not catastrophic, it seems reasonable that a $\sim 10^7\,M_{\odot}$ black hole can accrete a stellar mass in $\sim 10^6$ s with high radiative efficiency as long as a fraction $f$ of the binding energy dissipated in the corona is $\approx 1$." + The observed shape of the photou spectrum resenibles those of the brightest ULNs ie. a flat power-law in N-ravs.," The observed shape of the photon spectrum resembles those of the brightest ULXs i.e., a flat power-law in X-rays." + The ceutral οποίον source of Sw JI6111257 is heavily obscured., The central energy source of Sw J1644+57 is heavily obscured. + It is almost a certainty that. due to energv conservation. all of dust-obscured photon power will be re-enütted iu the IR wavebauds at some later time.," It is almost a certainty that, due to energy conservation, all of dust-obscured photon power will be re-emitted in the IR wavebands at some later time." + If the source is an isotropic ciuitter. such as the ULA-E model preseuted here. the total energy cinitted iu the IR is likely to exceed that of a beamed jet model.," If the source is an isotropic emitter, such as the ULX-E model presented here, the total energy emitted in the IR is likely to exceed that of a beamed jet model." + If a sizeable fraction of 1079 eres is absorbed by dust. then the reprocessed IR emissiou will casily out-shine the host as long as the thermal relaxation time of the dusty iiecium does not exceed several decades.," If a sizeable fraction of $10^{53}$ ergs is absorbed by dust, then the reprocessed IR emission will easily out-shine the host as long as the thermal relaxation time of the dusty medium does not exceed several decades." + As stellar debris draius iuto the black hole. the rate of accretion drops. as docs 7 of the deuse disk aud the bulk of the flow is eventually able to radiate efficientlv.," As stellar debris drains into the black hole, the rate of accretion drops, as does $\tau$ of the dense disk and the bulk of the flow is eventually able to radiate efficiently." + Sub-Eddington ACN and BUBs possess spectra that show strong thermal ciuission., Sub-Eddington AGN and BHBs possess spectra that show strong thermal emission. +" Once the accretion power drops vclow the Eddinetou Limit. the characteristic energy of he disk photons ~50 eV for Af,~LOCAL..."," Once the accretion power drops below the Eddington Limit, the characteristic energy of the disk photons $\sim 50$ eV for $M_{\bullet}\sim 10^7M_{\odot}$." + There may © Chough optical-UV. power in the thermal component at later times so that the ceutral source out-shines the rost galaxy., There may be enough optical-UV power in the thermal component at later times so that the central source out-shines the host galaxy. + Epochs of intense aud highly variable flaring N-ray power as well as radio cussion (Cüanuios Motzgor 2011). are most likely due to the production of a 1ος at early times.," Epochs of intense and highly variable flaring X-ray power as well as radio emission (Giannios Metzger 2011), are most likely due to the production of a jet at early times." + Swiffs wide-field BAT instrament was rigecred by these bright faring events. rather than the relatively dim persistent radiative cinissiou responsible or the bulk ofthe energy release AFy.," 's wide-field BAT instrument was triggered by these bright flaring events, rather than the relatively dim persistent radiative emission responsible for the bulk of the energy release $\Delta E_X$." + Ifthe jet openine- is sufficiently sinall. then the rate of tidal disruption events are in line with theoretical expectations (Blooms ot al.," If the jet opening-angle is sufficiently small, then the rate of tidal disruption events are in line with theoretical expectations (Bloom et al." + 2011: Burrows et al., 2011; Burrows et al. + 2011: see Magorriau Tremaine L999)., 2011; see Magorrian Tremaine 1999). + Even for sub-Eddinegton accretion flows. the nature of the transport mechauisin that enereizes the corona has uot been identified for thirty-five vears (e.g. Shapiro et al," Even for sub-Eddington accretion flows, the nature of the transport mechanism that energizes the corona has not been identified for thirty-five years (e.g., Shapiro et al." + 1976)., 1976). + Possibilities include magnetic buovaucy (Caleev ct al., Possibilities include magnetic buoyancy (Galeev et al. + 1979). wave excitation and turbulence (Socrates et al.," 1979), wave excitation and turbulence (Socrates et al." + 200 Thompson 2006)., 2004; Thompson 2006). + The high compactness of black hole aud neutrou star accretion Hows in comparison to other astroplivsical svstenis nay explain why their inferred value of f is so high (Goodman Uzceusky: Socrates 2010)., The high compactness of black hole and neutron star accretion flows in comparison to other astrophysical systems may explain why their inferred value of $f$ is so high (Goodman Uzdensky; Socrates 2010). + Nevertheless. he distance between a robust aud testable theory that quantifies the fractionf of binding energy dissipated im he corona aud our curent understandius sccms far.," Nevertheless, the distance between a robust and testable theory that quantifies the fraction of binding energy dissipated in the corona and our current understanding seems far." + The possibility that Sw JI1GIL]57 is powered by coroual enereizatiou reiuforces the general desire to ideutifv the physical πουλάστα» that power Conmptonized radiation of relativistic accretion flows., The possibility that Sw J1644+57 is powered by coronal energization reinforces the general desire to identify the physical mechanisms that power Comptonized radiation of relativistic accretion flows. + Let tage=Rog aud fag=rife where and AM is the accretion rate., Let $t_{\rm adv}\equiv R/v_R$ and $t_{\rm diff}\equiv \tau H/c$ where and $\dot{M}$ is the accretion rate. + Compute the ratio, Compute the ratio +the Holmberg diameter. compared to ~8.8 times the Holmberg diameter measured with the GMRT data alone.,"the Holmberg diameter, compared to $\sim8.3$ times the Holmberg diameter measured with the GMRT data alone." + In Paper T we had noted that NGC 3741 seemed to have a central bar. but this is not apparent in the lower resolution image in Fig. |.," In Paper I we had noted that NGC 3741 seemed to have a central bar, but this is not apparent in the lower resolution image in Fig. \ref{fig:overlay}." + On the other hand. the ΙΟ resolution image (Fig. H[[," On the other hand, the $^{''}$ resolution image (Fig. \ref{fig:overlay}[ [" +C]) shows the central bar clearly. and also shows a large one sided spiral arm of —9 (with no stellar counter part) on the western side of the galaxy. emanating from a central bar like region.,"C]) shows the central bar clearly, and also shows a large one sided spiral arm of $\sim$ $^\prime$ (with no stellar counter part) on the western side of the galaxy, emanating from a central bar like region." + A presence of an HI bar is also evident in the high resolution velocity field (Figure 2[[B] here and Figure.1[B] in Paper D from the oval distortion of the isovelocity contours in the center of the galaxy., A presence of an HI bar is also evident in the high resolution velocity field (Figure \ref{fig:mom1}[ [B] here and Figure.1[B] in Paper I) from the oval distortion of the isovelocity contours in the center of the galaxy. + Further. Gentile et αἱ007) also found evidence for a bar at the centre of this galaxy based on a harmonic decomposition of the velocity field.," Further, Gentile et al.(2007) also found evidence for a bar at the centre of this galaxy based on a harmonic decomposition of the velocity field." + On the other hand. near infra-red images of this galaxy shows no evidence for a stellar bar.," On the other hand, near infra-red images of this galaxy shows no evidence for a stellar bar." + Figure. | [[, Figure. \ref{fig:overlay}[ [ +B] shows the 10 resolution HI distribution (contours) overlayed on the J band emission (greyscale) from. Vaduvescu et al.(2005).,B] shows the $^{''}$ resolution HI distribution (contours) overlayed on the J band emission (greyscale) from Vaduvescu et al.(2005). +. Vaduvescu et al.(C2005) estimated an ellipticity and PA of the near infra-red disk emission to be 0.26 and 23 deg respectively., Vaduvescu et al.(2005) estimated an ellipticity and PA of the near infra-red disk emission to be 0.26 and 23 deg respectively. + On the other hand. PA and ellipticity of the HI bar derived from 10 resolution HI map is [OzES deg and 0.650.10.," On the other hand, PA and ellipticity of the HI bar derived from $^{''}$ resolution HI map is $-$ $\pm$ 5 deg and $\pm0.10$." + Thus. while the optical morphology of NGC 3741 implies a disk structure (Vaduvescu et αἱ2005). our HI data suggest a bar configuration in the center of the galaxy.," Thus, while the optical morphology of NGC 3741 implies a disk structure (Vaduvescu et al.(2005)), our HI data suggest a bar configuration in the center of the galaxy." + Such difference in the optical and HI morphology has been noted previously in a blue compact dwarf galaxy NGC 2915 (Meurer et al., Such difference in the optical and HI morphology has been noted previously in a blue compact dwarf galaxy NGC 2915 (Meurer et al. + 1996)., 1996). +" The velocity field of NGC 3741. as derived from a moment analysis of 71""TL” resolution data cube. is shown in Fig. 2[["," The velocity field of NGC 3741, as derived from a moment analysis of $''\times 71''$ resolution data cube, is shown in Fig. \ref{fig:mom1}[ [" +A].,A]. +viewing direction was chosen randomly here).,viewing direction was chosen randomly here). + However. when the estimators are not weighted (i.c. if equations 4 and 5 are used directIv). the computed light curve is significantIv overestimated at early. times («20 cays. in this case)," However, when the estimators are not weighted (i.e. if equations 4 and 5 are used directly), the computed light curve is significantly overestimated at early times $< 20$ days, in this case)." + As discussed. in Section 2.4. this is because the eric cells of the model are optically thick at early times: the maximum optical depth across one grid cell is plotted. as a function of time. in Figure 2.," As discussed in Section 2.4, this is because the grid cells of the model are optically thick at early times; the maximum optical depth across one grid cell is plotted, as a function of time, in Figure 2." + This shows that significant errors arise if the unweighted estimators are used when this optical depth is Tear 1., This shows that significant errors arise if the unweighted estimators are used when this optical depth is $\tau_{\mbox{\scriptsize cell}} > 1$ . + The 5-ray spectrum is obtained following the same principles as that used for the Light curve described above., The $\gamma$ -ray spectrum is obtained following the same principles as that used for the light curve described above. + The important dillerence being that the treatment of 5-rays is ull frequeney dependent., The important difference being that the treatment of $\gamma$ -rays is fully frequency dependent. + To deal with the frequency dependence. a grid. of requeney points is used. to divide the spectrum into small requency intervals.," To deal with the frequency dependence, a grid of frequency points is used to divide the spectrum into small frequency intervals." + One point in this grid is set to the rest [requeney of cach of the radioactive *5-rav emission ines in the range of interest and the remaining points are spaced logarithmically between., One point in this grid is set to the rest frequency of each of the radioactive $\gamma$ -ray emission lines in the range of interest and the remaining points are spaced logarithmically between. + To compute the spectrum. he same scheme of solving the radiative transfer equation along à set of rays trajectories through the model is used.," To compute the spectrum, the same scheme of solving the radiative transfer equation along a set of rays trajectories through the model is used." + Llere. however. the radiative transfer along each trajectory is computed. multiple times. once for cach frequency point in the frequency grid. thereby. determining the emergent radiation field as a function of both frequency and time.," Here, however, the radiative transfer along each trajectory is computed multiple times, once for each frequency point in the frequency grid, thereby determining the emergent radiation field as a function of both frequency and time." + As for the greyv-computations described. above. the opacity term in the radiative transfer equation. is known (the sum of Compton ancl photoelectric terms).," As for the grey-computations described above, the opacity term in the radiative transfer equation is known (the sum of Compton and photoelectric terms)." + Phere are again two emissivity terms which need. to be considered., There are again two emissivity terms which need to be considered. + The first. direct emission of ανν by radioactive decay can also be expressed analytically for every. eric cell in terms of the half-lives of the radioactive isotopes and their initial concentrations in the cell.," The first, direct emission of $\gamma$ -rays by radioactive decay can also be expressed analytically for every grid cell in terms of the half-lives of the radioactive isotopes and their initial concentrations in the cell." + The second. emissivity term is due to Compton down-scattering., The second emissivity term is due to Compton down-scattering. + The treatment of this term requires that both the angular- and. frequencv-dependence. of the Compton process be considered., The treatment of this term requires that both the angular- and frequency-dependence of the Compton process be considered. + Lt is determined via a set Monte Carlo estimators (one per frequeney interval per grid cell per time step): the estimator for the frequency. interval ¢ in the eric cell j for timestep & is given (in the observer rame) by where the sumruns over all 5-rav. trajectories which lie in cell j (having volume V;) and have frequency appropriate for scattering into the frequency interval £ (of width Av) during the timestep & (which has duration 2M)., It is determined via a set Monte Carlo estimators (one per frequency interval per grid cell per time step); the estimator for the frequency interval $i$ in the grid cell $j$ for timestep $k$ is given (in the observer frame) by where the sumruns over all $\gamma$ -ray trajectories which lie in cell $j$ (having volume $V_{j}$ ) and have frequency appropriate for scattering into the frequency interval $i$ (of width $\Delta\nu$ ) during the timestep $k$ (which has duration $\Delta t_{k}$ ). + n. is the number density of target electrons in the cell. ο is the observer-frame energy of the 5-ray. packet and (σαν is the Compton dilferential cross-section for scattering into the direction of the line-of-s1ght (2) in the observer frame.," $n_{e}$ is the number density of target electrons in the cell, $\epsilon$ is the observer-frame energy of the $\gamma$ -ray packet and $\left({{\d \sigma}/{\d \Omega}}\right)_{\mbox{\scriptsize obs}}$ is the Compton differential cross-section for scattering into the direction of the line-of-sight ) in the observer frame." + This cross-section depends upon the angle between the trajectory and αμα is determined by applying the IxIein-Nishina formula for the cross-section in the co-moving frame., This cross-section depends upon the angle between the trajectory and and is determined by applying the Klein-Nishina formula for the cross-section in the co-moving frame. + In this section. two toy models of elliptical supernovae are used to investigate possible observational consequences of large scale asphericity in supernova explosions.," In this section, two toy models of elliptical supernovae are used to investigate possible observational consequences of large scale asphericity in supernova explosions." + Such an investigation is motivated by observational evidence for global asphericity in SNla obtained via polarimetry (sec e.g. Lowell ct al., Such an investigation is motivated by observational evidence for global asphericity in SNIa obtained via polarimetry (see e.g. Howell et al. + 2001: Wang ct al., 2001; Wang et al. + 2003)., 2003). + The origin of this asphericity is not well known: mostly likely it is determined by the details of the explosion process itself but may have its roots in the properties of a rapidly rotating progenitor., The origin of this asphericity is not well known: mostly likely it is determined by the details of the explosion process itself but may have its roots in the properties of a rapidly rotating progenitor. + Lere. however. the objective is not to gain insight to the physical origin of such a geometry but rather to study how it might οσο both the amplitude ancl shape of observec light curves in Comparison with spherical explosions.," Here, however, the objective is not to gain insight to the physical origin of such a geometry but rather to study how it might effect both the amplitude and shape of observed light curves in comparison with spherical explosions." + Earlier calculations of radiation transport in elliptica supernovae have been discussed by Hólilich (1991)., Earlier calculations of radiation transport in elliptical supernovae have been discussed by Höfflich (1991). + In tha work. a multi-dimensional Monte Carlo code was also used.," In that work, a multi-dimensional Monte Carlo code was also used." + However. the treatment of energy packet ecnerallon anc emission was simplified. via the use of a parameterisec photosphere in contrast to the full treatment of >-transpor ancl deposition emploved here.," However, the treatment of energy packet generation and emission was simplified via the use of a parameterised photosphere in contrast to the full treatment of $\gamma$ -transport and deposition employed here." + A simple. elliptical. model has been. constructed. closely related to the spherical model used as a test. case. in Section 2.," A simple elliptical model has been constructed, closely related to the spherical model used as a test case in Section 2." +" The adopted model has the same total mass ancl sume ""Ni mass as the spherical model.", The adopted model has the same total mass and same $^{56}$ Ni mass as the spherical model. + It is also assumed to be in homologous expansion and to have uniform density., It is also assumed to be in homologous expansion and to have uniform density. + Llowever. the maximum velocity (and hence spatial extent) is taken to be smaller in the z-direction than in the a and y- (symmetry is still assumed under rotation about the z-axis).," However, the maximum velocity (and hence spatial extent) is taken to be smaller in the $z$ -direction than in the $x$ - and $y$ -directions (symmetry is still assumed under rotation about the $z$ -axis)." + Such a mocel is intended as a simple description [or cases in which either the explosion. mechanism or the properties of the progenitor lead to a large-scale (low angular mode) departure from sphericity., Such a model is intended as a simple description for cases in which either the explosion mechanism or the properties of the progenitor lead to a large-scale (low angular mode) departure from sphericity. + Two particular realisations of the model will. be considered here., Two particular realisations of the model will be considered here. + For both the maximum velocity in the wr ane g-directions was kept at 10° em ο., For both the maximum velocity in the $x$ - and$y$ -directions was kept at $^9$ cm $^{-1}$ . + Phe models dilfer in the chosen maximum velocity in the z-direction: for one. this velocity was fixed at 5.r10 em thereby giving," The models differ in the chosen maximum velocity in the $z$ -direction: for one, this velocity was fixed at $5 \times 10^{8}$ cm $^{-1}$ , thereby giving" +"hand, reddening caused by any non-DLA absorption systems would statistically cancel out when the composite of absorber sample is compared with that of the matching non-DLA sample, giving an estimate of reddening due to the DLAs alone.","hand, reddening caused by any non-DLA absorption systems would statistically cancel out when the composite of absorber sample is compared with that of the matching non-DLA sample, giving an estimate of reddening due to the DLAs alone." +" For compiling the matching non-absorber sample, we selected from DR7, QSOs without any absorption systems of grade A and B. We chose to ignore any grade C, D, E systems that may be present in the QSO spectra as these are not likely to produce significant reddening as noted by Y06."," For compiling the matching non-absorber sample, we selected from DR7, QSOs without any absorption systems of grade A and B. We chose to ignore any grade C, D, E systems that may be present in the QSO spectra as these are not likely to produce significant reddening as noted by Y06." + Details of the system grades can be found in Y06., Details of the system grades can be found in Y06. + In Fig.2 we have plotted the difference in M; and Zem between the full sample S1 and the corresponding non-absorber sample., In Fig.2 we have plotted the difference in $_i$ and $_{em}$ between the full sample S1 and the corresponding non-absorber sample. +" For some QSOs, differences are large, reaching up to > 1."," For some QSOs, differences are large, reaching up to $>$ 1." +" As identification of absorption systems is difficult in the spectra of faint QSOs (which have smaller S/N) we constructed a subsample of S1 having QSOs with Galactic extinction corrected, i magnitude < 19.5 so that the S/N of the corresponding non-absorber spectra will be sufficiently high to ascertain the absence of absorption systems."," As identification of absorption systems is difficult in the spectra of faint QSOs (which have smaller S/N) we constructed a subsample of S1 having QSOs with Galactic extinction corrected, i magnitude $<$ 19.5 so that the S/N of the corresponding non-absorber spectra will be sufficiently high to ascertain the absence of absorption systems." + This subsample of S1 (S2) has 847 systems., This subsample of S1 (S2) has 847 systems. +" The values of the differences in M; and Zem of the pairs of QSOs in the absorber subsample S2 and the corresponding non-absorber sample are also as large as those for S1, and the match between M; and Ze; of the absorber and non-absorber QSO pairs is not as good as that obtained for the lower redshift Mg II sample of Y06 or the non-DLA-absorber sample of FP10."," The values of the differences in $_i$ and $_{em}$ of the pairs of QSOs in the absorber subsample S2 and the corresponding non-absorber sample are also as large as those for S1, and the match between $_i$ and $_{em}$ of the absorber and non-absorber QSO pairs is not as good as that obtained for the lower redshift Mg II sample of Y06 or the non-DLA-absorber sample of FP10." +" For better comparison of the composites, we therefore, chose two subsamples: S3 having 545 systems with | AM;|<0.1 and |Azem|«0.05 and S4 having 609 systems with |AM,|«0.15 and |Azem|«0.1."," For better comparison of the composites, we therefore, chose two subsamples: S3 having 545 systems with $|\Delta$ $_i|<0.1$ and $|\Delta$ $_{em}| < 0.05$ and S4 having 609 systems with $|\Delta$ $_i|<0.15$ and $|\Delta$ $_{em}| < 0.1$." + The redshift distributions for these subsamples are also shown in Fig.l., The redshift distributions for these subsamples are also shown in Fig.1. + About of the systems in these subsamples also have their redshifts between 2.25 and 4., About of the systems in these subsamples also have their redshifts between 2.25 and 4. + The points corresponding to subsample S3 are shown in red in Fig.2., The points corresponding to subsample S3 are shown in red in Fig.2. +" The histograms showing the distributions of |AM;| and |Az-,,| for these subsamples are shown in Fig.3.", The histograms showing the distributions of $|\Delta$ $_i|$ and $|\Delta$ $_{em}|$ for these subsamples are shown in Fig.3. + The values are mostly small and the subsamples can be used to get reliable estimates of reddening., The values are mostly small and the subsamples can be used to get reliable estimates of reddening. + We constructed the matching sample of non-DLAs in similar way., We constructed the matching sample of non-DLAs in similar way. +" The number of non-DLAs in SDSS DR7 being very large, better matches were obtained between the parameters of the QSOs in S1 and those of the matching non-DLA QSOs, with |Azem| and |AM;| being smaller than 0.32 and 0.4 respectively."," The number of non-DLAs in SDSS DR7 being very large, better matches were obtained between the parameters of the QSOs in S1 and those of the matching non-DLA QSOs, with $|\Delta$ $_{em}|$ and $|\Delta$ $_i|$ being smaller than 0.32 and 0.4 respectively." +that. for galaxies in the Poulain et al.,"that, for galaxies in the Poulain et al." + sample. around a half of those classified as I2 by. visual inspection of survey plates have Poulain et al.," sample, around a half of those classified as E by visual inspection of survey plates have Poulain et al." + types 80 or later., types S0 or later. + Spectroscopic observations were made using the 2.5m Isaac Newton Telescope (INT) on La Palma. in 1993 ancl 1994.," Spectroscopic observations were made using the 2.5m Isaac Newton Telescope (INT) on La Palma, in 1993 and 1994." + Dillerent detectors were used in each run: an LEW CCD in 1993. and the faster “PEW CCD in 1994.," Different detectors were used in each run: an EEV CCD in 1993, and the faster TEK CCD in 1994." + An EEV chip was used for one night of the 1994 run. due to technical problems.," An EEV chip was used for one night of the 1994 run, due to technical problems." + “Phis resulted in three spectroscopic datasets (hereafter denoted EEV93. EEVOL. TEINX94). which were cach treated separately. during the course of the data reduction.," This resulted in three spectroscopic datasets (hereafter denoted EEV93, EEV94, TEK94), which were each treated separately during the course of the data reduction." + Instrumental details for the three catasets are summarised in Table 3.., Instrumental details for the three datasets are summarised in Table \ref{instruments}. + Initial reduction of the CCD frames involved. bias and clark current subtraction. the removal of pixel-to-pixel sensitivity variations (using Hat field exposures provided by a tungsten calibration lamp) and correction for vignetting along the slit (using twilight skv-line exposures).," Initial reduction of the CCD frames involved bias and dark current subtraction, the removal of pixel-to-pixel sensitivity variations (using flat field exposures provided by a tungsten calibration lamp) and correction for vignetting along the slit (using twilight sky-line exposures)." + The spectra obtained covered 21000: ccentred. on the Aleb triplet. and were sampled with a resolution of X FEWLAL.," The spectra obtained covered $\sim$ centred on the Mgb triplet, and were sampled with a resolution of $\sim$ FWHM." + Wavelength calibration was performed using arelamp exposures. taken regularly in the course of the observations. ancl always after movement [from one cluster or region to another.," Wavelength calibration was performed using arc–lamp exposures, taken regularly in the course of the observations, and always after movement from one cluster or region to another." + A cubic fit between pixel number and wavelength for ~1S arc lines gave a maximum rms calibration error of ~O.LA.., A cubic fit between pixel number and wavelength for $\sim$ 18 arc lines gave a maximum rms calibration error of $\sim$. + Spectra were extracted from the frames by simple co-addition of the central 5 rows of the galaxy., Spectra were extracted from the frames by simple co-addition of the central 5 rows of the galaxy. + The resulting effective. aperture size is tabulatecl for. cach dataset. in ‘Table 3..., The resulting effective aperture size is tabulated for each dataset in Table \ref{instruments}. + After. application of a medianfilter to remove cosmic rav events. the carkest rows on the frame were usec to produce a sky spectrum.," After application of a median–filter to remove cosmic ray events, the darkest rows on the frame were used to produce a sky spectrum." + For some galaxies in the ELV9O3 dataset. sulficien signal-to-noise could be obtained only by co-accding spectra resulting from two separate exposures.," For some galaxies in the EEV93 dataset, sufficient signal-to-noise could be obtained only by co-adding spectra resulting from two separate exposures." + In almost all of these cases. the two exposures were taken in immediate subsequence. ensuring the validity of the co-adcdition.," In almost all of these cases, the two exposures were taken in immediate subsequence, ensuring the validity of the co-addition." + Cosmic ray events in the galaxy spectra were removec by a combination of automatic procedures before extraction. and interactive methods. applied. at. the onc-cimensiona spectrum stage.," Cosmic ray events in the galaxy spectra were removed by a combination of automatic procedures before extraction, and interactive methods applied at the one-dimensional spectrum stage." + Features in the spectrum resulting [rom noise in the subtraction of skv.line features (especially a 5577A)) were similarly removed after extraction., Features in the spectrum resulting from noise in the subtraction of sky–line features (especially at ) were similarly removed after extraction. + On cach run. spectra were obtained. for several Gs to WS giant stars. for use as template spectra.," On each run, spectra were obtained for several G8 to K3 giant stars, for use as template spectra." + These stars were trailed across the slit at a shallow anele during the exposure. to produce an extended illumination.," These stars were trailed across the slit at a shallow angle during the exposure, to produce an extended illumination." + Subsequent weighting of these frames. by a typical galaxy profile. effects a simulated observation of a galaxy with zero velocity dispersion.," Subsequent weighting of these frames, by a typical galaxy profile, effects a simulated observation of a galaxy with zero velocity dispersion." + The extension of illumination has the elfect. of woadening the stellar spectra by ~30to., The extension of illumination has the effect of broadening the stellar spectra by $\sim 30$. + The method. used. lor measurement of the velocity dispersion. σ. for cach galaxy. is based upon the well-known Fourier Quotient method of Sargent et al. (," The method used for measurement of the velocity dispersion, $\sigma$, for each galaxy, is based upon the well-known Fourier Quotient method of Sargent et al. (" +1977).,1977). + Lo »eparation for the application of this procedure. continum evels were subtracted from both the template spectrum and he galaxy spectrum. and both were submitted to a cosine xl modulation to fix the spectrum ends to zero.," In preparation for the application of this procedure, continuum levels were subtracted from both the template spectrum and the galaxy spectrum, and both were submitted to a cosine bell modulation to fix the spectrum ends to zero." + The latter step is necessary to avoid unphysical signals appearing at all requencies in the Fourier Transform., The latter step is necessary to avoid unphysical signals appearing at all frequencies in the Fourier Transforms. + The method requires also the removal from the spectra of signals resulting from noise. inadequate continuum removal and the application of the cosine bell.," The method requires also the removal from the spectra of signals resulting from noise, inadequate continuum removal and the application of the cosine bell." + Firstly. a cut is made at high frequencies. to remove noise.," Firstly, a cut is made at high frequencies, to remove noise." + The results of this method. seem to be fairly insensitive to the exact value. ημων. chosen for the high frequency. cut.," The results of this method seem to be fairly insensitive to the exact value, $k_{\rm{high}}$, chosen for the high frequency cut." + Anion=200z (5A)+ has been used throughout., $k_{\rm{high}} = 200\ \approx(5$ $)^{-1}$ has been used throughout. + Furthermore. a low frequency. filter must. be applied. to remove residual continuum features. and the effects of the cosine-bell modulation function described above.," Furthermore, a low frequency filter must be applied to remove residual continuum features, and the effects of the cosine-bell modulation function described above." + With the low-frequency eut. however. results are found. to exhibit a clear trend: velocity dispersions are measured to be smaller when Aya. is higher.," With the low-frequency cut, however, results are found to exhibit a clear trend: velocity dispersions are measured to be smaller when $k_{\rm{low}}$ is higher." + One must choose the cutoll (requenevy with care., One must choose the cutoff frequency with care. + The highest sensible Aya. is that which would preserve spectral features in spectra of velocity. dispersion <500, The highest sensible $k_{\rm{low}}$ is that which would preserve spectral features in spectra of velocity dispersion $\leq500$. + This is fiw=9 zm(110A) for our spectra.," This is $k_{\rm{low}} = +9$ $\approx(110{\rm \AA})^{-1}$ for our spectra." + “Phe lowest sensible Aj; is that which is necessary to remove the signal of the cosine-bell modulation., The lowest sensible $k_{\rm{low}}$ is that which is necessary to remove the signal of the cosine-bell modulation. + This is, This is +method (Tonry Davis. 1979). where robust measurements were obtained for galaxy spectra dominated by either emission lines or absorption lines.,"method (Tonry Davis, 1979), where robust measurements were obtained for galaxy spectra dominated by either emission lines or absorption lines." + For spectra dominated by absorption lines. we used galaxy templates anc stellar radial velocity standards. while for emission-line dominated spectra we used a synthetic template generated by the IRAF packagelinespec.," For spectra dominated by absorption lines, we used galaxy templates and stellar radial velocity standards, while for emission-line dominated spectra we used a synthetic template generated by the IRAF package." + Starting from a list of the stronger emission lines (Hf. [OIII]. [OI]. Ha. [NIL]. [SII]). the package creates a synthetic spectrum. which was then convolved with the instrumental A confidence parameter (see Kurtz Mink (1998) for a complete discussion) was used to assess the goodness of the estimated redshift: all redshifts with a confidence parameter > 5 were considered reliable. while measurements with 2.5 € € 5 were checked by hand.," Starting from a list of the stronger emission lines $\beta$, [OIII], [OI], $\alpha$, [NII], [SII]), the package creates a synthetic spectrum, which was then convolved with the instrumental A confidence parameter (see Kurtz Mink (1998) for a complete discussion) was used to assess the goodness of the estimated redshift: all redshifts with a confidence parameter $\ge$ 5 were considered reliable, while measurements with 2.5 $\le$ $\le$ 5 were checked by hand." + Measurements with < 2.5 are not reliable., Measurements with $\le$ 2.5 are not reliable. + All the confirmed member galaxies in our sample had ar> 3.3., All the confirmed member galaxies in our sample had a $>$ 3.5. + In some cases. failed to correctly identify the emission lines. which happened each time some emission lines were contaminated by underlying absorption.," In some cases, failed to correctly identify the emission lines, which happened each time some emission lines were contaminated by underlying absorption." + When this occurred. we measured the redshift by gaussian fitting the strongest emission lines visible and took the average of the results obtained from each line.," When this occurred, we measured the redshift by gaussian fitting the strongest emission lines visible and took the average of the results obtained from each line." + If two or more lines were blended. the IRAF command within thesplot package was The recession velocity errors. varied between I5 and 100kms!.. depending on the kind of the galaxy spectrum (emission or absorption dominated) and also the S/N of the target Corrections to produce heliocentric recession velocities were estimated using the IRAF task in the package Whenever possible. we checked the existing literature for other published redshifts: in. particular. we made extensive use of the overlapping area with the SDSS. SDSS-R7 (see Abazajian et al.. 2009)).," If two or more lines were blended, the IRAF command within the package was The recession velocity errors varied between 15 and 100, depending on the kind of the galaxy spectrum (emission or absorption dominated) and also the S/N of the target Corrections to produce heliocentric recession velocities were estimated using the IRAF task in the package Whenever possible, we checked the existing literature for other published redshifts; in particular, we made extensive use of the overlapping area with the SDSS, SDSS-R7 (see Abazajian et al., \cite{aba09}) )." + For galaxies that were well separated from other objects. we found a remarkable agreement with exisiting measurements within our measurements errors (see Fig.," For galaxies that were well separated from other objects, we found a remarkable agreement with exisiting measurements within our measurements errors (see Fig." + 1)., 1). + Some disagreements were found instead for galaxies close on the sky to either nearby stars or other galaxies with different redshifts., Some disagreements were found instead for galaxies close on the sky to either nearby stars or other galaxies with different redshifts. + We assumed that this happened mostly because of the fiber proximity limit. which prohibited the Sloan spectrograph from observing targets closer to each other on the sky than 60” at z=0.1 in a single pass.," We assumed that this happened mostly because of the fiber proximity limit, which prohibited the Sloan spectrograph from observing targets closer to each other on the sky than $\arcsec$ at z=0.1 in a single pass." + We note that when the only available redshifts were photometric. these frequently disagreed with our own spectroscopic measurements.," We note that when the only available redshifts were photometric, these frequently disagreed with our own spectroscopic measurements." + We briefly summarize here how we estimated the luminosity of each member galaxy: for a full description. the reader can consult paper I. The luminosity of each group was obtained by summing up all the luminosities of the member galaxies. after correction for Galactic extinction and k-correction.," We briefly summarize here how we estimated the luminosity of each member galaxy; for a full description, the reader can consult paper I. The luminosity of each group was obtained by summing up all the luminosities of the member galaxies, after correction for Galactic extinction and k-correction." + Only two values of correction were used. one for early-type galaxies (E- and another for late-type ones (Sb onward). identified by an EW(Ha) > 6À? and morphological evidence. 1.9. presence of spiral arms.," Only two values of correction were used, one for early-type galaxies (E-Sa), and another for late-type ones (Sb onward), identified by an $\alpha$ ) $>$ $\AA$ and morphological evidence, i.e. presence of spiral arms." + No correction for passive evolution was applied. both because not all galaxies in our sample can be characterized by a simple stellar population and owing to the large r.m.s which is comparable at z=0.1 to the amount of correction that would be applied. assuming the models from van Dokkum et al.," No correction for passive evolution was applied, both because not all galaxies in our sample can be characterized by a simple stellar population and owing to the large r.m.s which is comparable at z=0.1 to the amount of correction that would be applied, assuming the models from van Dokkum et al." + no., no. + 1. 2. and 3 (Longair. 2008).," 1, 2, and 3 (Longair, 2008)." + All R band luminosities were converted to B band luminosity using the transformation (Windhorst et al..," All R band luminosities were converted to B band luminosity using the transformation (Windhorst et al.," + 1991) based on the empirical relations of Kent (1985): and assuming that Mpc; = 5.48.," 1991) based on the empirical relations of Kent (1985): and assuming that $M_\mathrm{B,\sun}$ = 5.48." + Errors 1n the luminosity were estimated by assuming the maximum error in the photometric calibration of. DPOSS plates. t.e. an error of 0.19 magnitudes for an7 magnitude of 19 (Gal et al.," Errors in the luminosity were estimated by assuming the maximum error in the photometric calibration of DPOSS plates, i.e. an error of 0.19 magnitudes for an magnitude of 19 (Gal et al." + 2004)., 2004). + This section is divided into two parts., This section is divided into two parts. + The first part will describe our so-called sample cleaning. re. an analysis of the environment surrounding the spectroscopically confirmed groups. to determine whether they fulfil the isolatior criteria.," The first part will describe our so-called sample cleaning, i.e. an analysis of the environment surrounding the spectroscopically confirmed groups, to determine whether they fulfil the isolation criteria." + This basically divides the confirmed groups into two categories: (1) the objects really isolated on the sky. which cai be assumed to be compact groups: and. (2) objects close on the sky to larger scale structure. to whom they may be associated. or objects that part of a cluster of galaxies and have been selected as candidate CGs by In the second part of this section. we calculate the so-called characteristic parameters of the CGs. namely velocity dispersion. crossing time. radius. and mass. using various estimators. and we compare our measurements with other existing works and with the values of the same parameters obtained for compact groups in the nearby universe.," This basically divides the confirmed groups into two categories: (1) the objects really isolated on the sky, which can be assumed to be compact groups; and, (2) objects close on the sky to larger scale structure, to whom they may be associated, or objects that part of a cluster of galaxies and have been selected as candidate CGs by In the second part of this section, we calculate the so-called characteristic parameters of the CGs, namely velocity dispersion, crossing time, radius, and mass, using various estimators, and we compare our measurements with other existing works and with the values of the same parameters obtained for compact groups in the nearby universe." + We consider a candidate compact group to be spectroscopically confirmed if at least three of its members have accordant redshifts. i.e. are within + s7!of the median redshift of the group.," We consider a candidate compact group to be spectroscopically confirmed if at least three of its members have accordant redshifts, i.e. are within $\pm$ of the median redshift of the group." + The redshift of the confirmed group is assumed to be the median value of the measured redshift of its confirmed, The redshift of the confirmed group is assumed to be the median value of the measured redshift of its confirmed +larecr triplets were ejected first. rotation is in the sale sense as found for the galaxy and ceutral torus. with eas and water vapour niaser enission redshlifted iu the West aud blueshifted iu the East (Creeulilletal.1996).,"larger triplets were ejected first, rotation is in the same sense as found for the galaxy and central torus, with gas and water vapour maser emission redshifted in the West and blueshifted in the East \citep{gre96}." +. c) Pair-3iuglet separation velocilos. event ages and galaxy rotation rate.," c) Pair-singlet separation velocities, event ages and galaxy rotation rate." + Tf inside cach triplet the non-Doppler componcuts of the sinelet and mean pair redshifts are identical [which might be expected for similar masses if the intrinsic conrponeut is eravitationally xoduced. or if mass and intrinsic redshift are age related (NarlikarandDas1950:Dell2001). the differences between the singlet and imeau-pair redshifts will eive the Lo-s component of the pair-singlet separation velocity.," If inside each triplet the non-Doppler components of the singlet and mean pair redshifts are identical [which might be expected for similar masses if the intrinsic component is gravitationally produced, or if mass and intrinsic redshift are age related \citep{nar80,bel01}, the differences between the singlet and mean-pair redshifts will give the l-o-s component of the pair-singlet separation velocity." + Since the redshifts for all sources in triplets A and D have been measured. it is possible to test this.," Since the redshifts for all sources in triplets A and B have been measured, it is possible to test this." + Since the rotation angle of triplet Ais >90°(122° for>= 187). the yay 111 triplet A must be blueshifted relative to singlet A. For triplet D. with a position angle <90°C717 for 5=187). the opposite must be true.," Since the rotation angle of triplet A is $>-90\arcdeg (-122\arcdeg$ for $\gamma = 18\arcdeg$ ), the pair in triplet A must be blueshifted relative to singlet A. For triplet B, with a position angle $<-90\arcdeg (-71\arcdeg$ for $\gamma = 18\arcdeg)$, the opposite must be true." + From cols 2 and 3 of Table 3 this cau ρα seen to hold true. indicating that he assuuption of equal intrinsic redshift components may be a valid one. allowing the Lo-s siuglet-pair separation velocities to be estimated directly from the difference between the singlet aud mioean-pair redshifts.," From cols 2 and 3 of Table 3 this can be seen to hold true, indicating that the assumption of equal intrinsic redshift components may be a valid one, allowing the l-o-s singlet-pair separation velocities to be estimated directly from the difference between the singlet and mean-pair redshifts." + Alakiug this assmuption it is now possible to determine the xür-nuelet separation velocities and use them to calulate event ages., Making this assumption it is now possible to determine the pair-singlet separation velocities and use them to calulate event ages. + In Table 3 the separation redshift of the pairs aud singlets in triplets A and B ire listed in col 1., In Table 3 the separation redshift of the pairs and singlets in triplets A and B are listed in col 4. + These are produced by the l-o-s Doppler motion of the pairs and singlets as they move out from their respective centers-ofimass., These are produced by the l-o-s Doppler motion of the pairs and singlets as they move out from their respective centers-of-mass. +" They have heen calculated frou the following relations: aud Tere z, is the redshift of tre center of mass of the triplet relative to the oealaxy aud (Zineiu )sing?nal IS the intrinsic component of tie sóuelet. assumed to be equal to the intrinsic component of thepair Ziur hair."," They have been calculated from the following relations: and Here $_{\rm t}$ is the redshift of the center of mass of the triplet relative to the galaxy and $_{\rm int}$ $_{singl}$ is the intrinsic component of the singlet, assumed to be equal to the intrinsic component of thepair $_{\rm int}$ $_{\rm pair}$." + Siuce UZeparar pair Is asstuued to be equal to (-Zparatdsinel Oud zas aid Zp. are conuuon to the two equations. the oilv unknown is the separation velocity which cau then be solved. for.," Since $_{\rm separat}$ $_{\rm pair}$ is assumed to be equal to $_{\rm separat}$ $_{\rm singl}$, and $_{\rm sys}$ and $_{\rm t}$, are common to the two equations, the only unknown is the separation velocity which can then be solved for." + This must be divided by coss to take accorut of the tip angele o: the rotation axis., This must be divided by $\gamma$ to take account of the tip angle of the rotation axis. + The resiitiug values are liste in col I., The resulting values are listed in col 4. + The ejection redshifts iu col 1 are converted to Lo-s velocities iu co 5 of Table 3 using the non-relativistic relation v = cz., The ejection redshifts in col 4 are converted to l-o-s velocities in col 5 of Table 3 using the non-relativistic relation v = cz. + The radial separation velocity of the singlets aud udrs are listed iniu col 8., The radial separation velocity of the singlets and pairs are listed in col 8. +" Col 9 gives the velocity verpendicular to he Lo-« and col 10 the mica retlar displacement on the skv of the singlets id pair imuüdponts from each triplet’s center of Lass,", Col 9 gives the velocity perpendicular to the l-o-s and col 10 the mean angular displacement on the sky of the singlets and pair midpoints from each triplet's center of mass. + If the compact objects are located near NGC GS. the values ound for the ejection velocity crpeudicular to the Ίος (col 9). alone with the retlar displacement ou the sky (col 10) eive 1ο elapsed. time since each event occurred. and jerefore eive the approximate ageof cach triplet.," If the compact objects are located near NGC 1068, the values found for the ejection velocity perpendicular to the l-o-s (col 9), along with the angular displacement on the sky (col 10) give the elapsed time since each event occurred and therefore give the approximate ageof each triplet." + At the distance of NGC 1068 1 2 L2 kpe., At the distance of NGC 1068 $\arcmin$ = 4.2 kpc. + These miubers thus result in ages near 6.08«109 aud Γιος109 wrs for the A aud D triplets respectively or a tip anele of ~ = 18°)., These numbers thus result in ages near $6.08\times10^{6}$ and $4.46\times10^{6}$ yrs for the A and B triplets respectively (for a tip angle of $\gamma$ = $\arcdeg$ ). + Thus triplet D is vouuger than triplet A in agreement with the wstuuptions that larger triplets are older. aud that 16 rotation sequence is from A to D. Between the A and D events the position uele (eiven by 0) rotates through ~517.," Thus triplet B is younger than triplet A in agreement with the assumptions that larger triplets are older, and that the rotation sequence is from A to B. Between the A and B events the position angle (given by $\theta$ ) rotates through $\sim51\arcdeg$." + Since is amount of rotation takes 4109 vrs. one complete revolution will take ~1.1«10* vrs. or a actor of 25 shorter than the time it takes the Sun o 1iake 1 revolution in our own Calaxy.," Since this amount of rotation takes $\times10^{6}$ yrs, one complete revolution will take $\sim1.1\times10^{7}$ yrs, or a factor of 25 shorter than the time it takes the Sun to make 1 revolution in our own Galaxy." + This value is iu good agroocnieut with the value (6«109 vrs} calculated for the rotation period of the nucleus of NOC 10685 using recent kinematic results (Alloiuetal. 2001).. when i is kept iu mind that it applies Or 5=18 only. and this angle is not accurately shown.," This value is in good agreement with the value $\times10^{6}$ yrs) calculated for the rotation period of the nucleus of NGC 1068 using recent kinematic results \citep{all01}, when it is kept in mind that it applies for $\gamma = 18\arcdeg$ only, and this angle is not accurately known." + Furthermore. there may be some evideuce hat this angle cheives over LOS vrs (see below).," Furthermore, there may be some evidence that this angle changes over $10^{7}$ yrs (see below)." + This result is interpreted as imdicatiug that the changes in triplet rotation angle are tied closely o the rotation of the galaxy., This result is interpreted as indicating that the changes in triplet rotation angle are tied closely to the rotation of the galaxy. + The above imnibers eive an anguar rotation rate of <104 visfdee., The above numbers give an angular rotation rate of $\times10^{4}$ yrs/deg. +" The rotatkn aneles of riplets C aud D hus lead to ages for tjose triplets of «109 sis and «109 yes respectively. for οΞ 15”, "," The rotation angles of triplets C and D thus lead to ages for these triplets of $\times10^{6}$ yrs and $\times10^{6}$ yrs respectively, for $\gamma = 18\arcdeg$ ." +d) Quautizaticn in Ziican- , d) Quantization in $_{\rm mean}$ . +Examination of the zi components. [whore μια = (Zi| 22) 2| reveals that not oulv do they fall off ioothlv with increasing distance from, Examination of the $_{\rm mean}$ components [where $_{\rm mean}$ = $_{1}+$ $_{2})/2$ ] reveals that not only do they fall off smoothly with increasing distance from +them.,. + Note that this statement does not necessarily imply the minimum halo mass to be the only factor plaving a relevant role in the onset of radio emission [rom an AGN., Note that this statement does not necessarily imply the minimum halo mass to be the only factor playing a relevant role in the onset of radio emission from an AGN. + Also the threshold. may not be a sharp mass threshold. but could. be as a smooth transition between the racio-quict ancl racio-Ioud: regimes for halos near Alin.," Also the threshold may not be a sharp mass threshold, but could be as a smooth transition between the radio-quiet and radio-loud regimes for halos near $\rm M_{\rm min}$." + These results on the minimum halo mass can also be viewed in terms of a minimum black hole mass., These results on the minimum halo mass can also be viewed in terms of a minimum black hole mass. +" Ferrarese (2002) gives a simple prescription to convert the dark matter mass Alba; of a halo hosting a black hole into black hole mass Als: +pThus. a minimum""- halo mass Mui,~lo13.4CAL: corresponds to MPHmim;S10!‘ALL. which would represent 10 minimum black hole mass required to onset. racioAGN clivity at least for relatively faint/EBRE sources such as 16 overwhelming majority of those we have considered. in our analysis (see Section 3.1)."," Ferrarese (2002) gives a simple prescription to convert the dark matter mass $\rm M_{DM}$ of a halo hosting a black hole into black hole mass $\rm M_{BH}$: Thus, a minimum halo mass ${\rm M_{\rm min}}\sim 10^{13.4} \rm M{\sun}$ corresponds to $\rm M^{\rm BH}_{\rm min}\sim 10^9 \rm M_{\sun}$, which would represent the minimum black hole mass required to onset radio-AGN activity – at least for relatively faint/FRI sources such as the overwhelming majority of those we have considered in our analysis (see Section 3.1)." + Ho is interesting to note that lis estimate is in good agreement with both the results of Alarchesini. Ferrarese Celotti (2003) ancl also those of Dunlop et al. (," It is interesting to note that this estimate is in good agreement with both the results of Marchesini, Ferrarese Celotti (2003) and also those of Dunlop et al. (" +2003). despite the entirely different methods used in our analysis.,"2003), despite the entirely different methods used in our analysis." + Also our minimum black hole mass is noticeably larger than that obtained for raclio-quiet quasars: from an analysis of the 24k QSO dataset in the same redshift range spanned by the sources considered. in this work. Corbett et al. (," Also our minimum black hole mass is noticeably larger than that obtained for radio-quiet quasars; from an analysis of the 2dF QSO dataset in the same redshift range spanned by the sources considered in this work, Corbett et al. (" +2003) find 6.5τςloginμη/λ1E 8.3.,"2003) find $6.5\simlt {\rm log_{10}}[{\rm M_{\rm BH}}/{\rm +M_{\sun}}]\simlt 8.3$ ." + By making use of equation (7)). we can then conclude that αἱ least for moderately faint{FRI racio sources mass.," By making use of equation \ref{eq:mbh}) ), we can then conclude that – at least for moderately faint/FRI radio sources –." + Vhis is in agreement with other analyses of radio-Ioud quasars by Dunlop et al. (, This is in agreement with other analyses of radio-loud quasars by Dunlop et al. ( +2003) and Cirasuolo et al. (,2003) and Cirasuolo et al. ( +2003).,2003). + We note that. even though the connection between black hole mass and radio power has been obtained in our analvsis as à consequence of the connection between radio power and halo mass. this first relationship is supposed to be more fundamental and physically based as it is the black hole which actually powers the AGN.," We note that, even though the connection between black hole mass and radio power has been obtained in our analysis as a consequence of the connection between radio power and halo mass, this first relationship is supposed to be more fundamental and physically based as it is the black hole which actually powers the AGN." + Any correlation. between radio power and halo mass is then expected to arise as a secondary ellect. since black hole mass is observed to scale with bulge luminosity and this is turn is related — in the case of elliptical galaxies to halo mass (see e.g. Magorrian et al.," Any correlation between radio power and halo mass is then expected to arise as a secondary effect, since black hole mass is observed to scale with bulge luminosity and this is turn is related – in the case of elliptical galaxies – to halo mass (see e.g. Magorrian et al." + 1998: Ixormendsy Gebhardt 2001: MeLure Dunlop 2002: Archibald et al., 1998; Kormendy Gebhardt 2001; McLure Dunlop 2002; Archibald et al. + 2002: Ciranato et al., 2002; Granato et al. + 2004) This paper has presented the clustering properties of local. 5La46HzZd mJy radio sources by making use of a sample of N20 objects drawn from the joint use of the FIRST survey and the 2dkFCRS.," 2004) This paper has presented the clustering properties of local, $S_{1.4 +\rm GHz}\ge 1$ mJy radio sources by making use of a sample of 820 objects drawn from the joint use of the FIRST survey and the 2dFGRS." +" To this aim. we have introduced l new b,19.45 spectroscopic counterparts for FIRST radio sources to be added to those already obtained by Alaglioechetti et al. ("," To this aim, we have introduced 271 new $\bj \le 19.45$ spectroscopic counterparts for FIRST radio sources to be added to those already obtained by Magliocchetti et al. (" +2002).,2002). + Phese objects can be divided in two broad sub-classes: (1)) star-forming objects (66 sources. which include both late-tvpe and star-burst galaxies). which owe their radio activity to. processes connected to intense star formation and (2) racioNXGNs (202 sources). where the radio signal stems from aceretion processes onto a central black hole.," These objects can be divided in two broad sub-classes: (1) star-forming objects (66 sources, which include both late-type and star-burst galaxies), which owe their radio activity to processes connected to intense star formation and (2) radio-AGNs (202 sources), where the radio signal stems from accretion processes onto a central black hole." + In both cases. the redshift range range spanned extends up to z20.3 (with star-forming objects being relatively more local than ACGN-fuelled: sources) ancl racio luminosities cover the interval 107 1072) AGN-fuelled radio sources., We also find no significant differences in the clustering properties of faint ${\cal P}\le 10^{22}$ ) compared to brighter ${\cal P} > 10^{22}$ ) AGN-fuelled radio sources. + Comparisons with physicallv-motivated: models for the clustering properties of classes of galaxies show that ACGN-fuelleck sources have to reside in dark matter halos more massive than loginMiyiu/M.]213.4. higher than the figure recently measured. for. raclio-quict QSOs (see c.g. Girazian et al.," Comparisons with physically-motivated models for the clustering properties of classes of galaxies show that AGN-fuelled sources have to reside in dark matter halos more massive than $\rm +log_{10}[M_{min}/M_{\sun}]\simeq 13.4$, higher than the figure recently measured for radio-quiet QSOs (see e.g. Grazian et al." + 2003)., 2003). + Under certain assumptions. this value can be converted into a minimum black hole mass associated with radio-loud. AGN-fuelled objects of Mig10NL.. again larger than current estimates for the typical black hole mass associated with local 2dE (raclio-quiet) quasars (Corbett et al.," Under certain assumptions, this value can be converted into a minimum black hole mass associated with radio-loud, AGN-fuelled objects of $\rm +M_{BH}^{min}\sim 10^9 M_{\sun}$, again larger than current estimates for the typical black hole mass associated with local 2dF (radio-quiet) quasars (Corbett et al." + 2003)., 2003). + ‘The above results then suggest — at least for moderately [aint{ΕΠΙ radio sources such as those included in our sample the existence of a threshold. halo/black hole miss associated with the onset of significant radio activity such as that of. racio-loud ACGNs., The above results then suggest – at least for moderately faint/FRI radio sources such as those included in our sample – the existence of a threshold halo/black hole mass associated with the onset of significant radio activity such as that of radio-loud AGNs. + We stress that such threshold. is not necessarily a sharp one. as it could. as well identify an allowed range (in the high-mass regime) for the transition between radio-quiet and. raclio-loucl regimes.," We stress that such threshold is not necessarily a sharp one, as it could as well identify an allowed range (in the high-mass regime) for the transition between radio-quiet and radio-loud regimes." + Once the activity is triggered there seemsto be no evidence [or à connection betweenhalo/black hole mass and. racio luminosity., Once the activity is triggered there seemsto be no evidence for a connection betweenhalo/black hole mass and radio luminosity. +"lline ratio and the bbrightness temperature (for a source size of 10”) as a function of ny, and Nunco.","line ratio and the brightness temperature (for a source size of 10"") as a function of $n_{H_{2}}$ and $N_{HNCO}$." +" The same diagrams for a source size equal to the telescope main beam (using T;,») are shown in Fig. 5..", The same diagrams for a source size equal to the telescope main beam (using $T_{mb}$ ) are shown in Fig. \ref{fig:radex2}. + The kinetic temperature cannot be constrained since equally good solutions can be found just changing the hydrogen density by ~0.5 dex., The kinetic temperature cannot be constrained since equally good solutions can be found just changing the hydrogen density by $\sim 0.5$ dex. +" For a given source size and kinetic temperature, the Hz density is similar for B1 and B2."," For a given source size and kinetic temperature, the $_2$ density is similar for B1 and B2." +" The density varies from 10*—10*4 ffor a source size of 10"" and Τκ=250 K, to 10*9—10°? for sources filling the main beam and Tx=30 K. In mm, ng, is lower than that in B1 and B2 by 0.2—0.3 dex."," The density varies from $10^{4}-10^{4.4}$ for a source size of 10"" and $T_K=250$ K, to $10^{4.6}-10^{5.2}$ for sources filling the main beam and $T_K=30$ K. In L1157-mm, $n_{H_{2}}$ is lower than that in B1 and B2 by $0.2-0.3$ dex." +" 'The total HNCO columns densities are 0.2-1.3, 0.6-2.5 and 1.3-5.0 (in units of 1015. cm-2)) for mm, B1, and B2, respectively (Table 3))."," The total HNCO columns densities are 0.2-1.3, 0.6-2.5 and 1.3-5.0 (in units of $10^{13}$ ) for mm, B1, and B2, respectively (Table \ref{tab:results}) )." +" The lower limits are similar to those derived using LTE, while the upper limits for B1 and B2 are somewhat higher because opacity effects start playing a role."," The lower limits are similar to those derived using LTE, while the upper limits for B1 and B2 are somewhat higher because opacity effects start playing a role." + Table 3 also shows HNCO abundances computed with the estimations of the HNCO column density and the total Ho column density derived from CO by ?.., Table \ref{tab:results} also shows HNCO abundances computed with the estimations of the HNCO column density and the total $_2$ column density derived from CO by \cite{Bachiller97}. +" The HNCO abundances are (0.3—1.2)x107? for L1157-mm, (4.3—17.9)x10? for L1157-B1 and (25—96)x107? for L1157-B2 (Table 3))."," The HNCO abundances are $(0.3-1.2)\times10^{-9}$ for L1157-mm, $(4.3-17.9)\times10^{-9}$ for L1157-B1 and $(25-96)\times 10^{-9}$ for L1157-B2 (Table \ref{tab:results}) )." +" Therefore, there is a clear increase of the HNCO abundance in the shocked regions, by a factor of 6-14 in B1 and by a factor of in B2."," Therefore, there is a clear increase of the HNCO abundance in the shocked regions, by a factor of 6-14 in B1 and by a factor of 34-83 in B2." +"gas. In the range of physical conditions and HNCO column densities derived from the aand lines, the model predictions for the tto rratio is 0.6-0.7."," In the range of physical conditions and HNCO column densities derived from the and lines, the model predictions for the to ratio is 0.6-0.7." +" In contrast, the measured ratio is 0.3-0.4 for L1157-mm, and it is lower than 0.3 for B1 and B2."," In contrast, the measured ratio is 0.3-0.4 for L1157-mm, and it is lower than 0.3 for B1 and B2." +" Table 4 shows HNCO abundances with respect to Ho measured other Galactic sources as translucent clouds, photon-dominated regions (PDRs), dense cores and hot cores."," Table \ref{tab:comp} shows HNCO abundances with respect to $_2$ measured other Galactic sources as translucent clouds, photon-dominated regions (PDRs), dense cores and hot cores." + The highest HNCO abundance is found in hot cores and dense cores: up to ~8.710-?.," The highest HNCO abundance is found in hot cores and dense cores: up to $\sim 8.7\,10^{-9}$." +" The HNCO abundance in L1157-mm is similar to that measured in those dense cores and hot cores with the lowest HNCO abundance and in the only “hot corino"" where the molecule has been previously detected, IRAS 16293 (?).."," The HNCO abundance in L1157-mm is similar to that measured in those dense cores and hot cores with the lowest HNCO abundance and in the only “hot corino"" where the molecule has been previously detected, IRAS 16293 \citep{vanDishoeck95}." +" The HNCO abundance in the L1157-B1 shock is comparable, but can even be higher than that in hot cores and dense cores."," The HNCO abundance in the L1157-B1 shock is comparable, but can even be higher than that in hot cores and dense cores." +" Regarding the L1157-B2 shock, the HNCO abundance is"," Regarding the L1157-B2 shock, the HNCO abundance is" +binary companion. via tidal forces and by spinnine-up the AGB star.,"binary companion, via tidal forces and by spinning-up the AGB star." + Single ACB stars can also become very chaotic when their envelope mass is low. as the structure become less stable (Soker Harpaz 1999. 2002).," Single AGB stars can also become very chaotic when their envelope mass is low, as the structure become less stable (Soker Harpaz 1999, 2002)." + This is mainiv because the entropy profile becomes steeper and the clensity profile becomes shallower at the end of the AGB. and because the thermal (Ixelvin-Ielmholtz) time scale decreases and becomes comparable to the dynamical (pulsation) time scale (Soker 2008).," This is mainly because the entropy profile becomes steeper and the density profile becomes shallower at the end of the AGB, and because the thermal (Kelvin-Helmholtz) time scale decreases and becomes comparable to the dynamical (pulsation) time scale (Soker 2008)." + The behavior of the photospheric opacity can also contribute to the irregular behavior (Soker 2006)., The behavior of the photospheric opacity can also contribute to the irregular behavior (Soker 2006). + The effervescent zone will become extended when the radiation momentum flux is about equal to the wind momentum flix., The effervescent zone will become extended when the radiation momentum flux is about equal to the wind momentum flux. +" At that stage the mass loss rate in (he wind is L/(cve.). where e, is the terminal wind speed and £ the stellar Iuminositv."," At that stage the mass loss rate in the wind is $\dot M_{wc} = L/(c v_w)$ , where $v_w$ is the terminal wind speed and $L$ the stellar luminosity." + Substituting (vpical values gives ↕∐⊔∐↲∐≼↲⇀↸↥⊳∖⇁≼↲≺∢∐∪∐⊔∐↲≀↧↴∖↽≼↲↕⋅≀↧↴≸↽↔↴≼↲≼⋝∐↥≀↧↪∖⇁↕↽≻∐≼↲↕⋅↥≺∢≀↧↴↥⊳∖⇁∐≼↲∐⇄⋝≼⇂≼↲∐⊳∖⇁∐∡∖↽∪↓⋟⊔∐↲∣↽≻∪∏∐≼⇂≸↽↔↴≀↧↪∖⇁↕⊳∖⇁↓≯∪∏∐≼⇂ ↥∪∖↽≀↧↴↕⋅∡∖↽≀↧↪∖⇁∣⋮↱↗⊋⋅∖∖↽↥∐↲↕⋅≼↲∣⋮↕⊳∖⇁⊔∐↲↕⋅⋯∐≀↧↴↥≼∐⊳∖⇁↥≀↧↴∐," Substituting typical values gives In the next section the average (in a spherical shell) density of the bound gas is found to vary as $r^{-5/2}$, where $r$ is the radial distance measured from the center of the star." +≺∢≼↲∐∐↲≀↧↪∖⊽⋯⋅≼↲≼⇂∐⋅∪∐↓⊔∐↲≺∢≼↲∐∩↲↕⋅∪↓⋟⊔∐↲⊳∖⇁↥≀∐⋅⋅↳∖↡≀↧↴∐∐↲↥∡∖↽⋅ ⊔∐↲↕⋅≀↧↴∐∪∪↓≯⊔∐↲≀↧↴∖↽≼↲↕⋅≀↧↴≸≟≼↲≼⋝∐↥≀↧↴⊳∖⊽↕↽≻∐≼↲↕⋅↥≺∢≀↧↴↥⊳∖⇁↥∐↲∐⇄⋝≼⇂≼↲∐⊳∖⊽∐⋡∖↽∪↓≯⊔∐↲∐⋯↪∖⇁⊳∖⊽↕∐⊔∐↲≼↲∐⋡≼↲↕⋅∖↽≼↲⊳∖⊽≺∢≼↲∐↥∠∪∐≼↲ ⊔↥≀↧↴⊓⇂⋯↲⊳∖⇁∐∪↥≼↲⋝∖⊽≺∢≀↧↴↕↽≻≼↲↓⋟↕⋅∪∐↓⊔∐↲⊳," Namely, the ratio of the average (in a spherical shell) density of the mass in the effervescent zone that does not escape from the star to the wind averaged density $\eta(r)$, is found to vary as $\eta(r) \sim r^{-1/2}$." +∖⇁↥≀↧↴↕⋅↥∪⊔∐↲∖∖↽↕∐≼⇂≀↧↴∖↽≼↲↕⋅≀↧↴≸≟≼↲≼⇂≼⇂≼↲∐⊳∖⇁∐⋡∖↽∣∣≼⋝∣⋮↕⋝⋅↕⊳∖⊽↓⋟⋯∐∐⇂↥∪∖↽≀↧↴↕⋅∡∖⇁≀↧⊔∖⊽ ∣∣⋜⋝∣⋮↕⋝↴∿↴∣⋮↓⊽−⋟⋅↴∏∐↲≀↧↴∖↽≼↲↕⋅≀↧↴≸↽↔↴≼↲∪↕↽≻∐≺∢≀↧↴↥≼⇂≼↲↕↽≻⊔↥∐⋅∪↕∐⊔∐↲∪∣↽≻⊳∖⇁≼↲↕⋅∖↽≼↲↕⋅≼⇂∪∖∖↽∐↥∪↕⋅≀↧↴≼∐∏⊳∖⇁∣⋮↕⊳∖⇁ where & is the opacity of the dusty wind., The average optical depth from the observer down to radius $r$ is where $\kappa$ is the opacity of the dusty wind. + The effervescent zone becomes extended {ο tens of AUwhen the mass loss rate is high (eq. 1))., The effervescent zone becomes extended to tens of $\AU$when the mass loss rate is high (eq. \ref{mwc1}) ). + From equation (2)) it is seen that the optical depth to the effervescent zone becomes very large. and ils inner parts cannol be observed directly.," From equation \ref{tau1}) ) it is seen that the optical depth to the effervescent zone becomes very large, and its inner parts cannot be observed directly." + For example. we can take alr) Lat r~50AU. and find 7~1.," For example, we can take $\eta (r) \sim 1$ at $r \sim 50 \AU$, and find $\bar \tau \sim 1$." + In general. only the outer regions that are dominated by the wind can be observed clirectly (depending on the wavelength).," In general, only the outer regions that are dominated by the wind can be observed directly (depending on the wavelength)." + The carbon AGB star IIRC--10216. for example. has such a mass loss rate and cannol be observed directly. (e.$.. Fonfria οἱ al.," The carbon AGB star IRC+10216, for example, has such a mass loss rate and cannot be observed directly (e.g., Fonfria et al." + 2008)., 2008). + Strong pulsations can eject dense clumps to large distances before (hey are accelerated to high speeds., Strong pulsations can eject dense clumps to large distances before they are accelerated to high speeds. + For the clumps to fall back the gravitational force must be larger than that due to radiation pressure., For the clumps to fall back the gravitational force must be larger than that due to radiation pressure. + Let us consider a dense clump (a blob). e.g.. as the one mocelled bv Lopez et al. (," Let us consider a dense clump (a blob), e.g., as the one modelled by Lopez et al. (" +1997) inMira. A. It has a cross section lacing the star of area 2L. a length,"1997) inMira A. It has a cross section facing the star of area $A_b$ , a length" +is determined by the competition between acceleration time and age of the svstem. rather than svachrotron losses (lower panel of Fig. 1)).,"is determined by the competition between acceleration time and age of the system, rather than synchrotron losses (lower panel of Fig. \ref{fig:f1}) )." + The adopted value £=3.7 corresponds to a fraction of injected particles ga;=12-10.7., The adopted value $\xi= 3.7$ corresponds to a fraction of injected particles $\eta_{\rm inj}= 1.2\cdot 10^{-4}$. + Phe resulting acceleration ellicieney. e. defined as the percentage of the energy. Dux crossing the shock that ends up in. relativistic particles. varies from ~δα (for By=0.1 μα) to ~36% (Lor By=10 nC).," The resulting acceleration efficiency, $\epsilon$, defined as the percentage of the energy flux crossing the shock that ends up in relativistic particles, varies from $\sim 68\%$ (for $B_0=0.1\ \mu$ G) to $\sim 36\%$ (for $B_0=10\ \mu$ G)." + tis very important to notice that 10 solutions corresponding to the curves in the upper panel of Fig., It is very important to notice that the solutions corresponding to the curves in the upper panel of Fig. +" 1 ave characterized. by moderately low values. of. the compression factor in the precursor (Aya,ος 12). despite the high acceleration elliciencies."," \ref{fig:f1} are characterized by moderately low values of the compression factor in the precursor $R_{tot}\lesssim 12$ ), despite the high acceleration efficiencies." + This result. is purely the consequence of the dynamical. reaction of the amplified magnetic field on the shock., This result is purely the consequence of the dynamical reaction of the amplified magnetic field on the shock. + No turbulent heating has been introduced in these calculations., No turbulent heating has been introduced in these calculations. + One may wonder how the results would change if no cosmic rav induced magnetic field amplification were present. so that the magnetic field. in the precursor and at the shock would only be produced by compression of a turbulent field at upstream infinity. with 0B~ By.," One may wonder how the results would change if no cosmic ray induced magnetic field amplification were present, so that the magnetic field in the precursor and at the shock would only be produced by compression of a turbulent field at upstream infinity, with $\delta B\sim B_0$ ." + In this case the turbulent field. (assumed to be perpendicular to Ly) is compressed. according to ByGr)υπο ute)., In this case the turbulent field (assumed to be perpendicular to $B_0$ ) is compressed according to $B_\perp(x)= B_0 (u_0/u(x))$ . + In the bottom panel in Fig., In the bottom panel in Fig. + we show the cutoll energies obtained in this situation (we still assume £=3.7)., \ref{fig:f1} we show the cutoff energies obtained in this situation (we still assume $\xi=3.7$ ). + For 0.18oLO"")."," \ref{fig:f2} we illustrate the dependence of $B_2$ (upper panel) and of the cutoff energies (lower panel) on the injection parameter $\xi$, varying between 3.4 and 4.1 (corresponding to $6\times 10^{-4} > \eta_{\rm inj} > 8\times 10^{-6}$ )." + Phe upstreans magnetic field is By=2iG. Phe curves are labelled as in Fie. 1..," The upstream magnetic field is $B_0=2\ \mu$ G. The curves are labelled as in Fig. \ref{fig:f1}," + with the addition of two thin solid lines representing he cutoll energy. ⋅for zt decay when the maximum. energy of the parent protons is calculated. with a=S% and a=15% in Eq. (1))., with the addition of two thin solid lines representing the cutoff energy for $\pi^0$ decay when the maximum energy of the parent protons is calculated with $\alpha=8\%$ and $\alpha=15\%$ in Eq. \ref{eq:pmax}) ). + The vertical thick solid line in the upper panel shows the solution providing the central value of the measured rim thickness (corresponding to D»=LOO pC) while the dashed: vertical lines bound the allowed: region corresponding to UC 1000$ and $T < 3\times 10^{4}$ K \citep[e.g.][]{2009MNRAS.399..650S}." +" ? also used SKID and introduced “virtual galaxies"" in order to account for the fragmentation of baryonic structure between consecutive outputs.", \citet{2006ApJ...647..763M} also used SKID and introduced “virtual galaxies” in order to account for the fragmentation of baryonic structure between consecutive outputs. +" On the other hand, ?? used a modified version of SUBFIND to detect simultaneously dark matter and baryons, ending with a galaxy composed of DM, stars, and gas."," On the other hand, \citet{2009MNRAS.399..497D,2010MNRAS.405.1544D} + used a modified version of SUBFIND to detect simultaneously dark matter and baryons, ending with a galaxy composed of DM, stars, and gas." + They used dynamical criteria to distinguish between the central galaxy and the diffuse stellar component., They used dynamical criteria to distinguish between the central galaxy and the diffuse stellar component. +" Our approach here was slightly different: we detected on the one hand the hierarchy of DM haloes and subhaloes, and on the other hand the baryonic component consisting of central galaxies and satellites."," Our approach here was slightly different: we detected on the one hand the hierarchy of DM haloes and subhaloes, and on the other hand the baryonic component consisting of central galaxies and satellites." + We therefore also used AdaptaHOP to detect baryonic structures., We therefore also used AdaptaHOP to detect baryonic structures. +" While input parameters are known for DM detection, we had to find a more well-suited set of parameters in order to detect the baryonic structures."," While input parameters are known for DM detection, we had to find a more well-suited set of parameters in order to detect the baryonic structures." + We set the density threshold above which structures are considered to 1000 times the mean (baryonic) density., We set the density threshold above which structures are considered to 1000 times the mean (baryonic) density. +" We took f;=4, f;=5x107 in order to allow to detect structures with sizes of the order of 1 kpc, and kept α = 1."," We took $f_p = 4$, $f_\eps = 5\times 10^{-4}$ in order to allow to detect structures with sizes of the order of 1 kpc, and kept $\alpha$ = 1." +" Higher values of f, tend to remove the smallest structures, while lower values add unphysical substructures."," Higher values of $f_p$ tend to remove the smallest structures, while lower values add unphysical substructures." + An interesting question that we addressed is how much baryonic matter there is in DM haloes., An interesting question that we addressed is how much baryonic matter there is in DM haloes. +" To answer this question, we studied the link between galaxies and haloes, taking advantage of their independent detections."," To answer this question, we studied the link between galaxies and haloes, taking advantage of their independent detections." + We then set several rules to decide whether a galaxy and a halo are linked together., We then set several rules to decide whether a galaxy and a halo are linked together. + The first rule is that a galaxy should belong to at most one (sub)halo (and of course its host halo hierarchy if it is a subhalo)., The first rule is that a galaxy should belong to at most one (sub)halo (and of course its host halo hierarchy if it is a subhalo). +" The second rule is that the hierarchy of galaxies and satellites on the one hand and haloes and subhaloes on the other has to be respected, so that we avoid the case where a satellite is"," The second rule is that the hierarchy of galaxies and satellites on the one hand and haloes and subhaloes on the other has to be respected, so that we avoid the case where a satellite is" +We acknowledge the IRAM ancl DIMA stall for carrving out the observations.,We acknowledge the IRAM and BIMA staff for carrying out the observations. + We are especially grateful to Roberto Neri and Jerome Pety for coordinating remote reduction of the IRAM PdBI observations., We are especially grateful to Roberto Neri and Jerome Pety for coordinating remote reduction of the IRAM PdBI observations. + , +Section 3.,Section 3. + Phe results are presented and discussed in Section 4 and compared with other recent studies. particularly that of Bellochectal.(2003) who have recently demonstrated the presence of rotation in the more evolved Class 0 source. IRAAT 0419111522.," The results are presented and discussed in Section 4 and compared with other recent studies, particularly that of \citet{belloche.et.al02} who have recently demonstrated the presence of rotation in the more evolved Class 0 source, IRAM 04191+1522." + Lt is concluded in Section 5 that. the asvmmetric line profiles can be very well modelled if L168913 is undergoing rotation and that therefore rotation dominates anv infall motions in this source., It is concluded in Section 5 that the asymmetric line profiles can be very well modelled if L1689B is undergoing rotation and that therefore rotation dominates any infall motions in this source. + LIGSOB is a pre-stellar core located in Ophiuchus., L1689B is a pre-stellar core located in Ophiuchus. + Shirley6al.(2000). present SCUBA maps of L1689D that confirm ju there is no protostellar object in the centre of the core., \citet{shirley.et.al00} present SCUBA maps of L1689B that confirm that there is no protostellar object in the centre of the core. + Evansetal.(2001) use a ποconsistent clust emission =rodel to constrain the properties of LIGSOB ancl conclude ju the dust temperature decreases from the edge to the entre. a conclusion also reached by Andréetal.(1996). and Jessop&Ward-Phompson(2001).," \citet{evans.et.al01} use a self-consistent dust emission model to constrain the properties of L1689B and conclude that the dust temperature decreases from the edge to the centre, a conclusion also reached by \citet{andre.et.al96} and \citet{jessop&wardthompson01}." +. Phe density structure of 10 core is mildly [lattened in the centre ancl decreases for arger radii., The density structure of the core is mildly flattened in the centre and decreases for larger radii. + Phe density was well modelled by [Evansetal. using a Bonner-Ehert sphere density. clistribution (κου Mebaughlin&Pudritz1996: Alvesetal. 2001:: Evansetal.2001: Whitworth&Warcd-Phompson 20011: Wuehterl&‘Vscharnuter2003. for recent work involving Bonner-Ebert spheres)., The density was well modelled by \citet{evans.et.al01} using a Bonner-Ebert sphere density distribution (see \citealt{mclaughlin&pudritz96}; \citealt{alves.et.al01}; \citealt{evans.et.al01}; \citealt{whitworth&wardthompson01}; \citealt{wuchterl&tscharnuter03} for recent work involving Bonner-Ebert spheres). + Redmanetal.(2002) carried out oobservations towards the pre-stellar core. L1689D. By examining the relative —strengths of| the hvperfine components of this line the optical depth was calculated., \citet{redman.et.al02b} carried out observations towards the pre-stellar core L1689B. By examining the relative strengths of the hyperfine components of this line the optical depth was calculated. + This allowed accurate CO column densities. to be determined., This allowed accurate CO column densities to be determined. + Phe hydrogen column densities. that these measurements imply are substantially smaller than those calculated from SCUBA clust) emission. data of Shirleyetal.(2000) and Evansetal.(2001)., The hydrogen column densities that these measurements imply are substantially smaller than those calculated from SCUBA dust emission data of \citet{shirley.et.al00} and \citet{evans.et.al01}. +.. Furthermore. the ccolumnο densities are approximately constant across L1689D whereas the SCUBA column densities are peaked towards the centre.," Furthermore, the column densities are approximately constant across L1689B whereas the SCUBA column densities are peaked towards the centre." + The most likely explanation is that CO is depleted. [rom the central regions of LI689D. as also suggested. by Jessop&Ward-Phompson(2001).," The most likely explanation is that CO is depleted from the central regions of L1689B, as also suggested by \citet{jessop&wardthompson01}." +. Evidence of CO depletion. has also been found in. several other prestellar cores (Casellietal.1999:Bacmann2002:Jorgensenetal.2002:Tafalla 2002).," Evidence of CO depletion has also been found in several other prestellar cores \citep{caselli.et.al99,bacmann.et.al02,jorgensen.et.al02,tafalla.et.al02}." +. LO was estimated by Redmanetal.(2002) that within about 5000 AU of the centre of LIGSOD. over ofthe CO has frozen onto grains.," It was estimated by \citet{redman.et.al02b} that within about 5000 AU of the centre of L1689B, over of the CO has frozen onto grains." + This level of depletion can only be achieved after a duration of time that is at least comparable to the free-fall timescale., This level of depletion can only be achieved after a duration of time that is at least comparable to the free-fall timescale. + While the CO emitting gas appears to be quiescent. line profiles obtained. by Creeersen&Evans(2000) show the presence of both blueend τοῦ asvnimetric line profiles in this source.," While the CO emitting gas appears to be quiescent, line profiles obtained by \citet{gregersen&evans00} show the presence of both blue red asymmetric line profiles in this source." + New ΔΙ observations. described. below. confirm. the observational results of Ciregersen.&Evans(2000) and reveal an underlying order to the locations of the blue and red asymmetric profiles.," New JCMT observations, described below, confirm the observational results of \citet{gregersen&evans00} and reveal an underlying order to the locations of the blue and red asymmetric profiles." + The bulk of the observations were carried. out. using the heterodvne. receiver BRxA3 at the James Clark Maxwell Telescope. (JONUE). Mauna Wea. Hawaii on the nights of 2001 Feburary 24-26. 2001 August 19-21. 2003 Alay 3-5.," The bulk of the observations were carried out using the heterodyne receiver RxA3 at the James Clark Maxwell Telescope (JCMT), Mauna Kea, Hawaii on the nights of 2001 Feburary 24-26, 2001 August 19-21, 2003 May 3-5." + Additional data were collected. on various dates in 2001. (, Additional data were collected on various dates in 2001. ( +(267.5665 GLIZ) line. profiles were obtained. for seventeen positions across the centre of LI689B. Some of the data points were collected. as part of a larger survey of infall candidate objects. the results of which will be reported in Hedman ct al. (,"267.5665 GHZ) line profiles were obtained for seventeen positions across the centre of L1689B. Some of the data points were collected as part of a larger survey of infall candidate objects, the results of which will be reported in Redman et al. (" +2004).,2004). +" The cata were reduced in the stancard manner using theSPECN software package and were converted to the Zi, scale using a main beam elliciency of 0.", The data were reduced in the standard manner using the software package and were converted to the $T_{\rm mb}$ scale using a main beam efficiency of 0.7. + The seventeen positions are at different olfsets ancl at shorter spacings than those of Gregersen&Evans(2000)., The seventeen positions are at different offsets and at shorter spacings than those of \citet{gregersen&evans00}. +. The line profiles are cisplaved in Fig 1.., The line profiles are displayed in Fig \ref{data}. + Again. the presence of both blue and red. asymmetric line profiles is apparent.," Again, the presence of both blue and red asymmetric line profiles is apparent." + The two datasets cover dillerent. though overlapping. parts of the cloud. (note that. as is often the case for prestellar cores. the position of the centre of the cloud. is somewhat uncertain - see. e.g. the SCUBA cust emission. map of Shirley et al 2000)," The two datasets cover different, though overlapping, parts of the cloud (note that, as is often the case for prestellar cores, the position of the centre of the cloud is somewhat uncertain - see, e.g., the SCUBA dust emission map of Shirley et al 2000)." + While in our map the majority of the profiles are red asvmmetrie line profiles. the opposite is the case for the CGregersen&Evans(2000). dataset.," While in our map the majority of the profiles are red asymmetric line profiles, the opposite is the case for the \citet{gregersen&evans00} dataset." + Where the pointing positions between the Cregersen&Evans(2000) dataset and the present study overlap (in the north-cast top right] corner) it was verified that the datasets match each other., Where the pointing positions between the \citet{gregersen&evans00} dataset and the present study overlap (in the north-east [top right] corner) it was verified that the datasets match each other. + Inspection of the data of Gregersen&Evans(2000) and Fie P. reveals that the blue and red. asymmetric line profiles are found on either side of an axis that runs from SW to NEE.," Inspection of the data of \cite{gregersen&evans00} and Fig \ref{data} + reveals that the blue and red asymmetric line profiles are found on either side of an axis that runs from SW to NE." + This axis is displaced to the NW of the zero ollset. position of our dataset but would run through the centre of the combined datasets., This axis is displaced to the NW of the zero offset position of our dataset but would run through the centre of the combined datasets. + The change in asymmetry is in broad accord with the lower spatial resolution CS2.+1 data of Leeetal.(1999). (obtained with FCRAQO) in which the sense of asymmetry of the line profiles switches from blue in the north of LIGSOB to red in the south.," The change in asymmetry is in broad accord with the lower spatial resolution ${\rm +CS~{2\rightarrow 1}}$ data of \citet{lee.et.al99} (obtained with FCRAO) in which the sense of asymmetry of the line profiles switches from blue in the north of L1689B to red in the south." + This indicates that there is dynamical activity in the HCO— emitting gas., This indicates that there is dynamical activity in the ${\rm HCO^+}$ emitting gas. + Since the outer lavers of the cloud. as traced by CHO. are quiescent (the hyperfine structure is well resolved - Redmanetal. 2002)) the dynamically active gas must lie within the CO depleted. region.," Since the outer layers of the cloud, as traced by ${\rm +C^{17}O}$, are quiescent (the hyperfine structure is well resolved - \citealt{redman.et.al02b}) ) the dynamically active gas must lie within the CO depleted region." + A blue asymmetric line profile in an infalling core will be ormect if (i) the infall velocity increases less slowly than lír and (i) the excitation temperature increases. towards he centre (e.g. Evans 1999))., A blue asymmetric line profile in an infalling core will be formed if (i) the infall velocity increases less slowly than $1/r$ and (ii) the excitation temperature increases towards the centre (e.g. \citealt{evans99}) ). + The cust radiative transfer modelling carried out by Evansetal.(2001). demonstrates hat the second of these conditions may not be met in an object like LIGSOB since the dust temperature (and. if they are well coupled. the gas temperature) decreases. towards he centre of the cloud.," The dust radiative transfer modelling carried out by \citet{evans.et.al01} demonstrates that the second of these conditions may not be met in an object like L1689B since the dust temperature (and, if they are well coupled, the gas temperature) decreases towards the centre of the cloud." + Furthermore. of course. the presence of red. asvmametrie line profiles as well as blue asymmetric xolfiles toward the centre of the cloud means that simple infall cannot explain the observational data.," Furthermore, of course, the presence of red asymmetric line profiles as well as blue asymmetric profiles toward the centre of the cloud means that simple infall cannot explain the observational data." + Since star. formation is usually accompanied by outllows. one possible explanation is that an outllow is the cause of the changes in the sense of the asvnunetry.," Since star formation is usually accompanied by outflows, one possible explanation is that an outflow is the cause of the changes in the sense of the asymmetry." + Llowever. this can be discounted here since the CO would be," However, this can be discounted here since the CO would be" +for most search strategies.,for most search strategies. + In principle the παπα. of candidate galaxies could be reduced if the distance cau be constrained from the CW signal: however. distance estimates for individual eveuts are rather uucertain. especially at that low SNRs that will characterize most cleteetions CNissaukeetal.2010).," In principle the number of candidate galaxies could be reduced if the distance can be constrained from the GW signal; however, distance estimates for individual events are rather uncertain, especially at that low SNRs that will characterize most detections \citep{Nissanke+10}." +. Moreover. οποια! ealaxy catalogs are incomplete withiu the ALIGO/Vireo vole (e.g. Iulkuni&Kaslial 2009)). especially at lower huuinosities.," Moreover, current galaxy catalogs are incomplete within the ALIGO/Virgo volume (e.g. \citealt{Kulkarni&Kasliwal09}) ), especially at lower luminosities." + Finally. some merecrs may also occur outside of their host galaxies (Berger20102:Kelley 2010).," Finally, some mergers may also occur outside of their host galaxies \citep{Berger10,Kelley+10}." +. At the present there are no optical or radio facilities that can provide all-sky coverage at a cadence and depth aatched to the expected light curves of EM counterparts., At the present there are no optical or radio facilities that can provide all-sky coverage at a cadence and depth matched to the expected light curves of EM counterparts. + As we show in this paper. even the Large Synoptic Survey Telescope (LSST}. with a planned all-sky cadence of 1 d and a depth of rz2L7 mag. is unlikely to effectively capture the range of expected EM counterparts.," As we show in this paper, even the Large Synoptic Survey Telescope (LSST), with a planned all-sky cadence of 4 d and a depth of $r\approx 24.7$ mag, is unlikely to effectively capture the range of expected EM counterparts." + Thus. targeted follow-up of GW eor regions is required. whether the aim is to detect optical or radio counterparts," Thus, targeted follow-up of GW error regions is required, whether the aim is to detect optical or radio counterparts." + Even with this approach. the follow-up observations will still require l]lauege field-of-view telescopes to cover tens of square degrees: targeted observations of galaxies are unlikely το substantially reduce the large amount of time to scan the full error reelon.," Even with this approach, the follow-up observations will still require large field-of-view telescopes to cover tens of square degrees; targeted observations of galaxies are unlikely to substantially reduce the large amount of time to scan the full error region." + Our investigation of EM counterparts is organize as follows., Our investigation of EM counterparts is organized as follows. + We beeiu by comparing various types of LM counterparts. cach illustrated by the scliematic diagram in Figure 1..," We begin by comparing various types of EM counterparts, each illustrated by the schematic diagram in Figure \ref{fig:cartoon}." + The first is au SCRB. powere * accretion. following the merger (52).," The first is an SGRB, powered by accretion following the merger $\S\ref{sec:GRB}$ )." + Even if no SCRB is produced or detected. the merger may stil © accompanied by relativistic ejecta. which will power ron-thermal afterglow ciuission as it interacts with the sarounding medium.," Even if no SGRB is produced or detected, the merger may still be accompanied by relativistic ejecta, which will power non-thermal afterglow emission as it interacts with the surrounding medium." + Iu 63 we explore the properties of such “orphan afterelows from bursts with jets noarlv aligned towards Earth (optical afterelows: 63.1) aud for arecr viewing angeles (late radio afterelows: 63.2)., In $\S\ref{sec:ag}$ we explore the properties of such “orphan afterglows” from bursts with jets nearly aligned towards Earth (optical afterglows; $\S\ref{sec:oa}$ ) and for larger viewing angles (late radio afterglows; $\S\ref{sec:ra}$ ). + We constrain our models using the existing observations of SCRB afterelows. coupled with off-axis afterglow models.," We constrain our models using the existing observations of SGRB afterglows, coupled with off-axis afterglow models." + We also provide a realistic assessineut of the required 6serving fiue and achievable depths in the optical and radio bands., We also provide a realistic assessment of the required observing time and achievable depths in the optical and radio bands. +" In 51 we consider isotropic optical transicuts powered by the radioactive decay of heavy elements svuthesized iu the ejecta (""lilonovac"").", In $\S\ref{sec:kilonova}$ we consider isotropic optical transients powered by the radioactive decay of heavy elements synthesized in the ejecta (“kilonovae”). + Iu 55 we conrpare aud contrast the potential counterparts iu the context of our four Cardinal Virtues., In $\S\ref{sec:compare}$ we compare and contrast the potential counterparts in the context of our four Cardinal Virtues. + Although some of these counterparts have been discussed previously in the literature. we examine them together to better highleht their relative strengths and weaknesses.," Although some of these counterparts have been discussed previously in the literature, we examine them together to better highlight their relative strengths and weaknesses." + Drawing ou the properties of the various counterparts. iu retsec:strateey we make specific reconunuendatious for optimizing the follow-up with 5-raw satellites. wicle-field optical telescopes (PTF. Pau-STARRS. LSST). and radio telescopes (EVLA. ASIXAP).," Drawing on the properties of the various counterparts, in \\ref{sec:strategy} + we make specific recommendations for optimizing the follow-up with $\gamma$ -ray satellites, wide-field optical telescopes (PTF, Pan-STARRS, LSST), and radio telescopes (EVLA, ASKAP)." + We sunuuarize our conclusions i 87., We summarize our conclusions in $\S\ref{sec:conclusion}$. + The most commonly discussed EXD counterpart of NS-NS/NS-DII 1iergers is an SCRD. powered bv accretion outo the ceutral compact object (e.g.. Paczvuski1986:etal 2011))," The most commonly discussed EM counterpart of NS-NS/NS-BH mergers is an SGRB, powered by accretion onto the central compact object (e.g., \citealt{Paczynski86,Eichler+89,Narayan+92,Rezzolla+11}) )." + TheSuvfé satellite. and rapid follow- observations with eround-hased telescopes. have revolutionized our understanding of SGRDs by detecting and localizing a significant umber of their afterglows for the first time (e.c. Dergeretal.2005:Foxoet2005:Tjorthetal.Bloom 20063).," The satellite, and rapid follow-up observations with ground-based telescopes, have revolutionized our understanding of SGRBs by detecting and localizing a significant number of their afterglows for the first time (e.g., \citealt{Berger+05,Fox+05,Hjorth+05,Bloom+06}) )." + This has enabled the discovery that SGBDs originate from more evolved stellar populations than those of long-«duration GRBs. consistent with au origin associated withNS-NS nerecrs (Bergerctal.2005:Bloomet2006:Leibler&Berger2010:2011b:Fongetal. 2011a).," This has enabled the discovery that SGRBs originate from more evolved stellar populations than those of long-duration GRBs, consistent with an origin associated withNS-NS mergers \citep{Berger+05,Bloom+06,Leibler&Berger10,Berger11,Fong+11}." +. The study of SGRD afterglows has also established a scale or the energy release and circmmbiurst density that are ower than for long CRBs. with Ez10°! erg and nS0.1 cmt? (Bergeretal.2005:Soderberg2006:Berger 2007a).," The study of SGRB afterglows has also established a scale for the energy release and circumburst density that are lower than for long GRBs, with $E\lesssim 10^{51}$ erg and $n\lesssim 0.1$ $^{-3}$ \citep{Berger+05,Soderberg+06,Berger+07}." +. These observations have also provided evidence ‘or collimation im at least oue case (GRDB0051221A). with a jet halfopening angle of 0;z0.12 (Burrowsotal.2006:Soderbergetal. 2006).. aud upper or lower limits in additional cases (Foxetal.2005:Cape2006:)horger 20075).. overall suggestive of wider opening angles than for long CRBs.," These observations have also provided evidence for collimation in at least one case 051221A), with a jet half-opening angle of $\theta_j\approx +0.12$ \citep{Burrows+06,Soderberg+06}, and upper or lower limits in additional cases \citep{Fox+05,Grupe+06,Berger07}, overall suggestive of wider opening angles than for long GRBs." + Despite this progress. it is not vet established that all SCRDs are uniquely associated with DII mereers (e.g. Iurlewvetal.2005:Moetzeer 2008b)). nor that all mergers lead to an energetic GRD.," Despite this progress, it is not yet established that all SGRBs are uniquely associated with NS-NS/NS-BH mergers (e.g., \citealt{Hurley+05,Metzger+08}) ), nor that all mergers lead to an energetic GRB." + The οποιον of the CRB jet. for instance. may depend sensitively on the mass of the remnant accretion disk. which from nmnnerical siaulations appears to vary by ordersof anagnitude (~10°0.1 ML). dependingon the properties of the binary and the high-density equation of state (Ruffertctal.1997:Janka1999:Lee2001: 2010)..," The energy of the GRB jet, for instance, may depend sensitively on the mass of the remnant accretion disk, which from numerical simulations appears to vary by orders of magnitude $\sim +10^{-3}-0.1$ $_\odot$ ), depending on the properties of the binary and the high-density equation of state \citep{Ruffert+97,Janka+99,Lee01,Rosswog+03,Shibata&Taniguchi08,Duez+09,Chawla+10}. ." + Although SCRBs are bright. they occur relatively rarely within the range of ALICO/Vireo.," Although SGRBs are bright, they occur relatively rarely within the range of ALIGO/Virgo." +" To illustrate this poit. in Figure 2 we plot the cumulative rate at which SCRDs are currently detected: above a redshift 2. οπώνi). 7), "," To illustrate this point, in Figure \ref{fig:redshift} we plot the cumulative rate at which SGRBs are currently detected above a redshift $z$ , $\dot{N}_{\rm GRB,obs} +(>z)$ ." +This distribution iucludes 19, This distribution includes 19 +where we usecl that 944=3.,where we used that $\delta_{\alpha \alpha}=3$. + Here O is the augle between the filament direction (aud ποια! to the shock lor GRBs) aud the particle velocity Gin an observer's frame). which is approximately the direction toward an observer. that is vik for an ultra-relativistie particle (because of relativistic beaming. the emitted radiation is localized withiu a narrow cone of angle 1/5).," Here $\Theta$ is the angle between the filament direction (and normal to the shock for GRBs) and the particle velocity (in an observer's frame), which is approximately the direction toward an observer, that is ${\bf v\|k}$ for an ultra-relativistic particle (because of relativistic beaming, the emitted radiation is localized within a narrow cone of angle $\sim 1/\gamma$ )." + Eq. (1)), Eq. \ref{w1s}) ) + becomes πμ... pdhea., becomes ) ) d^2. + Equatious (3)).3)) fully determine the spectrum of jitter radiation from relativistic electrous propagating through the Weibel turbulence., Equations \ref{dW-1}) \ref{w-main}) ) fully determine the spectrum of jitter radiation from relativistic electrons propagating through the Weibel turbulence. + First. we cau simplify tle vector expression iu ) (3)).," First, we can simplify the vector expression in \ref{dW-1}) )." + Indeed. iu the ultrarelativistic case. the longitudinal compouent o “the acceleration is small coupared to the Tablisvelse Colp¢μοι. σεjαςcadiταςoul.," Indeed, in the ultrarelativistic case, the longitudinal component of the acceleration is small compared to the transverse component, $w_\|/w_\bot\sim1/\gamma^2\ll1$." + Therefore. Viald νν are approximately perpeixicular to each other., Therefore ${\bf v}$ and ${\bf w}$ are approximately perpendicular to each other. + Second. the dominant contribution to the iweg‘al over dQ comes fromstiall aieles 0~l/5 with respect to the particle’s velocity.," Second, the dominant contribution to the integral over $d\Omega$ comes fromsmall angles $\theta\sim1/\gamma$ with respect to the particle's velocity." + Therefore. we approximately write i2uwου..jte(P+> 7).," Therefore, we approximately write $\omega'\simeq\omega\left(1-v/c+\theta^2/2\right) \simeq\frac{1}{2}\omega\left(1-v^2/c^2+\theta^2\right) +=\frac{1}{2}\omega\left(\theta^2+\gamma^{-2}\right)$ ." + We now can rejxace integration over the solid auge dQ~0dOdo with integration over dodaω aud integrate equation (3)) over the azimutlal angle. ©. [rou 0 to 2x.," We now can replace integration over the solid angle $d\Omega\simeq\theta\,d\theta\,d\phi$ with integration over $d\phi\,d\omega'/\omega$ and integrate equation \ref{dW-1}) ) over the azimuthal angle, $\phi$, from $0$ to $2\pi$." + The spectral power emited » a relativistic particle moviig through sinall-scale. raucom magnetic fields. uuder the assumj»tjon that the deflection angle is negligible aud the particle trajectory is a stratelit line. has been derived elsewhere (Laudau&Lifshitz1971:Medvedev 2000):: Judd.," The angle-averaged spectral power emitted by a relativistic particle moving through small-scale random magnetic fields, under the assumption that the deflection angle is negligible and the particle trajectory is a straight line, has been derived elsewhere \citep{LL,M00}: : ." +?..,\cite{Spitzer}. + In the case of adiabatic expansion this equation reads: where InA is the Coulomb logarithm., In the case of adiabatic expansion this equation reads: where $\ln\Lambda$ is the Coulomb logarithm. + The first term in Eq., The first term in Eq. +" A] corresponds to the heating of electrons due to Coulomb interactions with the protons of temperature T;, and the second one corresponds to the cooling of the electron gas due to the adiabatic expansion of the SNR.", \ref{eq-Spitzer-Te} corresponds to the heating of electrons due to Coulomb interactions with the protons of temperature $T_p$ and the second one corresponds to the cooling of the electron gas due to the adiabatic expansion of the SNR. +" This equation has to be coupled with the equation that connects Τρ and Τε with macroscopic parameters such as the gas pressure and density and with the equation that allows us to change coordinate system from the system moving with the gas to the system connected with the center of the explosion: Together with the boundary condition T.(€=1,t)/T,(€1,t)=m./m; this forms a complete set of equations for determining the electron temperature T;(£,t) inside a SNR."," This equation has to be coupled with the equation that connects $T_p$ and $T_e$ with macroscopic parameters such as the gas pressure and density and with the equation that allows us to change coordinate system from the system moving with the gas to the system connected with the center of the explosion: Together with the boundary condition $T_e(\xi=1,t)/T_p(\xi=1,t)=m_e/m_p$ this forms a complete set of equations for determining the electron temperature $T_e(\xi,t)$ inside a SNR." + By solving Eq., By solving Eq. +" we derive the electron temperature T;(£,t) in the radial coordinate[ή] £."," \ref{eq-Spitzer-Te} we derive the electron temperature $T_e(\xi,t)$ in the radial coordinate $\xi$." + In order to compare this profile with observations we have to take into account projection effects., In order to compare this profile with observations we have to take into account projection effects. +" To do this we use the following formula for the thermal bremsstrahlung (TB) emission of the volume element dV at distance D (?)): where gr; — is the thermal Gaunt factor, gy;7:1, and the electron temperature Τε here is a function of the distance £ to the SNR The integration of this expression along the line of sight gives the flux from an area dS at a projected distance x=r'/T'sp from the SNR center."," To do this we use the following formula for the thermal bremsstrahlung (TB) emission of the volume element $dV$ at distance $D$ \citealt{Rybicki-Lightman}) ): where $g_{ff}$ – is the thermal Gaunt factor, $g_{ff}\approx 1$, and the electron temperature $T_e$ here is a function of the distance $\xi$ to the SNR The integration of this expression along the line of sight gives the flux from an area dS at a projected distance $\chi=r/r_{sh}$ from the SNR center." + The red points in Fig., The red points in Fig. + [5] represent the expected flux as a function of energy for x=0.7., \ref{fig:spectra-chi=05} represent the expected flux as a function of energy for $\chi=0.7$. +" As it can be easily seen this spectrum is not exactly thermal, being the superposition of different thermal spectra characterized by different temperatures."," As it can be easily seen this spectrum is not exactly thermal, being the superposition of different thermal spectra characterized by different temperatures." +" However, a thermal bremsstrahlung spectrum gives a very good approximation to the predicted points."," However, a thermal bremsstrahlung spectrum gives a very good approximation to the predicted points." +" This is shown in Fig. D],"," This is shown in Fig. \ref{fig:spectra-chi=05}," + where the solid line represents the thermal bremsstrahlung emission for an effective temperature defined as the peak of the expected x-ray emission., where the solid line represents the thermal bremsstrahlung emission for an effective temperature defined as the peak of the expected x-ray emission. + The dependence of this effective temperature from x is shown in Fig. B]., The dependence of this effective temperature from $\chi$ is shown in Fig. \ref{fig:Te-chi}. +" This figure shows that, for a broad range of parameters such as explosion energy, SNR age and CR acceleration efficiency, such an effective electron temperature is almost constant in the inner (x< 0.9) region of the SNR."," This figure shows that, for a broad range of parameters such as explosion energy, SNR age and CR acceleration efficiency, such an effective electron temperature is almost constant in the inner $\chi<0.9$ ) region of the SNR." +" So, it is reasonable to study the dependence of Τε on other parameters not for all the values of x, but only for some fixed x<0.9."," So, it is reasonable to study the dependence of $T_e$ on other parameters not for all the values of $\chi$, but only for some fixed $\chi<0.9$." + In the following we will adopt x=0.7., In the following we will adopt $\chi=0.7$. +" Finally, the triangles in Fig."," Finally, the triangles in Fig." + B| show the temperature one would observe by integrating the whole X-ray emission from the SNR., \ref{fig:Te-chi} show the temperature one would observe by integrating the whole X-ray emission from the SNR. + The discrepancy between the triangles and the curves is always below 5%.., The discrepancy between the triangles and the curves is always below . +Iu this paper. we only cousider the evolution of iron aud oxveen.,"In this paper, we only consider the evolution of iron and oxygen." +" The oxveen aud wou production for Type II SNs and Type Ia SNs ire taken frou: Woosley Weaver (1995) and Woosley (1997). respectively,"," The oxygen and iron production for Type II SNs and Type Ia SNs are taken from Woosley Weaver (1995) and Woosley (1997), respectively." + Recently. using the evolutionary tracks of Cóoneva eroup up to the carly asvinptotic giant brauch. (ACB) in combination with a svuthetic thermal-pulsing ACD model. van den Dock Crocuewegen (1997) calculated in detail the chemical evolution and vields of six eleiieuts up to the cud of ACB.," Recently, using the evolutionary tracks of Geneva group up to the early asymptotic giant branch (AGB) in combination with a synthetic thermal-pulsing AGB model, van den Hock Groenewegen (1997) calculated in detail the chemical evolution and yields of six elements up to the end of AGB." + Their results showed that the low-nass stars (20< 23M.) produce simall amounts of oxveenu. vot the intermediate mass stars (BAL.90 and are plotted as red dots in the color-magnitude diagram of Figure 1., All 11 UCD candidates have a $S/N>90$ and are plotted as red dots in the color-magnitude diagram of Figure 1. +" In color and magnitude most UCDs overlap with the brightest globular clusters, the very same is the case for UCDs in the core of the Coma cluster, tthey share the same parameter space of the brightest globular clusters associated with NGC 4874 (Paper I)."," In color and magnitude most UCDs overlap with the brightest globular clusters, the very same is the case for UCDs in the core of the Coma cluster, they share the same parameter space of the brightest globular clusters associated with NGC 4874 (Paper I)." +" The brightest UCD candidate is a M32-like object located, in projection, ~6.6 kpc away from the center of the galaxy."," The brightest UCD candidate is a M32-like object located, in projection, $\sim$ 6.6 kpc away from the center of the galaxy." +" Its effective radius is rj=77.1 pc, its magnitude masonLp=18.49, or two magnitudes brighter than the second brightest UCD candidate, and its is color particularly red (F475W—F850LP)=2.28."," Its effective radius is $r_h=77.1$ pc, its magnitude $m_{F850LP}=18.49$, or two magnitudes brighter than the second brightest UCD candidate, and its is color particularly red $(F475W-F850LP)= 2.28$." + In the framework of a dual formation mechanism for UCDs proposed by Da Rocha et ((2011) and Norris Kannappan (2011) this candidate is the remaining nucleus of a stripped companion of NGC 1132 due to the clear gap of two magnitudes between the brightest globular clusters and this UCD., In the framework of a dual formation mechanism for UCDs proposed by Da Rocha et (2011) and Norris Kannappan (2011) this candidate is the remaining nucleus of a stripped companion of NGC 1132 due to the clear gap of two magnitudes between the brightest globular clusters and this UCD. +" This object is similar to SDSS J124155.3--114003.7, the UCD reported by Chilingarian Mamon (2008) at a distance of 9 kpc from M59."," This object is similar to SDSS J124155.3+114003.7, the UCD reported by Chilingarian Mamon (2008) at a distance of 9 kpc from M59." + As stated by Norris Kannappan (2011) no globular cluster system has a luminosity function continuously extending up to such high luminosity., As stated by Norris Kannappan (2011) no globular cluster system has a luminosity function continuously extending up to such high luminosity. +" As shown in Paper I, not even the extremely rich globular cluster system of NGO 4874 in the core of the Coma cluster has members with magnitudes similar to the brightest UCD candidate."," As shown in Paper I, not even the extremely rich globular cluster system of NGC 4874 in the core of the Coma cluster has members with magnitudes similar to the brightest UCD candidate." +" This object was catalogued by the Two Micron All Sky Survey as 2MASS-02525121-0116193, its K band magnitude is My=13.505 mag (Skrutskie et 22006)."," This object was catalogued by the Two Micron All Sky Survey as 2MASS-02525121-0116193, its K band magnitude is $M_K=13.505$ mag (Skrutskie et 2006)." + A size estimate for the M32 counterpart was also carried out with (Peng et 22002) using a Sersic model with an initial Sersic index of n—2 (Sersic 1968)., A size estimate for the M32 counterpart was also carried out with (Peng et 2002) using a Sersic model with an initial Sersic index of $n=2$ (Sersic 1968). +" Using the best fit for this object has a reduced y?=1.008 and yields n=2.4, and rj=89.2 pc."," Using the best fit for this object has a reduced $\chi^2$ =1.008 and yields $n=2.4$, and $r_h=89.2$ pc." + The original image of the brightest UCD and the residual after model subtraction with both andISHAPE is given in Figure 2., The original image of the brightest UCD and the residual after model subtraction with both and is given in Figure 2. + The best fit of two different analytical models and different software leaves a small residual in the core., The best fit of two different analytical models and different software leaves a small residual in the core. + Similar residuals are found by Price et ((2009) studying several compact elliptical galaxies in the core of the Coma Cluster., Similar residuals are found by Price et (2009) studying several compact elliptical galaxies in the core of the Coma Cluster. +" The brightest UCD candidate is comparable, but slightly smaller than the compact elliptical galaxies studied by Price et al. ("," The brightest UCD candidate is comparable, but slightly smaller than the compact elliptical galaxies studied by Price et al. (" +2009) which have effective radii of rj~200 pc.,2009) which have effective radii of $r_h\sim200$ pc. + This object is also fainter than the Price compact ellipticals which have magnitudes ranging from mg=18.34 to mg=21.33 mag., This object is also fainter than the Price compact ellipticals which have magnitudes ranging from $m_B=18.34$ to $m_B=21.33$ mag. + Photometric and structural parameters of the eleven UCD candidates are presented in Table 1., Photometric and structural parameters of the eleven UCD candidates are presented in Table 1. +" An additional 39 sources are positively resolved in both bands and have effective radii between 8.2 pc and 59.7 pc, with a median r,=11.6 pc."," An additional 39 sources are positively resolved in both bands and have effective radii between 8.2 pc and 59.7 pc, with a median $r_h =11.6$ pc." + While these sources have the size characteristic of UCDs their magnitudes fall short of the minimum threshold for the selection criteria., While these sources have the size characteristic of UCDs their magnitudes fall short of the minimum threshold for the selection criteria. +" These extended stellar systems have received several denominations, here we refer to them as extended star clusters."," These extended stellar systems have received several denominations, here we refer to them as extended star clusters." + Extended star clusters are plotted as blue squares on the CMD of Figure 1., Extended star clusters are plotted as blue squares on the CMD of Figure 1. +" Even if these extended star clusters are not as bright as UCDs, in luminosity some of these objects are comparable to w Centauri."," Even if these extended star clusters are not as bright as UCDs, in luminosity some of these objects are comparable to $\omega$ Centauri." +nder very coustraimed conditions. as described in detail in Dussoetal(2001).,"under very constrained conditions, as described in detail in \cite{busso01}." +. The weal s-process. also involved in Zr production. utilizes 7?Ne as the neutron source.," The weak $s$ -process, also involved in Zr production, utilizes $^{22}$ Ne as the neutron source." + Iwarakas&Lattanzio(2007) provides an cstimate of ιο total vield of clemeuts heavier than the Fe-peak (i.e. bevoud the maximi atomic mass included im their reaction network) in ACB stars., \cite{karakas08} provides an estimate of the total yield of elements heavier than the Fe-peak (i.e. beyond the maximum atomic mass included in their reaction network) in AGB stars. + Their results suggest iat the production of Zr is biased towards lower mass ACB stars than those within which the heavy isotopes of Mg ofare made. which could explain why |Zr/Fe| docs rot appear to vary among the M71 eiauts im our sample.," Their results suggest that the production of Zr is biased towards lower mass AGB stars than those within which the heavy isotopes of Mg are made, which could explain why [Zr/Fe] does not appear to vary among the M71 giants in our sample." + Better models to verify the consistency of our results witli he predicted behavior of Zr aud La vs the Mg isotope ratios in ACB stars as a function of mass are needed., Better models to verify the consistency of our results with the predicted behavior of Zr and La vs the Mg isotope ratios in AGB stars as a function of mass are needed. + Eu serve the same role for the process of neutron capture which produces selected. isotopes of heavy elements bevoud the Fe peak., Eu serve the same role for the $r$ -process of neutron capture which produces selected isotopes of heavy elements beyond the Fe peak. + No credible star-to-star variations could be detected among the huuinous MTI giants in [Eu/Fe} based on the strength of the 6615 line of Eu II., No credible star-to-star variations could be detected among the luminous M71 giants in [Eu/Fe] based on the strength of the 6645 line of Eu II. + With the aid of exquisite spectral resolution aud very luigh signal-to-noise spectra combined with a very careful analysis. we lave deteriuned Meg isotopic ratios for 9 huninous elauts iu the metalrvich Calactic elobular cluster M71.," With the aid of exquisite spectral resolution and very high signal-to-noise spectra combined with a very careful analysis, we have determined Mg isotopic ratios for 9 luminous giants in the metal-rich Galactic globular cluster M71." + We have also used these spectra to determüne precision abundances for several other elements in this GC. including the light clements O. Na. Me. and AT.," We have also used these spectra to determine precision abundances for several other elements in this GC, including the light elements O, Na, Mg, and Al." +" The abunudauces of Si, Ca. Ti. Ni aud Fe do not show any star-to-star variations."," The abundances of Si, Ca, Ti, Ni and Fe do not show any star-to-star variations." + The total range for the absolute Fe abundance. log|e(Fe)]. amoug the sample of 9 eiauts in MTI is only 0.08 dex.," The total range for the absolute Fe abundance, $\epsilon$ (Fe)], among the sample of 9 giants in M71 is only 0.08 dex." + Once the depeudence ou iis removed. all the M71 giants have identical [Fe/TI]. [Si/Fe|. |Ca/Fe]. [Ti/Fe|] aud [Ni/Fo] to within σ=0.01 dex (105€)).," Once the dependence on is removed, all the M71 giants have identical [Fe/H], [Si/Fe], [Ca/Fe], [Ti/Fe] and [Ni/Fe] to within $\sigma = 0.04$ dex )." + This places a strong coustraint ou the nuiformity of mixing in the vouug GC., This places a strong constraint on the uniformity of mixing in the young GC. + These clemeuts cannot have been produced in auvthing other than the first eeneratiou of GC stars., These elements cannot have been produced in anything other than the first generation of GC stars. + We see the expected correlations aud auticorrelatious iunones the light clements O. Na. Me. and Alin the MT1 eqauts.," We see the expected correlations and anticorrelations among the light elements O, Na, Mg, and Al in the M71 giants." + But the amplitude of the stir-to-star variations among these clementsis small. 0.3 dex for |O/Fe}. 0.6 dex for 0.2 dex for aud at most 0.1 dex for [Na/Fe|.," But the amplitude of the star-to-star variations among these elements is small, 0.3 dex for [O/Fe], 0.6 dex for [Na/Fe], 0.2 dex for [Al/Fe], and at most 0.1 dex for [Mg/Fe]." +"""Fel. Carrettaet|Al/Fe|.al(2007). lave looked for a luk [Mgbetween chemical anomalies along the RGB and other properties of GCs.", \cite{carretta07} have looked for a link between chemical anomalies along the RGB and other properties of GCs. + Tn addition to the obvious suggestion that higher amplitude star-to-star variations should be found iu higher mass GCs. which with their lugher binding energies wav be better able to retain stellar ejecta. they sugeest that the hieh temperature extension of the horizoutal brauchblue tailis lonegcr iu GCs with higher amplitudeNa-O anticorrclatious.," In addition to the obvious suggestion that higher amplitude star-to-star variations should be found in higher mass GCs, which with their higher binding energies may be better able to retain stellar ejecta, they suggest that the high temperature extension of the horizontal branch blue tail is longer in GCs with higher amplitude Na-O anticorrelations." + The latter is attributed to a spread in He. aud hence max again be tied to the ability to retain ejectecl gas. see the discussion in Carrettaetal(2007).," The latter is attributed to a spread in He, and hence may again be tied to the ability to retain ejected gas, see the discussion in \cite{carretta07}." +. We suggest that oue additional parameter is relevant. the Feanetallicitv of the GC.," We suggest that one additional parameter is relevant, the Fe-metallicity of the GC." + As the stellar iiectallicity becomes higher. the effect of the addition of AGB processed material. whose uucleosvutliesis proceeds among the light elements ii a manner which is somewhat independent of their initial metallicity. would be diluted. and the resulting vield. asstuned to be positive. reduced.," As the stellar metallicity becomes higher, the effect of the addition of AGB processed material, whose nucleosynthesis proceeds among the light elements in a manner which is somewhat independent of their initial metallicity, would be diluted, and the resulting yield, assumed to be positive, reduced." + Such an effect is apparent iu the calculation of ACB vields by Karalas&Lattanzio(2007).. amone others.," Such an effect is apparent in the calculation of AGB yields by \cite{karakas08}, among others." + This would explain why the most prominent cases of star-to-star variations within GCs are seen among the lower moetallicitv. COCs (i.c. M15. AILS. ete) even though there are a umber of quite massive high-uetallicity. GCs such as 1? Tuc for which Carrettaetal(2001). found ouly modest star-to-star variations among the light elements.," This would explain why the most prominent cases of star-to-star variations within GCs are seen among the lower metallicity GCs (i.e. M15, M13, etc) even though there are a number of quite massive high-metallicity GCs such as 47 Tuc for which \cite{carretta04} found only modest star-to-star variations among the light elements." + In this context it is iuteresting to note that the behavior of CII aud CN bands in these relatively high metallicity COCs teuds to be bimodal. while in more metal-poor GCs. stars fill the eutire rauge of € aud N abundances without being so concentrated towards the upper aud lower extremes of [C/Fe] (see.c.g.Fig.11ofCohen.Briley&Stetson2005)..," In this context it is interesting to note that the behavior of CH and CN bands in these relatively high metallicity GCs tends to be bimodal, while in more metal-poor GCs, stars fill the entire range of C and N abundances without being so concentrated towards the upper and lower extremes of [C/Fe] \citep[see, e.g. Fig.~11 of][]{cohen_m15_c}." + The heavy Ale isotopes among the CN weak eiauts in our M71 sample have very low Ale isotopic ratios PO°\ ToEe (© )) which are consistent with models of ealactic chemical1% evolution with no contribution frou ACD stars., The heavy Mg isotopes among the CN weak giants in our M71 sample have very low Mg isotopic ratios $^{26}$ Mg/Mg $\sim$ ) which are consistent with models of galactic chemical evolution with no contribution from AGB stars. + These stars are both CN weak and have ight clement abundances typical of field Calactic halo uetal-poor stars of similar Feanetallicitv: we call them he “normal” stars., These stars are both CN weak and have light element abundances typical of field Galactic halo metal-poor stars of similar Fe-metallicity; we call them the “normal” stars. + Rroupa&Boily(2002)— discuss orniue the Galactic halo field via dissolved. COCs: our results sugeest that this must have involved the “normal” CC stars from clusters which dissolved. early ou before heir intermediate-mass stars reached the ACB., \cite{kroupa02} discuss forming the Galactic halo field via dissolved GCs; our results suggest that this must have involved the “normal” GC stars from clusters which dissolved early on before their intermediate-mass stars reached the AGB. + The CN strong M71 eiants have higher Me isotopic ratios PONTeAle (~8%)). but these are far below previously miblished values by Yongetal.(2006) and references herein for more metal-poor GC giants.," The CN strong M71 giants have higher Mg isotopic ratios $^{26}$ Mg/Mg $\sim$ ), but these are far below previously published values by \cite{2006ApJ...638.1018Y} and references therein for more metal-poor GC giants." + This group of stars. iu addition to a higher fraction of the heavier Mg isotopes. shows chhanced Na aud Al accompanied by ower ο abuudances.," This group of stars, in addition to a higher fraction of the heavier Mg isotopes, shows enhanced Na and Al, accompanied by lower O abundances." + The behavior of the Me isotopes iu the “normal” stars is reproduced by models of galactic chemical evolution by Fenneretal(2003) without auv coutribution from ACD stars.," The behavior of the Mg isotopes in the “normal” stars is reproduced by models of galactic chemical evolution by \cite{fenner03} + without any contribution from AGB stars." + Their models with the ACD coutribution expected in the normal course of stellar evolution reproduce the behavior of the heavy Ale isotope rich AIT] eiauts., Their models with the AGB contribution expected in the normal course of stellar evolution reproduce the behavior of the heavy Mg isotope rich M71 giants. + These stars naust represent a later generation of stars formed sufficiently long after the first that the AGB coutributiou to their chemical inventory was iuchided., These stars must represent a later generation of stars formed sufficiently long after the first that the AGB contribution to their chemical inventory was included. + Alternatively. the CN-vich aud CN-weak stars mav have formed at the same tine. but the CNoweak stars could have becu formed in an Wuuixed euviromneut. while the CN-stroug stars were born from material polluted by ACD stars.," Alternatively, the CN-rich and CN-weak stars may have formed at the same time, but the CN-weak stars could have been formed in an unmixed environment, while the CN-strong stars were born from material polluted by AGB stars." + With the present work. we believe we have demonstrated convincingly that the difference between the geueratious of GC stars is consistent in detail with the coutribution of ACB stars.," With the present work, we believe we have demonstrated convincingly that the difference between the generations of GC stars is consistent in detail with the contribution of AGB stars." + Furthermore. we have extended our previous results from Moléndez&Co-—ren(2007). based. on imetalpoor halo field dwarts to still higher metallicity. up to the Fe-metallicity of MTI.," Furthermore, we have extended our previous results from \cite{2007ApJ...659L..25M} based on metal-poor halo field dwarfs to still higher metallicity, up to the Fe-metallicity of M71." + d ou the calculations of stellar vields for AGB stars by DasἹνατακας&Lattauzio(2003).. updated im Iarakas&Lattauzio (2007).. stars of initial mass 36 AL. are required to contribute sàiguificaut amounts of the heavier Ale isotopes.," Based on the calculations of stellar yields for AGB stars by \cite{karakas03}, updated in \cite{karakas08}, stars of initial mass 3–6 $_{\odot}$ are required to contribute significant amounts of the heavier Mg isotopes." + Stellar evolutionary tracks establish that stars du this mass range reach the upper ACB at an age of ~0.3 Cor., Stellar evolutionary tracks establish that stars in this mass range reach the upper AGB at an age of $\sim$ 0.3 Gyr. + Asstuning uniform mixing within the eas iu this GC. for a GC as imetalerich as is MTI. this timescale waist reflect the minimi age differeuce," Assuming uniform mixing within the gas in this GC, for a GC as metal-rich as is M71, this timescale must reflect the minimum age difference" +Strong interactions and mergers between galaxies occur more efficiently in the low velocity dispersion environment of galaxy groups (Milesetal.2004).,Strong interactions and mergers between galaxies occur more efficiently in the low velocity dispersion environment of galaxy groups \citep{b105}. +. Therefore in old. relatively isolated groups. most massive galaxies have sufficient time to merge via dynamical friction.," Therefore in old, relatively isolated groups, most massive galaxies have sufficient time to merge via dynamical friction." + If X-ray fossil groups are indeed systems that formed at an earlier epoch. we should be able to verify this from the merger histories of present-day fossils in the Millennium simulation: an exercise that is not directly possible to perform with observational surveys.," If X-ray fossil groups are indeed systems that formed at an earlier epoch, we should be able to verify this from the merger histories of present-day fossils in the Millennium simulation: an exercise that is not directly possible to perform with observational surveys." + In Fig., In Fig. + 6 we trace the mass evolution of present-day X-ray fossil systems backwards fromz— 0. to z—0.52 ," \ref{aadfig7} + we trace the mass evolution of present-day X-ray fossil systems backwards from$z\!=\!0$ , to $z\!=\!0.82$ " +a disk blackbody + power-law or a blackbody + power-law model give acceptable fits to the XIS data alone.,a disk blackbody + power-law or a blackbody + power-law model give acceptable fits to the XIS data alone. + It is important to note the iron line profile recovered from these different continuum models is robust and changes very little in shape., It is important to note the iron line profile recovered from these different continuum models is robust and changes very little in shape. + This demonstrates that the line is not due to continuum components crossing in the iron band., This demonstrates that the line is not due to continuum components crossing in the iron band. +" For slowly rotating neutron stars, the gravitational potential around a neutron star is expected to be very close to a simple Schwarzschild potential."," For slowly rotating neutron stars, the gravitational potential around a neutron star is expected to be very close to a simple Schwarzschild potential." +" In fact, the neutron star spin for 4U 1820—30 and GX 349-+2 inferred from the difference between the freqencies of the kHz QPOs is less than 300 Hz, which would imply that the spin parameter j=cJ/GM?<0.3 (Milleretal.1998)."," In fact, the neutron star spin for 4U $-$ 30 and GX 349+2 inferred from the difference between the freqencies of the kHz QPOs is less than 300 Hz, which would imply that the spin parameter $j\equiv cJ/GM^2 < 0.3$ \citep{miller98}." +. Frame-dragging corrections for such spins should give errors of much less than (Milleretal.1998)., Frame-dragging corrections for such spins should give errors of much less than \citep{miller98}. +". We therefore fit the iron line profiles with a model of line emission from relativistic accretion disk assuming the Schwarzschild ametric (the‘diskline’model,Fabian 1989)."," We therefore fit the iron line profiles with a model of line emission from a relativistic accretion disk assuming the Schwarzschild metric \citep[the `diskline' model,][]{fabian89}." +. The line profiles in all objects can be well fit by this model., The line profiles in all objects can be well fit by this model. + When fitting the lines we restrict the line energy to between 6.4—6.97 keV (the allowed range for different ionization states of Fe K emission)., When fitting the lines we restrict the line energy to between $6.4-6.97$ keV (the allowed range for different ionization states of Fe K emission). +" The inner radius, inclination and disk emissivity are free parameters in the fit, whilst the outer disk radius is fixed at a large value (1000 Ra)."," The inner radius, inclination and disk emissivity are free parameters in the fit, whilst the outer disk radius is fixed at a large value (1000 $R_G$ )." +" The inner radius, Rin, of the accretion disk (in units of gravitational radii, Ra— GM/c?) is important for shaping the line, and is a parameter of the line fit."," The inner radius, $R_{in}$, of the accretion disk (in units of gravitational radii, ${\mathrm R_G = GM/c^2}$ ) is important for shaping the line, and is a parameter of the line fit." + We are therefore able to measure the inner radius of the accretion disk in the three objects., We are therefore able to measure the inner radius of the accretion disk in the three objects. + The full 'diskline' parameters are given in Table 3.., The full `diskline' parameters are given in Table \ref{tab:linefits}. + The inner radius of the accretion disk places an upper limit on the neutron star radius., The inner radius of the accretion disk places an upper limit on the neutron star radius. +" In general, we find that these inner disk radii are in the range 7—8Rc, which is equivalent to 14.5—16.5 km for a 1.4 Mo neutron star."," In general, we find that these inner disk radii are in the range $7 - 8~{\mathrm R_G}$, which is equivalent to $14.5 - 16.5$ km for a 1.4 $_\odot$ neutron star." + We checked that the ‘diskline’ is the appropriate line model to use., We checked that the `diskline' is the appropriate line model to use. + Alternative models have been developed for emission lines formed in the space-time around a spinning, Alternative models have been developed for emission lines formed in the space-time around a spinning +in (he input data stream and performs error detection and reporting with a simple parity check scheme.,in the input data stream and performs error detection and reporting with a simple parity check scheme. + A 5-bit [rame counter in the input frame format is used to svnchronize the three channels., A 5-bit frame counter in the input frame format is used to synchronize the three channels. + The data are then organized into the format required by the correlator., The data are then organized into the format required by the correlator. + A major requirement of the project is to continue scientific observations with the VLA as the EVLA electronies svstems are installed., A major requirement of the project is to continue scientific observations with the VLA as the EVLA electronics systems are installed. + To accommodate (his transition requirement. a cieital filler was implemented in the deformatter FPGAs that selects a 64 MIIz sub-band from the 1 Giz bandwidth available.," To accommodate this transition requirement, a digital filter was implemented in the deformatter FPGAs that selects a 64 MHz sub-band from the 1 GHz bandwidth available." + The sub-band is converted to analog and passed on to ihe VLA baseband svstem (see Figure 5))., The sub-band is converted to analog and passed on to the VLA baseband system (see Figure \ref{fig:dts}) ). + Digitization al the antenna avoids the distortions contributed by an analog (transmission svslem. but raises concerns regarding sell-generated REI.," Digitization at the antenna avoids the distortions contributed by an analog transmission system, but raises concerns regarding self-generated RFI." + Therefore. several features. were implemented in the formatter module (ο suppress REI.," Therefore, several features were implemented in the formatter module to suppress RFI." + Packaging of the digitizers and associated electronics into a single Formatter module avoids the routing of high-speed digital signals between modules and shortens signal runs., Packaging of the digitizers and associated electronics into a single formatter module avoids the routing of high-speed digital signals between modules and shortens signal runs. + Clock signals and RE digitizer inputs enter the module via coaxial cables bonded: at the module wall., Clock signals and RF digitizer inputs enter the module via coaxial cables bonded at the module wall. + Power to the module is provided by a single. heavily filtered. 48 volt supply.," Power to the module is provided by a single, heavily filtered, 48 volt supply." + All operating voltages for electronics inside (he module are obtained from regulators internal (ο the module., All operating voltages for electronics inside the module are obtained from regulators internal to the module. + The high speed digital output. data exit the module via three single-mode optical fibers., The high speed digital output data exit the module via three single-mode optical fibers. + All fiber-optie signals penetrate (he module wall through connectors chosen for their RF attenuation., All fiber-optic signals penetrate the module wall through connectors chosen for their RF attenuation. + The penetrations act as waveguides bevond cutoff and provide eood shielding characteristics., The penetrations act as waveguides beyond cutoff and provide good shielding characteristics. + The hieh-speed electronics in (he module ave cooled by air (lowing trough honevcomb REI filters on the top and bottom of the module enclosure., The high-speed electronics in the module are cooled by air flowing through honeycomb RFI filters on the top and bottom of the module enclosure. + The formatter module is heavily shielded., The formatter module is heavily shielded. + The main module enclosure consists of a welded aluminum box with one open end and the honevconb filters attached on its top and bottom by screws with absorbing RF easkets., The main module enclosure consists of a welded aluminum box with one open end and the honeycomb filters attached on its top and bottom by screws with absorbing RF gaskets. + The major electronics assemblies are attached to a single aluminum bulkhead that runs down the center of the module., The major electronics assemblies are attached to a single aluminum bulkhead that runs down the center of the module. + Final assembly of the module consists of sliding the bulkheacl into the box and securing its [ront cover with an absorbing RF gasket and a large number of screws., Final assembly of the module consists of sliding the bulkhead into the box and securing its front cover with an absorbing RF gasket and a large number of screws. + The shielding effectiveness of the entire assembly has been measured at 85 dB. The EVLA WIDAR (Wideband Interferometer Digital Architecture) correlator is the final destination for all of the real-time wideband signals carefully collected. down-convertecd. and sampled by all of the antennas.," The shielding effectiveness of the entire assembly has been measured at 85 dB. The EVLA WIDAR (Wideband Interferometer Digital Architecture) correlator is the final destination for all of the real-time wideband signals carefully collected, down-converted, and sampled by all of the antennas." + It calculates the cross-correlation Iunction for every pair ol antennas (baseline) in the array., It calculates the cross-correlation function for every pair of antennas (baseline) in the array. + This is no small feat considering the number of antennas in the EVLA (27). the bandwidths observed (16 GIIz per antenna). and the 10 to 10° spectral channels needed per baseline.," This is no small feat considering the number of antennas in the EVLA (27), the bandwidths observed (16 GHz per antenna), and the $10^3$ to $10^6$ spectral channels needed per baseline." +on the quasar SEDs of Elvis et al. (,on the quasar SEDs of Elvis et al. ( +1994) and the UV spectrum of quasars of Telfer et al. (,1994) and the UV spectrum of quasars of Telfer et al. ( +2002) and Richards et al. (,2002) and Richards et al. ( +2003) we inferred the ratio of observed 0.52.0 keV flux to Lya flux of 1.57 and 1.51 for radio-quiet and radio-loud quasars. respectively.,"2003) we inferred the ratio of observed $0.5 - 2.0$ keV flux to $\alpha$ flux of $1.87$ and $1.51$ for radio-quiet and radio-loud quasars, respectively." + For the flux limit in the X-ray band. the maximum magnitude observed for Lya is then 23.34.," For the flux limit in the X-ray band, the maximum magnitude observed for $\alpha$ is then 23.34." + In our complete GALEX and non-GALEX-detected samples. nine objects have magnitudes brighter than this. four of which are GALEX-detected.," In our complete GALEX and non-GALEX-detected samples, nine objects have magnitudes brighter than this, four of which are GALEX-detected." + Of the nine objects. six have X-ray detections (all four GALEX-detected sources and two LAE candidates).," Of the nine objects, six have X-ray detections (all four GALEX-detected sources and two LAE candidates)." + Thus. if we exclude the four GALEX-detected sources. two out of five Lya bright galaxies host AGN and the fraction of X-ray detected AGN in the non-GALEX-detected sample is40%.. four times the fraction found by Ouchi et al. (," Thus, if we exclude the four GALEX-detected sources, two out of five $\alpha$ bright galaxies host AGN and the fraction of X-ray detected AGN in the non-GALEX-detected sample is, four times the fraction found by Ouchi et al. (" +2008) Του: ~3 LAEs.,2008) for $z\sim3$ LAEs. + To conclude. our detection of a AGN contribution in the non-GALEX-detected LAE sample is consistent with previous results. but is indicative of a higher AGN fraction being present at this redshift.," To conclude, our detection of a AGN contribution in the non-GALEX-detected LAE sample is consistent with previous results, but is indicative of a higher AGN fraction being present at this redshift." + For the surface density determination. we included both the GALEX-detected and non-detected objects to obtain as complete as possible à measure of the number density.," For the surface density determination, we included both the GALEX-detected and non-detected objects to obtain as complete as possible a measure of the number density." + Since our image has areas of poorer signal-to-noise. as well as stellar artifacts. we selected sub-images of superior quality with a total area of ~288 aremin?. corresponding to ~28% of the total surveyed area. to use for the surface and volume density calculations.," Since our image has areas of poorer signal-to-noise, as well as stellar artifacts, we selected sub-images of superior quality with a total area of $\sim 288$ $^2$, corresponding to $\sim 28$ of the total surveyed area, to use for the surface and volume density calculations." + In these areas. the selection is complete. and we found 54 candidates within these sub-images.," In these areas, the selection is complete, and we found 54 candidates within these sub-images." + This implies a surface density of LAE candidates of 0.19 ? A+ο or 1.91 ? :!.," This implies a surface density of LAE candidates of $0.19$ $^{-2}$ $\Delta z^{-1}$, or $1.91$ $^{-2}$ $z^{-1}$." + The volume density is 0.00062 7. which is in the lower range of that observed at redshift 2~3.," The volume density is $0.00062$ $^{-3}$, which is in the lower range of that observed at redshift $z \sim 3$." + Fynbo et al. (, Fynbo et al. ( +2001) summarise the surface densities of several early :~3 surveys.,2001) summarise the surface densities of several early $z \sim 3$ surveys. + With the exception of the Steidel et al. (, With the exception of the Steidel et al. ( +2000) survey in the overdense SSA2? field. these surveys all determined. values of 2.115.9 ? ! to the flux limit of this survey. but with large error bars.,"2000) survey in the overdense SSA22 field, these surveys all determined values of $2.11 - 5.9$ $^{-2}$ $z^{-1}$ to the flux limit of this survey, but with large error bars." + Hence. the values at :23 are consistently higher than our value. but in most cases the measurements agree to within 10.," Hence, the values at $z \gtrsim 3$ are consistently higher than our value, but in most cases the measurements agree to within $1\sigma$." + For LAE candidates brighter than the (57) luminosity limit of this survey. Nilsson et al. (," For LAE candidates brighter than the $5\sigma$ ) luminosity limit of this survey, Nilsson et al. (" +2007) identified six candidates im their survey. corresponding to 0.0018 . which represents a decrease of roughly a factor of three although based on a small sample.,"2007) identified six candidates in their survey, corresponding to $0.0018$ $^{-3}$, which represents a decrease of roughly a factor of three although based on a small sample." + Gronwall et al. (, Gronwall et al. ( +2007) determined a space density of 0.00057 ? above the 5e luminosity limit of our survey. which is consistent with the space density found here.,"2007) determined a space density of $0.00057$ $^{-3}$ above the $5\sigma$ luminosity limit of our survey, which is consistent with the space density found here." + Stiavelli et al. (, Stiavelli et al. ( +2001) presented a survey of :=2.1 LAEs and found a volume density of 0.0001 ° above a luminosity limit of logL=12.93 erg +.,2001) presented a survey of $z = 2.4$ LAEs and found a volume density of $0.0001$ $^{-3}$ above a luminosity limit of $\log{L} = 42.93$ erg $^{-1}$. + The same number for this survey is 0.00009 °., The same number for this survey is $0.00009$ $^{-3}$. + The numbers agree reasonably well with previous results., The numbers agree reasonably well with previous results. + Finally. Prescott et al. (," Finally, Prescott et al. (" +2008) completed a survey of ;~2.7 LAEs around a so-called Lya blob (e.g. Steidel et al.,2008) completed a survey of $z \sim 2.7$ LAEs around a so-called $\alpha$ blob (e.g. Steidel et al. + 2000: Matsuda et al., 2000; Matsuda et al. + 2004: Dey et al., 2004; Dey et al. + 2005: Nilsson et al., 2005; Nilsson et al. + 2006)., 2006). + They argued that the central part of their field is overdense. and determined a number density of 0.0021 °.," They argued that the central part of their field is overdense, and determined a number density of $0.0021$ $^{-3}$." + This is roughly three and half times higher than in our survey., This is roughly three and half times higher than in our survey. + At the edge of their field. the density ts instead 0.0012 . in closer agreement with. but still higher than. our result.," At the edge of their field, the density is instead $0.0012$ $^{-3}$, in closer agreement with, but still higher than, our result." + Thus. the surface density in this survey is in almost all cases lower than in higher redshift surveys. but could also be consistent with previous results.," Thus, the surface density in this survey is in almost all cases lower than in higher redshift surveys, but could also be consistent with previous results." + If one considers that number densities have been found to vary by factors of 2.5 in 0.2 deg? fields at redshift :=3 (Ouchi et al., If one considers that number densities have been found to vary by factors of $2 - 5$ in $0.2$ $^2$ fields at redshift $z = 3$ (Ouchi et al. + 2008). it is clear that more data at both higher and lower redshifts ts needed to resolve this issue finally.," 2008), it is clear that more data at both higher and lower redshifts is needed to resolve this issue finally." + As in Nilsson et al. (, As in Nilsson et al. ( +2007). the sizes of the candidate Lyo and GALEX-detected objects measured in the narrow-band and +! broad-band images are presented in Fig. 7..,"2007), the sizes of the candidate $\alpha$ and GALEX-detected objects measured in the narrow-band and $r^+$ broad-band images are presented in Fig. \ref{sizes}." + Six LAE objects are excluded due to non-detections in the +! band., Six LAE objects are excluded due to non-detections in the $r^+$ band. + The FWHM was calculated using the RRADIUS output from SExtractor. and the PSF in the narrow-band image was caleulated by using 9 objects in the image with fluxes in the range of the candidates and the SExtractor parameter SSTAR larger than 0.8. which inferred a PSF of 0.96”.," The FWHM was calculated using the RADIUS output from SExtractor, and the PSF in the narrow-band image was calculated by using 9 objects in the image with fluxes in the range of the candidates and the SExtractor parameter STAR larger than 0.8, which inferred a PSF of $0.96''$." +" The PSF of the r! image is similar to that of the narrow-band image PSF (the PSF of the »! image is 1.06"").", The PSF of the $r^+$ image is similar to that of the narrow-band image PSF (the PSF of the $r^+$ image is $1.06''$ ). +" As can be seen in the figure. we have two marginal Ενα blob detections in this survey (of FWHM 23.16"" and 3.70""). if a Ένα blob ts defined to have a radius larger than 15 kpe (corresponding to a diameter of 3.75"")."," As can be seen in the figure, we have two marginal $\alpha$ blob detections in this survey (of FWHM $3.46''$ and $3.70''$ ), if a $\alpha$ blob is defined to have a radius larger than $15$ kpc (corresponding to a diameter of $3.75''$ )." +" These two (candidates 54 and 66) are also extended in the broad-band images with FWHM ~2"" and are thus ""normal"" extended Lye emitters.", These two (candidates 54 and 66) are also extended in the broad-band images with FWHM $\sim 2''$ and are thus “normal” extended $\alpha$ emitters. + We conclude that we have no blobs in this survey., We conclude that we have no blobs in this survey. + Using the results from Matsuda et al. (, Using the results from Matsuda et al. ( +2004). Saito et al (20006). Gronwall et al. (,"2004), Saito et al (2006), Gronwall et al. (" +2007). and Prescott et al. (,"2007), and Prescott et al. (" +2008). the expected number density of Lyman-alpha blobs ranges from a few to a few hundred «109 .,"2008), the expected number density of Lyman-alpha blobs ranges from a few to a few hundred $\times 10^{-6}$ $^{-3}$ ." + The upper limit to the survey is ~3«105 7. and hence at the low end of the predictions from previous results.," The upper limit to the survey is $\sim 3 \times 10^{-6}$ $^{-3}$, and hence at the low end of the predictions from previous results." + Matsuda et al. (, Matsuda et al. ( +2004) and Prescott et al. (,2004) and Prescott et al. ( +2008) argued that Lya blobs reside in overdense regions of space.,2008) argued that $\alpha$ blobs reside in overdense regions of space. + If this assumption is correct. it agrees well with the two results from this survey that we detect a tentatively lower number density of LAEs at this redshift than expected from +~3 observations. and no Lya blobs are found in this survey.," If this assumption is correct, it agrees well with the two results from this survey that we detect a tentatively lower number density of LAEs at this redshift than expected from $z \sim 3$ observations, and no $\alpha$ blobs are found in this survey." + Both these observations indicate that the COSMOS field is under-dense at ;=2.25., Both these observations indicate that the COSMOS field is under-dense at $z = 2.25$. + We also note that there is a rapid decline in FWHM at larger radii in Fig. 7..," We also note that there is a rapid decline in FWHM at larger radii in Fig. \ref{sizes}," + indicating that Lya blobs and LAEs are two separate categories of Ένα emitting objects., indicating that $\alpha$ blobs and LAEs are two separate categories of $\alpha$ emitting objects. + If this was not the case. a tail of objects should be seen towards larger radi.," If this was not the case, a tail of objects should be seen towards larger radii." + No sample has yet been sufficiently large to confirm whether Ένα blobs and LAEs are separate populations., No sample has yet been sufficiently large to confirm whether $\alpha$ blobs and LAEs are separate populations. + It is also apparent that the candidate emitters are in general always more extended in the narrow-band image than their broad-band counterparts. 1.8. the broad-band counterparts are consistent with being pure point- Whereas the narrow-band objects are significantly more extended than point-sources (cf.," It is also apparent that the candidate emitters are in general always more extended in the narrow-band image than their broad-band counterparts, i.e. the broad-band counterparts are consistent with being pure point-sources whereas the narrow-band objects are significantly more extended than point-sources (cf." + Moller Warren 1998: Fynbo et al., ller Warren 1998; Fynbo et al. + 2001. 2003).," 2001, 2003)." + This may arise from diffuse scattering of Lya within thegalaxy (see also Laursen Sommer- 2007) and/or due to the diffuse ISM (Osstlin et al., This may arise from diffuse scattering of $\alpha$ within thegalaxy (see also Laursen Sommer-Larsen 2007) and/or due to the diffuse ISM (Össtlin et al. +CMB (PCM).,CMB (PCM). + As one can see from refpcmxcorr for reconstructed CMB signal the quadrupole component has smaller power than the simulated CMB., As one can see from \\ref{pcmxcorr} for reconstructed CMB signal the quadrupole component has smaller power than the simulated CMB. +" The reason for that is that the peculiar phases of the quadrupole component Qoo, Φοι and Φορ."," The reason for that is that the peculiar phases of the quadrupole component $Q_{20}$, $Q_{21}$ and $Q_{22}$." +" Accidentally, in our simulated realization of the CMB (see Fig.6)) the phases of the component («20 and «Φ9οι are zero whereas for the Q22 component the corresponding phase is close to 37/2 with only deviation."," Accidentally, in our simulated realization of the CMB (see \ref{simulator}) ) the phases of the component $Q_{20}$ and $Q_{21}$ are zero whereas for the $Q_{22}$ component the corresponding phase is close to $3\pi/2$ with only deviation." + That is why the reconstructed phase of Qo» component has £29=6.227 radians., That is why the reconstructed phase of $Q_{22}$ component has $\ks_{22}=6.227$ radians. + In Fig.9 we plot the cross correlation of the phases between the reconstructed CMB signal (PCM) and the simulator foregrounds at all 5 simulated bands., In \ref{simulatorxcorr} we plot the cross correlation of the phases between the reconstructed CMB signal (PCM) and the simulator foregrounds at all 5 simulated bands. + The scattering of points in all 5 panels indicates that the phases of the PCM display no serious correlations with those of the foregrounds., The scattering of points in all 5 panels indicates that the phases of the PCM display no serious correlations with those of the foregrounds. + The simulator therefore confirms the usefulness of our “blind” PCM method for the CMB extraction without any assumptions about the statistical properties of the foregrounds., The simulator therefore confirms the usefulness of our “blind” PCM method for the CMB extraction without any assumptions about the statistical properties of the foregrounds. +" For the reconstruction of the CMB signal at £<50 from the K-W bands of the data we use the three pairs of the maps: Ka-Q, Q-V and Ka-V. We repeat the steps b and c of the “blind” PCM method: each of them has been convolved by the weighting coefficients, Eq.(17)) and then by the coefficients Eq.(19)) using only 2 iterations."," For the reconstruction of the CMB signal at $\ell \le 50$ from the K–W bands of the data we use the three pairs of the maps: Ka–Q, Q–V and Ka–V. We repeat the steps ${\bf b}$ and ${\bf c}$ of the “blind” PCM method: each of them has been convolved by the weighting coefficients, \ref{eq16}) ) and then by the coefficients \ref{eq18}) ) using only 2 iterations." + All the next iterations do not change significantly the Gem coefficients (the corresponding error being less than 10-396)., All the next iterations do not change significantly the $\alm$ coefficients (the corresponding error being less than $10^{-3}\%$ ). +" The results are present in Fig.10, in which all the 3 cleaned-up maps have pronounced similarity in morphology, albeit with some residues from the galactic foregrounds."," The results are present in \ref{cleanedup}, in which all the 3 cleaned-up maps have pronounced similarity in morphology, albeit with some residues from the galactic foregrounds." +" In Fig.11 we show the result after the step d, the MIN-MAX filtering."," In \ref{minmax} we show the result after the step ${\bf d}$, the MIN-MAX filtering." +" The top panel is our CMB signal (the PCM), the middle is the ILC map for comparison and the bottom is the difference of the two."," The top panel is our CMB signal (the PCM), the middle is the ILC map for comparison and the bottom is the difference of the two." +" In Fig.12 we plot the CMB angular power spectra from different methods: the thick solid line is the PCM, the dashed line the ILC map, the dash-dot line the TOH foreground-cleaned map, and the thin solid line the TOH Wiener-filtered map."," In \ref{pcmpw} we plot the CMB angular power spectra from different methods: the thick solid line is the PCM, the dashed line the ILC map, the dash-dot line the TOH foreground-cleaned map, and the thin solid line the TOH Wiener-filtered map." + The PCM power spectrum is smaller then ILC power spectrum at the whole multipole range 4<50 and it reproduces a similar power spectrum as the TOH filtered map.," The PCM power spectrum is smaller then ILC power spectrum at the whole multipole range $\ell +\le 50$ and it reproduces a similar power spectrum as the TOH Winer-filtered map." + In Fig.13 we show the cross correlation of the phases between the PCM and the foreground maps of the bands., In \ref{pcmwmapxcorr} we show the cross correlation of the phases between the PCM and the foreground maps of the bands. + Again the scattering of the points shows that the phases of the PCM practically have no correlations with those of the foregrounds., Again the scattering of the points shows that the phases of the PCM practically have no correlations with those of the foregrounds. +Llowever. these studies have identified. some degeneracies between sets of cosmological estimated. from the linear CALB power spectra alone.,"However, these studies have identified some degeneracies between sets of cosmological estimated from the linear CMB power spectra alone." + Since the entire statistical information on the CAIB anisotropies in Ciaussian theories is contained. in the power spectrum. such parameter cegencracies impose serious limitations on the ability of CAIB experiments to constrain cosmological parameters. without invoking additional external constraints.," Since the entire statistical information on the CMB anisotropies in Gaussian theories is contained in the power spectrum, such parameter degeneracies impose serious limitations on the ability of CMB experiments to constrain cosmological parameters without invoking additional external constraints." + In particular. Bond (1997) and Zaldarriaga al.(1997) have emphasized that cosmological models with identical Ductuation spectra. matter content. anc angular chameter distance to the scattering surface (see Section 2. below) will produce statistically almost. incistinguishable power spectra of CM fluctuations.," In particular, Bond (1997) and Zaldarriaga (1997) have emphasized that cosmological models with identical fluctuation spectra, matter content and angular diameter distance to the scattering surface (see Section 2.1 below) will produce statistically almost indistinguishable power spectra of CMB fluctuations." + This property (which we call thedegeneracy hereafter) means tha in the limit of validity of linear perturbation theory. CMD measurements cannot set strong independent. bounds. on the spatial curvature and cosmological constant ancl hence cannot unambiguously constrain the spatial geometry of the Universe.," This property (which we call the hereafter) means that in the limit of validity of linear perturbation theory, CMB measurements cannot set strong independent bounds on the spatial curvature and cosmological constant and hence cannot unambiguously constrain the spatial geometry of the Universe." + In fact there are many adelitional observational constraints that can be usec to break the ecometrical degeneracy., In fact there are many additional observational constraints that can be used to break the geometrical degeneracy. + Examples include. accurate measurements. of the Llubble constant. the age of the Universe and the geometrical constraints imposed. by Type La. supernovae light curves sce Figure L and the more detailed discussions by White (1998). Tegmark. Eisenstein llliu (1998) and. Efstathiou BBond (1998)].," Examples include accurate measurements of the Hubble constant, the age of the Universe and the geometrical constraints imposed by Type Ia supernovae light curves [see Figure \ref{fig1} and the more detailed discussions by White (1998), Tegmark, Eisenstein Hu (1998) and Efstathiou Bond (1998)]." + Llowever. before invoking more conventiona astronomical observations. it is worthwhile analysing whether there are non-linear. contributions to the CMD anisotropies that can break the geometrical degeneracy.," However, before invoking more conventional astronomical observations, it is worthwhile analysing whether there are non-linear contributions to the CMB anisotropies that can break the geometrical degeneracy." + Lf such cllects are present. then it may be possible to break the ecometrical degeneracy using measurements of the CMD alone.," If such effects are present, then it may be possible to break the geometrical degeneracy using measurements of the CMB alone." + In this paper. we analyse the effect of eravitationa lensing on the CALB anisotropies.," In this paper, we analyse the effect of gravitational lensing on the CMB anisotropies." + Although acknowledge to be small (Blanchard SSchneicer 1987. Cole Iibfstathiou 1989. Sasaki 1989. Seljak 1996). the eravitational lensing ellect may be detectable. by. the high precision observations of the CALB anisotroples expected from. future satellite experiments.," Although acknowledged to be small (Blanchard Schneider 1987, Cole Efstathiou 1989, Sasaki 1989, Seljak 1996), the gravitational lensing effect may be detectable by the high precision observations of the CMB anisotropies expected from future satellite experiments." + The possibility of utilising gravitational lensing to break the geometrical degeneracy has heen noticed independently by. Aleteall SSilk (1998)., The possibility of utilising gravitational lensing to break the geometrical degeneracy has been noticed independently by Metcalf Silk (1998). + In this paper. we analyse the effects. of eravitational lensing on the temperature. polarisation and tomperature-polarisation cross-correlation power spectra and assess whether it is possible to observe these effects with the NLAP (Bennett L997) and Planck (Bersanclli 1996) satellites.," In this paper, we analyse the effects of gravitational lensing on the temperature, polarisation and temperature-polarisation cross-correlation power spectra and assess whether it is possible to observe these effects with the MAP (Bennett 1997) and Planck (Bersanelli 1996) satellites." + In this paper we restrict. ourselves to cold. dark matter (CDM) cosmologies with adiabatic scalar. perturbations. an arbitrary value of the curvature (οςWfliz) ane cosmological constant (£24A/315).," In this paper we restrict ourselves to cold dark matter (CDM) cosmologies with adiabatic scalar perturbations, an arbitrary value of the curvature $\Omega_K\equiv -K/H_0^2$ ) and cosmological constant $\Omega_\Lambda\equiv \Lambda/3 H_0^2$ )." +. Following Boned (1997) we use physical densities. d;=Q;h7. o define the matter content of the universe ... with i=Widow... and OQ). Qo. O.... are the density xwanmeters of barvons. cold dark matter (CDAD). photons ote.," Following Bond (1997) we use physical densities, $\omega_i\equiv\Omega_ih^2$, to define the matter content of the universe , with $i=K,\Lambda$ $\gamma$ $\dots$, and $\Omega_{\rm b}$, $\Omega_{\rm c}$, $\Omega_{\gamma}$ $\dots$ are the density parameters of baryons, cold dark matter (CDM), photons etc." + We assume the standard. thermal history throughout his paper with recombination at recshift z1100 (Pechles LOGS) and ignore the possibility. of. reionization., We assume the standard thermal history throughout this paper with recombination at redshift $z\sim 1100$ (Peebles 1968) and ignore the possibility of reionization. + In. the numerical examples. described. below. we have assumed a scale-invariant (Llarrison-Zelcdovich) power spectrum. of primordial scalar and acliahatic Lluctuations lexYAS|A. where a wavenumber & is the separation constant of the Uchuholtz equation (c.g. Harrisson 1967).," In the numerical examples described below, we have assumed a scale-invariant (Harrison-Zel'dovich) power spectrum of primordial scalar and adiabatic fluctuations $\propto +\sqrt{k^2+K},$ where a wavenumber $k$ is the separation constant of the Helmholtz equation (e.g. Harrisson 1967)." +" As is well known. the power spectrum of the CMD anisotropies in such mocels displays prominent ""Doppler peaks (see. Figures 2a.b)."," As is well known, the power spectrum of the CMB anisotropies in such models displays prominent `Doppler' peaks (see, Figures 2a,b)." + The shape of the CALB power spectrum and. in particular. the locations and relative heights of the peaks. depend: sensitively on cosmological parameters (e.g. Hu SSugivama 1995).," The shape of the CMB power spectrum and, in particular, the locations and relative heights of the peaks, depend sensitively on cosmological parameters (e.g. Hu Sugiyama 1995)." + Phe Doppler peak structure is imprinted into the present dav CAIB power spectrum at the time of recombination., The Doppler peak structure is imprinted into the present day CMB power spectrum at the time of recombination. + Since recombination occurs at a hieh redshift. no plausible value of the cosmological constant or spatial curvature can influences the dynamical evolution of he universe at that time.," Since recombination occurs at a high redshift, no plausible value of the cosmological constant or spatial curvature can influences the dynamical evolution of the universe at that time." +. Phe statistical properties of the CMD anisotropies at the time of last scattering are therefore determined by the form of the initial Huctuations spectrum (mode. shape and amplitude) and by the physical densities hat determine the sound speed prior to recombination.," The statistical properties of the CMB anisotropies at the time of last scattering are therefore determined by the form of the initial fluctuations spectrum (mode, shape and amplitude) and by the physical densities that determine the sound speed prior to recombination." + After last scattering. (assuming that the universe remains neutral) the only mechanism that can alfect a freelv-alling CAIB photon is the gravitational interaction with he evolving matter field.," After last scattering, (assuming that the universe remains neutral) the only mechanism that can affect a freely-falling CMB photon is the gravitational interaction with the evolving matter field." + In the linear approximation this is sometimes called the integrated Sachs-Wolle effect scc. e.g. the review by Bone (1996)] and is of importance only or temperature f[uctuations on the largest angular scales.," In the linear approximation this is sometimes called the integrated Sachs-Wolfe effect [see, e.g. the review by Bond (1996)] and is of importance only for temperature fluctuations on the largest angular scales." + Since the large-scale. anisotropies have large statistical uncertainties (cosmic variance). the integrated Sachs-Wolfe οσοι cannot. break the &eometrical. degeneracy except for extreme values of the cosmological parameters see Efstathiou Μο (1998) for detailed caleulations].," Since the large-scale anisotropies have large statistical uncertainties (cosmic variance), the integrated Sachs-Wolfe effect cannot break the geometrical degeneracy except for extreme values of the cosmological parameters [see Efstathiou Bond (1998) for detailed calculations]." + La linear theory. the ecometrical degeneracy canbe assumed to be exact for most practical purposes.," In linear theory, the geometrical degeneracy canbe assumed to be exact for most practical purposes." +within our Local Group although it is much less well-studied than the Milky Way (MW). the Magellanie Clouds or Andromeda (M31).,"within our Local Group although it is much less well-studied than the Milky Way (MW), the Magellanic Clouds or Andromeda (M31)." + In addition to the well-known stream [rom the cdisruptin£g Sagittarius dwarl galaxy. other evidence for substructure within the Milkv. Wax includes the Monoceros ring. the Orphan stream. and other more subtle overdensities (e.g.. ?22??)).," In addition to the well-known stream from the disrupting Sagittarius dwarf galaxy, other evidence for substructure within the Milky Way includes the Monoceros ring, the Orphan stream, and other more subtle overdensities (e.g., \citealt{1995MNRAS.277..781I, 2002ApJ...569..245N, 2006ApJ...642L.137B, + 2007ApJ...658..337B}) )." + M31s substructure is being revealed in more and more detail with large-scale structures of very low surface e," M31's substructure is being revealed in more and more detail with large-scale structures of very low surface brightness, including several arcs, shells and streams \citep{2002AJ....124.1452F, 2005ApJ...634..287I, 2007ApJ...671.1591I, 2006ApJ...648..389K, 2008AJ....135.1998R, + 2009Natur.461...66M}." +Subdivisions within the NW GCS have been observed (e.g.. ??)) with evidence that at least some are the result of accretions of dwarf satellite galaxies (?227).. ," Subdivisions within the MW GCS have been observed (e.g., \citealt{1978ApJ...225..357S, 2004MNRAS.355..504M}) ) with evidence that at least some are the result of accretions of dwarf satellite galaxies \citep{2003AJ....125..188B, 2004MNRAS.355..504M, 2004AJ....127.3394F}." +Certain clusters still appear to be associated with their accreted satellites: most prominently. clusters associated with Sagittarius (e.g.. 2??)).," Certain clusters still appear to be associated with their accreted satellites: most prominently, clusters associated with Sagittarius (e.g., \citealt{2000AJ....119.1760L, 2003ApJ...596L.191N, + 2003AJ....125..188B}) )." + The most distant GC known in the MW is still AM-IL. first discovered by ? αἱ à galactocentric distance of 22120 kpc.," The most distant GC known in the MW is still AM-1, first discovered by \cite{1979ApJ...227L.103M} at a galactocentric distance of $\approx$ 120 kpc." +" In other galaxies. clusters with largeealactocentric radii (se 120 kpe) reside in the AM, - +, parameter space between Palomar-0vpe clusters and ultra-Iaint. cdwarls. and this overlap is now well-established (e.g.. 7.. ? and ?))."," In other galaxies, clusters with largegalactocentric radii $\approx$ 120 kpc) reside in the $M_v$ - $r_h$ parameter space between Palomar-type clusters and ultra-faint dwarfs, and this overlap is now well-established (e.g., \citealt{2005MNRAS.360.1007H}, \citealt{2006A&A...447..877G} and \citealt{2007ApJ...658..337B}) )." + Within M31. there are now over 60 known clusters wilh a projected radius greater than t," Within M31, there are now over 60 known clusters with a projected radius greater than 30 kpc \citep{2005MNRAS.360.1007H, 2006MNRAS.371.1983M, + 2007ApJ...655L..85M, 2008MNRAS.385.1989H, + 2010ApJ...717L..11M}." +hev are found to be both more luminous and have larger sizes (?).., Some of these distant clusters are rather unlike their MWcounterparts as they are found to be both more luminous and have larger sizes \citep{2007ApJ...655L..85M}. + Most recently it has been shown that the outer halo clusters appear to follow other substructure (streams of enhanced surface brightness). with the probability of chance alignment less than 1," Most recently it has been shown that the outer halo clusters appear to follow other substructure (streams of enhanced surface brightness), with the probability of chance alignment less than $\%$ \citep{2010ApJ...717L..11M}." +" (?).. ? conclude (hat the majority of these clusters are accreted along will their host satellite ealaxv. as first proposed by ο, Observations of the M33 clusters - both voung and old - have been collated in the calalogue by 7. (7: SM hereafter)."," \citeauthor{2010ApJ...717L..11M} conclude that the majority of these clusters are accreted along with their host satellite galaxy, as first proposed by \cite{1978ApJ...225..357S}.. Observations of the M33 clusters - both young and old - have been collated in the catalogue by \citeauthor{2007AJ....134..447S} \citeyear{2007AJ....134..447S}; ; SM hereafter)." + This catalogue includes cluster identifications and data. from ground-based observations (?????).. ILST' imaging (7???7?7?7).. andfurther data," This catalogue includes cluster identifications and data from ground-based observations \citep{1960ApJ...131..163H, + 1978A&AS...34..249M, 1982ApJS...49..405C, 1988AJ.....95..704C, + 1998AcA....48..455M}, , $HST$ imaging \citep{1999ApJS..122..431C, + 2001A&A...366..498C, 2005A&A...444..831B, 2007AJ....134.2168P, + 2007AJ....133..290S, 2008AJ....135.1482S, 2009ApJ...698L..77H, 2009ApJ...699..839S}, , andfurther data" +of emission features such as Io. since we would expect the strength of this emission to vary spatially across the galaxy.,of emission features such as $\alpha$ since we would expect the strength of this emission to vary spatially across the galaxy. + However. because the random positioning errors are much smaller than the scale. lengths of the galaxies this isn't a large problem.," However, because the random positioning errors are much smaller than the scale lengths of the galaxies this isn't a large problem." + For this reason the information contained in the emission/absorption line strengths shoulc be relatively robust., For this reason the information contained in the emission/absorption line strengths should be relatively robust. + Perhaps our greatest concern regarding the representativeness of the spectra is due to the limite size of the aperture with respect to the galaxy., Perhaps our greatest concern regarding the representativeness of the spectra is due to the limited size of the aperture with respect to the galaxy. + Surprisingly. we have found it eillicult to isolate any svstematic bias from. this elfect.," Surprisingly, we have found it difficult to isolate any systematic bias from this effect." +" Of course this elfect will be substantially clilutec in the observed spectra due to the significant seeing presen at the Anelo-Australian Telescope in Siding Springs. which is of the order of 1.5"""" ↓⋅↖∖⊳↓⊔"," Of course this effect will be substantially diluted in the observed spectra due to the significant seeing present at the Anglo-Australian Telescope in Siding Springs, which is of the order of $1.5''-1.8''$." +⋯∐∐↓∪⊔∣⇂↥⋖⋅↓≻↓⋅⋖⋅≱∖⋖⋅⊔≼∙⋖⋅∪- differential atmospheric refraction may also assist. us., In addition the presence of differential atmospheric refraction may also assist us. +" We discuss the impact of this ""fibre-aperture bias’ on our results in more στα in Section 5.3.", We discuss the impact of this `fibre-aperture bias' on our results in more detail in Section 5.3. + We are presented with several options in attempting to derive a Classification for the observed. 2dE galaxies. based upon their spectra., We are presented with several options in attempting to derive a classification for the observed 2dF galaxies based upon their spectra. +" However. there are several issues that one must first consider: ὃν projecting the pe, and pes components of each ealaxy onto the linear combination which maximises the cllect of emission/absorption line features we are in effect high-pass filtering the spectra."," However, there are several issues that one must first consider: By projecting the $pc_1$ and $pc_2$ components of each galaxy onto the linear combination which maximises the effect of emission/absorption line features we are in effect high-pass filtering the spectra." + Thus we would expect. (and indeed we find) this projection to be relatively stable to uncertainties in continuum measurements., Thus we would expect (and indeed we find) this projection to be relatively stable to uncertainties in continuum measurements. + )v using this projection we are determining a measure of the average emissionabsorption line strength of a galaxy which is casily quantifiable and robust., By using this projection we are determining a measure of the average emission/absorption line strength of a galaxy which is easily quantifiable and robust. + In. addition this projection is also representative of the spectral sequence of the galaxy population since it is composed of the two most significant principal components (representing of the total variance over the population)., In addition this projection is also representative of the spectral sequence of the galaxy population since it is composed of the two most significant principal components (representing of the total variance over the population). + We therefore choose to adopt this projection. which we shall denote a. as our continuous measure of spectral type The value of «a which niaximises the emission/absorption features is essentially identical to that we would. find from. identifying the most stable projection in the (pey.pes) plane between repeated: pairs of spectral observations.," We therefore choose to adopt this projection, which we shall denote $\eta$, as our continuous measure of spectral type The value of $a$ which maximises the emission/absorption features is essentially identical to that we would find from identifying the most stable projection in the $pc_1$ $pc_2$ ) plane between repeated pairs of spectral observations." + Using this method we find a—0.5cx0.1., Using this method we find $a = 0.5 \pm 0.1$. + In Fig., In Fig. + 4 the distribution of the 7 projections is shown for the galaxies observed to date in the 2dbkCRS., \ref{eta} the distribution of the $\eta$ projections is shown for the galaxies observed to date in the 2dFGRS. + Also shown in the same figure is the morphology relation for a sample of galaxies from the WKennieutt Atlas (Ixennicut 1992)., Also shown in the same figure is the $\eta$ -morphology relation for a sample of galaxies from the Kennicutt Atlas (Kennicutt 1992). + Comparing the two data sets shows that there is a correspondence between the sequence of a ancl tha of morphology., Comparing the two data sets shows that there is a correspondence between the sequence of $\eta$ and that of morphology. + Note that this correspondence. can only be treated as an approximation since our sample of ]xennicutt galaxies is not complete anc only represents a few high signal-to-noise ratio spectra with well determine morphologies., Note that this correspondence can only be treated as an approximation since our sample of Kennicutt galaxies is not complete and only represents a few high signal-to-noise ratio spectra with well determined morphologies. + However. the trend is clear.," However, the trend is clear." + ]t is important to have an understanding of the uncertainties in the principal component analvsis as this will allect the reliability of our classification., It is important to have an understanding of the uncertainties in the principal component analysis as this will affect the reliability of our classification. + Using a sample of (~ 2000) repeated spectral observations we can attempt to quantify these uncertainties., Using a sample of $\sim 2000$ ) repeated spectral observations we can attempt to quantify these uncertainties. +" The dilferences in the PCA projections (pe, and pes) and in the spectral classification between repeated: pairs is shown in Fig. 5..", The differences in the PCA projections $pc_1$ and $pc_2$ ) and in the spectral classification between repeated pairs is shown in Fig. \ref{errors}. + Note that. for clarity we show here the Gaussian fits mace to these error distributions., Note that for clarity we show here the Gaussian fits made to these error distributions. +" It is clear [rom this figure that the uncertainty in the pe, and pes projections is substantial (Lo clispersions of 2.9 and 1.7 respectively). however. this dispersion. is ereatly reduced by using the + parameterisation (la= 0.7)."," It is clear from this figure that the uncertainty in the $pc_1$ and $pc_2$ projections is substantial $1\sigma$ dispersions of 2.9 and 1.7 respectively), however, this dispersion is greatly reduced by using the $\eta$ parameterisation $1\sigma=0.7$ )." +where fis the number of data points.,where $n$ is the number of data points. + For constraining our free parameters we used only Stokes Q// as intensity is not very sensitive to variations of f and ou and the line depths depend on the line blanketing parameters which can be slightly adjusted (see Sect. 231)., For constraining our free parameters we used only Stokes $Q/I$ as intensity is not very sensitive to variations of $f$ and $\delta_{\rm th}^{\rm min}$ and the line depths depend on the line blanketing parameters which can be slightly adjusted (see Sect. \ref{sec:obs}) ). + To compute y we used 120 data points chosen under the condition to avoid blending with atomic lines., To compute $\chi^2$ we used 120 data points chosen under the condition to avoid blending with atomic lines. + The y-contours for different f parameter values are presented in Fig. 6.., The $\chi^2$ -contours for different $f$ parameter values are presented in Fig. \ref{fig:contour00}. + For each f£ value we have drawn three contours which correspond to the confidence limits68.3%..90%... and 99.," For each $f$ value we have drawn three contours which correspond to the confidence limits, and ." +73%... Of course. the errors In our case are not necessarily distributed normally and there are definitely some systematic errors.," Of course, the errors in our case are not necessarily distributed normally and there are definitely some systematic errors." + The deduced magnetic field strengths corresponding to y minima are listed in Table 1..., The deduced magnetic field strengths corresponding to $\chi^2$ minima are listed in Table \ref{table:bestfit}. + The main conclusion from Fig., The main conclusion from Fig. + 6 and Table | is that the magnetic field strength appears to be model dependent., \ref{fig:contour00} and Table \ref{table:bestfit} is that the magnetic field strength appears to be model dependent. + A larger additional anisotropy leads to a stronger field because the collisional rates enter into the denominator of Eq. (6))., A larger additional anisotropy leads to a stronger field because the collisional rates enter into the denominator of Eq. \ref{eq:gamma}) ). + It implies that their increase will lead to weaker Hanle sensitivity. so for obtaining the same Hanle depolarization a higher field is needed.," It implies that their increase will lead to weaker Hanle sensitivity, so for obtaining the same Hanle depolarization a higher field is needed." + Moreover. the overall polarizatior growth can also be partially compensated by the Hanle depolarization (however. only within a limit which is constrained by the differential behavior of the Hanle effect).," Moreover, the overall polarization growth can also be partially compensated by the Hanle depolarization (however, only within a limit which is constrained by the differential behavior of the Hanle effect)." + For a fixed f value both the magnetic field and collision rate are well constrained., For a fixed $f$ value both the magnetic field and collision rate are well constrained. + Even though decreasing the collisional rate (and hence mereasing scattering) can be partly compensated by the growth of Hanle depolarization. the magnetic field strength is constrained due to the differential behavior of the Hiile effect.," Even though decreasing the collisional rate (and hence increasing scattering) can be partly compensated by the growth of Hanle depolarization, the magnetic field strength is constrained due to the differential behavior of the Hanle effect." + Knowing collisional rates more precisely would help to obtain a unique solution., Knowing collisional rates more precisely would help to obtain a unique solution. + Here we present our results for the spectral region close to the (1.1) bandhead (3868.8-3871.5ÀJ).," Here we present our results for the spectral region close to the (1,1) bandhead )." + A comparison of the observed and calculated spectra with7., A comparison of the observed and calculated spectra with. + This region contains many CN lines from both (1.1) and (0.0) bands and also several strong atomic blends (among them two strong iron lines at about A)) as well as one CH line at aboutΑ.," This region contains many CN lines from both (1,1) and (0,0) bands and also several strong atomic blends (among them two strong iron lines at about ) as well as one CH line at about." +. Therefore. the overall quality of the fit is worse than that for the (0.0) bandhead region.," Therefore, the overall quality of the fit is worse than that for the (0,0) bandhead region." + The y minimum values and corresponding magnetic field strengths are listed in Table I. the y-contours are shown in Fig. 8...," The $\chi^2$ minimum values and corresponding magnetic field strengths are listed in Table \ref{table:bestfit}, the $\chi^2$ -contours are shown in Fig. \ref{fig:contour11}." + The observatios with higher µ values sample deeper layers of the solar atmosphere where the collisional rates and. consequently. the denominator of Eq. (6))," The observations with higher $\mu$ values sample deeper layers of the solar atmosphere where the collisional rates and, consequently, the denominator of Eq. \ref{eq:gamma}) )" + are larger., are larger. + Therefore. these lies are less affected by the Hanle effect and less depolarized.," Therefore, these lines are less affected by the Hanle effect and less depolarized." + This can be clearly seen in Fig. 7:, This can be clearly seen in Fig. \ref{fig:IQ3872_1}: + for Ho0.4 the O/T οιrve is strongly depolarized in presence of aG. while for =0.5 it i5 almost unaffected by the Hanle effect.," for $\mu=0.1$ the $Q/I$ curve is strongly depolarized in presence of a, while for $\mu=0.5$ it is almost unaffected by the Hanle effect." + The height dependence of the collisional rates and the deduced magnetic field are strongly coupled with each other., The height dependence of the collisional rates and the deduced magnetic field are strongly coupled with each other. + For example à steeper collision rate dependence on temperature (and hence height) will lead to magnetic field strength., For example a steeper collision rate dependence on temperature (and hence height) will lead to magnetic field strength. + decreasing with height., decreasing with height. + Thus taken the current uncertainties in collisional rates. and radiation field anisotropy it is not possible to unambiguously determine the depth dependence of the magnetic field strength., Thus taken the current uncertainties in collisional rates and radiation field anisotropy it is not possible to unambiguously determine the depth dependence of the magnetic field strength. + Improvements in collision theory. 3D modeling ofthe radiation field anisotropy. and observations at a greater number of limb positions would be required for better constraints of the model atmosphere and the free parameters.," Improvements in collision theory, 3D modeling of the radiation field anisotropy, and observations at a greater number of limb positions would be required for better constraints of the model atmosphere and the free parameters." + Interestingly. there is one more mechanism which constrains the deduced magnetic field strength for this region.," Interestingly, there is one more mechanism which constrains the deduced magnetic field strength for this region." + The alteration. of the oe coefficient affects Ο// curves at all ye values in approximately the same way., The alteration of the $\delta_{\rm th}^{\rm min}$ coefficient affects $Q/I$ curves at all $\mu$ values in approximately the same way. + The magnetic field however mainly depolarizes lines observed at small µ., The magnetic field however mainly depolarizes lines observed at small $\mu$. + This differential behavior significantly helps to constrain both the magnetic field strength and the collisional coefficient (assuming that we employ the correct dependency of the collisional rates on depth)., This differential behavior significantly helps to constrain both the magnetic field strength and the collisional coefficient (assuming that we employ the correct dependency of the collisional rates on depth). + the considered mechanism is even more important than the differential Hanle effect as this region contains a crowded mixture of lines with different 7 numbers. and the differential line behavior in the magnetic field is not clearly seen.," the considered mechanism is even more important than the differential Hanle effect as this region contains a crowded mixture of lines with different $J$ numbers, and the differential line behavior in the magnetic field is not clearly seen." + This mechanism is illustrated in Fig., This mechanism is illustrated in Fig. + 9 where the dependence of the mean polarization on py is plotted for several values of the collisional coettcient oe and magnetic field strength B., \ref{fig:dep} where the dependence of the mean polarization on $\mu$ is plotted for several values of the collisional coefficient $\delta_{\rm th}^{\rm min}$ and magnetic field strength $B$. + The observed five points best coincide with the curve which corresponds to B=45 Gand o???=0.3., The observed five points best coincide with the curve which corresponds to $B=45$ G and $\delta_{\rm th}^{\rm min}=0.3$. + From Figs., From Figs. + 6 and 8 and Table 1 one can see that the magnetic field streeth deduced with the same f parameter for both spectral regioas differ by a factor of two. with the one for the (0.0) bandhead being larger.," \ref{fig:contour00} and \ref{fig:contour11} and Table \ref{table:bestfit} one can see that the magnetic field strength deduced with the same $f$ parameter for both spectral regions differ by a factor of two, with the one for the (0,0) bandhead being larger." + This can be a signature of spatial magnetic field variations as the observations of these spectral regions were made on different days and sample accordingly different regions on the solar surface., This can be a signature of spatial magnetic field variations as the observations of these spectral regions were made on different days and sample accordingly different regions on the solar surface. + We also nterpreted the data from the atlas by Gandorfer(2005). for the (0.0) bandhead region and found a weaker magnetic field of about 40 G compared to the 82 G obtained from our ew observations with f=0.6.," We also interpreted the data from the atlas by \citet{gandorfer2005atlas} for the (0,0) bandhead region and found a weaker magnetic field of about 40 G compared to the 82 G obtained from our new observations with $f=0.6$." +" However. since the applied osonstraints are sensitive to the amount of available data (e.g.. imb angles) only simultaneous measurements at the same limb ""Sistances in both regions can clarify the situation."," However, since the applied constraints are sensitive to the amount of available data (e.g., limb angles) only simultaneous measurements at the same limb distances in both regions can clarify the situation." + We have employed a new computational scheme to interpret. simultaneously center-to-limb variations of the intensity and linear polarization in the CN violet system., We have employed a new computational scheme to interpret simultaneously center-to-limb variations of the intensity and linear polarization in the CN violet system. + An analysis of these variations improves our understanding of the scattering. polarization in the CN violet system., An analysis of these variations improves our understanding of the scattering polarization in the CN violet system. + In our model we solve the statistical equilibrium equations and self- account for multiple scattering in optically thick, In our model we solve the statistical equilibrium equations and self-consistently account for multiple scattering in optically thick +2006).,. +. Additional evidence of widespread silicates are provided by models of the erain populations. in terms of size and composition. required to fit exiinction measurements. diffuse infrared emission. and abuucdanuce constraints for the diffuse ISM ZDA).," Additional evidence of widespread silicates are provided by models of the grain populations, in terms of size and composition, required to fit extinction measurements, diffuse infrared emission, and abundance constraints for the diffuse ISM ." +". The ZDA COMP-GR-FG model. consisting of silicates (MgFeSiO,). eraphite. and a small amount PAIIs. provides a good fit to the extinction and II. emission data if ISM abundances are comparable to Ε and G star abundances."," The ZDA COMP-GR-FG model, consisting of silicates $_4$ ), graphite, and a small amount PAHs, provides a good fit to the extinction and IR emission data if ISM abundances are comparable to F and G star abundances." + The silicates in the ZDA model have α<0.25yon.. with most of the grain mass contained in grains with ao0.06—0.25yan.. however a significant fraction of silicate grains with aZ50.01 aare present.," The silicates in the ZDA COMP-GR-FG model have $a < 0.25$, with most of the grain mass contained in grains with $a \sim 0.06 - 0.25$, however a significant fraction of silicate grains with $a \lesssim 0.01$ are present." + The small amount of PÀISs required by the COMP-GR-FG are allowed by the LIC C data. depending on the assumed solar CC abundance.," The small amount of PAHs required by the COMP-GR-FG are allowed by the LIC C data, depending on the assumed solar C abundance." + The above arguments used (o derive grain composition asstme (hat dust and gas have been fully mixed over the cloud lifetime., The above arguments used to derive grain composition assume that dust and gas have been fully mixed over the cloud lifetime. + A check on this assumption is the eas-to-dust mass ratio.Roya. in local ISM. which can be examined in several wavs. (," A check on this assumption is the gas-to-dust mass ratio, in local ISM, which can be examined in several ways. (" +1) The first method compares spacecraft znsifu measurements of the ISDG mass with the gas mass determined from RT models.,1) The first method compares spacecraft $in~situ$ measurements of the ISDG mass with the gas mass determined from RT models. + Updating the E99 discussion with more recent spacecralt results vields 44130. wheretheupperlimitholdsbecausesmallchargedI5 DGsart ," Updating the F99 discussion with more recent spacecraft results yields $<$ 130, where the upper limit holds because small charged ISDGs are excluded from the solar system. (" +ccan also be determined [rom comparisons between (the RT models and solar abundances.,2) can also be determined from comparisons between the RT models and solar abundances. +" For the L03 solar abundances. model 8 vields B,;4,-11836."," For the L03 solar abundances, model 8 yields 186." + If instead the [SAL reference O abundance is O/II—520 (see above). model 3 gives Ryjq=2210.," If instead the ISM reference O abundance is O/H=520 (see above), model 8 gives 210." + For either case the 7nsitu measurements and model 8 predictions disagree., For either case the $in~situ$ measurements and model 8 predictions disagree. + For comparison. the Asplund et al.," For comparison, the Asplund et al." + abundances vield q=3330. due to the lower solar abundances for Mg. Si. and Fe of ~20%.. compared to L03.," abundances yield 330, due to the lower solar abundances for Mg, Si, and Fe of $\sim$, compared to L03." + The difference between (1) and (2) estimates of mnmaxv indicate a grain population is present (hat has not been coupled to the gas over the cloud lifetime. such as expected if the LIC has been shocked to high LSB. velocitiesE99).," The difference between (1) and (2) estimates of may indicate a grain population is present that has not been coupled to the gas over the cloud lifetime, such as expected if the LIC has been shocked to high LSR velocities." +. Evidently the (nv grains are disproportionallv destroved by sputtering so that dderived [rom nsiZu data may not be significantly overestimatec., Evidently the tiny grains are disproportionally destroyed by sputtering so that derived from $in~situ$ data may not be significantly overestimated. + A third basis for understanding iin (he LIC uses the silicate component of the ZDA COMP-GR-FG model as a model for LIC dust., A third basis for understanding in the LIC uses the silicate component of the ZDA COMP-GR-FG model as a model for LIC dust. +" The silicate component in the COMP-GR-FG model alone vields R,;,4,—2251. while the silicate and PAIIs together give 4,722323."," The silicate component in the COMP-GR-FG model alone yields 251, while the silicate and PAHs together give 233." + The other constituents in the COAMP-GR-FG moclel. eraphile. water ice. and organics. are nol required by missing atoms of RT models," The other constituents in the COMP-GR-FG model, graphite, water ice, and organics, are not required by “missing” atoms of RT models" +the cluster at a similar distance from the center.,the cluster at a similar distance from the center. + This argues in favor of these regions being embedded in the cluster gas and maintaining the pressure equilibrium. therefore revealing a medium survived from the accretion shock heating.," This argues in favor of these regions being embedded in the cluster gas and maintaining the pressure equilibrium, therefore revealing a medium survived from the accretion shock heating." + Existence of this effect has been suggested by the simulations (e.g. Motl et al., Existence of this effect has been suggested by the simulations (e.g. Motl et al. + 2004). but has so far only been reported for A85 (Durret et al.," 2004), but has so far only been reported for A85 (Durret et al." + 2005)., 2005). + Incomplete (in. à sense of being on-going) shock propagation m clusters soon after the major merging event could also be a cause of the low entropies seen at the outskirts., Incomplete (in a sense of being on-going) shock propagation in clusters soon after the major merging event could also be a cause of the low entropies seen at the outskirts. + In fact. the clusters in the advanced stage of interaction have systematically higher entropy at Γρ compared to the average trend.," In fact, the clusters in the advanced stage of interaction have systematically higher entropy at $r_{500}$ compared to the average trend." +Usine the photometric sample. Iwataetal.(2007) derived the UV Iuminosity hunction (UVLF) of LBGs at 2~5 in the region including (he GOODS-N and the JO053+1234 region.,"Using the photometric sample, \citet{iwa07} derived the UV luminosity function (UVLF) of LBGs at $z \sim 5$ in the region including the GOODS-N and the J0053+1234 region." +" Thev found that there is a significant population of bright (Ap,<—22.0 mag) LBGs αἱ zo5 comparable to that of z~3—4. while the faint. CM:>—21.0 mag) end of their UVLF shows a gradual increase [rom z~5 lo ο3 (Sawicki&Thompson2006)."," They found that there is a significant population of bright $M_{UV} < -22.0$ mag) LBGs at $z \sim 5$ comparable to that of $z \sim 3-4$, while the faint $M_{UV} > -21.0$ mag) end of their UVLF shows a gradual increase from $z \sim 5$ to $z \sim 3$ \citep{saw06}." +. 50 Iwata suggest luminosity dependent evolution of LDGs at these redshifts., So \citet{iwa07} suggest luminosity dependent evolution of LBGs at these redshifts. + ILowever. different results are derived from other studies of UVLE of LBGs at z5.," However, different results are derived from other studies of UVLF of LBGs at $z \sim 5$." + The UVLFs in Subaru Deep Field and Subaru XMM-Newton Deep Field derived by Ouchietal.(2004) and by Yoshidaetal.(2006) show a smaller number density of bright LBGs than that found by Iwataetal.(2003.2007).. and suggest an evolution of the number density in (the bright part of the UVLF from 2:~5 to ze3.," The UVLFs in Subaru Deep Field and Subaru XMM-Newton Deep Field derived by \citet{ouc04a} and by \citet{yos06} show a smaller number density of bright LBGs than that found by \citet{iwa03,iwa07}, and suggest an evolution of the number density in the bright part of the UVLF from $z \sim 5$ to $z \sim 3$." + The UVLFs by Beckwithetal.(2006) and also show a similar trend to those by Ouchietal.(2004) ancl Yoshida (2006)., The UVLFs by \citet{bec06} and \citet{bou07} also show a similar trend to those by \citet{ouc04a} and \citet{yos06}. +. The difference between the number clensitv of bright (Αν.<—22.0 mag) LBCs ol Iwataetal.(2003.2007). ancl that of Ouchietal.(2004). ancl Yoshidaetal.(2006) is 0.5—1.0 dex.," The difference between the number density of bright $M_{UV} < -22.0$ mag) LBGs of \citet{iwa03,iwa07} and that of \citet{ouc04a} and \citet{yos06} + is $0.5-1.0$ dex." + The cause of the divergence of UVLFs is still unknown., The cause of the divergence of UVLFs is still unknown. + Field-to-field variance may exist., Field-to-field variance may exist. + Or different filter sets used in various LBG survevs may cause the difference 2008a)., Or different filter sets used in various LBG surveys may cause the difference \citep{sta08a}. +. The spectroscopic sample helps to constrain the UVLF., The spectroscopic sample helps to constrain the UVLF. +" We derived (he lower limit ol the number densitv of LBGs at z~5 in the GOODS-N region and the J00532-1234 region. using (he spectroscopically confirmed LBGs including the spectroscopy [rom the literature (Dawsoneto2001.2002:Fernández-5otoal.2001:Spinrad1998:Bargeretal."" 2003).. but not ineluclingz5 galaxies outside of the color selection window."," We derived the lower limit of the number density of LBGs at $z \sim 5$ in the GOODS-N region and the J0053+1234 region, using the spectroscopically confirmed LBGs including the spectroscopy from the literature \citep{daw01,daw02,fer01,spi98,ste99,bar08}, but not including $z\sim5$ galaxies outside of the color selection window." + We derived the er limits for each field bv dividing the numbers of spectroscopically confirmed LBCs by the effective volume in each magnitude bin from Dwataetal.(2007)., We derived the lower limits for each field by dividing the numbers of spectroscopically confirmed LBGs by the effective volume in each magnitude bin from \citet{iwa07}. +. Then we averaged the lower limits of two fields weighting with their survey areas., Then we averaged the lower limits of two fields weighting with their survey areas. + When we calculate the UV absolute magnitude of the spectroscopic sample. we used (he fixed redshift of 2=4.8 for consistenev with the estimation of the effective volume.," When we calculate the UV absolute magnitude of the spectroscopic sample, we used the fixed redshift of $z = 4.8$ for consistency with the estimation of the effective volume." + The difference of the UV absolute magnitude by this assumption and that from spectroscopic redshift is <0.2 mag., The difference of the UV absolute magnitude by this assumption and that from spectroscopic redshift is $\lesssim 0.2$ mag. + Figure 4. shows the derived lower limits on the number clensitv of LBGs at z~5 in ihe GOODS-N region. the J00532-1234 region. and their average.," Figure \ref{UVLF} shows the derived lower limits on the number density of LBGs at $z \sim 5$ in the GOODS-N region, the J0053+1234 region, and their average." + The solid and the dashed line shows the Schechter function fit to the UVLE of Iwataetal.(2007). and (2006).. respectively with the data points (small crosses and pluses. respectively).," The solid and the dashed line shows the Schechter function fit to the UVLF of \cite{iwa07} and \cite{yos06}, respectively with the data points (small crosses and pluses, respectively)." + The conservalive estimation of the lower limits bv using only the spectroscopic sample gives the nunmber density of LBGs comparable to that by Yoshidaetal.(2006) in the magnitude range of 23.5«z'24.0 mae. and a slightly smaller value in 24.0<2!24.5 mag.," The conservative estimation of the lower limits by using only the spectroscopic sample gives the number density of LBGs comparable to that by \citet{yos06} in the magnitude range of $23.5 < z' < 24.0$ mag, and a slightly smaller value in $24.0 < z' < 24.5$ mag." + The fractions, The fractions +processes lead (to positive ancl negative chareine of the surface. but on much smaller spatial scales corresponding to the scale of the local topography. leading to locally high electric field eradients.,"processes lead to positive and negative charging of the surface, but on much smaller spatial scales corresponding to the scale of the local topography, leading to locally high electric field gradients." + Near a shadow edge. the photoelectrons produced in sunlight can travel to and stick in unilluminated regions. causing local electric [ield gradients estimated al E— 10 to 100 V ! (Colwell et al.," Near a shadow edge, the photoelectrons produced in sunlight can travel to and stick in unilluminated regions, causing local electric field gradients estimated at $E \sim$ 10 to 100 V $^{-1}$ (Colwell et al." + 2007)., 2007). + The positive. sunlit surface attracts a cloud of electrons. effectively neutralizing the gradient on length scales 6Z1 m. The electrostatic processes that move dust particles on the Moon presumably operate also on the asteroids.," The positive, sunlit surface attracts a cloud of electrons, effectively neutralizing the gradient on length scales $\ell \gtrsim$ 1 m. The electrostatic processes that move dust particles on the Moon presumably operate also on the asteroids." + The charging time on the Moon is 10? to 10* s (de and Criswell 1977): photoelectron charging eiurents will be 9 times weaker at 3 AU and the charging times will be 9 times longer but the potentials attained. for a given dielectric constant. will remain the same.," The charging time on the Moon is $\sim$ $^2$ to $^3$ s (de and Criswell 1977); photoelectron charging currents will be 9 times weaker at 3 AU and the charging times will be 9 times longer but the potentials attained, for a given dielectric constant, will remain the same." + The principal difference in the asteroid belt is that. whereas levitated Iunar cust is retained by (he gravitv of the Moon. dust ejection speeds on small bodies can exceed. the escape velocitv. ος.," The principal difference in the asteroid belt is that, whereas levitated lunar dust is retained by the gravity of the Moon, dust ejection speeds on small bodies can exceed the escape velocity, $v_e$." + Therefore. electrostatic processes are potentially capable of leading to mass loss from asteroids.," Therefore, electrostatic processes are potentially capable of leading to mass loss from asteroids." + The charge on a spherical grain of radius @ is related to the potential on (he erain. V. by (q = περίa. where ἐμ = 8.854x Fin | is the pernullivily of ree space.," The charge on a spherical grain of radius $a$ is related to the potential on the grain, $V$, by $q$ = $4\pi\epsilon_0 V a$, where $\epsilon_0$ = $\times$ $^{-12}$ F $^{-1}$ is the permittivity of free space." +The force on a charged particle exposed to an electric field E (V +) is just F=qE.,The force on a charged particle exposed to an electric field $E$ (V $^{-1}$ ) is just $F_e = q E$. +" As our criterion for dust ejection. we demand ο>V;. where v is the erain speed achieved by accelerating across the shielding distance ( and V, is the gravitational escape speed at the surface."," As our criterion for dust ejection, we demand $v > V_e$, where $v$ is the grain speed achieved by accelerating across the shielding distance $\ell$ and $V_e$ is the gravitational escape speed at the surface." +" Assuming that the grain and (the asteroid are spherical. of radius e ancl r. respectively. and that both have densitv p. this criterion gives the critical grain size for electrostatic ejection as eSubstituting the lunar values. = 10 Volts. f= lin. E = 1010 100 V . and using p = 2000 ke as the canonical asteroid density. Equation (13)) gives a, = 1.5 to 5 un for a r = 1 km asteroid (c.f."," Assuming that the grain and the asteroid are spherical, of radius $a$ and $r$, respectively, and that both have density $\rho$, this criterion gives the critical grain size for electrostatic ejection as Substituting the lunar values, $V$ = 10 Volts, $\ell$ = 1 m, $E$ = 10 to 100 V $^{-1}$, and using $\rho$ = 2000 kg $^{-3}$ as the canonical asteroid density, Equation \ref{electro}) ) gives $a_e$ = 1.5 to 5 $\mu$ m for a $r$ = 1 km asteroid (c.f." + Figure 5))., Figure \ref{critical}) ). + These sizes are somewhat smaller than the 10 jam particle sized particles inferred [rom observations of some active asteroids (e.g. 1991): Hsieh et al., These sizes are somewhat smaller than the $\sim$ 10 $\mu$ m particle sized particles inferred from observations of some active asteroids (e.g. 133P; Hsieh et al. + 2004) but. given the many uncertainties in both the model and in the interpretation of observations. perhaps the differences are acceptable.," 2004) but, given the many uncertainties in both the model and in the interpretation of observations, perhaps the differences are acceptable." + In contrast. Equation (13)) shows that on the Moon (r = 1600 km). only nanometer-sized grains can be ejected. meaning that the process is irrelevant there.," In contrast, Equation \ref{electro}) ) shows that on the Moon $r$ = 1600 km), only nanometer-sized grains can be ejected, meaning that the process is irrelevant there." +" Even for asteroid (596) Scheila (r = 56 km and a, = 0.04 to 0.1 jn). any electrostatically ejected particles would be smaller than a wavelength and inefficient optical scatterers."," Even for asteroid (596) Scheila $r$ = 56 km and $a_e$ = 0.04 to 0.1 $\mu$ m), any electrostatically ejected particles would be smaller than a wavelength and inefficient optical scatterers." +" Figure (5)) shows that a,~LO Ja. for a given asteroid radius."," Figure \ref{critical}) ) shows that $a_e \sim 10^{-4} a_c$ , for a given asteroid radius." + We conclude (hat electrostatic ejection of particles large enough to scatter optical photons is a plausible mass-loss mechanism only for smaller asteroids., We conclude that electrostatic ejection of particles large enough to scatter optical photons is a plausible mass-loss mechanism only for smaller asteroids. +have higher huninosities aud steeper values of Jj.,have higher luminosities and steeper values of $\beta$. + Luuinous ealaxies on average coutain older stellar populatious., Luminous galaxies on average contain older stellar populations. + Iu the next paper iu this series (Baldryetal.2003) πο preseut a detailed analysis of this differcutial ΕΤ iu today's Universe.," In the next paper in this series \citep{BAL03} + we present a detailed analysis of this differential SFH in today's Universe." + One limitation of this work is the assmuption of a universal Salpeter IME., One limitation of this work is the assumption of a universal Salpeter IMF. + The lieh-anass IMF can be constrained by cosmic spectra. if uear-IR data is included.," 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 ct al..," This will be addressed by a forthcoming paper (Baldry et al.," + 2003)., 2003). + Another limitation of the current work is the depeudence ou relatively low resolution (20A)}) models of evolutionary svuthesis. whereas the SDSS data has resolution.," Another limitation of the current work is the dependence on relatively low resolution ) models of evolutionary synthesis, whereas the SDSS data has resolution." + The SDSS cosmic spectrum resolves niuiy low equivalent width metal lines which are not exploited by the curent low resolution analysis aud will help to break the ageanetalliitv degeneracy., The SDSS cosmic spectrum resolves many low equivalent width metal lines which are not exploited by the current low resolution analysis and will help to break the age-metallicity degeneracy. + We are working toward beige able to construct ligh-resolution models to resolve further the question of the star-formation history of the Universe., We are working toward being able to construct high-resolution models to resolve further the question of the star-formation history of the Universe. +such a disk is powered by a black hole and has an infinite efficiency.,Such a disk is powered by a black hole and has an infinite efficiency. +" We emphasize (hat ""radiation without accretion” is a specilic feature of our model: a disk coupled to a black hole with a magnetic field.", We emphasize that “radiation without accretion” is a specific feature of our model: a disk coupled to a black hole with a magnetic field. + A standard aceretion disk radiates only if the accretion rate is non-zero. and the efficienev. of a standard: accretion disk is always V.naller than 0.42. (," A standard accretion disk radiates only if the accretion rate is non-zero, and the efficiency of a standard accretion disk is always smaller than $0.42$. (" +The πιαΙΙΙ ellicieney 0.42 can be reached only [or a disk around an extreme Ixerr black hole with α=Mj.),The maximum efficiency $0.42$ can be reached only for a disk around an extreme Kerr black hole with $a = M_H$ .) + For the model of a disk magnetically coupled to je Material in the transition region. though it has been demonstrated that the efficiency. of 1ο disk is unbounded. from above if the black hole rotates faster than the disk 2000).. a state with a zero accretion rate and a finite power can never be realized V.ince in (hat model in order to extract energy [rom the black hole material with negative energv must fall into the black hole thus aceretion must exist (Ganmuie1999).," For the model of a disk magnetically coupled to the material in the transition region, though it has been demonstrated that the efficiency of the disk is unbounded from above if the black hole rotates faster than the disk \citep{ago00}, a state with a zero accretion rate and a finite power can never be realized since in that model in order to extract energy from the black hole material with negative energy must fall into the black hole thus accretion must exist \citep{gam99}." +". Suppose (he magnetic field touches the disk at a circle wilh a radius r=rp>75,4. Le. where ly is a constant and 9Cr) is a Dirac 9-[unction which satisfies for anv 7z0. and for anv smooth function ο)."," Suppose the magnetic field touches the disk at a circle with a radius $r=r_0 > +r_{ms}$ , i.e. where $A_0$ is a constant and $\delta (x)$ is a Dirac $\delta$ -function which satisfies for any $x\neq 0$, and for any smooth function $y(x)$." + Though this is a simple and highly ideal case. it is fundamental in wuclerstanding the effect of (he magnetic coupling on the energetic process of the disk.," Though this is a simple and highly ideal case, it is fundamental in understanding the effect of the magnetic coupling on the energetic process of the disk." + For any given distribution of a magnetic field on the disk. the corresponding ff(1) can alwavs be written as since (he energv flux and the internal torque given bv equation (16)) and equation (17)) are linear functionals of H(r). the results for any given distribution of a magnetic field can be obtained [rom (theresults for the simple in equation (29)) bx linear superpositions.," For any given distribution of a magnetic field on the disk, the corresponding $H(r)$ can always be written as Since the energy flux and the internal torque given by equation \ref{flux1}) ) and equation \ref{torque1}) ) are linear functionals of $H(r)$, the results for any given distribution of a magnetic field can be obtained from theresults for the simple in equation \ref{hdel}) ) by linear superpositions." +detection of 11989: Meisenheimer. Yates Rósser 1997: Looney Hardcastle. 2000).,"detection of 1989; Meisenheimer, Yates Rösser 1997; Looney Hardcastle, 2000)." +" Throughout this letter we use //,= 50km s+ and qu=0.", Throughout this letter we use $H_0 = 50$ km $^{-1}$ $^{-1}$ and $q_0 = 0$. + At the redshift of 1123. | arcsee corresponds to 4.74 kpe.," At the redshift of 123, 1 arcsec corresponds to 4.74 kpc." + We observed 1123 with the for 46.7 ks on 2000 March 21., We observed 123 with the for 46.7 ks on 2000 March 21. + The source was near the aim point for the $3 ACIS chip., The source was near the aim point for the S3 ACIS chip. + After filtering for intervals of high background. the usable exposure time was 38.5 ks.," After filtering for intervals of high background, the usable exposure time was 38.5 ks." + We considered events in the energy range 0.5—7.0 keV. as the spectral response of the instrument is uncertain outside this range.," We considered events in the energy range 0.5–7.0 keV, as the spectral response of the instrument is uncertain outside this range." + refimage shows the exposure-corrected image of 1123 in this band., \\ref{image} shows the exposure-corrected image of 123 in this band. + Diffuse cluster emission. an X-ray nucleus and the eastern hotspot are all detected in X-rays.," Diffuse cluster emission, an X-ray nucleus and the eastern hotspot are all detected in X-rays." + We discuss each component in turn., We discuss each component in turn. + In each case. spectra were extracted. usingCIAO. with the best available responses being constructed for euch extraction region. and analysed usingXSPEC.," In each case, spectra were extracted using, with the best available responses being constructed for each extraction region, and analysed using." + Spectra were binned such that every bin had =20 net counts., Spectra were binned such that every bin had $>20$ net counts. + The X-ray counts from 1123 are dominated by diffuse cluster-scale emission. which is detectable above the background more than an areminute away from the central source.," The X-ray counts from 123 are dominated by diffuse cluster-scale emission, which is detectable above the background more than an arcminute away from the central source." +" The source was Known to be extended fromROSAT images (Hardcastle Worrall 1999), and there are many faint optical objects in the field of 1123 which may be cluster members LLongair Gunn 1975). though strong galactic reddening (the source isatb 12”. and see below) means that this cluster has not been studied in detail in the optical."," The source was known to be extended from images (Hardcastle Worrall 1999), and there are many faint optical objects in the field of 123 which may be cluster members Longair Gunn 1975), though strong galactic reddening (the source is at $b \approx -12^\circ$, and see below) means that this cluster has not been studied in detail in the optical." + We detect around 5.000 counts in a 75- radius circle centred on the nucleus. excluding the core and hotspot.," We detect around 5,000 counts in a 75-arcsec radius circle centred on the nucleus, excluding the core and hotspot." + The overall spectrum of this region is well fitted with an absorbed MEKAL spectrum with AY=5.0(1 keV. abundance of 0.47m solar and a galactic hydrogen column density of 4.5U.2UU.107* ? terrors ure 1o for one interesting parameter).," The overall spectrum of this region is well fitted with an absorbed MEKAL spectrum with $kT += 5.0^{+0.6}_{-0.4}$ keV, abundance of $0.47^{+0.12}_{-0.11}$ solar and a galactic hydrogen column density of $4.3_{-0.3}^{+0.2} \times +10^{21}$ $^{-2}$ (errors are $1\sigma$ for one interesting parameter)." + 1123 lies behind a well-known molecular cloud system in Taurus UUngerechts Thaddeus 1987). and our derived column density is consistent with the total hydrogen column inferred from radio observations of the molecular cloud system.," 123 lies behind a well-known molecular cloud system in Taurus Ungerechts Thaddeus 1987), and our derived column density is consistent with the total hydrogen column inferred from radio observations of the molecular cloud system." +" From HI absorption against 1123. Colgan. Salpeter Terzian (1988) derive Nyy=1.97>107+ 7? at the velocity of the cloud system. while the molecular hydrogen column can be inferred from CO measurements [Mco2LOK kms +. Megeath (private communication)] to be Ny,=1.6107 7, with a large systematic uncertainty [We use a recent estimate of the conversion factor averaged over the galactic plane. due to Hunter ((1997). but this may not be appropriate for the Taurus region]."," From HI absorption against 123, Colgan, Salpeter Terzian (1988) derive $N_{\rm HI} = 1.97 \times 10^{21}$ $^{-2}$ at the velocity of the cloud system, while the molecular hydrogen column can be inferred from CO measurements $W_{\rm CO} \approx 10$ K km $^{-1}$, Megeath (private communication)] to be $N_{\rm H_2} \approx 1.6 \times +10^{21}$ $^{-2}$, with a large systematic uncertainty [we use a recent estimate of the conversion factor averaged over the galactic plane, due to Hunter (1997), but this may not be appropriate for the Taurus region]." + We adopt a galactic absorption column of 4.3...107. =. unless otherwise stated. from now on.," We adopt a galactic absorption column of $4.3 +\times 10^{21}$ $^{-2}$, unless otherwise stated, from now on." + The X-ray spectral fif implies a rest-frame 2-10. keV luminosity from the cluster within a radius of 75 aresee (360 kpe) of 2.1011 eres 1+. consistent with the fitted temperature on the temperature-luminosity relation (determined largely for Abell clusters) of David ((1993).," The X-ray spectral fit implies a rest-frame 2–10 keV luminosity from the cluster within a radius of 75 arcsec (360 kpc) of $2 \times +10^{44}$ ergs $^{-1}$, consistent with the fitted temperature on the temperature-luminosity relation (determined largely for Abell clusters) of David (1993)." + refimage shows a plateau of X-ray emission on scales comparable to those of the radio source. with clear structure in the emission (note particularly X-ray voids to the E and SW of the nucleus) although there is no evidence for interaction between the X-ray sus and the radio lobes.," \\ref{image} shows a plateau of X-ray emission on scales comparable to those of the radio source, with clear structure in the emission (note particularly X-ray voids to the E and SW of the nucleus) although there is no evidence for interaction between the X-ray gas and the radio lobes." + The voids may represent large-scale iihomogeneity in the cluster gas: if so. they would help to explain the peculiar radio structure.," The voids may represent large-scale inhomogeneity in the cluster gas; if so, they would help to explain the peculiar radio structure." + The central cooling time is a few .100 yeurs. so we might expect to see a cooling flow around the source.," The central cooling time is a few $\times 10^{9}$ years, so we might expect to see a cooling flow around the source." + But there is no strong evidence for cooling in the temperature fits: the best-titting temperature for the material within [5 aresec of the nucleus (fixing the abundance to the value obtained for the whole cluster) is 4.4+0.3 keV. Since gas with temperatures below ~3 keV is not observed even in the centres of well-studied cooling flows FFabian 22000. Peterson 22000) this is perhaps not surprising.," But there is no strong evidence for cooling in the temperature fits; the best-fitting temperature for the material within 15 arcsec of the nucleus (fixing the abundance to the value obtained for the whole cluster) is $4.4\pm 0.3$ keV. Since gas with temperatures below $\sim 3$ keV is not observed even in the centres of well-studied cooling flows Fabian 2000, Peterson 2000) this is perhaps not surprising." + Our preliminary. analysis implies particle densities around the lobes which are similar to those reported by Hardcastle Worrall (2000) using data. and the measured temperature. implies comparable. but slightly larger. external pressures.," Our preliminary analysis implies particle densities around the lobes which are similar to those reported by Hardcastle Worrall (2000) using data, and the measured temperature implies comparable, but slightly larger, external pressures." + The point-like nucleus contains 517+36 0.5—7.0 keV counts. measured in a 2.5-aresee region about the centroid. with the background being taken from a 3—S aresec concentric annulus.," The point-like nucleus contains $517 \pm 36$ 0.5–7.0 keV counts, measured in a 2.5-arcsec region about the centroid, with the background being taken from a 3–5 arcsec concentric annulus." +(he iclentification with the highest FoM value.,the identification with the highest FoM value. + Though the 0.25 cutoff is perhaps arbitrary. 1 is clear (hat well below this limit (at about. 0.1). the probability for chance associations ereally increases (Sowarcls-Emunercl.Romani.&Michelson2003).," Though the 0.25 cutoff is perhaps arbitrary, it is clear that well below this limit (at about 0.1), the probability for chance associations greatly increases \citep{sow03}." +. These authors ancl (heir current working group have not vet published an analvsis for (he sources between -40 ancl -90 declination., These authors and their current working group have not yet published an analysis for the sources between -40 and -90 declination. + For these sources. we included. all of the original catalog identilieations. with the caveat that (he more marginal identifications (i.e. counterparts wilh 8.4 GIIz racio [lux density <0.5 Jv) could possibly not hold up to the analysis using the FoM criterion.," For these sources, we included all of the original catalog identifications, with the caveat that the more marginal identifications (i.e. counterparts with 8.4 GHz radio flux density $< 0.5$ Jy) could possibly not hold up to the analysis using the FoM criterion." + The total munher of such sources in this declination range is ten. with (wo below 0.5 Jv (the remainder all have flux density greater than 1 Jv al 8.4 GIIz).," The total number of such sources in this declination range is ten, with two below 0.5 Jy (the remainder all have flux density greater than 1 Jy at 8.4 GHz)." + We also note that we could be excluding candidate identifications heretolore unmentioned in this declination range., We also note that we could be excluding candidate identifications heretofore unmentioned in this declination range. + A summary of the available data used in our statistical aualvsis has been compiled in Table 1., A summary of the available data used in our statistical analysis has been compiled in Table 1. + Colunn(1) indicates the EGRET source name. column (2) indicates the best radio identification. lollowed by the redshift in coliumn(3).," Column(1) indicates the EGRET source name, column (2) indicates the best radio identification, followed by the redshift in column(3)." +" Colinns (4)-(6) give the monochromatic radio. optical and gamma ray luminosities. respectively (all have units of joulessecIz4),"," Columns (4)-(6) give the monochromatic radio, optical and gamma ray luminosities, respectively (all have units of $ {\rm joules\, sec^{-1} \,Hz^{-1}}$ )." + If the redshift is unknown. we substitute with 251.," If the redshift is unknown, we substitute with z=1." + There are no significant changes in the results if we use other assumptions. such as z=0.5.," There are no significant changes in the results if we use other assumptions, such as z=0.5." + To calculate the radio Iuminositv we use (he 8.4 GIIz flux densities aud spectral indices (Column (7))between 1.4 and 8.4 Gllz of Sowards-Emumerd.Romani.&Michelson(2003.2004). except for the lowest declination sources cdiscussecl above.," To calculate the radio luminosity we use the 8.4 GHz flux densities and spectral indices (Column (7))between 1.4 and 8.4 GHz of \citet{sow03,sow04} except for the lowest declination sources discussed above." + For (hese. we extract the similar radio data from the NASA Extragalactic Database (NED) to calculate the spectral index between 1.4 and 8.4 GlIIz.," For these, we extract the similar radio data from the NASA Extragalactic Database (NED) to calculate the spectral index between 1.4 and 8.4 GHz." +" Henceforth we use P,xv"" For defining spectral indices.", Henceforth we use ${F_{\nu}} \propto {\nu^{-\alpha}}$ for defining spectral indices. + In. caleulating the optical huminositlies we use recent. V. magnitudes extracted fom NED (when available). and we derive an optical flux density and monochromatic luminosity [rom this magnitude using the conversions of Bessel (1919).," In calculating the optical luminosities we use recent V magnitudes extracted from NED (when available), and we derive an optical flux density and monochromatic luminosity from this magnitude using the conversions of \citet{bes79}." +. Sowards-Emunercd.Romani.&Michelson(2003.2004) also provide archival Rand D nagnitudes [rom the USNO catalog (Monet.efa£.2003).. which we have used to interpolate a V value if we did not otherwise have a relerence for a V magnitude.," \citet{sow03,sow04} also provide archival R and B magnitudes from the USNO catalog \citep{mon03}, which we have used to interpolate a V value if we did not otherwise have a reference for a V magnitude." + In à lew cases we only vad O magnitudes from the POSS-I survey or 2MASS infraved magnitudes. and thus need to extrapolate to the V. band.," In a few cases we only had O magnitudes from the POSS-I survey or 2MASS infrared magnitudes, and thus need to extrapolate to the V band." + For sources that have no optical or near infrared magnitudes in the literature. and that were not detected in the POSS-I. SERC-J. or POSS-II we assume nagnitude upper limits equal to the appropriate plate limits ofthe survey (eg..," For sources that have no optical or near infrared magnitudes in the literature, and that were not detected in the POSS-I, SERC-J, or POSS-II we assume magnitude upper limits equal to the appropriate plate limits of the survey (eg.," + O-21.5.E-—20 or POSS-I MeMahlon.efa£. (2002))) ancl derive upper limits to the optical luminosities accordinglv.," O=21.5,E=20 for POSS-I \citet{mcm02}) ) and derive upper limits to the optical luminosities accordingly." + The eamumna-ray Dhuminosities are determined [rom the flux and spectral index (Column (3)) given in Hartmanefa£.(1999)., The gamma-ray luminosities are determined from the flux and spectral index (Column (8)) given in \citet{har99}. +. We use the lormula of to derive an exact 400 MeV. Πας., We use the formula of \citet{tho96} to derive an exact 400 MeV flux. + If the spectral index is not known. we assume it is 1.0 mote that we are referring to (he energy spectral index and not the photon index).," If the spectral index is not known, we assume it is 1.0 (note that we are referring to the energy spectral index and not the photon index)." + In. all cases we use (he co-added fIux over all viewing periods., In all cases we use the co-added flux over all viewing periods. + In the absence of simultaneous data ab all wavelengths. Chis is a better representation of broad band properties than any single value.," In the absence of simultaneous data at all wavelengths, this is a better representation of broad band properties than any single value." + Each of the Iuminosities is calculated using equation (2) of, Each of the luminosities is calculated using equation (2) of +We will estimate the projected mass associated with the CI component under some simple assuuptious for the purpose of constraining its possible contribution to the N-rav ass estimate.,We will estimate the projected mass associated with the G1 component under some simple assumptions for the purpose of constraining its possible contribution to the X-ray mass estimate. + Firstly. we cousider the mass of the two bright elliptical galaxies inside CUI.," Firstly, we consider the mass of the two bright elliptical galaxies inside G1." +" Their velocity dispersious aud effective radii were measured to bee =317 lan/s andr,=5.9hij1kpe for⊳∙∖ #3380 aud 0=⊲↼275 lau/s.; ad rs=3.1.lkpe forJ #33727L. respectively: (uiDoklaunetal. 1996)."," Their velocity dispersions and effective radii were measured to be $\sigma=317$ km/s and $r_e=5.9 ~h_{50}^{-1}{\rm kpc}$ for 380 and $\sigma=275$ km/s, and $r_e = 3.4 ~h_{50}^{-1}{\rm kpc}$ for 374, respectively \citep{VANDOKKUM_ETAL.1996}." +" fayThen calculating the projected leusine mass under the Sineular Isothermal Sphere model. we obtain Maps~wat/(2Gr,.)=Li«101NE, for 43380 and Maps=1.915% flux change wouldbe6054.," Assuming that the $K$ -band variations are sufficiently sampled, the probability of seeing a $>$ flux change would be." +. In one extreme case. a Iv flux decrease occured within oue dav.," In one extreme case, a $K$ flux decrease occured within one day." + Our observations were plauued so that such strong variability would have been detected., Our observations were planned so that such strong variability would have been detected. + Correlated flux changes between the MIR aud A bands are expected iu the proposed dust disk model for (Figure 1:: Waneetal. 2006)).i£ X-ray flux chanecs are considered as the primary cause of the variability.," Correlated flux changes between the MIR and $K$ bands are expected in the proposed dust disk model for (Figure \ref{fig:disk}; \citealt{wck06}) ), if X-ray flux changes are considered as the primary cause of the variability." + We did not detect the Av-like flux variations in our MIR observatious., We did not detect the $K$ -like flux variations in our MIR observations. + The TRAC fluxes were cousisteut with being a constant within the uncertainties., The /IRAC fluxes were consistent with being a constant within the uncertainties. +" Caven that the nuit ou the MIR. 1.5 flux variations was οτον, upperthe MIR enüssion variabilityAber was similar to the NIR 7/7 bands aud less variable than in the A baud."," Given that the upper limit on the MIR 4.5 $\mu$ m flux variations was $\lesssim 13$, the MIR emission variability was similar to the NIR $JH$ bands and less variable than in the $K$ band." + We note that in à A-baud observation made one dav prior to our first oobservation. the source had A/—19.940.l imag (Gonzalezetal.2007).. approximately the average A magnitude of0112161.," We note that in a $K$ -band observation made one day prior to our first observation, the source had $K=19.9\pm0.1$ mag \citep{gon+07}, approximately the average $K$ magnitude of." +. Because the time scale of the A fux variations is uot determined. this could sugecstCoco that the source was in a stable state in the NIR durig our observations. which could be a reason for the absence of MIR. variability.," Because the time scale of the $K$ flux variations is not determined, this could suggest that the source was in a stable state in the NIR during our observations, which could be a reason for the absence of MIR variability." + To further coustrain the relation between the MIB aud NIR cussion. frequent. simultaneous observations are needed.," To further constrain the relation between the MIR and NIR emission, frequent, simultaneous observations are needed." + If the MIR. enuüssioun ds truly less variable. the restricted A-baud variability would deumaud explanation.," If the MIR emission is truly less variable, the restricted $K$ -band variability would demand explanation." +" Tuterestinely. simular NIB variability is seen iu a few dust disk systenis around voung stars has](οι,Eiroa etal.2002))."," Interestingly, similar NIR variability is seen in a few dust disk systems around young stars (e.g., \citealt{eir+02}) )." + Tu those svsteiis. the variability con sugeested to be caused by structural changes of the immer disk.," In those systems, the variability has been suggested to be caused by structural changes of the inner disk." + If this is the case for61.. the properties in the sources IR variability might be explainable.," If this is the case for, the properties in the source's IR variability might be explainable." + Since cussion in the A baud would mainly arise from the inner edge of the disk aud thus be more seusitive to iuner disk chanees. it would vary more stronglv than cussion iu the 77 aud AIMIR bands.," Since emission in the $K$ band would mainly arise from the inner edge of the disk and thus be more sensitive to inner disk changes, it would vary more strongly than emission in the $JH$ and MIR bands." + It is not clear what would be the cause of the structural changes in the disk inGI., It is not clear what would be the cause of the structural changes in the disk in. +. One possibility is variable Nav. heatiug. such as due to burst-related N-rav. brightening.," One possibility is variable X-ray heating, such as due to burst-related X-ray brightening." + However. no siguificaut short-term. flux wanriationus have been found iu the observatious of the source (Duraut&vanIerkwijk20063.. aud thus far oulv a few bursts have Όσο found in bieweckly N-rav imionitoriug observatious (Dib 2007).. indicating iufrequeucy of the burst events.," However, no significant short-term flux variations have been found in the X-ray observations of the source \citep{dv06}, and thus far only a few bursts have been found in bi-weekly X-ray monitoring observations \citep{dkgw06,gav+07}, indicating infrequency of the burst events." + Thus iu the absence of N-ray variability. the A-band variability challenges the dust disk model (Duraut&vanI&erkwijk200600).," Thus in the absence of X-ray variability, the $K$ -band variability challenges the dust disk model \citep{dv06}." + Tn addition. we did not detect any sieuificant MIR flux chanees from in our TRAC MMobservatious following the large X-ray burst.," In addition, we did not detect any significant MIR flux changes from in our IRAC observations following the large X-ray burst." + The 1.5/8.0 pau fluxes were nearly the same as those obtained in 2005., The 4.5/8.0 $\mu$ m fluxes were nearly the same as those obtained in 2005. + As demoustrated by N-ray observations of the source that were made several days prior to our first oobservation (Couzalez ct al, As demonstrated by X-ray observations of the source that were made several days prior to our first observation (Gonzalez et al. + 2007). the ANP uufortunately lad already returned το quiesceuce during our observations.," 2007), the AXP unfortunately had already returned to quiescence during our observations." + Also as shown iu the loue-term N-rav nonitorime observations. the quiesceut N-rav fiux of has been nearly constaut and stable over the past decade (Dib.Kaspi.&Cuowrul2007: Gonzalez et al.," Also as shown in the long-term X-ray monitoring observations, the quiescent X-ray flux of has been nearly constant and stable over the past decade \citealt*{dkg07}; Gonzalez et al." + 2007)., 2007). + Therefore. our nou-detection is cousisteut with the sources state at X-ray energies at the time.," Therefore, our non-detection is consistent with the source's state at X-ray energies at the time." + We thauls theSpitzer Sciouce Center for erautiug us the observations aud the Helpdesk at Spitzer Scieuce Centerfor help with data reduction aud aualvsis., We thank the Science Center for granting us the observations and the Helpdesk at Science Centerfor help with data reduction and analysis. + This research was supported by NSERC sia a Discovery Grant aud by the FORNT aud ci&£u., This research was supported by NSERC via a Discovery Grant and by the FQRNT and cifar. + VAUX holds a Canada Research Chair aud the Lorne Trottier Chair in Astroplivsics Cosimmologv. aud is a R. Toward Webster Fouudatiou Fellow of citar.," VMK holds a Canada Research Chair and the Lorne Trottier Chair in Astrophysics Cosmology, and is a R. Howard Webster Foundation Fellow of cifar." +panel) it seems that the direction of degeneracy is slightly changed for the potential-based temperature functions so that og can be constrained more tightly compared to the upper panel.,"panel), it seems that the direction of degeneracy is slightly changed for the potential-based temperature functions so that $\sigma_8$ can be constrained more tightly compared to the upper panel." +" For the mass-based temperature function, there is no such effect."," For the mass-based temperature function, there is no such effect." +" Overall, the potential-based functions yield slightly smaller best-fit values for σᾳ compared to their mass-based counterparts."," Overall, the potential-based functions yield slightly smaller best-fit values for $\sigma_8$ compared to their mass-based counterparts." +" If merger effects are taken into account, cg is significantly lowered while OQ is increased for all temperature functions."," If merger effects are taken into account, $\sigma_8$ is significantly lowered while $\Omega_\mathrm{m0}$ is increased for all temperature functions." +" Consequently, the confidence contours of the results including and excluding mergers do not overlap."," Consequently, the confidence contours of the results including and excluding mergers do not overlap." +" This result is in good agreement with the work by ?,, who also found using numerical simulations that mergers do have a drastic impact on the results for those two parameters."," This result is in good agreement with the work by \citet{Randall2002}, who also found using numerical simulations that mergers do have a drastic impact on the results for those two parameters." + First converting the measured temperature according to Eq., First converting the measured temperature according to Eq. + and then comparing it to the theoretical potential-based temperature function incorporating spherical collapse (green contours) has a similar effect as mergers: og is decreased while O9 is increased., and then comparing it to the theoretical potential-based temperature function incorporating spherical collapse (green contours) has a similar effect as mergers: $\sigma_8$ is decreased while $\Omega_\mathrm{m0}$ is increased. +" Interestingly, using the potential-based temperature function including merger effects but without temperature conversion (blue solid contours) and using the potential-based temperature function with temperature conversion but merger effects (green dashed contours) give almost identical (asfor?) or at least similar (for?) confidence contours."," Interestingly, using the potential-based temperature function including merger effects but without temperature conversion (blue solid contours) and using the potential-based temperature function with temperature conversion but merger effects (green dashed contours) give almost identical \citep[as for][]{Vikhlinin2009a} or at least similar \citep[for][]{Ikebe2002} confidence contours." +" Hence, the effects of temperature conversion and cluster mergers turn out to be highly degenerate."," Hence, the effects of temperature conversion and cluster mergers turn out to be highly degenerate." +" Additionally, merger boosts increase the uncertainty on Ὃπιρ since the confidence contours become more elongated in this direction."," Additionally, merger boosts increase the uncertainty on $\Omega_\mathrm{m0}$ since the confidence contours become more elongated in this direction." +" The confidence contours inferred from the potential-based temperature functions built on ellipsoidal-collapse dynamics (magenta contours) are shifted towards higher Ojo compared to those built on spherical collapse, both including and excluding mergers."," The confidence contours inferred from the potential-based temperature functions built on ellipsoidal-collapse dynamics (magenta contours) are shifted towards higher $\Omega_\mathrm{m0}$ compared to those built on spherical collapse, both including and excluding mergers." + This can easily be understood considering Fig., This can easily be understood considering Fig. + l1 again., \ref{fig:sphEllFunc} again. +" There, the temperature function based on ellipsoidal collapse lies always below the spherical-collapse case for the same cosmological parameters."," There, the temperature function based on ellipsoidal collapse lies always below the spherical-collapse case for the same cosmological parameters." +" The reasons are a significantly enlarged 6, and a smaller A, that leads to a smaller ratio of the non-linearly to the linearly evolved potential.", The reasons are a significantly enlarged $\delta_\cc$ and a smaller $\Delta_\vv$ that leads to a smaller ratio of the non-linearly to the linearly evolved potential. + The result of the former is a decrease of the temperature function's amplitude while the latter shifts the curve towards smaller temperatures., The result of the former is a decrease of the temperature function's amplitude while the latter shifts the curve towards smaller temperatures. +" Hence, to arrive at a similar fit for a given data set, a higher O49 is needed."," Hence, to arrive at a similar fit for a given data set, a higher $\Omega_\mathrm{m0}$ is needed." +" Additionally, the contours based on ellipsoidal collapse are more extended especially in the OQmo- direction compared to both the spherical case and the based temperature function."," Additionally, the contours based on ellipsoidal collapse are more extended especially in the $\Omega_\mathrm{m0}$ -direction compared to both the spherical case and the mass-based temperature function." + This implies that the potential-based temperature function built upon ellipsoidal collapse is the least sensitive to changes in Oo., This implies that the potential-based temperature function built upon ellipsoidal collapse is the least sensitive to changes in $\Omega_\mathrm{m0}$. +" The contours are not in agreement with a joint analysis of the five-year data release of the (WMAPS5), and data from baryonic acoustic oscillations (BAO) and supernovae (SN) by ? (black solid contour)."," The contours are not in agreement with a joint analysis of the five-year data release of the (WMAP5), and data from baryonic acoustic oscillations (BAO) and supernovae (SN) by \citet{Komatsu2009} (black solid contour)." + The reason for this discrepancy might be that the ellipsoidal case describes temperature functions very well which are based on the mass-weighted temperature SSect. 3.2))., The reason for this discrepancy might be that the ellipsoidal case describes temperature functions very well which are based on the mass-weighted temperature Sect. \ref{subsec:propTemp}) ). +" The latter, however, is different from the temperature that is actually inferred from observations (see Sect. 3.1))."," The latter, however, is different from the temperature that is actually inferred from observations (see Sect. \ref{subsec:probAnalysis}) )." + A detailed study of this problem is therefore crucial., A detailed study of this problem is therefore crucial. + It will be carried out in a forthcoming paper., It will be carried out in a forthcoming paper. +" Besides the aforementioned contours from the potential-based temperature function including ellipsoidal collapse, all confidence contours are in agreement with the WMAPS-«BAO-SN analysis except one: if both the temperature conversion. Eq."," Besides the aforementioned contours from the potential-based temperature function including ellipsoidal collapse, all confidence contours are in agreement with the WMAP5+BAO+SN analysis except one: if both the temperature conversion Eq." +" and merger effects are included in the calculation of the X-ray temperature function (green solid contour), the resulting confidence contour no longer overlaps with that given by ?.."," and merger effects are included in the calculation of the X-ray temperature function (green solid contour), the resulting confidence contour no longer overlaps with that given by \citet{Komatsu2009}. ." +formation becomes (he mass accretion rate as given bv equation (3).,formation becomes the mass accretion rate as given by equation (3). + Because the mass accretion rate depends on total mass square. the accretion rate is higher (han in a single-star case.," Because the mass accretion rate depends on total mass square, the accretion rate is higher than in a single-star case." + Consider (wo equal mass main sequence stars of Mj;=Mis1.M.. and demanding that each star accretes at a rale of 10TAL.vr.|.," Consider two equal mass main sequence stars of $M_{b1}=M_{b2}=1 M_\odot$, and demanding that each star accretes at a rate of $> 10^{-7} M_\odot \yr^{-1}$." + For the mass loss rate and wind velocity as in equation (3). the constraint from the mass accretion rate becomes ay<400AU.," For the mass loss rate and wind velocity as in equation (3), the constraint from the mass accretion rate becomes $a_0 \lesssim 400 \AU$." + For accreting. WD stars. Le.. al least one of the stars in the binary svstem is a white cwarl which accretes half of the mass. I take Mj;=Mis0.6.M.. and as in section 1 requires the accretion rate to be >10.“AL.vr.+.," For accreting WD stars, i.e., at least one of the stars in the binary system is a white dwarf which accretes half of the mass, I take $M_{b1}=M_{b2}=0.6 M_\odot$, and as in section 1 requires the accretion rate to be $> 10^{-8} M_\odot \yr^{-1}$." + The constraint [rom the mass accretion rate becomes ayS800AU., The constraint from the mass accretion rate becomes $a_0 \lesssim 800 \AU$. + These numbers should be compared with the constraint on accreting single stellar companion (first section) of ayο<40AU and ayο<150AU. for main sequence and WD single companions. respectively.," These numbers should be compared with the constraint on accreting single stellar companion (first section) of $a_0 \lesssim 40 \AU$ and $a_0 \lesssim 150 \AU$, for main sequence and WD single companions, respectively." +" In (he later case (he constraint is the accreted specific angular moment, (", In the later case the constraint is the accreted specific angular momentum. ( +6) The constraint on the mass accretion rate can be eased if we consider the nature of ihe Dondi-Hovle-Lyttleton accretion flow.,6) The constraint on the mass accretion rate can be eased if we consider the nature of the Bondi-Hoyle-Lyttleton accretion flow. + The flow along the accretion column is unstable. with large variation in density. hence in the mass accretion rate on short time scales (Cowie 1971: Soker 1991).," The flow along the accretion column is unstable, with large variation in density, hence in the mass accretion rate on short time scales (Cowie 1977; Soker 1991)." + This implies that even when the average accretion rate is lower (han the critical value. on short time scales it can be higher. leading possibly to sporadic jet formation. (," This implies that even when the average accretion rate is lower than the critical value, on short time scales it can be higher, leading possibly to sporadic jet formation. (" +7) The formation of jets at large distance ου (he mass losing star will lead to departure from axisvmmnietry. even when jets are blown perpendicular to the triple-star orbital plane (Soker 2001).,"7) The formation of jets at large distance from the mass losing star will lead to departure from axisymmetry, even when jets are blown perpendicular to the triple-star orbital plane (Soker 2001)." + Here there is another effect., Here there is another effect. + Because the accretion disk is almost perpendicular to the orbital plane. i.e.. ils axis. hence the jets if are formed. is close to the triple-star orbital plane and pointing from the the accreting binary svstem to the mass-losing star.," Because the accretion disk is almost perpendicular to the orbital plane, i.e., its axis, hence the jets if are formed, is close to the triple-star orbital plane and pointing from the the accreting binary system to the mass-losing star." + This means that one jet expands toward lower density medium and expands almost undisturbed., This means that one jet expands toward lower density medium and expands almost undisturbed. + The opposite jet. on the other hand. expands toward the mass losing star and encounters dense medium.," The opposite jet, on the other hand, expands toward the mass losing star and encounters dense medium." + This jet can be deflected and/or slowed down by the dense wind [rom the mass losing star. (, This jet can be deflected and/or slowed down by the dense wind from the mass losing star. ( +3) In addition to the accreting binary svstem which can reside at a large orbital separation dy. the mass losing eiut star may have a close companion.,"8) In addition to the accreting binary system which can reside at a large orbital separation $a_0$, the mass losing giant star may have a close companion." + That closer companion will cause axisvmmetrical mass loss as well. but most likely with a different axis of svimimetry. (," That closer companion will cause axisymmetrical mass loss as well, but most likely with a different axis of symmetry. (" +9) When q~1. ie.. almost equal mass companions. both stars can blow jets. each stars on ils turn.,"9) When $q \sim 1$, i.e., almost equal mass companions, both stars can blow jets, each stars on its turn." + This may further complicate the structure of the nebula., This may further complicate the structure of the nebula. +from the estimations based on [SII].,from the estimations based on [SII]. + The values ofXa/a obtained from [Nel] are significantly different from zero., The values of$\Delta \alpha/\alpha$ obtained from [NeIII] are significantly different from zero. + We have checked that (his departure from zero keeps along all the range in redshift analyzed usine that doublet., We have checked that this departure from zero keeps along all the range in redshift analyzed using that doublet. + The wide range in redshift covered by (his sample ancl the absence of the effect for other lines (for instance. the lines of the [OHI] doublet or the atmospheric OI line) precludes possible svstematic errors in wavelength calibration.," The wide range in redshift covered by this sample and the absence of the effect for other lines (for instance, the lines of the [OIII] doublet or the atmospheric OI line) precludes possible systematic errors in wavelength calibration." + Figure 8. (righ!) shows a comparison between the estimations of Aa/a from the ΟΠΗ and [Nell] respectively using only common spectra to both samples., Figure \ref{compara_especies} $right$ ) shows a comparison between the estimations of $\Delta \alpha/\alpha$ from the [OIII] and [NeIII] respectively using only common spectra to both samples. + Clearly. the results from [Nel] are not compatible with those from [OLI].," Clearly, the results from [NeIII] are not compatible with those from [OIII]." + For the distribution of the centroids of each member of the [Nell] doublet. we have estimated mean values of 3869.61 and 3969.05 and rms of 0.51 and 0.58 respectively.," For the distribution of the centroids of each member of the [NeIII] doublet, we have estimated mean values of 3869.61 and 3969.05 and rms of 0.51 and 0.58 respectively." + The comparison with the theoretical local values (3869.86 and 3968.59 respectively) shows discrepancies οἱ 0.25 and 0.46 to the blue and to the red respectively., The comparison with the theoretical local values (3869.86 and 3968.59 respectively) shows discrepancies of 0.25 and 0.46 to the blue and to the red respectively. + If we restrict the sample according to stronger constraints on the SNR. of both lines. these shifts tend to decrease only for the line at 3870A.," If we restrict the sample according to stronger constraints on the SNR of both lines, these shifts tend to decrease only for the line at 3870." +. Although this could indicate inaceuraey in the tabulated wavelengths of both transitions. we think the main reason is (hat the estimated wavelengths for the line [Nel] (2970 A)) are affected by the proximity of several lines like lle and the absorption line of Call. Nevertheless. if (his is (he case it would remain unclear why the rms of the the distributions of both members of the doublet are so similar. and why the shift in the 3970 line does not decrease when only spectra with relatively high SNR are considered.," Although this could indicate inaccuracy in the tabulated wavelengths of both transitions, we think the main reason is that the estimated wavelengths for the line [NeIII] (3970 ) are affected by the proximity of several lines like $\epsilon$ and the absorption line of CaII-H. Nevertheless, if this is the case it would remain unclear why the rms of the the distributions of both members of the doublet are so similar, and why the shift in the 3970 line does not decrease when only spectra with relatively high SNR are considered." + Curiously enough. the high value found for Aa/a using [Nell] is similar to (he mean value found by Grupe et al.," Curiously enough, the high value found for $\Delta \alpha/\alpha$ using [NeIII] is similar to the mean value found by Grupe et al." + using Chis pair., using this pair. + In Section 1 we have mentioned the different astronomical methods used to constrain the variation in a with particular emphasis on those based on fine structure splitting., In Section 1 we have mentioned the different astronomical methods used to constrain the variation in $\alpha$ with particular emphasis on those based on fine structure splitting. + Here. we make comparisons only with previous observations based on the relative splitting of pairs ol emission lines in QSOs or AGN in general.," Here, we make comparisons only with previous observations based on the relative splitting of pairs of emission lines in QSOs or AGN in general." + The analvsis bv. Baheall οἱ iis based on the Early Data Release of SDSS. which comprises a sub sample of the sample analyzed in (his paper. so il is worth making a comparison of both studies.," The analysis by Bahcall et is based on the Early Data Release of SDSS, which comprises a sub sample of the sample analyzed in this paper, so it is worth making a comparison of both studies." + There are 38(10) shared objects between (he sample of these authors and our raw(clean) sample., There are 38(10) shared objects between the sample of these authors and our raw(clean) sample. + Figure 10. shows a comparison between our estimates of Aa/a and those by Baheall et al., Figure \ref{bahcall} shows a comparison between our estimates of $\Delta \alpha/\alpha$ and those by Bahcall et al. + The comparison shows a very good agreement between both studies., The comparison shows a very good agreement between both studies. + The distribution of Aa/a obtained from objects in common between our raw sample and the Baheall et ssample is similar. while the rms of Aa/a [rom our clean sample is 0.5xI0. 7. slightly better than the sample of Dahcall et (0.7x10. 77).," The distribution of $\Delta \alpha/\alpha$ obtained from objects in common between our raw sample and the Bahcall et sample is similar, while the rms of $\Delta +\alpha/\alpha$ from our clean sample is $0.5\times 10^{-3}$ , slightly better than the sample of Bahcall et $0.7\times 10^{-3}$ )." + So. although," So, although" +Given that a smaller branching fraction limits this patloway. electron impact excitation iuto the triplet manifold will be a competing formation imechaisin.,"Given that a smaller branching fraction limits this pathway, electron impact excitation into the triplet manifold will be a competing formation mechanism." + Cross sections for ionization and excitation of helium bv electrous in the 10.—1000 eV range are shown in Dalgaruoetal.(1999). figures 2a 2b., Cross sections for ionization and excitation of helium by electrons in the $10-1000$ eV range are shown in \citet{dal99} figures 2a 2b. + To compute the rate of ionization and excitation. one must perform an integral in energv space over the product of cach cross section with the differential energy spectrui of electrons in the ISM.," To compute the rate of ionization and excitation, one must perform an integral in energy space over the product of each cross section with the differential energy spectrum of electrons in the ISM." + This full caleulatiou is hiudered by the fact that the spectru of secondary clectrous (those produced during ionization events] is unknown. aud cannot be derived from the differential energyspectrum of cosimic-rav protons which is also unknown below ~1 GeV. The complexity associated with deriving the spectrum of secondary electrons is bevoud the scope of this paper. lus we make some simplificatious in estimating the inportance of electron inipact excitation iuto the triplet uanifold of helimm.," This full calculation is hindered by the fact that the spectrum of secondary electrons (those produced during ionization events) is unknown, and cannot be derived from the differential energyspectrum of cosmic-ray protons which is also unknown below $\sim1$ GeV. The complexity associated with deriving the spectrum of secondary electrons is beyond the scope of this paper, thus we make some simplifications in estimating the importance of electron impact excitation into the triplet manifold of helium." + Assunidug that all secondary. electrous have the same energv. the ratio between the rate of excitation iuto all riplet states and the rate of ionization can be determined o» taking the ratio of the respective cross sectious af a elven enerev.," Assuming that all secondary electrons have the same energy, the ratio between the rate of excitation into all triplet states and the rate of ionization can be determined by taking the ratio of the respective cross sections at a given energy." + We take this ratio at 30 eV (the mean value given by Cravens&Dalearuo (1978))). aud fiud he rate of excitation iuto all triplet states to be 2 times aster than the rate of ionization by secondary electrons.," We take this ratio at 30 eV (the mean value given by \citet{cra78}) ), and find the rate of excitation into all triplet states to be 2 times faster than the rate of ionization by secondary electrons." + To determine the overall importance of electron mipact excitation then. we need to find a relatiouship between he total ionization rate of helm aud the ionization rate due to secondaries.," To determine the overall importance of electron impact excitation then, we need to find a relationship between the total ionization rate of helium and the ionization rate due to secondaries." +" Using relations between the xumnary iouization rates of hydrogen aud belium (Wabing&Goldsmith1971:Liszt2003) aud between the primary ionization rate of hydrogen aud the total ionization rate of heliuun. (Classeold&Langer1971:Tieleus2005).. we estimate that iouization by secoudary electrons accounts for about 1/6 of the total ionization rate of ποια,"," Using relations between the primary ionization rates of hydrogen and helium \citep{hab71,lis03} and between the primary ionization rate of hydrogen and the total ionization rate of helium \citep{gla74,tie05}, we estimate that ionization by secondary electrons accounts for about 1/6 of the total ionization rate of helium." + This. in turn. leads to the approximation that the rate for electron imupact excitation iuto the triplet manifold and thus the metastable state (which we denote ài ) should be roughly 1/3 that of the total ionization rate of helium (i0. 8j29Qu/3: we use this relation for the remmauder of this paper).," This, in turn, leads to the approximation that the rate for electron impact excitation into the triplet manifold — and thus the metastable state (which we denote $\delta_{\rm He^*}$ ) — should be roughly 1/3 that of the total ionization rate of helium (i.e. $\delta_{\rm He^*}\approx \zeta_{\rm He}/3$; we use this relation for the remainder of this paper)." + Mathematically. these additional formation aud destruction reactions can casily be included. by altering— the steady state equations in 811.2. resulting in 2 changes to our analysis.," Mathematically, these additional formation and destruction reactions can easily be included by altering the steady state equations in 1.2, resulting in 2 changes to our analysis." +" First. due to the additional destruction pathways of Tle). the branching fraction. b. must be redefined as Iu many cases. however. absolute abundances are not known auditis thus convenient to recast equation (15)) in ternis of fractional abundances as where s;— sg—VCD)|20(0ID. aud the inolecubu: hydrogen njfng.fraction fj,(Πο)ng."," First, due to the additional destruction pathways of $^+$, the branching fraction, $b$, must be redefined as In many cases, however, absolute abundances are not known and it is thus convenient to recast equation \ref{eqbranch}) ) in terms of fractional abundances as where $x_j\equiv~n_j/n_{\rm H}$, $n_{\rm H}\equiv n({\rm H})+2n({\rm H_2})$, and the molecular hydrogen fraction $f_{\rm H_2}\equiv 2n({\rm H_2})/n_{\rm H}$." + Second. equation (6)) must be recast to include electron impact excitation into the metastable state. aud becomes While the analysis now iucludes many more paralcters. wei can still caleulate the fractional abundance of metastable heli. aud thus the expected lue strength. toward IID 183112.," Second, equation \ref{eqfmapprox}) ) must be recast to include electron impact excitation into the metastable state, and becomes While the analysis now includes many more parameters, we can still calculate the fractional abundance of metastable helium, and thus the expected line strength, toward HD 183143." + We assume that fractional abuudances are constant throughout the cloud. allowing us to substitute column densities for nunber deusities when available (ie. ο/Nip).," We assume that fractional abundances are constant throughout the cloud, allowing us to substitute column densities for number densities when available (i.e. $x_j=N_j/N_{\rm H}$ )." + Using the color excess as in 822.1 eives Ny=7.1<107 cin7., Using the color excess as in 2.1 gives $N_{\rm H}=7.4\times10^{21}$ $^{-2}$. + This is used in conjunction with spectroscopic observations of CO which indicate NICO)z102? ? (MeCalletal.2002) to compute weg., This is used in conjunction with spectroscopic observations of CO which indicate $N({\rm CO})\approx 10^{15}$ $^{-2}$ \citep{mcc02} to compute $x_{\rm CO}$ . +" The assumption that there are equal amounts of atomic and molecular bydrogcu is quantified by fi,=2/3.", The assumption that there are equal amounts of atomic and molecular hydrogen is quantified by $f_{\rm H_2}=2/3$. +" Finally. observations of C in diffuseclouds have shown that. ~1.4«101, assuniue that ucarly all electrous come from this sinely ionized carbon (Cardellietal.1996)."," Finally, observations of $^+$ in diffuseclouds have shown that $x_e\sim1.4\times10^{-4}$, assuming that nearly all electrons come from this singly ionized carbon \citep{car96}." +. Combining these data ancl assumptions with the rate coofficieuts in Table 3.. the new branching fraction is b=0.08. about one-cighth of the value considering clectrous alouc.," Combining these data and assumptions with the rate coefficients in Table \ref{tblrates}, the new branching fraction is $b=0.08$, about one-eighth of the value considering electrons alone." +" Substituting this branching fraction and the relevant paralucters from 822.1-2.2 iuto equation (17)) results in values of f,,1.3«10£7, N,,=9.3«10% em7. and Wa=0.1611À."," Substituting this branching fraction and the relevant parameters from 2.1-2.2 into equation \ref{eqfmBZDA}) ) results in values of $f_m=1.3\times10^{-12}$, $N_m=9.3\times10^8$ $^{-2}$, and $W_{\lambda}=0.46$." +. Again splitting the material iuto 2 equal cloud. components decreases the equivalent widths to Wy20.2311À.. which would require a S/N~2000 for a 37 detection.," Again splitting the material into 2 equal cloud components decreases the equivalent widths to $W_{\lambda}=0.23$, which would require a $\sim 2000$ for a $\sigma$ detection." + Re-arraneing equation (17)). we can turn this problem around and compute an upper luit to the cosmic-ray ionization rate of elim using our observations.," Re-arranging equation \ref{eqfmBZDA}) ), we can turn this problem around and compute an upper limit to the cosmic-ray ionization rate of helium using our observations." +" Cüven the upper limit to the metastable coli density. IN,<3.2.10? 7. and the estimated total helimm colunu. ΑΠΟ=JAMIVE(BV)7.ς10°"" cm2. the 30 upper unit to the fractional metastable population is fn t_{\rm nuc}$ excludes significantly higher masses." + Figs., Figs. + 3. 4 show the evolution of such a system: a 1.5M. AIS star was allowed to evolve and fill its Roche lobe in a 15 hr binary with a 7M.DIL.," 3, 4 show the evolution of such a system: a $1.5 \, \msun$ MS star was allowed to evolve and fill its Roche lobe in a 15 hr binary with a $7 \, \msun$." + The predicted mass transfer rate throughout the evolution. including its current value 35H10IN.Ivr+. shows that the system would. indeedH lave appeared as à soft. NXrav. transient. according to the irradiateddisc criterion. for blackhole. svstems given. by Ixing. Kolb Szuszkiewicz (1997).," The predicted mass transfer rate throughout the evolution, including its current value $3 \times 10^{-10} \, \msun {\rm yr}^{-1}$, shows that the system would indeed have appeared as a soft X–ray transient, according to the irradiated–disc criterion for black–hole systems given by King, Kolb Szuszkiewicz (1997)." +" It should be noted that he change in CAN is mostly due to a drastic depletion of 12g""C. supplemented by à more modest increase. in. N. DoThe otal O abundance at the surface has only decreased: very ittle: in fact the ON ratio is reduced. by only a. factor of 3 to 5 at most. predominantly due to the increase of N. Interestingly. this mioclel also passes through £244=TAab5hr at around. A»zO.GAL.. showing much weaker N enhancements almost normal abundances. cf Fig."," It should be noted that the change in C/N is mostly due to a drastic depletion of $^{12}$ C, supplemented by a more modest increase in $^{14}$ N. The total O abundance at the surface has only decreased very little; in fact the O/N ratio is reduced by only a factor of 3 to 5 at most, predominantly due to the increase of N. Interestingly, this model also passes through $P_{\rm orb} = 7.75 \, +{\rm hr}$ at around $M_2 \approx 0.6 \, \msun$, showing much weaker N enhancements almost normal abundances, cf Fig." + 3)., 3). +" Thus it can also be considered. a reasonable model fe""n A0G62000.", Thus it can also be considered a reasonable model for A0620–00. + A subsequent. paper (Schenker et al..," A subsequent paper (Schenker et al.," + 20025) will explore this and related evolutions in detail., 2002b) will explore this and related evolutions in detail. + Finally we can compare further. properties. of. the secondary in our model to observations: Figure 4 shows rw evolution of elective temperature with orbital period. ogether with a simple mapping to spectral types.," Finally we can compare further properties of the secondary in our model to observations: Figure 4 shows the evolution of effective temperature with orbital period, together with a simple mapping to spectral types." + The procedure is based on a conversion of observed: colours to spectral types (Beucrmann et al.," The procedure is based on a conversion of observed colours to spectral types (Beuermann et al.," + 1998) and a set of non-grev stellar atmospheres (Llauschildt et al..," 1998) and a set of non-grey stellar atmospheres (Hauschildt et al.," +. 1999). providing the colours for cach set of stellar boundary conditions., 1999) providing the colours for each set of stellar boundary conditions. + For solar metallicity the resulting SpT turns out to be only a function of clicctive temperature with a very weak dependence on surface gravity., For solar metallicity the resulting SpT turns out to be only a function of effective temperature with a very weak dependence on surface gravity. + Llowever this mapping should. only be considered a first estimate. as the evolutionary code in its current forni still uses grey atmospheres.," However this mapping should only be considered a first estimate, as the evolutionary code in its current form still uses grey atmospheres." + Furthermore the whole conversion is based on an observed. set of unevolved stars. and. theoretical ZAAIS models. nno fully selt-consistent application to a partially evolved. ALS star such as shown in Fig.," Furthermore the whole conversion is based on an observed set of unevolved stars and theoretical ZAMS models, no fully self-consistent application to a partially evolved MS star such as shown in Fig." + 4 is possible for the time being., 4 is possible for the time being. + Allowing for the uncertainties described above. our model may be slightlv too cool (M2 rather than Ix5-Ml. as mentioned in MeClintock. et al (2001). or W7-ALO by Wagner et al (2000).," Allowing for the uncertainties described above, our model may be slightly too cool (M2 rather than K5-M1 as mentioned in McClintock et al (2001), or K7-M0 by Wagner et al (2000)." + Similar evolutionary tracks of strongly evolved CVs, Similar evolutionary tracks of strongly evolved CVs +We have obtained optical spectrophotometry of the evolution of comet 9P/Tempel 1 alter (he impact of the Deep Impact probe. using the Supernova Integral Field Spectrograph (SNIFS) at the UII 2.2m telescope. as well as simullaneous optical and infrared spectra using the Lick Visible-to-Near-Infrared Inaeing Spectrograph (VNIRIS) spectrograph.,"We have obtained optical spectrophotometry of the evolution of comet 9P/Tempel 1 after the impact of the Deep Impact probe, using the Supernova Integral Field Spectrograph (SNIFS) at the UH 2.2m telescope, as well as simultaneous optical and infrared spectra using the Lick Visible-to-Near-Infrared Imaging Spectrograph (VNIRIS) spectrograph." +" The spatial distribution and temporal evolution of the ""violet band” CN (0-0) emission and of the 630 nm [OI] emission was studied.", The spatial distribution and temporal evolution of the “violet band” CN (0-0) emission and of the 630 nm [OI] emission was studied. + We found that CN emission centered on the nucleus increased in the (wo hours alter impact. but that (his CN emission was celaved compared to the light curve of dust-scattered sunlight.," We found that CN emission centered on the nucleus increased in the two hours after impact, but that this CN emission was delayed compared to the light curve of dust-scattered sunlight." + The CN emission also expanded faster than the cloud of scattering dust., The CN emission also expanded faster than the cloud of scattering dust. + The emission of [OI] at 630 nm rose similarly to the scattered light. but then remained nearly constant for several hours alter impact.," The emission of [OI] at 630 nm rose similarly to the scattered light, but then remained nearly constant for several hours after impact." + On Che day following the impact. both CN and [OI] emission concentrated on the comet nucleus had returned nearly {ο pre-impact levels.," On the day following the impact, both CN and [OI] emission concentrated on the comet nucleus had returned nearly to pre-impact levels." + We have also searched for differences in the scattering properties of the dust ejected by (he impact compared to the dust released under normal conditions., We have also searched for differences in the scattering properties of the dust ejected by the impact compared to the dust released under normal conditions. + Compared to the pre-impact state of the comet. we find evidence that the color of the comet was slightly bluer during the post-impact rise in briehtness.," Compared to the pre-impact state of the comet, we find evidence that the color of the comet was slightly bluer during the post-impact rise in brightness." + Long alter the impact. in the following nights. the comet colors returned (o their pre-impact values.," Long after the impact, in the following nights, the comet colors returned to their pre-impact values." + This can be explained by postulating a change to a smaller particle size distribution in the ejecta cloud. in agreement with the findines from mid-infrared observatons. or bv postulating a large fraction of clean ice particles. or by a combination of (hese (wo.," This can be explained by postulating a change to a smaller particle size distribution in the ejecta cloud, in agreement with the findings from mid-infrared observatons, or by postulating a large fraction of clean ice particles, or by a combination of these two." + Kev Words: Comets: 9P/Tempel 1: Deep Impact: Photometry: Spectroscopy, Key Words: Comets; 9P/Tempel 1; Deep Impact; Photometry; Spectroscopy +While Tvpe la supernovae (la SNe) plav a Fundamental role in cosmology auc chemical evolution of the Universe. (heir exact origin remains greatly uncertain.,"While Type Ia supernovae (Ia SNe) play a fundamental role in cosmology and chemical evolution of the Universe, their exact origin remains greatly uncertain." + One of the leading, One of the leading +central surface brightness is fy=16.20 in Jay.,central surface brightness is $\mu_0=16.20$ in $I_{AB}$. + At a redshift of 2=0.938 this corresponds lo puplrestframe)=pi—7.5log(1+2)0.13 where the latter term is the correction from observed wavelength to B-band.," At a redshift of $z=0.938$ this corresponds to $\mu_{0,B}(restframe)=\mu_{0,I}-7.5\log(1+z) -0.13$ where the latter term is the correction from observed wavelength to $B$ -band." +" This value. jip(restframe)=13.92. converts to ρω=13.24 and surface brightness αἱ H2—Re. _r=20.18$." + Using the relations eiven by Jorgensen.Franx&Njaergaard(1996) vields a velocity dispersion of ¢=380$5., Using the relations given by \citet{Jor96} yields a velocity dispersion of $\sigma=380^{+65}_{-60}$. + This is im verv good agreement with the mass parameter derived [rom the lensing model above., This is in very good agreement with the mass parameter derived from the lensing model above. + The [act that it agrees so well. however. poses another problem in that it apparently represents a contradiction to the passive evolution moclel for elliptical galaxies.," The fact that it agrees so well, however, poses another problem in that it apparently represents a contradiction to the passive evolution model for elliptical galaxies." + For example. Schadeοἱal.(1999). claim evolution of nearly 1: magnitude in luminosity (or. equivalently. surface brightness) for an elliptical at this redshift.," For example, \citet{Sch99} claim evolution of nearly 1 magnitude in luminosity (or, equivalently, surface brightness) for an elliptical at this redshift." + In fact. the lensing galaxy is one of the sample of elliptical galaxies in (he CFRS/LDSS imagine survey (hat was used to derive the evolution.," In fact, the lensing galaxy is one of the sample of elliptical galaxies in the CFRS/LDSS imaging survey that was used to derive the evolution." +" In order (o estimate mass from the photometric parameters of (his galaxy the observed surface brightness should be ""de-evolved. that is. the central surface brightness should be made one magnitude fainter before it is compared to thelocal (2=0) fundamental plane."," In order to estimate mass from the photometric parameters of this galaxy the observed surface brightness should be “de-evolved"", that is, the central surface brightness should be made one magnitude fainter before it is compared to thelocal $z=0$ ) fundamental plane." + Lf this is done. a mass estimate of 6=2143 is obtained. obviously very. significantly lower than the mass estimate from the lens moclel.," If this is done, a mass estimate of $\sigma=214^{+35}_{-30}$ is obtained, obviously very significantly lower than the mass estimate from the lens model." + This result for CFRSO3.1077 is contrary to results [rom studies of the evolution of the fhuudamental plane at moderate redshift (Ixelson.Hlingworth.vanDokkum&Franx2000:vanDokkum.Frans.Nelson.&Ulinegworth2001) and of lensing galaxies on average.," This result for CFRS03.1077 is contrary to results from studies of the evolution of the fundamental plane at moderate redshift \citep{kel00,vd01} and of lensing galaxies on average." + ]xochaneketal.(2000) present data from 30 lenses and conclude that the fundamental plane for both field galaxies ancl cluster galaxies are similar and that (μον are representative of passively evolving populations formed at z > 2.," \citet{Koc00} + present data from 30 lenses and conclude that the fundamental plane for both field galaxies and cluster galaxies are similar and that they are representative of passively evolving populations formed at z $>$ 2." + That view is consistent with the fundamental plane studies., That view is consistent with the fundamental plane studies. + The reason (hat CERS03.1077 does not appear to share (his behavior is nol obvious., The reason that CFRS03.1077 does not appear to share this behavior is not obvious. + Is there substantial variance in (he evolution history of massive elliptical galaxies?, Is there substantial variance in the evolution history of massive elliptical galaxies? + An examination of Figure 3 [rom Schadeοἱal.(1999). shows that this particular galaxy lies within ils lo error bar of the no evolution locus for elliptical galaxies in the Mp(15)—logFH plane and is one of the most deviant points from (he evolving relation., An examination of Figure 3 from \citet{Sch99} shows that this particular galaxy lies within its $1\sigma$ error bar of the no evolution locus for elliptical galaxies in the $M_B(AB)-\log R_e$ plane and is one of the most deviant points from the evolving relation. + The only other very luminous elliptical galaxy in the study by Schadeetal.(1999) (CEBRS 14.1811 at 2=0.807) also appears in Figure 3 of that paper and lies exactly on the evolving Ap(AB)—logFH relation implying an evolution in huminositwv (or. equivalenilv. in surface briehtness) of ~1 magnitude.," The only other very luminous elliptical galaxy in the study by \citet{Sch99} (CFRS 14.1311 at $z=0.807$ ) also appears in Figure 3 of that paper and lies exactly on the evolving $M_B(AB)-\log R_e$ relation implying an evolution in luminosity (or, equivalently, in surface brightness) of $\sim 1$ magnitude." + Remarkably. (hat galaxy is an Einstein Cross lens discovered by Ratnattnga and studied by Cramptonοἱal.(1996). who report a velocity dispersion of 230 km ! as implied by Che lens model.," Remarkably, that galaxy is an Einstein Cross lens discovered by \citet{Rat95} and studied by \citet{Cra96} who report a velocity dispersion of 230 km $^{-1}$ as implied by the lens model." + If the observed values of A and _e$ for CFRS 14.1311 are converted into a velocity dispersion via the local fundamental plane then a value of $\sigma=537$ km $^{-1}$ is obtained. + If an evolution of one magnitude in surface brightness is (hen applied this is reduced to o= 290km |. roughly consistent with the value derived [rom the lens model.," If an evolution of one magnitude in surface brightness is then applied this is reduced to $\sigma=290$ km $^{-1}$ , roughly consistent with the value derived from the lens model." + In other words. CERS14.1311 behaves as expected but CERSO2.1077 does not.," In other words, CFRS14.1311 behaves as expected but CFRS03.1077 does not." + It should, It should +Tables L. 5 aud 6 compare the observed shape parameters measured by the various observations with the predictions from the two models derived. above.,"Tables \ref{modcompe}, , \ref{modcompi} and \ref{modcompel} compare the observed shape parameters measured by the various observations with the predictions from the two models derived above." + While the moclel j»arameters were derived using weighted averages of data (roi dillerent observatious. these comiparisous do not cousider variations in the uncertainties iu the observatious.," While the model parameters were derived using weighted averages of data from different observations, these comparisons do not consider variations in the uncertainties in the observations." + This is jecause. as noted above. these simplified models were unable to fit the [4.4] data to within ie error bars.," This is because, as noted above, these simplified models were unable to fit the $[h,k]$ data to within the error bars." + Thus au unweighted aualysis will provide a couservative estimate of how well jese models describe the data., Thus an unweighted analysis will provide a conservative estimate of how well these models describe the data. + Table L preseuts the moclel predictious for the eccentricity aud periceuter locations rou the loneitucinal scaus., Table \ref{modcompe} presents the model predictions for the eccentricity and pericenter locations from the longitudinal scans. + Note that the only observation where the more complex Moclel lo does a better job predicting the eccentricity aud pericenter than tle simpler Model 1 is in the Orbit 30 data., Note that the only observation where the more complex Model 2 does a better job predicting the eccentricity and pericenter than the simpler Model 1 is in the Orbit 30 data. + This is consistent. with Fig 6.. where the dashed circle (Model 2) gets closer to the point iu the upper left Crom Orbit 30) than the solid circle (Model 1). but or all the other data points the dashed circle is not obviously a better fit than the solid one.," This is consistent with Fig \ref{charmpar}, where the dashed circle (Model 2) gets closer to the point in the upper left (from Orbit 30) than the solid circle (Model 1), but for all the other data points the dashed circle is not obviously a better fit than the solid one." + Note the Orbit 30 ata were taken at a substautially hielier phase angle than the other observations. so this observation may probe a cdillerent part of the size distribution and the shape parameters may uot be perfectly comparable to the others.," Note the Orbit 30 data were taken at a substantially higher phase angle than the other observations, so this observation may probe a different part of the size distribution and the shape parameters may not be perfectly comparable to the others." + Therelore. we conclude that the simpler moclel that assumes the forced component of the pericenter is perlectly anti-alignecd with the Sun is a preferable moclel for the shape of the ring.," Therefore, we conclude that the simpler model that assumes the forced component of the pericenter is perfectly anti-aligned with the Sun is a preferable model for the shape of the ring." + This model recovers the eccentricity of the ringlet with au rvs residual of 1 kin and the pericenterlocation with an ris vesicdual of E, This model recovers the eccentricity of the ringlet with an $rms$ residual of 1 km and the pericenterlocation with an $rms$ residual of $^\circ$. + Table 5 presents the model preclictious for the inclinations aud nodes for the longitudiual scans., Table \ref{modcompi} presents the model predictions for the inclinations and nodes for the longitudinal scans. + La this case. there is not a clear differeuce between the two inodels.," In this case, there is not a clear difference between the two models." + Given that including a forced inclination does uot substantially reduce the scatter in the observations. for the sake of simplicity we favor the use of the simpler Model 1 in this case as well.," Given that including a forced inclination does not substantially reduce the scatter in the observations, for the sake of simplicity we favor the use of the simpler Model 1 in this case as well." + Here the inodel predicts the inclination with au rics residual of 0.3 ku and the node location with an rins residual of LI., Here the model predicts the inclination with an $rms$ residual of 0.3 km and the node location with an $rms$ residual of $^\circ$. + Finally. Table 6 compares the model predictious for the z aud C yarameters for the elevation scau (see Eqs 7 aud 8)).," Finally, Table \ref{modcompel} compares the model predictions for the $z$ and $C$ parameters for the elevation scan (see Eqs \ref{zeq} and \ref{ceq}) )." + This is a critical check ou the model. wuch was developed uxing only the longitudinal scan data.," This is a critical check on the model, which was developed using only the longitudinal scan data." + Here. we can see that both uodes give values for z aud C that are reasonably cousisteut with the observed. values.," Here, we can see that both models give values for $z$ and $C$ that are reasonably consistent with the observed values." + Iu couclusiou. while Model 1 is clearly over-simplifiecd aud does uot »xovkle a perfectly accurate description of the observed data. it nevertheless appears to bea welul approximate description of the ringlet's shape and time variability.," In conclusion, while Model 1 is clearly over-simplified and does not provide a perfectly accurate description of the observed data, it nevertheless appears to be a useful approximate description of the ringlet's shape and time variability." + We can uow compare tlie observed shape parameters of this rinelet with theoretical expectatious., We can now compare the observed shape parameters of this ringlet with theoretical expectations. + Theforced eccentricity aud inclination cau be relatively easily uuderstood iu terms of the solar radiation forces cliscussed above., The eccentricity and inclination can be relatively easily understood in terms of the solar radiation forces discussed above. +By contrast. the components of the,"By contrast, the components of the" +an index a=(2—p)/2 (corresponding to a particle index p+1) above it.,an index $\alpha=(2-p)/2$ (corresponding to a particle index $p+1$ ) above it. + The cooling break corresponds to the electron energy (or Lorentz factor y;) at which the escape time Τεις from the system is equal to the (synchrotron) cooling time Του]., The cooling break corresponds to the electron energy (or Lorentz factor $\gamma_b$ ) at which the escape time $\tau_{esc}$ from the system is equal to the (synchrotron) cooling time $\tau_{cool}$. +" The cooling timescale is given as (Pacholczyk 1970) but the escape timescale depends on several factors, including B and the ambient particle density n,."," The cooling timescale is given as (Pacholczyk 1970) but the escape timescale depends on several factors, including $B$ and the ambient particle density $n_e$." +" Nonetheless, detailed calculations of the acceleration process (see Nayakshin Melia 1998, Liu et al."," Nonetheless, detailed calculations of the acceleration process (see Nayakshin Melia 1998, Liu et al." +" 2004, 2006) indicate that for a broad range of conditions, T,,. corresponds roughly to 3 times the light transit time in the system. ("," 2004, 2006) indicate that for a broad range of conditions, $\tau_{esc}$ corresponds roughly to 3 times the light transit time in the system. (" +"For an analogous, though much smaller system than Sgr A*, see also Misra Melia 1993.)","For an analogous, though much smaller system than Sgr A*, see also Misra Melia 1993.)" +" Thus, if the emission region is near the marginally stable orbit (see below), we would expect for a black hole mass 4x10°Mo."," Thus, if the emission region is near the marginally stable orbit (see below), we would expect for a black hole mass $4\times 10^6\;M_\odot$." +" In the overall spectrum, the cooling break is therefore expected to occur at a frequency i.e., somewhere above the NIR component and well below the X-ray, as long as the magnetic field intensity is of order 30 G, essentially the value required to produce Sgr A*’s quiscent emission."," In the overall spectrum, the cooling break is therefore expected to occur at a frequency i.e., somewhere above the NIR component and well below the X-ray, as long as the magnetic field intensity is of order 30 G, essentially the value required to produce Sgr A*'s quiscent emission." +" For the simulations reported in thisLetter, we will therefore assume that the relativistic particle distribution producing the NIR/X-ray flare has the following form: where the choice of p, y; (or, equivalently, B in Equation 3), and the normalization constant No, are all based on earlier fits to the data (see, e.g., Dodds-Eden et al."," For the simulations reported in this, we will therefore assume that the relativistic particle distribution producing the NIR/X-ray flare has the following form: where the choice of $p$ , $\gamma_b$ (or, equivalently, $B$ in Equation 3), and the normalization constant $N_0$, are all based on earlier fits to the data (see, e.g., Dodds-Eden et al." +" 2009, Trap et al."," 2009, Trap et al." + 2011)., 2011). +" An additional constraint on the flaring region is provided by the temporal substructure seen in typical bursts, particularly in the NIR."," An additional constraint on the flaring region is provided by the temporal substructure seen in typical bursts, particularly in the NIR." +" For example, one sees L’-band flux variations up to ~30% of the peak value on a timescale of only ~20 minutes."," For example, one sees $L^\prime$ -band flux variations up to $\sim 30\%$ of the peak value on a timescale of only $\sim 20$ minutes." +" Taken at face value, these fluctuations could be telling us that most of the burst activity is occurring near the marginally stable orbit surrounding a 4x105Μο black hole (see, e.g., Melia et al."," Taken at face value, these fluctuations could be telling us that most of the burst activity is occurring near the marginally stable orbit surrounding a $\sim 4\times 10^6\;M_\odot$ black hole (see, e.g., Melia et al." + 2001a)., 2001a). +" However, light-travel arguments constrain the size of the emitting region even further when one uses the shortest time-scale variations seen, e.g., in the 4 April, 2007 burst reported by Dodds-Eden et al. ("," However, light-travel arguments constrain the size of the emitting region even further when one uses the shortest time-scale variations seen, e.g., in the 4 April, 2007 burst reported by Dodds-Eden et al. (" +"2009).There, in the L’ lightcurve,","2009).There, in the $L^\prime$ lightcurve," +"As for the standard ellipticals, even our dwarf early- galaxies display a flat (Fe)o distribution MMgo.","As for the standard ellipticals, even our dwarf early-type galaxies display a flat $\langle Fe \rangle_2$ distribution $_2$." +" This apparent decoupling between Iron and the other a elements (as traced by Magnesium) is a well recognized feature (Gorgas,Efstathiou,&AragonSalamanca1990;&Gariboldi 1994),, and probably the most direct evidence of the different enrichment channels that provided metals to the galaxies in the past."," This apparent decoupling between Iron and the other $\alpha$ elements (as traced by Magnesium) is a well recognized feature \citep{gorgas90,worthey92,buzzoni94}, and probably the most direct evidence of the different enrichment channels that provided metals to the galaxies in the past." +" According to stellar evolution theory, in fact, we know that a-elements are important yields for high-mass stars (M=8 Mc) dying as Type II SNe; on the contrary, the Fe-Ni enrichment is more efficiently carried on by the Type Ia SNe, likely related to the binary- environment."," According to stellar evolution theory, in fact, we know that $\alpha$ -elements are important yields for high-mass stars $M\gtrsim 8~M_\odot$ ) dying as Type II SNe; on the contrary, the Fe-Ni enrichment is more efficiently carried on by the Type Ia SNe, likely related to the binary-star environment." +" A steady trend of (Fe)2 MMg might therefore be resilient of a constant abundance of Iron, that is of a constant rate of Type Ia SNe (Buzzoni,Mantegazza,&Gariboldi 1994)."," A steady trend of $\langle Fe \rangle_2$ Mg might therefore be resilient of a constant abundance of Iron, that is of a constant rate of Type Ia SNe \citep{buzzoni94}." +". Apparently at odds with previous conclusions, however, the study of the (Fe)s meta-index reports a more explicit correlation between Fe and Mg along the entire mass range of standard and dwarf ellipticals."," Apparently at odds with previous conclusions, however, the study of the $\langle Fe \rangle_5$ meta-index reports a more explicit correlation between Fe and Mg along the entire mass range of standard and dwarf ellipticals." +" To a finer detail, this puzzling behaviour is mostly induced by a trend in place among the “bluer” Fe indices (namely Fe4383 and Fe4531)."," To a finer detail, this puzzling behaviour is mostly induced by a trend in place among the “bluer” Fe indices (namely Fe4383 and Fe4531)." +" Contrary to the “red” indices FFe5270, Fe5335 and Fe5406), when split into the different elemental contributions (see,forinstance,Table2inTrageretal. 1998),, all the “blue” indices are actually blends including an important presence of Ti and Mg, and this may eventually explain the apparent correlation between (Fe)s and Mg»."," Contrary to the “red” indices Fe5270, Fe5335 and Fe5406), when split into the different elemental contributions \citep[see, for instance, Table 2 in][]{trager98}, all the “blue” indices are actually blends including an important presence of Ti and Mg, and this may eventually explain the apparent correlation between $\langle Fe \rangle_5$ and $_2$." +" As a final remark dealing with Fig. 18,,"," As a final remark dealing with Fig. \ref{f18}," + one has to note the somewhat unexpected general correlation of galaxy indices along the different morhological types., one has to note the somewhat unexpected general correlation of galaxy indices along the different morhological types. +" Although with larger individual uncertainties, in fact, also spirals and dwarf irregulars seem to obey in the plots the established relationship as for ellipticals."," Although with larger individual uncertainties, in fact, also spirals and dwarf irregulars seem to obey in the plots the established relationship as for ellipticals." +" This interesting behaviour is largely in consequence of the much poorer (and similar) response of both Mg and Fe indices to SSP age, that simply displaces their location in the plots along the SSP ""universal"" locus independently from the galaxy star-formation history."," This interesting behaviour is largely in consequence of the much poorer (and similar) response of both Mg and Fe indices to SSP age, that simply displaces their location in the plots along the SSP “universal” locus independently from the galaxy star-formation history." +" 'The natural correlation among o elements within our galaxy sample can be verified by means of the two molecular features of Carbon, namely CH (alias G4300) and C» at 4668 ((see the two upper panels of Fig. 19)),"," The natural correlation among $\alpha$ elements within our galaxy sample can be verified by means of the two molecular features of Carbon, namely CH (alias G4300) and $_2$ at 4668 (see the two upper panels of Fig. \ref{f19}) )," + and the Calcium Ca4455 feature (as in the lower panel of the same figure)., and the Calcium Ca4455 feature (as in the lower panel of the same figure). +" In both cases, a beautiful trend is in place with the NGC 5044 dwarf-galaxy population linking standard ellipticals with globular clusters."," In both cases, a beautiful trend is in place with the NGC 5044 dwarf-galaxy population linking standard ellipticals with globular clusters." +" A slightly more scattered plot may be noticed for the G4300 index, however, perhaps in some cases affected by the influence of the closeby Hy emission."," A slightly more scattered plot may be noticed for the G4300 index, however, perhaps in some cases affected by the influence of the closeby $\gamma$ emission." +" Overall, one has also to report in the different panels of Fig."," Overall, one has also to report in the different panels of Fig." + 18 and 19 a tendency for NGC 5044 itself to display slightly shallower absorption features compared to the expected strength for standard ellipticals of similar Mg» value.," \ref{f18} and \ref{f19} + a tendency for NGC 5044 itself to display slightly shallower absorption features compared to the expected strength for standard ellipticals of similar $_2$ value." + We are inclined to ascribe this effect to the larger, We are inclined to ascribe this effect to the larger +normalization condition (14)) is satisfied.,normalization condition \ref{norms}) ) is satisfied. +" The fact that S.(7) has a fairly simple power law form, will allow us to calculate an expression for thens attenuation, by direct integration of the formal solution (16))."," The fact that $S_*(\tau)$ has a fairly simple power law form, will allow us to calculate an expression for the attenuation, by direct integration of the formal solution \ref{Ans}) )." +" Inserting S.(T) in (16)) we obtain which becomes, using the function WV;(x) defined as in Appendix B, This result is in agreement with the solution obtained by Disney et ((1989)."," Inserting $S_*(\tau)$ in \ref{Ans}) ) we obtain which becomes, using the function ${\cal W}_\zeta(x)$ defined as in Appendix B, This result is in agreement with the solution obtained by Disney et (1989)." +" Knowing this expression, we immediately also have an expression for the fs andai attenuation curves For ¢>0 and for all values of x, we define the function Wec(x) by the integral For natural values of C, the integral can immediately be solved in terms of elementary functions, for example For non-integer values of ¢ the integral canbe calculated by expanding the cosh function, (10))"," Knowing this expression, we immediately also have an expression for the and attenuation curves For $\zeta>0$ and for all values of $x$, we define the function ${\cal{W}}_\zeta(x)$ by the integral For natural values of $\zeta$, the integral can immediately be solved in terms of elementary functions, for example For non-integer values of $\zeta$ the integral canbe calculated by expanding the cosh function, \ref{app_defW})" +aud whether estimates of AL41 from observations at N-rav aud other wavelengths can be reconciled.,and whether estimates of $\Mdot_{1}$ from observations at X-ray and other wavelengths can be reconciled. + Future X-ray erating observations should also help us to fix the value of the wind momentum ratio more accurately., Future X-ray grating observations should also help us to fix the value of the wind momentum ratio more accurately. + As the secondary wind dominates the X-ray spectrin. and its terminal velocity appears to be high (53000kins 3). we should expect to see signs of Doppler broadening and shifts in the line profiles.," As the secondary wind dominates the X-ray spectrum, and its terminal velocity appears to be high $\approx 3000\;\kmps$ ), we should expect to see signs of Doppler broadening and shifts in the line profiles." + While there is little evidence for this iu the current spectrum. other orbital phases may be more favourable in this regard.," While there is little evidence for this in the current spectrum, other orbital phases may be more favourable in this regard." + The addition of Doppler effects has already been incorporated in modelled X-ray. spectra (Pittard alii preparation). and should provide further information ou wind velocities and the structure of the wind-wind collision region.," The addition of Doppler effects has already been incorporated in modelled X-ray spectra (Pittard in preparation), and should provide further information on wind velocities and the structure of the wind-wind collision region." + The over-prediction of the N-ray. liues in our models verhaps indicates tha the companion has /sub-solar abunudauces. which favours an O-tvpe over a WR classification. although we would need to perform a nore detailed analysis to coufin this possibility.," The over-prediction of the X-ray lines in our models perhaps indicates that the companion has sub-solar abundances, which favours an O-type over a WR classification, although we would need to perform a more detailed analysis to confirm this possibility." + As the oxmnuary has slightly cnhauced abundances of € aud N compared to solar. this sugeestsOO that to date there has ο. no lass exchanee between the stars.," As the primary has slightly enhanced abundances of C and N compared to solar, this suggests that to date there has been no mass exchange between the stars." + Lamers (1998)) sugeested that the star which dominates the UV GIRS spectrum is not the star which ejected the rebula since the abundances in the GIIRS spectrum are rot as evolved as the abundances in the nebula (which are indicative of CNO-cvcle products}., Lamers \cite{LLPW1998}) ) suggested that the star which dominates the UV GHRS spectrum is not the star which ejected the nebula since the abundances in the GHRS spectrum are not as evolved as the abundances in the nebula (which are indicative of CNO-cycle ). + As the UV bright source is probably the companion (IlBer 2001)) lis indicates that it was the primary which ejected the rebula., As the UV bright source is probably the companion (Hillier \cite{HDIG2001}) ) this indicates that it was the primary which ejected the nebula. + There are also some caveats about the analysis in Laiers (1998)) since strong C lines (which Lamers took to indicate rormal CNO abuudauces in the GIIRS spectrum) also appear in stars kuown to be deficient in C (see the discussion in Willer 2001))., There are also some caveats about the analysis in Lamers \cite{LLPW1998}) ) since strong C lines (which Lamers took to indicate normal CNO abundances in the GHRS spectrum) also appear in stars known to be deficient in C (see the discussion in Hillier \cite{HDIG2001}) ). + Tt is also interesting to note that the UV spectrmm brightened iu 1999.1]. vs. 1998.2. which is suggestive of au eclipse of the UV source near poriastrou in 1998.," It is also interesting to note that the UV spectrum brightened in 1999.1 vs. 1998.2, which is suggestive of an eclipse of the UV source near periastron in 1998." + Iu conchision. the high energy photons (UV and X-ray) secu to be telling us about the companion.," In conclusion, the high energy photons (UV and X-ray) seem to be telling us about the companion." + We cuplhasize that coutrary to the vast majority of colliding wiud svstems. our X-ray analysis of yy Car ΠΑΝ probes the couditious of the shocked wind of he companion.," We emphasize that contrary to the vast majority of colliding wind systems, our X-ray analysis of $\eta$ Car primarily probes the conditions of the shocked wind of the companion." + X-ray observations of jj Car are therefore unique iu this regard since at other wavelengths (with the xossible exception of the far UV) the wine of the ouv dominates the observed phenomena., X-ray observations of $\eta$ Car are therefore unique in this regard since at other wavelengths (with the possible exception of the far UV) the wind of the primary dominates the observed phenomena. + While our analysis ias for the first time provided a direct estimate of the wind parameters of the companion star. relating these to he stellar parameters (nass. radius. luninosity) of the colupanion star requires niore work.," While our analysis has for the first time provided a direct estimate of the wind parameters of the companion star, relating these to the stellar parameters (mass, radius, luminosity) of the companion star requires more work." + It is anticipated that he continued multi-wwavelength study of jj Car through and bevoud the next periastron passage will further reveal he hidden secrets of this most enignatie svsteni., It is anticipated that the continued multi-wavelength study of $\eta$ Car through and beyond the next periastron passage will further reveal the hidden secrets of this most enigmatic system. +picture of the QLF resulting from the application of realistic. lummosity-dependent quasar lifetimes. accurately predicts the faint-end slope of the QLF at all observed redshifts.,"picture of the QLF resulting from the application of realistic, luminosity-dependent quasar lifetimes, accurately predicts the faint-end slope of the QLF at all observed redshifts." + Our modeling provides a simple. direct physical motivation for both the break luminosity L. and faint-end slope +.," Our modeling provides a simple, direct physical motivation for both the break luminosity $\lstar$ and faint-end slope $\slope$." + The break L. corresponds to the in the rate at which quasars with a given peak luminosity (final BH mass) are being created or activated at any given time. and is determined (to first order) by the differential lifetime of these objects. as they spend substantial time at low L«ρω. either in early stages of rapid BH growth to larger £L or in sub-Eddington states in transition into or out of the brief period of peak quasar activity.," The break $\lstar$ corresponds to the in the rate at which quasars with a given peak luminosity (final BH mass) are being created or activated at any given time, and $\slope$ is determined (to first order) by the differential lifetime of these objects, as they spend substantial time at low $L\ll\Lp$, either in early stages of rapid BH growth to larger $L$ or in sub-Eddington states in transition into or out of the brief period of peak quasar activity." + The observed ~ and its evolution with redshift are a simple consequence of L. and its evolution., The observed $\slope$ and its evolution with redshift are a simple consequence of $\lstar$ and its evolution. + At high-z. Z.. is larger. implying most quasars have higher peak luminosity.," At $z$, $\lstar$ is larger, implying most quasars have higher peak luminosity." +" From our simulations and analytical modeling of quasar feedback. we expect objects to both grow and expel gas more rapidly and higher-Lpea,violently. when they reach their final mass and feedback unbinds nearby material."," From our simulations and analytical modeling of quasar feedback, we expect $\Lp$ objects to both grow and expel gas more rapidly and violently, when they reach their final mass and feedback unbinds nearby material." +" Thus. objects ""die"" more quickly. resulting 1n a flatterbrighter-Lpoa, > as they spend less relative time in any given L at Lo," Our model can predict $\slope$ as a simple function of $\lstar$, itself tied to the characteristic quasars being created at any time, and is thus immediately useful for modeling the quasar contribution to reionization, which depends on $\slope$ at $z$." +" For purposes where 5 is important. the quasar lifetimes fitted in Hopkinsetal.(200569). should be slightly modified to be Schechter functions with faint-end slopes [the weak dependence of normalization on [ρε found >(Lpea,)therein is entirely contained in "," For purposes where $\slope$ is important, the quasar lifetimes fitted in \citet{H05e} should be slightly modified to be Schechter functions with faint-end slopes $\slope(\Lp)$ [the weak dependence of normalization on $\Lp$ found therein is entirely contained in $\slope(\Lp)$ ]." +"We have also provided simple analytical forms for the 2Lj4,)].quasar light curve. for use in semi-analytical models and other theoretical models of which require the time-dependent quasar light curve (not simply the statistical properties contained in the quasar lifetime fits we have previously calculated). and which cannot resolve the detailed time dependence of quasar activity in individual mergers and interactions."," We have also provided simple analytical forms for the quasar light curve, for use in semi-analytical models and other theoretical models of which require the time-dependent quasar light curve (not simply the statistical properties contained in the quasar lifetime fits we have previously calculated), and which cannot resolve the detailed time dependence of quasar activity in individual mergers and interactions." +" We have demonstrated that the observed evolution of 5 and corresponding ""Iuminosity-dependent density evolution"" of the quasar population are not just accounted for. but actually in our model of the QLF. às a consequence of quasar feedback being more violent in higher peak luminosity (larger BH mass) systems. and the fact that the observed faint-end QLF is dominated by sources with intrinsically brighter peak luminosity (Lp,~ L.C in dimmer stages of their evolution."," We have demonstrated that the observed evolution of $\slope$ and corresponding ``luminosity-dependent density evolution” of the quasar population are not just accounted for, but actually in our model of the QLF, as a consequence of quasar feedback being more violent in higher peak luminosity (larger BH mass) systems, and the fact that the observed faint-end QLF is dominated by sources with intrinsically brighter peak luminosity $\Lp\sim\lstar(z)$ ) in dimmer stages of their evolution." + While more accurate predictions require additional detailed modeling. the results presented here allow future observations of 5 to directly constrain the differential quasar lifetime. even at L« as our modeling shows that the faint-end QLF ρω.effectively traces the quasar of Loyc9Ls sources.nof the intrinsic source ppeak L or BH mass) distribution.," While more accurate predictions require additional detailed modeling, the results presented here allow future observations of $\slope$ to directly constrain the differential quasar lifetime, even at $L\ll\Lp$, as our modeling shows that the faint-end QLF effectively traces the quasar of $\Lp\sim\lstar$ sources, the intrinsic source peak $L$ or BH mass) distribution." + Such observations will. further limit models of the distribution of quasar masses and host properties [through Γρ]. and models of quasar fueling mechanisms and accretion (through the form of the lifetime/slope at low-L).," Such observations will further limit models of the distribution of quasar masses and host properties [through $\nLp$ ], and models of quasar fueling mechanisms and accretion (through the form of the lifetime/slope at $L$ )." + As is clear in Figure 3.. the QLF faint-end slope as a function of redshift is. still only poorly constrained by observations.," As is clear in Figure \ref{fig:slope.v.z}, , the QLF faint-end slope as a function of redshift is still only poorly constrained by observations." + Improved observational constraints. in. particular samples with a uniform. selection criteria Which can span the range of redshifts z=0—6. for which the selection criteria could be accurately modeled and compared in detail with observations. would provide very valuable constraints on theoretical models of quasar feedback. ddetermining the relative contributions to the faint-end QLF from quasars growing to larger luminosities or relaxing after their peak. and constraining the efficiency of coupling between accretion energy and the surrounding ISM.," Improved observational constraints, in particular samples with a uniform selection criteria which can span the range of redshifts $z=0-6$, for which the selection criteria could be accurately modeled and compared in detail with observations, would provide very valuable constraints on theoretical models of quasar feedback, determining the relative contributions to the faint-end QLF from quasars growing to larger luminosities or relaxing after their peak, and constraining the efficiency of coupling between accretion energy and the surrounding ISM." + Samples which cover the relevant redshift range in a uniform rest frame wavelength are also especially valuable. and measurements in different wavelengths can provide different constraints.," Samples which cover the relevant redshift range in a uniform rest frame wavelength are also especially valuable, and measurements in different wavelengths can provide different constraints." + For example. the faint-end hard X-ray QLF may be more robust against obscuration effects and so provide a better indicator of the bolometric luminosity function. tracing rrelatively low-luminosity stages hidden by cireumnuclear starbusts.," For example, the faint-end hard X-ray QLF may be more robust against obscuration effects and so provide a better indicator of the bolometric luminosity function, tracing relatively low-luminosity stages hidden by circumnuclear starbusts." + The optical QLF. on the other hand. is in our modeling more closely associated with the peak quasar luminosity and “blowout” phase. meaning that the faint-end optical QLF (measurement of which would require extending the completeness of current high-redshift optical surveys by several magnitudes) can provide an valuable constraint on the underlying peak luminosity distribution. a particularly valuable quantity in itself because it determines. in our modeling. the QLF in all other bands. and reflects (as well as constrains) much more directly the underlying cosmological context. such as merger rates as a funetion of host galaxy mass.," The optical QLF, on the other hand, is in our modeling more closely associated with the peak quasar luminosity and “blowout” phase, meaning that the faint-end optical QLF (measurement of which would require extending the completeness of current high-redshift optical surveys by several magnitudes) can provide an valuable constraint on the underlying peak luminosity distribution, a particularly valuable quantity in itself because it determines, in our modeling, the QLF in all other bands, and reflects (as well as constrains) much more directly the underlying cosmological context, such as merger rates as a function of host galaxy mass." +" The combination of the two. yielding a reliable bolometric faint-end luminosity function slope and underlying peak luminosity distribution. would allow measurements of 7(z) to be translated reliably into 2(L4,). and could be de-convolved to construct an entirely observational determination of the quasar lifetime as a function of luminosity."," The combination of the two, yielding a reliable bolometric faint-end luminosity function slope and underlying peak luminosity distribution, would allow measurements of $\gamma(z)$ to be translated reliably into $\gamma(\Lp)$, and could be de-convolved to construct an entirely observational determination of the quasar lifetime as a function of luminosity." +" These observations. though difficult at very high z. can probe redshifts at which direct observations of quasar hosts and masses are inaccessible. constraming theories of early quasar evolution,"," These observations, though difficult at very high $z$, can probe redshifts at which direct observations of quasar hosts and masses are inaccessible, constraining theories of early quasar evolution." + Combined with the modeling presented in Hopkins et ((2005a-f). this motivates a completely self-consistent picture of the quasar lifetime and luminosity function. derived from the input physics of our simulations and without arbitrary tunable parameters.," Combined with the modeling presented in Hopkins et (2005a-f), this motivates a completely self-consistent picture of the quasar lifetime and luminosity function, derived from the input physics of our simulations and without arbitrary tunable parameters." + With the eritical recognition that the quasar lifetime Is/uminosity-dependent. with quasars spending more time at low luminosities than their peak lummosities (as has now also been suggested by observations. AAdelberger SSteidel 2005). we have shown that a large range of observed properties of the quasar and spheroid population are predicted to high accuracy. over a wide range of observed redshifts.," With the critical recognition that the quasar lifetime is, with quasars spending more time at low luminosities than their peak luminosities (as has now also been suggested by observations, Adelberger Steidel 2005), we have shown that a large range of observed properties of the quasar and spheroid population are predicted to high accuracy, over a wide range of observed redshifts." + These works also provide several simple tests of our model of the quasar lifetime. and correspondingly the model of the faint-end slope presented here.," These works also provide several simple tests of our model of the quasar lifetime, and correspondingly the model of the faint-end slope presented here." + In Hopkins et ((2005a-e). we explicitly demonstrate that these predictions include. tthe QLF at frequencies from optical to hard X-ray and at many observed redshifts. the distribution of Eddington ratios as a function of luminosity and redshift. the column density distribution at various wavelengths. the fraction of broad-line quasars as a function of luminosity and redshift. the active BH mass function of both Type IL and Type II quasars. the relic BH mass function and total density. the cosmic X-ray background spectrum. the anti-hierarchical evolution of BH mass. the radio source population at high redshift. correlations between IR emission. star formation. and quasar obscuration. and the quasar lifetime as a function of luminosity and host galaxy properties.," In Hopkins et (2005a-e), we explicitly demonstrate that these predictions include, the QLF at frequencies from optical to hard X-ray and at many observed redshifts, the distribution of Eddington ratios as a function of luminosity and redshift, the column density distribution at various wavelengths, the fraction of broad-line quasars as a function of luminosity and redshift, the active BH mass function of both Type I and Type II quasars, the relic BH mass function and total density, the cosmic X-ray background spectrum, the anti-hierarchical evolution of BH mass, the radio source population at high redshift, correlations between IR emission, star formation, and quasar obscuration, and the quasar lifetime as a function of luminosity and host galaxy properties." + The distribution of Eddington ratios as a function of luminosity is adirect test of this model. and the degree to," The distribution of Eddington ratios as a function of luminosity is adirect test of this model, and the degree to" +the log N-log $ distribution.,the log $N$ -log $S$ distribution. + Clearly. to begin to uucderstaud and inodel the prompt energy release clistributiou. we need to determine GBRB energies in a common co-moving baudpass.," Clearly, to begin to understand and model the prompt energy release distribution, we need to determine GRB energies in a common co-moving bandpass." + In this paper. we find the &-corrected euergies of GRBs with kuown redshifts iu order to homogenize the set of GRB energies to a comunon co-moving bandpass.," In this paper, we find the $k$ -corrected energies of GRBs with known redshifts in order to homogenize the set of GRB energies to a common co-moving bandpass." + The correction methodology. described in 82.. is straightforward when information on the GRB spectrum is known.," The correction methodology, described in \ref{sec:method}, is straightforward when information on the GRB spectrum is known." + However. a number of GRBs have only a fluence aud a redshift published: to estimate the A-correction. then. we use au eusemble of template GRB spectra. expanding upon the earlier work of Bloometal.(1996).," However, a number of GRBs have only a fluence and a redshift published; to estimate the $k$ -correction, then, we use an ensemble of template GRB spectra, expanding upon the earlier work of \citet{bfi96}." +. lu δ we present the &-corrected euergies [or 17 cosinological GRBs (plus 6 additional well-studied GRBs with au assured redshift) in both a co-moving baudpass of 20-2000 keV and a bolometric bandpass., In \ref{sec:results} we present the $k$ -corrected energies for 17 cosmological GRBs (plus 6 additional well-studied GRBs with an assumed redshift) in both a co-moving bandpass of 20–2000 keV and a bolometric bandpass. + We employ a number of tests to show that A-correctious derived (rom the template spectra method are robust., We employ a number of tests to show that $k$ -corrections derived from the template spectra method are robust. +" Lastly. we poiut out that by assuming that the total prompt energy release is simply E=IxD?S,{1+2). where S44; is the quoted fluence in some detector bandpass. wacdercouuts the bolometric energy release by to6005c.. depending on the particular CRB."," Lastly, we point out that by assuming that the total prompt energy release is simply $E = 4 \pi D_l^2 S_{\rm obs}/(1+z)$, where $S_{\rm +obs}$ is the quoted fluence in some detector bandpass, undercounts the bolometric energy release by to, depending on the particular GRB." +" The relatiouship of the bolometric energy (Ενω) to the bolometric [Iuence(55,4) is where D, is the luminosity clistance to the source at redshift z.", The relationship of the bolometric energy $E_{\rm bol}$ ) to the bolometric fluence$S_{\rm bol}$ ) is where $D_l$ is the luminosity distance to the source at redshift $z$. + The bolometric fluence is difficult GE not impossible) to measure directly., The bolometric fluence is difficult (if not impossible) to measure directly. + Lustead fIuence (energy per unit area) is typically measurect iu some detector bandpass bracketed by the euergies. eq aud e».," Instead fluence (energy per unit area) is typically measured in some detector bandpass bracketed by the energies, $e_1$ and $e_2$." +" The Burst aud Trausieut Source Experiment (BATSE). for instance. was capable of measuring llueuce in the baudpass ey=20 keV to e»=2000 keV. We now define this baudpass f[lueuce. S,=5|eyes]: as where the (time-iutegrated) spectral shape of the GRB. oóCE). aud the normalization Sy(units olf photon per unit area per unit enerey) are fouud (rom measurements."," The Burst and Transient Source Experiment (BATSE), for instance, was capable of measuring fluence in the bandpass $e_1 = 20$ keV to $e_2 = +2000$ keV. We now define this bandpass fluence, $S_{\rm obs} \equiv +S_{[e_1,e_2]}$, as where the (time-integrated) spectral shape of the GRB, $\phi(E)$, and the normalization $S_0$(units of photon per unit area per unit energy) are found from measurements." + In. general. however. we wish to measure the energy. Eppjj. in some fixed co-moving bandpass. bracketed by two arbitrary euergies Ej aud E».," In general, however, we wish to measure the energy, $E_{[E_1, E_2]}$, in some fixed co-moving bandpass, bracketed by two arbitrary energies $E_1$ and $E_2$." + In this case. Note that by letting Ej—0 aud E»—x we recover the bolometric result in equation 1..," In this case, Note that by letting $E_1 \rightarrow 0$ and $E_2 \rightarrow \infty$ we recover the bolometric result in equation \ref{eq:edef}. ." + Iu reality. we can only measure. ΡΕ the prompt energy release per unit solid augle in," In reality, we can only measure, $d E_{[E_1, E_2]}/d \Omega$ , the prompt energy release per unit solid angle in" +of the population at ?45 mmin or a pile-up of systems around. £2?z45 mmin. depending on whether they become Lully detached.,"of the population at $P>45$ min or a pile-up of systems around $P\approx45$ min, depending on whether they become fully detached." + The current saniple of six. of which orbital periods have only been measured for four. at. present prevents us from drawing conclusions.," The current sample of six, of which orbital periods have only been measured for four, at present prevents us from drawing conclusions." + The fact that AAI CVns at orbital periods. well above 45 minutes have been observed. indicates that at least not all of them become detached indefinitely.," The fact that AM CVns at orbital periods well above 45 minutes have been observed, indicates that at least not all of them become detached indefinitely." + In addition. even if this were the case. it is clear [rom figure 2. that this could at most have caused a suppression of the population by a factor of 3. based on he fraction of observed. systems that is expected to be at orbital periods P45 mmin.," In addition, even if this were the case, it is clear from figure \ref{completeness_colours} that this could at most have caused a suppression of the population by a factor of 3, based on the fraction of observed systems that is expected to be at orbital periods $P>45$ min." + The LHle-star models take into account. optimistic and »essimistic estimates for the destruction of AM. CVn stars ov edge-Iit. detonations of the accreting CO white cwarl (Nelemansetal.2001)., The He-star models take into account optimistic and pessimistic estimates for the destruction of AM CVn stars by edge-lit detonations of the accreting CO white dwarf \citep{nelemans}. +. Although recent. studies question he existence of such IZLDs altogether citealtvoon)). their. possible non-existence is not very relevant for the AM CVn population since it is of relatively ittle influence on the number of XM CVn stars produced in the Lle-star channel (see table 1)).," Although recent studies question the existence of such ELDs altogether \\citealt{yoon}) ), their possible non-existence is not very relevant for the AM CVn population since it is of relatively little influence on the number of AM CVn stars produced in the He-star channel (see table \ref{densities}) )." + What could be of inlluence is the suggestion that the IIe-star. channel may iarcldly work at all clue to the poor ellicieney for ejecting the common envelope in such a configuration., What could be of influence is the suggestion that the He-star channel may hardly work at all due to the poor efficiency for ejecting the common envelope in such a configuration. + This is thought to »e due to the hvdrodynamies of the relatively weak density eracdient between the Le-burning core and its hydrogen mantle. which together form the Lle-star progenitor (see Sandeuistetal.(2000). for a studs of how this may prevent the formation of low-mass (κ 0.247.) lle WDs from a common envelope).," This is thought to be due to the hydrodynamics of the relatively weak density gradient between the He-burning core and its hydrogen mantle, which together form the He-star progenitor (see \citet{sandquist} for a study of how this may prevent the formation of low-mass $<0.2\,M_\odot$ ) He WDs from a common envelope)." + ln a variation on the ELL) theme. Bildstenetal.(2007) have recently shown that a substantial fraction of XM CVins. and. possibly all of them. could host a strong thermonuclear event due to the ignition of a sullicientlv. thick laver. of accreted helium. on the accretor's. CO. core.," In a variation on the ELD theme, \citet{.Ia} have recently shown that a substantial fraction of AM CVns, and possibly all of them, could host a strong thermonuclear event due to the ignition of a sufficiently thick layer of accreted helium on the accretor's CO core." + This could destrov the binary and thus remove AM. CVns [rom the population they have started their evolution towards longer orbital periods as stable mass-transferring binaries., This could destroy the binary and thus remove AM CVns from the population they have started their evolution towards longer orbital periods as stable mass-transferring binaries. + In the WD channel. the ellect of the unknown tidal coupling between. the aceretor and. the donor on. their survival as stable mass-transferring white dwarls (Nelomansetal.2001:Marsh.2004) jw been taken into account by modelling an optimistic (perfect coupling) and a pessimistic (no coupling) scenario.," In the WD channel, the effect of the unknown tidal coupling between the accretor and the donor on their survival as stable mass-transferring white dwarfs \citep{nelemans,masstransfer} has been taken into account by modelling an optimistic (perfect coupling) and a pessimistic (no coupling) scenario." + In the latter case. the WD channel is so much suppressed due to the mass transfer becoming unstable that the observed. space density is too high for this channel to be the only contributor.," In the latter case, the WD channel is so much suppressed due to the mass transfer becoming unstable that the observed space density is too high for this channel to be the only contributor." + An acieitional. relatively unstucied elect is the possible ignition of Le-core white dwarls upon accretion. of a substantial amount of helium from their helium-white-cdwarl donors. either through a series of inward-moving helium Lashes (Saio&Jeffery2000) or via an inward-moving burning [ront (Bildsten in preparation: private communication).," An additional, relatively unstudied effect is the possible ignition of He-core white dwarfs upon accretion of a substantial amount of helium from their helium-white-dwarf donors, either through a series of inward-moving helium flashes \citep{saio} or via an inward-moving burning front (Bildsten in preparation; private communication)." + Such Ile|Le WD binaries represent up to of the AM CVn gaar progenitors in the WD channel for the optimistic model (but note again the arguments by Sandquistctal.(2000) eainst the formation of low-mass Ho WDs in such binaries): the possible non-existence of AML CVans descending. [rom Le|He WD binaries should therefore be of limited influcnce., Such He+He WD binaries represent up to of the AM CVn star progenitors in the WD channel for the optimistic model (but note again the arguments by \citet{sandquist} against the formation of low-mass He WDs in such binaries); the possible non-existence of AM CVns descending from He+He WD binaries should therefore be of limited influence. + In the pessimistic model. only WD binaries of extreme mass ratio survive the initial mass transfer. leaving no XM CVn gazs from Ie|He white chwarl binarics anvwav.," In the pessimistic model, only WD binaries of extreme mass ratio survive the initial mass transfer, leaving no AM CVn stars from He+He white dwarf binaries anyway." + With the lower space densities reported in this paper. we note that the evolved-CV. channel for the formation of AAL CVn stars (Podsiadlowskietal.2003).. which was previously estimated to contribute at the. 30$ min could cause us to underestimate the short-period population." + Nevertheless it would. seem reasonable. based. on the results shown in table 1.. to lower the estimate of ~11.000 Galactic AM CVn stars that can be resolved with to about —1.000. for a mission cluration of one vear (Nelemansetal.2004).," Nevertheless it would seem reasonable, based on the results shown in table \ref{densities}, to lower the estimate of $\sim$$11,000$ Galactic AM CVn stars that can be resolved with to about $\sim$$1,000$, for a mission duration of one year \citep{nelemans2004}." +". We have investigated the population of helium-emission-line AAL CVn stars based on the sample of six. new systems from the Sloan Digital Sky Survey,", We have investigated the population of helium-emission-line AM CVn stars based on the sample of six new systems from the Sloan Digital Sky Survey. + We have compared the observed. sample to. predicted: samples as obtained from. population svathesis models., We have compared the observed sample to predicted samples as obtained from population synthesis models. +" For cdilferent model populations we have derived: local. space of densities1.3.10."" ppe7.", For different model populations we have derived local space densities of $1-3\times 10^{-6}$ $^{-3}$. + In addition to the variations in observed space density for the dillerent. models. we estimate uncertainties of a factor of 2 due to Poisson noise and (assumed) uncertainties in the colours anc absolute magnitudes of the emission-lino AAL CVn stars.," In addition to the variations in observed space density for the different models, we estimate uncertainties of a factor of 2 due to Poisson noise and (assumed) uncertainties in the colours and absolute magnitudes of the emission-line AM CVn stars." + In. the standard: evolutionary picture. where all AAL CVn stars evolve to become emission-line svstems at orbital periods above ~30 minutes. this corresponds to à space density of the entire population that is very nearly identical to this value (within 24)).," In the standard evolutionary picture, where all AM CVn stars evolve to become emission-line systems at orbital periods above $\sim$ 30 minutes, this corresponds to a space density of the entire population that is very nearly identical to this value (within )." + A further refinement of the space density would. require additional follow-up. spectroscopy of photometric candidates in the SDSS. to increase. the spectroscopic sample and bring clown the Poisson noise.," A further refinement of the space density would require additional follow-up spectroscopy of photometric candidates in the SDSS, to increase the spectroscopic sample and bring down the Poisson noise." + Since there are relatively few other types of objects, Since there are relatively few other types of objects +Evolution of single stars is now well modelled (seeforexample1995).,"Evolution of single stars is now well modelled \citep[see for + example][]{pols1995}." +". There remain concerns with mass loss, rotation and convection but appropriate and successful empirical treatments exist."," There remain concerns with mass loss, rotation and convection but appropriate and successful empirical treatments exist." + Evolution of a binary star has several additional complications associated with interaction between the components., Evolution of a binary star has several additional complications associated with interaction between the components. +" Since solving the mystery of Algol systems [Crawford][1955]... the prototype of semi-detached Algol-type binary stars with one evolved and one main-sequence component, we realize that there are some stages of evolution when interaction between the components is unavoidable."," Since solving the mystery of Algol systems \citep{hoyle1955,crawford1955}, the prototype of semi-detached Algol-type binary stars with one evolved and one main-sequence component, we realize that there are some stages of evolution when interaction between the components is unavoidable." +" We must therefore take into account, in our calculations, the mass transfer and mass loss together with any angular momentum and magnetic interaction between the components, at least in some critical phases, to fully understand evolution of a binary system."," We must therefore take into account, in our calculations, the mass transfer and mass loss together with any angular momentum and magnetic interaction between the components, at least in some critical phases, to fully understand evolution of a binary system." +" Over the last few decades, the evolution of Algols has been modelled with well defined approximations such as conservation of total mass and total orbital angular momentum."," Over the last few decades, the evolution of Algols has been modelled with well defined approximations such as conservation of total mass and total orbital angular momentum." + The effect of mass transfer on the structure of both stars can be modelled reasonably well., The effect of mass transfer on the structure of both stars can be modelled reasonably well. +" The angular momentum transfer during mass exchange, however, is not well understood."," The angular momentum transfer during mass exchange, however, is not well understood." + As we shall see in section [2.1] there are some episodes of mass transfer in Algols when accretion discs or disc-like structures form around the mass gainer., As we shall see in section \ref{accdiscs} there are some episodes of mass transfer in Algols when accretion discs or disc-like structures form around the mass gainer. + Current approximations of binary star evolution do not adequately explain the spin angular momentum of the mass-gaining components because the high specific angular momentum of the disc material should easily spin these stars up to their critical break-up rotational velocities in less than the time needed to reverse the mass ratio of system and enter the Algol phase., Current approximations of binary star evolution do not adequately explain the spin angular momentum of the mass-gaining components because the high specific angular momentum of the disc material should easily spin these stars up to their critical break-up rotational velocities in less than the time needed to reverse the mass ratio of system and enter the Algol phase. +" Here we discuss formation of discs in classical Algol systems and consider the spin angular momentum evolution of mass accreting components, taking into account discs, tides and magnetic stellar winds."," Here we discuss formation of discs in classical Algol systems and consider the spin angular momentum evolution of mass accreting components, taking into account discs, tides and magnetic stellar winds." + We demonstrate that tidal effects play a minor role in the, We demonstrate that tidal effects play a minor role in the +We now describe how (he marked point bootstrap can be used with estimators of the two-point correlation fanction.,We now describe how the marked point bootstrap can be used with estimators of the two-point correlation function. + The common estimators of (he two-point correlation function &(r) are which are. respectively. (he natural estimator (Ixerscheretal.2000).. and estimators due to Davis&Peebles(1983):Hamilton(1993):LandySzalavILewett(1952).. where ris some distance of oe," The common estimators of the two-point correlation function $\xi(r)$ are which are, respectively, the natural estimator \citep{kerscher2000}, and estimators due to \citet{davis83, hamilton93, landy93, hewett82}, where $r$ is some distance of interest." +" In these RN ddr)=DD(ry/N?.dr(r)DRG/NNg and rr(r)=RBE(r)/Ns. where ""ΣΣ”(f—dr.r4dr)""me DROP)ΣΣ""rdi)NNg and RRO)'=$5,venusy|€(r—dr.r+dr) NP. Ris a set of randomly. generated vials PPoisson) in the observation region “1. and IN and Ny are respectively the number of soils in the real and random data sets."," In these expressions, $dd(r) = DD(r)/N^2, dr(r) = +DR(r)/NN_R$ and $rr(r)=RR(r)/N_R^2$, where $DD(r)=\sum_{x\in D} \sum_{y\in D: y\ne + x} 1\{ |x-y| \in (r-dr, r+dr)\}/N^2$, $DR(r)=\sum_{x\in D} \sum_{y\in R} 1\{ |x-y| \in (r-dr, r+dr)\}/NN_R$ and $RR(r)=\sum_{x\in R} \sum_{y\in R: y\ne x} 1\{ |x-y| \in (r-dr, r+dr)\}/N_R^2$ , $R$ is a set of randomly generated points Poisson) in the observation region $A$, and $N$ and $N_R$ are respectively the number of points in the real and random data sets." + To apply the marked poit bootstrap. assign to each point .r of the dataset marks υπla=PyepyesHiecyl€(edie υπ”," To apply the marked point bootstrap, assign to each point $x$ of the dataset marks $m_{x,1}=\sum_{y\in D: y\ne + x} 1\{ |x-y| \in (r-dr, r+dr)\}$ and $m_{x,2}=\sum_{y\in R} 1\{ +|x-y| \in (r-dr, r+dr)\}$." + proceeds by resampling blocks of points and recording the marks associated with them., Bootstrap proceeds by resampling blocks of points and recording the marks associated with them. +" For a bootstrap sample.27.—L....:V"" owe then have and bootstrap estimates of the two-point correlation functions are (hen obtainedby subsütuting the above into (3))-(7))."," For a bootstrap sample, $x^*_j, j=1, \ldots N^*$, we then have and bootstrap estimates of the two-point correlation functions are then obtainedby substituting the above into \ref{eqn:nat}) \ref{eqn:hewett}) )." + If each point cc; of the actual data is resampled η*i (imes. so that A*=»ni. DD'(r) and DR(r) can also be written as," If each point $x_i$ of the actual data is resampled $n_i^*$ times, so that $N^* = \sum_i n_i^*$ , $DD^*(r)$ and $DR^*(r)$ can also be written as" +to observe at low[Fe/I]].. this problem could be solved by measuring individual element abundances rather than molecular bandstrengtlis.,"to observe at low, this problem could be solved by measuring individual element abundances rather than molecular bandstrengths." + Perhaps the most intriguing observations of the CN bimodality phenomenon are to be found among stars in the relatively unevolvecl regions of cluster CMDs., Perhaps the most intriguing observations of the CN bimodality phenomenon are to be found among stars in the relatively unevolved regions of cluster CMDs. + Contrary to predictions of standard stellar evolutionary models. significant. variations in CN bandstrengths have been reported lor stars prior to their undergoimeg first dredge-up 2002).. even down to the main sequence in 47 Tuc 2003a).," Contrary to predictions of standard stellar evolutionary models, significant variations in CN bandstrengths have been reported for stars prior to their undergoing first dredge-up , even down to the main sequence in 47 Tuc ." +. ILowever. searches within other cluster MS stars have produced mixed results.," However, searches within other cluster MS stars have produced mixed results." + reported no significant CN variation for MS5/MSTO stars belonging to M12. although (the CN features in their spectra were shown to be too weak [or reliable measurement 2001).," reported no significant CN variation for MS/MSTO stars belonging to M13, although the CN features in their spectra were shown to be too weak for reliable measurement ." +. Carbon and nitrogen abundance analvses of these stars by showed that this was likely due to the fact Chat there is very little change in bandstrength [or a given change in abundance at luminosities near the turnoff. where effective temperatures are relatively high compared to MS and giant stars (see their Figure 2).," Carbon and nitrogen abundance analyses of these stars by showed that this was likely due to the fact that there is very little change in bandstrength for a given change in abundance at luminosities near the turnoff, where effective temperatures are relatively high compared to MS and giant stars (see their Figure 2)." + Main sequence stars in M71 have been claimed to exhibit CN bimodality at a level larger than the measurement uncertainty. as well as an anticorrelation between CN aud CII 1999b).," Main sequence stars in M71 have been claimed to exhibit CN bimodality at a level larger than the measurement uncertainty, as well as an anticorrelation between CN and CH ." +. Follow-up analysis of Chis data further showed that the variation is al the same level as that observed for RGB stars in that cluster. leading the authors to elaàm that no significant mixing is occurring on the RGB (although this could also simply mean that first dredge-up did not significantly affect the surface carbon and nitrogen abundances). and that the abundance variations were in place at (he lime the stars formed 2001).," Follow-up analysis of this data further showed that the variation is at the same level as that observed for RGB stars in that cluster, leading the authors to claim that no significant mixing is occurring on the RGB (although this could also simply mean that first dredge-up did not significantly affect the surface carbon and nitrogen abundances), and that the abundance variations were in place at the time the stars formed ." +. In their sample of eight GC's.," In their sample of eight GCs," +The two leading candidate mechanisms to explain the alignment of the BCC with their parent cluster are tha roth are formed. from infall along preferred. directions in ilaments (e.g.?).. and that DCCGs are aligned by tida interactions (e.g.?7).,"The two leading candidate mechanisms to explain the alignment of the BCG with their parent cluster are that both are formed from infall along preferred directions in filaments \citep[e.g.][]{Dubinski:1998p366}, and that BCGs are aligned by tidal interactions \citep[e.g.][]{Faltenbacher:2008p67}." +. The points in cosmic history a which these mechanisms act are very clillerent: whereas ilamentary infall is likely to allect alignments curing anc immecdiatelv after cluster virialization tidal allects can ac during the cluster's entire lifetime., The points in cosmic history at which these mechanisms act are very different: whereas filamentary infall is likely to affect alignments during and immediately after cluster virialization tidal affects can act during the cluster's entire lifetime. + ? have shown tha he time scale on which a prolate galaxw's orientation is allected by a clusters tidal field. is much shorter than a Llubble time., \citet{Ciotti:1994p478} have shown that the time scale on which a prolate galaxy's orientation is affected by a cluster's tidal field is much shorter than a Hubble time. + Present-day. alignments may therefore either »e the result of. primordial alignments stemming from the veriod of cluster formation or can have grown during the cluster's lifetime., Present-day alignments may therefore either be the result of primordial alignments stemming from the period of cluster formation or can have grown during the cluster's lifetime. + By studying the redshift evolution of the alignment effect we can hope to distinguish these two cases., By studying the redshift evolution of the alignment effect we can hope to distinguish these two cases. + In this paper we use Sloan Digital Sky Survey Data Release 6 data (22) to study the alignment elfect in 12.755 clusters extending out to 2=0.44.," In this paper we use Sloan Digital Sky Survey Data Release 6 data \citep{York:2000p367,AdelmanMcCarthy:2008p362} to study the alignment effect in $12,755$ clusters extending out to $z=0.44$." + In €2 we describe our cluster selection and in €3 we analyse the dependence of alignment on BCC dominance. cluster richness. and redshift.," In 2 we describe our cluster selection and in 3 we analyse the dependence of alignment on BCG dominance, cluster richness, and redshift." + We discuss the implications of our findings in ΚΕ and summarise in £5., We discuss the implications of our findings in 4 and summarise in 5. + Throughout this paper we assume an Ον20.3. Q420.T. and dy—τὸ kms + * cosmology.," Throughout this paper we assume an $\Omega_m=0.3$, $\Omega_{\Lambda}=0.7$, and $H_0 = 70$ km $^{-1}$ $^{-1}$ cosmology." + The Sloan Digital Sky Survey (SDSS:7) is an imagine ancl spectroscopic survey that has covered: one-quarter of the celestial sphere., The Sloan Digital Sky Survey \citep[SDSS;][]{York:2000p367} is an imaging and spectroscopic survey that has covered one-quarter of the celestial sphere. + Lt is carricd out with a dedicated 2.5m telescope (7) using a large format CCD camera (?).., It is carried out with a dedicated 2.5m telescope \citep{2006AJ....131.2332G} using a large format CCD camera \citep{Gunn:1998p1435}. + The imaging data are collected in clrift-sean mode in five band. passes (u.g.r.£.2) with ellective wavelengths of 3551.4686.6165.7481. and 8931Α.," The imaging data are collected in drift-scan mode in five band passes $u$ $g$ $r$ $i$ $z$ ) with effective wavelengths of $3551,\;4686,\;6165,\;7481$, and $8931$." +. Phe imagine data are automatically reduced through a series of software pipelines which find. and. measure objects and. provide photometric and astrometric calibrations (τηλ. ," The imaging data are automatically reduced through a series of software pipelines which find and measure objects and provide photometric and astrometric calibrations \citep{Lupton:2001p1436,Lupton:2002SPIE.4836..350L,Pier:2003p1437,Tucker:2006p1438}. ." +Phe photometric calibrations are accurate to about 1% rms in g. r. ancl /. 3% in s and δα in z for bright (<20 mag) point sources (?2)..," The photometric calibrations are accurate to about $1\%$ rms in $g$, $r$, and $i$, $3\%$ in $u$ and $2\%$ in $z$ for bright $< 20$ mag) point sources \citep{Ivezic:2004p1443}." + We restrict ourselves to the objects that have reliable photometric cata by using the SDSS clean. photometry Ilags., We restrict ourselves to the objects that have reliable photometric data by using the SDSS clean photometry flags. + Targets for spectroscopy are selected from the imaging data on the basis of their photometric properties., Targets for spectroscopy are selected from the imaging data on the basis of their photometric properties. + A pair of dual fibre-fed spectrographs (7). can observe 640 spectra at a time with a wavelength coverage of 3800 /09200.1 and a resolution of 1800 /02100.4., A pair of dual fibre-fed spectrographs \citep{Uomoto1999} can observe 640 spectra at a time with a wavelength coverage of $3800$ $\;$ to $9200$ $\;$ and a resolution of $1800$ $\;$ to $2100$. +. The SDSS data are described in the data release papers (?.fortheSixthDataReleasewhichweuse) and are documented at//www., The SDSS data are described in the data release papers \citep[][for the Sixth Data Release which we use]{AdelmanMcCarthy:2008p362} and are documented at. +sdss.org.. In this paper we use two catalogues of clusters of galaxies., In this paper we use two catalogues of clusters of galaxies. +" One by ??) takes advantage of the concentration of cluster galaxies in colour-magnitude space on the red. sequence. and the other. by ? identifies clusters by matching galaxy distributions in position-magnitude space to an a priori filter,"," One by \citet{Koester:2007p484,Koester:2007p485} takes advantage of the concentration of cluster galaxies in colour-magnitude space on the red sequence, and the other, by \citet{Dong:2008p220} identifies clusters by matching galaxy distributions in position-magnitude space to an a priori filter." + The two catalogues are likely to have cülferent systematic errors such as miscentering ancl problems caused by cluster overlap. so computing results from the two allows us to reduce the severity such problems are.," The two catalogues are likely to have different systematic errors such as miscentering and problems caused by cluster overlap, so computing results from the two allows us to reduce the severity such problems are." + There is à well known bimodality of galaxies in colour-colour space (e.g.22???) with red quiescent) spheroidal galaxies occupying what is known as the red sequence. and blue actively star-forming galaxies concentrated. in the blue cloud.," There is a well known bimodality of galaxies in colour-colour space \citep[e.g.][]{Strateva:2001p504,Baldry:2004p481,Bell:2004p497,Cassata:2008p507} with red quiescent spheroidal galaxies occupying what is known as the red sequence, and blue actively star-forming galaxies concentrated in the blue cloud." + As first noted by 2. red sequence galaxies are. predominantly found. in. clusters of galaxies.," As first noted by \citet{Baum:1959PASP...71..106B}, red sequence galaxies are predominantly found in clusters of galaxies." + Since the location of the red. sequence in. colour-colour space is dependent on redshift via the W-eorrection it is a viable photometric redshift’ indicator for galaxy clusters and field ealaxies (οσο...?2?7?77.andreferencestherein).," Since the location of the red sequence in colour-colour space is dependent on redshift via the K-correction it is a viable photometric redshift indicator for galaxy clusters and field galaxies \citep[e.g..][and references therein]{Annis:1999AAS...195.1202A,Gladders:2000p360,Koester:2007p484,Koester:2007p485,Eisenhardt:2008p1444}." + These properties make the red sequence an ideal tool for identifving galaxy clusters in surveys (e.g.272?7)..," These properties make the red sequence an ideal tool for identifying galaxy clusters in surveys \citep[e.g..][]{Yee:1999ASPC..191..166Y,Gladders:2000p360,Lubin:2000ApJ...531L...5L,Gladders:2005ApJS..157....1G,Koester:2007p484}." + The red sequence allows one to isolate galaxies at a given redshift and thus remove contamination by projected foreground and background galaxies., The red sequence allows one to isolate galaxies at a given redshift and thus remove contamination by projected foreground and background galaxies. + 7T? follow ? and 7? using a technique known as maxBCG to search directly for over-clensitics of red sequence galaxies.," \citet{Koester:2007p484,Koester:2007p485} follow \citet{Gladders:2000p360} and \citet{Annis:1999AAS...195.1202A} using a technique known as maxBCG to search directly for over-densities of red sequence galaxies." + They take advantage of the uniform colours and luminosities of BCGs in the selection procedure., They take advantage of the uniform colours and luminosities of BCGs in the selection procedure. + The likelihood that cach galaxy in a photometric sample ws the photometric properties of a BCC ancl resides in an over-cdensity of red. sequence galaxies is evaluated at a evicl of assumed. redshifts., The likelihood that each galaxy in a photometric sample has the photometric properties of a BCG and resides in an over-density of red sequence galaxies is evaluated at a grid of assumed redshifts. + Phe redshift which maximises he likelihood (thence the name maxBCC) is used as a first estimate of the cluster redshift., The redshift which maximises the likelihood (hence the name maxBCG) is used as a first estimate of the cluster redshift. + Using this centre. all red sequence galaxies within 1 h Alpe projected radius are »otential cluster members.," Using this centre, all red sequence galaxies within $1$ $^{-1}$ Mpc projected radius are potential cluster members." + A percolation technique is then used. in order to determine if the galaxy in question is in act the cluster centre., A percolation technique is then used in order to determine if the galaxy in question is in fact the cluster centre. + The catalogue sample we employed contains 12.τοῦ clusters with photometric redshifts between V1 and 0.3 and is approximately volume limited.," The catalogue sample we employed contains $12,766$ clusters with photometric redshifts between $0.1$ and $0.3$ and is approximately volume limited." + Ixoester at al., Koester at al. + use the maxBCG algorithm on realistic mock catalogues and find that the sample is more than 90% pure and more han S54 complete for clusters with masses =110AL., use the maxBCG algorithm on realistic mock catalogues and find that the sample is more than $90\%$ pure and more than $85\%$ complete for clusters with masses $\geq 1\times10^{14}\;M_{\odot}$. + We extract BCC positions (which are defined to be at the cluster centres in this catalogue) and redshifts in order to select. red. sequence galaxies from the SDSS., We extract BCG positions (which are defined to be at the cluster centres in this catalogue) and redshifts in order to select red sequence galaxies from the SDSS. + Koester ct al., Koester et al. + [lind an rms scatter of only o=0.015 between the clusters? photometric redshift estimates ancl spectroscopic redshifts of the BCC for the 7813 clusters in their catalogue with spectroscopy in the SDSS., find an rms scatter of only $\sigma = 0.015$ between the clusters' photometric redshift estimates and spectroscopic redshifts of the BCG for the 7813 clusters in their catalogue with spectroscopy in the SDSS. + 2 use à variant of the matched. filter. technique weviously used by 227777... among others. which fits the distribution of galaxies in. magnitude and. position. space o a standard spatial profile (suchasthat.predicted:by 7).. using prior knowledge of spectroscopic or photometric ealaxy redshifts and the galaxy luminosity function.," \citet{Dong:2008p220} use a variant of the matched filter technique previously used by \citet{Postman:1996AJ....111..615P,Kawasaki:1998A&AS..130..567K,Schuecker:1998p521,Kepner:1999ApJ...517...78K,Bramel:2000p520,Kim:2002p370}, among others, which fits the distribution of galaxies in magnitude and position space to a standard spatial profile \citep[such as that predicted by][]{Navarro:1996p399}, using prior knowledge of spectroscopic or photometric galaxy redshifts and the galaxy luminosity function." + The echnique does not explicitly fit for the red sequence to select ealaxies and hence can identify clusters of blue galaxies. (f hey exist)., The technique does not explicitly fit for the red sequence to select galaxies and hence can identify clusters of blue galaxies (if they exist). + Phe algorithm: generates a cluster. likelihood map in position-redshift space whose peaks correspond. to »oxitions where the matches between the survey data and he cluster. filter are optimised., The algorithm generates a cluster likelihood map in position-redshift space whose peaks correspond to positions where the matches between the survey data and the cluster filter are optimised. + Using a realistic mock SDSS catalogue Dongct al., Using a realistic mock SDSS catalogue Donget al. + show that the catalogue is zzS5S% complete and over 90% pure for clusters with masses, show that the catalogue is $\approx 85\%$ complete and over $90\%$ pure for clusters with masses +The low-energy electron spectrum resulting from this analysis is shown in Fig.,The low-energy electron spectrum resulting from this analysis is shown in Fig. + 2 together with previous data of H.E.S.S. and direct measurements.," \ref{fig2} + together with previous data of H.E.S.S. and direct measurements." +" The spectrum is well described by a broken power law dN/dE=k-(E/E,)™'-(1+(E/Ey)!/2)-T?1% (42/d.o.f.=5.6/4, p= 0.23) with a normalization k=(1.5-:0.1)x107 TeV-! mm ssr! ss?!, and a break energy Ey=0.90.1 TeV, where the transition between the two spectral indices Γι=3.0€0.1 and I?=4.1€0.3 occurs."," The spectrum is well described by a broken power law $dN/dE = k \cdot (E/E_{\mathrm{b}})^{-\Gamma_1}\cdot(1+(E/E_{\mathrm{b}})^{1/\alpha})^{-(\Gamma_2-\Gamma_1) \alpha}$ $\chi^2/\mathrm{d.o.f.} = 5.6/4$, $p=0.23$ ) with a normalization $k=(1.5 \pm 0.1) \times 10^{-4}$ $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$, and a break energy $E_{\mathrm{b}} = 0.9 \pm 0.1$ TeV, where the transition between the two spectral indices $\Gamma_1 = 3.0\pm0.1$ and $\Gamma_2 = 4.1\pm0.3$ occurs." +" The parameter o denotes the sharpness of the transition, the fit prefers a sharp transition, α<0.3."," The parameter $\alpha$ denotes the sharpness of the transition, the fit prefers a sharp transition, $\alpha<0.3$." + The shaded band indicates the uncertainties in the flux normalization that arise from uncertainties in the modeling of hadronic interactions and in the atmospheric model., The shaded band indicates the uncertainties in the flux normalization that arise from uncertainties in the modeling of hadronic interactions and in the atmospheric model. +" The uncertainties amount to about and are derived in the same fashion as in the initial paper (Aharonianetal. 2008)), i.e. by comparison of the spectra derived from two independent data sets taken in summer and autumn 2004 for the effect of atmospheric variations and by comparison of the spectra derived using the SIBYLL and QGSJET-II hadronic interaction model for the effect of the uncertainties in the proton simulations."," The uncertainties amount to about and are derived in the same fashion as in the initial paper \cite{paper1}) ), i.e. by comparison of the spectra derived from two independent data sets taken in summer and autumn 2004 for the effect of atmospheric variations and by comparison of the spectra derived using the SIBYLL and QGSJET-II hadronic interaction model for the effect of the uncertainties in the proton simulations." + The band is centered around the broken power law fit., The band is centered around the broken power law fit. + The systematic error on the spectral indices ΓΙ. Γ2 is Al'(syst.)<0.3.," The systematic error on the spectral indices $\Gamma_1$, $\Gamma_2$ is $\Delta \Gamma (\mathrm{syst.})\lesssim 0.3$." + The H.E.S.S. energy scale uncertainty of 1596 is visualized by the double arrow., The H.E.S.S. energy scale uncertainty of $15\%$ is visualized by the double arrow. +" The H.E.S.S. measurement yields a smooth spectrum with a steepening towards higher energies, confirming the earlier findings above 600 GeV (Aharonianetal.2008)). When compared to ATIC, the H.E.S.S. data show no indication of an excess and sharp cutoff in the electron spectrum as reported by the ATIC collaboration."," The H.E.S.S. measurement yields a smooth spectrum with a steepening towards higher energies, confirming the earlier findings above 600 GeV \cite{paper1}) When compared to ATIC, the H.E.S.S. data show no indication of an excess and sharp cutoff in the electron spectrum as reported by the ATIC collaboration." +" Since H.E.S.S. measures the electron spectrum only above 340 GeV, one cannot test the rising section of the ATIC-reported excess."," Since H.E.S.S. measures the electron spectrum only above 340 GeV, one cannot test the rising section of the ATIC-reported excess." +" Although different in shape, an overall consistency of the ATIC spectrum with the H.E.S.S. result can be obtained within the uncertainty of the H.E.S.S. energy scale of about 1520."," Although different in shape, an overall consistency of the ATIC spectrum with the H.E.S.S. result can be obtained within the uncertainty of the H.E.S.S. energy scale of about $15\,\%$." + The deviation between the ATIC and the H.E.S.S. data is minimal at the 20% confidence level (assuming Gaussian errors for the systematic uncertainty dominating the H.E.S.S. measurement) when applying an upward shift of 10% in energy to the H.E.S.S. data.," The deviation between the ATIC and the H.E.S.S. data is minimal at the $20\,\%$ confidence level (assuming Gaussian errors for the systematic uncertainty dominating the H.E.S.S. measurement) when applying an upward shift of $10\,\%$ in energy to the H.E.S.S. data." + The shift is well within the uncertainty of the H.E.S.S. energy scale., The shift is well within the uncertainty of the H.E.S.S. energy scale. +" In this case the H.E.S.S. data overshoot the measurement of balloon experiments above 800 GeV, but are consistent given the large statistical errors from balloon experiments at these energies."," In this case the H.E.S.S. data overshoot the measurement of balloon experiments above 800 GeV, but are consistent given the large statistical errors from balloon experiments at these energies." +" However, the nominal H.E.S.S. data are in very good agreement with the high precision"," However, the nominal H.E.S.S. data are in very good agreement with the high precision" +and underestimated in wide ones.,and underestimated in wide ones. + One explanation is that the jet break time is uot necessarily within the limited time range used in the fits. but it could also be due torj crossing the observing frequency. especially in narrow jets.," One explanation is that the jet break time is not necessarily within the limited time range used in the fits, but it could also be due to$\nu_m$ crossing the observing frequency, especially in narrow jets." +" In the latter case. those eveuts cau be identified from) a πα value of the smoothucss factor. nv. because the break around 7, Is much smoother than the jet break."," In the latter case, those events can be identified from a small value of the smoothness factor, $n$, because the break around $\nu_m$ is much smoother than the jet break." +" This crossing of v,,, through the observing frequency is also the cause of the small wines iu the distribution of Apy/p aud Apo/p seeu around the value -0.1 in figure 2..", This crossing of $\nu_m$ through the observing frequency is also the cause of the small wings in the distribution of $\Delta p_1/p$ and $\Delta p_2/p$ seen around the value -0.1 in figure \ref{fig:differences}. +" By looking at the individual spectra. we can ideutify those events where v,, or rm. cross the observing frequency."," By looking at the individual spectra, we can identify those events where $\nu_m$ or $\nu_c$ cross the observing frequency." + We find that the latter case does uot have a significant effect on our results., We find that the latter case does not have a significant effect on our results. + We have shown that results from the standaxd procedure of fitting afterglow light curves with| a broken power lav inust be interpreted with caution., We have shown that results from the standard procedure of fitting afterglow light curves with a broken power law must be interpreted with caution. + There can be systematic cifferences in the evaluation of the clectron energy distribution iudex from the slope of the fitted curves and a strong correlation between the relative difference in the opemime augle estimated from the liebt curve break time and the initial openius augle of the jet., There can be systematic differences in the evaluation of the electron energy distribution index from the slope of the fitted curves and a strong correlation between the relative difference in the opening angle estimated from the light curve break time and the initial opening angle of the jet. + These fiudiugs are partly due to the approximations used in deriving equations (1)-CL) being used out of their validity lamits., These findings are partly due to the approximations used in deriving equations (1)-(4) being used out of their validity limits. + This applies to approxiuatious in both he dyvauauical (Bianco&Ruffui2005) aud the radiation xoperties of the expanding shell., This applies to approximations in both the dynamical \citep{Bianco2005} and the radiation properties of the expanding shell. + These differences aud owtieululv the correlation is also a consequence of difficultics iu accurately deteriuiuiug the jet break time roni the afterglow light curves., These differences and particularly the correlation is also a consequence of difficulties in accurately determining the jet break time from the afterglow light curves. + The fitting procedure we used was completely automatic and often did not converge., The fitting procedure we used was completely automatic and often did not converge. + Tn some cases it resulted iu erroneous xuineter values iud we therefore adopted a threshold o1 the reduced 47P to eliminate.+ those bad fits., In some cases it resulted in erroneous parameter values and we therefore adopted a threshold on the reduced $\chi^2$ to eliminate those bad fits. + To test the effect of this threshold. we removed it from the selection cyiteria and re-examined the data. still considering only hose eveuts where the lieht curve break time was within the time rauge of our data.," To test the effect of this threshold, we removed it from the selection criteria and re-examined the data, still considering only those events where the light curve break time was within the time range of our data." + This left us with over of the original population., This left us with over of the original population. + The most significant changes we fud iu the results. were slightly laregcr standard deviations in the relative difference distributions aud more spread in the Ad;/0y - (y correlation thereby weakening it.," The most significant changes we find in the results, were slightly larger standard deviations in the relative difference distributions and more spread in the $\Delta \theta_j/\theta_0$ - $\theta_0$ correlation thereby weakening it." + The spike around | seen in the Αθ0 distribution for the sharp fits in fieure 2 (diamonds) also becomes a dominating feature., The spike around 0 seen in the $\Delta \theta_j/\theta_0$ distribution for the sharp fits in figure \ref{fig:differences} (diamonds) also becomes a dominating feature. + This indicates that by using the 4? as the strougest filter. we remove the bad fits from the ensemble but may also ose sole useful fits.," This indicates that by using the $\chi^2$ as the strongest filter, we remove the bad fits from the ensemble but may also lose some useful fits." + It is known theoretically that the magnitude of the jet break. Aaἂνay. can be used to differentiate vefween a wind like or a constant density euvirouimenut (e.g.Panaitescuetal.1998).," It is known theoretically that the magnitude of the jet break, $\Delta +\alpha = \alpha_2 - \alpha_1$, can be used to differentiate between a wind like or a constant density environment \citep[e.g.][]{Panaitescu1998}." +".. The svsteimatic differences we find in the evaluation of p indicate that Aa is nuderestimated m most of our events,", The systematic differences we find in the evaluation of $p$ indicate that $\Delta \alpha$ is underestimated in most of our events. +" Similar conclusion is obtained for a population of afterglow light curves iu a wind πουπια, the main difference beige that pj did not show a systematic deviation iu that case."," Similar conclusion is obtained for a population of afterglow light curves in a wind medium, the main difference being that $p_1$ did not show a systematic deviation in that case." + This renders he method of using Aa to distinguish between density xofiles inpractical., This renders the method of using $\Delta \alpha$ to distinguish between density profiles impractical. + The correlation between the opening augle estimate and the known opemme augle puts a strong lint on interpretations of the beaming corrected enerev of the must (ce.Frailctal.2001:ChirlaudaetFricdinan&Bloom2005).," The correlation between the opening angle estimate and the known opening angle puts a strong limit on interpretations of the beaming corrected energy of the burst \citep[e.g.][]{Frail2001, Ghirlanda2004, +Friedman2005}." +. The clustering of the jet weak time due to limited time span of the data ogether with a generous use of the approximations used 3n deteriuimime ϐ vesults du a bias towards noderate opening angles. approximately between 2°-107.," The clustering of the jet break time due to limited time span of the data together with a generous use of the approximations used in determining $\theta_j$ results in a bias towards moderate opening angles, approximately between -." +. The rather large standard deviation iu the A0;0) distribution also makes the results unreliable., The rather large standard deviation in the $\Delta \theta_j/\theta_0$ distribution also makes the results unreliable. + Using the ροής corrected energv as a basis for cosmological studies therefore calls for a very careful determination of f; aud 6j., Using the beaming corrected energy as a basis for cosmological studies therefore calls for a very careful determination of $t_j$ and $\theta_j$. + The svuthetic burst population studied iu this paper Is coniputer eenerated aud the power law fit should iu heory be perfect., The synthetic burst population studied in this paper is computer generated and the power law fit should in theory be perfect. + The fact that the differences between he parameters derived from the fits aud the known nodel parameters are so significant. males the accuracy of power law fits to real iieasurenmieuts of afterglow lieht curves a concern.," The fact that the differences between the parameters derived from the fits and the known model parameters are so significant, makes the accuracy of power law fits to real measurements of afterglow light curves a concern." + In real bursts. effects such as density Huctuations aud energv injection. can change the shape of afterglow light curves as may for example be the case or GRD 021001 (ee.Lazzatietal.2002) and CRB 30329 (e.g.Shethetal.2003).," In real bursts, effects such as density fluctuations and energy injection, can change the shape of afterglow light curves as may for example be the case for GRB 021004 \citep[e.g.][]{Lazzati2002} and GRB 030329 \citep[e.g.][]{Sheth2003}." + These were deuselv sampled aud were uot well fitted with a broken power aw due to bumps in the Πο curves., These were densely sampled and were not well fitted with a broken power law due to bumps in the light curves. + It is uot hard ο see that grainicr measurements of the same eveuts could have been fitted with a broken power law. leading o even larecr uncertaiutics iu the paramcter estimates han discussed here.," It is not hard to see that grainier measurements of the same events could have been fitted with a broken power law, leading to even larger uncertainties in the parameter estimates than discussed here." + It should also be noted that other uodels are capable of explüniug light curve breaks he most popular απο the structured jet model (Bossietal. 2002)..," It should also be noted that other models are capable of explaining light curve breaks, the most popular being the structured jet model \citep{Rossi2002}. ." + There the lght curve break depends ou he observers viewiug angle rather than the jet opening auele., There the light curve break depends on the observer's viewing angle rather than the jet opening angle. + Hence the methodology adopted in this letter is rot directly applicable to that model., Hence the methodology adopted in this letter is not directly applicable to that model. +as redshift increases.,as redshift increases. + Scenarios favouring low metallicity progenitors tend to produce LGRBs further out from the central regions than those allowing high metallicity progenitors., Scenarios favouring low metallicity progenitors tend to produce LGRBs further out from the central regions than those allowing high metallicity progenitors. +" The confrontation of our models with available observations supports scenarios with low metallicity cut-offs, in agreement with previous results (Nuzaetal.2007;Camp-isietal.2009;Chisari 2010)."," The confrontation of our models with available observations supports scenarios with low metallicity cut-offs, in agreement with previous results \citep{Nuz07,Cam09,Chisari2010}." +. Particulary we best reproduce current available observations for a model where LGRB progenitors are massive stars with Z<0.3., Particulary we best reproduce current available observations for a model where LGRB progenitors are massive stars with $Z<0.3$. + Further precise LGRB position measurements would help to confirm these trends., Further precise LGRB position measurements would help to confirm these trends. +" Regarding [Fe/H] abundances of the stellar populations producing LGRBs, we found that in all our scenarios [Fe/H] increases as redshift decreases."," Regarding [Fe/H] abundances of the stellar populations producing LGRBs, we found that in all our scenarios [Fe/H] increases as redshift decreases." +" This effect is less conspicuous in the scenarios with low metallicity progenitors, as in these cases the metallicity cut-off restricts the chemical abundances of the stellar populations producing LGRBs."," This effect is less conspicuous in the scenarios with low metallicity progenitors, as in these cases the metallicity cut-off restricts the chemical abundances of the stellar populations producing LGRBs." +" The o-enhancement decreases with redshift in all our scenarios, as a result of the different contributions of SNIT and SNIa."," The $\alpha$ -enhancement decreases with redshift in all our scenarios, as a result of the different contributions of SNII and SNIa." +" Contrary to the detected trend in [Fe/H], the a-enhancement shows a stronger evolution with redshift as Ζο decreases."," Contrary to the detected trend in [Fe/H], the $\alpha$ -enhancement shows a stronger evolution with redshift as $Z_{\rm c}$ decreases." +" As previously discussed, these chemical trends can be understood within the context of chemical evolution in hierarchical clustering scenarios."," As previously discussed, these chemical trends can be understood within the context of chemical evolution in hierarchical clustering scenarios." +" Considering that the results on the spatial distribution of LGRB progenitors favours low-metallicity progenitor models, one would expect that the iron abundance of the stellar populations producing LGRBs remains low at all redshifts with little variations ([Fe/H]~ —1)."," Considering that the results on the spatial distribution of LGRB progenitors favours low-metallicity progenitor models, one would expect that the iron abundance of the stellar populations producing LGRBs remains low at all redshifts with little variations ${\rm [Fe/H]}\sim-1$ )." +" On the other hand, one would expect that the a-enhancement strongly decreases with redshift (by 0.2 dex between z=3 and z= 0)."," On the other hand, one would expect that the $\alpha$ -enhancement strongly decreases with redshift (by 0.2 dex between $z=3$ and $z=0$ )." +" This means that, if LGRBs are produced by low metallicity massive stars, their location will be shifted on average from the central regions to the outskirts of galaxies."," This means that, if LGRBs are produced by low metallicity massive stars, their location will be shifted on average from the central regions to the outskirts of galaxies." +" If LGRBs can trace the chemical properties of the interestelar medium, they may map different regions of galaxies at different redshifts."," If LGRBs can trace the chemical properties of the interestelar medium, they may map different regions of galaxies at different redshifts." + A test of these prediction could be set up as further dust-corrected measurements of the chemical abundances of the stellar populations producing LGRBs become available., A test of these prediction could be set up as further dust-corrected measurements of the chemical abundances of the stellar populations producing LGRBs become available. +" LJP acknowledges funding by Argentine ANPCyT, through grant PICT 2006-02015 and 2007-00848."," LJP acknowledges funding by Argentine ANPCyT, through grant PICT 2006-02015 and 2007-00848." +" This work was partially supported by PICT 2005-32342, PICT 2006-245 Max Planck and PIP 2009-0305."," This work was partially supported by PICT 2005-32342, PICT 2006-245 Max Planck and PIP 2009-0305." +eccentricity.,eccentricity. +" The situation is completely different however for the inclination, because the duration of a transit is very sensitive to it."," The situation is completely different however for the inclination, because the duration of a transit is very sensitive to it." +" According to the published values of the inclination, respectively the errors (¢=80.1+0.3? )), a shift of several tenth of degrees should be observable."," According to the published values of the inclination, respectively the errors $i = 80.1 \pm 0.3 $ ), a shift of several tenth of degrees should be observable." + In this section we will describe the numerical experiments and the results we obtained., In this section we will describe the numerical experiments and the results we obtained. + It is particularly interesting whether one could determine how much the transiting planet would be influenced with respect to its inclination; this would have consequences for the transit time and the transit time duration., It is particularly interesting whether one could determine how much the transiting planet would be influenced with respect to its inclination; this would have consequences for the transit time and the transit time duration. + Therefore different test computations have been undertaken numerically (see Section ??)) as well as using an analytical approach (see Section ??)) for inclined planets in the system., Therefore different test computations have been undertaken numerically (see Section \ref{sec:numerical2}) ) as well as using an analytical approach (see Section \ref{sec:analytical}) ) for inclined planets in the system. + In this section we considered only the two confirmed planets in the System; an extension to the possible case of three planets can be found in Section ??.., In this section we considered only the two confirmed planets in the system; an extension to the possible case of three planets can be found in Section \ref{sec:numerical3}. . +" In Figs. 2,,"," In Figs. \ref{fig:31a}, \ref{fig:31b}," +" 3,,4 and 5 we show the effect on the inclination of CoRoT-7b caused by a difference in the ascending node (Q7,=20° and Ωπ.=140° =A, respectively vice versa = B)."," \ref{fig:31c} and \ref{fig:31d} we show the effect on the inclination of CoRoT-7b caused by a difference in the ascending node $\Omega_{7b}=20^{\circ}$ and $\Omega_{7c}=140^{\circ}$ =, respectively vice versa = )." +" For each run, the following initial inclinations wereused: i7,=1? and i5,=30°, the time scale for the integration was 3.104 years."," For each run, the following initial inclinations wereused: $i_{7b}=1^{\circ}$ and $i_{7c}=30^{\circ}$, the time scale for the integration was $3.10^4$ years." + In Fig., In Fig. +" 2 there is no visible difference betweenA and over a time period of 30,000 years; note that CoORoT-7b reaches inclinations up to 17,=47°."," \ref{fig:31a} there is no visible difference between and over a time period of 30,000 years; note that b reaches inclinations up to $i_{7b}=47^{\circ}$." +" A closer look at a shorter period of time (1,000 years) shows a slight time shift for the evolution of the inclination of CoRoT-7b (Fig. 3))."," A closer look at a shorter period of time (1,000 years) shows a slight time shift for the evolution of the inclination of b (Fig. \ref{fig:31b}) )." +" Zooming into the first 100 years of the integration it turns out that the time shift is caused by a different behaviour during the first ten years: while i7; increases immediately inA, in it decreases at first, but starts to increase after about ten years."," Zooming into the first 100 years of the integration it turns out that the time shift is caused by a different behaviour during the first ten years: while $i_{7b}$ increases immediately in, in it decreases at first, but starts to increase after about ten years." + From this point on the dynamical behaviour is qualitatively and quantitatively the same.:, From this point on the dynamical behaviour is qualitatively and quantitatively the same.: + The thick and thin line in Fig., The thick and thin line in Fig. + 4 show the same slope after the initial ten years., \ref{fig:31c} show the same slope after the initial ten years. +" This time shift remains during the whole time which can be seen in Fig. 5,,"," This time shift remains during the whole time which can be seen in Fig. \ref{fig:31d}," + where we plotted the respective evolution of the inclinations after several thousand years., where we plotted the respective evolution of the inclinations after several thousand years. + We analytically estimate the change of the orbital elements in the two planet case (subscripts and j)using the differential equations for thesecular perturbation of the orbital elements, We analytically estimate the change of the orbital elements in the two planet case (subscripts and )using the differential equations for thesecular perturbation of the orbital elements +of the distortiou over the full extent of the field of view (FOV).,of the distortion over the full extent of the field of view (FOV). + We solved for these global terms in several stages., We solved for these global terms in several stages. + First. we put the two chips iuto a meta coordinate frame.," First, we put the two chips into a meta coordinate frame." + Next. we solved for the linear skew terms present in the combined system.," Next, we solved for the linear skew terms present in the combined system." + Then we solved for the overall scaling. so that all filters would have the same scaliug. in terius of pixels per aresecond.," Then we solved for the overall scaling, so that all filters would have the same scaling, in terms of pixels per arcsecond." + Finally. we solved for the positional offset between the filters.," Finally, we solved for the positional offset between the filters." + We based our meta-coordinate rane on the cistortiou-corrected frame of the bottom chip (chip[1])., We based our meta-coordinate frame on the distortion-corrected frame of the bottom chip (chip[1]). + The bottom chip is already in this system. so we situply ueecled to find the transformation that put the top clip (chip[2]) into this sale systeim.," The bottom chip is already in this system, so we simply needed to find the transformation that put the top chip (chip[2]) into this same system." + Siuce there is a gap of about 35 pixels between the frames. the two chips of a single exposure uaturally have uo sources in common.," Since there is a gap of about 35 pixels between the frames, the two chips of a single exposure naturally have no sources in common." + This means that we will have O use an intermectiate set of observations to accomplish the mappiug., This means that we will have to use an intermediate set of observations to accomplish the mapping. + We took all the F606W observatious and identified all pairs of observations that had either au offset of more that 200 pixels or auo‘jentation difference of more than 10 degrees. (, We took all the F606W observations and identified all pairs of observations that had either an offset of more than 500 pixels or an orientation difference of more than 10 degrees. ( +If the poiutiugs are too similar then the overlap will 100 be sufficient.),If the pointings are too similar then the overlap will not be sufficient.) + Since we wanted as many different pairs of exposures as possije. we also iucorp«ated images Trou PID-12001 (PI-IXozhurina-Platais). whieh provides additional roll angles.," Since we wanted as many different pairs of exposures as possible, we also incorporated images from PID-12094 (PI-Kozhurina-Platais), which provides additional roll angles." + There were a total of 32 variously overlapping FOOOW exposures. so in general we could work with 992 overlapping pairs.," There were a total of 32 variously overlapping F606W exposures, so in general we could work with 992 overlapping pairs." + For each qualifviug pair. we found which chip(s) in the first exposure had significant overlap with both chips in tlie second exposure.," For each qualifying pair, we found which chip(s) in the first exposure had significant overlap with both chips in the second exposure." + We first corrected. all positions for distortion using the, We first corrected all positions for distortion using the +quasars iu more detail using traditional type-1 ACN diagnostics.,quasars in more detail using traditional type-1 AGN diagnostics. + ILlowever. even the measurement of the most basic ACN parameters such as Mp and the Eddington ratio he accretion rate) is a difficult task for the red. dustv AGNs.," However, even the measurement of the most basic AGN parameters such as $M_{\rm BH}$ and the Eddington ratio (the accretion rate) is a difficult task for the red, dusty AGNs." + Iu general. Afpy are derived from the optical or the ultraviolet (UV) part of AGN spectra for which spectral diagnostics are well established.," In general, $M_{\rm BH}$ are derived from the optical or the ultraviolet (UV) part of AGN spectra for which spectral diagnostics are well established." + Iu the case of AGNs. the dust obscures or significantly reduces the utyaromUV or the optical light coniuge from the region SMBUs. making the popular ACN optical/UV spectroscopic diagnostics useless;," In the case of dusty AGNs, the dust obscures or significantly reduces the UV or the optical light coming from the region around SMBHs, making the popular AGN optical/UV spectroscopic diagnostics useless." + For example. popular Adpy estimators arebased upon a virial relation between two parameters - the velocity width of the broad. Ia or ILJ lines. aud the size of BLR estimated from the contin hunuiuositv at 5100 ναοίetal.2000). or the luminosities of Πα or IL? (Careene&Πο2005).," For example, popular $M_{\rm BH}$ estimators are based upon a virial relation between two parameters - the velocity width of the broad, $\alpha$ or $\beta$ lines, and the size of BLR estimated from the continuum luminosity at 5100 ${}$ \citep{kaspi00} or the luminosities of $\alpha$ or $\beta$ \citep{greene05}." +.. If the light from a red. dusty ACN is extincted by a color excess of E(B|V) =2 mag (Glikimanetal.2007:ταrutiaetal. 2009).. its Πα aud line fluxes would be suppressed by a factor of LOO and 1000 respectively.," If the light from a red, dusty AGN is extincted by a color excess of $E(B-V)$ =2 mag \citep{glikman07,urrutia09}, its $\alpha$ and $\beta$ line fluxes would be suppressed by a factor of 100 and 1000 respectively." + One can try to estimate the amount of the dust extinction from a contimun fitting of the opticaL spectra or through the Balmer decrement. but suchlV estimates are often inconsistent with each other and accomupanice with uncertainties of order of AE(BW)~0.5 mag or more which are related to the dispersion im the intrinsic properties of ACGNs.," One can try to estimate the amount of the dust extinction from a continuum fitting of the optical-UV spectrum or through the Balmer decrement, but such estimates are often inconsistent with each other and accompanied with uncertainties of order of $\delta E(B-V) \sim + 0.5$ mag or more which are related to the dispersion in the intrinsic properties of AGNs." + The dust obscuration can arise from the Calacitic extinction for AGNs at low galactic latitude (e... hu et al.," The dust obscuration can arise from the Galacitic extinction for AGNs at low galactic latitude (e.g., Im et al." + 2007: Lee et al., 2007; Lee et al. + 2008)., 2008). + The problem cau be substantially alleviated if we cau use NIR lines instead of optical or UV lines. since NIR Ih«droseu lines such as the Pa aud Po are much less affected by the dust extinction than the UV/optical light.," The problem can be substantially alleviated if we can use NIR lines instead of optical or UV lines, since NIR Hydrogen lines such as the $\alpha$ and $\beta$ are much less affected by the dust extinction than the UV/optical light." + For the red. dusty ACN with the color excess ofE(B1) = 2inag. the line fluxes of Pa and Pj are suppressed by a actor of ouly 2.3 aud L.7 respectively.," For the red, dusty AGN with the color excess of $E(B-V)$ = 2 mag, the line fluxes of $\alpha$ and $\beta$ are suppressed by a factor of only 2.3 and 4.7 respectively." + This is a siguificaut oeuprovement over the optical lines., This is a significant improvement over the optical lines. + Since ApixZP? where £ is a luminosity of the conti or iui eliuission ine. the suppression in the Paschen Lue buuinosities oeitroduces uncertainties m Mp estimates only at the evel of a factor of 2 or less. even without correcting for je dust extinction with the Paschen decrement.," Since $M_{\rm BH} \propto L^{0.5}$ , where $L$ is a luminosity of the continuum or an emission line, the suppression in the Paschen line luminosities introduces uncertainties in $M_{\rm BH}$ estimates only at the level of a factor of 2 or less, even without correcting for the dust extinction with the Paschen decrement." + Iu this paper. we will derive the A/py estimators sed on the NIR ITydrogeu lines of Type-l ACNs aud investigate the Lue ratios of the Paschen lines. keeping in mund future applications of such relations to studies of dusty. red Αννα with broad emission lines.," In this paper, we will derive the $M_{\rm BH}$ estimators based on the NIR Hydrogen lines of Type-1 AGNs and investigate the line ratios of the Paschen lines, keeping in mind future applications of such relations to studies of dusty, red AGNs with broad emission lines." + Iu order to construct mass estimators based on the NIB. Ivcdrogeu lines. we used two sauples of low redshitt Type-l AGNs with NIR spectra at 0.5.L1 pau. One is from Lancdt et al. (," In order to construct mass estimators based on the NIR Hydrogen lines, we used two samples of low redshift Type-1 AGNs with NIR spectra at 0.8–4.1 $\mu$ m. One is from Landt et al. (" +2008: hereafter LOS) who studied 23 well-known Type-l ACNs in the local universe.,2008; hereafter L08) who studied 23 well-known Type-1 AGNs in the local universe. + Among these. we use 16 and 21 ACNs that have line flux aud width measurements in Po or P Hines respectively.," Among these, we use 16 and 21 AGNs that have line flux and width measurements in $\alpha$ or $\beta$ lines, respectively." + Note that we excluded four objects. Myrk 590. NGC 5518. Ark 5bG6l. aud NGC 7169 in all or some of our analysis even though Pa aud P. line flux aud FWITIM nuüeasureiaents were available.," Note that we excluded four objects, Mrk 590, NGC 5548, Ark 564, and NGC 7469 in all or some of our analysis even though $\alpha$ and $\beta$ line flux and FWHM measurements were available." + For Ark 561 and NGC 7169. the PWHAL values of Pa and Po) lines listed iu Los are too discrepant from each other differing by more han a factor of 1.5.," For Ark 564 and NGC 7469, the FWHM values of $\alpha$ and $\beta$ lines listed in L08 are too discrepant from each other differing by more than a factor of 1.5." + This suggests that one of the two measurements is erroneous., This suggests that one of the two measurements is erroneous. + Therefore. these two objects are excluded from all of the analysis performed below.," Therefore, these two objects are excluded from all of the analysis performed below." + For Mrk 590 and NGC 55Ls. the Πα aud the I) widths isted in LOs differ by more than a factor of 1.5. but the Paschen line widths axe consistent with each other.," For Mrk 590 and NGC 5548, the $\alpha$ and the $\beta$ widths listed in L08 differ by more than a factor of 1.5, but the Paschen line widths are consistent with each other." + These wo objects are excluded in the analysis of the correlation vetween the Pascheu aud the Balmer lines. but their reverberationanuappiug derived Mp are rezined for the derivation of the black hole estimators (of the method 2 and the method 3 in Section 3.2).," These two objects are excluded in the analysis of the correlation between the Paschen and the Balmer lines, but their reverberation-mapping derived $M_{\rm BH}$ are retained for the derivation of the black hole estimators (of the method 2 and the method 3 in Section 3.2)." + Another sample comes from Clikiman et al. (, Another sample comes from Glikman et al. ( +2006: hereafter C06).,2006; hereafter G06). + The C06 sample is made of 26 Tvpe-1l AGNs that were selected froii a cross-inatch between the SDSS-DR1 quasar catalog (Schucideretal.2003) and the 2 microu All Sky Survey. (2\LASS: Skrutskie ct al., The G06 sample is made of 26 Type-1 AGNs that were selected from a cross-match between the SDSS-DR1 quasar catalog \citep{schneider03} and the 2 micron All Sky Survey (2MASS; Skrutskie et al. + 2006). with the criteria of K < 115 imag. redshift z < 0.5 and the absolute magnitude in band. M; d to nae.," 2006), with the criteria of K $<$ 14.5 mag, redshift z $<$ 0.5 and the absolute magnitude in $i$ -band, $M_{i}$ $<$ -23 mag." + Tere. the absolute magnitude lait is inpose uinimuze contaiumation of the quasar light due to the jost. galaxy.," Here, the absolute magnitude limit is imposed to minimize contamination of the quasar light due to the host galaxy." + The C06 sample provides LL ACNs with Pa ines and LL ACONsS with P.J lines showing up in their NTR spectra., The G06 sample provides 11 AGNs with $\alpha$ lines and 14 AGNs with $\beta$ lines showing up in their NIR spectra. +" Iu all. we use 27 and 35 Type-l AGNs for the Po and he Po} line analysis. respectively,"," In all, we use 27 and 35 Type-1 AGNs for the $\alpha$ and the $\beta$ line analysis, respectively." + Table 1 swmunarizes xoperties of these ACNSs.," Table \ref{tbl1} + summarizes properties of these AGNs." + For Afpy of our sample AGNs. we use the following values.," For $M_{\rm BH}$ of our sample AGNs, we use the following values." + First. we use Afpg derived with the reverberation napping inethod from literatures if available.," First, we use $M_{\rm BH}$ derived with the reverberation mapping method from literatures if available." + This applics to LOAGNs with Pa and 11 AGNs data in LOS or Which A/py are taken frou Vestergaard Peterson (2006)., This applies to 10 AGNs with $\alpha$ and 11 AGNs $\beta$ data in L08 for which $M_{\rm BH}$ are taken from Vestergaard Peterson (2006). + Secoud. if Apu from the reverberation imzapping nethod are not available. we derived AZpg from the optical spectral information using sinele epoch Mp estimators.," Second, if $M_{\rm BH}$ from the reverberation mapping method are not available, we derived $M_{\rm BH}$ from the optical spectral information using single epoch $M_{\rm BH}$ estimators." + For the LOS sample without the reverberation napping derived Apu. we used the luminosity aud FWIIM listed in the Table 5 of LOS to derive their My.," For the L08 sample without the reverberation mapping derived $M_{\rm BH}$, we used the $\beta$ luminosity and FWHM listed in the Table 5 of L08 to derive their $M_{\rm BH}$." + For this. we adopted a Mp; estimator in Greene Πο (2005). after adjusting their relation to have the virial factor of 5.5 (Oukenetal.2001:Wooot2010) by multipliug their relation bv a factor of 1.δ.," For this, we adopted a $M_{BH}$ estimator in Greene Ho (2005), after adjusting their relation to have the virial factor of 5.5 \citep{onken04, woo10} by multiplying their relation by a factor of 1.8." + We also made a small correction to the LOS FWIINE aud Iuninuositv values. since the wav how Curoeue Ilo (2005) derived EWIIMSs aud Ipyuuinosities is different from what LOS did - Greene IIo (2005) adopted a multiple Gaussian component fitting to the broad line while LOs adopted a single componeut fitting of the broad line after removing narrow line compoucuts.," We also made a small correction to the L08 FWHM and luminosity values, since the way how Greene Ho (2005) derived FWHMs and luminosities is different from what L08 did - Greene Ho (2005) adopted a multiple Gaussian component fitting to the broad line while L08 adopted a single component fitting of the broad line after removing narrow line components." +" We fud that the correction factor to FWOAL44; ΤΝΤgi 0.9 ANd L,,45:5;/ Lai qi—1.08 on average through. fitting of the SDSS spectra of the G06 sample with the two uicthods (See below).", We find that the correction factor to be $_{multi}$ $_{single}$ =0.9 and $L_{multi}$ $L_{single}$ =1.08 on average through fitting of the SDSS spectra of the G06 sample with the two methods (See below). + For the (106 sample. none of the objects have {μι derived from the reverberation mapping method.," For the G06 sample, none of the objects have $M_{\rm BH}$ derived from the reverberation mapping method." + Some of the G06 sample have them IL2line hDunuinosities and FWIIAIs listed in Shen et al. (, Some of the G06 sample have their $\beta$line luminosities and FWHMs listed in Shen et al. ( +2008). but after checking EWIIM. values in Shen et al. (,"2008), but after checking FWHM values in Shen et al. (" +2008) and the optical spectra. we find cases where EWIIMS appear to be overestimated.,"2008) and the optical spectra, we find cases where FWHMs appear to be overestimated." + Therefore. we used our own spectral fitting routine (sim ot al.," Therefore, we used our own spectral fitting routine (Kim et al." + 2006) to obtain the 11.) , 2006) to obtain the $\beta$ +The most metal-poor stars carry the fossil record of the chemical compostion of the Galaxy. and hence allow one to study the ealiest epochs of Galactic chemical evolution.,"The most metal-poor stars carry the fossil record of the chemical compostion of the Galaxy, and hence allow one to study the ealiest epochs of Galactic chemical evolution." + Moreover. there are also applications for metal-poor stars. e.g. the determination of the primordial Lithium abundance (??).. constraining the baryon density parameter. or individual age determinations (e.g..?).. thus setting a lower limit to the age of the Universe.," Moreover, there are also applications for metal-poor stars, e.g. the determination of the primordial Lithium abundance \citep {Spite/Spite:1982,Ryanetal:2000}, constraining the baryon density parameter, or individual age determinations \cite [e.g.,][] {Cowanetal:1999}, thus setting a lower limit to the age of the Universe." + Therefore. in the past decade there has been a fast-growing interest in these stars within the astronomical community.," Therefore, in the past decade there has been a fast-growing interest in these stars within the astronomical community." + With VLT-UT2 and UVES now being in operation. it has become feasible to study large samples of metal-poor stars at high resolution and high S/N In à very reasonable tin=e.," With VLT-UT2 and UVES now being in operation, it has become feasible to study large samples of metal-poor stars at high resolution and high $S/N$ in a very reasonable time." + For the past decade. the major source of metal-poor stars has been the so-called HK survey of Beers and collaborators (???).," For the past decade, the major source of metal-poor stars has been the so-called HK survey of Beers and collaborators \citep {BPSI,BPSII,TimTSS} ." +" Now, an ever larger survey volume within which to search for metal-deficient stars has been opened up by use of the digital objective-prism spectra of the Hamburg/ESO Survey (HES:???).. since the HES ts more than one magnitude deeper than the HK survey."," Now, an even larger survey volume within which to search for metal-deficient stars has been opened up by use of the digital objective-prism spectra of the Hamburg/ESO Survey \citep [HES;][] {HESpaperI,heshighlights,HESpaperIII}, since the HES is more than one magnitude deeper than the HK survey." + ? has shown that the selection of metal- candidates in the HES by automatic spectral classification is much more efficient than the manual selection applied to the HK survey. so that the amount of telescope time needed for follow-up spectroscopy is reduced. and afi// exploitation of the ~8« larger HES volume (compared to the HK survey alone) becomes feasible.," \cite {Christlieb:2000} has shown that the selection of metal-poor candidates in the HES by automatic spectral classification is much more efficient than the manual selection applied to the HK survey, so that the amount of telescope time needed for follow-up spectroscopy is reduced, and a exploitation of the $\sim 8\times$ larger HES volume (compared to the HK survey alone) becomes feasible." + Àn alternative selection method in the HES ts the so-called Ca K index method (?).. which looks for stars characterized by a III K line weaker than expected for their B...V color.," An alternative selection method in the HES is the so-called Ca K index method \citep {nctss}, which looks for stars characterized by a II K line weaker than expected for their $B-V$ color." + This method is almost as efficient in selecting metal-poor stars as automatic classification (?).., This method is almost as efficient in selecting metal-poor stars as automatic classification \citep {Christliebetal:2000}. + In this paper we report or the first. high-resolution observations of metal-poor stars from the HES., In this paper we report on the first high-resolution observations of metal-poor stars from the HES. + Two stars. and1353-2735.. were observed with VLT- in the course of UVES Science Verification in February 2000.," Two stars, and, were observed with VLT-UT2 in the course of UVES Science Verification in February 2000." + The two starsdescribed in this paper were selected by the Ca method (?).., The two starsdescribed in this paper were selected by the Ca K-index method \citep {nctss}. + As is obvious from Fig. 1.. a," As is obvious from Fig. \ref {Fig:lowres_spectra}," +nd were both selected because they show Ill K (A3933 A)) line in the HES spectra.," and were both selected because they show II K $\lambda\,3933$ ) line in the HES spectra." + Tab., Tab. + | lists. coordinates (derived from the DSS-I. see e.g. dss). and photometry for the two stars.," \ref {Tab:HESCoordPhot} lists coordinates (derived from the DSS-I, see e.g. ), and photometry for the two stars." + Spectroscopic follow-up observations were obtained in April 1999 using EMMI attached to the ESO-NTT., Spectroscopic follow-up observations were obtained in April 1999 using EMMI attached to the ESO-NTT. + From these moderate-resolution (~5 FWHM). but good quality spectra (see Fig. 1)).," From these moderate-resolution $\sim 5\,$ FWHM), but good quality spectra (see Fig. \ref {Fig:lowres_spectra}) )," + having S/N~50 at Call K and S/N>60 at the, having $S/N\sim 50$ at II K and $S/N>60$ at the +llong. gave a total projected slit length of oon the sky.,"long, gave a total projected slit length of on the sky." +" ""Seeing"" varied between dduring these observations.", `Seeing' varied between during these observations. + Six overlapping slit positions were obtained along cach of the two cuts 4 and 5 in Fig., Six overlapping slit positions were obtained along each of the two cuts 4 and 5 in Fig. + 1., 1. + These were each merged to form the single positional- velocity (pv) arrays of aand pprofiles using the Starlink KAPPA CCDPACK MAKEMOS routines., These were each merged to form the single positional– velocity (pv) arrays of and profiles using the Starlink KAPPA CCDPACK MAKEMOS routines. + Only the aarrays after this process are shown in Figs 2 3 for PA = aand respectively for the pprofiles are emitted by the whole of the internal expanding volumes of NGC 7293 (Mceaburn et al 2005b) and the final picture becomes confused., Only the arrays after this process are shown in Figs 2 3 for PA = and respectively for the profiles are emitted by the whole of the internal expanding volumes of NGC 7293 (Meaburn et al 2005b) and the final picture becomes confused. +" The slit was 150 jm wide (= 11 aand 1.9"")) for ten of the separate slit positions and 300 jim wide for only the two positions at either end of cut 5.", The slit was 150 $\mu$ m wide $\equiv$ 11 and ) for ten of the separate slit positions and 300 $\mu$ m wide for only the two positions at either end of cut 5. +" Integration times were 1800 s in all cases and the spectra were calibrated in wavelength to+ 1 aaccuracy when converted to heliocentric radial velocity (15,0) against the spectrum of a Th/Ar arc lamp.", Integration times were 1800 s in all cases and the spectra were calibrated in wavelength to $\pm$ 1 accuracy when converted to heliocentric radial velocity ) against the spectrum of a Th/Ar arc lamp. +" Incidentally, there is an error in the velocity scale of figs 3-5 in Meaburn et al (2005b) for the pv arrays from slit positions 1-3 (shown here in Fig."," Incidentally, there is an error in the velocity scale of figs 3–5 in Meaburn et al (2005b) for the pv arrays from slit positions 1-3 (shown here in Fig." + 1)., 1). +" The heliocentric correction had not been applied to the velocity scale, consequently the zero of the erroneous scales in these previous figures should be -26.1 tto convert them to heliocentric radial velocity."," The heliocentric correction had not been applied to the velocity scale, consequently the zero of the erroneous scales in these previous figures should be -26.1 to convert them to heliocentric radial velocity." + This has been carried out for the pv array of pprofiles for slit position 2 in Fig., This has been carried out for the pv array of profiles for slit position 2 in Fig. + | and shown here in Fig., 1 and shown here in Fig. + 5., 5. + The pprofiles are compared in Fig., The profiles are compared in Fig. + 5 with the systemic heliocentric radial velocity ==-27+2 ffor the whole nebula (Meaburn et al 2005b - and see therein details of these previous observations)., 5 with the systemic heliocentric radial velocity = -27 $\pm$ 2 for the whole nebula (Meaburn et al 2005b - and see therein details of these previous observations). + Note that for comparison with the CO observations of Young et al (1999) their relationship == —-32, Note that for comparison with the CO observations of Young et al (1999) their relationship = - 3.2 +on a stellar cluster would be as low as 3-10? GeV cm?.,on a stellar cluster would be as low as $3\cdot10^{5}\;$ GeV $^{-3}$. +" Both the low mass of these WIMPs (m,=8 GeV) and especially their large SD scattering cross section with protons (σχαρ=10:56 cm?) contribute to producing effects on the stellar cluster at lower DM halo densities."," Both the low mass of these WIMPs $m_{\chi}=8\;$ GeV) and especially their large SD scattering cross section with protons $\sigma_{\chi,SD}=10^{-36}\;$ $^2$ ) contribute to producing effects on the stellar cluster at lower DM halo densities." + We have shown that a cluster of stars that evolves in a dense halo of DM shows strong signatures in its appearance due to the self-annihilation of captured DM particles in the interior of stars., We have shown that a cluster of stars that evolves in a dense halo of DM shows strong signatures in its appearance due to the self-annihilation of captured DM particles in the interior of stars. +" In comparison to the classical case, the cluster within a dense DM halo looks younger than its true age, due to the slower evolution of the stars when these are partially powered by DM annihilation."," In comparison to the classical case, the cluster within a dense DM halo looks younger than its true age, due to the slower evolution of the stars when these are partially powered by DM annihilation." +" This is visible only for old clusters (e.g. for clusters older than 1 Gyr within a DM halo of density px=10° GeV cm), because their RGB is populated by low-mass stars, which are the type of stars most affected by DM."," This is visible only for old clusters (e.g. for clusters older than 1 Gyr within a DM halo of density $\rho_{\chi}=10^9\;$ GeV $^{-3}$ ), because their RGB is populated by low-mass stars, which are the type of stars most affected by DM." +" Our work focuses on environments with very high DM densities, which may be present only in specific locations, such as near the centers of galaxies (Gondolo&Silk "," Our work focuses on environments with very high DM densities, which may be present only in specific locations, such as near the centers of galaxies \citep{art-GondoloSilk1999}. ." +"In particular, considering an adiabatically contracted 1999)..DM profile (Bertone&Merritt2005),, the DM densities discussed here may be found at the following distances from the GC: p,=3x10° GeV cm-? at rac£1 pc and px=1010 GeV cm-? at recF20.01 pc."," In particular, considering an adiabatically contracted DM profile \citep{art-BertoneMerritt2005}, the DM densities discussed here may be found at the following distances from the GC: $\rho_{\chi}=3\times10^5\;$ GeV $^{-3}$ at $r_{GC}\approx 1\;$ pc and $\rho_{\chi}=10^{10}\;$ GeV $^{-3}$ at $r_{GC}\approx 0.01\;$ pc." +" The shape of the central profiles of galactic DM halos is still a topic of discussion (deBlok while simulations predict the existence of cusps, observations2010):: favor constant-density DM cores."," The shape of the central profiles of galactic DM halos is still a topic of discussion \citep{art-deBlok2010}: while simulations predict the existence of cusps, observations favor constant-density DM cores." +" Our results indicate that the age of a cluster may be underestimated if embedded in a dense DM halo, which goes towards solving the “paradox of youth” in the center of the Milky Way, a possibility that was first suggested by Moskalenko&Wai(2007) in the context of compact stars."," Our results indicate that the age of a cluster may be underestimated if embedded in a dense DM halo, which goes towards solving the “paradox of youth"" in the center of the Milky Way, a possibility that was first suggested by \cite{art-MoskalenkoWai2007} in the context of compact stars." +" However, there are many astrophysical uncertainties, such as the velocities of stars and DM particles, that may change the rate at which stars capture DM particles and therefore change the overall influence of DM on a cluster."," However, there are many astrophysical uncertainties, such as the velocities of stars and DM particles, that may change the rate at which stars capture DM particles and therefore change the overall influence of DM on a cluster." + Although our results do not explain the depletion of giants observed in the nuclear central cluster of the Milky Way (Doetal.2009;Buchholz2009;Bartkoetal.2010) they show that the influence of DM on stellar evolution must be taken into account when studying nuclear clusters.," Although our results do not explain the depletion of giants observed in the nuclear central cluster of the Milky Way \citep{art-Doetal2009ApJ,art-Buchholzetal2009A&A,art-Bartkoetal2010ApJ} they show that the influence of DM on stellar evolution must be taken into account when studying nuclear clusters." +" A DM halo density gradient inside the stellar cluster would result in a broader MS, turn-off and RGB regions."," A DM halo density gradient inside the stellar cluster would result in a broader MS, turn-off and RGB regions." +" 'This effect is usually attributed to photometric errors, variable reddening (Carraroetal. extended star formation (Twarogetal.2011) and 2002),,binaries (Zhao&Bailyn 2005)."," This effect is usually attributed to photometric errors, variable reddening \citep{art-Carraroetal2002MNRAS}, extended star formation \citep{art-Twarogetal2011ApJL} and binaries \citep{art-Zhao2005AJ}." +" In the case of nuclear star clusters it could also be associated with the annihilation of DM particles inside the stars, given that within the typical size of nuclear clusters the DM density is expected to vary several orders of magnitude depending on the proximity of the galactic center."," In the case of nuclear star clusters it could also be associated with the annihilation of DM particles inside the stars, given that within the typical size of nuclear clusters the DM density is expected to vary several orders of magnitude depending on the proximity of the galactic center." +" For stellar clusters embedded in halos with extremely high DM densities we found an additional very strong signature: the bottom of the computed isochrones in the H-R diagram rises to higher luminosities because the low-mass stars, powered only withenergy from DM annihilation, inflate and become fully convective."," For stellar clusters embedded in halos with extremely high DM densities we found an additional very strong signature: the bottom of the computed isochrones in the H-R diagram rises to higher luminosities because the low-mass stars, powered only withenergy from DM annihilation, inflate and become fully convective." + As this, As this +in the larger table there has been no effort to remove sources based on the SE error flag.,in the larger table there has been no effort to remove sources based on the SE error flag. + Due (to space constraints only the first few columnis of the table are present in the printed Verslon., Due to space constraints only the first few columns of the table are present in the printed version. + Although the extraction parameters were adjusted conservativelv. independent assessments ol the source reliability are required.," Although the extraction parameters were adjusted conservatively, independent assessments of the source reliability are required." + The following analyses ancl tests were performed to judge the realitv of the catalog sources., The following analyses and tests were performed to judge the reality of the catalog sources. + The source extraction program. SE. returns (hax errors as well as [Iuxes.," The source extraction program, SE, returns flux errors as well as fluxes." + Figure 5 shows (he measured signal to noise values for the faint end of the catalog., Figure \ref{fig-snv} shows the measured signal to noise values for the faint end of the catalog. + The ratio of the isophotal Εν to isophotal flix error is ploted versus isophotal magnitude., The ratio of the isophotal flux to isophotal flux error is ploted versus isophotal magnitude. + There is signilicant scatter in the values as expected., There is significant scatter in the values as expected. + The average magnitude for a signal to noise ratio of 5 appears to be around an isophotal magnitude of 28.4 significantly fainter than the aperture test value of 27.7 found in 5.1.., The average magnitude for a signal to noise ratio of 5 appears to be around an isophotal magnitude of 28.4 significantly fainter than the aperture test value of 27.7 found in \ref{ss-noise}. + The details of how SE computes its [lux errors are not immeciately obvious so (he value of 27.7 will be used., The details of how SE computes its flux errors are not immediately obvious so the value of 27.7 will be used. + The rms images supplied to SE were multiplied by 1.8 for the expected correlation due to drizzling so that should not be an explanation for the difference., The rms images supplied to SE were multiplied by 1.8 for the expected correlation due to drizzling so that should not be an explanation for the difference. + As a check on noise induced sources we ran the identical extraction procedure on the negative of (he original source detection image., As a check on noise induced sources we ran the identical extraction procedure on the negative of the original source detection image. + The procedure produced no detections from (he negative image., The procedure produced no detections from the negative image. + This indicates that (le number of sources produced by noise is very low., This indicates that the number of sources produced by noise is very low. + The presence of the much higher signal to noise ACS images provided a second test of source reliabilitv., The presence of the much higher signal to noise ACS images provided a second test of source reliability. +" We checked for catalog sources that. had ACS F850LP. 0.6"" aperture diameter AD magnitudes fainter than 29.5.", We checked for catalog sources that had ACS F850LP $0.6\arcsec$ aperture diameter AB magnitudes fainter than 29.5. + The smallest aperture was chosen to minimize [lux from overlapping sources., The smallest aperture was chosen to minimize flux from overlapping sources. + We identified 22 sources out of the total 1293 sources that, We identified 22 sources out of the total 1293 sources that +l]lere. we compare this previously derived MOND fundamental plane to the mass-based. fundamental. plane of Bolton et al.,"Here, we compare this previously derived MOND fundamental plane to the mass-based fundamental plane of Bolton et al." + and find that they are entirely consistent., and find that they are entirely consistent. + Using the theoretical fundamental plane relation to calculate the mass from the observed. ellective radius and: velocity dispersion. it is found that the projected MOND FP mass. presumably entirely. baryonic. is proportional to the observed lensing mass with a small olfset. due to the οσοι of moclifiecd gravity on the deflection of photons along the line of sight.," Using the theoretical fundamental plane relation to calculate the mass from the observed effective radius and velocity dispersion, it is found that the projected MOND FP mass, presumably entirely baryonic, is proportional to the observed lensing mass with a small offset due to the effect of modified gravity on the deflection of photons along the line of sight." + Moreover. the implied MOND AL/L-colour relationship for these svstems is entirely consistent with population svnthesis models.," Moreover, the implied MOND M/L-colour relationship for these systems is entirely consistent with population synthesis models." + In other words. we find that AIOND requires no dark matter on galaxy scale in lensing ealaxies. in contrast to recent claims (Ferreras et al.," In other words, we find that MOND requires no dark matter on galaxy scale in lensing galaxies, in contrast to recent claims (Ferreras et al." + 2008)., 2008). + The fundamental plane of elliptical galaxies (Dressler οἱ al., The fundamental plane of elliptical galaxies (Dressler et al. + 1987. Djorgovski Davis 1987) is a scaling relationship involving the observed effective radius. roy. the central πο velocity dispersion. e. ancl. in the original form. the mean surface brightness within an effective radius. Z.," 1987, Djorgovski Davis 1987) is a scaling relationship involving the observed effective radius, $r_{eff}$, the central line-of-sight velocity dispersion, $\sigma_0$, and, in the original form, the mean surface brightness within an effective radius, $I$." + This is usually expressed. as (it may alternatively be written as ai relationship between total luminosity. effective. radius. and velocity dispersion).," This is usually expressed as (it may alternatively be written as a relationship between total luminosity, effective radius, and velocity dispersion)." + The analysis of Sloan data on elliptical galaxies implies that e=1.5 and bzOS (Denardi et al., The analysis of Sloan data on elliptical galaxies implies that $a\approx 1.5$ and $b\approx -0.8$ (Benardi et al. + 2003). while the expectations from the Newtonian virial theorem. assuming homology and constant M/L. would be @=2 and b=1.," 2003), while the expectations from the Newtonian virial theorem, assuming homology and constant M/L, would be $a=2$ and $b=-1$." + Phe observed deviation from these expectations is eencrally thought to be due to systematic deviations [roni homology or [rom constant M/L. The significant achievement of Bolton et al., The observed deviation from these expectations is generally thought to be due to systematic deviations from homology or from constant M/L. The significant achievement of Bolton et al. + was to use eravitational lensing in order to eliminate the dependence on Mj/L. The strong gravitational lensing provides the mass surface density within the Einstein ring radius (ri): therefore surface density. X. may. be substituted for surface brightness in the above relationship.," was to use gravitational lensing in order to eliminate the dependence on M/L. The strong gravitational lensing provides the mass surface density within the Einstein ring radius $r_{ein}$ ); therefore surface density, $\Sigma$, may be substituted for surface brightness in the above relationship." + The Einstein ring radius in their sample is generally about half the effective radius. so the surface density is taken by Bolton et al.," The Einstein ring radius in their sample is generally about half the effective radius, so the surface density is taken by Bolton et al." +" to be that within r.rr/2 (the correction fromthe rj, to riqr/2 is done either by assuming a mass distribution like that of an isothermal sphere or that light traces mass).", to be that within $r_{eff}/2$ (the correction from the $r_{ein}$ to $r_{eff}/2$ is done either by assuming a mass distribution like that of an isothermal sphere or that light traces mass). + “Phis was then combined with spectroscopic and. photometric observations of the lens galaxies to generate a “mass” fundamental plane., This was then combined with spectroscopic and photometric observations of the lens galaxies to generate a “mass” fundamental plane. + The resulting relation exhibits considerably less scatter and the exponents are close to the virial expectations: @= LSG4EOAT. b=0.03d:0.09. d=5440.9 with the mass traces light assumption (here the elfective radius is in kpe. the velocity dispersion in 1 and the surface density in Al. kpe5 7).," The resulting relation exhibits considerably less scatter and the exponents are close to the virial expectations: $a=1.86\pm 0.17$ , $b=-0.93\pm 0.09$, $d=5.4\pm 0.9$ with the mass traces light assumption (here the effective radius is in kpc, the velocity dispersion in $^{-1}$ and the surface density in $_\odot$ $^{-2}$ )." + The Newtonian virial theorem: implies that the mass within raclius r is given by where e is à constant determined. by the structure of the object., The Newtonian virial theorem implies that the mass within radius $r$ is given by where $c$ is a constant determined by the structure of the object. + Therefore Bolton et al., Therefore Bolton et al. +" also express their result by plotting the mass of the lens (within r. 55/2) against a ""dimensional"" mass variable given bv o7rq(260) where σ is the mean line-of-sight. velocity dispersion. within {νε9.", also express their result by plotting the mass of the lens (within $r_{eff}/2$ ) against a “dimensional” mass variable given by $\sigma^2 r_{eff}/(2G)$ where $\sigma$ is the mean line-of-sight velocity dispersion within $r_{eff}/2$. + The result. of this is shown by the points in Fig., The result of this is shown by the points in Fig. + 1 which are well ft by with 6=0.98 and Coz0.6., 1 which are well fit by with $\delta=0.98$ and $C\approx 0.6$. + Therefore. these observations are consistent with the Newtonian virial heorem and no variation of the structure constant: elliptical galaxies would appear to be quite homologous over a wide range of mass.," Therefore, these observations are consistent with the Newtonian virial theorem and no variation of the structure constant; elliptical galaxies would appear to be quite homologous over a wide range of mass." + Moreover. the lensing M/L values (r-xu) for these galaxies range from about two to cight in solar units and are somewhat higher than predicted. by »»pulation svnthesis models. (Fig.," Moreover, the lensing M/L values (r-band) for these galaxies range from about two to eight in solar units and are somewhat higher than predicted by population synthesis models (Fig." + 3. upper panel).," 3, upper panel)." + This σοι! ds addressed: further below. but. overall. for. early-vpe galaxies M/L values in this range would not constitute compelling evidence for dark matter within rr5/2.," This point is addressed further below, but, overall, for early-type galaxies M/L values in this range would not constitute compelling evidence for dark matter within $r_{eff}/2$." + By solving the structure equation. Alilerom (1984). has demonstrated. that. with MOND. isothermal spheres with a fixed degree of anisotropy have finite mass. an upper limit to the surface density (& ay/C) anc exhibit a Alat relationship (the basis of the Faber-Jackson law): therefore. such objects might constitute sensible miocels for elliptical galaxies.," By solving the structure equation, Milgrom (1984) has demonstrated that, with MOND, isothermal spheres with a fixed degree of anisotropy have finite mass, an upper limit to the surface density $\approx a_0/G$ ) and exhibit a $M-\sigma^4$ relationship (the basis of the Faber-Jackson law); therefore, such objects might constitute sensible models for elliptical galaxies." + However. the observed. properties. of ellipticals in particular. their distribution and scatter on the a-r.yy plane (Jorgensen1999:Jorgensen.Franx&Ixzrgard1995a:Jorgensen.Franx&Ivorgard.1905b)-. cannot be matched by isothermal spheres or any strictly homologous class of objects.," However, the observed properties of ellipticals– in particular, their distribution and scatter on the $\sigma$ $r_{eff}$ plane \cite{jor99,jfk95a,jfk95b}- – cannot be matched by isothermal spheres or any strictly homologous class of objects." + The MOND isothermal sphere is too inllated for à, The MOND isothermal sphere is too inflated for a +uxing interinediate-baud photometric abtuucdauces lor an order-of-1iuaguitude sinaller sample. aud the prediction of stellar isochrones used to celine the cluster distauce scale as detailed in and Anetal.(2007).. but disagrees weakly with the aualysis of a comparable databset of hotter stars using abuudances derived [rom UBV iudices (Ixaratas&Schuster2006).,"using intermediate-band photometric abundances for an order-of-magnitude smaller sample, and the prediction of stellar isochrones used to define the cluster distance scale as detailed in \citet{pi04} and \citet{an07}, but disagrees weakly with the analysis of a comparable databset of hotter stars using abundances derived from $UBV$ indices \citep{ka06}." +. However. the scatter in the results becomes apparent when the specific values of the slope are comparecl.," However, the scatter in the results becomes apparent when the specific values of the slope are compared." + Because the techuique adopted is au expanded version of the teclinique laid ou by (2003).. we will translate our change in Ady with [Fe/H] at a given B—V to a chauge iu B- Vowith [Fe/H] at a givenἾν Ady to allow a direct comparison with their result.," Because the technique adopted is an expanded version of the technique laid out by \citet{pe03}, , we will translate our change in $M_V$ with [Fe/H] at a given $B-V$ to a change in $B-V$ with [Fe/H] at a given $M_V$ to allow a direct comparison with their result." + Siice the main sequence slope at a given. |Fe/H] is assumed to be linear. these comparisons are equivaent.," Since the main sequence slope at a given [Fe/H] is assumed to be linear, these comparisons are equivalent." + From 51 stars. Percivaletal.(2003)) lind .NCB— V)/.N[Fe/H] = 0.15L. with a very weak sensitivity of the [ina value to the adopted main sequence slope.," From 54 stars, \citet{pe03} find $\Delta(B-V)/\Delta$ [Fe/H] = 0.154, with a very weak sensitivity of the final value to the adopted main sequence slope." +" With a main sequeuce slope of L.77. 1lis translates into AA,-/A[Fe/H] = 0.73."," With a main sequence slope of 4.77, this translates into $\Delta M_V/\Delta$ [Fe/H] = 0.73." + For our two relations above. .N(B—V)/.N[Fe/H] =0.21LE and 0.218. respectively.," For our two relations above, $\Delta(B-V)/\Delta$ [Fe/H] $= 0.214$ and 0.218, respectively." + Chaneine the fixed main sequence slope to L2 aud 5.5 produces ACB—V)/.NA[Fe/H]— and 0.20. respectively. coufirniug the ise:sitivity of the color gradieut to the adopted main sequence slope bul clearly iidicating that the vaue of Percivaletal.(2003) umlerestinuates the metallicity effect by29%.," Changing the fixed main sequence slope to 4.5 and 5.5 produces $\Delta(B-V)/\Delta$ $ = 0.217$ and 0.208, respectively, confirming the insensitivity of the color gradient to the adopted main sequence slope but clearly indicating that the value of \citet{pe03} underestimates the metallicity effect by." +. Note that because ACB—V)/. NFe/H] is constant. XM/N[Fe/H] will vary directly wit ithe acloped slope for the mait sequence.," Note that because $\Delta(B-V)/\Delta$ [Fe/H] is constant, $\Delta M_V/\Delta$ [Fe/H] will vary directly with the adopted slope for the main sequence." + A the other end of the scale. Pinsonneaultetal.(200:)).2001) have coustructed adjusted isoclirores {ο Use LL cefiniug cluster distaices through main sequence fitting.," At the other end of the scale, \citet{pi03, pi04} have constructed empirically-adjusted isochrones to use in defining cluster distances through main sequence fitting." + The iso‘hroues are built upou the moclels o Sillsetal.(2000) 1ic trausformect to the observational plane Isle a variety ol T;-color relations that are empi‘ically adjusted to eusure au ideal match to the Hyacdes., The isochrones are built upon the models of \citet{si00} and transformed to the observational plane using a variety of $T_e$ -color relations that are empirically adjusted to ensure an ideal match to the Hyades. + Piusoiueaultetal.(2001) include a COL241150 o ‘the impact of the various Z;-color relatiOLS Oll he absolute magnitude of a star at a given color as [Fe/H] is varied between —0.3 and. +0.2 over he coor range B—V — 0.10 to 1.0., \citet{pi04} include a comparison of the impact of the various $T_e$ -color relations on the absolute magnitude of a star at a given color as [Fe/H] is varied between $-0.3$ and +0.2 over the color range $B-V$ = 0.40 to 1.0. +" For heir 1οςels. the zero-poiuts of the absolute relations vary with the 7;-color yeation adopted. but tie slopes are extrenely Consistent: AM, /.N[Fe/H]21.1. 35% larger than «erived iu tUs luvestigaion aud almost. double that found Nw Percivaletal.(2003)."," For their models, the zero-points of the absolute magnitude-[Fe/H] relations vary with the $T_e$ -color relation adopted, but the slopes are extremely consistent: $\Delta M_V/\Delta$ $ = 1.4$, $\%$ larger than derived in this investigation and almost double that found by \citet{pe03}." +. Tle eculvaleri ACB—ΕλAT Fe/H.] =0.29., The equivalent $\Delta(B-V)/\Delta$ [Fe/H] $= 0.29$. + It shouk e empliasized hat these numbers are {ied to a specihie set of 1iodels., It should be emphasized that these numbers are tied to a specific set of models. + Α cleck of the many . aud hence cannot arise m the foreground.," We will estimate the contribution to $N$ ) by the dense envelopes by modeling emission lines of which have critical densities of $\sim 10^6$, and hence cannot arise in the foreground." + Iu the dense euvelopes. the main destruction route of iis the reaction with CO iuto .," In the dense envelopes, the main destruction route of is the reaction with CO into ." +". The concentration of iis given bv (ΠΟ ect COIL hoof [Crlelke. | (ΠΟ ΜΗ νΟ]. with &, the rate coefficient for dissociative recombination ofTCO!."," The concentration of is given by $n$ $x$ $n$ $k_{\rm CO}$ / $(x(e)k_{e}$ + $x$ $k_{{\rm H}_2{\rm O}}$ ], with $k_e$ the rate coefficient for dissociative recombination of." +. The electron fraction (e) has been calculated at cach point in the envelopes with a «λα. chemical network dde Doisauger et 11996)) based on the UMIST reaction rates CMillar et ).., The electron fraction $x(e)$ has been calculated at each point in the envelopes with a small chemical network de Boisanger et \nocite{bois96}) ) based on the UMIST reaction rates (Millar et \nocite{mill97}. + The main difference with the analysis of de Doisauger et ((1996) is the use of a detailed physical structure to interpretthe hieli-excitation lines., The main difference with the analysis of de Boisanger et (1996) is the use of a detailed physical structure to interpretthe high-excitation lines. + We assiune that Os aud [umrave neglieible (210©) abundances in the bulk of the envelopes. but that at To100 IK. ΠΟΥ jumps to 5«107 due to erain mantle evaporation.," We assume that $_2$ and have negligible $\ltsim 10^{-6}$ ) abundances in the bulk of the envelopes, but that at $T>100$ K, $x$ ) jumps to $5\times 10^{-5}$ due to grain mantle evaporation." + We neelec uctals such as Meg. Fe aud S as contributors to ο) aud aree molecules such as polveyelie aromatic hiydrocarbous as snuks of οὓς usiug the low metal abundances iuferrec youn dark cloud ονομασαν models would increase (ο) by a factor of 23 (Lee et 11996).," We neglect metals such as Mg, Fe and S as contributors to $x(e)$ and large molecules such as polycyclic aromatic hydrocarbons as sinks of $x(e)$; using the low metal abundances inferred from dark cloud chemistry models would increase $x(e)$ by a factor of 2–3 (Lee et 1996)." +" The values of delerived above eive (ο)10 ""oat the outer radii anc ~10? at the inner radii. as illustrated im Fig. d"," The values of derived above give $x(e) \sim 10^{-7}$ at the outer radii and $\sim 10^{-9}$ at the inner radii, as illustrated in Fig. \ref{fig:gl2136}." + The precipitous drop of aat LOO Is. caused by reactions with evaporated water. occurs at too μα] radii to affect our results.," The precipitous drop of at $100$ K, caused by reactions with evaporated water, occurs at too small radii to affect our results." + Tn the comparison with data. we use the GO. less abundant isotope tto avoid optical depth effects.," In the comparison with data, we use the $60\times$ less abundant isotope to avoid optical depth effects." + The maxima optical depth in the lines is z1 im our models., The maximum optical depth in the lines is $\approx 1$ in our models. +" Table 2 lists the caleulated fluxes of the J 552 aud 93 lines in ls” and 11"" beams."," Table \ref{t:hco+} + lists the calculated fluxes of the $J$ $\to$ 2 and $\to$ 3 lines in $18''$ and $14''$ beams." +" Observations are from vanderTaketal.(1999) for GL 2591 and from deDoisaugeretal.(1996) for NGC 2261] and W 3 Προ,"," Observations are from \cite{fvdt99} + for GL 2591 and from \cite{bois96} for NGC 2264 and W 3 IRS5." + The data for W 33A. GL 190. S 110 and CL 2136 were obtained with the James Clerk Maxwell Telescope in the wav described in vanderTaketal.(2000).," The data for W 33A, GL 490, S 140 and GL 2136 were obtained with the James Clerk Maxwell Telescope in the way described in \cite{fvdt00}." +. Usine dderived fromILL. the models overproduce bby factors of 2.T.," Using derived from, the models overproduce by factors of $2-7$." +" Adjusting the models to the ddata vields refined estimates for ((Table 2)) which pertain strictly to the deuse molecular eas, unaffected by any intervening clouds aloug the line of sight."," Adjusting the models to the data yields refined estimates for (Table \ref{t:hco+}) ) which pertain strictly to the dense molecular gas, unaffected by any intervening clouds along the line of sight." +" The data for the various sources span therauge of =(2.6ELS).10bos 1, in eood agreement with the diffuse. cloud estimates 1)). and also consistent with recent data from the Vovager aud Pioneer spacecraft at distances up to 60 AU from the Sun (Webber 1998))."," The data for the various sources span therange of $=(2.6 \pm 1.8) \times 10^{-17}$ $^{-1}$ , in good agreement with the diffuse cloud estimates \ref{s:intro}) ), and also consistent with recent data from the Voyager and Pioneer spacecraft at distances up to $60$ AU from the Sun \cite{webb98}) )." +in the Sloan e' filter were also obtained on the night of June 26.,in the Sloan $g^{\prime}$ filter were also obtained on the night of June 26. + XTE J1550-564 has been monitored extensively by the Im YALO telescope (Bailyn et 22000) at Cerro Tololo Interamerican Observatory since the discovery of the optical counterpart in 1998 September (Orosz.Jain.&Bailyn 1998)., XTE J1550-564 has been monitored extensively by the 1m YALO telescope (Bailyn et 2000) at Cerro Tololo Interamerican Observatory since the discovery of the optical counterpart in 1998 September \citep{oro98a}. . +. The V-band data from 2001 discussed here were collected and reduced in a similar manner to previous data from this source described by Jainetal.(20010).," The $V$ -band data from 2001 discussed here were collected and reduced in a similar manner to previous data from this source described by \citet{jai01b,jai01c}." +. As part of the normal acquisitionb.c procedure for spectroscopy we obtained a total of nine direct V images with exposure times of 30 to 90 seconds with VLT/FORS in its imaging mode., As part of the normal acquisition procedure for spectroscopy we obtained a total of nine direct $V$ images with exposure times of 30 to 90 seconds with VLT/FORS1 in its imaging mode. + In addition. two additional direct imagesI in B with exposure times of 120 and 200 seconds were taken.," In addition, two additional direct images in $B$ with exposure times of 120 and 200 seconds were taken." + The image scale of FORS is 072 per pixel. and the field of view is 6.86.5 square areminutes.," The image scale of FORS1 is 2 per pixel, and the field of view is $6.8\times 6.8$ square arcminutes." +| Finally. photometry of XTE J1550-564 was obtained 2001 June | using the SuSI2 instrument on the Nasmyth focus of the 3.5m New Technology Telescope (NTT) located at the European Southern Observatory. La Silla.," Finally, photometry of XTE J1550-564 was obtained 2001 June 1 using the SuSI2 instrument on the Nasmyth focus of the 3.5m New Technology Telescope (NTT) located at the European Southern Observatory, La Silla." + SuSI2 is a mosaic of two 2048« 4096. thinned. anti-reflection coated EEV CCDs.," SuSI2 is a mosaic of two $2048 \times 4096$ , thinned, anti-reflection coated EEV CCDs." + We used 3« on-chip binning. yielding a scale of 0724 per pixel and a field of view of 5.5 square areminutes.," We used $3\times 3$ on-chip binning, yielding a scale of 24 per pixel and a field of view of $5.5 \times 5.5$ square arcminutes." + The observing conditions were quite poor: the seeing was between 175 and 270 and there were passing clouds., The observing conditions were quite poor: the seeing was between 5 and 0 and there were passing clouds. + We obtained a total of 51 usable R-band images and 4 usable V-band images with exposure times of 3 to 5 minutes., We obtained a total of 51 usable $R$ -band images and 4 usable $V$ -band images with exposure times of 3 to 5 minutes. + The image processing routines in IRAP were used to correct for the electronic bias and to apply the flat-field corrections to the ΝΕΤ NTT. and Magellan images.," The image processing routines in IRAF were used to correct for the electronic bias and to apply the flat-field corrections to the VLT, NTT, and Magellan images." + The programsIle. and (Stetson 1987: Stetson. Davis. Crabtree 199]; Stetson 1992a.b) were used to compute the instrumental magnitudes of XTE 564 and all of the field stars within about a 1.2 areminute radius.," The programs, and (Stetson 1987; Stetson, Davis, Crabtree 1991; Stetson 1992a,b) were used to compute the instrumental magnitudes of XTE J1550-564 and all of the field stars within about a 1.2 arcminute radius." +" The comparison stars ""A7. ""B"". and ""C"" shown in Figure 2 of Jainetal.(2001b) were used to place the B- and V- instrumental magnitudes on the standard scales."," The comparison stars “A”, “B”, and “C” shown in Figure 2 of \citet{jai01b} were used to place the $B$ - and $V$ -band instrumental magnitudes on the standard scales." + The R- photometry and the Magellan photometry were left on the instrumental magnitude scales., The $R$ -band photometry and the Magellan photometry were left on the instrumental magnitude scales. + Since some of the V-band images from the VLT and NTT were slightly under-exposed. we averaged groups of two to four consecutive exposures together. yielding two measurements from 24 May. and one measurement each from the nights of 25-27 May and 1 June.," Since some of the $V$ -band images from the VLT and NTT were slightly under-exposed, we averaged groups of two to four consecutive exposures together, yielding two measurements from 24 May, and one measurement each from the nights of 25-27 May and 1 June." + Figure laa shows the complete YALO V-band light curve together with our VLT photometry., Figure \ref{fig0}a a shows the complete YALO $V$ -band light curve together with our VLT photometry. + The 2-12 keV X-ray light curve from the All Sky Monitor (ASM) on is shown in Figure Ibb. XTE 1550-564 had an optical reflare in 2001 January (Jain.Bailyn.&Tomsick2001a.Fig.laa)., The 2-12 keV X-ray light curve from the All Sky Monitor (ASM) on is shown in Figure \ref{fig0}b b. XTE J1550-564 had an optical reflare in 2001 January \citep[Fig.\ \protect\ref{fig0}a. + Strangely enough. the corresponding outburst in X-rays was quite weak. with a peak level of less than 10 ASM counts per second.," Strangely enough, the corresponding outburst in X-rays was quite weak, with a peak level of less than 10 ASM counts per second." + The source returned to its quiescent level by about April 20. and our V-band magnitudes from May 24-27 are fully consistent with the quiescent level: 21.8324.0+0.1.," The source was not detected in $B$, and we place a conservative lower limit of $B>24.0\pm 0.1$." + Jainetal.(1999) had estimated B=22.0+0.5 for the quiescent level based on a detection (near the plate limit) of the source on the SERC J survey print., \citet{jai99} had estimated $B=22.0\pm 0.5$ for the quiescent level based on a detection (near the plate limit) of the source on the SERC J survey print. + The effective bandpass of the SERC J print is actually much redder than the standard Johnson Bfilter.. so the quiescent magnitude given in. Jainetal.(1999) is not a proper B magnitude but is closer to a V magnitude.," The effective bandpass of the SERC J print is actually much redder than the standard Johnson $B$, so the quiescent magnitude given in \citet{jai99} is not a proper $B$ magnitude but is closer to a $V$ magnitude." + We measured the radial velocities of the secondary star using thefvcor task within IRAF. which is an implementation of the technique of Tonry&Davis(1979).," We measured the radial velocities of the secondary star using the task within IRAF, which is an implementation of the technique of \citet{ton79}." +. The eross correlations were computed over the wavelength range 5000-6850A.. excluding the Ho emission line. interstellar lines (Na D and the diffuse band near 5876 A)). and a tellurie feature near 6280A.," The cross correlations were computed over the wavelength range 5000-6850, excluding the $\alpha$ emission line, interstellar lines (Na D and the diffuse band near 5876 ), and a telluric feature near 6280." +. The spectra were continuum-subtracted prior to computing the cross correlation. and a Fourier filter was used to remove high frequency noise.," The spectra were continuum-subtracted prior to computing the cross correlation, and a Fourier filter was used to remove high frequency noise." + With the exception of one spectrum from the end of the night of May 27 which had poor signal-to-notse. the cross correlation peaks were generally quite significant.," With the exception of one spectrum from the end of the night of May 27 which had poor signal-to-noise, the cross correlation peaks were generally quite significant." + The value of the Tonry Davis 777 parameter. which 15 à measure of the signal-to-noise in a eross correlation. was generally in the range of 3.0-4.8.," The value of the Tonry Davis $r$ ” parameter, which is a measure of the signal-to-noise in a cross correlation, was generally in the range of 3.0-4.8." + The spectrum of the K3III star HD 181110 usually gave the best cross correlation peaks as judged by the value of the r parameter. and the spectrum of the KA4III star HD 181480 generally gave the second-best cross correlation peaks.," The spectrum of the K3III star HD 181110 usually gave the best cross correlation peaks as judged by the value of the $r$ parameter, and the spectrum of the K4III star HD 181480 generally gave the second-best cross correlation peaks." + In the analysis below we adopt the velocities measured using the K3III template., In the analysis below we adopt the velocities measured using the K3III template. + Since the source was at or very near quiescence. we believe our radial velocities are not biased by X-ray heating.," Since the source was at or very near quiescence, we believe our radial velocities are not biased by X-ray heating." + To search for the spectroscopic period we computed a three-parameter sinusoidal fit to the 17 velocities for a dense range of trial periods between 0 and 4 days., To search for the spectroscopic period we computed a three-parameter sinusoidal fit to the 17 velocities for a dense range of trial periods between 0 and 4 days. +The reduced 4 values for these fits are shown in 2aa. The free parameters at each trial period are the velocity semiamplitude A>. the epoch of maximum velocity 7o(spect). and the systemic velocity +.,"The reduced $\chi^2$ values for these fits are shown in \ref{fig1}a a. The free parameters at each trial period are the velocity semiamplitude $K_2$, the epoch of maximum velocity $T_0$ (spect), and the systemic velocity $\gamma$." + The best fit is at a period. of Ap=1.5520.010 days (le error). where vc1.38.," The best fit is at a period of $P_{\rm sp}=1.552\pm 0.010$ days $1\sigma$ error), where $\chi^2_{\nu}=1.38$." + The two alias periods near 0.7 and 2.5 days are ruled out by their large values of 47 and by inspection of the folded velocity curves., The two alias periods near 0.7 and 2.5 days are ruled out by their large values of $\chi^2_{\nu}$ and by inspection of the folded velocity curves. +" We adopt the following spectroscopic elements with lo errors: P4,=1.552+0.010 days. Ky=349E12 km sl. and 7o(spect)=HJD2.452.054.296[+0.014."," We adopt the following spectroscopic elements with $1\sigma$ errors: $P_{\rm sp}=1.552\pm +0.010$ days, $K_2=349\pm 12$ km $^{-1}$, and $T_0({\rm +spect})={\rm HJD~}2,452,054.296\pm 0.014$." + In order to find the true systemic velocity we must know the radial velocity of the template star., In order to find the true systemic velocity we must know the radial velocity of the template star. + We cross correlated the spectrum of HD 181110 with 47 template spectra of stars with a radial velocity measurement listed in the SIMBAD database., We cross correlated the spectrum of HD 181110 with 47 template spectra of stars with a radial velocity measurement listed in the SIMBAD database. + The median heliocentric velocity for HD 181110 was —71 km s! and the standard deviation of the velocities was 18 km s!., The median heliocentric velocity for HD 181110 was $-71$ km $^{-1}$ and the standard deviation of the velocities was 18 km $^{-1}$. + Based on this. we adopt 2—68£19 km s! for XTE J1550-564.," Based on this, we adopt $\gamma=-68\pm 19$ km $^{-1}$ for XTE J1550-564." + The velocities and the best fitting sinusoid are shown in 2bb. and the spectroscopic elements are listed in Table ].. (," The velocities and the best fitting sinusoid are shown in \ref{fig1}b b, and the spectroscopic elements are listed in Table \ref{tab2}. (" +The velocity plotted as an open circle in 2bb was excluded fromthe fit since it deviatesby more than 4c from the fit.),The velocity plotted as an open circle in \ref{fig1}b b was excluded fromthe fit since it deviatesby more than $4\sigma$ from the fit.) +" We note that our spectroscopic pertod is consistent with the photometric period of P,=1.541XE0.009 days found by Jainetal. (2001b).", We note that our spectroscopic period is consistent with the photometric period of $P_{\rm ph}=1.541\pm 0.009$ days found by \citet{jai01b}. +. The optical mass function is then (lo error)., The optical mass function is then $1\sigma$ error). + The optical mass function places an immediate lower limit on the mass of the compact object. and since this mmimum mass of the compact object is well above the," The optical mass function places an immediate lower limit on the mass of the compact object, and since this minimum mass of the compact object is well above the" +Tuteractious play an nmuportaut role in the ealaxy evolution.,Interactions play an important role in the galaxy evolution. + Even a ΠΟΥ lucrger with the mias ratio less than 1/5Γ 1/10 which docs uot disturb the overall structure of the salaxw disk. lav cause a eas concentration 1n its coutra reelon. trigecringao the nuclear activity or a nuclear starburst.," Even a minor merger with the mass ratio less than $1/5$ $1/10$ which does not disturb the overall structure of the galaxy disk, may cause a gas concentration in its central region, triggering the nuclear activity or a nuclear starburst." + According to the hierarchical xwadieui such evens happened mnany times mine a galaxy lifetinie. however. it is difficult to detect nünor merge footpriuts. even he recent ones. against the backgrotud of a high surface xiehtuess galaxy.," According to the hierarchical paradigm, such events happened many times during a galaxy lifetime, however, it is difficult to detect minor merging footprints, even the recent ones, against the background of a high surface brightness galaxy." + Deep nuages. revealing low-contrast tidal feaures (see.for 2010).. Or (etaed studies of scllar populations and iuterwl kinematics of the galaxy are reqπου.," Deep images, revealing low-contrast tidal features \citep*[see, for +example][]{Martinez-Delgado2010, Smirnova2010b}, or detailed studies of stellar populations and internal kinematics of the galaxy are required." + The consequeuces of a minor mcrecr may be quite jverse., The consequences of a minor merger may be quite diverse. + Owji gas of a larger eaaxv nav be disturbed bv a satellite iutrusioi hence it may inflow iuto the center. resulting in a strong σας colpression iu the nucleus arid a subsequeit unclear star formation burst.," Own gas of a larger galaxy may be disturbed by a satellite intrusion, hence it may inflow into the center, resulting in a strong gas compression in the nucleus and a subsequent nuclear star formation burst." + A rather voung current age of the nuclear star Ῥοριlation luside au older bulge may be the signature of such event., A rather young current age of the nuclear star population inside an older bulge may be the signature of such event. + If the initial direction of the orbital augular nomentuu of the satellite significantly differed frou he niu ealaxv disk rotation momentum. then we Μαν LOW have a situation when some fraction of stars OY gas €ouds iu the ealaxy are rotating on orbits ited (or orthogonal) to the main galactic disk. or even counter-crotatius within it.," If the initial direction of the orbital angular momentum of the satellite significantly differed from the main galaxy disk rotation momentum, then we may now have a situation when some fraction of stars or gas clouds in the galaxy are rotating on orbits tilted (or orthogonal) to the main galactic disk, or even counter-rotating within it." + Long-«lit aud iuceral-field specral observations gave a 111ber of evidences or the οποιασα) iisaligniueuts in circunmuclear reeions of carly-type disk galaxies mceludius the cases of due.tically decoupled cores., Long-slit and integral-field spectral observations gave a number of evidences for the kinematical misalignments in circumnuclear regions of early-type disk galaxies including the cases of kinematically decoupled cores. + Numerous examples aud detaied discussions aud references can be fouud. for instance. in the papers by Afanasicyeal.(1989):CorsiniCoccatoetal (2007).," Numerous examples and detailed discussions and references can be found, for instance, in the papers by \citet{weall89,Corsini2003, Moiseev2004,Sarzi2006,Coccato2007}." +" Uunfortuuatelv. observational evidences of large-scale. (σος, one kiloparsec central region) kinematically decoupled suwvstenas are still quite ra| (seeSilchenkoetal.209.andreferences thereiu).."," Unfortunately, observational evidences of large-scale (beyond one kiloparsec central region) kinematically decoupled subsystems are still quite rare \citep[see][and +references therein]{Silchenko2009}." + Therefore. every new exaltale of the similarly peculiar objects is interesting.," Therefore, every new example of the similarly peculiar objects is interesting." +"In the early Universe, before z~2x10° double Compton and destroy any spectral distortions and maintain the Planck spectrum of CMB.","In the early Universe, before $z\sim 2\times 10^6$ double Compton and destroy any spectral distortions and maintain the Planck spectrum of CMB." +" For small distortions due to single, quasi-instantaneous episode of energy release, we can write the ratio of final-to-initial µ as an exponential function of redshift defined by the square root of the product of Comptonization and absorption rates (?).."," For small distortions due to single, quasi-instantaneous episode of energy release, we can write the ratio of final-to-initial $\mu$ as an exponential function of redshift defined by the square root of the product of Comptonization and absorption rates \citep{sz1970}." +" For a double Compton process, thisformula gives (?) where za,31.98x10° defines the “surface of the blackbody photosphere""."," For a double Compton process, thisformula gives \citep{dd1982} + where $z_{\rm dc}\approx 1.98\times 10^6$ defines the “surface of the blackbody photosphere""." + We call this function G(z) the blackbody visibility function for spectral distortions., We call this function ${G}(z)$ the blackbody visibility function for spectral distortions. +" We call the region z>za. where the initial µ distortion can be reduced by a factor of more than e the “blackbody photosphere""."," We call the region $z>z_{\rm{dc}}$ where the initial $\mu$ distortion can be reduced by a factor of more than $e$ the “blackbody photosphere""." +" Thus inside the blackbodyphotosphere, a Planckian spectrum can be established efficiently."," Thus inside the blackbodyphotosphere, a Planckian spectrum can be established efficiently." + Figure5] shows how the µ distortion at high redshifts decreases due to the double Compton and Compton scattering., Figure \ref{bbfig} shows how the $\mu$ distortion at high redshifts decreases due to the double Compton and Compton scattering. + The regions of the blackbody photosphere allowed by different experiments are shaded., The regions of the blackbody photosphere allowed by different experiments are shaded. +" At redshifts 10°1, and the spectrum with a negative chemical potential is established at x= 0ο."," At redshifts $10^51$, and the Bose-Einstein spectrum with a negative chemical potential is established at $x\gtrsim 0.01$ ." +" At lower frequencies, bremsstrahlung and double Compton create a Planck spectrum corresponding to"," At lower frequencies, bremsstrahlung and double Compton create Planck spectrum corresponding to" +the way. you have the option of saving an intermediate state in order to restore it later.,"the way, you have the option of saving an intermediate state in order to restore it later." + This can be a great help when you are searching for à parameter value to accomplish some specific outcome and the parameter only influences later stages of evolution (such as rate of envelope ejection)., This can be a great help when you are searching for a parameter value to accomplish some specific outcome and the parameter only influences later stages of evolution (such as rate of envelope ejection). + The data interface is simply a Fortran) module with declarations and lots of comments., The data interface is simply a Fortran module with declarations and lots of comments. + The interface includes evolution parameters and their default values., The interface includes evolution parameters and their default values. + Most will go untouched. but as needed they can be changed either at initialization or between steps.," Most will go untouched, but as needed they can be changed either at initialization or between steps." + There are parameters such as 4 for Reimers’ wind. with mass loss rate equal to 4« 107σας ()RL/M)/(ROL../M..) (Reimers. 1975). 6. for convectiveM mixing length. and more.," There are parameters such as $\eta $ for Reimers' wind, with mass loss rate equal to $4 \times 10^{-13} \Msun$ /year $( \eta R L / M)/(\Rsun \Lsun / \Msun)$ (Reimers, 1975), $\alpha $ for convective mixing length, and more." + There are also parameters unrelated to the physies. such as error tolerances and time step controls.," There are also parameters unrelated to the physics, such as error tolerances and time step controls." + In addition to legitimate evolution. there are parameters to let you do “pseudo-evolution™.," In addition to legitimate evolution, there are parameters to let you do “pseudo-evolution”." + You can add or remove mass from the surface at arbitrary rates. you can artificially inject energy. you can turn off convective overshooting. and you can do other arcane things às well.," You can add or remove mass from the surface at arbitrary rates, you can artificially inject energy, you can turn off convective overshooting, and you can do other arcane things as well." + Such pseudo-evolution can be useful in constructing models., Such pseudo-evolution can be useful in constructing models. + The third demo uses artificial mass loss to mimic envelope ejection during the common envelope phase of a binary. with the resulting star then allowed to evolve normally after the envelope is gone.," The third demo uses artificial mass loss to mimic envelope ejection during the common envelope phase of a binary, with the resulting star then allowed to evolve normally after the envelope is gone." + The demo programs. which can be downloaded as part of the software distribution from the website. illustrate the use of EZ and provide templates for your applications.," The demo programs, which can be downloaded as part of the software distribution from the website, illustrate the use of EZ and provide templates for your applications." + The first demo explores the ZAMS for two different metallicities., The first demo explores the Zams for two different metallicities. + The second demo surveys a wide range of masses evolving from the main sequence for Z=0.02., The second demo surveys a wide range of masses evolving from the main sequence for Z=0.02. + The third considers a | M.. star under different scenarios of mass loss including one that leads to a late helium flash when the star is well along the track to becoming à white dwarf., The third considers a 1 $\Msun$ star under different scenarios of mass loss including one that leads to a late helium flash when the star is well along the track to becoming a white dwarf. + The web site has details. as well as figures in pdf format for downloading.," The web site has details, as well as figures in pdf format for downloading." + Take a look at the on-line figures: they may be useful supplements to the standard textbook fare., Take a look at the on-line figures; they may be useful supplements to the standard textbook fare. + Here are a few more details., Here are a few more details. + Demol computes the zero age main sequences for Z=0.02 and Z=0.0001., Demo1 computes the zero age main sequences for Z=0.02 and Z=0.0001. + The variation with mass along the ZAMS Is shown for luminosity. surface temperature. central temperature. central density. radius. P-P versus CNO nuclear reactions. opacity. nuclear burning time scale. and convection zones.," The variation with mass along the Zams is shown for luminosity, surface temperature, central temperature, central density, radius, p-p versus cno nuclear reactions, opacity, nuclear burning time scale, and convection zones." + Demo2 shows the HR diagram tracks and central temperature and density tracks for a sample of Z=0.02 stars over a wide range of initial mass., Demo2 shows the HR diagram tracks and central temperature and density tracks for a sample of Z=0.02 stars over a wide range of initial mass. + The tracks are marked to show the location of break-even for the net power from nuclear reactions beyond hydrogen burning minus the total power lost to neutrino cooling (1.e.. the onset of significant helium burning).," The tracks are marked to show the location of break-even for the net power from nuclear reactions beyond hydrogen burning minus the total power lost to neutrino cooling (i.e., the onset of significant helium burning)." + The demo also looks in detail at a large number of stars. all simulated with convective overshooting and Reimers’ wind (7=1).," The demo also looks in detail at a large number of stars, all simulated with convective overshooting and Reimers' wind $\eta = 1$ )." + In addition to the usual HR diagram and central temperature-density tracks. the figures include histories of the later values for radius. neutino losses. power from triple-alpha. power from alpha-capture. power from carbon burning. center degeneracy. and total metal fraction.," In addition to the usual HR diagram and central temperature-density tracks, the figures include histories of the later values for radius, neutino losses, power from triple-alpha, power from alpha-capture, power from carbon burning, center degeneracy, and total metal fraction." + There are plots that trace the evolution of convection zones. burning zones. central abundances. nuclear power sources. and neutrino cooling.," There are plots that trace the evolution of convection zones, burning zones, central abundances, nuclear power sources, and neutrino cooling." + In addition. there. are figures showing sets of profiles by mass coordinate taken at key moments along the evolution.," In addition, there are figures showing sets of profiles by mass coordinate taken at key moments along the evolution." + Demo3 treats a | M.. PAstar with Z=0.02., Demo3 treats a 1 $\Msun$ star with Z=0.02. + It takes the star from the main sequence and saves state near the tip of the giant branch., It takes the star from the main sequence and saves state near the tip of the giant branch. + Then it continues the evolution in three different ways., Then it continues the evolution in three different ways. + First. it evolves with no mass loss up to the helium flash.," First, it evolves with no mass loss up to the helium flash." + Then. it restores the saved state and evolves the star again with the envelope ejected quickly.," Then, it restores the saved state and evolves the star again with the envelope ejected quickly." + This gives a smaller core and produces a white dwarf., This gives a smaller core and produces a white dwarf. + Finally. it restores state and tries again with a reduced rate of mass loss. which gives a slightly larger core and a late helium flash.," Finally, it restores state and tries again with a reduced rate of mass loss, which gives a slightly larger core and a late helium flash." + If you would like to learn more about EZ. the next step is to visit the website.," If you would like to learn more about EZ, the next step is to visit the website." + Even if you don't plan to download the code. you might enjoy looking at some of the figures.," Even if you don't plan to download the code, you might enjoy looking at some of the figures." + If you do decide to download it. there is a tar file with data and source code and a README file to help you along.," If you do decide to download it, there is a tar file with data and source code and a readme file to help you along." + It includes instructions for building and running EZ. for testing the results. and for making your own applications.," It includes instructions for building and running EZ, for testing the results, and for making your own applications." + Please e-mail me with comments. questions. and suggestions for improvements.," Please e-mail me with comments, questions, and suggestions for improvements." + Lars Bildsten. at the University of California. Santa Barbara. Kavli Institute for Theoretical Physics (KITP). has been a teacher. advisor. and friend for a retired computer scientist with a desire to learn some astrophysics.," Lars Bildsten, at the University of California, Santa Barbara, Kavli Institute for Theoretical Physics (KITP), has been a teacher, advisor, and friend for a retired computer scientist with a desire to learn some astrophysics." + Phil Arras. a post-doe at KITP. kindly provided code for neutrino cooling (based on Itoh et al..," Phil Arras, a post-doc at KITP, kindly provided code for neutrino cooling (based on Itoh et al.," + 1996) and volunteered to be the first beta-user., 1996) and volunteered to be the first beta-user. + And special thanks to Peter Eggleton himself for providing the current version of his code and e-mail support while I was getting into 1t., And special thanks to Peter Eggleton himself for providing the current version of his code and e-mail support while I was getting into it. + This work was partially supported by the National Science Foundation under grants PHY99-07949 and ASTO2-05956., This work was partially supported by the National Science Foundation under grants PHY99-07949 and AST02-05956. +Modern Cosmic Microwave Background (CMB) observations provide a powerful test of our understanding of the Universe.,Modern Cosmic Microwave Background (CMB) observations provide a powerful test of our understanding of the Universe. + Within the generally accepted framework of a XCDM model. the 5- measurements by the Wilkinson Microwave Anisotropy Probe (WMAP) constrain the fundamental cosmological parameters with a relative accuracy of 1θέ (Dunkleyetal.2009:Komatsual. 2009)... while the upcoming observations by the Planck satellite are expected to improve these numbers by at least a factor ~3.4 (e.g.ThePlanckCollaboration2006:Colomboetal.2009).," Within the generally accepted framework of a $\Lambda$ CDM model, the 5-year measurements by the Wilkinson Microwave Anisotropy Probe (WMAP) constrain the fundamental cosmological parameters with a relative accuracy of $1-10\%$ \citep{2009ApJS..180..306D,2009ApJS..180..330K}, while the upcoming observations by the Planck satellite are expected to improve these numbers by at least a factor $\sim 3-4$ \citep[e.g.][]{2006astro.ph..4069T,2009MNRAS.398.1621C}." +. One of the main scientific goals of Planck. and other proposed future CMB missions (e.g.EPIC.Bocketal.2009).. is understanding the nature of Inflation.," One of the main scientific goals of Planck, and other proposed future CMB missions \citep[e.g. EPIC,][]{2009arXiv0906.1188B}, is understanding the nature of Inflation." + Detection of the B-mode of CMB polarization would provide direct evidence of a primordial background. of Gravitational Waves arising from Inflation (Kamionkowskietal.1997:Spergel&Zaldarriaga 1997).," Detection of the B-mode of CMB polarization would provide direct evidence of a primordial background of Gravitational Waves arising from Inflation \citep{1997PhRvL..78.2058K,1997PhRvL..79.2180S}." +. Even without such detection the CMB remains the most powerful probe of Inflation currently accessible., Even without such detection the CMB remains the most powerful probe of Inflation currently accessible. +" A general prediction of inflationary models is that the fractional amplitude of density fluctuations would be nearly scale independent. so that the corresponding power spectrum could be well approximated by an Harrison-Zeldovich form P(&)xA"" where the spectral index ns21."," A general prediction of inflationary models is that the fractional amplitude of density fluctuations would be nearly scale independent, so that the corresponding power spectrum could be well approximated by an Harrison-Zeldovich form $P(k) \propto +k^{n_s}$, where the spectral index $n_s \simeq 1$." + The amount of deviation n. leonstrains the shape of the inflationary potential. and current WMAP results already allow to rule out several models (Komatsuetal. 2009)..," The amount of deviation $n_s -1$ constrains the shape of the inflationary potential, and current WMAP results already allow to rule out several models \citep{2009ApJS..180..330K}." + Significant improvements will come from Planck and the next generation CMB missions., Significant improvements will come from Planck and the next generation CMB missions. + However. exploitation of the full potential of CMB measurements requires a deep understanding of instrumenta systematics and a careful cleaning of foreground contaminants.," However, exploitation of the full potential of CMB measurements requires a deep understanding of instrumental systematics and a careful cleaning of foreground contaminants." + On small angular scales. extragalactic point sources are an importan source of contamination.," On small angular scales, extragalactic point sources are an important source of contamination." + Bright sources. which can be detectec with high significance in CMB maps. are typically accountec for by masking a small area around the source position during the estimation of the CMB angular power spectra. ©.," Bright sources, which can be detected with high significance in CMB maps, are typically accounted for by masking a small area around the source position during the estimation of the CMB angular power spectra, $C_\ell$." + On the xher hand. to a first approximation. undetected. and therefore unmasked. point sources provide a Poisson noise contribution to the measured C'; as well as a non-Gaussian signature in the maps (e.g.Toffolattietal.1998:Pierpaoli2003:&Perna2004:Cooray2008:Babich&Pierpaoli 2008).. ," On the other hand, to a first approximation, undetected, and therefore unmasked, point sources provide a Poisson noise contribution to the measured $C_\ell$ as well as a non-Gaussian signature in the maps \citep[e.g.][]{1998MNRAS.297..117T,2003ApJ...589...58P,2004MNRAS.354.1005P,2008PhRvD..77j7305S,2008PhRvD..77l3011B}. ." +An incorrec determination of this contamination can lead to relevant biases on the estimated cosmological parameters. in particular on ης Huffenbergeretal.2006.2008).. whose accurate measuremen depends on a careful estimate of C; over the largest range of scales probed by an experiment.," An incorrect determination of this contamination can lead to relevant biases on the estimated cosmological parameters, in particular on $n_s$ \citep{2006ApJ...651L..81H,2008ApJ...688....1H}, whose accurate measurement depends on a careful estimate of $C_\ell$ over the largest range of scales probed by an experiment." + In this respect the greates expectations are now on Planck. which is a whole sky survey with a small instrumental beam and low noise level.," In this respect the greatest expectations are now on Planck, which is a whole sky survey with a small instrumental beam and low noise level." + If foregrounds anc systematics are well under control. Planck will be able to confirmor falsify the WMAP findings about ης being signiticantly smaller," If foregrounds and systematics are well under control, Planck will be able to confirmor falsify the WMAP findings about $n_s$ being significantly smaller" +for NGC 1700. and suggesting that the merger was a faseous one.,"for NGC 1700, and suggesting that the merger was a gaseous one." + ? have shown that in a merger between two spirals with bulges the main starburst occurs at the time of nuclear coalescence while the tails form ~0.5 ανν earlier., \scite{mihos96} have shown that in a merger between two spirals with bulges the main starburst occurs at the time of nuclear coalescence while the tails form $\sim0.5$ Gyr earlier. + Lf this is the case. we might expect the ‘dvwnamical/structural’ age estimates to be slightly higher than the “starburst” ones.," If this is the case, we might expect the `dynamical/structural' age estimates to be slightly higher than the `starburst' ones." + We have decided to adopt an age for NGC 1700 of 3.031.0 Cir as our best estimate., We have decided to adopt an age for NGC 1700 of $3.0\pm1.0$ Gyr as our best estimate. + This may also correspond to the time since the nuclei of the progenitors merged., This may also correspond to the time since the nuclei of the progenitors merged. + Given the fieldofview. our Week observations are ideal for defining the outer reaches of the GC system.," Given the field–of–view, our Keck observations are ideal for defining the outer reaches of the GC system." + We have calculated the surface density (8D) profile for the GC system in the Keck images within 9 annuli centred on the galaxy., We have calculated the surface density (SD) profile for the GC system in the Keck images within 9 annuli centred on the galaxy. +" For objects in the corner of the CCD. the SD was calculated by taking into account the area of the annulus ""missing oll the edges of the chip."," For objects in the corner of the CCD, the SD was calculated by taking into account the area of the annulus `missing' off the edges of the chip." + This method allowed us to calculate the density out to a radius of 232 aresec (~60 kpe)., This method allowed us to calculate the density out to a radius of 232 arcsec $\sim60$ kpc). + The resulting surface density profile is shown in Fie. 14..., The resulting surface density profile is shown in Fig. \ref{fig:sdprofilek}. + The error bars simply rellect the Poisson errors on the number of GCs in each bin., The error bars simply reflect the Poisson errors on the number of GCs in each bin. + At laree radii the surface density decreases ike a power-law with radius (open squares)., At large radii the surface density decreases like a power-law with radius (open squares). + At radii «140 aresee however. there appears to be a significant deficit in he number of GC's detected in our Keck images (shown bv open circles).," At radii $<140$ arcsec however, there appears to be a significant deficit in the number of GCs detected in our Keck images (shown by open circles)." + Phe most likely cause for this is the fact that GCs at small racii are superimposed on the bright body of he galaxy which also possesses à steep radial gradient at jese distances., The most likely cause for this is the fact that GCs at small radii are superimposed on the bright body of the galaxy which also possesses a steep radial gradient at these distances. + Although an elliptical model of the galaxy was subtracte from each of the initial images. this cllect seems to have caused a reduction in our ability to detect GCs as our surface density continues to rise towards he centre at these radii as shown in Fig. 15..," Although an elliptical model of the galaxy was subtracted from each of the initial images, this effect seems to have caused a reduction in our ability to detect GCs as our surface density continues to rise towards the centre at these radii as shown in Fig. \ref{fig:sdprofileh}." + In addition. we were unable to detect GCs in the Ixeck. images within he central 33 aresee due to the [arge saturated. region a he centre of the £ band image.," In addition, we were unable to detect GCs in the Keck images within the central 33 arcsec due to the large saturated region at the centre of the $I$ band image." + To quantify the outer SD xofile of the GCs detected in our Week images. we fittec he outer-most points in Fig.," To quantify the outer SD profile of the GCs detected in our Keck images, we fitted the outer-most points in Fig." + 1H. with a function of the form p=por’., \ref{fig:sdprofilek} with a function of the form $\rho=\rho_{0}r^{\alpha}$. + Εις fit is shown by the dashed line in Fig. 14.., This fit is shown by the dashed line in Fig. \ref{fig:sdprofilek}. + We ind that pj—0.543.3 and à=107£0.25., We find that $\rho_{0}=0.5\pm3.3$ and $\alpha=-1.07\pm0.25$. + Dackgrounm contamination of the sample would add a constant SD leve o the profile., Background contamination of the sample would add a constant SD level to the profile. + Although this contamination is likely to be small. ideally it would be taken into consideration when computing the fit.," Although this contamination is likely to be small, ideally it would be taken into consideration when computing the fit." + Llowever. our data are not sullicien o calculate the level of contamination and the caleulatec slope of the profile should. be treated: with caution.," However, our data are not sufficient to calculate the level of contamination and the calculated slope of the profile should be treated with caution." + The solid line in Fig., The solid line in Fig. + 14 represents the stellar. profile of the galaxy., \ref{fig:sdprofilek} represents the stellar profile of the galaxy. + The galaxy profile used is not in the usual units of surface brightness but has been converted to and arbitrarily shifted in the Y. direction to allow simple comparison of the slopes., The galaxy profile used is not in the usual units of surface brightness but has been converted to and arbitrarily shifted in the Y direction to allow simple comparison of the slopes. + We measure a slope of 190. for the galaxy profile using the measured. intensities at. all radii., We measure a slope of $-1.9\pm0.1$ for the galaxy profile using the measured intensities at all radii. + It thus appears that the GC profile is Patter than the uncerlving stellar profile., It thus appears that the GC profile is flatter than the underlying stellar profile. + In order to investigate the SD profile within the central regions of the galaxy. we use the images.," In order to investigate the SD profile within the central regions of the galaxy, we use the images." + This profile is shown in Fig., This profile is shown in Fig. + 15. after correction for the areas of the annular bins missing from the ΑΕΡΟΣ field.ofview., \ref{fig:sdprofileh} after correction for the areas of the annular bins missing from the WFPC2 field–of–view. + Each annulus contains 25 GCs with the exception of the two inner bins which contain ~LO GCs., Each annulus contains $\sim25$ GCs with the exception of the two inner bins which contain $\sim10$ GCs. + We find that the surface density follows a power-law profile exterior tor11 aresec (Le. the outer 6 data points)., We find that the surface density follows a power-law profile exterior to $r\sim11$ arcsec (i.e. the outer 6 data points). +" We again fitted these points with a function of the form p=por"" and find a=098-Ε0.15 and po=0.27dE0.19 GC=.", We again fitted these points with a function of the form $\rho=\rho_{0}r^{\alpha}$ and find $\alpha=-0.90\pm0.15$ and $\rho_0=0.27\pm0.19$ GC. + The slope of this fit is within the range of values measured. for other ellipticals bv other authors (e.g. 2)) and also consistent with the slope calculated from the Ixeck sample., The slope of this fit is within the range of values measured for other ellipticals by other authors (e.g. \pcite{forbes97}) ) and also consistent with the slope calculated from the Keck sample. + Also shown in Fig., Also shown in Fig. + 15. is the stellar profile of the galaxy., \ref{fig:sdprofileh} is the stellar profile of the galaxy. + This has a slope of. —1.9d:0.1., This has a slope of $-1.9\pm0.1$. + The GC profile is significantly. Latter han that of the galaxy. which is often the case in other systems (e.g. Crillmair. Pritehet van den οσα 1986: 7:0071 7?)).," The GC profile is significantly flatter than that of the galaxy, which is often the case in other systems (e.g. Grillmair, Pritchet van den Bergh 1986; \pcite{harris86,lauer86,forbes98,ashman98}) )." +" Within ~11 aresee there is evidence for a latteningὃν of the profile indicatingo the presence of a ""core region.", Within $\sim11$ arcsec there is evidence for a flattening of the profile indicating the presence of a `core region'. + The core radius of the NGC 1700 GC distribution was also measured by ?. to | +1.6 kpe corresponding Oo Il aresec. although only 89 GC's were detected.," The core radius of the NGC 1700 GC distribution was also measured by \scite{forbes96} to be $2.7\pm1.6$ kpc corresponding to $\sim11$ arcsec, although only 39 GCs were detected." + The oesence of à core region is also commonly seen in other ellipticals and 7. define a relationship between GC system core radius and parent galaxy luminosity., The presence of a core region is also commonly seen in other ellipticals and \scite{forbes96} define a relationship between GC system core radius and parent galaxy luminosity. + This relation is in, This relation is in +"by the dashed. curve in 44 for ο=0.006 cm7. 3= 0.62. and 7,=6.5 keV. The required. core radius is 436 kpe.","by the dashed curve in 4 for $n_o = 0.006$ $^{-3}$, $\beta = 0.62$ , and $T_o=6.5$ keV. The required core radius is 436 kpc." + It is evident from 44 that the model still deviates significantly. from. pure isothermal. with a roughly a factor of two variation around the central temperature.," It is evident from 4 that the model still deviates significantly from pure isothermal, with a roughly a factor of two variation around the central temperature." + Moreover. compared to actual elusters. the implied core radius for this temperature is too large by a factor of two.," Moreover, compared to actual clusters, the implied core radius for this temperature is too large by a factor of two." + For these near isothermal 4οὐ mocels. E determined. the mean emission. weighted temperature. the total gas mass within the cut-oll radius ane the X-ray. luminosity within the 0.1 to 2.4 keV band.," For these near isothermal $\beta$ models, I determined the mean emission weighted temperature, the total gas mass within the cut-off radius and the X-ray luminosity within the 0.1 to 2.4 keV band." + Phe resulting gas mass-temperature relation is almost identical to that of MOND isothermal spheres (the dashed curve in 11) and thus again much larger than the observationally inferred. gas mass of X-ray emitting clusters The Iuminositv-tempoerature relation for these MOND j models is shown in 22 by the dotted. curve., The resulting gas mass-temperature relation is almost identical to that of MOND isothermal spheres (the dashed curve in 1) and thus again much larger than the observationally inferred gas mass of X-ray emitting clusters The luminosity-temperature relation for these MOND $\beta$ models is shown in 2 by the dotted curve. + Unsurprisingly. this nearly coincides with the caleulated relation for MOND isothermal spheres and. is clearly an equally poor description of reality.," Unsurprisingly, this nearly coincides with the calculated relation for MOND isothermal spheres and is clearly an equally poor description of reality." + “Phe basic problem. is that. for both MOND isothermal spheres and MOND 3 nmiocels. the core radii are too large.," The basic problem is that, for both MOND isothermal spheres and MOND $\beta$ models, the core radii are too large." + Ht is evident that some ingredient is missing from these models: that an additional mass component must be added to decrease the gas core radius at à given temperature., It is evident that some ingredient is missing from these models; that an additional mass component must be added to decrease the gas core radius at a given temperature. + For à cluster with an observed. density and. temperature distribution. 11 and 2 directly vielel Mr). the interior dynamical mass as a function of radius.," For a cluster with an observed density and temperature distribution, 1 and 2 directly yield M(r), the interior dynamical mass as a function of radius." +" In the Newtonian regime this is given simply by ∖∖⇢⊔↓↕↳∖↓↻↓∖⊽∐⊳⇂⋜↧↓∡⊲↓⊔⋏∙≟∕∣↿⇁≀⋅↴↿∪⋡⋖⋅⋏∙≟⊀↓∖⇁∢⊾⊔∣⋡∙∖⇁∢⋅⊏↥⋡⇉⇉≼⋱⇂↓↕⋖⋅ ∠⇂∙∖⇁↓↥⋜↧↓↥↓↕≼∼⋜↧↓⊔↓⋜↧⊳∖⊳∖⊲↓⊳∖ where a is the ""observed? acceleration Obviously. from 99 in the limit of large accelerations (e>> a.) the MOND clvnamical mass is equivalent to the Newtonian dynamical mass."," In the Newtonian regime this is given simply by With MOND, taking $\mu(x)$ to be given by 2c, the dynamical mass is where a is the “observed"" acceleration Obviously, from 9 in the limit of large accelerations $a>>a_o$ ) the MOND dynamical mass is equivalent to the Newtonian dynamical mass." +" We may apply these relations to the Coma cluster which has a density. clistribution well-lit by a ;-mocdel with 3 = 0.71. ες 216 kpe. n, = 00386 (Reiprich 2001). an observed racial temperature profile (Arnaud οἱ al."," We may apply these relations to the Coma cluster which has a density distribution well-fit by a $\beta$ -model with $\beta$ = 0.71, $r_c$ = 276 kpc, $n_o$ = .0036 (Reiprich 2001), an observed radial temperature profile (Arnaud et al." + 2001) and average emission. weighted. temperature of 8.6 keV. The results are shown in 55 which is the cumulative Newtonian dynamical mass (dotted line). the MOND dynamical mass (solid. line). and the gas mass (dashed line).," 2001) and average emission weighted temperature of 8.6 keV. The results are shown in 5 which is the cumulative Newtonian dynamical mass (dotted line), the MOND dynamical mass (solid line), and the gas mass (dashed line)." + Here it is evident that while the Newtonian dvnamical mass continues to increase at radius of 1 Alpe. the MOND mass has essentially converged.," Here it is evident that while the Newtonian dynamical mass continues to increase at radius of 1 Mpc, the MOND mass has essentially converged." + Llowever. the total MOND mass is still a factor of four times larger than the mass in gas alone.," However, the total MOND mass is still a factor of four times larger than the mass in gas alone." + This discrepancy cannot. be accounted. for by the stellar content of the galaxies which. assuming a mass-to-light ratio of seven. amounts only to about 1075 M. within 1 Mpe CEhe White 1988).," This discrepancy cannot be accounted for by the stellar content of the galaxies which, assuming a mass-to-light ratio of seven, amounts only to about $10^{13}$ $_\odot$ within 1 Mpc (The White 1988)." +" This is. in fact. the discrepancy pointed out by The and White a discrepancy which can be resolved. by increasing e, bv a factor of 3 or 4 over the value required [or galaxy rotation curves. or bv admitting the presence of non-Iuminous mass which MOND does not remove."," This is, in fact, the discrepancy pointed out by The and White– a discrepancy which can be resolved by increasing $a_o$ by a factor of 3 or 4 over the value required for galaxy rotation curves, or by admitting the presence of non-luminous mass which MOND does not remove." + The density of this non-Iuminous component is roughly constant and contained within two gas core radii., The density of this non-luminous component is roughly constant and contained within two gas core radii. + In other words the missing mass is essentially present in the inner regions of the cluster as implied. in the work of Aguirre. Shave. anc Quataert (2001).," In other words the missing mass is essentially present in the inner regions of the cluster as implied in the work of Aguirre, Shaye, and Quataert (2001)." + Επι suggests that. with AIOND. clusters might be described by a two component model: a gas component with a density. distribution given w the z;-model and a dark central component of constant density and a radius of about two times the core radius of he the gas clistribution.," This suggests that, with MOND, clusters might be described by a two component model: a gas component with a density distribution given by the $\beta$ -model and a dark central component of constant density and a radius of about two times the core radius of the the gas distribution." +" In Coma. the central surface densitv of the dark component is about Sy=240AL. /pc. which is comparable o the MOND surface density of a,2700AL. pe."," In Coma, the central surface density of the dark component is about $\Sigma_d = 240\,\,M_\odot$ $^2$ , which is comparable to the MOND surface density of $a_o/G \approx 700\,\,M_\odot$ $^2$." + This is the characteristic central surface densitv o£ NOND selt-eravitating isothermal svstems (Alilerom 1984)., This is the characteristic central surface density of MOND self-gravitating isothermal systems (Milgrom 1984). + Therefore. o determine scaling relations. Lo assume that the non-uminous Component is a rigid sphere having a central surface surface density equal to that in the Coma eluster and radius twice that of the σας core radius. as in Coma.," Therefore, to determine scaling relations, I assume that the non-luminous component is a rigid sphere having a central surface surface density equal to that in the Coma cluster and radius twice that of the gas core radius, as in Coma." + Then the constant densityof the second component is, Then the constant densityof the second component is +magnetic energy residing in large scale fields. 1.8.. where we have used that (Q~9/5 for a Keplerian disks.,"magnetic energy residing in large scale fields, i.e., where we have used that $Q\sim 9/8$ for a Keplerian disks." +" The lower limit for f£, depends on the dimensionless parameters characterizing the angular momentum transport efficiency. a. and magnetic pressure support. 0. though the product αὐ."," The lower limit for $f_{\rm s}$ depends on the dimensionless parameters characterizing the angular momentum transport efficiency, $\alpha$, and magnetic pressure support, $\beta$ , though the product $\alpha\beta$." + This result is very encouraging because. despite the fact that both quantities vary over several orders of magnitude across simulations carried out in domains with various sizes and with different field strengths and geometries (seePessahetal.2006a.andreferencestherein).. their product remains nearly constant with a3~0.5 (seeBlackmanetal.2008.andreferences therein)..," This result is very encouraging because, despite the fact that both quantities vary over several orders of magnitude across simulations carried out in domains with various sizes and with different field strengths and geometries \citep[see][and +references therein]{PCP06a}, their product remains nearly constant with $\alpha \beta \simeq 0.5$ \citep[see][and references therein]{BPV08}." + The upper limits for the fraction of magnetic energy associated with large scale field structures are shown in Figure 2 for three values of the product o.j=[1.0.0.5.0.1].," The upper limits for the fraction of magnetic energy associated with large scale field structures are shown in Figure \ref{fig:fs_vs_q} for three values of the product $\alpha\beta = \{1.0,0.5,0.1\}$." + The minimum constraints on f. illustrated. show that. if the observed non-thermal emission is interpreted as coronal emission due to magnetic dissipation from buoyant fields that were produced within a turbulent disk. then a significant fraction of the energy budget of the magnetic field build in the disk must be produced in fields of scale />7...," The minimum constraints on $f_{\rm s}$ illustrated show that, if the observed non-thermal emission is interpreted as coronal emission due to magnetic dissipation from buoyant fields that were produced within a turbulent disk, then a significant fraction of the energy budget of the magnetic field build in the disk must be produced in fields of scale $l>l_{\rm c}$." + Since Figure | shows that in general />. together these figures highlight the importance of large scale magnetic fields in powering coronae.," Since Figure \ref{fig:lc_to_H} shows that in general $l>l_{\rm t}$, together these figures highlight the importance of large scale magnetic fields in powering coronae." + Finally we note that MHD jets models typically invoke global scale fields. c.f. Ferreira(2007).," Finally we note that MHD jets models typically invoke global scale fields, c.f. \citet{f07}." +. If these fields arise from the opening of coronal fields (as in the sun: Wang Sheeley 2003: Blackman Tan 2004) then the mechanical luminosities of Jets would represent an additional contribution to that which results from the buoyant rise of magnetic fields., If these fields arise from the opening of coronal fields (as in the sun; Wang Sheeley 2003: Blackman Tan 2004) then the mechanical luminosities of jets would represent an additional contribution to that which results from the buoyant rise of magnetic fields. +" Specifically. D,. in Equation (9)) would be repalced by D,| where the latter is the jet power."," Specifically, $D_c$ in Equation \ref{q}) ) would be repalced by $D_c +D_j$ where the latter is the jet power." + This would further increase Djour lower limits on fy., This would further increase our lower limits on $f_s$. +" In our physical picture. the coronal emission fraction 4 depends on the fraction of magnetic energy f, produced in scales larger than the critical scale {ο."," In our physical picture, the coronal emission fraction $q$ depends on the fraction of magnetic energy $f_{\rm s}$ produced in scales larger than the critical scale $l_{\rm c}$." + We incorporate the density contrast between buoyant structures and the ambient medium required for coronal feeding., We incorporate the density contrast between buoyant structures and the ambient medium required for coronal feeding. +" Also. our lower limit on f, employs c, as an upper limit for the buoyant rise time."," Also, our lower limit on $f_{\rm s}$ employs $c_s$ as an upper limit for the buoyant rise time." + We use the a-viscosity prescription only for dissipation inside the disk: the coronal dissipation is modeled as a distinct contribution (see Eqs. [7]], We use the $\alpha$ -viscosity prescription only for dissipation inside the disk; the coronal dissipation is modeled as a distinct contribution (see Eqs. \ref{eq:D_d}] ] + and [8]])., and \ref{eq:D_c}] ]). + These features differ from those of Merloni Fabian (2002) and the ones summarized in Wang et al. (, These features differ from those of Merloni Fabian (2002) and the ones summarized in Wang et al. ( +2004).,2004). + In those treatments. there ts no explicit distinction between the density inside and outside the buoyant structures or the role of large and small scale magnetic fields.," In those treatments, there is no explicit distinction between the density inside and outside the buoyant structures or the role of large and small scale magnetic fields." + Furthermore. the coronal emission fraction is considered to be a subset of the total dissipation. modeled entirely with the o-viscosity prescription.," Furthermore, the coronal emission fraction is considered to be a subset of the total dissipation, modeled entirely with the $\alpha$ -viscosity prescription." + Also. the buoyant rise time is taken to be the Alfvénn speed: less than our upper limit value of e..," Also, the buoyant rise time is taken to be the Alfvénn speed; less than our upper limit value of $c_{\rm s}$." + In the present work we implicitly consider systems with low enough aceretion rates such that radiation pressure is unimportant., In the present work we implicitly consider systems with low enough accretion rates such that radiation pressure is unimportant. + A subtlety associated with radiation pressure is that the thermal photosphere can be significantly higher than the scale at which the magnetic pressure dominates the thermal pressure (e.g. Hirose et al., A subtlety associated with radiation pressure is that the thermal photosphere can be significantly higher than the scale at which the magnetic pressure dominates the thermal pressure (e.g. Hirose et al. + 2009)., 2009). + Thus the non-thermal coronal emission arises at larger scale heights compared to when radiation pressure is 1gnorable., Thus the non-thermal coronal emission arises at larger scale heights compared to when radiation pressure is ignorable. + The reduction of the coronal emission fraction for such large accretion rate systems is observed in Wang et al. (, The reduction of the coronal emission fraction for such large accretion rate systems is observed in Wang et al. ( +2004).,2004). + For a fixed magnetic spectrum. this would also be expected in our paradigm. because /7 in Equation (2)) is the scale that we consider a buoyant structure must rise to contribute to coronal emission.," For a fixed magnetic spectrum, this would also be expected in our paradigm, because $H$ in Equation \ref{eq:lc}) ) is the scale that we consider a buoyant structure must rise to contribute to coronal emission." + If the buoyant structure has to move higher. then /; would be larger and less of the magnetic energy would survive the buoyant rise.," If the buoyant structure has to move higher, then $l_{\rm c}$ would be larger and less of the magnetic energy would survive the buoyant rise." + In Merloni Fabian (2002) the reduction in coronal emission for large radiation pressure occurs because their coronal emission fraction depends inversely on the total disk pressure., In Merloni Fabian (2002) the reduction in coronal emission for large radiation pressure occurs because their coronal emission fraction depends inversely on the total disk pressure. + Starting with the assumption that coronal luminosity from a turbulent accretion disk results from buoyant magnetic structures that survive. turbulent shredding for at least one vertical density scale height. we derived lower limits on: (i) the scale of such magnetic structures and (/j) the fraction of magnetic energy that needs to be produced above this scale within. the disk to account for observed values of coronal to bolometric luminosity.," Starting with the assumption that coronal luminosity from a turbulent accretion disk results from buoyant magnetic structures that survive turbulent shredding for at least one vertical density scale height, we derived lower limits on: ) the scale of such magnetic structures and ) the fraction of magnetic energy that needs to be produced above this scale within the disk to account for observed values of coronal to bolometric luminosity." +" In our minimalist model. we considered the buoyant structures to be in pressure equilibrium with the ambient medium but to have an additional magnetic energy contribution from scales above the critical scale /,. and a lower density."," In our minimalist model, we considered the buoyant structures to be in pressure equilibrium with the ambient medium but to have an additional magnetic energy contribution from scales above the critical scale $l_{\rm c}$, and a lower density." + We find that typical ratios of coronal to. bolometric luminosity observed in AGN require the critical scale for buoyancy to robustly exceed the characteristic scale set by turbulent motions and that double digit percentages of magnetic energy should reside in fields above this scale., We find that typical ratios of coronal to bolometric luminosity observed in AGN require the critical scale for buoyancy to robustly exceed the characteristic scale set by turbulent motions and that double digit percentages of magnetic energy should reside in fields above this scale. + This is consistent with recent work highlighting the importance of in situ large scale dynamos in feeding coronae (Blackman 2007: Vishniac 2009)., This is consistent with recent work highlighting the importance of in situ large scale dynamos in feeding coronae (Blackman 2007; Vishniac 2009). + Our results complement growing motivation to consider larger domains in. stratified MRI simulations and motivate analysis of the magneticenergy spectra produced therein., Our results complement growing motivation to consider larger domains in stratified MRI simulations and motivate analysis of the magneticenergy spectra produced therein. + The results also resonate with models of accretion disks in which buoyancy and coronal dissipation play a primary role for transport (Lynden-Bell 1969: Field Rogers 1993)., The results also resonate with models of accretion disks in which buoyancy and coronal dissipation play a primary role for transport (Lynden-Bell 1969; Field Rogers 1993). +but the extreme far-UV extinction is not observed along anv line of sight in the galaxy.,but the extreme far-UV extinction is not observed along any line of sight in the galaxy. + The peak/platean at 1400 is also not observed in extinction proliles., The peak/plateau at 1400 is also not observed in extinction profiles. + Therefore. pure nanodiamoncds are highly unlikely in ISM.," Therefore, pure nanodiamonds are highly unlikely in ISM." + Using the optical properties given by Lewisetal.(1939).. Aannestacl(1995) incorporated iuodiamond in modeling (the extinction curve and predicted a very low percentage of 1anocdiamond dust.," Using the optical properties given by \citet{lewis89}, , \citet{aannestad95} incorporated nanodiamond in modeling the extinction curve and predicted a very low percentage of nanodiamond dust." + Nanodiamonds may occur inside carbonaceous matter in ISAM and manilest (heir presence by modifving the overall extinction profile., Nanodiamonds may occur inside carbonaceous matter in ISM and manifest their presence by modifying the overall extinction profile. + latοἱal.(2008) report. triple avered erainwith silicate. sp? and sp? carbonaceous material and Yastrebov&Smith(2009) report nanodiamond enveloped in glassv carbon shells.," \citet{iati08} report triple layered grainwith silicate, $sp^2 $ and $sp^3 $ carbonaceous material and \citet{yastrebov09} report nanodiamond enveloped in glassy carbon shells." + Considering (hat surface eraphitization of nanodiamond leads to core-mantle like shell structure (INsvonetal.2008:Lietal. 2008).. extinction efficiency. ealeulations are reported for spherical nanocdiamond inskle eraphite ellipsoidal mantle.," Considering that surface graphitization of nanodiamond leads to core-mantle like shell structure \citep{kwon08, li08}, extinction efficiency calculations are reported for spherical nanodiamond inside graphite ellipsoidal mantle." + Extinction properties of graphitic particles are well studied (Draine&Lee1984:DraineMalhotra 1993).," Extinction properties of graphitic particles are well studied \citep{draine-lee84,draine93}." +. The (2/3—1/3) approximation for dielectric anisotropy is found to be &ood for small particles and can also be used for graphite with coatings 1993)., The $(2/3 - 1/3)$ approximation for dielectric anisotropy is found to be good for small particles and can also be used for graphite with coatings \citep{draine93}. +. Belractive index data of 10nim graphite at 20 Ix is taken from D. T. Draines website and the (2/3—1/3) approximation applied., Refractive index data of $10 ~nm$ graphite at 20 K is taken from B. T. Draine's website and the $(2/3 - 1/3)$ approximation applied. + The nanodiamond-graphite core-mantle extinction efficiency and normalized) extinction are shown in fig.6.. for mantle shape 432 and size 5nm.," The nanodiamond-graphite core-mantle extinction efficiency and normalized extinction are shown in \ref{fig6}, for mantle shape 432 and size $5 ~nm$." + The volume percentage of core nanodiamond is also mentioned., The volume percentage of core nanodiamond is also mentioned. + It is seen that the 2175 peak in graphite gets modified due to the presence of nanocdiamond core., It is seen that the 2175 peak in graphite gets modified due to the presence of nanodiamond core. + On increasing the nanodiamond percentage. the peak is lowered. broadened ancl slightly blue shifted.," On increasing the nanodiamond percentage, the peak is lowered, broadened and slightly blue shifted." + In the Fu-UV region there is sharp rise in extinction (liat is steeper for larger nanocdiamond percentage., In the far-UV region there is sharp rise in extinction that is steeper for larger nanodiamond percentage. + Observed extinction along various lines of sight show similar 2175 feature lowering and broadening associated with enhanced far-UV rise (Carclelli&Savage1988:FitzpatrickMassa1990.2005.2007).," Observed extinction along various lines of sight show similar 2175 feature lowering and broadening associated with enhanced far-UV rise \citep{cardelli88, fitz-massa90, fitz-massa05, fitz-massa07}." +. Some such stellar regions. viz.," Some such stellar regions, viz." + IID210121. IID204327. IID29641. that do not follow the CCM rule (Carclellietal.1989). are termed as non-CCM sites (Valencieetal.2004).," HD210121, HD204827, HD29647, that do not follow the CCM rule \citep{CCM89} are termed as non-CCM sites \citep{valencic04}." +.. Also there are some sighi-lines. e.g. IID3191. ILD284339. ILD284841. ILD287150 ete. 2007)..," Also there are some sight-lines, e.g. HD3191, HD284839, HD284841, HD287150 etc. \citep{fitz-massa07}, ," + that exhibit similar broad bump and steep[ir-UV. rise., that exhibit similar broad bump and steepfar-UV rise. + Incorporating a mantle broadens the 2175 peak and to model this feature, Incorporating a mantle broadens the 2175 peak and to model this feature + Incorporating a mantle broadens the 2175 peak and to model this feature., Incorporating a mantle broadens the 2175 peak and to model this feature +debate.,debate. + What is not in dispute is the observational evidence of galaxies at the brieht-end of the galaxy luminosity function with ongoing. low-luminosity active nuclei.," What is not in dispute is the observational evidence of galaxies at the bright-end of the galaxy luminosity function with ongoing, low-luminosity active nuclei." + It is thus no surprise that most. current. scmiu-analytie naioclels incorporate active galactic nucle: (AGN) heating as a kev ingredient., It is thus no surprise that most current semi-analytic models incorporate active galactic nuclei (AGN) heating as a key ingredient. +" ? called this the ""radio mode of AGN evolution.", \cite{Croton2006} called this the “radio mode” of AGN evolution. +" Another process which can shut olf star formation in subhalos is the stripping of gas when a satellite falls into a larger halo. called ""strangulation."," Another process which can shut off star formation in subhalos is the stripping of gas when a satellite falls into a larger halo, called “strangulation”." +" There is clear evidence of a population of “rec and dead"" earlv-tvpe. even in voids (7). vet db is not obvious whether either or both of these mechanisms (ie. AGN heating and strangulation) can operate cllicientLy in voids or whether some other mechanism is needed."," There is clear evidence of a population of “red and dead” early-type even in voids \citep{Croton2005}, yet it is not obvious whether either or both of these mechanisms (i.e. AGN heating and strangulation) can operate efficiently in voids or whether some other mechanism is needed." + We investigate this question via semi-analvtic simulations. and find that strangulation plavs a minor role.," We investigate this question via semi-analytic simulations, and find that strangulation plays a minor role." + We find that heating when the central galaxy passes the critical mass is sullicient to account for the observed abundance of carly-twpe galaxies. in. voids., We find that heating when the central galaxy passes the critical mass is sufficient to account for the observed abundance of early-type galaxies in voids. + The different luminosity. functions of earlv-tvpe galaxies. between voids. ancl mean densitv environments can thus be entirely. attributed. to the dilference. in the halo mass. function. in the two environments. within the accuracy of present measurements.," The different luminosity functions of early-type galaxies between voids and mean density environments can thus be entirely attributed to the difference in the halo mass function in the two environments, within the accuracy of present measurements." + This explanation for the earlv-tvpe luminosity function has observable consequences as. discussed: below., This explanation for the early-type luminosity function has observable consequences as discussed below. + LE these are verified. it will lend credence to the physical interpretation of the semi-analvtie model.," If these are verified, it will lend credence to the physical interpretation of the semi-analytic model." + This paper is organised. as follows., This paper is organised as follows. + Sections 2 and 3 describe the galaxy. formation. model and our measure of environment within the Millennium Simulation. respectively.," Sections \ref{sec:model} and \ref{sec:density} describe the galaxy formation model and our measure of environment within the Millennium Simulation, respectively." + We present our void galaxy analysis in Section and discuss our results in light. of recent work ancl also within the broader context of galaxy formation theory., We present our void galaxy analysis in Section \ref{sec:results} and discuss our results in light of recent work and also within the broader context of galaxy formation theory. + Finally. Section 5 provides a brief summary.," Finally, Section \ref{sec:summary} provides a brief summary." +" Throughout we assume a standard WNLAD first vear ACDAL cosmology (?2) and Lubble parameter 44,=1005.thms 1 |."," Throughout we assume a standard WMAP first year $\Lambda$ CDM cosmology \citep{Spergel2003, Seljak2005} and Hubble parameter $H_0=100\,h^{-1}$ $^{-1}$ $^{-1}$." + The ealaxy formation model we use {ο study void environments is identical to that described in 2. (including parameter choices)., The galaxy formation model we use to study void environments is identical to that described in \cite{Croton2006} (including parameter choices). + This model is implemented on top of the Millennium Run ACDAIL dark matter simulation (2).., This model is implemented on top of the Millennium Run $\Lambda$ CDM dark matter simulation \citep{Springel2005}. + Below we briellv outline the relevant aspects of the simulation anc model to our current work. and refer the interested. reader to the above references for further information.," Below we briefly outline the relevant aspects of the simulation and model to our current work, and refer the interested reader to the above references for further information." + The Millennium Run simulation follows the cvnamica evolution. of Sly107 dark matter particles. in. a periodicMN box o side-leneth 5005. 1NMpe with a mass resolution per particle of 8.6.107ΝΤΟ.," The Millennium Run simulation follows the dynamical evolution of $10^{10}$ dark matter particles in a periodic box of side-length $500\,h^{-1}$ Mpc with a mass resolution per particle of $8.6\times +10^8\,h^{-1}{\rm M}_{\odot}$." + DH adopts cosmological parameter values consistent with a combined analysis of the 2dFGRS (7). anc first vear WALADP data (22).," It adopts cosmological parameter values consistent with a combined analysis of the 2dFGRS \citep{Colless2001} + and first year WMAP data \citep{Spergel2003, Seljak2005}." + Priends-ot-£riends (FOR) halos are identified in the simulation using a linking length of 0.2 the mean particle separation. while substructure each FOP halo is found with an improved. and extended: version of the algorithm of ?..," Friends-of-friends (FOF) halos are identified in the simulation using a linking length of 0.2 the mean particle separation, while substructure each FOF halo is found with an improved and extended version of the algorithm of \citet{Springel2001}." + Having determined. all halos and subhalos at all output snapshots. the hierarchical merging trees are constructed: these deseribe in detail how structures grow as the universe evolves.," Having determined all halos and subhalos at all output snapshots, the hierarchical merging trees are constructed; these describe in detail how structures grow as the universe evolves." + These trees form the backbone onto which we couple our model of galaxy formation., These trees form the backbone onto which we couple our model of galaxy formation. + Inside each tree. virialised dark matter halos at. each redshift are assumed to attract ambient eas from the surrounding medium. from which galaxies form and evolve.," Inside each tree, virialised dark matter halos at each redshift are assumed to attract ambient gas from the surrounding medium, from which galaxies form and evolve." + Our model ellectively tracks ai wide range of galaxy formation physics in cach halo using simple paranietrised forms. including reionization of the inter-galactic medium at high redshift. radiative cooling of hot gas and the formation of cooling Hows. star formation in the cold. disk and the resulting supernova feedback. black hole growth ancl [GN feedback through the ‘quasar’ ancl radio! epochs of AGN evolution. metal enrichment of the inter-ealactic and intra-cluster. medium. anc galaxy morphology shaped: through mergers and merger-induced starbursts.," Our model effectively tracks a wide range of galaxy formation physics in each halo using simple parametrised forms, including reionization of the inter-galactic medium at high redshift, radiative cooling of hot gas and the formation of cooling flows, star formation in the cold disk and the resulting supernova feedback, black hole growth and AGN feedback through the `quasar' and `radio' epochs of AGN evolution, metal enrichment of the inter-galactic and intra-cluster medium, and galaxy morphology shaped through mergers and merger-induced starbursts." +" At 2-0 the galaxy formation model contains approximately 9 million galaxies brighter than our completeness limit of Mi,οσμή=15.8 (representing the mean luminosity of a central galaxy in a halo containing 64 particles)."," At $z\!=\!0$ the galaxy formation model contains approximately 9 million galaxies brighter than our completeness limit of $M_{\rm b_J}\!-\!5\log_{10}\! +h\!=\!-15.8$ (representing the mean luminosity of a central galaxy in a halo containing 64 particles)." +" A critical feature for the success of this model is the inclusion ofan AGN component and the separation of AGN into their high and low aceretion states. called the “quasar mode” and. ""radio mode” respectively."," A critical feature for the success of this model is the inclusion of an AGN component and the separation of AGN into their high and low accretion states, called the “quasar mode” and “radio mode” respectively." + Within this picture the two ACN modes are distinct in their cause and. effect., Within this picture the two AGN modes are distinct in their cause and effect. + Importantly for the work of ?.. the radio mode was used to suppress the cooling of gas onto central galaxies living in eroup and cluster-sized halos. and is primarily important at late times (tvpically z« 1) and not earlier (where the SET density of the universe peaks. e.g. 2)).," Importantly for the work of \cite{Croton2006}, the radio mode was used to suppress the cooling of gas onto central galaxies living in group and cluster-sized halos, and is primarily important at late times (typically $z\!<\!1$ ) and not earlier (where the SFR density of the universe peaks, e.g. \citealt{Madau1996}) )." + This model was tuned to provide a good match to the local luminosity function and. colours of galaxies., This model was tuned to provide a good match to the local luminosity function and colours of galaxies. + Phe assumed radio mode black hole accretion rate. is very ellicient above a critical halo mass threshol which is approximately constant with time.," The assumed radio mode black hole accretion rate, is very efficient above a critical halo mass threshold which is approximately constant with time." +" Εις mass turns out to be Ale,z1007.MAL."," This mass turns out to be $M_{\rm +vir} \approx 10^{12 - 13} M_{\odot}$." + From this point-of-view. halos grow with time until they cross the critical halo mass. alter which the radio mode dominates. cooling gas slows.then stops. and star formation shut-down follows.," From this point-of-view, halos grow with time until they cross the critical halo mass, after which the radio mode dominates, cooling gas slows,then stops, and star formation shut-down follows." + Note that no environment dependence has been assumed. in this implementation of radio mode heating., Note that no environment dependence has been assumed in this implementation of radio mode heating. + We will return to this point in Section 4.., We will return to this point in Section \ref{sec:results}. + ‘To facilitate a fair comparison between the model. and observed Luminosity functions we determine environments in the Millennium Simulation box in the same way as ο eid forthe 20GIBS., To facilitate a fair comparison between the model and observed luminosity functions we determine environments in the Millennium Simulation box in the same way as \cite{Croton2005} did forthe 2dFGRS. + This is actually much simpler to do than with a magnitude limited redshift survey. as one has a perfect measure of survey geometry (a box in our case with volume Vig) and selection function. (uniform: ancl complete).," This is actually much simpler to do than with a magnitude limited redshift survey, as one has a perfect measure of survey geometry (a box in our case with volume $V_{\rm box}$ ) and selection function (uniform and complete)." + We consider the redshift zero snapshot of the mocel. which we call the 7Iocal population.," We consider the redshift zero snapshot of the model, which we call the “local” population." + Note that. although the 2dECGLIUS has a median redshift o£ 2 70.1. all 2dPORS magnitudes are k-corrected to 2 —0. and for our purposes we assume that the evolution of structure between z—0.1 and z—0 is negligible.," Note that, although the 2dFGRS has a median redshift of $z\!\sim\!0.1$ , all 2dFGRS magnitudes are k-corrected to $z\!=\!0$ and for our purposes we assume that the evolution of structure between $z\!=\!0.1$ and $z\!=\!0$ is negligible." +rowever. vield a Consistent result of 0.43 for the mass ratio of LP Pee (Fig. 2)).,"however, yield a consistent result of 0.43 for the mass ratio of IP Peg (Fig. \ref{fig:mratio}) )." + This is in disagreement with q = anc q = 0.55)0.62 found by ? ancl 7.. but agrees with )35«q«0.49 (2).. q = 0.3940.04 (7). and q = 0.32—0.08 (?)..," This is in disagreement with $q$ = 0.55--0.63 and $q$ = 0.55–0.62 found by \citet{martin89} and \citet{marsh88a}, , but agrees with $<$ $<$ 0.49 \citep{wood86}, $q$ = $\pm$ 0.04 \citep{catalan99b} and $q$ = $\pm$ 0.08 \citep{beekman00}." + AIL the authors. except 2.. mace corrections for the ellects of irradiation where appropriate.," All the authors, except \citet{beekman00}, made corrections for the effects of irradiation where appropriate." + Although we cannot determine the inclination using he surface maps alone. LP Peg is an eclipsinge svstem. and its geometry is further constrainedIn] by the observed.eclipse width. which is dependent upon the inclination and size of the secondary stars Roche lobe.," Although we cannot determine the inclination using the surface maps alone, IP Peg is an eclipsing system, and its geometry is further constrained by the observedeclipse width, which is dependent upon the inclination and size of the secondary star's Roche lobe." + Fig., Fig. + 3. shows the entropy landscape constructed. by varving the inclination at. each different mass pairing in order to match the eclipse width of Ad = 0.0863 C2)., \ref{fig:landscapes} shows the entropy landscape constructed by varying the inclination at each different mass pairing in order to match the eclipse width of $\Delta\phi$ = 0.0863 \citep{wood86}. +" This results in optimum masses of AJ, = 18 M. and AJ» = 0.50 M.at an inclination of 82.3.", This results in optimum masses of $M_1$ = 1.18 $_{\odot}$ and $M_2$ = 0.50 $_{\odot}$at an inclination of $^{\circ}$. +" Altering the eclipse width to the other extreme of AG = 0.0018 given by ? changes this determination to M, = 1.16 Al. andAf; = 0.50 M. and the optimum inclination to S4.4°.", Altering the eclipse width to the other extreme of $\Delta\phi$ = 0.0918 given by \citet{wood86} changes this determination to $M_1$ = 1.16 $_{\odot}$ and$M_2$ = 0.50 $_{\odot}$ and the optimum inclination to $^{\circ}$ . + Our best estimates are therefore AZ; = 1.16. 1.18 AL... Ado = 0.50 M. and 82 85.," Our best estimates are therefore $M_1$ = 1.16 – 1.18 $_{\odot}$ , $M_2$ = 0.50 $_{\odot}$ and $i$ = $^{\circ}$ $^{\circ}$ ." +Due to its proximity. the Galactic center (GC) offers the only opportunity to spatially resolve astrophysical phenomena in the immediate vicinity of a massive black hole (MBH:??) and provides seminal knowledge for understanding spatially unresolved extra-galactic nuclei.,"Due to its proximity, the Galactic center (GC) offers the only opportunity to spatially resolve astrophysical phenomena in the immediate vicinity of a massive black hole \citep[MBH;][]{1996Natur.383..415E,1998ApJ...509..678G} + and provides seminal knowledge for understanding spatially unresolved extra-galactic nuclei." + For the past decade. it has been possible to achieve diffraction-limited observations of the GC with 8-10m class telescopes. and therefore to probe the details of processes. such as star and dust formation at galacto-centric radii where the ~4-10°M. black hole generates a strong tidal field. at a unique angular resolution of about AAU/mas (??)..," For the past decade, it has been possible to achieve diffraction-limited observations of the GC with 8-10m class telescopes, and therefore to probe the details of processes, such as star and dust formation at galacto-centric radii where the $\sim 4 \cdot 10^6\,M_\odot$ black hole generates a strong tidal field, at a unique angular resolution of about AU/mas \citep{2003ApJ...586L.127G,2005ApJ...628..246E}." + However. even at this resolution source confusion is a significant effect.," However, even at this resolution source confusion is a significant effect." + With sufficient intensity sensitivity. optical long baseline interferometry (OLBI) offers today. in the pre-ELT era. the capability to study this region at even higher angular resolution. increased by about an order of magnitude over single-telescope experiments.," With sufficient intensity sensitivity, optical long baseline interferometry (OLBI) offers today, in the pre-ELT era, the capability to study this region at even higher angular resolution, increased by about an order of magnitude over single-telescope experiments." + Large apertures as offered by the and the Keck Interferometer (KI 7)) have provided a breakthrough in sensitivity enabling first interferometric studies at 10 jim of the brightest (N.>I Jy) GC sources (?)..," Large apertures as offered by the and the Keck Interferometer (KI ) have provided a breakthrough in sensitivity enabling first interferometric studies at 10 $\mu$ m of the brightest $N\,\gtrsim 1$ Jy) GC sources \citep{2005Msngr.119...43P}." + In the NIR the sensitivity constraints are even tighter due to significantly shorter atmospheric coherence times. and higher sensibility to instrumental vibrations along the optical path (Kin~10 mag).," In the NIR the sensitivity constraints are even tighter due to significantly shorter atmospheric coherence times, and higher sensibility to instrumental vibrations along the optical path $K_{\rm lim}\,\sim10$ mag)." + If such a bright and mostly unresolved source within the isoplanatic patch of the science target can be observed with the interferometer. the atmospheric piston-noise can be monitored enabling longer integration. times and boosting the sensitivity. equivalent to natural-guide-star adaptive optics for single telescopes.," If such a bright and mostly unresolved source within the isoplanatic patch of the science target can be observed with the interferometer, the atmospheric piston-noise can be monitored enabling longer integration times and boosting the sensitivity, equivalent to natural-guide-star adaptive optics for single telescopes." + Such phase-referencing facilities are in the making (VLTI: PRIMA. GRAVITY: KI: ASTRA). and have anticipated limiting K-magnitudes of about 15-19.," Such phase-referencing facilities are in the making (VLTI: PRIMA, GRAVITY; KI: ASTRA), and have anticipated limiting $K$ -magnitudes of about $15\,-19$." + These facilities should allow studies ofÀA*.. which is the emission source associated with the MBH (e.g. ?).. and of orbits deeper in the gravitational potential of the MBH. which could test general relativity in the strong gravity regime (??).. ," These facilities should allow studies of, which is the emission source associated with the MBH \citep[e.g.][]{2003Natur.425..934G}, and of orbits deeper in the gravitational potential of the MBH, which could test general relativity in the strong gravity regime \citep{2001A&A...374...95R, 2005ApJ...622..878W}." +It. therefore. appears to be timely to characterize the primary candidate of phase-referencing experiments at the GC.?.," It, therefore, appears to be timely to characterize the primary candidate of phase-referencing experiments at the GC,." +. This MI supergiant (?) is the brightest near-infrared star in the central parsec (K.~7 mag). and is located only 6 away from the MBH.," This M1 supergiant \citep{1996AJ....112.1988B} is the brightest near-infrared star in the central parsec $K\,\sim 7$ mag), and is located only 6 $\arcsec$ away from the MBH." + While photometrie variability of IRS 7 implies a possible change of its diameter (and visibility) over time (??).. the average K magnitude suggests an average stellar photospheric diameter of about | mas at NIR wavelengths.," While photometric variability of IRS 7 implies a possible change of its diameter (and visibility) over time \citep{1996ApJ...470..864B,1999ApJ...523..248O}, the average $K$ magnitude suggests an average stellar photospheric diameter of about 1 mas at NIR wavelengths." + IRS 7 is therefore expected to be at the very limit of resolution for VLTI and KI. with maximum baseline lengths of 130 m and 85 m. respectively. and should be suitably compact to serve às an OLBI phase-reference source for the GC until regular fringe tracking on fainter stars becomes possible as proposed for the GRAVITY instrument (?)..," IRS 7 is therefore expected to be at the very limit of resolution for VLTI and KI, with maximum baseline lengths of 130 m and 85 m, respectively, and should be suitably compact to serve as an OLBI phase-reference source for the GC until regular fringe tracking on fainter stars becomes possible as proposed for the GRAVITY instrument \citep{2006SPIE.6268E..33G}." + While single-dish observations of IRS 7 show it to be point-like at NIR wavelengths. similar observations in the MIR wavelengths regime reveal that a small fraction of the light is from an extended dust distribution.," While single-dish observations of IRS 7 show it to be point-like at NIR wavelengths, similar observations in the MIR wavelengths regime reveal that a small fraction of the light is from an extended dust distribution." + Specifically. ? detect in an 8.6 um-image a tail-like structure directed away from the center of the galaxy (seeFig.|in.?)..," Specifically, \citet{2007A&A...462L...1S} detect in an 8.6 $\mu$ m-image a tail-like structure directed away from the center of the galaxy \citep[see Fig.~1 in ][]{2007arXiv0711.0249P}." + This raises the concern that hotter dust may contribute substantially to the source size at 2 jm. Furthermore. such features are interesting in their own right. as they suggest an ongoing interaction of the circumstellar dust with impinging external stellar winds from," This raises the concern that hotter dust may contribute substantially to the source size at 2 $\mu$ m. Furthermore, such features are interesting in their own right, as they suggest an ongoing interaction of the circumstellar dust with impinging external stellar winds from" +SER in the next section.,SFR in the next section. + We compute the SFR for all I catalogues from the total unminositv deusities σου in the 1500 ybaucd., We compute the SFR for all 4 catalogues from the total luminosity densities $l_{1500}$ in the 1500 band. +" First. we derive συ af a eiven redshift vo sunumudne the completeness corrected (usingaV/V, ΕΟΟου LES up to he absolute magnitude limits,"," First, we derive $l_{1500}$ at a given redshift by summing the completeness corrected \citep[using a $V/V_{max}$ correction, LFs up to the absolute magnitude limits." + Second. we apply a further correction (to zero galaxy ποσατν). ZGL. o take into account the iissine contribution to the inuinositv density of the fainter galaxies.," Second, we apply a further correction (to zero galaxy luminosity) ZGL, to take into account the missing contribution to the luminosity density of the fainter galaxies." + To this eund we use the best-fittiue Schechter fiction., To this end we use the best-fitting Schechter function. + For the FDF catalogues the ZGL corrections are ouly in size., For the FDF catalogues the ZGL corrections are only in size. + The sinall ZGL correction curploved here owes itself to the faint maenitude limits probed by our deep FDF data set aud the relatively flat slopes (az—1.07 of the Schechter function., The small ZGL correction employed here owes itself to the faint magnitude limits probed by our deep FDF data set and the relatively flat slopes $\alpha\approx -1.07$ ) of the Schechter function. + Due to the brighter macuitud limut. the ZGL corrections for the GOODS catalogue cau be as hieli as5," Due to the brighter magnitude limit, the ZGL corrections for the GOODS catalogue can be as high as." +0 Note that if we follow ie. Steidel(1999) who find..—1.6 (excludedat26withourfits.seeGabaschlietal.200 [).. we would eet unich larger ZCL corrections for the same Mi. d$. (see the dotted line iu Fig.," Note that if we follow i.e. \citet{steidel:1} who find $\alpha=-1.6$ \citep[excluded +at 2$\sigma$ with our fits, see ][]{gabasch:1}, we would get much larger ZGL corrections for the same $M_\ast$, $\Phi_\ast$ (see the dotted line in Fig." + 2 aud the discussion below)., \ref{fig:sfr:sfr_fdf_goods} and the discussion below). + Finally. following Aladauetal.(1998) we derive the SER by scaling the UW luninosity densitics: SFRysy9=1.25«1078&lisgj im units of Mgr.HAZP. where the coustant is computed for a Salpeter peIMF.," Finally, following \citet{mad_poz_dick1} we derive the SFR by scaling the UV luminosity densities: ${\rm + SFR}_{1500}=1.25\times10^{-28}\times l_{1500}$ in units of $M_\odot +yr^{-1}Mpc^{-3}$, where the constant is computed for a Salpeter IMF." + The resulting values of SFRysyo ave shown in Fig., The resulting values of ${\rm SFR}_{1500}$ are shown in Fig. + 2 as a function of redshift., \ref{fig:sfr:sfr_fdf_goods} as a function of redshift. + Errors are computed from Monte Carlo simulations that take iuto account the probability distributions of photometric redshifts aud the Poissoniau error (Cabaschetal.2001)., Errors are computed from Monte Carlo simulations that take into account the probability distributions of photometric redshifts and the Poissonian error \citep{gabasch:1}. +. Following Adelberger&Steidel (2000)... we assume that dust extinction docs not evolve with redshift aud is about a factor of ~5. 9in the rest-frame UV.," Following \citet{adelberger:1}, we assume that dust extinction does not evolve with redshift and is about a factor of $\sim 5-9$ in the rest-frame UV." + A more detailed discussion of the role of dust will be given iu a future paper. like an analysis based on the SFR derived at 2800A.," A more detailed discussion of the role of dust will be given in a future paper, like an analysis based on the SFR derived at 2800." +". Thauks to the large area covered and the faint limiting magnitudes probed. our deteriuuatioun of the SER is the most precise to date. with statistical errors less than 0.1 dex for the single redshift bius spanuing the range 0.5<2<4,"," Thanks to the large area covered and the faint limiting magnitudes probed, our determination of the SFR is the most precise to date, with statistical errors less than 0.1 dex for the single redshift bins spanning the range $0.5< z<5$." +" The considerations of refsec, hotomctrytranslateinthe followingeonelusionsaboutt ake hh", The considerations of \\ref{sec_photometry} translate in the following conclusions about the SFR. +tou&tevcedahitWézpossble the SERs derived. from the I and DB. selected. FDF. or the mereed I) catalogue. are identical within the errors Cz0.1 dex: seeB plot at the bottom left of Fig. 2)).," Out to redshift $z\approx 3$ the SFRs derived from the I and B selected FDF, or the merged I+B catalogue, are identical within the errors $\lsim 0.1$ dex; see plot at the bottom left of Fig. \ref{fig:sfr:sfr_fdf_goods}) )." + At larecr redshifts the B-selected SFRs underestimate the true values. since D drop-outs are not taken iuto account.," At larger redshifts the B-selected SFRs underestimate the true values, since B drop-outs are not taken into account." + The strong evolution in both the AL. aud o paralucters of the Schechter LF ueasured as a function of vedshitt bv Gabaschetal.(2001) results iu a ucarly constant SFR. because the strong brightening of AL is colmpcusated by the dramatic decrease of o4 with +.," The strong evolution in both the $M_\ast$ and $\phi_\ast$ parameters of the Schechter LF measured as a function of redshift by \citet{gabasch:1} results in a nearly constant SFR, because the strong brightening of $M_\ast$ is compensated by the dramatic decrease of $\phi_\ast$ with $z$." + Comparing the two lower panels of shows that huninous galaxies (L> L.) coutribute only a third of the total SFR at all observed +. incdepeudent of the selection baud.," Comparing the two lower panels of shows that luminous galaxies $L>L_\ast$ ) contribute only a third of the total SFR at all observed $z$, independent of the selection band." + The ER-solected SFRs are similar in shape. but systematically lower by z0.2 dex at ιτ> 1.," The K-selected SFRs are similar in shape, but systematically lower by $\approx 0.2$ dex at $z>1$ ." + This result holds indepeudeutlv of our completeness correction., This result holds independently of our completeness correction. + If we consider oulv the contributions to the SER down to the limiting magnitude set by the K-baud. we find the sale 0.2 dex difference for 1<:x3. and 0.15 dex at 2>X," If we consider only the contributions to the SFR down to the limiting magnitude set by the K-band, we find the same 0.2 dex difference for $1 3$." + Fie., Fig. + d shows that this result originates frou he lower density of ἁπου719 ealaxies in the R-selected catalogue. as intermediate and low bunünositv due galaxies contributing to the SFR budget are more easily detected i the bluer bands than im EK. In fact. he contributions to the SFR coming from the galaxics xiehter than LÍ are identical within the errors for the I and EK selected. catalogues (see Fig. 2..," \ref{fig:sfr:cont_absmag_fdf_goods} shows that this result originates from the lower density of $M_{1500}>-19$ galaxies in the K-selected catalogue, as intermediate and low luminosity blue galaxies contributing to the SFR budget are more easily detected in the bluer bands than in K. In fact, the contributions to the SFR coming from the galaxies brighter than $L_\ast^I$ are identical within the errors for the I and K selected catalogues (see Fig. \ref{fig:sfr:sfr_fdf_goods}," + bottom-right uel)., bottom-right panel). + Therefore. cosiuiie variance does not play a vole. as we also verified by comparing the B-baud uuuber counts in the 2 fields.," Therefore, cosmic variance does not play a role, as we also verified by comparing the B-band number counts in the 2 fields." + They agree within 0.1 dex. which is the expected variation derived by Somervilleetal.(2001). sealed to the area of the COODS-Soutl field.," They agree within 0.1 dex, which is the expected variation derived by \citet{somerville:2} scaled to the area of the GOODS-South field." + On the other hand. Gabaschetal.(2001) show that the E-baud FDF catalogue night be missing only about 10 of the galaxies that would be detected in a deep Is-band selected survey with maeuitude limit A(pzx26 (likeinLabbéetal.2003)..," On the other hand, \citet{gabasch:1} show that the I-band FDF catalogue might be missing only about 10 of the galaxies that would be detected in a deep K-band selected survey with magnitude limit $K_{AB}\approx 26$ \citep[like in][]{labbe:1}." + The missiug galaxies would ve faint and likely not contributing siguificautly to the SER provided thei dust extinction is not exceedingly arec., The missing galaxies would be faint and likely not contributing significantly to the SFR provided their dust extinction is not exceedingly large. + Indepeudent of the selection baud the SFR declines vevoud zo15., Independent of the selection band the SFR declines beyond $z \sim 4.5$. + Our results coufirm the conjecture of Ikashikawactal.(2003). that the Is-selected UV. LES natch the optically selected. LFs at high huuinosities., Our results confirm the conjecture of \citet{kashikawa:1} that the K-selected UV LFs match the optically selected LFs at high luminosities. + The comparison with the literature shows that our results are dex lower. independent of the selection sand.," The comparison with the literature shows that our results are dex lower, independent of the selection band." +" This difference stems frou the large completcucss corrections applied by. c.g.. Steideletal.(1999).. derived roni the steep slopes fitted to the LF (sce retsec,hotometyy) )"," This difference stems from the large completeness corrections applied by, e.g., \citet{steidel:1}, derived from the steep slopes fitted to the LF (see \\ref{sec_photometry}) )." +Ourresultsscaletotheliteraturecaliuc sifsinilar and o.., Our results scale to the literature values if similar slopes are used for the same $M_\ast$ and $\phi_\ast$. + This is shown by the dotted lines of Fig. 2..," This is shown by the dotted lines of Fig. \ref{fig:sfr:sfr_fdf_goods}," + where we have assumed a slope of =1.6 for our data set while keeping M. aud ως the same as in our fit., where we have assumed a slope of $-1.6$ for our data set while keeping $M_\ast$ and $\phi_\ast$ the same as in our fit. + The overall agrecinent between the SFRs derived over a wide wavelength range (within 0.2 dex). from the optical D aud Ito the NIR Is. sampling at :zL the rest-frame UV aud D. shows that we are approaching (in the optical) the complete census of the galaxies contributing to the stellar production of the universe up to this redshift.," The overall agreement between the SFRs derived over a wide wavelength range (within 0.2 dex), from the optical B and I to the NIR K, sampling at $z\approx 4$ the rest-frame UV and B, shows that we are approaching (in the optical) the complete census of the galaxies contributing to the stellar production of the universe up to this redshift." + Therefore. we can expect possible biases iuduced by mussing stellar cherey distributions with redshift (bertetal.2001). to be small. when deep enough optical or NIR catalogues are available.," Therefore, we can expect possible biases induced by missing stellar energy distributions with redshift \citep{ilbert:1} to be small, when deep enough optical or NIR catalogues are available." + IToscever. we mielt still not contribution to the SFR conine from faint. hiellv dust-absorbed red star-forming ealaxies (IIughesctal.1998:Genzelet2001) which are likely missing from optically or uear-infrared selected sunples.," However, we might still not take into account the possible contribution to the SFR coming from faint, highly dust-absorbed red star-forming galaxies \citep{hughes:98,genzel:1} which are likely missing from optically or near-infrared selected samples." + Nevertheless. it is encouraging to find that recent Spitzer results (0.5. Eganetal. 2001)) indicate that the majority of the star formation has already Όσοι accounted for using the dust-corrected SFR derived frou optical studies.," Nevertheless, it is encouraging to find that recent Spitzer results (e.g. \citealt{egami:1}) ) indicate that the majority of the star formation has already been accounted for using the dust-corrected SFR derived from optical studies." + We have measured the SER ofthe universe out to DomLS with unprecedented accuracy from the FORS Deep Field aud the GOODS-South Field (90 arciniu? iu total)., We have measured the SFR ofthe universe out to $z\approx 4.5$ with unprecedented accuracy from the FORS Deep Field and the GOODS-South Field $90$ $^2$ in total). + Our main conclusions e The cosiüc variance in the SER history between the FDF and GOODS-South field is neeligibly small., Our main conclusions $\bullet$ The cosmic variance in the SFR history between the FDF and GOODS-South field is negligibly small. + The difference between these fields is <0.1 dex. consistent with theoretical," The difference between these fields is $\lsim 0.1$ dex, consistent with theoretical" +the less likely is the distribution to have a single peak aud the more likely it is to have at least two significant peaks.,the less likely is the distribution to have a single peak and the more likely it is to have at least two significant peaks. + A p-value of <0.05 inclicates that the mull-hyvpothesis is very unlikelv. aud that the given distribution has more (han one peak.," A p-value of $<0.05$ indicates that the null-hypothesis is very unlikely, and that the given distribution has more than one peak." + We applied the dip test to (he eccentricity distribution of our sample of 931 main belt asteroids: we determined that the (est statistic is 0.0107. From Iartigan&Ilartigan(1955).. (his corresponds to a p-value range of 0.6«p0.7 (based on a sample size of 1000).," We applied the dip test to the eccentricity distribution of our sample of 931 main belt asteroids; we determined that the test statistic is $0.0107$ From \cite{Hartigan:1985p3924}, this corresponds to a p-value range of $0.6350 which implies E,<100 keV exactly in the range of BAT (Swift)."," For example, in order to have $\sim 1$ GeV emission for $t_v=1$ ms, we need $\Gamma>350$ which implies $E_p<100$ keV exactly in the range of BAT (Swift)." + Therefore we expect that a good fraction of the bursts detected by Swift can produce GeV emission which will be detected by AGILE and GLAST., Therefore we expect that a good fraction of the bursts detected by Swift can produce GeV emission which will be detected by AGILE and GLAST. + We have taken the LIS as the mechanism responsible for the flare emission., We have taken the LIS as the mechanism responsible for the flare emission. +" In this model the average interval between consecutive shell ejection ¢,, has a fundamental role in determining the radius of the collision and therefore the emission properties (i.e. the peak energy) of X-ray flares."," In this model the average interval between consecutive shell ejection $t_v$ , has a fundamental role in determining the radius of the collision and therefore the emission properties (i.e. the peak energy) of X-ray flares." +" We initially considered a range of t, (10 ms-1 s) and a Lorentz factor (T 100) similar to the prompt emission, and found that the peak of the emission is between the optical and the X-ray bands, consistent with the observations."," We initially considered a range of $t_v$ (10 ms-1 s) and a Lorentz factor $\Gamma \sim$ 100) similar to the prompt emission, and found that the peak of the emission is between the optical and the X-ray bands, consistent with the observations." +" This implies that the X-ray flare light curve should contain some substructures of f,~100 ms such as the prompt emission.", This implies that the X-ray flare light curve should contain some substructures of $t_v\sim 100$ ms such as the prompt emission. + An accurate search of these flux variations is mandatory to understand the physics of the flares and to check the LIS model., An accurate search of these flux variations is mandatory to understand the physics of the flares and to check the LIS model. + If no flux variation on a small time scale is detected the implication would be that the shellsare ejectedwith an average interval similar to the durationof the single flare (t;~ 40s).In this case the collisions between the shells happen at a large distance from, If no flux variation on a small time scale is detected the implication would be that the shellsare ejectedwith an average interval similar to the durationof the single flare $t_f\sim 40 s$ ).In this case the collisions between the shells happen at a large distance from +feedback ellieienev.,feedback efficiency. + As for the Fe production and cdilusion. its behaviour is similar to that of Model D. thought with 30 per cent more Fe due to the higher IME over the mass range relevant for SNla.," As for the Fe production and diffusion, its behaviour is similar to that of Model D, thought with $\sim 30$ per cent more Fe due to the higher IMF over the mass range relevant for SNIa." + In the upper panels of Fig.l we show the profiles of O/Fe]., In the upper panels of \ref{fi:metprof} we show the profiles of [O/Fe]. + Since Oxygen is mostly produced by SNIL. O/Le] is usually considered as a ciagnostic for the relative role played by the (wo SN types.," Since Oxygen is mostly produced by SNII, [O/Fe] is usually considered as a diagnostic for the relative role played by the two SN types." + So far. robust measurements of the O abundance have been realized with the NMM-NEMWTON CRS. and are limited to the very central regions of galaxy clusters.," So far, robust measurements of the O abundance have been realized with the XMM-NEWTON GRS, and are limited to the very central regions of galaxy clusters." + Gastaldello Alolendi (2002) ancl Matsushita. οἱ al. (, Gastaldello Molendi (2002) and Matsushita et al. ( +2003) found O/Le}s0.3 around. AIST out to about 60 kpe. which corresponds to 20.047/95 for our simulated cluster.,"2003) found $\simeq -0.3$ around M87 out to about 60 kpc, which corresponds to $\simeq 0.04\,R_{200}$ for our simulated cluster." + On larger scales. the dillicult detection of the OVILL emission line at 0.67 keV makes the determination of O/Fe] more uncertain. although values in the range between 0.2 and 0.2 seem to be preferred. (see. Renzini 1997 [for à discussion).," On larger scales, the difficult detection of the OVIII emission line at 0.67 keV makes the determination of [O/Fe] more uncertain, although values in the range between $-0.2$ and 0.2 seem to be preferred (see Renzini 1997 for a discussion)." + The negative gradients of our O/Fe]. proliles are the signature of recent. star formation episodes in the central region., The negative gradients of our [O/Fe] profiles are the signature of recent star formation episodes in the central region. + This arises because SNIL already had: time to explode. while SNlIa. which are. generated: by longerliving stars. still have to release Iron.," This arises because SNII already had time to explode, while SNIa, which are generated by longer--living stars, still have to release Iron." + As à consequence. the ICM for Models A and D turns out to be overabundant in Oxveen. in the central regions. with respect to what observed for AIST. while being consistent with data on larger scales.," As a consequence, the ICM for Models A and B turns out to be over–abundant in Oxygen, in the central regions, with respect to what observed for M87, while being consistent with data on larger scales." + Assuming an AY ΕΛΣ provides a relatively larger number of SNIL. thus exacerbating the problem of Oxvecn overabundance.," Assuming an AY IMF provides a relatively larger number of SNII, thus exacerbating the problem of Oxygen overabundance." + As [or the overall metallicity. we obtain emissionweighted. Zp. values in the range 0.250.55. with the only exception of Model €. which produces a lower Fe abundance.," As for the overall metallicity, we obtain emission--weighted $Z_{\rm +Fe}$ values in the range 0.25–0.55, with the only exception of Model C, which produces a lower Fe abundance." +" Lt is worth noticing that. although Mocels A and E produces vw highest Zp"" values (sec Table 1). they have dilferen cassweighted Fo abundances."," It is worth noticing that, although Models A and F produces the highest $Z_{\rm Fe}^{ew}$ values (see Table 1), they have different mass–weighted Fe abundances." + In particular. the high Zi of Lelodel A corresponds to a fairly small massweighted value. 1¢ large cillerence being due to the steep profile of the Fe abundance.," In particular, the high $Z_{\rm Fe}^{ew}$ of Model A corresponds to a fairly small mass–weighted value, the large difference being due to the steep profile of the Fe abundance." + In their compilation of ASCA cata. BOS finc wt Zp. tends to decrease with cluster temperature. with Zyo=OF for T23 keV. down to Zp.5OB at Tx10 keV (οἱ.," In their compilation of ASCA data, B03 find that $Z_{\rm Fe}$ tends to decrease with cluster temperature, with $Z_{\rm Fe}\simeq 0.7$ for $T\simeq 3$ keV, down to $Z_{\rm Fe}\simeq 0.3$ at $T\simeq 10$ keV (cf." + also Renzini 2003. who claims a roughly constan Zp.0.3 over the same temperature range).," also Renzini 2003, who claims a roughly constant $Z_{\rm Fe}\sim 0.3$ over the same temperature range)." + Therefore. or our Virgolike cluster we should expect a Fe enrichmen which is sensibly larger than found in simulations.," Therefore, for our Virgo–like cluster we should expect a Fe enrichment which is sensibly larger than found in simulations." + However. we note that the procedure. of stacking NXrav. spectra of clusters with similar temperature. as followed: by DO3. corresponds to assuming that all clusters having the same T also have the same metallicity. and. therefore. that the fairly large scatter observed is only due to measurement errors.," However, we note that the procedure of stacking X–ray spectra of clusters with similar temperature, as followed by B03, corresponds to assuming that all clusters having the same $T$ also have the same metallicity, and, therefore, that the fairly large scatter observed is only due to measurement errors." + Since some amount of intrinsic scatter is anyway expected. it ds dillieult. to assess. with only one cluster simulated. how discrepant are our Zp. values with respect to the observed ones.," Since some amount of intrinsic scatter is anyway expected, it is difficult to assess, with only one cluster simulated, how discrepant are our $Z_{\rm Fe}$ values with respect to the observed ones." + Another feature of the simulated. be production is that the ICM contains between about 25 and 40 per cent of the total amount of produced Ee. at odds with observational indications for. Mpaesr/Mps;2 (Itenzini 2003).," Another feature of the simulated Fe production is that the ICM contains between about $25$ and 40 per cent of the total amount of produced Fe, at odds with observational indications for $M_{\rm Fe,ICM}\,/M_{\rm Fe,*}\sim 2$ (Renzini 2003)." + This further suggests that a mechanism is still lacking in simulations to transport metals away from star.forming regions., This further suggests that a mechanism is still lacking in simulations to transport metals away from star–forming regions. + Unlike Oxveen. which is cillieult to detect in the Xrav spectra of the hot ICM. Silicon is now detected [for à fair number of clusters.," Unlike Oxygen, which is difficult to detect in the X--ray spectra of the hot ICM, Silicon is now detected for a fair number of clusters." + Since a sizeable fraction. of Si is produced: also by SNla. depending on the choice for the WALK. it could. be a useful tool to investigate the relative contribution to metal enrichment from the two SNe types (c.g. Lowenstein 2003).," Since a sizeable fraction of Si is produced also by SNIa, depending on the choice for the IMF, it could be a useful tool to investigate the relative contribution to metal enrichment from the two SNe types (e.g. Lowenstein 2003)." + In. Figure 2 we show Si/EFce] vs. οΕΕ for our simulations. compared to the observational values from. D03.," In Figure 2 we show [Si/Fe] vs. [Fe/H] for our simulations, compared to the observational values from B03." + Several of our runs produce a relative SiFe] ratio which falls on the correlation indicated by data. although the observed absolute Ee abundance for ~3 keV clusters (marked. by the filled. circle) is significantly larger than that produced. by several of our models.," Several of our runs produce a relative [Si/Fe] ratio which falls on the correlation indicated by data, although the observed absolute Fe abundance for $\simeq 3$ keV clusters (marked by the filled circle) is significantly larger than that produced by several of our models." + We note that the models. better approximating observational data are A and E. which. besides providing a realistic emissionweighted Fe abundance. also produce an acceptable amount of Si.," We note that the models better approximating observational data are A and F, which, besides providing a realistic emission--weighted Fe abundance, also produce an acceptable amount of Si." + As a word of caution. we note that the resolution of the simulations presented here could. prevent the treatment of some physical effects. which may change final results.," As a word of caution, we note that the resolution of the simulations presented here could prevent the treatment of some physical effects, which may change final results." + For instance. cHeets of dynamical stripping may. play a significant role in removing metalrich. gas from. cluster galaxies and. therefore. to enrich. the diffuse ICM. (e.g. CGnedin. 1998: Toniazzo Schindler 2001).," For instance, effects of dynamical stripping may play a significant role in removing metal–rich gas from cluster galaxies and, therefore, to enrich the diffuse ICM (e.g., Gnedin 1998; Toniazzo Schindler 2001)." + While tidal stripping should. be well represented. in our simulations. a oper treatment of ranipressure stripping would. require a substantially higher. resolution in an SPILL simulation.," While tidal stripping should be well represented in our simulations, a proper treatment of ram–pressure stripping would require a substantially higher resolution in an SPH simulation." + Aguirre et al. (, Aguirre et al. ( +2001) claim that rampressure. stripping rom galaxies of mass 23LOCAL.Lu accounts for. a small raction of the LOCAL metal content.,"2001) claim that ram–pressure stripping from galaxies of mass $>3\times +10^{10}M_\odot$ accounts for a small fraction of the ICM metal content." + Furthermore. Renzini (2003) argues that. if ram.pressure stripping were cllicicnt. hen clusters with larger velocity dispersion should have a relatively higher metallicity. a trend which is not observed.," Furthermore, Renzini (2003) argues that, if ram–pressure stripping were efficient, then clusters with larger velocity dispersion should have a relatively higher metallicity, a trend which is not observed." + Furthermore. in. order to have reliable estimates of he LOCAL metal enrichment. we have to make sure that our simulation has high enough resolution to provide a correct representation of the star formation history. (see also Tornatore ct al.," Furthermore, in order to have reliable estimates of the ICM metal enrichment, we have to make sure that our simulation has high enough resolution to provide a correct representation of the star formation history (see also Tornatore et al." + 2003)., 2003). + We postpone a detailed. study of numerical convergence of star formation and metal production within clusters in a forthcoming paper., We postpone a detailed study of numerical convergence of star formation and metal production within clusters in a forthcoming paper. + We have presented results from hyvdrodsnamical simulations of the LOCAL. realized with a chemodynamical. version of he GADGET coce.," We have presented results from hydrodynamical simulations of the ICM, realized with a chemodynamical version of the GADGET code." + We used a version of this code that. vesicles a fairly advanced treatment of star formation anc eedback from galactic winds (Springel Llernquist 2O008a. 511039). also correctly accounts Lor [ifetimes of cilleren stellar populations. as well as for metal and energy. release roni SNla and LE ClLornatore et al.," We used a version of this code that, besides a fairly advanced treatment of star formation and feedback from galactic winds (Springel Hernquist 2003a, SH03), also correctly accounts for life–times of different stellar populations, as well as for metal and energy release from SNIa and II (Tornatore et al." + 2004. in. preparation).," 2004, in preparation)." + Dv simulating one single. cluster. having temperature. of about 3 keV. we looked at the effect. of feedback. strength and IMI on the resulting. metal production.," By simulating one single cluster, having temperature of about 3 keV, we looked at the effect of feedback strength and IMF on the resulting metal production." + Our main, Our main +that unrelated intrinsic quasar-to-quasar SED variations are combining to reproduce a feature and overall shape thatÀ reproduces the form of the LMC-extinction curve to the accuracy shown in Fig. 15..,that unrelated intrinsic quasar-to-quasar SED variations are combining to reproduce a feature and overall shape that reproduces the form of the LMC-extinction curve to the accuracy shown in Fig. \ref{cap:lmccoadd}. + 'The objects contributing to the composite are indicated in Fig. 11.., The objects contributing to the composite are indicated in Fig. \ref{cap:ebvz}. +" With only half of these objects present in the restricted sample used to investigate redshift evolution (Section ??)), it is not possible to say anything useful about the strength of the bump with redshift."," With only half of these objects present in the restricted sample used to investigate redshift evolution (Section \ref{sec:redevol}) ), it is not possible to say anything useful about the strength of the bump with redshift." +" ? perfomed a statistical analysis of 809 absorption systems from SDSS DR1, and searched for the feature in the dustiest 111 systems with an observed frame A(g—4)> 0.2."," \citet{2006MNRAS.367..945Y} perfomed a statistical analysis of 809 absorption systems from SDSS DR1, and searched for the feature in the dustiest 111 systems with an observed frame $\Delta \left(g-i\right)>0.2$ ." + They find an average E(B—V)suc=0.0805 and no evidence of a MW dust signature in their composite spectrum., They find an average $E(B-V)_{\mathrm{SMC}}=0.0805$ and no evidence of a MW dust signature in their composite spectrum. +" They also provide an estimate of the fraction of lines of sight that could have MW-type extinction, and provide an upper limit of 30 per cent."," They also provide an estimate of the fraction of lines of sight that could have MW-type extinction, and provide an upper limit of 30 per cent." +" Although we have reached a similar conclusion regarding the nature of dust, our sample of aabsorbers is an order of magnitude larger, and we have created a composite spectrum with a much larger average E(B— V)smc."," Although we have reached a similar conclusion regarding the nature of dust, our sample of absorbers is an order of magnitude larger, and we have created a composite spectrum with a much larger average $E(B-V)_{\mathrm{SMC}}$ ." + The sample used has also been carefully constructed to ensure that only objects with accurate estimates of E(B—V) (ie. those with Dimas«0.04) are allowed to contribute to the composite., The sample used has also been carefully constructed to ensure that only objects with accurate estimates of $E(B-V)$ (i.e. those with $D_\mathrm{max}^{\mathrm{smc}}<0.04$ ) are allowed to contribute to the composite. +" We provide a tighter constraint on the fraction of lines of sight with (the much less extreme) LMC-type extinction, as 35-410 per cent, compared to ?""s upper limit of 30 per cent with MW-type extinction."," We provide a tighter constraint on the fraction of lines of sight with (the much less extreme) LMC-type extinction, as $\pm10$ per cent, compared to \citeauthor{2006MNRAS.367..945Y}' 's upper limit of 30 per cent with MW-type extinction." +" A recent study by ? produced a catalogue of 39 candidate strong aabsorbers, with EW>1A and 1.0«z1.86, showing evidence for the presence of a weak feature."," A recent study by \citet{2011ApJ...732..110J} produced a catalogue of 39 candidate strong absorbers, with $>1$ and $1.0A$, as can easily be obtained from the magnification curve (Schneider et al." + 1992)., 1992). +" For large magnifications. however. we predict that o, is much larger for à SIS plus disk lens as compared with a SIS alone."," For large magnifications, however, we predict that $\sigma_\mu$ is much larger for a SIS plus disk lens as compared with a SIS alone." +" Magnification maps derived at inclinations of 60. TO and ddeg for à lens similar to the Milky Way are presented in refmaps.. and clearly show the distinctive shape of the caustic. with an elliptical component due to the halo and a diamond. shaped: component. the ""astroid. due to the disk."," Magnification maps derived at inclinations of 60, 70 and deg for a lens similar to the Milky Way are presented in \\ref{maps}, and clearly show the distinctive shape of the caustic, with an elliptical component due to the halo and a diamond shaped component, the “astroid”, due to the disk." +" For large inclinations. the size of the astroid increases significantly. leading to the increase of the multiple-imaging CLOSS section Oy, cliscussedl above."," For large inclinations, the size of the astroid increases significantly, leading to the increase of the multiple-imaging cross section $\sigma_{\rm m}$ discussed above." +" The cross section ratio a),an for magnifications &ereater than A for a galaxy lens similar to the Milkv Way are presented in 44.", The cross section ratio $\sigma_\mu/\sigma_\mu^{\mathrm{SIS}}$ for magnifications greater than A for a galaxy lens similar to the Milky Way are presented in 4. + The cross sections are derived » adding up the area of all pixels on the source plane with magnifications greater than A. The calculated ratios come less smooth at large magnifications because the number of high-magnilication pixels on the source plane is relatively small: onky about 20 pixels in the source. plane ve magnifications larger than of=NO., The cross sections are derived by adding up the area of all pixels on the source plane with magnifications greater than A. The calculated ratios become less smooth at large magnifications because the number of high-magnification pixels on the source plane is relatively small; only about 20 pixels in the source plane have magnifications larger than $A=80$. + The magnitude of he lluctuations in the ratios can be used as an estimate of he uncertainty in the results of these computations., The magnitude of the fluctuations in the ratios can be used as an estimate of the uncertainty in the results of these computations. + A Large increase in the cross section ratio Is predicted for inclinations hat exceed dades. at magnilications greater than a certain hreshold.," A large increase in the cross section ratio is predicted for inclinations that exceed deg, at magnifications greater than a certain threshold." + This threshold magnification is a strong function of inclination. and is reduced. as the inclination increases.," This threshold magnification is a strong function of inclination, and is reduced as the inclination increases." + The cross section ratios shown in bies.44 5 also have a characteristic peak beyond. this threshold) magnification., The cross section ratios shown in 4 5 also have a characteristic peak beyond this threshold magnification. + Lence. although the largest cross section ratios are preclicted for almost edge-on disks at magnifications greater than 50. at magnifications of about 10 a disk at 6=TO ddoeg is expected. to produce a larger cross section than a clisk at 9Odedee.," Hence, although the largest cross section ratios are predicted for almost edge-on disks at magnifications greater than 50, at magnifications of about 10 a disk at $\theta = 70$ deg is expected to produce a larger cross section than a disk at deg." + Hence. nearly ecee-on disks are more ellective in. producing large magnifications as compared with disks at smaller inclinations.," Hence, nearly edge-on disks are more effective in producing large magnifications as compared with disks at smaller inclinations." + This is because points interior to the astroicl caustic lie closer to caustic lines ancl experience larger average magnifications when the caustic is smaller. as it is at mocoerate inclinations.," This is because points interior to the astroid caustic lie closer to caustic lines and experience larger average magnifications when the caustic is smaller, as it is at moderate inclinations." + This ellect is clearly demonstrated in 33: although the area of the astroid caustic is larger in the lower panels. the mean magnification in the enclosed region is smaller.," This effect is clearly demonstrated in 3; although the area of the astroid caustic is larger in the lower panels, the mean magnification in the enclosed region is smaller." +" The inclination-averaged high-magnilication cross section 7, shown in refhighl— was derived by evaluating c, at [ive-degree intervals. from O to 90ddegrees. ancl approximating the integral (equation +) bv a sum.", The inclination-averaged high-magnification cross section $\bar{\sigma}_\mu$ shown in \\ref{high1} was derived by evaluating $\sigma_\mu$ at five-degree intervals from 0 to degrees and approximating the integral (equation 4) by a sum. +" The result is) very significant: 7, is greatly increased by a randomlv-oriented galaxy similar to the Milky Way as compared with a SIS lens. and ofosis710 at magnifications greater than about"," The result is very significant: $\bar{\sigma}_\mu$ is greatly increased by a randomly-oriented galaxy similar to the Milky Way as compared with a SIS lens, and $\bar{\sigma}/\sigma_{\mathrm{SIS}} \approx 10$ at magnifications greater than about" +optical we utilise public DRT release of the Subaru NMM-newton Deep Field Survey ((Purusawa 2008).,optical we utilise public DR1 release of the Subaru XMM-newton Deep Field Survey \nocite{Furusawa2008}( 2008). +" SNDS observed. 5 fields in a ‘plus’ shaped pattern centered: on Right Ascension-02I8""00. and. Declination—-050000"" with the SuprimeC'am instrument on the Subaru telescope.", SXDS observed 5 fields in a 'plus' shaped pattern centered on Right $02^h18^m00^s$ and $05^{\circ}00'00''$ with the SuprimeCam instrument on the Subaru telescope. + The SILADES field is wholly contained. within the single central SuprimeC'am pointing., The SHADES field is wholly contained within the single central SuprimeCam pointing. + Observations were performed in 5 optical bands. B. V. I. 7. z with 3o. 2 aperture. AB mag depths of 27.5. 27.5. 21. 27. and 26 respectively.," Observations were performed in 5 optical bands, B, V, R, $i'$, $z'$, with $\sigma$, 2” aperture, AB mag depths of 27.5, 27.5, 27, 27, and 26 respectively." + In the near-LR we utilise data from the UlXIDSS (UINIICE. Infrared. Deep Sky Survey: Lawrence 2007) Ultra Deep Survey. (UDS)., In the near-IR we utilise data from the UKIDSS (UKIRT Infrared Deep Sky Survey; \nocite{Lawrence2007}{ 2007) Ultra Deep Survey (UDS). +. UIXIDSS. uses the ντ) Wide Field Camera (WECAAL: Casali ct al. and a photometric system. described in. Llewett et al. (2006).," UKIDSS uses the UKIRT Wide Field Camera (WFCAM; Casali et al, \nocite{Casali2007} and a photometric system described in Hewett et al \nocite{Hewett2006}." +. The pipeline processing and science archive are described in Irwin ct al (2008. in prep) and Llamibly et al (2008).," The pipeline processing and science archive are described in Irwin et al (2008, in prep) and Hambly et al \nocite{Hambly2008}." +. We utilise the DRS release of the UDS dataset. which contains photometry in JL and [x t0 a 5m depth of 23.7. 23.5. and 23.7 AD mags respectively.," We utilise the DR3 release of the UDS dataset, which contains photometry in J,H and K to a $\sigma$ depth of 23.7, 23.5, and 23.7 AB mags respectively." + Ehe UDS field is coincident with the SADE. covering the extent of the ΗΛΙΟΣ SCUBA observations.," The UDS field is coincident with the SXDF, covering the extent of the SHADES SCUBA observations." + For the mid-Far. Hi we utilise data [from the SWIRL survey., For the mid-far IR we utilise data from the SWIRE survey. + SWIRL contains imaging of the entire NALAI-LSS lield in both the IRAC and. MIPS instruments on SWIRL., SWIRE contains imaging of the entire XMM-LSS field in both the IRAC and MIPS instruments on SWIRE. + This results in a5 band dataset. with [lux measurements centred on 3.6. 4.5. 5.8.8.0. 24.0 yam. While the MIDS 70/4 and. 1607/0 clata is included in the analysis only a very small number of SHADES sources are found to have nearby 70 and/or L60yma sources in SWIBIS and thus it is of little use in the vast majority of cases.," This results in a 5 band dataset, with flux measurements centred on 3.6, 4.5, 5.8, 8.0, 24.0 $\mu$ m. While the MIPS $\mu$ m and $\mu$ m data is included in the analysis only a very small number of SHADES sources are found to have nearby 70 and/or $\mu$ m sources in SWIRE and thus it is of little use in the vast majority of cases." + Asan initial test we trey to recreate in sipulated data the real scenario that will be considered later in this paper the matching of S50fn sources to deep optical ancl UM MIPS data with no redshift information., As an initial test we try to recreate in simulated data the real scenario that will be considered later in this paper the matching of $\mu$ m sources to deep optical and IRAC MIPS data with no redshift information. + The use of the simulations at this stage is vital as it ollers the convienence ofa perfect truth list to test against. Le. we know the true underlying association for each object apriori. something which is never truly possible with real data.," The use of the simulations at this stage is vital as it offers the convienence of a perfect truth list to test against, i.e. we know the true underlying association for each object apriori, something which is never truly possible with real data." + We select. 1: cone (Cone 1: 1 sq., We select 1 cone (Cone 1: 1 sq. + deg.), deg.) + of (ια10 simulations with photometry in 5 optical bands (D.V.lti.z). 3 Neu-IHlt. bands (JEN). the 4.Spifzer IRAC bands. and the MIPS. 24 τοι bands.," of GaLICS simulations with photometry in 5 optical bands (B,V,R,i',z'), 3 Near-IR bands (J,H,K), the 4 IRAC bands, and the MIPS 24 $\mu$ m bands." + The simulated data is then broken up into three catalogues. an optical-near LI catalogue. a “SWIRL” Spitzer HUAC'|MIPS 245m catalogue and a SCUBA S505 catalogue.," The simulated data is then broken up into three catalogues, an optical-near IR catalogue, a “SWIRE” Spitzer IRAC+MIPS $\mu$ m catalogue and a SCUBA $\mu$ m catalogue." + Flux limits are introduced. to make these catalogues. resemble. those ound in the SANDE., Flux limits are introduced to make these catalogues resemble those found in the SXDF. + All objects with B«21. S557LO dy and Sao 2 mw are kept in the catalogues.," All objects with $B<27$, $_{3.6}>10\mu$ Jy and $_{850}>$ 2 mJy are kept in the catalogues." + Additional imits are placed on the fluxes in the 7SWIBIZ catalogue o take into account the varying sensitivity between the IRAC channels and. ALPS 24 jn. Catalogued objects with lux values less than μὴν at LRAC δα yum. or « 5üjy at άμα are treated. as undetected: at. these wavelength in the analysis.," Additional limits are placed on the fluxes in the “SWIRE” catalogue to take into account the varying sensitivity between the IRAC channels and MIPS 24 $\mu$ m. Catalogued objects with flux values less than $\mu$ Jy at IRAC $\mu$ m $\mu$ m, or $<50\mu$ Jy at $\mu$ m are treated as undetected at these wavelength in the analysis." + While these limits are somewhat ower than the real data in SXDE they better match the observed. number density of objects in cach catalogue., While these limits are somewhat lower than the real data in SXDF they better match the observed number density of objects in each catalogue. + This mismatch is a result of a natural disparity. between the number clensity of far-LRo luminous sources in the Gables simulations compared to the real Universe., This mismatch is a result of a natural disparity between the number density of far-IR luminous sources in the GaLICS simulations compared to the real Universe. + These cuts result in catalogues of 253 SCUBA S50; sources. 34932 Spitzer sources (10817 with 24jum). and 306842 optical|near-ir sources. respectively.," These cuts result in catalogues of 253 SCUBA $\mu$ m sources, 34932 Spitzer sources (10817 with $\mu$ m), and 306842 optical+near-ir sources, respectively." + As the flux limits for cach catalogue are imposed. in different wavelength: regimes there is a natural clisparity between the catalogues. this is rellected by the fact that not all of the sources in one catalogue have matches in the other two.," As the flux limits for each catalogue are imposed in different wavelength regimes there is a natural disparity between the catalogues, this is reflected by the fact that not all of the sources in one catalogue have matches in the other two." + Specifically. only 129 of the 253 mock SCUBA sources have corresponding entries in thecatalogue.," Specifically, only 129 of the 253 mock SCUBA sources have corresponding entries in the catalogue." +" Of these 117 are ""detected at 24 (im (1e. model S44,>505v).", Of these 117 are “detected” at 24 $\mu$ m (i.e. model $_{24\mu m}>50\mu$ Jy). + The positions of objects in the three catalogues are independently scattered. by Gaussian random: errors. with the positional uncertainty in cach case being: Optical 0.1. Spitzer 0.27 and SCUBA 85050 37.," The positions of objects in the three catalogues are independently scattered by Gaussian random errors, with the positional uncertainty in each case being: Optical 0.1”, Spitzer 0.2” and SCUBA $\mu$ m 3”." + For our first test we try and find associations between our three catalogues requiring that a 245. detection is present in theSpiüzer catalogue (Le. ομη5041] )., For our first test we try and find associations between our three catalogues requiring that a $\mu$ m detection is present in the catalogue (i.e. $_{24\mu m}>50\mu$ Jy). + bor comparison we also find the best άμα association for each mock SCUBA source using the p-statistic ((Downes 1986)., For comparison we also find the best $\mu$ m association for each mock SCUBA source using the p-statistic \nocite{Downes1986}( 1986). + Table 1. summarises the our results in ternis of completeness (total number of correct. matches over all true associations) and reliability (number of correct matches over total made)., Table \ref{tab:sims24um} summarises the our results in terms of completeness (total number of correct matches over all true associations) and reliability (number of correct matches over total made). + Like the pestatistic our approach relies on a single statistic to determine the believability of an association: the Bavesian evidence InB., Like the p-statistic our approach relies on a single statistic to determine the believability of an association; the Bayesian evidence $\ln B$. + Three InP selection thresholds are presented: none. InD.>5. and InDx»2.2.," Three $\ln B$ selection thresholds are presented; none, $\ln B>5$, and $\ln B>2.2$." +" The lnD75 selection is consistent with ""strong evidence"" for à match according to the οσονs! scale JJelfrevs (1961).", The $\ln\ B>5$ selection is consistent with “strong evidence” for a match according to the Jeffery's' scale \nocite{Jeffreys1961}J Jeffreys (1961). + A [inal selection (InD> 2.3) which matches the number of associations found. via the p«0.05 selection is also shown., A final selection $\ln B>2.2$ ) which matches the number of associations found via the $p<0.05$ selection is also shown. + This is to enable a fair and direct comparison between the two methods., This is to enable a fair and direct comparison between the two methods. + From Table 1 it can be seen that the Bayesian analysis performs similarly to the p-statistic in correctly associating sub-mm to shorter. wavelength: counterparts. with both achieving a completeness of around. ancl a reliability of —90..," From Table \ref{tab:sims24um} it can be seen that the Bayesian analysis performs similarly to the p-statistic in correctly associating sub-mm to shorter wavelength counterparts, with both achieving a completeness of around and a reliability of $\sim$." + One advantage of the Bavesian approach over the p-statistic is its abilitv to make correct. identifications at the highest redshifts., One advantage of the Bayesian approach over the p-statistic is its ability to make correct identifications at the highest redshifts. + Vhis can be seen in Figure which shows the redshift. distribution for the correct. DBavesian ancl pestatistic matches., This can be seen in Figure \ref{fig:simsNz} which shows the redshift distribution for the correct Bayesian and p-statistic matches. + The Davesian approach correctly recovers 38/42 associations at z21.5 while the p-statistic only. recovers 20/42., The Bayesian approach correctly recovers 38/42 associations at $z>1.5$ while the p-statistic only recovers 20/42. + Phe reason for this is clear. the 24//m Hux of these sources drops. dramatically as a function of redshift. whereas the 850542 flux. as a result of the negative A correction. stavs the relatively constant.," The reason for this is clear, the $\mu$ m flux of these sources drops dramatically as a function of redshift, whereas the $\mu$ m flux, as a result of the negative $k$ correction, stays the relatively constant." + Thus the 245m associations for high-z SCUBA sources will always be very, Thus the $\mu$ m associations for $z$ SCUBA sources will always be very +used decision trees to provide star/galaxy classification for the entire Sloan Digital Sky Survey (SDSS) data release.,used decision trees to provide star/galaxy classification for the entire Sloan Digital Sky Survey (SDSS) data release. + Applied agglomerative hierarchichal clustering and A-means clustering have also been used for spectral classification in. X-rays (seeHojnackietal.2006.andrefer-encestherein).., Applied agglomerative hierarchichal clustering and $K$ -means clustering have also been used for spectral classification in X-rays \citep[see][and references therein]{hojnacki}. +" Here we describe an application of K-means clustering as a classifier of objects inside the error regions of unassociated oobjects and the subsequent estimate of the ""exotic? fraction among the catalogued ppopulation.", Here we describe an application of $K$ -means clustering as a classifier of objects inside the error regions of unassociated objects and the subsequent estimate of the `exotic' fraction among the catalogued population. + Given the extreme dust extinetion and source crowding close to the Galactic plane. we restrict our analysis to high Galactic latitude.," Given the extreme dust extinction and source crowding close to the Galactic plane, we restrict our analysis to high Galactic latitude." +" Further. and in order to maximise the likelihood of association. we turn to one of the most intensively studied areas of the sky away from the Galactic plane. namely the ""overlap region’ (Kimball&Ivezié2008)."," Further, and in order to maximise the likelihood of association, we turn to one of the most intensively studied areas of the sky away from the Galactic plane, namely the `overlap region' \citep{kimball}." +. This ~000 deg area is defined by the overlap of four radio catalogues: Green Bank 6 em Survey (GB6). Faint Images of the Radio Sky at Twenty Centimeters (FIRST). NRAO-VLA Sky Survey (NVSS). and the Westerbork Northern Sky Survey (WENSS). as well as photometry and spectroscopy collected by the SDSS.," This $\sim 3000$ $^{2}$ area is defined by the overlap of four radio catalogues: Green Bank 6 cm Survey (GB6), Faint Images of the Radio Sky at Twenty Centimeters (FIRST), NRAO–VLA Sky Survey (NVSS), and the Westerbork Northern Sky Survey (WENSS), as well as photometry and spectroscopy collected by the SDSS." + The structure of the paper is as follows: $2 summarises the data selection. $3 describes the A-means classification algorithm.," The structure of the paper is as follows: 2 summarises the data selection, 3 describes the $K$ -means classification algorithm." + $4 details the results of the classification process., 4 details the results of the classification process. + $5 discusses spectral typing., 5 discusses spectral typing. + Discussion and conclusions are presented in $6 and $7., Discussion and conclusions are presented in 6 and 7. +" The ‘overlap region’ is a ~3000deg? strip around the North Galactic Cap extending between 7.6” 92%)). FIRST-GB6 (379% )). and FIRST-SDSS (2 95%)) respectively.," For the samples used here, the estimated efficiencies are FIRST-WENSS $\geq 92$ ), FIRST-GB6 $\geq 79$ ), and FIRST-SDSS $\geq 95$ ) respectively." + Thus. we can safely assume that at least >79% of all the radio sources are properly matched.," Thus, we can safely assume that at least $\geq 79$ of all the radio sources are properly matched." + Internally. we further validate the reported efficiency of the matching procedure of Kimball&Ivezié(2008) within our sample.," Internally, we further validate the reported efficiency of the matching procedure of \citet{kimball} within our sample." + All of the 110 associated ssources have a 1.4 GHz FIRST counterpart brighter than 2.5 mJy. are detected by WENSS to a limiting flux of 18 mJy. and roughly show a GB6 source brighter than 18 mJy.," All of the 110 associated sources have a 1.4 GHz FIRST counterpart brighter than 2.5 mJy, are detected by WENSS to a limiting flux of 18 mJy, and roughly show a GB6 source brighter than 18 mJy." + The of WENSS and GB6 counterparts occurs predominantly for BL Lae associations at the faint end of the FIRST radio density distribution ($4.4<31 mJy)., The of WENSS and GB6 counterparts occurs predominantly for BL Lac associations at the faint end of the FIRST radio density distribution $S_{1.4} \lax 31$ mJy). + But for the most part. the radio regime excels at capturing the non-thermal emission from y-ray sources (seealsoKovalev2009:Giro- 20100. ," But for the most part, the radio regime excels at capturing the non-thermal emission from $\gamma$ -ray sources \citep[see also][]{kovalev,giroletti,mahony,ghir}. ." +Figure 2. shows the distribution of FIRST radio fluxes for the associated ssources., Figure \ref{figure2} shows the distribution of FIRST radio fluxes for the associated sources. +constrain the star formation histories of these galaxies.,constrain the star formation histories of these galaxies. + Iu particulary. the Nal index has been shown to be a uctallicity indicator as good as C668 in the optical range. while the iudex can be used as tracer of intermecdiate-age stellar »pulatious.," In particular, the NaI index has been shown to be a metallicity indicator as good as C4668 in the optical range, while the index can be used as tracer of intermediate-age stellar populations." + The differences iu CL668. Nal. audDew... when studving low-mass galaxies in Foruax cluster aud in low cdensitv cuviroumeuts. can be interpreted as Ποια galaxies having undergone later stellar formation episodes than Fornax galaxies.," The differences in C4668, NaI, and, when studying low-mass galaxies in Fornax cluster and in low density environments, can be interpreted as field galaxies having undergone later stellar formation episodes than Fornax galaxies." + Once svuthesis stellar »»pulatiou models in the near-IR range are available. nore detailed aud quantitative predictions will be made using this interesting waveleugth region.," Once synthesis stellar population models in the near-IR range are available, more detailed and quantitative predictions will be made using this interesting wavelength region." +" The authors acknowledge the referee. Balraim Mobasher. Lis useful comments,"," The authors acknowledge the referee, Bahram Mobasher, his useful comments." + EMO acknowledges the SMES for a EPI PhD fellowship., EMQ acknowledges the SMES for a FPI PhD fellowship. + This work has been partially supported by the SMES through the research project AYA2007-67752-CO3-01., This work has been partially supported by the SMES through the research project AYA2007-67752-C03-01. +. NC) also acknowledges financial support from the research project AYA2006-L5698-C02-02., NC also acknowledges financial support from the research project AYA2006-15698-C02-02. + PSB acknowledges the flnanutial support from ai Marie Curie European Reintegration Ciraut within the 7th Enropean Community Framework, PSB acknowledges the finantial support from a Marie Curie European Reintegration Grant within the 7th European Community Framework +the order of the typical dispersion of cach iudividual Gaussian.,the order of the typical dispersion of each individual Gaussian. + The prior density for one covariate is then pU.0guoDwt)xpida.d)pbΠΩple[i): and isH summarizedB hierarchicallyH. as The prior density for multiple covariates is just the multivariate extcusion of Equations (13)) (19)).," The prior density for one covariate is then $p(\theta,\psi,\mu_0,u^2,w^2) \propto p(\pi) p(\mu|\mu_0,u^2) + p(\tau^2|w^2) p(u^2|w^2)$ and is summarized hierarchically as The prior density for multiple covariates is just the multivariate extension of Equations \ref{eq-coefprior}) \ref{eq-wsqrprior}) )." + The posterior distribution stuumarizes our knowledge about the parameters in the statistical model. eiven the observed data and the priors.," The posterior distribution summarizes our knowledge about the parameters in the statistical model, given the observed data and the priors." + Direct computation of the posterior distribution is too computationally intensive for the model described in this work., Direct computation of the posterior distribution is too computationally intensive for the model described in this work. + However. we can obtain any πο of radon draws frou the posterior using Markov chain moute carlo (AICAIC) methods.," However, we can obtain any number of random draws from the posterior using Markov chain monte carlo (MCMC) methods." + In MCMXC' methods. we simulate a Markov chain that performs a random walk through the parameter space. saving the locations of the walk at cach iteration.," In MCMC methods, we simulate a Markov chain that performs a random walk through the parameter space, saving the locations of the walk at each iteration." + Eventually. the Markov. chain couverges to the posterior distribution. aud the saved parameter values can be treated as a zaudonm draw from the posterior.," Eventually, the Markov chain converges to the posterior distribution, and the saved parameter values can be treated as a random draw from the posterior." + The random draws can then be used to estimate posterior medians. standard errors. of plot histogriun estimates of the posterior.," The random draws can then be used to estimate posterior medians, standard errors, of plot histogram estimates of the posterior." + The easiest method for sampling from the posterior is to construct a Cübbs sampler., The easiest method for sampling from the posterior is to construct a Gibbs sampler. + The basic idea belind the Cabbs sampler is to construct a Markov. Chain. where new values of the model parameters aud nissius data are simulated at cach iteration. conditional on the values of the observed data aud the current values of the model parameters and the missing data.," The basic idea behind the Gibbs sampler is to construct a Markov Chain, where new values of the model parameters and missing data are simulated at each iteration, conditional on the values of the observed data and the current values of the model parameters and the missing data." + Within the coutext ofthe measurement error model considered in this work. the Cibbs Sampler undergoes four differeut stages.," Within the context of the measurement error model considered in this work, the Gibbs Sampler undergoes four different stages." + The first stage of the Cabbs sampler simulates values of the missing data. given the measured data and current parameter values. a process kuown as data augmentation.," The first stage of the Gibbs sampler simulates values of the missing data, given the measured data and current parameter values, a process known as data augmentation." + In this work the nüssiug data are i£. and auv non-detectious.," In this work the missing data are $\eta, \xi,$ and any non-detections." + In addition. [introduce an additional latent variable. G;. which gives the class ienmbership for the /'? data point.," In addition, I introduce an additional latent variable, ${\bf G}_i$, which gives the class membership for the $i^{\rm th}$ data point." +" The vector G; has A clements. where Gy,=1 if the i! data point comes from the 18 Gaussian. and G;j—ο mκ."," The vector ${\bf G}_i$ has $K$ elements, where $G_{ik} = 1$ if the $i^{\rm th}$ data point comes from the $k^{\rm th}$ Gaussian, and $G_{ij} = 0$ if $j \neq + k$." + Twill use G to refor to the set of η vectors G;.," I will use $G$ to refer to the set of $n$ vectors ${\bf + G}_i$." + Noting that πε gives the probability of drawing a data poit from the A79 Gaussian. the mixture model for © may then be expressed. Licrarchically as Tere. Multinoim(imn.pj...PK) is a multinonial distribution with i» trials. where pj is the probability," Noting that $\pi_k$ gives the probability of drawing a data point from the $k^{\rm th}$ Gaussian, the mixture model for $\xi$ may then be expressed hierarchically as Here, ${\rm Multinom}(m,p_1,\ldots,p_K)$ is a multinomial distribution with $m$ trials, where $p_k$ is the probability" +which is similar to equation 7 in Harding.Usov.&Muslimov(2005).,which is similar to equation 7 in \citet{Hard05}. +". This expression can be integrated from €, —100 MeV to the high-energy cut off ec to give the expression which provides (he number of curvature photons emitted alone the line of sight 9, from an open field line £ al a radial distance r per primary parücle. where r is given bv the expression The Goldreich-Julian. current of primary particles from the polar cap is uniformly distributed over the polar cap and is given by (he expression The number of primary particles in a particular patch on the stellar surface al R. ϐ.. and y. which gives the number of primaries along a particular field line £. is provided by the expression The total photon Iuminosity from one pole can be obtained by integrating over the open field volume to give With ihe integral over r can be written as an integral over ϐ to give where the integral over € (the 6, has been included in the integrand) is over the open lied lines and &6,,.pe is the angle at the footpoint of the field line on the stellar surface."," This expression can be integrated from $\epsilon_\gamma$ =100 MeV to the high-energy cut off $\epsilon_{CR}$ to give the expression which provides the number of curvature photons emitted along the line of sight $\theta_\gamma$ from an open field line $\xi$ at a radial distance $r$ per primary particle, where $r$ is given by the expression The Goldreich-Julian current of primary particles from the polar cap is uniformly distributed over the polar cap and is given by the expression The number of primary particles in a particular patch on the stellar surface at R, $\theta_s$, and $\varphi$, which gives the number of primaries along a particular field line $\xi$, is provided by the expression The total photon luminosity from one pole can be obtained by integrating over the open field volume to give With the integral over $r$ can be written as an integral over $\theta$ to give where the integral over $\xi$ (the $\theta_{pc}$ has been included in the integrand) is over the open field lines and $\xi\theta_{pc}$ is the angle at the footpoint of the field line on the stellar surface." + The expression in parentheses represents the photon emission from a particular field line at € and, The expression in parentheses represents the photon emission from a particular field line at $\xi$ and +with the simple standard model. aud then cousider a fit that takes iuto account both parallax aud blending.,"with the simple standard model, and then consider a fit that takes into account both parallax and blending." +" Most mucroleusing light curves are well described by the standard form (e.g.. Paczvüsski 1986): Aeliptie =uol, utyJetty, where 0g is the nuüpacet parameter Gu units of the Einstein radius) aud wiic =te. T FeTheley; with fy being the tine of the closest approach (Quasi mmaeniication). Re the Eiustein radius. e; the lens transverse velocity relative to the observer-source Ine of sight. and fg the Einstein radius crossing time."," Most microlensing light curves are well described by the standard form (e.g., Paczyńsski 1986): A(t) =, u(t), where $\u0$ is the impact parameter (in units of the Einstein radius) and w(t) =, t_E R_E/v_t with $t_0$ being the time of the closest approach (maximum magnification), $R_E$ the Einstein radius, $v_t$ the lens transverse velocity relative to the observer-source line of sight, and $t_E$ the Einstein radius crossing time." +" The Eiusteiu radius is clefined as ,Apeposition. where M is the leus mass. D, the distance to the source aud.r=DasDy is the ratio of the distance to the leus aud the clistance to the source."," The Einstein radius is defined as R_E = , where $M$ is the lens mass, $\Ds$ the distance to the source and $x=\Dd/\Ds$ is the ratio of the distance to the lens and the distance to the source." + To fit both the Lbaud and V-baud data with the standard model. we need five parameters. namely. WO lint for pen," To fit both the I-band and V-band data with the standard model, we need five parameters, namely, 0, t_0, t_E, 0, 0." + Best-fit parameters are found by minimizing the usual P using the MINUIT program iu the CERN library aud are tabulated in Table 1., Best-fit parameters are found by minimizing the usual $\chi^2$ using the MINUIT program in the CERN library and are tabulated in Table 1. + The resulting 47 is 893.9 Or 196 degrees of freedom., The resulting $\chi^2$ is 893.9 for 496 degrees of freedom. +" For couveuence. we divide the data mto one ""unuleused! part aud one ‘lensed part: the ormner has f£—JD.2150000<1150d ancl the latT ias foc1150d."," For convenience, we divide the data into one `unlensed' part and one `lensed' part; the former has $t={\rm J.D.}-2450000<1150\d$ and the latter has $t>1150\d$." +" For the standard fit. the lensed rt has v=107.9 for 161 data poiis, and the wneused part has (=ING.! for 310 data pons: the SOLLCWrat high 4? OY his xwt nav be due to contamina10115 ο “nearby bright stars (as can be seen in the finding ¢wat). particularly at poor secing conditious."," For the standard fit, the lensed part has $\chi^2=407.9$ for 161 data points, and the unlensed part has $\chi^2=486.0$ for 340 data points; the somewhat high $\chi^2$ for this part may be due to contaminations of nearby bright stars (as can be seen in the finding chart), particularly at poor seeing conditions." +" The 47 per degree of freedom or the ""leused! part is about 2.5. iudicatiug that the fit is rot satisfactory."," The $\chi^2$ per degree of freedom for the `lensed' part is about 2.5, indicating that the fit is not satisfactory." + This cau also be seen from Fie., This can also be seen from Fig. + 1. where we show the model light «rve together with the data )0lns.," 1, where we show the model light curve together with the data points." + As can be seen. the observed vales are consisteutlv xiehter tfiui the predicted ones for f>1325« in the Lbaud.," As can be seen, the observed values are consistently brighter than the predicted ones for $t>1325\d$ in the I-band." + Further. the preiction is fainer bv about 0.05 naeutude at the peak iu the V-baud.," Further, the prediction is fainter by about 0.05 magnitude at the peak in the V-band." + We show next hat both inconsistencies can be removed by incorporating xwallax effect and bleuding., We show next that both inconsistencies can be removed by incorporating parallax effect and blending. + To take into account the Earth motion around the Sun. we have to modify the expression for «(f) in eq. (1)).," To take into account the Earth motion around the Sun, we have to modify the expression for $u(t)$ in eq. \ref{amp}) )." + This modification. to the first order of the Earth’s orbital eccentricity (e= 0.017). is eiven by Alcock et al. (," This modification, to the first order of the Earth's orbital eccentricity $\epsilon=0.017$ ), is given by Alcock et al. (" +1995) and Dominik (1998): w(t} = ay?|w(t}ο qp ays | aud the line formed by the north axis projected outo the lens plane. aj is now more appropriately the minima distance between the lens aud he Suu-source line.,"1995) and Dominik (1998): u^2(t) = 0^2+w(t)^2 + ^2 + and the line formed by the north ecliptic axis projected onto the lens plane, $\u0$ is now more appropriately the minimum distance between the lens and the Sun-source line." +" The expression of 7j, aud c are given N prrojected to the solar QOQu=25ailvr. and © is the longitude measured in ecliptic plane from the peribelion toward the Earth's motion: this is eiven in the appendix of Dominik (1998).bol. where o. is the longitude of the vernal equiON yueasnredty.CE. frongU. theιο iclion."," The expression of $\re$ and $\psi$ are given by = rojected to the solar position, $\Omega_0=2\pi/{\rm yr}$ , and $\phi$ is the longitude measured in the ecliptic plane from the perihelion toward the Earth's motion; this is given in the appendix of Dominik (1998), where $\phi_\gamma$ is the longitude of the vernal equinox measured from the perihelion." + o.=1.33 (Gad). aud the 1 daynn '»Siliélion is t2151181.57: the reacOCLs are referred to the (1999) for he relevant data.," $\phi_\gamma=1.33$ (rad), and the Julian day for Perihelion is $\tp=2451181.57$; the readers are referred to the (1999) for the relevant data." + Note hat the inclusion of the parallax effect introduces two more parameters. ¢ and 0.," Note that the inclusion of the parallax effect introduces two more parameters, $\tv$ and $\theta$." + The two-color ight curves show that the leised object )ecanne bluer by zz0.05 nag at the peak of magnification: suci chromaticity is easily produced by blexdiic., The two-color light curves show that the lensed object became bluer by $\approx 0.05$ mag at the peak of magnification; such chromaticity is easily produced by blending. + The acitional source of light may be from the lens itself alcfor it can come from another star which Les in the secing disk of the leused star by chance aligineu., The additional source of light may be from the lens itself and/or it can come from another star which lies in the seeing disk of the lensed star by chance alignment. + When Taleidlingc» is present. the observed maeuificationOo is Ooeiveu by fei To model the blending in two colors. we need two furher parameters the fraction of light contributed bv the uuleused. compoucut in I and V. f; aud fy. at the baseline.," When blending is present, the observed magnification is given by A_i = f_i + (1-f_i) A(t), i=I, V. To model the blending in two colors, we need two further parameters – the fraction of light contributed by the unlensed component in I and V, $f_I$ and $f_V$, at the baseline." + Therefore. a fit that takes into account both parallax and bleudius effects reqives 9 parameters: πριfy.te.imyzy. ΠΕνο. C0.fp. and f.," Therefore, a fit that takes into account both parallax and blending effects requires 9 parameters: $\u0, t_0, t_E, \mI0$, $\mV0$, $\tv, \theta, f_I$, and $f_V$ ." + The best-fit paramcters for this model are given in Table 1., The best-fit parameters for this model are given in Table 1. + Compared with the standard fi. the y 5.is reduced from 893.9 to 610.5.," Compared with the standard fit, the $\chi^2$ is reduced from 893.9 to 640.8." + The reduction iu the lensed part is dramatic: the 4? drops from 107.9 to 177.7 for 161 data points., The reduction in the lensed part is dramatic: the $\chi^2$ drops from 407.9 to 177.7 for 161 data points. + The 4? for the nulensed part is 163.2 (as compared to [86.0 for the standard fit) for 310 data points., The $\chi^2$ for the unlensed part is 463.2 (as compared to 486.0 for the standard fit) for 340 data points. + The u per deeree of freedom dis satisfactory., The $\chi^2$ per degree of freedom is satisfactory. + The predictedlight curve (solid line inFig., The predictedlight curve (solid line inFig. + 1) matches the observed data both in theT-baud and V-baud., 1) matches the observed data both in theI-band and V-band. + From Table 1. the bleudiug," From Table 1, the blending" +Anisotropic emission. in Active Galactic Nuclei (AGN). and. in particular. Sevlert ealaxies. has become [air well established although the mechanisms of fuelling and collimating cjecta remain problematic.,"Anisotropic emission in Active Galactic Nuclei (AGN), and, in particular, Seyfert galaxies, has become fairly well established although the mechanisms of fuelling and collimating ejecta remain problematic." + In Sevfert galaxies. the closest and a very common type of AGN. both the racio and optical emission are often observed to be emitted in a collimatecl fashion.," In Seyfert galaxies, the closest and a very common type of AGN, both the radio and optical emission are often observed to be emitted in a collimated fashion." + Sevlert galaxies are classified. according to the width of their emission lines (Ixhachikian Weedman 1971). into wo main tvpes: Tvpe Es (with broad permitted and narrow orbidden lines) and Type 25 (with narrow permitted and orbidden lines).," Seyfert galaxies are classified, according to the width of their emission lines (Khachikian Weedman 1971), into two main types: Type 1's (with broad permitted and narrow forbidden lines) and Type 2's (with narrow permitted and forbidden lines)." + The discovery ο [à hidden Broad Line teeion (BLY CXntonucei Miller. 1985). and non-stellar continuum in the polarised [lux speetrum of the Sevfert vpe 2 galaxy. NGC LOGS. Led to he present dav Unified Schemes in which the cillerent observed properties of Sevfert vpes Land 2 may be account for by viewinge angele.," The discovery of a hidden Broad Line Region (BLR) (Antonucci Miller 1985) and non-stellar continuum in the polarised flux spectrum of the Seyfert type 2 galaxy, NGC 1068, led to the present day Unified Schemes in which the different observed properties of Seyfert types 1 and 2 may be accounted for by viewing angle." +o Antonucci Miller. (1985). suggesed that. the nucleus. in Seyfert type 2's are obscured from direct view by an optically ancl ecometrically thick disk or torus but that the hidden BLR. can be seen when nuclear radiation is scattered. by electrons above and. below the poles of the torus. into the observer's line of sight.," Antonucci Miller (1985) suggested that the nucleus in Seyfert type 2's are obscured from direct view by an optically and geometrically thick disk or torus but that the hidden BLR can be seen when nuclear radiation is scattered, by electrons above and below the poles of the torus, into the observer's line of sight." + This obscuring torus would also give rise to an anisotropic nuclear radiation field., This obscuring torus would also give rise to an anisotropic nuclear radiation field. + Direct optical evidence for this anisotropic radiation [ield was provided by the discovery ofthe Extended Narrow Line Region (IZNLIU) (Unger ct al., Direct optical evidence for this anisotropic radiation field was provided by the discovery of the Extended Narrow Line Region (ENLR) (Unger et al. + 1987)., 1987). + Ehe physical and kinematic properties of the ENL~ (e.g. PWNIIM. < 45 km 1. Αν ~ 10) implied that it is ambient galactic gas photoionized by the nuclear UV. continuum radiation.," The physical and kinematic properties of the ENLR (e.g., FWHM $\le$ 45 km $^{-1}$, $_{\beta}$ $\sim$ 10) implied that it is ambient galactic gas photoionized by the nuclear UV continuum radiation." + Dhis was confirmed by the discovery of a number of extended emission line regions (Meaburn. Whitehead Pecllar 1989. Pogee 1989. Pedlar et al.," This was confirmed by the discovery of a number of extended emission line regions (Meaburn, Whitehead Pedlar 1989, Pogge 1989, Pedlar et al." + 1989. Tadhunter Tsvetanov 1989. Unger et al.," 1989, Tadhunter Tsvetanov 1989, Unger et al." + 1992. Wilson Tsvetanov 1904). ranging in size from -—370 pc to —20 kpe (Wilson WVsvetanov. 1994). consistent with ionisation by a UV. radiation Cone.," 1992, Wilson Tsvetanov 1994), ranging in size from $\sim$ 70 pc to $\sim$ 20 kpc (Wilson Tsvetanov 1994), consistent with ionisation by a UV radiation cone." +"with a high-pass filter, within the sensitivity limits of the MWA.","with a high-pass filter, within the sensitivity limits of the MWA." + The difference between the two for k Mpc? is due to the loss of large-scale contrast owing to <0.04continuum foreground subtraction., The difference between the two for $k \lsim 0.04$ $^{-1}$ is due to the loss of large-scale contrast owing to continuum foreground subtraction. + The up-turn at large k (small scales) arises from the residual fluctuations present at the edges of the bandpass (as a result of polarised foreground removal)., The up-turn at large $k$ (small scales) arises from the residual fluctuations present at the edges of the bandpass (as a result of polarised foreground removal). + Apodisation of the bandwidth is required in order to eliminate spurious power in the power spectra due to the band-edge effects discussed in Section 8.2.., Apodisation of the bandwidth is required in order to eliminate spurious power in the power spectra due to the band-edge effects discussed in Section \ref{Full data cube}. +" No overall power is lost through this procedure, however, because the sampled volume is smaller, there will be a decreased effective sensitivity due to decreased number of Fourier modes, V [see Equation (73))]."," No overall power is lost through this procedure, however, because the sampled volume is smaller, there will be a decreased effective sensitivity due to decreased number of Fourier modes, $N_{\rm m} \propto V$ [see Equation \ref{sigmaP}) )]." +" In this paper, we have shown how polarised signals can contaminate the non-polarised signal—and therefore contaminate the signature of cosmic reionisation—through the process of instrumental polarisation leakage."," In this paper, we have shown how polarised signals can contaminate the non-polarised signal—and therefore contaminate the signature of cosmic reionisation—through the process of instrumental polarisation leakage." +" We have also demonstrated how, in principle, RM synthesis may be used to recover the cosmic signal by applying an RM synthesis technique to a three-dimensional synthetic data cube."," We have also demonstrated how, in principle, RM synthesis may be used to recover the cosmic signal by applying an RM synthesis technique to a three-dimensional synthetic data cube." +" In demonstrating this, we have assumed that the brightest point sources have been sufficiently removed, and modelled the brightest astrophysical sources of foreground contamination only, for the simplest case of a single, thin Faraday screen."," In demonstrating this, we have assumed that the brightest point sources have been sufficiently removed, and modelled the brightest astrophysical sources of foreground contamination only, for the simplest case of a single, thin Faraday screen." + Our results show that it is possible to accurately, Our results show that it is possible to accurately +output was performed using SEXtractor (Bertin Arouts 1996).,output was performed using SEXtractor (Bertin Arnouts 1996). +" Instead of using a fixed aperture. we decided to use SEXtractor's ""best"" estimate for the magnitude. which starts with an 3truein +0.2truein adaptive aperture and checks whether nearby sources are expected to bias the magnitude by more than 0.1 mag. in which case an isophotal estimate is chosen instead."," Instead of using a fixed aperture, we decided to use SEXtractor's “best” estimate for the magnitude, which starts with an 3truein +0.2truein adaptive aperture and checks whether nearby sources are expected to bias the magnitude by more than 0.1 mag, in which case an isophotal estimate is chosen instead." + This method allows us to get an estimate for the flux that is closest to the actual “total” magnitude., This method allows us to get an estimate for the flux that is closest to the actual “total” magnitude. + Our F702W magnitudes agree with Smail et al. (, Our F702W magnitudes agree with Smail et al. ( +1997) to better than 0.1 mag but differ significantly from Buson et al. (,1997) to better than 0.1 mag but differ significantly from Buson et al. ( +2000) who used a fixed 1.2” aperture.,2000) who used a fixed $1.2\arcsec$ aperture. + Additional optical photometry in g and + was retrieved from Dressler Gunn (1992)., Additional optical photometry in $g$ and $r$ was retrieved from Dressler Gunn (1992). + Out of the 72 galaxies classified as early-type systems in the F702W images. we detected 42both in F300W and F702W out of which 30 (down to F702W— 22) are listed in Dressler Gunn (1992).," Out of the 72 galaxies classified as early-type systems in the F702W images, we detected 42 in F300W and F702W out of which 30 (down to $\sim 22$ ) are listed in Dressler Gunn (1992)." + Figure | shows the NUV—optical and optical CM relations., Figure 1 shows the $-$ optical and optical CM relations. + The latter are compatible with a single burst at high redshift as shown in the figure by the thick solid and dashed lines. which give the CM of a simple stellar population formed at redshifts of zp=10 and I. respectively.," The latter are compatible with a single burst at high redshift as shown in the figure by the thick solid and dashed lines, which give the CM of a simple stellar population formed at redshifts of $z_F=10$ and $1$, respectively." + The prediction for a more recent burst at zj;20.5 is also shown as a dotted line., The prediction for a more recent burst at $z_F=0.5$ is also shown as a dotted line. + These estimates use the L/—V CM relation observed in Coma and Virgo as a constraint (Bower. Lucey Ellis. 1992).," These estimates use the $U-V$ CM relation observed in Coma and Virgo as a constraint (Bower, Lucey Ellis, 1992)." + However. in the top panel. the F300W—-F702W color magnitude relation is much steeper than the prediction for a monolithic stellar population.," However, in the top panel, the $-$ F702W color magnitude relation is much steeper than the prediction for a monolithic stellar population." + A least squares fit to the data points gives a slope of —0.83. significantly steeper than for a single stellar population (—0.16 at zy= 10).," A least squares fit to the data points gives a slope of $-0.83$, significantly steeper than for a single stellar population $-0.16$ at $z_F=10$ )." + However. we should caution our readers by adding in figure 1 a conservative do. detection limit from the F300W images (shaded line).," However, we should caution our readers by adding in figure 1 a conservative $4\sigma$ detection limit from the F300W images (shaded line)." + The limiting magnitude in F702W (< 28) is safely away from the galaxies presented in this sample., The limiting magnitude in F702W $\simlt 28$ ) is safely away from the galaxies presented in this sample. + This implies many faint galaxies have not been detected and thus would appear red., This implies many faint galaxies have not been detected and thus would appear red. +" Hence. the robust assumption that we can make with the present data is that there is an increased 3truein zzero redshift, evolved galaxiesaccording to the bybest estimate for 5: and fj, luminosityMarked by eireled +0.2truein seatter in the faint end of the color-magnitude relation. showing a significant fraction of blue early-type systems in NUV-optical colors."," Hence, the robust assumption that we can make with the present data is that there is an increased 3truein zero redshift, evolved according to the best estimate for $t_Y$ and $f_M$, marked by circled +0.2truein scatter in the faint end of the color-magnitude relation, showing a significant fraction of blue early-type systems in NUV-optical colors." + This excess blueness of the fainter early-type systems can only be explained by a younger stellar component., This excess blueness of the fainter early-type systems can only be explained by a younger stellar component. + This is a feature which goes unnoticed in optical wavebands since the flux of small fractions in young stars is negligible compared to the contribution from the bulk of — older — stars in the galaxy., This is a feature which goes unnoticed in optical wavebands since the flux of small fractions in young stars is negligible compared to the contribution from the bulk of — older — stars in the galaxy. + However. the F300W filter maps rest frame which is a spectral range where the flux from a large mass in old stars can be overwhelmed by a small fraction of young stars.," However, the F300W filter maps rest frame which is a spectral range where the flux from a large mass in old stars can be overwhelmed by a small fraction of young stars." + In order to estimate the fraction of young stars we consider a simple two-stage star formation history (SEH). where stars are instantaneously formed at two different epochs (1.e. we add two simple stellar populations).," In order to estimate the fraction of young stars we consider a simple two-stage star formation history (SFH), where stars are instantaneously formed at two different epochs (i.e. we add two simple stellar populations)." +" The old component is formed at a redshift zj/=3 which gives an age of 7 Gyr at the redshift of the cluster for a A-dominated flat cosmology (Q,,20.3. Hp=70km s! Mpe7! used hereafter)."," The old component is formed at a redshift $z_F=3$ which gives an age of 7 Gyr at the redshift of the cluster for a $\Lambda$ -dominated flat cosmology $\Omega_m=0.3$ , $H_0=70$ km $^{-1}$ $^{-1}$ used hereafter)." + The age (5j) and the mass fraction Cfaj). of the young component are explored in a wide range (0.05«ty/Gyr7.0: 107«fy<1)., The age $t_Y$ ) and the mass fraction $f_M$ ) of the young component are explored in a wide range $0.05 < t_Y/Gyr < 7.0$; $10^{-4} -1.8$." + The Rossby number at which coronal activity saturates is also broadly similar across a wide range of masses., The Rossby number at which coronal activity saturates is also broadly similar across a wide range of masses. + These facts suggest that X-ray, These facts suggest that X-ray +can sliaiuk faster than it expauds due to mass loss.,can shrink faster than it expands due to mass loss. + In this particular example the core reached almost exactly the divergence point. shedding O.LAL.. during the MIT so that the Πτα iiass was ie).," In this particular example the core reached almost exactly the divergence point, shedding $\sim 0.4 M_\odot$ during the MT so that the final mass was $m_{\rm cp}$." + We also performed a MT calculation in the fully non-conservative regine., We also performed a MT calculation in the fully non-conservative regime. + Iu this case the final mass of the core after the TR phase is the sale as in the conservative calculations., In this case the final mass of the core after the TR phase is the same as in the conservative calculations. + We also considered the case when the compauion is a NS., We also considered the case when the companion is a NS. +" We note that with a 2041, donor then. even for ace=Ll. the energy requirements for envelope ejection would not be satisfied if the core expands as mich as we find after our fast mass loss (i.e. the binary would merece)."," We note that with a $20 M_\odot$ donor then, even for $\alpha_{\rm CE}=1$, the energy requirements for envelope ejection would not be satisfied if the core expands as much as we find after our fast mass loss (i.e. the binary would merge)." + The final mass of the remnant of the massive eiut is the same. {ου as for the 3AL. companion.," The final mass of the remnant of the massive giant is the same, $m_{\rm cp}$, as for the $3~M_\odot$ companion." + If the lnass transfer is fully conservative. the NS is prestmably spun-up. as it would acctunulate ΕΕ ," If the mass transfer is fully conservative, the NS is presumably spun-up, as it would accumulate $0.34 M_\odot$." +Again. in the case of a fully nou- conservative regine. we find that the final mass of the post-CE roiuaut is Hie).," Again, in the case of a fully non- conservative regime, we find that the final mass of the post-CE remnant is $m_{\rm cp}$ ." + Next we considered a svstem witha 10A. giant (same as shown in Fie. 2)).," Next we considered a system with a $10\ M_\odot$ giant (same as shown in Fig. \ref{core_10_caseA}) )," +" considering as the post-CE core 2.5LAL. (na,= 2.01).", considering as the post-CE core $2.54~M_\odot$ $m_{\rm cp} = 2.04$ ). +" In our MT sinulatious with a NS colmpalion. less material above ie, has been trausterred. oulv 0.21.AZ... the final remmaut mass is 2.3AL..."," In our MT simulations with a NS companion, less material above $m_{\rm cp}$ has been transferred, only $0.24~M_\odot$, the final remnant mass is $2.3 ~M_\odot$." + It nuelt be connected to the fact that LO AY.. star does uot have such a sharp profile as a 20A in the post-CE thermal pulse zoue. aud its post-CE expansion.. is more flatter until about this mass (see Fig. 2)).," It might be connected to the fact that 10 $M_\odot$ star does not have such a sharp profile as a $20 M_\odot$ in the post-CE thermal pulse zone, and its post-CE expansion is more flatter until about this mass (see Fig. \ref{core_10_caseA}) )." + With a smaller colupalion mass. more of the post-CE remnanut mass is stripped. off.," With a smaller companion mass, more of the post-CE remnant mass is stripped off." + The MT rates that we encounter in the post-CE TR phase are highly super-Eddington aud we face the obvious question whether the AIT is approximately conservative or almost non-conservative. as this is crucial for a companion.," The MT rates that we encounter in the post-CE TR phase are highly super-Eddington and we face the obvious question whether the MT is approximately conservative or almost non-conservative, as this is crucial for a companion." + The question what happens if the mass-accretion rate ou a NS exceeds Eddington limit has becu discussed exteusivelv in the literature. in particular. the reeinue in which it excecds Algaqmagnitude.," The question what happens if the mass-accretion rate on a NS exceeds Eddington limit has been discussed extensively in the literature, in particular, the regime in which it exceeds $\dot M_{\rm Edd}$." + Beechuan(1979) showed that if the accretion rate is exticiielv high. few times LOMAL.wr|. then within some volume (the“trappingradius”.e.g.Kine&Beeclman1999) around the star the diffusion of photons outward cannot overcome the advection of photons inward.," \cite{1979MNRAS.187..237B} showed that if the accretion rate is extremely high, few times $10^{-4}M_\odot~{\rm yr}^{-1}$, then within some volume \citep[the ``trapping radius'', e.g.][]{1999ApJ...519L.169K} around the star the diffusion of photons outward cannot overcome the advection of photons inward." + While a black hole can swallow all the material in this case. if the accretor is a NS. radiation pressure near the NS surface resists inflow idu excess of the Eddington limit. likely leading to creation of a Thorne-Zxttkov object.," While a black hole can swallow all the material in this case, if the accretor is a NS, radiation pressure near the NS's surface resists inflow in excess of the Eddington limit, likely leading to creation of a Thorne-Z\'yttkov object." + Blondin(1986). has also found that when AIT rates exceed the Eddington rate by 105&Lage? or more. the accretion proceeds in a liypereritical regime.," \cite{Blondin1986} has also found that when MT rates exceed the Eddington rate by $10^{3}\times L_{\rm Edd}/c^2$ or more, the accretion proceeds in a hypercritical regime." + Uspereritical accretion was then argued to. be responsible for such efficient material acceunuulation duriug a CE event. that a NS is likely to convert to a black hole (Chevalier1989)..," Hypercritical accretion was then argued to be responsible for such efficient material accumulation during a CE event, that a NS is likely to convert to a black hole \citep{1989ApJ...346..847C}." + Brown(1995) used this argunueut to understand double NS formation., \cite{Brown1996} used this argument to understand double NS formation. + Ie showed that indeed in a CE event the Doudi-IHovle-Lyttleton accretion rate is about 104&Mg aud a NS can accumulate up to 13..., He showed that indeed in a CE event the Bondi-Hoyle-Lyttleton accretion rate is about $10^4 \times \dot M_{\rm Edd}$ and a NS can accumulate up to $1~M_\odot$. + We avened that iu this case. considering that a number of the discovered double NS have masses closer to the lowest possible NS mass lint. a double NS can be formed only from a binary with almost simular initial masses. evolving then via double CE eveut. before either of tle NSs was formed.," He argued that in this case, considering that a number of the discovered double NS have masses closer to the lowest possible NS mass limit, a double NS can be formed only from a binary with almost similar initial masses, evolving then via double CE event, before either of the NSs was formed." + IIouck&Chevalier(1991). cousicdered neutriuo losses during accretion on a NS., \cite{1991ApJ...376..234H} considered neutrino losses during accretion on a NS. + Thev studied iu detail the regimes of the mass accretion 10.1 msun)) have considerably shorter lifetimes (about 10 Myr) than massive stars that produce the UV continuum."," Moreover, the massive stars that can produce measurable amounts of ionising photons (stars with M $>$ ) have considerably shorter lifetimes (about 10 Myr) than massive stars that produce the UV continuum." +" Of the Balmer lines, is the most directly proportional to the ionising UV stellar spectra, because the weaker lines are much more affected by the equivalent absorption lines produced in stellar atmospheres."," Of the Balmer lines, is the most directly proportional to the ionising UV stellar spectra, because the weaker lines are much more affected by the equivalent absorption lines produced in stellar atmospheres." +" This SFR indicator is sensitive to the high end of the IMF, much more than the UV continuum, to dust extinction and to the possible leakage of ionising photons."," This SFR indicator is sensitive to the high end of the IMF, much more than the UV continuum, to dust extinction and to the possible leakage of ionising photons." +" Moreover, it is also susceptible to the stochastic formation of high mass stars and may not reliably measure the SFR when the activity is low (?).."," Moreover, it is also susceptible to the stochastic formation of high mass stars and may not reliably measure the SFR when the activity is low \citep{Lee2009}." +" FIR luminosity is a SFR tracer complementary to the UV and optical ones if we assume that much of the stellar light from new-born stars is absorbed, reprocessed by dust (since the cross section of the dust peaks in UV) and emerges in the FIR wavelength region."," FIR luminosity is a SFR tracer complementary to the UV and optical ones if we assume that much of the stellar light from new-born stars is absorbed, reprocessed by dust (since the cross section of the dust peaks in UV) and emerges in the FIR wavelength region." + The efficacy of this SFR diagnostic depends on the fraction of obscured SF and on the optical depth of the dust in star forming regions., The efficacy of this SFR diagnostic depends on the fraction of obscured SF and on the optical depth of the dust in star forming regions. +" The timescale for FIR emission is set by the time it takes massive stars to remove their surrounding material by radiation pressure, expansion of giant HII regions or SN explosions (about 2 Myr)."," The timescale for FIR emission is set by the time it takes massive stars to remove their surrounding material by radiation pressure, expansion of giant HII regions or SN explosions (about 2 Myr)." +" However, this SFR indicator is affected by the contribution to dust heating by older stars and AGNs."," However, this SFR indicator is affected by the contribution to dust heating by older stars and AGNs." +" Although the FIR luminosity can provide a reliable measure of the SFR only in the most obscured circumnuclear starburst, the combination of the dust-attenuated fluxes in the UV and with measurements of the dust emission in the FIR in the same galaxy sample can provide consistent extinction-corrected SFRs (?).."," Although the FIR luminosity can provide a reliable measure of the SFR only in the most obscured circumnuclear starburst, the combination of the dust-attenuated fluxes in the UV and with measurements of the dust emission in the FIR in the same galaxy sample can provide consistent extinction-corrected SFRs \citep{Kennicutt2009}." + An alternative and complementary approach to trace the SFR is based on the direct observation of the numbers of CC SNe occurring in a sample of galaxies or in a given volume., An alternative and complementary approach to trace the SFR is based on the direct observation of the numbers of CC SNe occurring in a sample of galaxies or in a given volume. +" The CC SN rate (Rcc)) is given, following the formalism by ?,, by: where t is the time elapsed since the beginning of SF in the galaxy under analysis, y is the SFR, k(t—τ) is the number of stars per unit mass of the stellar generation born at epoch (t— 1), Acc(t-T) is the number fraction ofstars from this stellar generation that end up as CC SNe,"," The CC SN rate ) is given, following the formalism by \citet{Blanc2008}, by : where t is the time elapsed since the beginning of SF in the galaxy under analysis, $\psi$ is the SFR, $k(t-\tau)$ is the number of stars per unit mass of the stellar generation born at epoch $(t-\tau)$ , $(t-\tau)$ is the number fraction ofstars from this stellar generation that end up as CC SNe," +"In the case of weak lensing, the transformation in Equation |l| is expanded in a Taylor series valid in the neighborhood of the position of the image (9 in the image plane, 0 in the source plane) in question.","In the case of weak lensing, the transformation in Equation \ref{eq:exactlensing} is expanded in a Taylor series valid in the neighborhood of the position of the image $\theta_0$ in the image plane, $\beta_0$ in the source plane) in question." +" To include the flexion fields, this expansion must extend to quadratic order, and yields The first-order lensing fields (convergence and shear) are &—IVV* and y=IV? the-second order fields (flexion) are F=VkV*y and G=Vy."," To include the flexion fields, this expansion must extend to quadratic order, and yields The first-order lensing fields (convergence and shear) are $\kappa=\frac{1}{2}\nabla\nabla^*\psi$ and $\gamma=\frac{1}{2}\nabla^2\psi$; the-second order fields (flexion) are $\fflex=\nabla\kappa=\nabla^*\gamma$ and $\gflex=\nabla\gamma$." +" Throughout this paperwe will refer to F as 1-flexion and G as 3-flexion, refering to the spin symmetry of the fields with respect to coordinate rotations."," Throughout this paperwe will refer to $\fflex$ as 1-flexion and $\gflex$ as 3-flexion, refering to the spin symmetry of the fields with respect to coordinate rotations." +" Elsewhere in literature, these lensing fields are called “first flexion” and “second flexion”, respectively."," Elsewhere in literature, these lensing fields are called “first flexion” and “second flexion”, respectively." +" We prefer the spin-based notation because it indicates a physical property of the flexion fields, rather than an arbitrary ordering."," We prefer the spin-based notation because it indicates a physical property of the flexion fields, rather than an arbitrary ordering." + All derivatives of the lensing potential are evaluated at 69., All derivatives of the lensing potential are evaluated at $\theta_0$. +" This notation follows that of(2008),, which simplifies the tensor notation of(2005)."," This notation follows that of, which simplifies the tensor notation of." +". When considering a single lensed image, the constant terms in Equation B| are degenerate and unmeasureable, and can be neglected in favor of small deviations 0 about the observed image center 69."," When considering a single lensed image, the constant terms in Equation \ref{eq:lensingexpansion} are degenerate and unmeasureable, and can be neglected in favor of small deviations $\theta$ about the observed image center $\theta_0$." + This gives a second-order local lensing equation This local lensing equation is sufficient for producing “arced” images from intrinsically circular or elliptical ones., This gives a second-order local lensing equation This local lensing equation is sufficient for producing “arced” images from intrinsically circular or elliptical ones. +" It is valid in the regime where the dimensionless products of the image size and the flexion fields, a;|F| and a;|G|, are small with respect to unity."," It is valid in the regime where the dimensionless products of the image size and the flexion fields, $a_I|\fflex|$ and $a_I|\gflex|$ , are small with respect to unity." + The, The +The Chandra spectra were fitted in the 0.3-7 keV energy range (at higher energies no source emission is detected).,The $Chandra$ spectra were fitted in the 0.3-7 keV energy range (at higher energies no source emission is detected). + We first analysed the spectrum of the extended emission alone] (taken from an annulus with inner and outer radit of and. respectively).," We first analysed the spectrum of the extended emission alone (taken from an annulus with inner and outer radii of and, respectively)." + The count rate of this region. over the adopted 0.3-7 keV energy range. is 0.017 cts/s. The spectrum is quite soft. and it is reasonably well fitted either by an absorbed power law with 23.0 7: and Nyz14 12x107! dm (y7=1.0/6 d.o.f.).," The count rate of this region, over the adopted 0.3-7 keV energy range, is 0.017 cts/s. The spectrum is quite soft, and it is reasonably well fitted either by an absorbed power law with $\Gamma$ $^{+0.7}_{-0.5}$ and $N_H$ $^{+1.2}_{-0.5}\times10^{21}$ $^{-2}$ $\chi^2_{\rm r}$ =1.0/6 d.o.f.)," + or by a thermal plasma spectrum (modelMEKAL: (y7=1.2/5 d.o.f.), or by a thermal plasma spectrum (model; $\chi^2_{\rm r}$ =1.2/5 d.o.f.) + with kT=1.27)5 keV: for the latter model. only upper limits of 0.19 solar and of 0.9%107! em ean be put on the metal abundance and the absorber column density. respectively.," with $kT$ $^{+1.2}_{-0.7}$ keV; for the latter model, only upper limits of 0.19 solar and of $\times10^{21}$ $^{-2}$ can be put on the metal abundance and the absorber column density, respectively." + Given the implausibly low metal abundance. in the following we will adopt the power law mode] (even if. of course. the low metal abundance may derive from à too simple thermal plasma model: however. statistics is nof good enough to test more complex models).," Given the implausibly low metal abundance, in the following we will adopt the power law model (even if, of course, the low metal abundance may derive from a too simple thermal plasma model; however, statistics is not good enough to test more complex models)." + In this Case. ibsorption in excess of the Galactic one (1.8109 em. Dickey Lockman 1990) is required. and may be due to the dust lane observed by HST (Malkan et al.," In this case, absorption in excess of the Galactic one $\times10^{20}$ $^{-2}$, Dickey Lockman 1990) is required, and may be due to the dust lane observed by HST (Malkan et al." + 1998)., 1998). +" The value of the Nj, is broadly in agreement with the reddening to the NLR. which i$ Av 21.4[ (Murayama et al."," The value of the $N_H$ is broadly in agreement with the reddening to the NLR, which is $A_V$ =1.4 (Murayama et al." + 1998)., 1998). + We then analyzed the spectrum extracted from a circular cell with a radius of (count rate of 0.14 cts/s). (, We then analyzed the spectrum extracted from a circular cell with a radius of (count rate of 0.14 cts/s). ( +We choose te-anályze the unresolvedt+textended spectrum. instead of the nuclear spectrum alone. to make easier the comparison with the XMM-Newton spectrum. as well as with spectra from previous satellites.,"We choose to analyze the unresolved+extended spectrum, instead of the nuclear spectrum alone, to make easier the comparison with the $Newton$ spectrum, as well as with spectra from previous satellites." + In any case. unresolved emisstor dominates at all energies.)," In any case, unresolved emission dominates at all energies.)" + Following Iwasawa et al. (, Following Iwasawa et al. ( +2001) we adopted a model composed of: a nuclear power law absorbed by a cold screen of 2x107 em™*: a cold reflection component model: the illuminating power law index has been initially fixed to 2. given the limited statistics available): a 6.4 keV narrow iron line: a soft X-ray emission component. parameterized by a power law: and Galactic absorption.,"2001) we adopted a model composed of: a nuclear power law absorbed by a cold screen of $\times10^{24}$ $^{-2}$; a cold reflection component model; the illuminating power law index has been initially fixed to 2, given the limited statistics available); a 6.4 keV narrow iron line; a soft X-ray emission component, parameterized by a power law; and Galactic absorption." + The fit is completely unacceptable (y7=4.4/36 d.o.£.:, The fit is completely unacceptable $\chi^2_{\rm r}$ =4.4/36 d.o.f.; + see Fig. 3)).," see Fig. \ref{ch_badsp}) )," + partly due to two emission features at about 0.55 and 0.9 keV (the latter was indeed already found by Iwasawa et al 2001 in the ASCA spectrum)., partly due to two emission features at about 0.55 and 0.9 keV (the latter was indeed already found by Iwasawa et al 2001 in the ASCA spectrum). + The inclusion of these two lines improves the fit significantly: however. the y is still unacceptable (y722.3/32 d.o.f.).," The inclusion of these two lines improves the fit significantly; however, the $\chi^2$ is still unacceptable $\chi^2_{\rm r}$ =2.3/32 d.o.f.)." + Adding a thermal plasma component further improves the quality of the fit (y7=1.68/29 d.o.£.).," Adding a thermal plasma component further improves the quality of the fit $\chi^2_{\rm r}$ =1.68/29 d.o.f.)," + which however remains poor., which however remains poor. + A much better. and fully acceptable. fit (y7=0.88/31 d.o.f.)," A much better, and fully acceptable, fit $\chi^2_{\rm r}$ =0.88/31 d.o.f.)" + is instead obtained by allowing the cold absorption. covering all components. to be larger than the Galactic value.," is instead obtained by allowing the cold absorption, covering all components, to be larger than the Galactic value." + Interestingly. the best fit value. ~3x107! ον”. is what is expected from the optical extinction.," Interestingly, the best fit value, $\sim3\times10^{21}$ $^{-2}$, is what is expected from the optical extinction." + No significant improvement is found after adding either a He-like or a H-like iron line., No significant improvement is found after adding either a He–like or a H–like iron line. + The best-fit values are summarized in Table 1. and the spectrum is shown in Fig. 4..," The best–fit values are summarized in Table 1, and the spectrum is shown in Fig. \ref{ch_goodsp}." + As the power law index of the soft component ts much larger than 2. the value we assumed for the hard X-ray component (both transmitted and reflected). we tried to link the two values to each other.," As the power law index of the soft component is much larger than 2, the value we assumed for the hard X-ray component (both transmitted and reflected), we tried to link the two values to each other." + The resulting value of E 1s 2.9. but the fit is unacceptable (y7=l96/31 d.o.f.).," The resulting value of $\Gamma$ is 2.9, but the fit is unacceptable $\chi^2_{\rm r}$ =1.96/31 d.o.f.)." + A fit with a thermal plasma model instead of the soft power law plus two lines also fails to give an acceptable fit (y7=1.8/34 d.o.f) mainly because the two lines remain unfitted., A fit with a thermal plasma model instead of the soft power law plus two lines also fails to give an acceptable fit $\chi^2_{\rm r}$ =1.8/34 d.o.f) mainly because the two lines remain unfitted. + Adding instead either the thermal, Adding instead either the thermal + ∐∢⋅↓⋜⋯⊾∠⇂≻∢⋟↓⇂⇂↿↕⋖≱↓↕≻≼⇍⋜⋯∣⋊⋅⋠⊔⇂⋖⋅⊔↿⊲↓∐∢⊾∠⇂↕↓↕≻⇂⋜↧⋡⇂∙∖⇁≱∖↥↓⋅⋜↧⊲↓∐⋖⋅∠⇂⊳∖∩⊾∐⋜⊔⋅ ⋜⊔⊔↓∪⊳∖↓≻↓∐⋅↓⋅∢⊾⊳∖⊳∖∖⊽↓↕∢⋅↓⋅⋖⊾⇂↓↕⋖⋅∙∖⇁⋜⊔⋅∢⊾↓∡⊔∪∖∖⋎⊔∥⊳∖↓⋅⊔↓∪∠,"Related solutions can be identified in stably stratified stellar atmospheres, where they are known as r modes \citep{1978MNRAS.182..423P}." +⇂⋖⋅⊳∖∖↓↴⋜↧↓≻⋜↧↓⋖⋟↕∠⋖⋟⇂⇂ ⊾∖↽↓↴↓⋰↓⊔⋏∙≟↓⋖⋅↓≤⋗⊤↖∖⊐↣ ↾∐↕⋖⋅↓⋅⋖⊾⊳∖∪⊔⋜⋯≼∙⋖⋅∠⇂∢⋅≱∖≼∙↓⋰↓∣⋊⋅∠⇂⋜↧∣⋡∪∖⇁∢⋅⋯∙≼∙⊔↓⋅⊳∖∖∖⋰↓↿↥↿↓↥∢⊾↿∖⋯∶ ⇉," The resonance described above occurs with the $(m=2,n=3)$ Rossby wave or r mode at $\omega=-\Omega/3$. (" +⊳⊔∶∶↗≻∃↓⊰∪≱∖≱∖∣⋡∙∖⇁∖∖⋎⋜↧∖⇁∢⋅∪↓⋅↓⋅⊔↓⋯⇂∢⊾⋜∐∣∽↙⋎∶≤≥∶∫≻⋡⋃∖⊽∪↿⋖⋅ ⇂↓⋯↿↿⇂↥⊀↓⊳∖⊲↓⊳∖⊔∪↿∢⊾⊏↥⇂⇂↕∖⇁⋜↧↓∢⋅↓↕↿↿∪⇂↓↕∢⊾⊳∖↓≻⋖⊾≼⋰↓⋜↧↓⊳↓≻⊔↓⋅∢⊾↓∙∖⇁↿⋖⋟↓⋅∢≱↕∠⇂⋜↧↓ mode discussed in Section 2c 3.3... which has a frequency. of w= 20/3and involves no radial motion.),"Note that this is not equivalent to the special, purely toroidal mode discussed in Section \ref{s:modes}, , which has a frequency of $\omega=-2\Omega/3$ and involves no radial motion.)" +" The appropriate balance in equations (21)) and (22)) is then The boundary conditions. determine that da,αν=(ο)δν and we casily obtain 5, and ce, from the above equations."," The appropriate balance in equations \ref{cneq}) ) and \ref{dneq}) ) is then The boundary conditions determine that $\rmd a_n/\rmd r=(U/\epsilon +R)\delta_{n\ell}$ and we easily obtain $b_n$ and $c_n$ from the above equations." + In the case (=m2 investigated. here. the toroidal velocity component ο is excited ancl becomes large when zx is small. which occurs close to ο=1/3.," In the case $\ell=m=2$ investigated here, the toroidal velocity component $c_3$ is excited and becomes large when $\omega_3$ is small, which occurs close to $\omega/\Omega=-1/3$." + The resulting dissipation rate is This expression provides an excellent fit. to. the numerically determined. dissipation rate in the frictiona problem for a=0.99., The resulting dissipation rate is This expression provides an excellent fit to the numerically determined dissipation rate in the frictional problem for $\alpha=0.99$. + Note that 2 is inversely. proportiona to the thickness of the shell., Note that $D$ is inversely proportional to the thickness of the shell. + This result occurs because the fast barotropic Dow (i.e. horizontal motion independent. of depth) excited in a thin shell is efficiently. clamped by the artificial frictional force in this model: a dillerent behaviour would occur in à viscous [uil, This result occurs because the fast barotropic flow (i.e. horizontal motion independent of depth) excited in a thin shell is efficiently damped by the artificial frictional force in this model; a different behaviour would occur in a viscous fluid. + Nevertheless. it ds wel known from the case of the Earth that highly ellicient. tida dissipation can occur in a shallow ocean.," Nevertheless, it is well known from the case of the Earth that highly efficient tidal dissipation can occur in a shallow ocean." + The case of the ]5arth's ocean is of course enormously. complicated. by its irregular shape and depth., The case of the Earth's ocean is of course enormously complicated by its irregular shape and depth. + Mode conversion and turbulence provide channels for dissipation., Mode conversion and turbulence provide channels for dissipation. + The original tidal. problem. described in Section 2.. gives results very similar to those of the simplified. raclially forced xoblem.," The original tidal problem, described in Section \ref{s:tidal}, gives results very similar to those of the simplified, radially forced problem." + Some additional parameters are required. το set up the tidal problem: the ratio of the dynamical frequency (g/0).7 to the spin frequency ©. and the ratio 3 of the luid density to the mean density of the planet.," Some additional parameters are required to set up the tidal problem: the ratio of the dynamical frequency $(g/R)^{1/2}$ to the spin frequency $\Omega$, and the ratio $\beta$ of the fluid density to the mean density of the planet." + In Fig., In Fig. + 3 we compare the dissipation rates in the tidal ancl racdially orced. problems. with a=0.5. 4=1 and ο=10?," \ref{f:tidal} we compare the dissipation rates in the tidal and radially forced problems, with $\alpha=0.5$, $\beta=1$ and $\gamma/\Omega=10^{-3}$." +" In order to make the comparison we assume that the raclia velocity at the surface is determined by equation (27)) in he low-frequeney limit in which the WW), term (and also the viscous terni) is neglected.", In order to make the comparison we assume that the radial velocity at the surface is determined by equation \ref{tidalbc}) ) in the low-frequency limit in which the $W_n$ term (and also the viscous term) is neglected. + This is equivalent to saving tha he racial displacement of the surface is (5/2)/g. where he factor of 5/2 comes from the seli-gravityv of the uid.," This is equivalent to saying that the radial displacement of the surface is $-(5/2)\Psi/g$, where the factor of $5/2$ comes from the self-gravity of the fluid." + When the planet is slowly rotating. in the sense tha (οI)7 the agreement is excellent ancl shows tha he excitation of inertial waves is not allected by the freedom of the outer boundary.," When the planet is slowly rotating, in the sense that $\Omega\ll(g/R)^{1/2}$, the agreement is excellent and shows that the excitation of inertial waves is not affected by the freedom of the outer boundary." + For more rapidly rotating planets the influence of surface gravity waves becomes apparent in this range of frequencies., For more rapidly rotating planets the influence of surface gravity waves becomes apparent in this range of frequencies. + For such rapidly rotating planets the centrifugal distortion of the Iluid. ought to be taken intoaccount., For such rapidly rotating planets the centrifugal distortion of the fluid ought to be taken intoaccount. + In order to investigate the response in greater detail. we restrict our attention to the case of a fractional core radius o—0.5 and to a certain of rangefrequencies. |? (Table 2).," For instance, \citet{1995A&A...293..889P} found a mean $S\simeq 0.5$ from their sample of X-ray halos, which corresponds $\tau_{{\rm s,1keV}}\simeq0.24$ for LS 5039 where $N_H=6.4\times10^{21}$ $^{-2}$ (Table 2)." +" An even better correlation for 7, was obtained with the optical extinction towards the object. zj;45ey=0.056.447 (see Appendix A). which gives τοον=0.32 (for Ay=3.9: ?2)). in good agreement with the previous estimate."," An even better correlation for $\tau_{{\rm s}}$ was obtained with the optical extinction towards the object, $\tau_{{\rm s,1keV}}=0.056 A_V$ (see Appendix A), which gives $\tau_{{\rm s,1keV}}=0.22$ (for $A_V=3.9$; \citealt{2002A&A...384..954R}) ), in good agreement with the previous estimate." + The relatively low value of τοΊαν allows us to neglect the contributions of multiple scatteriugs [or EZlkkeV. We have calculated. the halo. profile in the siugle-scatteriug approximation by folkdiug[n] the spectral intensity of a halo (see e.g. ?.. also Appendix A) with the detector response in the SkkeV enerey range.," The relatively low value of $\tau_{{\rm s,1keV}}$ allows us to neglect the contributions of multiple scatterings for $E\ga1$ keV. We have calculated the halo profile in the single-scattering approximation by folding the spectral intensity of a halo (see e.g., \citealt{1991ApJ...376..490M}, also Appendix A) with the detector response in the keV energy range." +" We find that. for instance. for the parameters O=360"" and S=1. and the dust distribution function (Cr) defined in Appendix A. the dust halo model overall describes the observed radial profile (see Fie. 1)."," We find that, for instance, for the parameters $\Theta=360\arcsec$ and $S=1$, and the dust distribution function $f(x)$ defined in Appendix A, the dust halo model overall describes the observed radial profile (see Fig. \ref{rad}) )." + Although some deviations are noticeable. they might be attributed to the uuperlect. choice of the above parameters (we did uot perform rigorous fittiug) or to the inaccuracy of the ? ιούς] or the Rayleigh-Gaus (RG) approximation to the scattering Cross section at low energies (.39 keV).," Although some deviations are noticeable, they might be attributed to the imperfect choice of the above parameters (we did not perform rigorous fitting) or to the inaccuracy of the \citet{2003ApJ...598.1026D} model or the Rayleigh-Gans (RG) approximation to the scattering cross section at low energies $\lesssim 2$ keV)." +close to the epoch when we observe it.,close to the epoch when we observe it. + [tis still surprising that the combination of constants appearing in equation (8)) is roughly close to unity for a star like (he Sun. but (his coincidence now seems much less unlikely (han in the case when the two very small fundamental constants of nature are unrelated.," It is still surprising that the combination of constants appearing in equation \ref{trat}) ) is roughly close to unity for a star like the Sun, but this coincidence now seems much less unlikely than in the case when the two very small fundamental constants of nature are unrelated." + It should be noted that this explanation for the coincidence problem is unrelated to the anthropic principle., It should be noted that this explanation for the coincidence problem is unrelated to the anthropic principle. + The prediction that the expansion should start accelerating when the age ol the universe is of (he same order as (he lifetime of a star is à purely physical one xl bears no relation to our presence in (he universe., The prediction that the expansion should start accelerating when the age of the universe is of the same order as the lifetime of a star is a purely physical one and bears no relation to our presence in the universe. + The fact that the lifetime of the Sun and (he present age of the universe are comparable is known to be (rue. and it has not been considered a surprising coincidence: this may be related to a “weak”À and obvious form of { antliropic principle (hat says that we must appear in the universe al the epoch when most of the stars adequate for harboring planets with life ave in their main-sequence phase.," The fact that the lifetime of the Sun and the present age of the universe are comparable is known to be true, and it has not been considered a surprising coincidence: this may be related to a “weak”´ and obvious form of t anthropic principle that says that we must appear in the universe at the epoch when most of the stars adequate for harboring planets with life are in their main-sequence phase." + ] acknowledge support by the Spanish grant. AYA2009-09745., I acknowledge support by the Spanish grant AYA2009-09745. +between these (wo events has vet to be definitively established (Chapmanetal.2007:Cuketal.2010:Alalhotva&Strom 2010).,"between these two events has yet to be definitively established \citep{Chapman:2007p97,Cuk:2010p4126,Malhotra:2010}." +. Such migration would have enhanced (he impact [lux of both asteroids ancl comets onto the terrestrial planets in two wavs., Such migration would have enhanced the impact flux of both asteroids and comets onto the terrestrial planets in two ways. + First. many of the icv planetesimals scattered by the giant. planets would have crossed (he orbits of the terrestrial planets.," First, many of the icy planetesimals scattered by the giant planets would have crossed the orbits of the terrestrial planets." + Second. as (he giant. planets migrated. locations of mean motion and secular resonances would have swept across the asteroid belt. raising the eccentricilies of asteroids to planet-crossing values.," Second, as the giant planets migrated, locations of mean motion and secular resonances would have swept across the asteroid belt, raising the eccentricities of asteroids to planet-crossing values." + Recently. Minton&Malhotra(2009) showed that the patterns of depletion observed in the asteroid belt are consistent with the ellects of sweeping of resonances during the migration of (he giant planets.," Recently, \cite{Minton:2009p280} showed that the patterns of depletion observed in the asteroid belt are consistent with the effects of sweeping of resonances during the migration of the giant planets." + The Jupiter-lacing sides of some of the Kirkwood gaps (regions of the asteroid belt that are nearly empty due to strong jovian mean motion resonances) are depleted relative to the Sun-facing sides. as would be expected due to the inward mieration of Jupiter aud the associated inward sweeping of the jovian mean motion resonances.," The Jupiter-facing sides of some of the Kirkwood gaps (regions of the asteroid belt that are nearly empty due to strong jovian mean motion resonances) are depleted relative to the Sun-facing sides, as would be expected due to the inward migration of Jupiter and the associated inward sweeping of the jovian mean motion resonances." + The region within the inner asteroid belt between semimajor axis range 2.1 2.5AU also has excess depletion relative to a model asteroid bell (hat was uniformly. populated and then subsequently sculpted by the gravitational perturbations of the planets over 4Gv. as would be expected due to the outward migration of Saturn and (he associated inward sweeping of a strong secular resonance. (he so-called £j resonance. as explained below.," The region within the inner asteroid belt between semimajor axis range $2.1$ $2.5\AU$ also has excess depletion relative to a model asteroid belt that was uniformly populated and then subsequently sculpted by the gravitational perturbations of the planets over $4\Gy$, as would be expected due to the outward migration of Saturn and the associated inward sweeping of a strong secular resonance, the so-called $\nu_6$ resonance, as explained below." + Ii our 2009 study. we concluded that the semimajor axis distribution of asteroids in the main belt is consistent with the inward migration of Jupiter and outward migration of Saturn by amounts proposed in previous studies based on the Ixuiper belt resonance structure(e.g..Alalhotra1995)..," In our 2009 study, we concluded that the semimajor axis distribution of asteroids in the main belt is consistent with the inward migration of Jupiter and outward migration of Saturn by amounts proposed in previous studies based on the Kuiper belt resonance \citep[e.g.,~][]{Malhotra:1995p79}." + llowever. in that study (the migration timescale was not stronglv constrained. because only the relative depletion of asteroids in nearby semimajor axis bins could be determined. not (heir overall level of depletion.," However, in that study the migration timescale was not strongly constrained, because only the relative depletion of asteroids in nearby semimajor axis bins could be determined, not their overall level of depletion." + In the present paper. we explore in more detail the effect that planet migration would have had on the asteroil belt due (o asteroid eccentricitv excitation bv the sweeping of (he μη secular resonance.," In the present paper, we explore in more detail the effect that planet migration would have had on the asteroid belt due to asteroid eccentricity excitation by the sweeping of the $\nu_6$ secular resonance." + From the observed eccentricity distribution of main belt asteroids. we find that it is possible to derive constraints on (he secular resonance sweeping tümescale. and hence on the migration timescale.," From the observed eccentricity distribution of main belt asteroids, we find that it is possible to derive constraints on the secular resonance sweeping timescale, and hence on the migration timescale." + secular resonances plav an important role in the evolution of the main asteroid belt., Secular resonances play an important role in the evolution of the main asteroid belt. + The inner edge of the belt nearly coincides with the 4; secular resonance which is defined by 4g72ga. Where g is the rate of precession of the longitude of pericenter. az. of an asteroid and gs is (he sixth eigenlrequency of (he solar svstem planets (approximately the rate of precession of Saturn's longitude of pericenter).," The inner edge of the belt nearly coincides with the $\nu_6$ secular resonance which is defined by $g\approx g_6$, where $g$ is the rate of precession of the longitude of pericenter, $\varpi$, of an asteroid and $g_6$ is the sixth eigenfrequency of the solar system planets (approximately the rate of precession of Saturn's longitude of pericenter)." + The 4; resonance. is important lor (he delivery of Near Earth Asteroids (NEAs) to the inner solar svstem (Scholl&Froesehle1," The $\nu_6$ resonance, is important for the delivery of Near Earth Asteroids (NEAs) to the inner solar system \citep{Scholl:1991p680}." +"991).. Faulkner(1981). showed that the location of the ο resonance actually forms surfaces in (—e—sni space. and Milani&Ixnezevic(1990) showed that those surfaces approximately define the ""inner edge” of the main asteroid belt."," \cite{Williams:1981p532} showed that the location of the $\nu_6$ resonance actually forms surfaces in $a-e-\sin i$ space, and \cite{Milani:1990p531} showed that those surfaces approximately define the “inner edge"" of the main asteroid belt." + ILowever. as mentioned above.," However, as mentioned above," +Fig.,Fig. + 1), 1). + The heavy clement couteut m the cuveope is fouud to increase sustantially with decreasing total mass., The heavy element content in the envelope is found to increase substantially with decreasing total mass. + The envelope metallicity mass fraction Ζων Varies from fora Ll Mj. planet to for masses > 101 AL)., The envelope metallicity mass fraction $Z_{\rm env}$ varies from for a 14 $\mearth$ planet to for masses $>$ 100 $\mearth$. + Note that our calculationsnof take iuto account the probability of occiurence of the initial paraiieters leading to the formaticπι of these planets., Note that our calculations take into account the probability of occurrence of the initial parameters leading to the formation of these planets. + Therefore. the ποτ of light planets tha can actually form by this extended core accretion nieclianisai and its fraction compared to the uuiiber of mor Clnmassive planets cannot be interred from these caleulatinis.," Therefore, the number of light planets that can actually form by this extended core accretion mechanism and its fraction compared to the number of more massive planets cannot be inferred from these calculations." + Usine the inijab conditions provided by the planet formation niocel described iu 82. core mass aud heavy clement enrichnent for a total planet mass. we calculate the subsequeut evolutionary sequences for differeut values of these initia planetary masses.," Using the initial conditions provided by the planet formation model described in 2, core mass and heavy element enrichment for a total planet mass, we calculate the subsequent evolutionary sequences for different values of these initial planetary masses." + Evolutionary models take into acesmut irradiation effects from the pareut star ou tie planet atinospheric aud internal structure. as described i Baraffe et al. (," Evolutionary models take into account irradiation effects from the parent star on the planet atmospheric and internal structure, as described in Baraffe et al. (" +2003) and Chabrier ct al. (,2003) and Chabrier et al. ( +2001).,2004). +" The incident stellar flux received by f1ο planet atnosprere ds deternüued from the orbital axd stelax paraleers characteristic of the p-Ara svstenm (e = ().9 AU. nu LAr... OR,LR... Tow,5sOO I. cf."," The incident stellar flux received by the planet atmosphere is determined from the orbital and stellar parameters characteristic of the $\mu$ -Ara system $a$ = 0.09 AU, $m_\star$ = 1 $\msol$, $R_\star \, \simeq \, 1 \, R_\odot$, $_{\rm eff \star} \, \simeq \, 5800$ K, cf." + Saios © al., Santos et al. + 2001)., 2004). + Evaporation effects are also Tuded. as descYibed iu Baraffe et al. (," Evaporation effects are also included, as described in Baraffe et al. (" +2001). using. as our fiducjal model. the cnerev-liuited escape model derived by Lamner et al. {,"2004), using, as our fiducial model, the energy-limited escape model derived by Lammer et al. (" +2003. hereafter LO3).,"2003, hereafter L03)." + This model describes à lvdrodvuaiuc mass loss process due to he hich cherectic NUV. Hux of the parent star., This model describes a hydrodynamic mass loss process due to the high energetic XUV flux of the parent star. + We also consider sinalOY evaporajon rates., We also consider smaller evaporation rates. + Indeed. L3 assiuue that the planet underexjw inaxiual enerev-luited eva)oration. thus providing an upper hut for escape rates.," Indeed, L03 assume that the planet undergoes maximal energy-limited evaporation, thus providing an upper limit for escape rates." + Their predicted escae rate for TID 2095ish is ~ 100 times larger than the lueasurec w Vidal-Macdjar et al. (, Their predicted escape rate for HD 209548b is $\sim$ 100 times larger than the measured by Vidal-Madjar et al. ( +2003) fortlis planet.,2003) for this planet. +" Iu a receu study. Yelle (2001) iucluded: a beter troatiueit oof atimospheric chemistry. a crucial meredient for handling cooling processes. and found esca)o rates 20 or I0) times iualler than the ones estimated by 1,3."," In a recent study, Yelle (2004) included a better treatment of atmospheric chemistry, a crucial ingredient for handling cooling processes, and found escape rates 20 or 100 times smaller than the ones estimated by L03." + Talàug iuto account a two-dimensional. lvdrodvuawical energv deposition caculation iusead of the sinele-aver heating model used in LS. Tian et al. (," Taking into account a two-dimensional, hydrodynamical energy deposition calculation instead of the single-layer heating model used in L03, Tian et al. (" +2005)x fux OSCape rates for ΠΟ 209[Sab at leas ~ 16 times sal erthan LO3.,2005) find escape rates for HD 209458b at least $\sim$ 16 times smaller than L03. + Finally. ii a recent study. Jaritz et al. (," Finally, in a recent study, Jaritz et al. (" +2005) analyze Roche-Iobe effects on expander upper atnosplieres of close-in giant plancts.,2005) analyze Roche-lobe effects on expanded upper atmospheres of close-in giant planets. + They conclue that. iu SOMLC Cases. planets can undergo geometrical bow-ott. rather than classical. livdrodvuanue.blow-off.. because the critical level where blow-off occurs cauuot be reached before t1ο exobase level reaches the Roche-Lobe.," They conclude that, in some cases, planets can undergo geometrical blow-off, rather than classical hydrodynamic, because the critical level where blow-off occurs cannot be reached before the exobase level reaches the Roche-Lobe." + Jaritz et al. (, Jaritz et al. ( +2005) show that the transit planet OCLE-TR 26b is iu such a configuration and find al escape rate 25 times lower than the imaxiua enerev-linüted: mass loss calculated by LOS.,2005) show that the transit planet OGLE-TR 26b is in such a configuration and find an escape rate 25 times lower than the maximal energy-limited mass loss calculated by L03. + Caven the large uncertainties nu the esca2ο rate illusrated bv these differont studies. we performed. evolutionary calculatiois with l. 1/20 aud 1100 tiues the escape rate based onu the model ofLU. correspouding to vahes ranging frou «1072 &/s (2.6 10 Myr) to 1410? e/s (110 1 M 'vi) for planets older than 1 Cz.," Given the large uncertainties in the escape rate illustrated by these different studies, we performed evolutionary calculations with 1, 1/20 and 1/100 times the escape rate based on the model ofL03, corresponding to values ranging from $\times 10^{12}$ g/s (2.6 $10^{-8}$ $\mearth$ /yr) to $\times 10^{9}$ g/s (4 $10^{-11}$ $\mearth$ /yr) for planets older than 1 Gyr." + All our previois evolutionary caleulatious were done for coreless planets (Baratte et al., All our previous evolutionary calculations were done for coreless planets (Baraffe et al. + 2003. 2001. 2005. Chabrier ( al.," 2003, 2004, 2005, Chabrier et al." + 2001)., 2004). + Iu order for the evolution to ο consistent with our formaion model. we have now inchced a central rocky core in our structure and evoution calculations.," In order for the evolution to be consistent with our formation model, we have now included a central rocky core in our structure and evolution calculations." + Tustead of using a conustaut core deusity. as done ia Soule exo-planct nodels (e.g Bodenheimer e al.," Instead of using a constant core density, as done in some exo-planet models (e.g Bodenheimer et al." + 2003). we have oeuplemeuted tιο ANEOS equation of state Thompson Lausou 1972).," 2003), we have implemented the ANEOS equation of state (Thompson Lauson 1972)." + This equation of state (ECIS) describes je. thermodynamic properties o| differeut maternal of anuetarv imterest (ice. dunite. mon). derived from the IIeluiholtz ree enerev.," This equation of state (EOS) describes the thermodynamic properties of different material of planetary interest (ice, dunite, iron), derived from the Helmholtz free energy." + Even thougi this EOS has physical it gives a thermocdvuanic|o description of phase transitions aud theruodvuanc quawities relevant or the evoution of planets as wel as Rosseand opacities aud electron couductivitics.," Even though this EOS has physical, it gives a thermodynamic description of phase transitions and thermodynamic quantities relevant for the evolution of planets as well as Rosseland opacities and electron conductivities." + Iu he ewdutionarv codo. we integrate the structure cquatious from tie center o the surace and at the core/envelope bouudarw. the EOS switches fom ANEOS to the Samou-Chaπια EOS (Sammon. Chabrier Vaulloru 1995).," In the evolutionary code, we integrate the structure equations from the center to the surface and at the core/envelope boundary, the EOS switches from ANEOS to the Saumon-Chabrier EOS (Saumon, Chabrier VanHorn 1995)." + At this boundary. a deusitv jinip is preseut due to the change in couposition but continuity in pressure and temperature is euforced.," At this boundary, a density jump is present due to the change in composition but continuity in pressure and temperature is enforced." +" Iu order to check our iuplemeitation of ANEOS, we have conipared the mass-racdius relationships oltained for water Ice and oiviue (or dunite. MegoSiO) planets to the results cisplaved in Caillot (2005) aud Coullot et al. ("," In order to check our implementation of ANEOS, we have compared the mass-radius relationships obtained for water ice and olivine (or dunite, $_2$ $_4$ ) planets to the results displayed in Guillot (2005) and Guillot et al. (" +1996) based ou the same EOS.,1996) based on the same EOS. + We fiud a1 excellent agreement with these studies., We find an excellent agreement with these studies. + Asseeested bv the formation mode (c£., As suggested by the formation model (cf. + Fig., Fig. + 1). we adopt in the following a core nass of 6. AL). independent of the initial planet mass.," 1), we adopt in the following a core mass of 6 $\mearth$ independent of the initial planet mass." +" We assuue hat the core is made of dunite. as represeutative of roc5,"," We assume that the core is made of dunite, as representative of rock." + Plis material vields typical iieau densities in the core ~ 6-7 oο a., This material yields typical mean densities in the core $\sim$ 6-7 g $^{-3}$. +" We also performed comparative caleulatlous with water ice cores. corresponding to a lower mea1 clensity ~ oο Ὁ,"," We also performed comparative calculations with water ice cores, corresponding to a lower mean density $\sim$ 3 g $^{-3}$ ." + Adopting ice or dunite for the core composition, Adopting ice or dunite for the core composition +Now consider. the number of photons produced within r. SQ)=09M(«r).,"Now consider, the number of photons produced within $r$ , ${\cal S}(r) = \theta M(1 means (hat all of the photons are absorbed within the halo., This leads to the expression for the ionized fraction as a function of radius If we define quenching fraction then $\eta \geq 1$ means that all of the photons are absorbed within the halo. +" If 7 1. this factor is 0 all thephotons are consumed within the halo.," At high redshift, when $\eta \geq 1$ , this factor is 0 — all thephotons are consumed within the halo." +We test the hard thresholding algorithm by using it to remove artificially added Gaussian noise on the Virgo density field (the simulation is described in Section 5)).,We test the hard thresholding algorithm by using it to remove artificially added Gaussian noise on the Virgo density field (the simulation is described in Section \ref{section:WaveletTest}) ). +" To conduct this experiment, the original density field taken from the n-body simulation has been used to compute an initial set of SFB coefficients (with Ing,=1023 and N44,=512) and out to r=479h-!Mpc."," To conduct this experiment, the original density field taken from the n-body simulation has been used to compute an initial set of SFB coefficients (with $l_{max} = 1023$ and $N_{max} = 512$ ) and out to $r = 479 h^{-1}{\rm Mpc}$." + Figure 5(a) shows a slice of the 3D density field reconstructed from these coefficients., Figure \ref{Figure:fieldOriginal} shows a slice of the 3D density field reconstructed from these coefficients. +" A Gaussian noise was then added to the SFB coefficients, the reconstruction of this noisy density field is shown on Figure 5(b)."," A Gaussian noise was then added to the SFB coefficients, the reconstruction of this noisy density field is shown on Figure \ref{Figure:fieldNoisy}." + The hard thresholding algorithm was subsequently applied to the noisy SFB coefficients using 5 wavelet scales., The hard thresholding algorithm was subsequently applied to the noisy SFB coefficients using 5 wavelet scales. + The resulting density field is reconstructed on Figure 5(c).., The resulting density field is reconstructed on Figure \ref{Figure:fieldThresholded}. . + The residuals are shown on Figure 5(d).., The residuals are shown on Figure \ref{Figure:residuals}. +" The wavelet analysis means we can successfully remove the noise we artificially added on entry, Without much loss to the large scale structure, though some of the smaller structures are removed."," The wavelet analysis means we can successfully remove the noise we artificially added on entry, without much loss to the large scale structure, though some of the smaller structures are removed." +" Modern cosmology requires the analysis of 3D fields on large areas of the sky, i.e. where the field is best viewed in spherical coordinates."," Modern cosmology requires the analysis of 3D fields on large areas of the sky, i.e. where the field is best viewed in spherical coordinates." +" In this configuration, a Spherical Fourier Bessel (SFB) transform is the most natural way to statistically analyse the field."," In this configuration, a Spherical Fourier Bessel (SFB) transform is the most natural way to statistically analyse the field." +" Wavelet transforms have been shown to be ideally suited for cosmological fields, which tend to be sparse in wavelet space."," Wavelet transforms have been shown to be ideally suited for cosmological fields, which tend to be sparse in wavelet space." +" The wavelet transform can be used e.g. for denoising, but there is yet no 3D wavelet transform in spherical coordinates."," The wavelet transform can be used e.g. for denoising, but there is yet no 3D wavelet transform in spherical coordinates." +" We present in this paper a new 3D spherical wavelet transform, based on the undecimated wavelet transform (UWT) described in (?)."," We present in this paper a new 3D spherical wavelet transform, based on the undecimated wavelet transform (UWT) described in \citep{starck:sta05_2}." +" In order to perform operations on the wavelet transforms (such as denoising), we require a discrete version of the SFB transform for both the direct and inverse transforms."," In order to perform operations on the wavelet transforms (such as denoising), we require a discrete version of the SFB transform for both the direct and inverse transforms." + We show a novel way to perform such a fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme., We show a novel way to perform such a fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. +" Using the 3D wavelet transform and the DSFBT, both introduced in this paper, we denoise a test large scale structure data set, taken from the Virgo large box"," Using the 3D wavelet transform and the DSFBT, both introduced in this paper, we denoise a test large scale structure data set, taken from the Virgo large box." + GaussianWe find we can satisfactorily remove artificially added noise without much loss to the large scale structure., We find we can satisfactorily remove artificially added Gaussian noise without much loss to the large scale structure. + All the algorithms presented in this paper are available for download as a public code called atmrs3d., All the algorithms presented in this paper are available for download as a public code called at. +"html.. In order to have a better understanding of the SFB coefficients and of how to use them to perform filtering, the SFB transform can be related to the 3D Fourier transform."," In order to have a better understanding of the SFB coefficients and of how to use them to perform filtering, the SFB transform can be related to the 3D Fourier transform." +" We follow a similar definition as the one presented in ?,, but using our conventions for the different transforms."," We follow a similar definition as the one presented in \cite{DSFBT}, but using our conventions for the different transforms." +The following convention will be used for the Fourier transform: where F denotes the Fourier transform of f.,The following convention will be used for the Fourier transform: where $F$ denotes the Fourier transform of $f$. + This formulation does not assume any coordinate system., This formulation does not assume any coordinate system. +" However, to relate this transform to the SFB transform, it is possible to express this equation in spherical coordinates using the following expansion for the Fourier kernel: where (Kk,θι,$,.) and (r,6,,$,.) are respectively the spherical coordinates of vectors K and 7."," However, to relate this transform to the SFB transform, it is possible to express this equation in spherical coordinates using the following expansion for the Fourier kernel: where $(k, \theta_k,\phi_k )$ and $(r, \theta_r,\phi_r)$ are respectively the spherical coordinates of vectors $\vec{k}$ and $\vec{r}$." +" Substituting this expression for the kernel in the definition of the 3D Fourier transform yields: In the last equation, the expression of the Spherical Harmonics Expansion of F(k,0,,$4) for a given value of k can be recognised from Eq. (4b))."," Substituting this expression for the kernel in the definition of the 3D Fourier transform yields: In the last equation, the expression of the Spherical Harmonics Expansion of $F(k,\theta_k,\phi_k)$ for a given value of $k$ can be recognised from Eq. \ref{Inv_SHT}) )." +" In the Fourier space, the (-i)!fink) are the Spherical Harmonics coefficients of F on a sphere of given radius k."," In the Fourier space, the $(-i)^l \hat{f}_{l m}(k)$ are the Spherical Harmonics coefficients of $F$ on a sphere of given radius $k$." +" In other words, the Spherical Harmonics coefficients ΕΚ) of the 3D Fourier transform F(k,θε,6%) on a sphere of given radius k in Fourier space are the SFB coefficients fj,(k) for the same value k but multiplied by factor (—i)'."," In other words, the Spherical Harmonics coefficients $F_{l m}(k)$ of the 3D Fourier transform $F(k, \theta_k,\phi_k)$ on a sphere of given radius $k$ in Fourier space are the SFB coefficients $\hat{f}_{l m}(k)$ for the same value $k$ but multiplied by factor $(-i)^l$." + The relationship between 3D Fourier transform and SFB transform is therefore very simple., The relationship between 3D Fourier transform and SFB transform is therefore very simple. + The SFB transform can be sought of as a mere Fourier transform in spherical coordinates., The SFB transform can be sought of as a mere Fourier transform in spherical coordinates. +" In the next sections, this relationship will be used to derive convolution and filtering relations for the SFB transform using the well known relations verified bythe Fourier transform."," In the next sections, this relationship will be used to derive convolution and filtering relations for the SFB transform using the well known relations verified bythe Fourier transform." +transformations including the degeneracy between A and a discussed here.,transformations including the degeneracy between $\lambda$ and $a$ discussed here. +" With optimal values for A and a at hand, we compute the transformed Fisher matrix as given in equation (12) and subsequently the transformed posterior according to equation (9)."," With optimal values for $\lambda$ and $a$ at hand, we compute the transformed Fisher matrix as given in equation ) and subsequently the transformed posterior according to equation )." +" The resulting confidence contours and marginal distributions, with Box-Cox parameters obtained from the marginal distributions via rgo (1D) as well as from the full posterior via Lmax (2D), are also shown in 1."," The resulting confidence contours and marginal distributions, with Box-Cox parameters obtained from the marginal distributions via $r_{\rm QQ}$ (1D) as well as from the full posterior via $L_{\rm max}$ (2D), are also shown in $\,$." +" Furthermore we provide a quantitative statement on how accurately the Box-Cox transformed posterior matches the actual one by calculating the Kullback-Leibler divergence Dx as given by equation (7) between the two distributions in Table1, again for both the two-dimensional and marginal cases."," Furthermore we provide a quantitative statement on how accurately the Box-Cox transformed posterior matches the actual one by calculating the Kullback-Leibler divergence $D_{\rm KL}$ as given by equation ) between the two distributions in Table, again for both the two-dimensional and marginal cases." +" Both visual and quantitative inspection demonstrate that the Box-Cox-Fisher formalism excellently reproduces the actual posterior, for all variants of the implementation considered."," Both visual and quantitative inspection demonstrate that the Box-Cox-Fisher formalism excellently reproduces the actual posterior, for all variants of the implementation considered." +" Compared to the standard Fisher results, the Box-Cox-Fisher formalism improves κι, by a factor of 2 to 4in the case of the marginal distribution of og and by at least an order of magnitude for the marginal distribution of Qm."," Compared to the standard Fisher results, the Box-Cox-Fisher formalism improves $D_{\rm KL}$ by a factor of 2 to 4 in the case of the marginal distribution of $\sigma_8$ and by at least an order of magnitude for the marginal distribution of $\Omega_{\rm m}$." +" The decrease in Dr, can mainly be ascribed to the accurate modelling of the non-Gaussian wings of the distributions, but partly also to the shift in the maximum of the marginal"," The decrease in $D_{\rm KL}$ can mainly be ascribed to the accurate modelling of the non-Gaussian wings of the distributions, but partly also to the shift in the maximum of the marginal" +fluctuation as well as about the nature of the turbulence in the plasma.,fluctuation as well as about the nature of the turbulence in the plasma. + We present here the estimates of the power spectrum obtained directly from the interferometric measurements of the visibility function of the sources., We present here the estimates of the power spectrum obtained directly from the interferometric measurements of the visibility function of the sources. + The analysis technique is briefly described below in refsec:atech.., The analysis technique is briefly described below in \\ref{sec:atech}. . + In refsec:dar.. the details of the observational data and the results are given.," In \\ref{sec:dar}, the details of the observational data and the results are given." + Finally. we summarize and present our conclusions in refsec:con..," Finally, we summarize and present our conclusions in \\ref{sec:con}." + Assuming that the angular extent of the source is small. the angular power spectrum. {η0). of the intensity fluctuation of synchrotron radiation 0/(/.m) can be written as where (/.m) is the direction on the sky. (7.0) is the inverse angular separations and £ is the autocorrelation function of the intensity fluctuation Here the angular brackets imply an average across different positions and directions on the sky.," Assuming that the angular extent of the source is small, the angular power spectrum, $P(u,v)$, of the intensity fluctuation of synchrotron radiation $\delta I(l,m)$ can be written as where $(l,m)$ is the direction on the sky, $(u,v)$ is the inverse angular separations and $\xi$ is the autocorrelation function of the intensity fluctuation Here the angular brackets imply an average across different positions and directions on the sky." + If the angular extent of the source is not small enough then. instead of taking the Fourier transform. a spherical harmonie. decomposition of the autocorrelation function is to be done to get the angular power spectrum.," If the angular extent of the source is not small enough then, instead of taking the Fourier transform, a spherical harmonic decomposition of the autocorrelation function is to be done to get the angular power spectrum." + Throughout this analysis. it is assumed that the angular size of the source is small and the statistical properties of the small scale intensity fluctuations are homogeneous and isotropic.," Throughout this analysis, it is assumed that the angular size of the source is small and the statistical properties of the small scale intensity fluctuations are homogeneous and isotropic." + Hence. the intensity fluctuation power spectrum {η0) is a function of the magnitude (=Yue|e? only and is independent of the direction.," Hence, the intensity fluctuation power spectrum $P(u,v)$ is a function of the magnitude $U = +\sqrt{u^2+v^2}$ only and is independent of the direction." + Since the complex visibility function V(i.0) measured by an interferometer is the Fourier transform of the source brightness distribution /(/.ni). where (#20) is the baseline or the projected antenna separation in units of the wavelength of observation and is associated with an inverse angular scale. one can estimate the angular power spectrum directly from the measured. visibility function.," Since the complex visibility function $V(u,v)$ measured by an interferometer is the Fourier transform of the source brightness distribution $I(l,m)$, where $(u,v)$ is the baseline or the projected antenna separation in units of the wavelength of observation and is associated with an inverse angular scale, one can estimate the angular power spectrum directly from the measured visibility function." + It can be easily shown that the squared modulus of the visibility is a direct estimator of the intensity fluctuation power spectrum where the angular brackets denote an average over all possible orientations of the baselines., It can be easily shown that the squared modulus of the visibility is a direct estimator of the intensity fluctuation power spectrum where the angular brackets denote an average over all possible orientations of the baselines. + This method for estimating the power spectrum from the complex visibility function has been used earlier by Crovisier&Dickey(1983). and Green(1993)., This method for estimating the power spectrum from the complex visibility function has been used earlier by \citet{cr83} and \citet{gr93}. +. The technique of direct visibility based estimation of power spectrum has also been used and discussed in literature in various contexts like the analysis of interferometric Observations of the Cosmic Microwave Background Radiation (e.g.Hobsonetal.1995).. the large-scale H distribution at high redshifts (Bharadwaj&Sethi2001) and the interferometric H observations to detect the epoch of reionization2005).," The technique of direct visibility based estimation of power spectrum has also been used and discussed in literature in various contexts like the analysis of interferometric observations of the Cosmic Microwave Background Radiation \citep[e.g.][]{ho95}, the large-scale H distribution at high redshifts \citep{bh01} and the interferometric H observations to detect the epoch of reionization." +. The technical issues like the effect of the window function corresponding to the size of the source on the power spectrum estimator and the method of avoiding the noise bias by correlating the visibilities at two differen baselines are described in detail in Begumetal.(2006)., The technical issues like the effect of the window function corresponding to the size of the source on the power spectrum estimator and the method of avoiding the noise bias by correlating the visibilities at two different baselines are described in detail in \citet{ba06}. +.. The actua algorithm of estimating the power spectrum from the measurec visibility function is outlined in Duttaetal.(2008)., The actual algorithm of estimating the power spectrum from the measured visibility function is outlined in \citet{dp08}. +. Here. à very similar algorithm. slightly modified to further reduce the noise bias. is used for the present work.," Here, a very similar algorithm, slightly modified to further reduce the noise bias, is used for the present work." + To minimize the contribution of correlated noise power to the power spectrum estimator. visibilities are correlated at two different baselines with slightly different stamp for which the noise is expected to be uncorrelated.," To minimize the contribution of correlated noise power to the power spectrum estimator, visibilities are correlated at two different baselines with slightly different time-stamp for which the noise is expected to be uncorrelated." + Begumeal.(2006). has shown that the real part of the measured visibility correlation directly estimates the power spectrum at baselines large compared to the inverse angular size of the source and at smaller baselines the true power spectrum is convolved with the window function., \citet{ba06} has shown that the real part of the measured visibility correlation directly estimates the power spectrum at baselines large compared to the inverse angular size of the source and at smaller baselines the true power spectrum is convolved with the window function. + The error of the power spectrum is estimated accounting for both the noise in the measured visibility function and the finite number of independent estimates of the true power spectrum (cosmic variance)., The error of the power spectrum is estimated accounting for both the noise in the measured visibility function and the finite number of independent estimates of the true power spectrum (cosmic variance). + The Giant Metrewave Radio Telescope (GMRT:Swarupetal.1991) L-band (20 cm) receiver was used to observe the supernova remnant Cas A. The unique hybrid array configuration of the GMRT allows one to probe structures on both large and small angular scale in a single observation., The Giant Metrewave Radio Telescope \citep[GMRT;][]{gs91} L-band $20$ cm) receiver was used to observe the supernova remnant Cas A. The unique hybrid array configuration of the GMRT allows one to probe structures on both large and small angular scale in a single observation. + Scans on standard calibrators were used for flux calibration. phase calibration and also. to determine the bandpass shape.," Scans on standard calibrators were used for flux calibration, phase calibration and also to determine the bandpass shape." + The Very Large Array (VLA) archival C-band (6 cm) data are also used for both the supernova remnant Cas A and Crab Nebula., The Very Large Array (VLA) archival C-band $6$ cm) data are also used for both the supernova remnant Cas A and Crab Nebula. + A summary of the GMRT and tye VLA data used for this work with the observation band. the telescope array configuration. the original programme code and the dates of observation is given in Table 1).," A summary of the GMRT and the VLA data used for this work with the observation band, the telescope array configuration, the original programme code and the dates of observation is given in Table \ref{table:obs}) )." + Data analysis was carried out using standard AIPS., Data analysis was carried out using standard AIPS. + After flagging out bad data. the flux density scale and instrumental phase were calibrated.," After flagging out bad data, the flux density scale and instrumental phase were calibrated." + The calibrated visibility data of the target sources are then usedto estimate the angular power spectra and the errors., The calibrated visibility data of the target sources are then usedto estimate the angular power spectra and the errors. +Fig.,Fig. +" 3 we show a comparison of the apparent velocity £,,,,,,. caleulated with the helical model. and the apparent velocity Papp estimated from observations."," 3 we show a comparison of the apparent velocity $\beta_{app}^{'}$, calculated with the helical model, and the apparent velocity $\beta_{app}$ estimated from observations." + Points with error-bars and solid lines are corresponding to the observed data and helical model calculation. respectively.," Points with error-bars and solid lines are corresponding to the observed data and helical model calculation, respectively." + The model parameters of the helical fitting (e.g.. y. ω. o) listed in Table 2 are consistent for the three components.," The model parameters of the helical fitting (e.g., $\gamma$, $\omega$, $\phi$ ) listed in Table 2 are consistent for the three components." + Moreover. the single dish radio flux monitoring of this source at 22 GHz. reported by (Teraesrantaetal.1998;Teraesrantaetal. 2004)... lasting nearly twenty years from 1981 to 2000. shows three prominent peaks at about 1986.7. 1991.4 and 1995.3 in its light curve (Britzenetal.1999;Türleretal. 1999).," Moreover, the single dish radio flux monitoring of this source at 22 GHz, reported by \citep{Tera98,Tera04}, lasting nearly twenty years from 1981 to 2000, shows three prominent peaks at about 1986.7, 1991.4 and 1995.3 in its light curve \citep{Brit99, Turl99}. ." +. They can be considered as the ejection time [οι for each corresponding component. assuming that each new component appearance is accompanied by an outburst in the total intensity.," They can be considered as the ejection time $t_{ej}$ for each corresponding component, assuming that each new component appearance is accompanied by an outburst in the total intensity." + The ejection times derived by the helical model for these three components are 1986.6. 1990.1. and 1994.1.," The ejection times derived by the helical model for these three components are 1986.6, 1990.1, and 1994.1." + If component BI moves along a linear path. the 7; derived from proper motion extrapolation would be around 1989.7. three years later than the flaring time 1986.7.," If component B1 moves along a linear path, the $t_{ej}$ derived from proper motion extrapolation would be around 1989.7, three years later than the flaring time 1986.7." + Compared with the extrapolated ejection times from a linear fit. it seems that the ejection times derived. from the helical model are more consistent.," Compared with the extrapolated ejection times from a linear fit, it seems that the ejection times derived from the helical model are more consistent." + After combining the 14 epoch observations of this source. we find the kinematical motions of B3 1633-382 can be reasonably explained with both a simple linear and helical mode.," After combining the 14 epoch observations of this source, we find the kinematical motions of B3 1633+382 can be reasonably explained with both a simple linear and helical mode." + In the linear kinematical motion. the component B2 moves at significantly slower apparent velocity than the other two components in this compact jet.," In the linear kinematical motion, the component B2 moves at significantly slower apparent velocity than the other two components in this compact jet." + These low-pattern velocity or even stationary features have sometimes been explained as standing recollimation shocks m= an initially over-pressurized outflow. which have been reproduced in numerical simulations of AGN jets (e.g.. (Gómezetal.1995;Perucho&Martí2007:Listeretal.2009))).," These low-pattern velocity or even stationary features have sometimes been explained as standing recollimation shocks in an initially over-pressurized outflow, which have been reproduced in numerical simulations of AGN jets (e.g., \citep{Gmez95, Peru07, +List09}) )." +. Alternatively. it is possible that the quasi-stationary motion of the componer= is due to an extremely small viewing angle of the specific geometry (Alberdietal.2000).," Alternatively, it is possible that the quasi-stationary motion of the component is due to an extremely small viewing angle of the specific geometry \citep{Albe00}." +.. We roughly estimate à Doppler factor of approximately several tens by using both the average flux density and the average size of the core., We roughly estimate a Doppler factor of approximately several tens by using both the average flux density and the average size of the core. + Taking the apparent velocities into account. this implies that the jet is aligned at ~1° to our line of sight. and the Lorentz factor corresponding to the pattern velocity is [~18.," Taking the apparent velocities into account, this implies that the jet is aligned at $\sim1^{\circ}$ to our line of sight, and the Lorentz factor corresponding to the pattern velocity is $\rm \Gamma\sim18$." + Although it is an approximate estimation. the direction of the jet from our line of sight and the Lorentz factor fitted from linear model are consistent with the parameters from the helical model calculation.," Although it is an approximate estimation, the direction of the jet from our line of sight and the Lorentz factor fitted from linear model are consistent with the parameters from the helical model calculation." + As for the helical fitting. on the other hand. it has been applied for fitting both the projected trajectory and the apparent velocity of components in the compact jet of quasar B3 16334382.," As for the helical fitting, on the other hand, it has been applied for fitting both the projected trajectory and the apparent velocity of components in the compact jet of quasar B3 1633+382." + The model-calculated projected trajectories also well fit the significantly low apparent velocity for components B2 and B3 around a core-separation of ~ 0.5 mas., The model-calculated projected trajectories also well fit the significantly low apparent velocity for components B2 and B3 around a core-separation of $\sim$ 0.5 mas. + Helical motions combined with indications of a time-dependent ejection angle can be explained in the context of a binary core., Helical motions combined with indications of a time-dependent ejection angle can be explained in the context of a binary core. + Binary black hole (BBH) models have been employed to explain. similar component. motions in. other sources (e.g. 1803-784: (Britzenetal.2010;Roland2008).. 3C 345: (Lobanov&Roland 2005))).," Binary black hole (BBH) models have been employed to explain similar component motions in other sources (e.g., 1803+784; \citep{Brit10, Rola08}, 3C 345; \citep{Loba05}) )." + The component B3 16334382 has been shown to exhibit periodicities in the radio (Fanetal.2007) and in the optical (1) lighteurves. while also being variable in the y-rays (2).," The component B3 1633+382 has been shown to exhibit periodicities in the radio \citep{Fan07} and in the optical \citep{Bozy90} + lightcurves, while also being variable in the $\gamma$ -rays \citep{Fan02}." +. Quasi-pertodic variability across the spectrum is a further argument in favor of à BBH in the nucleus of this object (Karouzosetal. 2010:: e.g.. OJ 287; Sillanpaaetal.1988:: Lehto&Valtonen 1996.. 3C 454.3: Qianetal. 2007)).," Quasi-periodic variability across the spectrum is a further argument in favor of a BBH in the nucleus of this object \citealp{Karo10}; ; e.g., OJ 287; \citealp{Sill88}; \citealp{Leht96}, 3C 454.3; \citealp{Qian07}) )." + Helicity and precession of the jet can be explained in terms of Kelvin-Helmholtz instabilities (e.g.. Camenzing&Krockenberger1992.. Peruchoetal. 2006)). precession of the aceretion disk (e.g.. Capronietal. 2006)). or magnetic torques Lat2003..," Helicity and precession of the jet can be explained in terms of Kelvin-Helmholtz instabilities (e.g., \citealp{Came92}, \citealp{Peru06}) ), precession of the accretion disk (e.g., \citealp{Capr06}) ), or magnetic torques \citealp{Lai03}." + Although the stationary proper motion of components in B3 16334382 can also be explained with both linear and helical model in this study. the long-term VLBA study has indicated that the standing components may be in temporarily quiescent states (Listeretal. 2009)).," Although the stationary proper motion of components in B3 1633+382 can also be explained with both linear and helical model in this study, the long-term VLBA study has indicated that the standing components may be in temporarily quiescent states \citealp{List09}) )." + Future observations will provide new kinematical constraints., Future observations will provide new kinematical constraints. + The quasar B3 1633+382 shows two different kinds of proper motion for its components., The quasar B3 1633+382 shows two different kinds of proper motion for its components. + We note that it could be explained as two kinds of kinematical models when we use different classifications for the components., We note that it could be explained as two kinds of kinematical models when we use different classifications for the components. + In the first case. if component BI andB3 move outwards with a linear speed. then component B2 stays at a quasi-stationary state ~ 0.95mas from the core for the whole observation interval.," In the first case, if component B1 andB3 move outwards with a linear speed, then component B2 stays at a quasi-stationary state $\sim$ 0.5mas from the core for the whole observation interval." + Component, Component +fig~27 mag 7).,$\mu_B \sim 27$ mag $^{-2}$ ). + This in turn suggests that there do not exist [large numbers of galaxies with surface brightnesses just below this limit: Ipt (iii) No local galaxies with Alp«1l are known with such low surface brightnesses. although a small number of bulge-cominated galaxies have disk components this faint or fainter e.g. Malin 1 (Bothun et αἱ.," This in turn suggests that there do not exist large numbers of galaxies with surface brightnesses just below this limit; 1pt (iii) No local galaxies with $M_B < -11$ are known with such low surface brightnesses, although a small number of bulge-dominated galaxies have disk components this faint or fainter e.g. Malin 1 (Bothun et al." + LOST) and CP 1444 (Davies. Phillipps Disney 1988).," 1987) and GP 1444 (Davies, Phillipps Disney 1988)." + The giant. galaxy population in the Virgo Cluster is similar to that in the local Universe in terms of galaxy. structural parameters. so it is reasonable to expect that the dwarf galaxy population is similar too and that this absence in the field of cwarls with Alp«ll anc pg c 27 mag aresee7 extends to the Virgo Cluster.," The giant galaxy population in the Virgo Cluster is similar to that in the local Universe in terms of galaxy structural parameters, so it is reasonable to expect that the dwarf galaxy population is similar too and that this absence in the field of dwarfs with $M_B < -11$ and $\mu_B$ $>$ 27 mag $^{-2}$ extends to the Virgo Cluster." + Dwarf galaxies with very high surface brightnesses acking an extended: dilluse light) component arc another »otential source of contamination because they would be rejected. from the current sample since. they. look. Like uminous background galaxies (they have low 2 values)., Dwarf galaxies with very high surface brightnesses lacking an extended diffuse light component are another potential source of contamination because they would be rejected from the current sample since they look like luminous background galaxies (they have low $P$ values). + ‘These can either be blue LUE galaxies like Alarkarian 1460 (Trentham. Fully Verheijen 2001b) or red compact clhwarls ike M32 in the Local Group or UGC 6805 in the Ursa Major Cluster (Lully Verheijen 1997).," These can either be blue HII galaxies like Markarian 1460 (Trentham, Tully Verheijen 2001b) or red compact dwarfs like M32 in the Local Group or UGC 6805 in the Ursa Major Cluster (Tully Verheijen 1997)." + In the Virgo Cluster. VCC 1313 is an example of the former and VCC 1627 of the latter: were the velocities of these two objects not known we would have classified them as background objects.," In the Virgo Cluster, VCC 1313 is an example of the former and VCC 1627 of the latter; were the velocities of these two objects not known we would have classified them as background objects." + For Mg<—14 only these two galaxies of this tvpe were identified., For $M_B < -14$ only these two galaxies of this type were identified. + Were such objects to exist with Mgc—14. our sample could be incomplete.," Were such objects to exist with $M_B > -14$, our sample could be incomplete." + The fraction of detected galaxies that we assign to the cluster on surface brightnesss grounds ranged. [rom close to Lat the bright end of the sample (D«15) to about l per cent at the faint end (D~20)., The fraction of detected galaxies that we assign to the cluster on surface brightnesss grounds ranged from close to 1 at the bright end of the sample $B < 15$ ) to about 1 per cent at the faint end $B \sim 20$ ). + This is an important change of emphasis from what has classically been thought of as the main uncertainty in stuclies of cluster luminosity functions., This is an important change of emphasis from what has classically been thought of as the main uncertainty in studies of cluster luminosity functions. + Previously the results from this kind of studs were open to question because many very low surface-brightness galaxies could be missing from the sample since they are never detected. above the sky., Previously the results from this kind of study were open to question because many very low surface-brightness galaxies could be missing from the sample since they are never detected above the sky. + This is no longer a worry because deep surveys like this one and that of Trentham Tully (2001) ave not uncovering large numbers of LSB ealaxies that were missing in shallow ones., This is no longer a worry because deep surveys like this one and that of Trentham Tully (2001) are not uncovering large numbers of LSB galaxies that were missing in shallow ones. + Instead. the major concern is now that the sample may be missing many surface-brightness galaxies which we have culled from the sample because we think that they are background. galaxies.," Instead, the major concern is now that the sample may be missing many surface-brightness galaxies which we have culled from the sample because we think that they are background galaxies." + We do not however regard this as a serious worry., We do not however regard this as a serious worry. + Fistlv. at the bright end of our sample. where velocity measurements are available. galaxies with high surface brightnesses are rare (VCC 1313 and. VCC 1627 are the exceptions).," Firstly, at the bright end of our sample, where velocity measurements are available, galaxies with high surface brightnesses are rare (VCC 1313 and VCC 1627 are the exceptions)." + Secondly. high surlace-brightness galaxies do not appear to be present in substantial number in the Fornax Cluster else they would have been seen in the spectroscopic survey described by Drinkwater et al. (," Secondly, high surface-brightness galaxies do not appear to be present in substantial number in the Fornax Cluster else they would have been seen in the spectroscopic survey described by Drinkwater et al. (" +20008: this work uses he 341) spectrograph on the Anglo-Australian Telescope).,2000a; this work uses the 2dF spectrograph on the Anglo-Australian Telescope). + Small numbers of compact galaxies with carly-twpe spectra discovered. in that survey (Drinkwater ct al., Small numbers of compact galaxies with early-type spectra discovered in that survey (Drinkwater et al. +" 2000b. ""hillipps et al."," 2000b, Phillipps et al." + 2001) but they are too rare to contribute significantly to the Fornax LE., 2001) but they are too rare to contribute significantly to the Fornax LF. + Given the similarities ρου the Virgo and Fornax Clusters. we do not expect his to be a major souree of incompleteness in the current stuck.," Given the similarities between the Virgo and Fornax Clusters, we do not expect this to be a major source of incompleteness in the current study." + Another potential problem is that the Vireo data rut not. the North Galactic Cap background. data is contaminated by an anomalously [large number of nearby galaxies at comparable distances to the Virgo Cluster that are not bound to the cluster (the P? values computed. by comparing the numbers of low surface-hrightness galaxies in the two datasets would then be too high)., Another potential problem is that the Virgo data but not the North Galactic Cap background data is contaminated by an anomalously large number of nearby galaxies at comparable distances to the Virgo Cluster that are not bound to the cluster (the $P$ values computed by comparing the numbers of low surface-brightness galaxies in the two datasets would then be too high). + The contaminating ealaxies would need to be nearby or else they would. not look like Virgo Cluster galaxies., The contaminating galaxies would need to be nearby or else they would not look like Virgo Cluster galaxies. + We regard such a possibility as unlikely due to the paucity of. Duminous ealaxies with velocities between about 2000 km | and 3000 km tin the Virgo dataset. (see Figure 9)., We regard such a possibility as unlikely due to the paucity of luminous galaxies with velocities between about 2000 km $^{-1}$ and 3000 km $^{-1}$ in the Virgo dataset (see Figure 9). + Were such objects to be numerous. the satellite populations of these luminous Ingalaxies (only verv luminous Ingalaxies are [Bisted in the at these distances and. so would be included in Figure 9) could look like Virgo Cluster members (satellites of galaxies at higher velocities would be too small).," Were such objects to be numerous, the satellite populations of these luminous galaxies (only very luminous galaxies are listed in the at these distances and so would be included in Figure 9) could look like Virgo Cluster members (satellites of galaxies at higher velocities would be too small)." +of the gas mixture and (he quantum mechanical properties of the (transition.,of the gas mixture and the quantum mechanical properties of the transition. + The approximate shape of an absorption line is given bx the Voiet profile. V(z). which is the convolution of line broadening kernels due to Doppler and pressure (Lorentzian) broadening mechanisms.," The approximate shape of an absorption line is given by the Voigt profile, $V(\nu)$, which is the convolution of line broadening kernels due to Doppler and pressure (Lorentzian) broadening mechanisms." + At low pressure the motions of the absorbing molecules dominate (he broadening aud al higher pressure collisions between molecules come to dominate., At low pressure the motions of the absorbing molecules dominate the broadening and at higher pressure collisions between molecules come to dominate. + Both regimes occur al different levels in Earth's atmosphere., Both regimes occur at different levels in Earth's atmosphere. +" The Voigt profile is defined where ay is the Doppler half width of the line. a, is the Lorentzian half. width of the line. and vy. is the line center. each of which can depend on atmospheric temperature and/or pressure."," The Voigt profile is defined where $\alpha_{D}$ is the Doppler half width of the line, $\alpha_{L}$ is the Lorentzian half width of the line, and $\nu_{c}$ is the line center, each of which can depend on atmospheric temperature and/or pressure." + The cross section σ(ν) is a function of the line broadening as well as the line intensity. S=SVQ. where Q is a scaling factor based on the partition function of the molecule aud the temperature of the gas.," The cross section $\sigma(\nu)$ is a function of the line broadening as well as the line intensity, $S=S^{0}Q$, where $Q$ is a scaling factor based on the partition function of the molecule and the temperature of the gas." +" The total transmission can now be expressed as T,=e'"" where τι, is We retrieved line parameters including hall-widthlis. strengths. line centers. aud pressure shifts of those line centers. for transitions of TsO in the wavelength range 600 to 11000 nm [rom INTRAN 2008 and calculated atmospheric transmission at zenith in wavelength steps ol across a plane parallel atmosphere with 30 lavers logarithmically spaced between 0 km and 80 kin."," The total transmission can now be expressed as $T_{\nu}=e^{-\tau_{\nu}}$ where $\tau_{\nu}$ is We retrieved line parameters including half-widths, strengths, line centers, and pressure shifts of those line centers, for transitions of $_{2}$ O in the wavelength range 600 to 11000 nm from HITRAN 2008 and calculated atmospheric transmission at zenith in wavelength steps of across a plane parallel atmosphere with 30 layers logarithmically spaced between 0 km and 80 km." + This radiative transfer caleulation requires a model of the structure and composition of Earth's atmosphere. including temperature. pressure. and chemical composition. as a function of height.," This radiative transfer calculation requires a model of the structure and composition of Earth's atmosphere, including temperature, pressure, and chemical composition, as a function of height." + We used the NASA-MSFEC Earth Global Reference Atmospheric Model (EFarth-GRAAI 2010; ? and references therein) to approximate the average properties of ihe atmosphere above APO. located in southeastern New Mexico at an altitude of 2.780 m. Earth-GRAM combines a large number of historic atmospheric measurements with modern meteorological models to predict atmospheric properties. and the statistical distributions of (hose properties. as a function of altitude. location on the Earth. and month.," We used the NASA-MSFC Earth Global Reference Atmospheric Model (Earth-GRAM 2010; \citealt{justus2004} and references therein) to approximate the average properties of the atmosphere above APO, located in southeastern New Mexico at an altitude of 2,780 m. Earth-GRAM combines a large number of historic atmospheric measurements with modern meteorological models to predict atmospheric properties, and the statistical distributions of those properties, as a function of altitude, location on the Earth, and month." + While is often used for engineering applications. such as estimating the effect of Earth's abmosphere on trajectories. it is also a powerful resource for quantilving the impact of the atmosphere on astronomical observations.," While Earth-GRAM is often used for engineering applications, such as estimating the effect of Earth's atmosphere on trajectories, it is also a powerful resource for quantifying the impact of the atmosphere on astronomical observations." +The study of small starburst galaxies such as NGC 3077 has been favoured recently mainly. because of the implications that these objects have in thesfandard model of galaxy evolution (e.g. Baugh. Cole Frenk 1996).,"The study of small starburst galaxies such as NGC 3077 has been favoured recently mainly because of the implications that these objects have in the model of galaxy evolution (e.g. Baugh, Cole Frenk 1996)." + In the hierarchical scenario. smaller systems form first and. then become the building blocks of the massive galaxies that are (πονο in the local universe.," In the hierarchical scenario, smaller systems form first and then become the building blocks of the massive galaxies that are observed in the local universe." + These svsterms which are the most numerous type of galaxies. could. be responsible for an important. fraction of the reionization of the universe.," These systems which are the most numerous type of galaxies, could be responsible for an important fraction of the reionization of the universe." + Moreover. due to the low gravitational potential of. those galaxies the interstellar medium might be allowed to escape from the host more easily. contributing to the enrichment of the intergalactic medium at carly epochs.," Moreover, due to the low gravitational potential of those galaxies the interstellar medium might be allowed to escape from the host more easily contributing to the enrichment of the intergalactic medium at early epochs." + However the expelling of newly processed matter depends not only on the mass of the host and the power ofthe burst but also on the distribution ofthe interstellar medium and the presence ofa dark matter halo surrounding the host galaxy (c.g. Silich Tenorio-Tagle 2001)., However the expelling of newly processed matter depends not only on the mass of the host and the power of the burst but also on the distribution of the interstellar medium and the presence of a dark matter halo surrounding the host galaxy (e.g. Silich Tenorio-Tagle 2001). + Nearby compact starburst galaxies are excellent laboratories in which to study the starburst phenomenon., Nearby compact starburst galaxies are excellent laboratories in which to study the starburst phenomenon. + In fact. compact starburst’ galaxies have been used. to test the validity of cillerent star forming tracers (e.g. ltosa-Gonzállez. Ferlevich. Verlevich 2002): to study the interaction of the burst with the interstellar medium (e.g. Martin 1998: Silich. et al.," In fact, compact starburst galaxies have been used to test the validity of different star forming tracers (e.g. Rosa-Gonzállez, Terlevich Terlevich 2002); to study the interaction of the burst with the interstellar medium (e.g. Martin 1998; Silich et al." + 2002): and to study the enrichmen of the intergalactic medium due to the break out. of superbubbles (c.g. Ixunth et al., 2002); and to study the enrichment of the intergalactic medium due to the break out of superbubbles (e.g. Kunth et al. + 2002)., 2002). + lt is only in the nearby universe that the physica processes related. to the current starburst event. can. be studied in great. detail., It is only in the nearby universe that the physical processes related to the current starburst event can be studied in great detail. + The presence of a recent. starburs eventtrigeered by the interaction of NGC 3077 with ALS and M 82.has been confirmed. by several independen racers., The presence of a recent starburst event—triggered by the interaction of NGC 3077 with M 81 and M 82—has been confirmed by several independent tracers. + The IUIS ultraviolet (UV). spectra. revealed. the oesence of massive stars not. older. than years (Benacchio Galletta 1981)., The IUE ultraviolet (UV) spectra revealed the presence of massive stars not older than $\times$ $^7$ years (Benacchio Galletta 1981). + The peak ofthe Pa nebula a racer of voung star formation regions — (Meier. Turner and Deck 2001: Bokker et al.," The peak of the $\alpha$ nebula – a tracer of young star formation regions – (Meier, Turner and Beck 2001; Bökker et al." + 1999. Figure 1)) is located between wo CO complexes detected. by the Owens Valley. Hacdio Observatory (Walter et al.," 1999, Figure \ref{PaImage}) ) is located between two CO complexes detected by the Owens Valley Radio Observatory (Walter et al." + 2002)., 2002). + Walter et al., Walter et al. + conducted a comprehensive multiwavelength study of NCC 3077. relating he atomic and molecular gas with the observed. LIL regions.," conducted a comprehensive multiwavelength study of NGC 3077, relating the atomic and molecular gas with the observed HII regions." + Dv combining CO and emission. line observations. they," By combining CO and emission line observations, they" +the level populations to thermal equilibrium.,the level populations to thermal equilibrium. +" Therefore any NLTE emission lines will have maximum intrinsic widths comparable to the Doppler velocities of the emitting species, and when observed at low resolving power the apparent flux densities (ergs s! cm-? Hz-!) of emission lines will be greatly reduced because their intrinsic line widths are unresolved."," Therefore any NLTE emission lines will have maximum intrinsic widths comparable to the Doppler velocities of the emitting species, and when observed at low resolving power the apparent flux densities (ergs $^{-1}$ $^{-2}$ $^{-1}$ ) of emission lines will be greatly reduced because their intrinsic line widths are unresolved." +" This motivated our attempt to confirm the 910 results using data with a much higher spectral resolving power, obtained with theNear-IR Spectrograph (NIRSPEC; ?)) on the 10-m Keck II telescope."," This motivated our attempt to confirm the S10 results using data with a much higher spectral resolving power, obtained with theNear-IR Spectrograph (NIRSPEC; \citealt{mclean1998p566}) ) on the 10-m Keck II telescope." +" The peak intensities of NLTE emission lines wil be much greater when they are observed at high spectral resolving power, and S10's claim of bright emission at low spectral resolution implies that observations at high spectral resolution and sensitivity should easily produce a detection."," The peak intensities of NLTE emission lines will be much greater when they are observed at high spectral resolving power, and S10's claim of bright emission at low spectral resolution implies that observations at high spectral resolution and sensitivity should easily produce a detection." +" A description of our search for absorption signatures of the exoplanet in our data set will be presented in a future manuscript; the expected line depths based on standard atmospheric modeling are approximately 0.01—0.196 of the stellar continuum (?),, and a comprehensive analysis at that level is beyond the scope of this study."," A description of our search for absorption signatures of the exoplanet in our data set will be presented in a future manuscript; the expected line depths based on standard atmospheric modeling are approximately $0.01-0.1$ of the stellar continuum \citep{Burrows2008p1436}, and a comprehensive analysis at that level is beyond the scope of this study." + In this paper we limit our analysis and discussion to whether or not we can confirm the bright emission signal announced by S10., In this paper we limit our analysis and discussion to whether or not we can confirm the bright emission signal announced by S10. +" We present our observing and data analysis procedure in Section refobs, predict the expected emission features using excitation models of molecular emission at different rotational temperatures and compare the expected signal to our results in Section refres,, and conclude with a discussion of the potential explanations for the differences between our results and those of S10 in Section refdisc.."," We present our observing and data analysis procedure in Section \\ref{obs}, predict the expected emission features using excitation models of molecular emission at different rotational temperatures and compare the expected signal to our results in Section \\ref{res}, and conclude with a discussion of the potential explanations for the differences between our results and those of S10 in Section \\ref{disc}." +" We acquired spectra at A/AAzz 27,000 with NIRSPEC without AO on UT July 13, 2009 using the KL filter with a setting covering portions of the wavelength range between 3.27 and 4.0jm. Observing conditions were optimal, with low water vapor and clear skies."," We acquired spectra at $\lambda/\Delta\lambda \approx $ 27,000 with NIRSPEC without AO on UT July 13, 2009 using the KL filter with a setting covering portions of the wavelength range between 3.27 and $\mu$ m. Observing conditions were optimal, with low water vapor and clear skies." +" We observed 1189733 before, during and after a secondary eclipse of the planet, for a total integration time of 100 minutes between UT 10:00 and UT 14:00."," We observed 189733 before, during and after a secondary eclipse of the planet, for a total integration time of 100 minutes between UT 10:00 and UT 14:00." + A bright B-type comparison star 88634) was also observed immediately after the science target., A bright B-type comparison star 8634) was also observed immediately after the science target. +" We nodded the telescope 12 arcsec in an ABBA sequence, with 60-second integrations per beam for both stars."," We nodded the telescope 12 arcsec in an ABBA sequence, with 60-second integrations per beam for both stars." +" In total, we obtained 48 echelle spectra of 1189733 during eclipse, 52 spectra out of eclipse, and 40 spectra of 88634."," In total, we obtained 48 echelle spectra of 189733 during eclipse, 52 spectra out of eclipse, and 40 spectra of 8634." +" Since our spectra were acquired prior to the publication of the S10 results, the wavelength ranges of our echelle grating orders are not identical to the S10 work."," Since our spectra were acquired prior to the publication of the S10 results, the wavelength ranges of our echelle grating orders are not identical to the S10 work." +" Fortunately, our data include a spectral range from 3.27—3.31 um that overlaps the brightest bin in the emission feature claimed by S10."," Fortunately, our data include a spectral range from $3.27-3.31\,\mu$ m that overlaps the brightest bin in the emission feature claimed by S10." +" The wavelength structure of molecular bands is known unequivocally from quantum mechanics, with only the level populations affecting the intensity of lines in different spectral channels."," The wavelength structure of molecular bands is known unequivocally from quantum mechanics, with only the level populations affecting the intensity of lines in different spectral channels." +" Our modeling Section indicates(see that molecules emitting strongly in the refres))$10 um bin must also emit significantly in our 3.27—3.31 um region, and we test the 910 results on that basis."," Our modeling (see Section \\ref{res}) ) indicates that molecules emitting strongly in the S10 $\mu$ m bin must also emit significantly in our $3.27-3.31\,\mu$ m region, and we test the S10 results on that basis." +" We utilized custom data reduction algorithms, previously used to detect new molecular emission features from warm gas in circumstellar disks (7),, to extract and process spectra for each echelle order in each ABBA set."," We utilized custom data reduction algorithms, previously used to detect new molecular emission features from warm gas in circumstellar disks \citep{mandell2008pL25}, to extract and process spectra for each echelle order in each ABBA set." + We reduced the initial 2D spectral-spatial images to 1D spectra after first correcting for the slope of the beam due to cross-dispersion and subtracting A- and B-beam images to remove the contribution from telluric radiance., We reduced the initial 2D spectral-spatial images to 1D spectra after first correcting for the slope of the beam due to cross-dispersion and subtracting A- and B-beam images to remove the contribution from telluric radiance. +" We identified bad pixels and cosmic ray hits in each raw pixel column by comparing the beam profile to an average beam profile for nearby columns, allowing us to identify and replace single-pixel events without removing any enhancements due to emission or absorption features."," We identified bad pixels and cosmic ray hits in each raw pixel column by comparing the beam profile to an average beam profile for nearby columns, allowing us to identify and replace single-pixel events without removing any enhancements due to emission or absorption features." +" We corrected for changing airmass and telluric atmospheric conditions to high accuracy using a two-step process: 1) fitting the data for both the science star 1189733) and the comparison star 88634) with terrestrial spectral transmittance models synthesized with the LBLRTM atmospheric code (?) and subtracting the models to obtain spectral residuals for each star, and 2) differencing the residuals of the two stars."," We corrected for changing airmass and telluric atmospheric conditions to high accuracy using a two-step process: 1) fitting the data for both the science star 189733) and the comparison star 8634) with terrestrial spectral transmittance models synthesized with the LBLRTM atmospheric code \citep{clough2005p233} and subtracting the models to obtain spectral residuals for each star, and 2) differencing the residuals of the two stars." +" The subtraction of the telluric model compensates for the effects of changing airmass and atmospheric variability, and the differencing of the residuals removes remnant fringes and other instrumental artifacts, as well as minor errors in the telluric model such as imprecise pressure broadening, weak features missing from the line list, and inaccurate isotopic ratios."," The subtraction of the telluric model compensates for the effects of changing airmass and atmospheric variability, and the differencing of the residuals removes remnant fringes and other instrumental artifacts, as well as minor errors in the telluric model such as imprecise pressure broadening, weak features missing from the line list, and inaccurate isotopic ratios." +" For our LBLRTM models we utilized a standard tropical temperature profile and line parameters from the HITRAN2008 molecular database with updates from 2009 (?),, and we fitted for the abundance of three key atmospheric constituents (H20, CH4, and O3) and a scaling factor for the temperature of the troposphere."," For our LBLRTM models we utilized a standard tropical temperature profile and line parameters from the HITRAN2008 molecular database with updates from 2009 \citep{rothman2009p533}, and we fitted for the abundance of three key atmospheric constituents $_2$ O, $_4$, and $_3$ ) and a scaling factor for the temperature of the troposphere." +" Atmospheric models were fitted for wavelength sub-sections of each AB set, with the fully-resolved model convolved with the local instrumental resolving power derived for each sub-section to compensate for variability in the effective spectral resolving power due to the position of the spectrum on the detector."," Atmospheric models were fitted for wavelength sub-sections of each AB set, with the fully-resolved model convolved with the local instrumental resolving power derived for each sub-section to compensate for variability in the effective spectral resolving power due to the position of the spectrum on the detector." +" Additionally, using a telluric model provided us with an extremely well-calibrated wavelength solution for each sub-section (AA/A~ 1079)."," Additionally, using a telluric model provided us with an extremely well-calibrated wavelength solution for each sub-section $\Delta\lambda/\lambda\sim10^{-6}$ )." +" This process achieved results corresponding to S/N ~300 on the original stellar continuum for each AB set, and an rms noise only slightly larger (by than that expected from the photon statistics (see 20%))Figure 1))."," This process achieved results corresponding to S/N $\sim 300$ on the original stellar continuum for each AB set, and an rms noise only slightly larger (by ) than that expected from the photon statistics (see Figure \ref{reduction}) )." +" Stellar absorption features were removed by using the results for the in-eclipse data as a stellar template, with each AB set shifted to correct for changes in the heliocentric velocity and the stellar radial velocity variation due to the influence of the planet."," Stellar absorption features were removed by using the results for the in-eclipse data as a stellar template, with each AB set shifted to correct for changes in the heliocentric velocity and the stellar radial velocity variation due to the influence of the planet." +" We then subtracted this stellar template from each AB set in the out-of-eclipse data after shifting for changes in the radial velocity for that time interval, leaving final residuals for each out-of-eclipse AB set with only the signal from the planet Figure "," We then subtracted this stellar template from each AB set in the out-of-eclipse data after shifting for changes in the radial velocity for that time interval, leaving final residuals for each out-of-eclipse AB set with only the signal from the planet (see Figure \ref{example}) )." +"We combined(see all 2)).the out-of-eclipse residuals after shifting each set to correct for the radial velocity of the planet around the star, with velocity shifts calculated based on the ephemeris from ?.."," We combined all the out-of-eclipse residuals after shifting each set to correct for the radial velocity of the planet around the star, with velocity shifts calculated based on the ephemeris from \citet{knutson2009p822}. ." +" The radial velocity of the HD 189733 system relative to the telescope (accounting for Earth’s orbit and rotation) was -8 km/s,"," The radial velocity of the HD 189733 system relative to the telescope (accounting for Earth's orbit and rotation) was -8 km/s," +to the position angle and GC velocity data using a nonlinear. least-squares fit Sharplesetal. 1998).,"to the position angle and GC velocity data using a nonlinear, least-squares fit \citeANP{Sharples98} 1998)." + Gy ancl Vi; are [ree parameters. and represent the position angle of the line of nodes and the rotation velocity of the GC's respectively.," $\theta_0$ and $_{\rm rot}$ are free parameters, and represent the position angle of the line of nodes and the rotation velocity of the GCs respectively." + Vu is the svstemic velocity of the GC system our derived mean velocity), $_0$ is the systemic velocity of the GC system our derived mean velocity). + We find that the GC system shows rotation of 114+GOkms| (texeluding the outlving cluster). around a position angle of 22+27dee.," We find that the GC system shows rotation of $114\pm60 \kms$ (excluding the outlying cluster), around a position angle of $22\pm 27 \deg$." + We plot the radial velocities of these clusters against position angle. along with our best (weighted) sinusoidal [it in Figure 9..," We plot the radial velocities of these clusters against position angle, along with our best (weighted) sinusoidal fit in Figure \ref{fig:rotation}." + Interestinglv. the rotation we derive is similar to the maximum observed rotation velocity of the stellar. light of. 124+7kms," Interestingly, the rotation we derive is similar to the maximum observed rotation velocity of the stellar light of $124\pm7 \kms$." + Llowever this measurement is afonga position angle of 38deg (Simien&Prugniel2000).," However this measurement is a position angle of $38 +\deg$ \cite{Simien00}." +. Therefore. the stellar rotation appears to be at ~IsOcdeg to the GCs if the position angle Conventions are correct.," Therefore, the stellar rotation appears to be at $\sim 180 \deg$ to the GCs if the position angle conventions are correct." + Alany luminous earlv-twvpe. galaxies host at least two »opulations of GC's. as suggested. by their bimodal colour distributions Gebhardt&Ixissler-Patig L999: Ixundu&Whitmore 2001: Larsenetal. 2001) and increasingly by heir dillering kinematic properties Cohen&Itvzhov 1997: Zepfetal. 2000: Cotéetal. 2001: Geisleretal. 2001).," Many luminous early-type galaxies host at least two populations of GCs, as suggested by their bimodal colour distributions \citeANP{Gebhardt99} 1999; \citeANP{Kundu01} + 2001; \citeANP{Larsen01} 2001) and increasingly by their differing kinematic properties \citeANP{Cohen97} 1997; \citeANP{Zepf00} 2000; \citeANP{Cote01} 2001; \citeANP{Geisler01} + 2001)." + CC 524 also possesses a GC system with a bimodal colour clistribution Larsenctal. 2001 and see Figure 1))., NGC 524 also possesses a GC system with a bimodal colour distribution \citeANP{Larsen01} 2001 and see Figure \ref{fig:colours}) ). + We iive looked at the kinematics of these sub-populations in our present sample., We have looked at the kinematics of these sub-populations in our present sample. + We have separated the cluster sample into metal-poor (best < 1.0) and metal-rich (Fe/H] = 1) groups on the xwsls of the metallicities derived in Section 3.1.., We have separated the cluster sample into metal-poor ([Fe/H] $<$ –1.0) and metal-rich ([Fe/H] $\geq$ –1) groups on the basis of the metallicities derived in Section \ref{Metallicities}. + Performing he same analysis as described. above. we find that. the metal-poor GCs (17 clusters) dominate the rotation in our sample. with. a rotation. ofamo 147475kms1 around a position- angle of 6+26deg.," Performing the same analysis as described above, we find that the metal-poor GCs (17 clusters) dominate the rotation in our sample, with a rotation of $147\pm 75 \kms$ around a position angle of $6\pm 26 \deg$." + In contrast. we find that the metal-rich GCs (11 clusters excluding the outlier) show no significant rotation. with 68£8tkms+.," In contrast, we find that the metal-rich GCs (11 clusters excluding the outlier) show no significant rotation, with $68\pm84 \kms$." + Although the rotation of the wo metallicity groups are not stronglv constrainedat this »oint. this result seems to dilfer from that of the NGC 3115. he nearby lenticular galaxy studied by Ixuntschnerctal. (2002).," Although the rotation of the two metallicity groups are not strongly constrainedat this point, this result seems to differ from that of the NGC 3115, the nearby lenticular galaxy studied by \citeANP{Kuntschner02} (2002)." + From a total sample of 24 GCs. Ixuntschnerctal. (2002) found that the metal-poor and metal-rich GC's wel a similar rotation signal.," From a total sample of 24 GCs, \citeANP{Kuntschner02} (2002) found that the metal-poor and metal-rich GCs had a similar rotation signal." + lteturning to NGC 524. the velocity dispersions of the wo cluster populations. when neglecting rotation. clillers only slightly: 197339kms.+ for the metal-poor GCs. 169+43kms|! for the metal-rich GC sub-population.," Returning to NGC 524, the velocity dispersions of the two cluster populations, when neglecting rotation, differs only slightly: $197\pm39 \kms$ for the metal-poor GCs, $169\pm43 \kms$ for the metal-rich GC sub-population." + Moreover. when the rotational component is taken into account. the dispersion of the two sub-populations are very similar (201 kms+ versus 193. kms13.," Moreover, when the rotational component is taken into account, the dispersion of the two sub-populations are very similar (201 $\kms$ versus 193 $\kms$ )." + Phe kinematical results for the NGC 524 GC system are summarised in Table 6.., The kinematical results for the NGC 524 GC system are summarised in Table \ref{tab:kinematics}. . + The lack of rotation in the metal-rich population translates into a rather low value for Ví: fo. an often used diagnostic for the degree of rotation over anisotropy.," The lack of rotation in the metal-rich population translates into a rather low value for $_{\rm rot}$ $\sigma$, an often used diagnostic for the degree of rotation over anisotropy." +" For the metal-rich clusters we find Vi, fo = 0.40 + 0.64. where the rather large error reflects the small sample of clusters."," For the metal-rich clusters we find $_{\rm rot}$ $\sigma$ = 0.40 $\pm$ 0.64, where the rather large error reflects the small sample of clusters." + This is similar to the situation found by Zepfetal. (2000) for the NGC 4472 GC system. although they also found only a modest level of rotation in the metal-poor clusters.," This is similar to the situation found by \citeANP{Zepf00} (2000) for the NGC 4472 GC system, although they also found only a modest level of rotation in the metal-poor clusters." + These results hint at. either. dillerent. density profiga or different families of orbits for the GC sub-populations (e.g.sece Wissler-Patig&Cebhardt LO9S8 for ao similar situation in AIST)., These results hint at either different density profiles or different families of orbits for the GC sub-populations see \citeANP{KisslerPatig98a} 1998 for a similar situation in M87). + The most likely explanation is that this is due to the metal-poor clusters having a Latter density distribution than the metal-rich elusters. as observed. in luminous galaxies (o.g.see Rhode&Zepf 2001 for the specilie case of NGC 4472).," The most likely explanation is that this is due to the metal-poor clusters having a flatter density distribution than the metal-rich clusters, as observed in luminous galaxies see \citeANP{Rhode01} 2001 for the specific case of NGC 4472)." + Llowever. it does remain puzzling why the metal-poor globular clusters rotate at a right angle with respect to the stellar light of NGC 524.," However, it does remain puzzling why the metal-poor globular clusters rotate at a right angle with respect to the stellar light of NGC 524." + Integral field cata available for this ealaxy (see deZeeuwetal. 2002) will clarify whether or not it is connected to the kinematically decoupled core., Integral field data available for this galaxy (see \citeANP{deZeeuw02} 2002) will clarify whether or not it is connected to the kinematically decoupled core. + Clearly a larger sample of racial velocities for the NGC 524 GCs is desirable for a more detailed analysis of these issues., Clearly a larger sample of radial velocities for the NGC 524 GCs is desirable for a more detailed analysis of these issues. + Globular clusters can be used to good elfect as test-particles to probe the gravitational potential of their parent. galaxies Cohen&Byzhov. 1997: Wissler-Patigetal. 1998: ορal. 2000). ancl ave complementary to other techniques such as studies of planetary nebulae Huietal. 1995: Arnaboldietal. 1998) and integrated. light. Dressler 1984: Bender.Saglia.&Gerhard. 1994).," Globular clusters can be used to good effect as test-particles to probe the gravitational potential of their parent galaxies \citeANP{Cohen97} 1997; \citeANP{KisslerPatig98} 1998; \citeANP{Zepf00} 2000), and are complementary to other techniques such as studies of planetary nebulae \citeANP{Hui95} 1995; \citeANP{Arnaboldi98} 1998) and integrated light \citeANP{Dressler84} 1984; \citeANP{Bender94} 1994)." + Our present spectroscopic sample allows us to estimate 1ο total mass of the galaxy. within a radius of ~ within roughly 2 effective radii (~ 26 kpe) of NGC 524.," Our present spectroscopic sample allows us to estimate the total mass of the galaxy within a radius of $\sim$ , within roughly 2 effective radii $\sim$ 26 kpc) of NGC 524." + For this purpose we used the virial (VMIS) and. projected (PME) mass estimators.as described in Bahcall&Tremaine (1981) and Heisler.Tremaine.&Baheall(1985) respectively.," For this purpose we used the virial (VME) and projected (PME) mass estimators,as described in \citeANP{Bahcall81} (1981) and \citeANP{Heisler85} (1985) respectively." +" With our adopted. distance to NGC 524 of 28.2 Alpe (de 1991)... we obtain masses of ~4104 AL. (VALE) and between 4.Lott (PALE. purely tangential orbits) and 13.107 AL. (PME, purely radial orbits)."," With our adopted distance to NGC 524 of 28.2 Mpc \cite{RC3}, , we obtain masses of $\sim 4\times 10^{11}$ $_\odot$ (VME) and between $4\times 10^{11}$ (PME, purely tangential orbits) and $13\times 10^{11}$ $_\odot$ (PME, purely radial orbits)." + We, We +demonstrates the noise level of the identification procedure. which results from the S/N in the original spectra. the spectral mismatch. between star and. template and/or velocity. errors.,"demonstrates the noise level of the identification procedure, which results from the S/N in the original spectra, the spectral mismatch between star and template and/or velocity errors." + Most. of the features in this region of the diagram have FWIIMo and are indeed unlikely. to correspond to. true absorption (or emission) features given the spectral resolution of2., Most of the features in this region of the diagram have $\simeq$ and are indeed unlikely to correspond to true absorption (or emission) features given the spectral resolution of. +5... However. there are a few outlving points. both below (absorption) anc above (emission) this band. which have Wy]= and which were selected for further investigation.," However, there are a few outlying points, both below (absorption) and above (emission) this band, which have $|W_{\lambda}| \geq$ and which were selected for further investigation." + In. particular. there is à peak in the distribution of absorption features at and emission peaks at anclA.," In particular, there is a peak in the distribution of absorption features at and emission peaks at and." +.. The emission features at are due to A671. most probably originating in line-of-sight nebulosity in the LAIC.," The emission features at are due to $\lambda$ 6717, most probably originating in line-of-sight nebulosity in the LMC." + This. supposition is corroborated by the fact that the same stars also show strong Ho emission. as one would expect.," This supposition is corroborated by the fact that the same stars also show strong $\alpha$ emission, as one would expect." + The occasional appearance of nebular emission lines in the 2dE data is not surprising because there is patchy nebulosity across the LMC field. but the sky subtraction was done using the mean signal from a relatively small number of sky fibres chosen to lie in clear areas.," The occasional appearance of nebular emission lines in the 2dF data is not surprising because there is patchy nebulosity across the LMC field, but the sky subtraction was done using the mean signal from a relatively small number of sky fibres chosen to lie in clear areas." + However. the A6GT17 emission lines do help place limits on the acceptable values of the gaussian EWIIM.," However, the $\lambda$ 6717 emission lines do help place limits on the acceptable values of the gaussian ." + Most of these have 4 233A. and nonehas PWM; or {So," Most of these have $<$ $<$, and nonehas $<$ or $>$." +hC'onsequently. alldetectionswilh « were excluded. from. further consideration.," Consequently, all detections with $<$ were excluded from further consideration." + In. practice. no features rejected in this way were close to the position of the lithium line.," In practice, no features rejected in this way were close to the position of the lithium line." + Since small spectral mismatches in. the region around the lithium line can allect the wings of the detected lithium feature. as is the case with the strong line shown in Fig.," Since small spectral mismatches in the region around the lithium line can affect the wings of the detected lithium feature, as is the case with the strong line shown in Fig." + 2ec. an upper limit for the line width was set at 55A...," \ref{montage}c c, an upper limit for the line width was set at $\leq$." + Another wav to study these results is to consider big., Another way to study these results is to consider Fig. + 4 which shows histograms of the identifications plotted in Fie., \ref{hist} which shows histograms of the identifications plotted in Fig. + 3 which lic in the range S55AX.., \ref{lines} which lie in the range $\leq$ $\leq$. + Phe wavelength range is civiced into 2A--wide bins., The wavelength range is divided into -wide bins. + The three left-hancl panels are for absorption features and the three right-hand. panels are for. emission [eatures., The three left-hand panels are for absorption features and the three right-hand panels are for emission features. + The individual histograms are [for identifications with WA 2004 & LO00.dandM y," The individual histograms are for identifications with $_\lambda$ $>$, $<$ $_\lambda$ $<$ and $_\lambda$ $<$." + ;3:4. Wal Wert omgerabsecgly Pig., The predominance of the peak at in the stronger absorption features is obvious (Fig. + daa) ilcontainselevenstars., \ref{hist}a a): it contains eleven stars. +oncofwhich. 22832. ΠΟ ΠΕΡΣΙ 1g. 3. LE," one of which, 2832, has a very strong absorption line at and stands out clearly from the rest in Fig. \ref{lines}." + sspeclri, Its spectrum is plotted in Fig. + AGTOT that is strong enough to be seen even without the subtraction of the template spectrum., \ref{montage}c c and shows a $\lambda$ 6707 that is strong enough to be seen even without the subtraction of the template spectrum. + OF the remaining three features in Fig., Of the remaining three features in Fig. + daa. one appears at in star 22379. another is the blend of two smaller features at in star 33389 and the third is the consequence of a bad. pixel.," \ref{hist}a a, one appears at in star 2379, another is the blend of two smaller features at in star 3389 and the third is the consequence of a bad pixel." + Since none of the bins in Fig., Since none of the bins in Fig. + daa apart from. the bin has more than one star. it is reasonable to assume that no more than one of the eleven stars in the bin is there by chance.," \ref{hist}a a apart from the bin has more than one star, it is reasonable to assume that no more than one of the eleven stars in the bin is there by chance." + With only two out of 18 bins having single stars. the likelihood that this is happening is only —0.11.," With only two out of 18 bins having single stars, the likelihood that this is happening is only $\sim$ 0.11." + The same peak can be seen in the weaker lines of Fig., The same peak can be seen in the weaker lines of Fig. + 4bb. but here there are also significant. numbers of lines in the two neighbouring bins at lower wavelengths.," \ref{hist}b b, but here there are also significant numbers of lines in the two neighbouring bins at lower wavelengths." + Nevertheless. the histogram certainly rellects à non-random distribution.," Nevertheless, the histogram certainly reflects a non-random distribution." + It is unlikely that the detections shortward of are due to enhancements of individual metal [ines because related. metal lines are found in other wavelength bins as well (Barnbaunm1994). and. are relatively weak in LMC stars., It is unlikely that the detections shortward of are due to enhancements of individual metal lines because related metal lines are found in other wavelength bins as well \cite{barnbaum94} and are relatively weak in LMC stars. + Ht is more likely that they are associated with a general spectrum characteristic which also produces the relatively high numbers of weak lines found (bie., It is more likely that they are associated with a general spectrum characteristic which also produces the relatively high numbers of weak lines found (Fig. + dec) at the same two bins and also gives rise to a number of emission features at (Pie., \ref{hist}c c) at the same two bins and also gives rise to a number of emission features at (Fig. + tee)., \ref{hist}e e). +" This could be due to dillerences in the relative strengths of the οσο BCEC, ΤΟΝ and ΕΙΝ:€ molecular bands between some stars and the mean hepr"," This could be due to differences in the relative strengths of the $^{12}{\rmn C}^{12}{\rmn C}$, $^{13}{\rmn C}^{12}{\rmn C}$, $^{12}{\rmn C}^{14}{\rmn N}$ and $^{13}{\rmn C}^{14}{\rmn N}$ molecular bands between some stars and the mean spectrum." +edoménancepféelipanGoes dind«cadierkcninobat," In contrast, very few very weak lines are found at." +ous( hasarerystron ΟΙ Dite: , Nor are many emission lines found at. +Kern ΛΜ is likely. the weak lines give a measure of how errors in the method generate lines. two of the ten lines in the bin in Fig.," If, as is likely, the weak lines give a measure of how errors in the method generate lines, two of the ten lines in the bin in Fig." + 4bb are expected to have been caused in this way., \ref{hist}b b are expected to have been caused in this way. + Lf they do not. then the number of false detections at (at 0.3; 100.4: 4)conldbeashighasthenumberscenintheneighbouringbinalt Fie.," If they do not, then the number of false detections at (at $<$ $_{\lambda}$ $<$ ) could be as high as the number seen in the neighbouring bin at, i.e., five out of the ten detections at could be false." + 5, Fig. + is an example of a J star with a modest detection of AGTOTwith Woru7 OO4ASA.. (, \ref{Nstar_with_li} is an example of a J star with a modest detection of $\lambda$ 6707with $_{6707}$ . ( +his can be compared with the strongest lithium line detected. in our sample. shown in Fig.,"This can be compared with the strongest lithium line detected in our sample, shown in Fig." + σοι). The superimposed lines show the quadratic ‘continuum ancl the fitted eaussians., \ref{montage}c c.) The superimposed lines show the quadratic `continuum' and the fitted gaussians. + “Phis particular example includes gaussians fitted to two broad shallow, This particular example includes gaussians fitted to two broad shallow +IBerarchDical galaxy formation models predict frequent mteractions in a ealaxws history(6.8.Coleetal.2000:Wechsler 2002).,"Hierarchical galaxy formation models predict frequent interactions in a galaxy's history\citep[e.g.][]{cole00,wechsler02}." +. Some of these interactions may trigger star formation., Some of these interactions may trigger star formation. + Observational limits on the frequency and duration of triggeredCoco» star formation are an nmuportaut constraint ou the role of these interactions iu the evolution of stellar populations., Observational limits on the frequency and duration of triggered star formation are an important constraint on the role of these interactions in the evolution of stellar populations. + Evidence that galaxy interactions at low redshift trigecroo star formation was first detected in photometric observations bv Larsou&Tinsley (1978).. who," Evidence that galaxy interactions at low redshift trigger star formation was first detected in photometric observations by \citet{larson_tinsley}, , who" +galaxies on internal plivsical properties of galaxies and environmental factors.,galaxies on internal physical properties of galaxies and environmental factors. +" We used a volume-limuted saluple of galaxies. drawn from the SDSS DR7. brighter han AZ,=19.5 mag and at redshift 0.02<2.405189."," We used a volume-limited sample of galaxies, drawn from the SDSS DR7, brighter than $M_{r}=-19.5$ mag and at redshift $0.02\le z\le 0.05489$ ." + We classify the galaxies in our sample iuto xuvred or nou-barred ones by visual inspection., We classify the galaxies in our sample into barred or non-barred ones by visual inspection. + To reduce contamination by iuternal extinction effects; we use ouly 10.67L late-type galaxies with axis ratio b/a>0.60.," To reduce contamination by internal extinction effects, we use only 10,674 late-type galaxies with axis ratio $b/a>0.60$." + Our uajor fiidings are as follows., Our major findings are as follows. + 1., 1. +" We find33.210 barred ealaxies (fig,=30.1) that consist of2.5 strong bars (fapi=23.8% ) aud 698 weals ars "," We find 3,240 barred galaxies $\bfr=30.4\%$ ) that consist of 2,542 strong bars $\bfrsbo=23.8\%$ ) and 698 weak bars $\bfrsbw=6.5\%$ )." +, 2. +(fanostronglyj fan depends oud ¢ color: ων qnucreases sienificautly as the color becomes redder., $\bfrsbo$ strongly depends on $u-r$ color: $\bfrsbo$ increases significantly as the color becomes redder. + Ceutral velocity dispersion is another miportanut parameter deterinining fap., Central velocity dispersion is another important parameter determining $\bfrsbo$. + The bar fraction of SD1 galaxies has a maximal value at intermediate velocity dispersions of σι=125~175 hans +. hoste, The bar fraction of SB1 galaxies has a maximum value at intermediate velocity dispersions of $\sigma_{max}=125\sim175$ km $^{-1}$. +dThese results suggest that stroug bars aro dominautlv 1o» dutermiediate-nuass systems uudergoime long secular evolution with little experieuce of recent mteractions or niergers., These results suggest that strong bars are dominantly hosted by intermediate-mass systems undergoing long secular evolution with little experience of recent interactions or mergers. + , 3. +fape also depends on 4/—r and σ., $\bfrsbw$ also depends on $u-r$ and $\sigma$. + But unlike SBI ealaxies. Galaxies with bluer color or smaller σ are more likely to host weak bars.," But unlike SB1 galaxies, galaxies with bluer color or smaller $\sigma$ are more likely to host weak bars." + These results mean that weal bars iuainlv inhabit later type spirals with low mass aud blue color., These results mean that weak bars mainly inhabit later type spirals with low mass and blue color. + , 4. +fepo is higher iu lesseouceutrated svstems than lüuore-concentrated svstenüs., $\bfrsbw$ is higher in less-concentrated systems than more-concentrated systems. + fapi also shows a simular trend but oulv for high mass systems with 0>150 kin 1, $\bfrsbo$ also shows a similar trend but only for high mass systems with $\sigma>150$ km ${}^{-1}$. + , 5. +fepr imnonotonicallv iuereases as the backeround density poy/p increases., $\bfrsbo$ monotonically increases as the background density $\rtwenty/\brho$ increases. + Tlowever. this dependence disappears when «or or σα fixed.," However, this dependence disappears when $u-r$ or $\sigma$ is fixed." + This indicates that the backerouud density does not play a direct role in the bar formation., This indicates that the background density does not play a direct role in the bar formation. + Iu addition. we find that fapo also do not depend ou the backerouncl density.," In addition, we find that $\bfrsbw$ also do not depend on the background density." + , 6. +Tufiuence of the nearest neighbor galaxy on fypy appears when the separation to the neiglibor is smaller than 0.1 times the virial radius of the neighbor., Influence of the nearest neighbor galaxy on $\bfrsbo$ appears when the separation to the neighbor is smaller than 0.1 times the virial radius of the neighbor. +" μι decreases as Rafter, decreases regardless of ucighbor’s morphology.", $\bfrsbo$ decreases as $\distnei$ decreases regardless of neighbor's morphology. + It indicates that it is difficult for galaxies to maintain strong bars during stroug tidal iuteractions. and that this plenomenou is of eravitational origin.," It indicates that it is difficult for galaxies to maintain strong bars during strong tidal interactions, and that this phenomenon is of gravitational origin." +" The fraction of weak bars show little dependence ou HR,Voir", The fraction of weak bars show little dependence on $\distnei$. + We thank ILS.Ihwaus for helpful conunueuts aud are erateful to .LILLee aud J.D.Sohu for helping us with the morphology classification., We thank H.S.Hwang for helpful comments and are grateful to J.H.Lee and J.B.Sohn for helping us with the morphology classification. + C.B.P. ackuowledees the support of the National Research Foundation of lorea (NRF) evant funded bv the Korea goveruimoenut (MEST) (No., C.B.P. acknowledges the support of the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. + 2009-0062868)., 2009-0062868). + ALCOL. was supported iu part by Midecareer Research Program through NRF eraut funded bv the MEST (No.2010-0013575)., M.G.L. was supported in part by Mid-career Research Program through NRF grant funded by the MEST (No.2010-0013875). + YYC wes supported by the National Research Foundation of Tkorea to the Center for Galaxy Evolution Research., YYC wss supported by the National Research Foundation of Korea to the Center for Galaxy Evolution Research. + Funding for the SDSS aud SDSS-II has been provided by the Alfred P. Sloan Foundation. the Participating Tustitutions. the National Science Foundation. the U.S. Departineut of Energy. the National Acronauties aud Space Adininistration. the Japanese Alounbukasakusho. the Max Pluck Society. aud the Ilseher Education Fuudiug Council for Euglaud.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." + The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortiun for the Participating Lhustitutious., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. +" The Participating Tustitutions are the American Museu of Natural Tistory. Astrophysical Iustitute Potsdam. University of Basel. Cambridge Universitv. Case Western Reserve University. Uuiversity of Chicago. Drexel University. Formilah. the Institute for Advanced Study. the Japan Participation Group. Johus Hopkius University. the Joiut Iustitute for Nuclear Astrophysics. the Navli DIustitute for Particle Astroplivsies aud Cosmology. the Korean Scientist Caoup. the Chinese Academy of Sciences (LAMOST). Los Alamos National Laboratory. the Max- for Astrouauw (AIPIA). the Max- for Astrophysics (AIPA). New Mexico| State University, Olio. State University. University of Pittsburgh. University. of Portsmouth. Princetou University. the United States Naval Observatory. aud the University of Washington."," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, Cambridge University, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington." + clianges of the surace briginess of the reprocessed. radlation (eg. in ependentthe 6.4 keV line. sec| Sunvaev & Churazov. 1998).,"dependent changes of the surface brightness of the reprocessed radiation (e.g. in the 6.4 keV line, see Sunyaev & Churazov, 1998)." + Indeed. for ie short. [lare t10 leprocessit1g sites (bright at à given moment of time i[ter the primary Hare) should be located at the surface of the parabola with a focus at the position o ‘the primary source (Pig).," Indeed, for the short flare the reprocessing sites (bright at a given moment of time after the primary flare) should be located at the surface of the parabola with a focus at the position of the primary source (Fig.4)." + All s Over je surface cM this. have the same time delay for the poinpiotons from. the source to parabolathe site and then to the observer., All points over the surface of this parabola have the same time delay for the photons coming from the source to the reprocessing site and then to the observer. + Phe 'oming vwill evolve witi time reprocessingelfectively scanning the nonurΠΟΠΗ istribution parabol:of t10 medium around the A*., The parabola will evolve with time effectively scanning the nonuniform distribution of the scattering medium around the Sgr A*. + The apxvent motions could he εδ or scattering on Serthe mutual Lo¢“Allon m[ the primary source and tje superluminal. site.," The apparent motions could be sub or superluminal, depending on the mutual location of the primary source and the scattering site." + dependingShown in Piet are the ime of the surface scatteringbrightness of a spherical cleμις at illerent. dependentmornents of changestime anc different position of the cloud., Shown in Fig.4 are the time dependent changes of the surface brightness of a spherical cloud at different moments of time and different position of the cloud. +" For tje GC region One can ς “proper motion"" of the regions bright in the 6.4 keV line at z Lirae of xpectthe order of an areminute per vear (if the rise and fronts oftie [lare were enough).", For the GC region one can expect “proper motion” of the regions bright in the 6.4 keV line at a rate of the order of an arcminute per year (if the rise and decay fronts of the flare were sharp enough). + οσανan (inormation can be sharpobtained the spectra of the reflected Import, Important information can be obtained by studying the spectra of the reflected component. + Shown in Fig.r dis a by studyingrellected a slab of a component.molecular gas having solar spectrumabundance of heavy hyelements., Shown in Fig.5 is a spectrum reflected by a semi-infinite slab of a molecular gas having solar abundance of heavy elements. +svithetic spectrum (Zar=31.564IX) to the observed Ly α line than is true for the system svithetic spectrum. whose mean Zar is appreciably lower.,"synthetic spectrum $T_{\rm eff}=31,564$ K) to the observed Ly ${\alpha}$ line than is true for the system synthetic spectrum, whose mean $T_{\rm eff}$ is appreciably lower." + This indicates that the absorption lines are formed in a higher temperature environment (1.e.. corona or wind) (han is true for ihe continuum.," This indicates that the absorption lines are formed in a higher temperature environment (i.e., corona or wind) than is true for the continuum." + Fig., Fig. + 9 shows the Si IV doublet near: it is too weak in the svstem svithetic spectrum. and equivalent widths lor the overplotted annulus svnthetic spectrum (Toy=31. 5641X) are again a better fit.," 9 shows the Si IV doublet near; it is too weak in the system synthetic spectrum, and equivalent widths for the overplotted annulus synthetic spectrum $T_{\rm eff}=31,564$ K) are again a better fit." + The C IV doublet (Fig., The C IV doublet (Fig. + 10) in the svstem synthetic spectrum is also much (oo weak., 10) in the system synthetic spectrum is also much too weak. +" The doublet is stronger in both the overplotted annulus synthetic spectra (7,5—31.5641Ix. and 38.016). but not by enough when scaled to fit the observed profile."," The doublet is stronger in both the overplotted annulus synthetic spectra $T_{\rm eff}$ =31,564K, and 38,076K), but not by enough when scaled to fit the observed profile." + The C II line complex (Fig., The C II line complex (Fig. + 9) is slightlv too weak in the overplotted annulus spectrum. while the equivalent width of the svstem svntlietie spectrum appears comparable to the observed value.," 9) is slightly too weak in the overplotted annulus spectrum, while the equivalent width of the system synthetic spectrum appears comparable to the observed value." + The C HI line complex. Fig.," The C III line complex, Fig." + 8 in the overplotted annulus svuthelic spectrum. appears to have an equivalent width approximately matching the observed. value. while the svstem svuthetic spectrum is too weak.," 8 in the overplotted annulus synthetic spectrum, appears to have an equivalent width approximately matching the observed value, while the system synthetic spectrum is too weak." + The varving strengths of C lines in different ionization stages and the observed (large) strength of N V (Fig., The varying strengths of C lines in different ionization stages and the observed (large) strength of N V (Fig. + 8) max be due to composition ellects but we cannot exclude the possibility (hat it is an excitation elfect., 8) may be due to composition effects but we cannot exclude the possibility that it is an excitation effect. + Large N V/C IV ratios have been seen in several CV svstems (Gansickeetal.2003) and are likely related to evolutionary effects., Large N V/C IV ratios have been seen in several CV systems \citep{G2003} and are likely related to evolutionary effects. + Note that 112004 determines an overall metal composition for the MV Lay WD of Z=0.3xZ.. bul detailed elemental abundances. relative to solar values. of C=0.5. N=0.5. and Si=0.2. (," Note that H2004 determines an overall metal composition for the MV Lyr WD of $Z=0.3{\times}Z_{\odot}$, but detailed elemental abundances, relative to solar values, of C=0.5, N=0.5, and Si=0.2. (" +Since strong excitation effects are clearly present there is no conlliet between our assumed solar abundance for the present analysis and the WD composition determination in 2004.,Since strong excitation effects are clearly present there is no conflict between our assumed solar abundance for the present analysis and the WD composition determination in H2004.) + It is of interest to compare the emission line spectrum of the intermediate state and the absorption line spectrum of the high state (Fig., It is of interest to compare the emission line spectrum of the intermediate state and the absorption line spectrum of the high state (Fig. + 11)., 11). + Note that emission lines in the intermediate state match corresponding absorption lines in the high state., Note that emission lines in the intermediate state match corresponding absorption lines in the high state. + As well as can be judged. the relative strengths of the various resonance enission lines are similar to the relative strengths of the same absorption lines.," As well as can be judged, the relative strengths of the various resonance emission lines are similar to the relative strengths of the same absorption lines." + The IST spectu in Fig., The HST spectrum in Fig. + 11. has been displaced downward to superpose the C IV complex., 11 has been displaced downward to superpose the C IV complex. + The two broadened spectra fit accurately at the superposed line boundaries: if (here were a radial velocity difference between the emission line spectrum and the absorption line spectrum as large as the displacement of the emission line spectrum (e.e.. Fig.," The two broadened spectra fit accurately at the superposed line boundaries; if there were a radial velocity difference between the emission line spectrum and the absorption line spectrum as large as the displacement of the emission line spectrum (e.g., Fig." + 9) from the synthetic spectrum. that dillerence would be detectable.," 9) from the synthetic spectrum, that difference would be detectable." + Comparable fits result when other spectral regions are superposed. although the low signal level of theZUE spectrum produces some ambiguity.," Comparable fits result when other spectral regions are superposed, although the low signal level of the spectrum produces some ambiguity." + It is of particular interest that. the intermediate state spectrum is flatter than the high state spectrum., It is of particular interest that the intermediate state spectrum is flatter than the high state spectrum. + The two sets of lines in (he intermediate and high states appear to be produced in a wind with a similar velocity siructure in the two states., The two sets of lines in the intermediate and high states appear to be produced in a wind with a similar velocity structure in the two states. +The contünuum in the GTO spectrum is well approximated by 1.1 (mes the flux of the continuum in Sle.,The continuum in the GTO spectrum is well approximated by 1.1 times the flux of the continuum in SH2. + The SIII continuum is approximately 1.3 (mes the SII2 continuum. although it is shallower in slope than SII2 bevond ~1540n.," The SH1 continuum is approximately 1.3 times the SH2 continuum, although it is shallower in slope than SH2 beyond $\sim 15\micron$." + These differences may arise in part. [rom pointing errors (<20% photometric uncertainity in SII for the nominalSpilzer pointing accuracy: seeSpitzer Observers Manual. version 8.0) or (rue variability in (the T Tawi continuum (e.g.. Muzerolle et 22009) or a combination of these.," These differences may arise in part from pointing errors $< 20$ photometric uncertainity in SH for the nominal pointing accuracy; see Observer's Manual, version 8.0) or true variability in the T Tauri continuum (e.g., Muzerolle et 2009) or a combination of these." + The [Nell] line at 12.81an and III lines at 11.31yam and. 12.27jam are strongly in emission at each epoch., The [NeII] line at $12.81\micron$ and HI lines at $11.31\micron$ and $12.37\micron$ are strongly in emission at each epoch. + Notably. in none of the three epochs does TW Iva show strong mid-infrared molecular enission like (hat seen inSpilzer spectra of classical T Tauri stars that have been reported in (he literature (Carr Najita 2008: Salvk et 22008: see also Pascucei οἱ 22009).," Notably, in none of the three epochs does TW Hya show strong mid-infrared molecular emission like that seen in spectra of classical T Tauri stars that have been reported in the literature (Carr Najita 2008; Salyk et 2008; see also Pascucci et 2009)." + The Nell} line luminosity is a convenient reference. since TW Ilva and AA Tau (Carr Najita 2008) have similar (Nell) line Iuminosities. within a factor of 2.," The [NeII] line luminosity is a convenient reference, since TW Hya and AA Tau (Carr Najita 2008) have similar [NeII] line luminosities, within a factor of 2." + In AA Tau. the molecular emission is stronger than the [Nell] emission. whereas in TW Ilva. the [NelL] emission is. by far. one of the brightest lines in the spectrum.," In AA Tau, the molecular emission is stronger than the [NeII] emission, whereas in TW Hya, the [NeII] emission is, by far, one of the brightest lines in the spectrum." + Nevertheless. TW Iva does show a rich spectrum of weaker emission features.," Nevertheless, TW Hya does show a rich spectrum of weaker emission features." + To illustrate this. we show in Figure 2 the average of SILL and SII? after subtracting a high order polvnonual fit to the continuum.," To illustrate this, we show in Figure 2 the average of SH1 and SH2 after subtracting a high order polynomial fit to the continuum." + The features that are seen correspond well in wavelength with known atomic lines (Ill. Nell. NeIII) and other molecular features (IIs. ΟΠΗ. COs. HCO. and possibly Cll).," The features that are seen correspond well in wavelength with known atomic lines (HI, NeII, NeIII) and other molecular features $\Htwo$ , OH, $\COtwo$, $\HCOp$, and possibly $\CHthree$ )." + The transitions that dominate the detected: OIL features are listed in Table 3., The transitions that dominate the detected OH features are listed in Table 3. + The COs band has been detected both in emission (Carr Najita 2003: sSalvk et 22008) and in absorption (e.g.. Lahuis et 22006b) from T Tauri stars.," The $\COtwo$ band has been detected both in emission (Carr Najita 2008; Salyk et 2008) and in absorption (e.g., Lahuis et 2006b) from T Tauri stars." + We identify (he feature at 12.06jii as the νο fundamental Q-branch of HCO (Davies Rothwell 1934)., We identify the feature at $12.06\micron$ as the $\nu_2$ fundamental Q-branch of $\HCOp$ (Davies Rothwell 1984). + The detection of IICO emission is interesting. and (o our knowledge this band has not been reported. previously in anv voung stellar object.," The detection of $\HCOp$ emission is interesting, and to our knowledge this band has not been reported previously in any young stellar object." + There is also a weak feature observed in the SILL spectrum at 16.43jm that maa be the £5 Q-branch of the fundamental band of CIL; (Bezard οἱ 11999: Feuchtgruber et 22000)., There is also a weak feature observed in the SH1 spectrum at $16.48\micron$ that may be the $\nu_2$ Q-branch of the fundamental band of $\CHthree$ (Bezard et 1999; Feuchtgruber et 2000). + In addition. the Nell] line is marginally detected in the SII2 spectrum.," In addition, the [NeIII] line is marginally detected in the SH2 spectrum." +" Figure 3 gives an expanded. view of the region around the weak features [Nell] and. CLL, in the epoch in which they. were detected (S1I2 and SIL. respectively)."," Figure 3 gives an expanded view of the region around the weak features [NeIII] and $\CHthree$ in the epoch in which they were detected (SH2 and SH1, respectively)." + These features are more apparent in the individual spectra than in the average of SIL] and SIZ (Figure 2)., These features are more apparent in the individual spectra than in the average of SH1 and SH2 (Figure 2). + since filling and subtracting a high order polynomial can affect the strength of weak features (e.g.. iit incorrectly fits the local continuum). we did not measure line strengths from the continuuni-subtracted spectrum.," Since fitting and subtracting a high order polynomial can affect the strength of weak features (e.g., if it incorrectly fits the local continuum), we did not measure line strengths from the continuum-subtracted spectrum." + We instead used the continmmm-subtracted spectrum to identify (he approximate wavelengths of features to be fit. ancl we (hen measured feature strengths Irom the original spectrum.," We instead used the continuum-subtracted spectrum to identify the approximate wavelengths of features to be fit, and we then measured feature strengths from the original spectrum." + We made a least-squares fit to each [eature using a model of a Gaussian anda quadratic approximation to the local continuum., We made a least-squares fit to each feature using a model of a Gaussian anda quadratic approximation to the local continuum. + A Marquardt, A Marquardt +superluminal motions and are probably moving al relativistic speeds 1994).,superluminal motions and are probably moving at relativistic speeds . +. Flaves in (he jet components have also been observed wilh similar amplitudes: ancl (imescales as core Hares 2000)., Flares in the jet components have also been observed with similar amplitudes and timescales as core flares . +. There is. however. a small fraction of compact sources whose pe-seale structure is dominated by steep-spectrum extended emission on both sides of the core.," There is, however, a small fraction of compact sources whose pc-scale structure is dominated by steep-spectrum extended emission on both sides of the core." + These sources are known as Compact Svunmetric Objects (CSOs)., These sources are known as Compact Symmetric Objects (CSOs). + Recent measurements ol kinematic ages of ~ 1000 vears support the theory that CSOs are small by virtue of their vouth aud nol because (μον are [rustrated bv a dense environment., Recent measurements of kinematic ages of $\sim$ 1000 years support the theory that CSOs are small by virtue of their youth and not because they are frustrated by a dense environment. + This was the [avored interpretation bv who first drew attention to a group of compact double sources will steep or Gllz-peaked spectra and slow motions compared (o the majority of core-jet sources., This was the favored interpretation by who first drew attention to a group of compact double sources with steep or GHz-peaked spectra and slow motions compared to the majority of core-jet sources. + At about the same time. reported that GIIz-peaked spectrum (GPS) sources generally have low variability and low polarization.," At about the same time, reported that GHz-peaked spectrum (GPS) sources generally have low variability and low polarization." + Although there is some overlap belween sources Classified as CSOs and those classified as GPS sources. we emphasize that (here is no clear correspondence between (he (wo types of sources.," Although there is some overlap between sources classified as CSOs and those classified as GPS sources, we emphasize that there is no clear correspondence between the two types of sources." + In fact. a recent. survey of 47 GPS sources found that only 3 could be clearly classified as CSOs2000).," In fact, a recent survey of 47 GPS sources found that only 3 could be clearly classified as CSOs." +. The term GPS is purely a spectral classification while CSO is a physical one. requiring considerably greater observational effort (usually VLBI observations at multiple frequencies) in order to identify the location of the core component and extended jet and/or lobe emission on both sides of the core.," The term GPS is purely a spectral classification while CSO is a physical one, requiring considerably greater observational effort (usually VLBI observations at multiple frequencies) in order to identify the location of the core component and extended jet and/or lobe emission on both sides of the core." + Objects with vastly different powers. orientations. and evolutionary stages can be classified as GPS sources. while the CSOs are a much more homogeneous group.," Objects with vastly different powers, orientations, and evolutionary stages can be classified as GPS sources, while the CSOs are a much more homogeneous group." + The lack of correspondence between GPS and CSO sources is especially important (o keep in mind if one is choosing a sample of CSOs as flux density calibrators., The lack of correspondence between GPS and CSO sources is especially important to keep in mind if one is choosing a sample of CSOs as flux density calibrators. + The CsOs have «qualities which should make (hem excellent {his calibrator sources., The CSOs have qualities which should make them excellent flux calibrator sources. + One is (he relative unimportance of the presumably. variable core component., One is the relative unimportance of the presumably variable core component. + For 6 bright CSOs. found the core to comprise from. «0.4 to of ihe integrated flix density at 15 Gllz.," For 6 bright CSOs, found the core to comprise from $<$ to of the integrated flux density at 15 GHz." + Another quality is that the jets and lobes of CSOs are (hought to be relatively [ree of Doppler boosting elfects1994)., Another quality is that the jets and lobes of CSOs are thought to be relatively free of Doppler boosting effects. +. Thus. flix variations due to flares in the jet components should not be magnified.," Thus, flux variations due to flares in the jet components should not be magnified." + The physical properties of CSOs have been summarized bv(1996).. who pointed oul that the few CSOs known at that time exhibited both weak radio variability (< 10%)) and low polarization (< 0.5%)).," The physical properties of CSOs have been summarized by, who pointed out that the few CSOs known at that time exhibited both weak radio variability $<$ ) and low polarization $<$ )." + In addition. reported that the CSO 2208 varied bv less than Lover a period of 10 vears at 5 GlIz.," In addition, reported that the CSO 208 varied by less than $^{-1}$ over a period of 10 years at 5 GHz." + presented 8.4 GlIz VLBI observations showing that the polarization was less than in 21 CSOs and CSO candidates., presented 8.4 GHz VLBI observations showing that the polarization was less than in 21 CSOs and CSO candidates. + Yet another fortunate property of CSOs for calibration purposes is (hat thev generally exhibit, Yet another fortunate property of CSOs for calibration purposes is that they generally exhibit +common than what detections indicate.,common than what detections indicate. + In our sample. (he median distance to the SWPs is 35 pc. compared to the 15 pe for the SWOPs. ancl (wo-sample tests reveal these clistauces {ο be significantly different.," In our sample, the median distance to the SWPs is 35 pc, compared to the 15 pc for the SWOPs, and two-sample tests reveal these distances to be significantly different." + ILowever. our main analvsis quantity is Che distance-independent H. and we explicitly include information about sky confusion noise in the form of upper limits. which are taken into account in the survival analvsis.," However, our main analysis quantity is the distance-independent $R$, and we explicitly include information about sky confusion noise in the form of upper limits, which are taken into account in the survival analysis." + Therefore. our results do not support the presence of a large population of undiscovered debris disks around SWPs.," Therefore, our results do not support the presence of a large population of undiscovered debris disks around SWPs." + At jan. our detection limit (Eqn.," At $\,\mu$ m, our detection limit (Eqn." + Ll of Wyatt2008)) is Laws / Le £ ὃν, 11 of \citealt{wyatt2008}) ) is $_{\rm dust}$ / $_{*}$ $\approx$ $^{-6}$. + For these bright debris disks. (he null hypothesis implies (hat the population of planets αἱ distances where the sam emission comes from is Che same for SWPs and the SWOPs.," For these bright debris disks, the null hypothesis implies that the population of planets at distances where the $\,\mu$ m emission comes from is the same for SWPs and the SWOPs." + The mareinally higher incidence of debris disks around SWDPs suggests that in these svstems an outer planet might also exist. which stirs up the planetesimals producing a cold debris disk.," The marginally higher incidence of debris disks around SWPs suggests that in these systems an outer planet might also exist, which stirs up the planetesimals producing a cold debris disk." + The model by Wyattetal.(2007) for A-tvpe stars suggests that the sau emission should be larger for SWPs than for SWOPs. due to the larger mass of the protoplanetary disk in (he former.," The model by \citet{wyatt2007} for A-type stars suggests that the $\,\mu$ m emission should be larger for SWPs than for SWOPs, due to the larger mass of the protoplanetary disk in the former." + They speculate that a similar (rend holds for Sun-like stars., They speculate that a similar trend holds for Sun-like stars. + We found that the brightest debris disks in our SWPs sample are 2—2 times brighter than those in ihe SWODs sample. but the mean brightnesses are only slightly hisher in (he SWPs sample al a 1.66 level.," We found that the brightest debris disks in our SWPs sample are $-$ 3 times brighter than those in the SWOPs sample, but the mean brightnesses are only slightly higher in the SWPs sample at a $\,\sigma$ level." + Our results do not contradict with the prediction of Wyattetal.(2007). although the difference we found is less pronounced (than that expected for A-tvpe stars.," Our results do not contradict with the prediction of \citet{wyatt2007}, although the difference we found is less pronounced than that expected for A-type stars." + Note that disk mass is not the only variable that controls the likelihood of planet formation: disk lifetime. metallicity. aud surface clensity distribution are also important.," Note that disk mass is not the only variable that controls the likelihood of planet formation: disk lifetime, metallicity, and surface density distribution are also important." + Prior (o this studs. only a dozen stars were known to harbour both planets aud debris disks.," Prior to this study, only a dozen stars were known to harbour both planets and debris disks." + Our 10 new debris disks found around planet-bearing stars al jum doubled," Our 10 new debris disks found around planet-bearing stars at $\,\mu$ m doubled" +"moclel. also results in a very weak line (best-fit normalisation is an upper limit of "" photons ? 1) that does not provide any improvement in the quality of the fit (A\F=0.2 for 2 cot).","model, also results in a very weak line (best-fit normalisation is an upper limit of $\times$ $^{-6}$ photons $^{-2}$ $^{-1}$ ) that does not provide any improvement in the quality of the fit $\Delta\chi^{2}$ =0.2 for 2 d.o.f)." + Replacing the two line. profiles in these fits with a single line associated with emission from the accretion disk results in a similar 47 to that obtained with a narrow line., Replacing the two line profiles in these fits with a single line associated with emission from the accretion disk results in a similar $\chi^{2}$ to that obtained with a narrow line. +" However. in this case the derived inner radius of the accretion disk is r;. 71000 4, (qgz2. 6245 )). which results in a clisk-line profile that closely resembles a narrow Gaussian line profile."," However, in this case the derived inner radius of the accretion disk is $_{i}$, $\sim$ 1000 $_{g}$ $\approx$ 2, $\theta\approx$ ), which results in a disk-line profile that closely resembles a narrow Gaussian line profile." + ln summary. the high significance spectra reveal only a narrow iron. Ίνα line with no evidence for the presence of a strong relativistically broaclened iron νὰ feature.," In summary, the high significance spectra reveal only a narrow iron $\alpha$ line with no evidence for the presence of a strong relativistically broadened iron $\alpha$ feature." + This is contrary to the earlier conclusions of Yaqoob (1995) and Wang (1999. 2001). who on the basis of spectra. identified: broad iron Ίνα features in the NGC 4151 spectrum.," This is contrary to the earlier conclusions of Yaqoob (1995) and Wang (1999, 2001), who on the basis of spectra identified broad iron $\alpha$ features in the NGC 4151 spectrum." + However. we note that the presence ofa broad line was not required in the spectral modelling of the final long-Iook observation of NGC 4151 (Sehurch Warwick 2002: Takahashi 2002).," However, we note that the presence of a broad line was not required in the spectral modelling of the final long-look observation of NGC 4151 (Schurch Warwick 2002; Takahashi 2002)." + Lt remains possible that a relativistically broadened line appears in the X-ray spectrum of NGC 4151 only intermittently or for particular ‘states’ of the source., It remains possible that a relativistically broadened line appears in the X-ray spectrum of NGC 4151 only intermittently or for particular `states' of the source. + Further monitoring of NGC 4151 with and should help clarify whether this is the case., Further monitoring of NGC 4151 with and should help clarify whether this is the case. + The measured Hux in the narrow iron Ave line is 1.3. 10+ photons ? significantly lower than that. measured in earlier.αρνι and observations. where the line lux was more typically ~2.2- 1 photons 7s+: (Yaqoob Warwick 19901: Yacoob 1993: Schurch Warwick 2002).," The measured flux in the narrow iron $K\alpha$ line is $\sim$ $\times$ $^{-4}$ photons $^{-2}$ $^{-1}$, significantly lower than that measured in earlier, and observations, where the line flux was more typically $\sim$ $\times$ $^{-4}$ photons $^{-2}$ $^{-1}$; (Yaqoob Warwick 1991; Yaqoob 1993; Schurch Warwick 2002)." + The present measurenient is also somewhat lower than that reported. in. recent observations (1840.2. ! photons 7s 1: Ogle 20000., The present measurement is also somewhat lower than that reported in recent observations $\pm$ $\times$ $^{-4}$ photons $^{-2}$ $^{-1}$; Ogle 2000). + Ogle (2000) state that spatially resolves 659% of the iron line emission. placing its origin in the ENLR at a clistances of up to ~500 pe from the continuum source.," Ogle (2000) state that spatially resolves $\pm$ of the iron line emission, placing its origin in the ENLR at a distances of up to $\sim$ 500 pc from the continuum source." + “Phus an iron We line Lux of up to 12-107 photons em27 + could. be attributable to the ENLR. a value comparable to that. measured. in. the current observations.," Thus an iron $\alpha$ line flux of up to $\times10^{-4}$ photons $^{-2}$ $^{-1}$ could be attributable to the ENLR, a value comparable to that measured in the current observations." + The implication is tha a component of the iron. Ίνα line. produced. close το the central engine in NGC 4151 almost completely. clisappearec over the —10 month time interval betweenthe anc observations., The implication is that a component of the iron $\alpha$ line produced close to the central engine in NGC 4151 almost completely disappeared over the $\sim$ 10 month time interval betweenthe and observations. + However. we caution that this intriguing scenario may not be valid.," However, we caution that this intriguing scenario may not be valid." + The line intensity given by Ogle (2000) combined with the exposure time anc LETC: ellective area indicate. ~160 photons in the line., The line intensity given by Ogle (2000) combined with the exposure time and HETG effective area indicate $\sim$ 160 photons in the line. + MPhe central —17 Hoopof the cross-cdispersion. profile qosintegratec over the energy interval containing the line contains the majority of the photons from both line and continuum (whether extended or not)., The central $\sim$ of the cross-dispersion profile integrated over the energy interval containing the line contains the majority of the photons from both line and continuum (whether extended or not). + To determine whether any of the line emission is extended to a given level of confidence. one needs to show that the cross-cdispersion profile outside of the central 71 lies above the background. noise.," To determine whether any of the line emission is extended to a given level of confidence, one needs to show that the cross-dispersion profile outside of the central $\sim$ lies above the background noise." + Ogle (2000) do not give a confidence level to their. claim hat the interval either side of the peak of the cross-dispersion profile contains extended iron line emission. rowever a brief calculation of the cross-cdispersion prolile or the number of photons detected in the erating observation indicates that stronely significant (4e. 24e significance) spatially extended iron ivo line emissioncannol x detected in this relatively short observation.," Ogle (2000) do not give a confidence level to their claim that the interval either side of the peak of the cross-dispersion profile contains extended iron line emission, however a brief calculation of the cross-dispersion profile for the number of photons detected in the grating observation indicates that strongly significant i.e. $>$ $\sigma$ significance) spatially extended iron $\alpha$ line emission be detected in this relatively short observation." + Lf all the iron We line [ux instead originates close to the central engine. then the line Mux from this vicinity would only need to decrease by ~35% between the and observations.," If all the iron $\alpha$ line flux instead originates close to the central engine, then the line flux from this vicinity would only need to decrease by $\sim$ between the and observations." + The intensity of the neutral iron Ke ine in the spectra is Consistent with all the ine [lux originating in a nearly Compton thick molecular orus (the EQW with respect to the Compton rellection continuum. is. 1.06 keV).," The intensity of the neutral iron $\alpha$ line in the spectra is consistent with all the line flux originating in a nearly Compton thick molecular torus (the EQW with respect to the Compton reflection continuum, is 1.06 keV)." + The decrease in line [ux observed Yween the ancl observations is. however. in marked contrast with the behavior of the Compton rellection component. which remains at à similar lux-level or. if anvthing. is slightlv stronger. during the observation than it was in the January 1999 observation.," The decrease in line flux observed between the and observations is, however, in marked contrast with the behavior of the Compton reflection component, which remains at a similar flux-level or, if anything, is slightly stronger during the observation than it was in the January 1999 observation." + Εις decoupling of the iron We and he reflection continuum suggests that the additional iron Ixo line Lux observed in the earlier observations is formed in opticallv-thin. cool clouds located within about a light vear of the central source (i.e. closer than the material responsible [or the Compton rellection continuum).," This decoupling of the iron $\alpha$ and the reflection continuum suggests that the additional iron $\alpha$ line flux observed in the earlier observations is formed in optically-thin, cool clouds located within about a light year of the central source (i.e. closer than the material responsible for the Compton reflection continuum)." + In this setting the decline of the iron Ίνα line flux presumably coincides with the central source entering a fairly prolonged low-Iux. period. sampled only Latterly by the observations.," In this setting the decline of the iron Ka line flux presumably coincides with the central source entering a fairly prolonged low-flux period, sampled only latterly by the observations." + The variability constraints suggest that a significantly component of the iron We line may be associated with the complex absorbing medium. including the warm. absorber.," The variability constraints suggest that a significantly component of the iron $\alpha$ line may be associated with the complex absorbing medium, including the warm absorber." + Schurch Warwick (2002) note that the predicted range of iron ionization states in the warm medium. determined from a long-look observation. is Fe XVI-Fe NXI (for which the associated. Ίνα line energy is 6.4-6.6 keV).," Schurch Warwick (2002) note that the predicted range of iron ionization states in the warm medium, determined from a long-look observation, is Fe XVI-Fe XXI (for which the associated $\alpha$ line energy is 6.4-6.6 keV)." + Since the lino encreyv measured by (I2 =6.39540.012 keV). excludes much of this range. it was concluded. that the bulk of the line ux derives from less strongly photoionized material located: further from the nucleus than the warm medium.," Since the line energy measured by $_{K\alpha}$ $\pm$ 0.012 keV), excludes much of this range, it was concluded that the bulk of the line flux derives from less strongly photoionized material located further from the nucleus than the warm medium." + Comparison of the results with the present observations suggests the narrow ion |xa line may typically be composed. of a relatively constant component amounting to 1.2. 101 Ποοας cni2 s1 plus a more variable component of comparable magnitude., Comparison of the results with the present observations suggests the narrow iron $\alpha$ line may typically be composed of a relatively constant component amounting to $\sim$ $\times$ $^{-4}$ photons $^{-2}$ $^{-1}$ plus a more variable component of comparable magnitude. + In such a situation the line measurements clearly relate) predominantly to the. first. of. these two origins., In such a situation the line measurements clearly relate predominantly to the first of these two origins. +" The line equivalent width (~175 eV. referenced. to the observed: power-law but ~GO eV. for a more tvpica continuum level) anc energy derived. from the observations are consistent with an origin for the 7""constant line component in reflection from a neutral of lightly photoionized medium located outside the immediate proximity of the nucleus r1 pc.", The line equivalent width $\sim$ 175 eV referenced to the observed power-law but $\sim$ 60 eV for a more typical continuum level) and energy derived from the observations are consistent with an origin for the “constant” line component in reflection from a neutral of lightly photoionized medium located outside the immediate proximity of the nucleus $>$ 1 pc. + On the other hanc the variable line emission component may still be associate with the warm absorbing medium. provided. the dominan, On the other hand the variable line emission component may still be associated with the warm absorbing medium provided the dominant +projected number of stars per area surrounding the cluster centre.,projected number of stars per area surrounding the cluster centre. + RDPs are built with stars selected after applying the respective colour magnitude (CM) filter to the observed photometry., RDPs are built with stars selected after applying the respective colour magnitude (CM) filter to the observed photometry. +" CM filters isolate the probable cluster sequences excluding stars with colours different from those of the cluster sequences (e.g.Bonatto&Bica20072,andreferences therein)..", CM filters isolate the probable cluster sequences excluding stars with colours different from those of the cluster sequences \citep[e.g.][and references therein]{Bonatto07a}. +" However, residual field stars with colours similar to those of the cluster are expected to remain inside the CM filter."," However, residual field stars with colours similar to those of the cluster are expected to remain inside the CM filter." + They affect the intrinsic stellar radial distribution profile in a degree that depends on the relative densities of field and cluster., They affect the intrinsic stellar radial distribution profile in a degree that depends on the relative densities of field and cluster. + The contribution of these residual field stars to the RDPs is statistically quantified by means of comparison to the field., The contribution of these residual field stars to the RDPs is statistically quantified by means of comparison to the field. +" In practical terms, the use of the CM filters in cluster sequences enhances the contrast of the RDP with respect to the stellar field."," In practical terms, the use of the CM filters in cluster sequences enhances the contrast of the RDP with respect to the stellar field." + T'he CM filters are shown in Figs., The CM filters are shown in Figs. + 4 to 8 as the shaded area superimposed on the field-star decontaminated CMDs., \ref{fig:04} to \ref{fig:08} as the shaded area superimposed on the field-star decontaminated CMDs. +" 'To minimise oversampling near the centre and under-sampling for large radii, the RDPs are built by counting stars in concentric rings of increasing width with distance to the centre."," To minimise oversampling near the centre and under-sampling for large radii, the RDPs are built by counting stars in concentric rings of increasing width with distance to the centre." + The selected number and width of rings produce RDPs with adequate spatial resolution and moderate lo Poisson errors., The selected number and width of rings produce RDPs with adequate spatial resolution and moderate $1\sigma$ Poisson errors. + The residual background level of each RDP corresponds to the average number of CM-filtered stars measured in the comparison field., The residual background level of each RDP corresponds to the average number of CM-filtered stars measured in the comparison field. +" The cluster structure was derived by means of a King- profile, which is similar to a two-parameter King(1962) model that describes the intermediate and central regions of globular clusters."," The cluster structure was derived by means of a King-like profile, which is similar to a two-parameter \citet{King1962} model that describes the intermediate and central regions of globular clusters." + The fit was performed with a non-linear least-squares routine that uses the errors as weights., The fit was performed with a non-linear least-squares routine that uses the errors as weights. + The best-fit solutions are shown in Fig., The best-fit solutions are shown in Fig. + 12 for 3 relatively populous ECs as a solid line superimposed on the RDPs., \ref{fig:12} for 3 relatively populous ECs as a solid line superimposed on the RDPs. +" The profile is expressed as o(R)=ovg+00K/(1+(R/Reore)’, where op, is the stellar background surface density, σοκ is the central density relative to the background level and Reore is the core radius."," The profile is expressed as $\sigma(R)=\sigma_{bg}+\sigma_{0K}/(1+(R/R_{core})^{2}$, where $\sigma_{bg}$ is the stellar background surface density, $\sigma_{0K}$ is the central density relative to the background level and $R_{core}$ is the core radius." + The cluster radius (Rrpp) and uncertainty can be estimated by considering the RDP fluctuations with respect to the residual field., The cluster radius $R_{RDP}$ ) and uncertainty can be estimated by considering the RDP fluctuations with respect to the residual field. + Rapp is the distance from the cluster centre where RDP and comparison field become statistically indistinguishable., $R_{RDP}$ is the distance from the cluster centre where RDP and comparison field become statistically indistinguishable. + Small variations in the RDPs are probably due to the presence of other clusters and/or enhanced dust absorption., Small variations in the RDPs are probably due to the presence of other clusters and/or enhanced dust absorption. + The derived structural parameters are given in Table 3.., The derived structural parameters are given in Table \ref{tab5}. + In Fig., In Fig. +" 12 we show the RDPs of Sh2-235 Cluster, Sh2- East2, and FSR 784."," \ref{fig:12} we show the RDPs of Sh2-235 Cluster, Sh2-235 East2, and FSR 784." + For Sh2-235 Cluster and Sh2-235 East2., For Sh2-235 Cluster and Sh2-235 East2. + Overdensities show up in their RDPs., Overdensities show up in their RDPs. + Fig., Fig. +" 13. shows the RDPs of Sh2-235B Cluster, BDSB 71, BDSB 72, BDSB 73, Sh2-232 IR Cluster, KKC11, CBB 2 and the pairs CBB 1 and G 173, PCS 2 and Sh2-233 SE."," \ref{fig:13} shows the RDPs of Sh2-235B Cluster, BDSB 71, BDSB 72, BDSB 73, Sh2-232 IR Cluster, KKC11, CBB 2 and the pairs CBB 1 and G 173, PCS 2 and Sh2-233 SE." +" The RDPs are typical of ECs of low mass and/or initial evolutionary phases, and cannot be fitted by King's profile (Soaresetal.2005)."," The RDPs are typical of ECs of low mass and/or initial evolutionary phases, and cannot be fitted by King's profile \citep{Soares05}." +. They present bumps and dips as compared to field stars., They present bumps and dips as compared to field stars. +" The depression in star counts in the central region of some ECs is possibly due to strong dust absorption, crowding or structured cores."," The depression in star counts in the central region of some ECs is possibly due to strong dust absorption, crowding or structured cores." +" Sh2-232 IR Cluster has a high cluster/background density contrast, but the profile is irregular."," Sh2-232 IR Cluster has a high cluster/background density contrast, but the profile is irregular." +" The Sh2-235B cluster profile includes several of the small clusters nearby like BDSB 71, 72 and 73."," The Sh2-235B cluster profile includes several of the small clusters nearby like BDSB 71, 72 and 73." + A deeper photometry is required for the analysis of the structure of these objects., A deeper photometry is required for the analysis of the structure of these objects. + 'The structure of young populous ECs can be generally characterised by an RDP with multiple peaks on a large spatial scale or centrally condensed with an RDP that, The structure of young populous ECs can be generally characterised by an RDP with multiple peaks on a large spatial scale or centrally condensed with an RDP that +The intrinsic shape of galaxies is interesting from a variety of perspectives.,The intrinsic shape of galaxies is interesting from a variety of perspectives. + For a given galaxy the shape should be consistent with the dynamical model of the galaxy. while. for a sample of galaxies. one would expect that a correct evolutionary model should be able to reproduce the observed distribution of shapes.," For a given galaxy the shape should be consistent with the dynamical model of the galaxy, while, for a sample of galaxies, one would expect that a correct evolutionary model should be able to reproduce the observed distribution of shapes." + It is generally assumed that dise galaxies can be approximated to be oblate spheroids (e.g. Hubble(1926):Sandage.Freeman.&Stokes(1970):Ryden (2006))).," It is generally assumed that disc galaxies can be approximated to be oblate spheroids (e.g. \cite{hubble26,sandage70,ryden06}) )." + If one further assumes that the galaxies have a well defined mean axial ratio (qu). then the observed axial ratio can be used to determine the inclination of the disc.," If one further assumes that the galaxies have a well defined mean axial ratio $_0$ ), then the observed axial ratio can be used to determine the inclination of the disc." + In turn. the inclination is a crucial input in dynamical modeling (e.g. for the mass and structure of the dark matter halo). studying the Fisher relation ete.," In turn, the inclination is a crucial input in dynamical modeling (e.g. for the mass and structure of the dark matter halo), studying the Tully-Fisher relation etc." + The observed shape of a galaxy differs from the intrinsic shape because of projection effects., The observed shape of a galaxy differs from the intrinsic shape because of projection effects. + If one has a sample of galaxies drawn from a population with a well detined intrinsic axial ratio distribution and with random orientations with respect to the earth. then one can determine the distribution of intrinsic axial ratios from the observed axial ratio distribution (fore.g.Noerdlinger1979:1992:Ryden 2006).," If one has a sample of galaxies drawn from a population with a well defined intrinsic axial ratio distribution and with random orientations with respect to the earth, then one can determine the distribution of intrinsic axial ratios from the observed axial ratio distribution \citep[for e.g.~][]{noe79,bin81,lam92,ryden06}." +. It is worth noting that most of these studies have focused on large galaxies. and that there have been relatively few that focused on dwarfs.," It is worth noting that most of these studies have focused on large galaxies, and that there have been relatively few that focused on dwarfs." + For bright spiral galaxies. qo is often taken to be ~0.2 (seee.g.Haynes&Giovanelli1984:Verhei-jen&Sancisi 2001).," For bright spiral galaxies, $_0$ is often taken to be $\sim 0.2$ \citep[see e.g.~][]{haynes84,verheijen01}." + It has also long been appreciated that the axial ratio is a function of Hubble type., It has also long been appreciated that the axial ratio is a function of Hubble type. + For example. Heidmann.Heidmann.&deVaucouleurs(1972). found that while dises get thinner as one goes from galaxies of morphological type Sa to Sd. there is a rapid increase in dise thickness as one goes from Sd to dwarf Irregular galaxies.," For example, \cite{heidmann72} found that while discs get thinner as one goes from galaxies of morphological type Sa to Sd, there is a rapid increase in disc thickness as one goes from Sd to dwarf Irregular galaxies." + Similarly. Staveley-Smith.Davies&Kinman(1992). found that dwarf galaxies from the UGC catalog have qu.0.5.," Similarly, \cite{sta92} found that dwarf galaxies from the UGC catalog have $_0 \sim 0.5$." + Axial ratio is also a function of the wavelength of observation., Axial ratio is also a function of the wavelength of observation. + For example. Ryden(2006). showed that older populations as traced by redder stars have thicker ratios than the corresponding B band disc.," For example, \citet{ryden06} showed that older populations as traced by redder stars have thicker ratios than the corresponding B band disc." + But all of these studies refer to the stellar discs of the galaxies., But all of these studies refer to the discs of the galaxies. + Due to collisions between gas clouds.," Due to collisions between gas clouds," +The precision photometry For millions of faint stars observed »w the Sloan Digital Sky Survey (SDSS) led to the discovery of numerous tidal streams of halo stars.,The precision photometry for millions of faint stars observed by the Sloan Digital Sky Survey (SDSS) led to the discovery of numerous tidal streams of halo stars. + Many. of. these streams are certainly of tidal origin because the progenitor 1às been seen (Odenkirchenetal.2002:Majewski2004:Johnson2006) but in some other cases the progenitor is unknown and may no longer be extant. (Cirillmair2006:Be-okurovetal.2006b:Cirillmair&Dionatos 2006).," Many of these streams are certainly of tidal origin because the progenitor has been seen \citep{Odenkirchen02,Majewski04,N5466,Fellhauer07,Grillmair} but in some other cases the progenitor is unknown and may no longer be extant \citep{Grillmair06,Fieldstars,GD-1}." +. It. has ong been recognised that streams provide an important chagnostic of the still uncertain Galactic gravitational field ov virtue. of the closeness with which a thin stream approximates an orbit (Johnstonetal., It has long been recognised that streams provide an important diagnostic of the still uncertain Galactic gravitational field by virtue of the closeness with which a thin stream approximates an orbit \citep{JohnstonHB}. +1996).. Llowever. he traditional way of exploiting this connection. which is o search for orbits that are consistent with the data. has vieldecd fewer convincing fits to the data than one migh lave expected. and in any given case it is not clear why a »etter-fitting orbit has not been found.," However, the traditional way of exploiting this connection, which is to search for orbits that are consistent with the data, has yielded fewer convincing fits to the data than one might have expected, and in any given case it is not clear why a better-fitting orbit has not been found." + ltecentIy it was realised that given a Galactic potentia «9 and line-of-sight) velocities along ai stream. one can uniquely solve. for the six. phase-space coordinates tha points on the stream must. have if they are to trace an orbit in the given potential (Jin&Lyneen-Bell2007:Bin-nev2008.hereafterPaper D..," Recently it was realised that given a Galactic potential $\Phi$ and line-of-sight velocities along a stream, one can uniquely solve for the six phase-space coordinates that points on the stream must have if they are to trace an orbit in the given potential \citep[][hereafter +Paper I]{complexA,Binney08}." + I£ the wrong eravitationa potential is used in the reconstruction. the recovered. phase-space coordinates will in general be inconsistent. with conservation of energv (Paper 1) and will. violate the angential component of the equations of motion (I2vre&Binney2009.hereafterPaper LH..," If the wrong gravitational potential is used in the reconstruction, the recovered phase-space coordinates will in general be inconsistent with conservation of energy (Paper I) and will violate the tangential component of the equations of motion \citep[][hereafter Paper +II]{EyreB09}." + Hence the reconstruction echnique provides a powerful diagnostic of the gravitational »»ential. and. once the potential has been. determined. it will provide distances to stars that lie on streams that are as absolute as trigonometric parallaxes but very much more »ecise than will be possible for such distant objects in the oresceable future (Paper LH).," Hence the reconstruction technique provides a powerful diagnostic of the gravitational potential, and once the potential has been determined, it will provide distances to stars that lie on streams that are as absolute as trigonometric parallaxes but very much more precise than will be possible for such distant objects in the foreseeable future (Paper I)." + The main obstacles to attainment of these exciting goals are (a) the fact that streams diller slightly but significantly rom orbits. and (b) a lack of reliable line-of-sight velocities along streams.," The main obstacles to attainment of these exciting goals are (a) the fact that streams differ slightly but significantly from orbits, and (b) a lack of reliable line-of-sight velocities along streams." + Paper Lb addresses problem (a)., Paper II addresses problem (a). + This paper aclelresses problem (b) by showing that proper motions may x: emploved. instead of linc-ol-sight velocities., This paper addresses problem (b) by showing that proper motions may be employed instead of line-of-sight velocities. + Alany of the most promising streams have distances in he range LO5Okpe. so their distance moduli are 15.—18.5 and their solar-type stars have apparent. magnitudes. in he range {c1922.5.," Many of the most promising streams have distances in the range $10-50\kpc$, so their distance moduli are $15-18.5$ and their solar-type stars have apparent magnitudes in the range $I\simeq19-22.5$." + Perhaps the closest streams of interest are the GD-1 and Anticentre streams (Crillmalr&Dionatos2006:ομιαν 2006).. which are only LOkpe distant.," Perhaps the closest streams of interest are the GD-1 and Anticentre streams \citep{GD-1,Grillmair06}, which are only $\sim10\kpc$ distant." + Consequently ator«19 Ixoposov.et.al.(2009) were able to obtain velocities for 24 turnoll stars in the GD-1 stream. while at ο«20 CGrilmairetal.(2008) measured velocities for 20 stream stars in cach of two Ποιος.," Consequently at $r<19$ \cite{Koposov} were able to obtain velocities for 24 turnoff stars in the GD-1 stream, while at $g<20$ \cite{anticentre} measured velocities for $\sim20$ stream stars in each of two fields." + The situation regarding velocities of stars in the more distant Orphan stream is much less satisfactory Belokuroy conclude that indications of the line-of-ight velocity of the Orphan stream “are suggestive rather than conclusive’., The situation regarding velocities of stars in the more distant Orphan stream is much less satisfactory – \cite{orphans} conclude that indications of the line-of-sight velocity of the Orphan stream “are suggestive rather than conclusive”. + Even with an Sm telescope it is extremely," Even with an $8\,$ m telescope it is extremely" + , +Using rules of thumb from ?. ?..,"Using rules of thumb from \cite{1997ApJ...485..319S} \cite{2007A&A...473..983D}," +Several interpretations have been proposed for explaining the rebrightenings of these different GRBs but none of them is able to take into account all the characteristics shown by the different light-curves under a unique physical framework.,Several interpretations have been proposed for explaining the rebrightenings of these different GRBs but none of them is able to take into account all the characteristics shown by the different light-curves under a unique physical framework. + In this section we give a brief overview of the different proposed models and will then check if the broad-band light-curve of GRB 081029 can be explained in the framework of some of these models., In this section we give a brief overview of the different proposed models and will then check if the broad-band light-curve of GRB 081029 can be explained in the framework of some of these models. + In the external shock model. a sudden increase of the external medium density can. in principle. produce a rebrightening in the observed afterglow light-curve (Lazzati et al.," In the external shock model, a sudden increase of the external medium density can, in principle, produce a rebrightening in the observed afterglow light-curve (Lazzati et al." + 2002)., 2002). + Such a density profile can be found in the surroundings of a long GRB., Such a density profile can be found in the surroundings of a long GRB. + This is caused by the impact of the stellar wind on the interstellar medium (Kong et al., This is caused by the impact of the stellar wind on the interstellar medium (Kong et al. + 2010)., 2010). +" This effect should be prominent for frequencies between the typical synchrotron frequency and the cooling frequeney vq,«v photometry of E-tvpe stars., The disagreement was quite recently confirmed by Stello Nissen (2001) on the basis of Strömmgren photometry of F-type stars. + Naravanan Could (L999) used. Hipparcos proper motions to further investigate the parallaxes of Pleiades stars. finding a distance modulus with a rather large error (+ 0.18 mae.)," Narayanan Gould (1999) used Hipparcos proper motions to further investigate the parallaxes of Pleiades stars, finding a distance modulus with a rather large error $\pm$ 0.18 mag.)" + which they claimed to be in disagreemen with that derived directly from Llipparcos parallaxes and in agreement with that obtained through AIS fitting., which they claimed to be in disagreement with that derived directly from Hipparcos parallaxes and in agreement with that obtained through MS fitting. + However. the uncertainty is of the same order as that of the quote discrepancy.," However, the uncertainty is of the same order as that of the quoted discrepancy." + Thus the authors suggested the possibility of systematic errors due to spatial correlations over smal angular scales., Thus the authors suggested the possibility of systematic errors due to spatial correlations over small angular scales. + This) possibility was rejected by. Robichon οἳ al. (, This possibility was rejected by Robichon et al. ( +1999a.b) and van Leeuwen (1999b) who. on the basis of a range of statistical checks on the data and an evaluation of data reduction. methods. excluded. the occurrence of systematic errors (see also van Leeuwen Evans 1998).,"1999a,b) and van Leeuwen (1999b) who, on the basis of a range of statistical checks on the data and an evaluation of data reduction methods, excluded the occurrence of systematic errors (see also van Leeuwen Evans 1998)." + Aloreover. Stello Nissen (2001). quoted. the. recen photometric determination of the Pleiacles metallicity by Grenon (1999) based on about 62 stars: Fe/LJ=-0.1140.025 showing that with this choice of metallicity the Pleiades, Moreover Stello Nissen (2001) quoted the recent photometric determination of the Pleiades metallicity by Grenon (1999) based on about 62 stars: $\pm$ 0.025 showing that with this choice of metallicity the Pleiades +Neutron stars are excellent astrophysical laboratories (ο test matter above nuclear density (Page&Reddy.2006)..,Neutron stars are excellent astrophysical laboratories to test matter above nuclear density \citep{2006ARNPS..56..327P}. + Unfortunately. there is nowadays no wav for nuclear physicists to investigate matter al such extvemely high densities in laboratories.," Unfortunately, there is nowadays no way for nuclear physicists to investigate matter at such extremely high densities in laboratories." + Moreover. because of the lack of knowledge about the behavior of particles in (hese extreme regimes. (here is vet no consensus on a satisfactory equation of state for nucleons.," Moreover, because of the lack of knowledge about the behavior of particles in these extreme regimes, there is yet no consensus on a satisfactory equation of state for nucleons." + Many modern equations of state have been proposed. based ou non-elativistic approximations or with help on relativistic field theory (see ILaenseletal.(2007) and references therein).," Many modern equations of state have been proposed, based on non-relativistic approximations or with help on relativistic field theory (see \cite{2007ASSL..326.....H} and references therein)." + These equations of state at or above nuclear density. predict different mass to radius relations Lor neulron stars., These equations of state at or above nuclear density predict different mass to radius relations for neutron stars. + The answer or a piece of it could maxbe come not from terrestrial laboratories but [rom the skv (Lattimer&Prakash2007:Ozeletal.2010)..," The answer or a piece of it could maybe come not from terrestrial laboratories but from the sky \citep{2007PhR...442..109L, + 2010arXiv1002.3153O}." + Indeed. it has been claimed that measuring the mass and the radius of neutron stars will help to constrain the proposed equations of state ancl to reject some of them (Milleretal.1998:Lattimer20071)..," Indeed, it has been claimed that measuring the mass and the radius of neutron stars will help to constrain the proposed equations of state and to reject some of them \citep{1998ApJ...508..791M, 2007Ap&SS.308..371L}." + IIF-QPOs observations in LMXBDs is a unique tool to test gravity in (he strong field reeime and to learn about the behavior of particles at high densities., HF-QPOs observations in LMXBs is a unique tool to test gravity in the strong field regime and to learn about the behavior of particles at high densities. + Further detailed observations and modelling of QPOs for individual objects will help getng more insight into the properties of individual accreting neutron stars., Further detailed observations and modelling of QPOs for individual objects will help getting more insight into the properties of individual accreting neutron stars. + llow can we then estimate their mass and radius?, How can we then estimate their mass and radius? + In binary neutron stars showing up as pulsars. (he task is relatively easy (Thorsett&Chakrabarty1999)..," In binary neutron stars showing up as pulsars, the task is relatively easy \citep{1999ApJ...512..288T}." + The very. accurate clock furnished by the pulsar serves as an efficient mstrument to deduce the orbital motion and other parameters in (his svstem (Nice2006).., The very accurate clock furnished by the pulsar serves as an efficient instrument to deduce the orbital motion and other parameters in this system \citep{2006AdSpR..38.2721N}. + Such techniques have been successfully applied bv numerous authors. finding masses aggregating around 1.4A. (for a summary. see e.g. Lattimer&Prakash (2007))).," Such techniques have been successfully applied by numerous authors, finding masses aggregating around $1.4\,M_\odot$ (for a summary, see e.g. \cite{2007PhR...442..109L}) )." + For neutron stars in LMXDs. the situation is less favorable although some attempts have been made.," For neutron stars in LMXBs, the situation is less favorable although some attempts have been made." + For a recent. review on different methods (o compute neutron star, For a recent review on different methods to compute neutron star +where the approximate value is appropriate to the order they consider.,where the approximate value is appropriate to the order they consider. +" The // and fy Einstein equations are respectively The second equation is equivalent to the formula where thev have Thus the observed rotation curve becomes a boundary condition lor the solution to Laplace's equation (5)) which thev take in the form where the A, are chosen for orthogonalitv over the radius of the galaxy.", The $tt$ and $t\varphi$ Einstein equations are respectively The second equation is equivalent to the formula where they have Thus the observed rotation curve becomes a boundary condition for the solution to Laplace's equation \ref{lap}) ) which they take in the form where the $k_n$ are chosen for orthogonality over the radius of the galaxy. + Once ;N is found by fitting this function to the obsersved rotation curve. they derive the density by (4a)) and in (his wav thev obtain an excellent fit to (he data while obtaining a density profile that accords with observation.," Once $N$ is found by fitting this function to the obsersved rotation curve, they derive the density by \ref{dens}) ) and in this way they obtain an excellent fit to the data while obtaining a density profile that accords with observation." + llowever. it has been pointed out (IXorzevnski2005:Vogt&Letelier2005) that. since the solution depends on |:|. equation (4b)) is not satisfied. but rather vields a singular contribution to the 2=0 plane. which has the properties of an exotic form of matter.," However, it has been pointed out \citep{c1,c2} that, since the solution depends on $|z|$, equation \ref{neqn}) ) is not satisfied, but rather yields a singular contribution to the $z=0$ plane, which has the properties of an exotic form of matter." + H may be wondered whether (his singular disk can be removed by choosing a different solution form or by increasing the complexity of the model., It may be wondered whether this singular disk can be removed by choosing a different solution form or by increasing the complexity of the model. + However. in the following analvsis we will show that Chis is not possible aud (hat model fails to accord with general relativity.," However, in the following analysis we will show that this is not possible and that model fails to accord with general relativity." +" Assuming this form of the metric. aud without making any approximations. the scalar of volume expansion ο=u"", vanishes (a semicolon denotes covariant differentiation and a"," Assuming this form of the metric, and without making any approximations, the scalar of volume expansion $\Theta \equiv +u^\mu_{\phantom{\mu};\mu}$ vanishes (a semicolon denotes covariant differentiation and a" +Although a similar translation is found in Barr(1981).. th. these authors have taken some poctic liceuse with he text.,"Although a similar translation is found in \citet{Barr81}, both these authors have taken some poetic license with the text." + A iore literal trauslation of the key sentence and a slight modification of that given by Ramsey(2006) is “Even at midday. the marveling populace beheld a old. ancl unmistakable star. which was uot faint with dinuned rav. but as bright as Boottes is at night.," A more literal translation of the key sentence and a slight modification of that given by \cite{Ramsey2006} is: “Even at midday, the marveling populace beheld a bold and unmistakable star, which was not faint with dimmed ray, but as bright as Boöttes is at night." + It shone orth. a guest in παν regions at a strange hour. aud it could be recognized although the moou lay hidden.”," It shone forth, a guest in fiery regions at a strange hour, and it could be recognized although the moon lay hidden.”" + Although Clauciaw’s description concerning a star cine “bold” (audax) aud visible even at midday sugecsting a very bright object would seem cousisteu with our estimated peak magnitude around —[.5 for a RX J17123.7-3916. supernova. it appears unlikely tha it is a reference to the Chincse guest star of 393.," Although Claudian's description concerning a star being “bold” (audax) and visible even at midday suggesting a very bright object would seem consistent with our estimated peak magnitude around $-4.5$ for a RX J1713.7-3946 supernova, it appears unlikely that it is a reference to the Chinese guest star of 393." + The constellation Scorpius would set by 9 am in the morning of carly March 393 and hence no star located im its tai would be visible near midday., The constellation Scorpius would set by 9 am in the morning of early March 393 and hence no star located in its tail would be visible near midday. + One possibility is that Clauciau’s star is a sighting of a brilliant 15 or brighter SN in late 392 when Scorpius would be near conjuction with the Sun., One possibility is that Claudian's star is a sighting of a brilliant $-4.5$ or brighter SN in late 392 when Scorpius would be near conjuction with the Sun. + However. iu tha case the Chinese then should have reported it iun the early morning by mid-Januuw when Scorpius rises an hour before morning twilight.," However, in that case the Chinese then should have reported it in the early morning by mid-January when Scorpius rises an hour before morning twilight." + Additionally. there is no Chinese record concermue a davtime star m 392.," Additionally, there is no Chinese record concerning a daytime star in 392." + Tuterestinely Venus. which can be seeu during davlight when brighter than ~3.45 magnitude (Weaver1917).. was near its maximo brilliance of —L6 mag aud rear the meridian at 9 am on 23 January 393 when llouorius was declared einperor (Augustus) by lis father Theodosius.," Interestingly Venus, which can be seen during daylight when brighter than $\approx -3.5$ magnitude \citep{Weaver1947}, , was near its maximum brilliance of $-4.6$ mag and near the meridian at 9 am on 23 January 393 when Honorius was declared emperor (Augustus) by his father Theodosius." + Af noon ou that dav. Venus would still have 2ος. Visible some 25 degrees above the southnwesteru skies.," At noon on that day, Venus would still have been visible some 25 degrees above the southwestern skies." + The waning crescent Moon would have already sot woinidday and might explain Claudian’s reference to a stars visibility “though the moon lay lid”., The waning crescent Moon would have already set by midday and might explain Claudian's reference to a star's visibility “though the moon lay hid”. + So maybe a daytime sielting of Venus is what Claudiau was referring o in his poem of adoration to emperor Houorius., So maybe a daytime sighting of Venus is what Claudian was referring to in his poem of adoration to emperor Honorius. + Ideutifvine the remnants of historie SNe is often difficult aud this is especially true in the case of the 395 euest star., Identifying the remnants of historic SNe is often difficult and this is especially true in the case of the 393 guest star. + Caven the brief description of the eucst star in the Chinese records aud the nearly dozen Calactic supernova reninants currently kuown within the tail of Scorpius (Caeen2009).. doubts about auv SN 393 SNR association will likely persist.," Given the brief description of the guest star in the Chinese records and the nearly dozen Galactic supernova remnants currently known within the tail of Scorpius \citep{Green09}, doubts about any SN 393 – SNR association will likely persist." + A connection between the ancient euest star anc suspected supernova of 393 and the X-ray bright supernova remnant RX J17123.7-3916 has been propose by Waneetal.(1997)., A connection between the ancient guest star and suspected supernova of 393 and the X-ray bright supernova remnant RX J1713.7-3946 has been proposed by \citet{Wang97}. +. While this counectiou has been often cited in the literature on the RN. J1712.7-3916 τοι! audisiulnuesith some of its relatively vouthfu properties. the Wangetal.(1997). estimated AZ values between 12 and Ll imply a very subliuninous core-collapse SN event.," While this connection has been often cited in the literature on the RX J1713.7-3946 remnant and is in line with some of its relatively youthful properties, the \citet{Wang97} estimated $M_{\rm V}$ values between $-12$ and $-14$ imply a very subluminous core-collapse SN event." + Iun this paper. woe reviewed both the Chinese and Roman accounts and calculated probable visual brightuesses for a range of supernova subtype.," In this paper, we reviewed both the Chinese and Roman accounts and calculated probable visual brightnesses for a range of supernova subtype." + We conclude that neither the Chinese nor the Roman descriptions are casily recouciled with au expected RN JI713.7-39 supernova brightucss aud duration., We conclude that neither the Chinese nor the Roman descriptions are easily reconciled with an expected RX J1713.7-3946 supernova brightness and duration. + We further note 16that if RN. J17123.7-3916 were the SN 393 remnant. if would then rank as having been the nearest of all the known historic Galactic supernovae during the last 2000 vears.," We further note that if RX J1713.7-3946 were the SN 393 remnant, it would then rank as having been the nearest of all the known historic Galactic supernovae during the last 2000 years." + It’s relatively χα] distance of around 1 kpc plus a moderate amount of optical extinction also micas its supernova would have likely have been a visually brilliant object. certainly as bright as Jupiter aud maybe as bright as Venus.," It's relatively small distance of around 1 kpc plus a moderate amount of optical extinction also means its supernova would have likely have been a visually brilliant object, certainly as bright as Jupiter and maybe as bright as Venus." + Although a connection between SN 393 and RN J1713.7-3916. or for that matter anv other voune SNR lug within Scorpius tail. will likely remain uncertain due to limitations of the ancient records. such au association does not appear consistent with the available historical records.," Although a connection between SN 393 and RX J1713.7-3946, or for that matter any other young SNR lying within Scorpius' tail, will likely remain uncertain due to limitations of the ancient records, such an association does not appear consistent with the available historical records." + It is hoped that future studies of the RN J1713.7-3916. roumaut which provide better estimates as to its age iav. help resolvethe question of the remnant of the suspected SN of 393 AD., It is hoped that future studies of the RX J1713.7-3946 remnant which provide better estimates as to its age may help resolvethe question of the remnant of the suspected SN of 393 AD. +Il Zw 40 is a dwarl starburst galaxy. al a distance of 10.5 Mpc (Becketal.2002).,II Zw 40 is a dwarf starburst galaxy at a distance of 10.5 Mpc \citep{bec02}. +. It is known to be a Woll-Ravel galaxy (xunth&SargentL983:VaccaConti1992).. suggesting significant star formation 3-6 Myr in (he past and indicating the presence of a population of evolved massive stars (hal are temporally associated will the onset of supernovae.," It is known to be a Wolf-Rayet galaxy \citep{kun83,vac92}, suggesting significant star formation 3-6 Myr in the past and indicating the presence of a population of evolved massive stars that are temporally associated with the onset of supernovae." + From and optical imaging. Vanzietal.(1996) suggest that the bulk of (he recent starburst aclivily is less than 4 Myr old. which implies that (he galaxy sGll may be ramping up to its peak number of evolved massive stars and supernovae.," From near-infrared and optical imaging, \citet{van96} suggest that the bulk of the recent starburst activity is less than 4 Myr old, which implies that the galaxy still may be ramping up to its peak number of evolved massive stars and supernovae." + Based on their models. predict a supernova rate of <107 SN +.," Based on their models, \citet{van96} predict a supernova rate of $<10^{-3}$ SN $^{-1}$." + Neutral hydrogen observations indicate moclerate depressions associated will the active star lormine region. plausibly suggesting; the impact of mechanical feedback [rom stellar winds and/or supernovae (vanZeeetal.1998).," Neutral hydrogen observations indicate moderate depressions associated with the active star forming region, plausibly suggesting the impact of mechanical feedback from stellar winds and/or supernovae \citep{van98}." +.. Previous radio observations of II Zw 40 indicate a relative lack of non-thermal emission., Previous radio observations of II Zw 40 indicate a relative lack of non-thermal emission. + Sramek&Weedman(1986). find that the 5 GIIz flux is dominated by thermal emission. and estimate a total non-thermal flux at 1.49 GlIz of 2.4:3.9 mJv. which is consistent. with 11 Zw 40 only having a low level of recent supernovae activity.," \citet{sra86} find that the 5 GHz flux is dominated by thermal emission, and estimate a total non-thermal flux at 1.49 GHz of 2.4–3.9 mJy, which is consistent with II Zw 40 only having a low level of recent supernovae activity." + Becketal.(2002) [it a raclic spectrum to II Zw 40 indicating that most of the radio emission is optically (hin thermal emission. presumably energized by voung stars: from the radio source in the central 3”. they infer the presence of ~1.4x107 O7-equivalent stars.," \citet{bec02} fit a radio spectrum to II Zw 40 indicating that most of the radio emission is optically thin thermal emission, presumably energized by young stars; from the radio source in the central $3''$ , they infer the presence of $\sim 1.4\times 10^4$ O7-equivalent stars." + Larger scale emission inferred by (2002) is imaged more clearly in our Figure 1.. but this emission clearly is not compact on iilliareseconcl scales.," Larger scale emission inferred by \citet{bec02} is imaged more clearly in our Figure \ref{fig:vla}, but this emission clearly is not compact on milliarcsecond scales." + Thus. the region that we imaged using the HSA contains all the subarcsecond-seale [ux in 11 Zw 40.," Thus, the region that we imaged using the HSA contains all the subarcsecond-scale flux in II Zw 40." + The most compact 15 GlIIz sources in this region have flux densities of 0.40.6 mJy 1 inplving similar 5 Gllz flux densities for thermal sources. so i would be feasible for these sources to contain radio supernovae at the level of 0.10.3 mJv at 5 Gllz.," The most compact 15 GHz sources in this region have flux densities of 0.4–0.6 mJy $^{-1}$, implying similar 5 GHz flux densities for thermal sources, so it would be feasible for these sources to contain radio supernovae at the level of 0.1–0.3 mJy at 5 GHz." + Our conservative ISA upper limit of 0.09 mJy 1 is somewhat lower. and corresponds to an upper limit of 1.2xLO W hat 5 GllIz.," Our conservative HSA upper limit of 0.09 mJy $^{-1}$ is somewhat lower, and corresponds to an upper limit of $1.2\times 10^{18}$ W $^{-1}$ at 5 GHz." + We can compare this limit to the power of the galactic supernova remnant Cas A. which presently has à 5 GIIz flix clensity of 650 Jv (Baarsetal.1977).," We can compare this limit to the power of the galactic supernova remnant Cas A, which presently has a 5 GHz flux density of 650 Jy \citep{baa77}." +. For a distance of 3.4 kpc (eelοἱal.1995).. the Cas A power at 5 Gllz is 9.0x10 W !. so we conclude that there are no radio supernovae in IL Zw 40 with powers greater than 1.3 times Clas A. lle 2-10 is another dwarf galaxy. al a distance of 9 Ape.," For a distance of 3.4 kpc \citep{ree95}, the Cas A power at 5 GHz is $9.0\times 10^{17}$ W $^{-1}$, so we conclude that there are no radio supernovae in II Zw 40 with powers greater than 1.3 times Cas A. He 2-10 is another dwarf galaxy, at a distance of 9 Mpc." + Its current star formation is dominated by a star-forming region that contains several hundred. WollRavetstars, Its current star formation is dominated by a star-forming region that contains several hundred Wolf-Rayetstars +Supernova feedback is considered to be a crucial element for negative feedback in star formation in disk galaxies.,Supernova feedback is considered to be a crucial element for negative feedback in star formation in disk galaxies. +" The star formation history in massive spheroids requires, according to the prevalent view, negative feedback from AGN."," The star formation history in massive spheroids requires, according to the prevalent view, negative feedback from AGN." + Whether this is sufficient to explain the observed downsizing is far from clear., Whether this is sufficient to explain the observed downsizing is far from clear. + Here we reassess the Schmidt-Kennicutt (SK) star formation law and develop a simple multi-phase model in terms of the porosity formalism applied to disk galaxies 2001)., Here we reassess the Schmidt-Kennicutt (SK) star formation law and develop a simple multi-phase model in terms of the porosity formalism applied to disk galaxies \citep{sil01}. +.We extend the model to incorporate AGN-triggered star formation and provide an application to spheroid formation and ultraluminous starbursts., .We extend the model to incorporate AGN-triggered star formation and provide an application to spheroid formation and ultraluminous starbursts. + A cloud collision model of the SK law has been previously presented by who uses galactic shear to compute the cloud collision (1999).rate.," A cloud collision model of the SK law has been previously presented by \citet{tan99}, who uses galactic shear to compute the cloud collision rate." + One advantage of this approach is that it provides a natural explanation for the low star formation rates observed in the outer parts of disk galaxies and complements an alternative explanation which appeals to UV background radiation-controlled H» suppression in the dust-deprived outer disk , One advantage of this approach is that it provides a natural explanation for the low star formation rates observed in the outer parts of disk galaxies and complements an alternative explanation which appeals to UV background radiation-controlled $H_2$ suppression in the dust-deprived outer disk \citet{sch04}. +"We provide a simplified reformulation below, that we (2004)...will apply in the context of a multi-phase medium to incorporate star formation and supernova feedback (Section 2)."," We provide a simplified reformulation below, that we will apply in the context of a multi-phase medium to incorporate star formation and supernova feedback (Section 2)." +" In Section 3, we explore regulation of star formation by turbulent pressure and set an upper limit on the disk surface brightness due to star formation."," In Section 3, we explore regulation of star formation by turbulent pressure and set an upper limit on the disk surface brightness due to star formation." + Section 4 builds on the AGN feedback model and applies AGN triggering to star formation in protospheroids., Section 4 builds on the AGN feedback model \citet{sil05} and applies AGN triggering to star formation in protospheroids. + Scaling laws are derived for the black hole growth rate and the star formation rate., Scaling laws are derived for the black hole growth rate and the star formation rate. + Downsizing of both super-massive black holes and stellar mass is found to be a natural consequence of Bondi accretion-fed black holes and AGN-induced star formation Consider cloud collisions in the disk as a trigger of star formation., Downsizing of both super-massive black holes and stellar mass is found to be a natural consequence of Bondi accretion-fed black holes and AGN-induced star formation Consider cloud collisions in the disk as a trigger of star formation. + Cloud formation and collisions are driven by the non-axisymmetric gravitational instability of a cold self-gravitating gas-rich disk., Cloud formation and collisions are driven by the non-axisymmetric gravitational instability of a cold self-gravitating gas-rich disk. +" Let a typical cloud have pressure p,; and surface density X. We expect star-forming clouds to be marginally self-gravitating and also to be confined by ambient gas pressure.", Let a typical cloud have pressure $p_{cl}$ and surface density $\Sigma_{cl}.$ We expect star-forming clouds to be marginally self-gravitating and also to be confined by ambient gas pressure. +" Clouds form this way, and may be maintained if the cloud covering factor is of order unity, this condition guaranteeing that collisions occur on a local dynamical time-scale."," Clouds form this way, and may be maintained if the cloud covering factor is of order unity, this condition guaranteeing that collisions occur on a local dynamical time-scale." +" If the clouds are strongly bound, it is difficult to avoid a short lifetime, collapse and star formation."," If the clouds are strongly bound, it is difficult to avoid a short lifetime, collapse and star formation." + Our description is a statistical one where we are assuming a steady state ensemble of clouds although the clouds are being formed and reformed all the time in competition with cloud destruction and dispersal processes such as star formation and collisions., Our description is a statistical one where we are assuming a steady state ensemble of clouds although the clouds are being formed and reformed all the time in competition with cloud destruction and dispersal processes such as star formation and collisions. +" For typical parameters in the Galaxy, the disk crossing time normal to the disk and the cloud lifetimes are similar both of order 10Myr, although we assume in general a statistically steady state cloud population in this analysis."," For typical parameters in the Galaxy, the disk crossing time normal to the disk and the cloud lifetimes are similar both of order $10 \rm Myr,$ although we assume in general a statistically steady state cloud population in this analysis." +The cutting performance of the laser machine from the point of view of the slit edge rougluess nust be periodically controlled to be inside the specifications reported i1 2.1.,The cutting performance of the laser machine from the point of view of the slit edge roughness must be periodically controlled to be inside the specifications reported in 2.1. + We have defined the ollowiug quality control procedure: 9 square samples (30 tun side) are cu [rom an invar sheet uuder he same laser machine settines as the mask slits., We have defined the following quality control procedure: 9 square samples (30 mm side) are cut from an invar sheet under the same laser machine settings as the mask slits. + The roughluess of the sariple borders is measured 'v a Inechanical roughness The samples are placed vertically uner the measuring probe. which is à 1 nun wide chisel edge stvlus with 5in tip radius. that measres the roughness over the ull thickness of the 0.2 mu samples.," The roughness of the sample borders is measured by a mechanical roughness The samples are placed vertically under the measuring probe, which is a 1 mm wide chisel edge stylus with $5\,\mu$ m tip radius, that measures the roughness over the full thickness of the 0.2 mm samples." + The roughuess cau be due to both the laser cutting process itself aud the residual invar melting flashes., The roughness can be due to both the laser cutting process itself and the residual invar melting flashes. + The instrument is counected to a third PC where all ueasuremeuts carried out during the lifetime of the MAUL can be acquire. analyzed aud archivect.," The instrument is connected to a third PC where all measurements carried out during the lifetime of the MMU can be acquired, analyzed and archived." + The slit width is checked by a microscope with a calibrated reticle., The slit width is checked by a microscope with a calibrated reticle. + The SteucilMaster software by LPISF controls the whole cutting process. Le. the clisplaceme: of the worki1g platform. aud the laser parameter settings aud switchiug.," The StencilMaster software by LPKF controls the whole cutting process, i.e. the displacement of the working platform, and the laser parameter settings and switching." + The XY motion system S controlled by rotary encoders on tle motor shafts. but a calibration of tlie system itself can be dore wine the luear glass rules provided on the two axes.," The XY motion system is controlled by rotary encoders on the motor shafts, but a calibration of the system itself can be done using the linear glass rules provided on the two axes." + During sucli procedure the workiug platform. noves. backwards aud forwards. aoug the Y aud X direction. with a oedefiued step to cover tle whole traveine range.," During such procedure the working platform moves, backwards and forwards, along the Y and X direction, with a predefined step to cover the whole traveling range." + After each step the displacement is reac ou he rules aud the clillerence )elween the reqtested aud the actial positions Is storecl in a calibratio file., After each step the displacement is read on the rules and the difference between the requested and the actual positions is stored in a calibration file. + During normal cuttiiD>oO Operation stch correction is appliec to the requested position to take iο account this difference., During normal cutting operation such correction is applied to the requested position to take into account this difference. + A jew calibration of the motion systeu 1s reconunencled i£ a significant temperature variation occurres or if the machine is switched off for some days., A new calibration of the motion system is recommended if a significant temperature variation occurres or if the machine is switched off for some days. + A typical calibration fie is plotted in Fig., A typical calibration file is plotted in Fig. + To verily the accuracy of the working platform displacements afte: calibration. we used a laser interferometer with a resolution of 0.1 sam and an accuracy oL £0.5ppii.," To verify the accuracy of the working platform displacements after calibration, we used a laser interferometer with a resolution of $0.1\, \mu$ m and an accuracy of $\pm\,0.5\, ppm$." + Normally. the 'eadiugs [rom internal linear glass rules are uot accessible while the jachine is moving., Normally the readings from internal linear glass rules are not accessible while the machine is moving. + For this 'eason a sluele (uucalibrated) step displacement was commanded uauually aud. when done. the internal rule reacting was recorded together with the interferometer dispacement measurement.," For this reason a single (uncalibrated) step displacement was commanded manually and, when done, the internal rule reading was recorded together with the interferometer displacement measurement." +" The agreement between the two measures was within d -2,un. that confirms the accuracy of the LPIKE uachiue displacements."," The agreement between the two measures was within $\pm\, 2 \,\mu$ m, that confirms the accuracy of the LPKF machine displacements." + We cid further tests asking for selected linear €us along the interferometer jean (alternately mounted aloug X aud Y) aud readiug the interferoijeter reaclout aud the glass, We did further tests asking for selected linear cuts along the interferometer beam (alternately mounted along X and Y) and reading the interferometer readout and the glass +the orbital period of a transient. given only the observed values for its outburst amplitude.,the orbital period of a transient given only the observed values for its outburst amplitude. + For some of the X-ray transients. their quiescent magnitudes have proved too faint for one to obtain accurate radial velocity or photometric light curves of the secondary. star. which will allow one to determine the orbital period. of these systems.," For some of the X-ray transients, their quiescent magnitudes have proved too faint for one to obtain accurate radial velocity or photometric light curves of the secondary star, which will allow one to determine the orbital period of these systems." + In the next section we estimate quiescent magnitudes and/or the orbital periods of a few of the faint Lransients., In the next section we estimate quiescent magnitudes and/or the orbital periods of a few of the faint transients. + For a Roche-lobe [filling star the average density. pis simply a function. of the orbital period. (Frank. Wing ltaine 1985).," For a Roche-lobe filling star the average density, $\rho$ is simply a function of the orbital period (Frank, King Raine 1985)." +" For νοΟΤΙ676 with 7,253.82 hrs. p=7.54 ο cm7 which implies a M34V star (Allen 1981)."," For EXO0748–676 with $P_{orb}$ =3.82 hrs, $\rho$ =7.54 g $^{-3}$, which implies a M3–4V star (Allen 1981)." + This can be compared with the spectral type of the secondary star obtained by determining its absolute magnitude., This can be compared with the spectral type of the secondary star obtained by determining its absolute magnitude. +" Using equation (4) we find. M,.(2)210.2 mags. which implies an MP3 V star (Allen 1981)."," Using equation (4) we find $M_{v}(2)$ =10.2 mags, which implies an M2–3 V star (Allen 1981)." + Using equation (1) we can also predict. the quiescen magnitude. of ENOOTAS-676., Using equation (1) we can also predict the quiescent magnitude of EXO0748-676. + With Vo 2169. we. finc Vo 726.8 mags. which is consistent with the observed limi ol Vo 723 mags (see Table 1).," With $V_{O}$ =16.9, we find $V_{Q}\sim$ 26.8 mags, which is consistent with the observed limit of $V_{Q}>$ 23 mags (see Table 1)." + However. if the secondary star is sullicently evolved for it to be degenerate. then it woule not obey equation (4) and would probably be fainter.," However, if the secondary star is sufficently evolved for it to be degenerate, then it would not obey equation (4) and would probably be fainter." + Note that the models of Ixing. Kolb Durderi (1996) show tha neutron-star SNTs may require evolved companions.even a short orbital periods.," Note that the models of King, Kolb Burderi (1996) show that neutron-star SXTs may require evolved companions, even at short orbital periods." + We can estimate the orbital period for GIUS1354.64 by using equation. (1)., We can estimate the orbital period for GRS1354–64 by using equation (1). +" Since"" there are no . V-band measurements for⋅ the svstem in quiescence. we use the colors ofa INO.MO star in order to determine Vo."," Since there are no $V$ -band measurements for the system in quiescence, we use the colors of a K0–M0 star in order to determine $V_{Q}$." +" Using 720.3 mags (Martin 1996). feev —1.0 mags (van Paraclijs AleClintock 1994) and (V-RjJ=0.61.2 mags ΑθΑς Allen 1981). we estimate 1,9 —21.622.2. mags."," Using $R_{Q}$ =20.3 mags (Martin 1996), $E_{B-V}$ =1.0 mags (van Paradijs McClintock 1994) and (V-R)=0.6–1.2 mags $\sc v/iii$; Allen 1981), we estimate $V_{Q}$ =21.6–22.2 mags." + Then using equation (1) with τος] mags. (Pederson.," Then using equation (1) with $V_{O}$ =16.9 mags (Pederson," +The CANGABOO-II imaging atmospheric Cherenkov telescope has detected TeV &amma- emission [rom a nearby edge-on starburst galaxy. NGC 253 (Itohetal.2002a.b).,"The CANGAROO-II imaging atmospheric Cherenkov telescope has detected TeV gamma-ray emission from a nearby edge-on starburst galaxy, NGC 253 \citep{Itoh2002a, Itoh2002b}." +. This TeV emission is spatially extended and temporally steady. whose nature is different. from that of previously observed extragalactic objects of the active galactic nuclei (AGN) class.," This TeV emission is spatially extended and temporally steady, whose nature is different from that of previously observed extragalactic objects of the active galactic nuclei (AGN) class." + This is the first detection of TeV eamima-ravs [rom a normal-sized spiral galaxy like our Galaxy., This is the first detection of TeV gamma-rays from a normal-sized spiral galaxy like our Galaxy. + We can learn how high-energv particles propagate on the galactic scale [rom the observations of NGC 253 by TeV gamma-rays., We can learn how high-energy particles propagate on the galactic scale from the observations of NGC 253 by TeV gamma-rays. + The acceleration and propagation of galactic cosmic ravs (GCs). which are observed directly near the earth. are among the big topics in physics ancl astrophysics.," The acceleration and propagation of galactic cosmic rays (GCRs), which are observed directly near the earth, are among the big topics in physics and astrophysics." + The distribution, The distribution +(Campana 1997).,(Campana 1997). + ASCA aud ROSAT observations gave a first indication of the spectrum at such low rates: the ASCA spectu is well fit by a power law (photon index D— 2) plus a soft component. ce. a black body with temperature ~3 keV and equivalent radius of 2 kin.," ASCA and ROSAT observations gave a first indication of the spectrum at such low rates: the ASCA spectrum is well fit by a power law (photon index $\Gamma\sim 2$ ) plus a soft component, e.g. a black body with temperature $\sim 3$ keV and equivalent radius of $\sim 2$ km." + The ROSAT PSPC spectrum at a factor of 10.100 lower hpuninositv can be fit bv a black body mocel with much smaller temperature (~0.2 keV) aud larger radii (~70 ki)., The ROSAT PSPC spectrum at a factor of 10–100 lower luminosity can be fit by a black body model with much smaller temperature $\sim 0.2$ keV) and larger radii $\sim 70$ km). + The presence of a hard power law however cannot be excluded., The presence of a hard power law however cannot be excluded. + Recently. we obtained BeppoSAX observations of three fast spinning IIXNRTs (A 053866. V 0332|53 aud IU 0115163) during their quiesceut states (Castaldello et al.," Recently, we obtained BeppoSAX observations of three fast spinning HXRTs (A 0538–66, V 0332+53 and 4U 0115+63) during their quiescent states (Gastaldello et al." + 2000)., 2000). + The most siiiie results comes frou the observation of LU 0115163., The most striking results comes from the observation of 4U 0115+63. + A 15 hr BeppoSAX observation shows a variation in the count rate by a factor of ~250 (cf., A 15 hr BeppoSAX observation shows a variation in the count rate by a factor of $\sim 250$ (cf. + Fie., Fig. + 2: Campana et al., 2; Campana et al. + 20004)., 2000a). + A time-resolved spectral analysis reveals that this variation is lufriIsic o the source. which docs not chanec its spectruni (ard power law with photo jidex E~ 1) nor its column cleusity (a few “-1077cin>7. washing⋅ out any soft. componenuV.," A time-resolved spectral analysis reveals that this variation is intrinsic to the source, which does not change its spectrum (hard power law with photon index $\Gamma\sim 1$ ) nor its column density (a few $10^{22}\cmdue$, washing out any soft component)." + The mean 0.1.200 keV huuinositv in cach interval varies from ~ὃς10°!eyes Έποςὃς10°evesOoL1 (at Lkpe)., The mean 0.1–200 keV luminosity in each interval varies from $\sim 2\times 10^{34}\ergs$ to $\sim 2\times 10^{36}\ergs$ (at 4 kpc). + Pulsations were detected all the way dow ito he snaller fluxes., Pulsations were detected all the way down to the smaller fluxes. +discrepancy. at the line center: our model does not account for the laree apparent additional opacity centered at (he quasar redshift.,discrepancy at the line center: our model does not account for the large apparent additional opacity centered at the quasar redshift. + Llowever. this does not effect our conclusions drawn from the blue tail of the line.," However, this does not effect our conclusions drawn from the blue tail of the line." + The crucial feature of the observed spectrum of SDSS 1030-+-0524 is the presence of significant this down to8750À., The crucial feature of the observed spectrum of SDSS 1030+0524 is the presence of significant flux down to. +. Ànv model that allows for the presence of (his flux must have an HI region whose size is at least >4.5 Alpe. as is the case in (he example shown in Figure 1..," Any model that allows for the presence of this flux must have an HII region whose size is at least $>4.5$ Mpc, as is the case in the example shown in Figure \ref{spec}." + If the I] region was smaller. (he {lis αἱ wavelengths above would. be suppressed by an enormous factor [7-exp(10)] from the Gunn-Peterson opacity of the neutral IGM.," If the HII region was smaller, the flux at wavelengths above would be suppressed by an enormous factor $\sim \exp(10^6)$ ] from the Gunn-Peterson opacity of the neutral IGM." + As we have seen above. the presence of flix in the spectrum of SDSS 10302-0524 down (o implies that this quasar is surrounded by a large (4.5 proper Mpc) Stvommeren sphere.," As we have seen above, the presence of flux in the spectrum of SDSS 1030+0524 down to implies that this quasar is surrounded by a large (4.5 proper Mpc) Strömmgren sphere." + Assuming that its apparent [Iux rellects its true luminosity. this source is powered by a black hole whose mass is Mj=2x107M... and. [rom equation (1)). its age has to be at least 2x[0* llowever. the flux of SDSS 10304-0524 max be magnified through gravitational lensing bv foreground galaxies (or stars).," Assuming that its apparent flux reflects its true luminosity, this source is powered by a black hole whose mass is $M_{\rm +bh}=2\times10^9~{\rm M_\odot}$ and, from equation \ref{eq:Rt1}) ), its age has to be at least $2\times 10^7$ However, the flux of SDSS 1030+0524 may be magnified through gravitational lensing by foreground galaxies (or stars)." + As mentioned in the introduction. the probability for significant magnification can be appreciable. depending on the shape of (he unknown quasar luminosity function (Comerford et al.," As mentioned in the introduction, the probability for significant magnification can be appreciable, depending on the shape of the unknown quasar luminosity function (Comerford et al." + 2002: Writhe Loeb 2002)., 2002; Wyithe Loeb 2002). + Obviously. lor a given observed flux from the quasar. a larger gravitational lensing magnification would imply an intrinsically fainter quasar.," Obviously, for a given observed flux from the quasar, a larger gravitational lensing magnification would imply an intrinsically fainter quasar." + A fainter quasar would. in turn. require a longer age to produce a Strómmigren sphere with the required size of al least 4.5 Alpe.," A fainter quasar would, in turn, require a longer age to produce a Strömmgren sphere with the required size of at least 4.5 Mpc." + Thus. the minimum quasar age is an increasing function of gravitational lensing magnification.," Thus, the minimum quasar age is an increasing function of gravitational lensing magnification." +" Indeed. a constraint on fin NAV be most informativelv placed in the (/,4 0s magnification) plane."," Indeed, a constraint on $t_{\rm min}$ may be most informatively placed in the $t_{\rm min}$ $vs$ magnification) plane." + Figure 2. shows the constraints on the minimum age of SDSS 10302-0524 as a [function of ils gravitational lensing magnification., Figure \ref{tmin} shows the constraints on the minimum age of SDSS 1030+0524 as a function of its gravitational lensing magnification. +" The constraint is based on the requirement (hat (he radius of the St6mmeren sphere. computed from equation (3)). should be A,=4.5 Alpe."," The constraint is based on the requirement that the radius of the Strömmgren sphere, computed from equation \ref{eq:Ri}) ), should be $R_{\rm s}=4.5~$ Mpc." + The case presented here assumes that the IGM is still largely neutral at z= 6.28., The case presented here assumes that the IGM is still largely neutral at $z=6.28$ . + The four curves show [our cases with a=0 (ignoring recombinations. in this case μμ scales linearly with (he magnification). and with three dillerent gasclumping factors. C= 1.C=10 and," The four curves show four cases with $\alpha=0$ (ignoring recombinations, in this case $t_{\rm +min}$ scales linearly with the magnification), and with three different gasclumping factors, $C=1$ ,$C=10$ and" +Numerical simulation of the nonlinear evolution of collisiouless dark matter. usually by followiug a set of polnt masses as they move uuder tlieir mutual gravitational influence. lias; over the last [ew decades. played an uuportaut. role in increasiug our uxcderstanding of cosmological structure formation.,"Numerical simulation of the nonlinear evolution of collisionless dark matter, usually by following a set of point masses as they move under their mutual gravitational influence, has, over the last few decades, played an important role in increasing our understanding of cosmological structure formation." + Rather than attempt to make a summary of the exteusive literature avallable ou this subject here. we direct the reader to the recent reviews by Bertschiuger(1998). aud IxIypiu.(2000).," Rather than attempt to make a summary of the extensive literature available on this subject here, we direct the reader to the recent reviews by \citet{Bert98} + and \citet{Klypin00}." +. A search of the internet will reveal a cliverse set of N-body codes now available to be downloaded by those interested in carrying out cosmological simulatious., A search of the internet will reveal a diverse set of N-body codes now available to be downloaded by those interested in carrying out cosmological simulations. + Que of the first to be developed is the direct code of Aarseth(1999)., One of the first to be developed is the direct code of \citet{Aars99}. +. The operation count for ---implementing any such particle-particle code scales as D/N7. where NV roeis the nunber ofH particles.," The operation count for implementing any such particle–particle code scales as $N^2$, where $N$ is the number of particles." +H One cau reach larger NWH and thus higherH mass, One can reach larger $N$ and thus higher mass +files current as of 2011 May 25.,files current as of 2011 May 25. +" We also reprocessed the pn data from H+04,, which are taken with the same filter, but with the full window mode instead (we did not use their full-frame MOS data, since these do not resolve the We us"," We also reprocessed the pn data from , which are taken with the same filter, but with the full window mode instead (we did not use their full-frame MOS data, since these do not resolve the pulsations)." +edepchain and and selected source pulsations).events from a circular region of 37/5 radius., We used and and selected source events from a circular region of $37\farcs5$ radius. +" For the pn, we selected energies between 130 and eeV, where we set our lower energy cutoff slightly below the default of eeV to increase the net number of counts from our very soft target (by about2596; for even lower thresholds, the instrumental background increases too and the upper cutoff at the energy at which the rapidly),source becomes undetectable minimizing the effects of flares, which dominate the (thusbackground at higher energies)."," For the pn, we selected energies between 130 and eV, where we set our lower energy cutoff slightly below the default of eV to increase the net number of counts from our very soft target (by about; for even lower thresholds, the instrumental background increases too rapidly), and the upper cutoff at the energy at which the source becomes undetectable (thus minimizing the effects of flares, which dominate the background at higher energies)." +" Following standard practice, we included only one and two-pixel and double patterns events with no warning flags (singlefor pn, and single, double,0—4) and triple events (patterns 0-12) with the default flag mask for MOSI/2."," Following standard practice, we included only one and two-pixel (single and double patterns 0–4) events with no warning flags for pn, and single, double, and triple events (patterns 0–12) with the default flag mask for MOS1/2." + We barycentered the event times using theObservatory position from H+04:: a=0420*01:95 and ó=—50?22'48/1 (J2000).," We barycentered the event times using the position from : $\alpha=04^{\rm h}20^{\rm + m}01\fs95$ and $\delta=-50\degr22\arcmin48\farcs1$ (J2000)." +" We extracted background lightcurves for pn from similarly sized regions offset from the source, but at the same coordinate, as recommended by the SAS User For MOS1/2, the small-window mode does not permit such large background areas, but we used several smaller areas to compensate."," We extracted background lightcurves for pn from similarly sized regions offset from the source, but at the same coordinate, as recommended by the SAS User For MOS1/2, the small-window mode does not permit such large background areas, but we used several smaller areas to compensate." + Our timing analysis largely follows the procedure described inKvK05a., Our timing analysis largely follows the procedure described in. +". As a starting place, we first determined the frequency that maximized the power in a Z? periodogram for the EPIC-pn data from the longest observation in Rev. 1981."," As a starting place, we first determined the frequency that maximized the power in a $Z_1^2$ periodogram for the EPIC-pn data from the longest observation in Rev. 1981." + We then expanded the periodogram to include data from all observations in Revs., We then expanded the periodogram to include data from all observations in Revs. +" 1981 and 1983, finding a best-fit frequency of v=0.2896033+0.0000003 HHz, consistent with that found by for the earlier data."," 1981 and 1983, finding a best-fit frequency of $\nu=0.2896033\pm0.0000003$ Hz, consistent with that found by for the earlier data." +" In contrast to some of the other INSs,periodogram: there is no evidence for higher harmonics in the the Z? power is 33.8, while ZZ=34.7 and Z}=35.2, both of which are consistent with the additional power of 1 expected for noise."," In contrast to some of the other INSs, there is no evidence for higher harmonics in the periodogram: the $Z_1^2$ power is 33.8, while $Z_2^2=34.7$ and $Z_3^2=35.2$, both of which are consistent with the additional power of 1 expected for noise." +" We also checked to see if the true period was in fact 6.9ss (closer to that of the other INSs), but the pulse shape, hardness ratio, and median energy were all consistent with no variation between the first and second halves of the pulse (with 16 bins the lightcurve variation between the first and second halves has y?=10.6/8, while the hardness ratio variation has y?= "," We also checked to see if the true period was in fact s (closer to that of the other INSs), but the pulse shape, hardness ratio, and median energy were all consistent with no variation between the first and second halves of the pulse (with 16 bins the lightcurve variation between the first and second halves has $\chi^2=10.6/8$, while the hardness ratio variation has $\chi^2=4.1/8$ )." +"Using the above frequency, we determined the4.1/8). times-of-arrival (TOAs; see Table 1)) for the combined EPIC data from each observation by fitting the binned lightcurves (following KvK05b)) to a single sinusoid, appropriate given the results of the periodograms (Fig. 1));"," Using the above frequency, we determined the times-of-arrival (TOAs; see Table \ref{tab:obs}) ) for the combined EPIC data from each observation by fitting the binned lightcurves (following ) to a single sinusoid, appropriate given the results of the periodograms (Fig. \ref{fig:resids}) );" +" the best-fit sinusoid to the composite, background corrected pn data had a semi-amplitude of 15+2%,, where the uncertainty includes an estimate for the variation in the background correction over different background regions."," the best-fit sinusoid to the composite, background corrected pn data had a semi-amplitude of $15\pm2$, where the uncertainty includes an estimate for the variation in the background correction over different background regions." +" This is a little higher than the semi-amplitude of about fromH+04,, but differences in background-subtraction and energy selection could account for the difference (our best-fit to the 2002-2003 data has a semi-amplitude of 13.2-Ε 1.196))."," This is a little higher than the semi-amplitude of about from, but differences in background-subtraction and energy selection could account for the difference (our best-fit to the 2002–2003 data has a semi-amplitude of $13.2\pm1.1$ )." +" The x? for the fit to the composite profile was good, 14.4 for 13 dof."," The $\chi^2$ for the fit to the composite profile was good, 14.4 for 13 dof." +" Using our TOAs, we were able to identify a reasonably unambiguous coherent timing solution."," Using our TOAs, we were able to identify a reasonably unambiguous coherent timing solution." + This was possible as we restricted solutions to have|p|«9x10?Hzs! or Baip<2x 104G (based on the incoherent limits set /external/xmm_user-support/documentatjoriaberte 208G)o," This was possible as we restricted solutions to have$|\dot \nu|<\expnt{9}{-13}\,\Hzsec$ or $B_{\rm + dip}<\expnt{2}{14}\,$ G (based on the incoherent limits set by )." +"detatontgnitthose, the solution presented"," Among those, the solution presented" +et al.,et al. + 1981)., 1981). + The continuum is then [fixed by assuming a normalization for the spectrum. (parametrized) using thebolomefric luminosity Li) and the temperature of. the bump. Zee.," The continuum is then fixed by assuming a normalization for the spectrum (parametrized using the luminosity $L_{\rm ill}$ ) and the temperature of the bump, $T_{BB}$." + Using this model for the continuum we calculate the dilfuse emission of the BLIt for the hydrogen density and the hydrogen column density of the clouds in the ranges n=10—1075 ? and Ny=1072107! 7. respectively.," Using this model for the continuum we calculate the diffuse emission of the BLR for the hydrogen density and the hydrogen column density of the clouds in the ranges $n=10^9-10^{11}$ $^{-3}$ and $N_H=10^{22}-10^{24}$ $^{-2}$, respectively." + These intervals cover the region of the parameter space allowed by detailed modelling of the lines observed. for [ew selected. (raclio-quict) ACGNs (e.g. Ixorista Coad 2000: Ixaspi Netzer 1999)., These intervals cover the region of the parameter space allowed by detailed modelling of the lines observed for few selected (radio-quiet) AGNs (e.g. Korista Goad 2000; Kaspi Netzer 1999). + Αcareal Gwhbich applies also to the choice. of the spectral shape of the illaminating continuum) is that the present knowledge of he geometry and the physical state of the gas in the BLR mainl« relies on the studies of (ew) well-observec racio-quiet ACNs (mainly Sevfert galaxies)., A (which applies also to the choice of the spectral shape of the illuminating continuum) is that the present knowledge of the geometry and the physical state of the gas in the BLR mainly relies on the studies of (few) well-observed radio-quiet AGNs (mainly Seyfert galaxies). + Indeed: it is conceivable that for the sources for which we are interestec rere. namely powerful. raclio-loucl quasars. the conditions could be different.," Indeed it is conceivable that for the sources for which we are interested here, namely powerful, radio-loud quasars, the conditions could be different." + Note moreover that. for. simplicity. we model the BLR with a unique value of the physica xwameters. although the recent detailed models of emission ines quoted above seem to support the presence of a stratified BLR. with the parameters (censity. column densitv. covering factor) varving with distance from the central source.," Note moreover that, for simplicity, we model the BLR with a unique value of the physical parameters, although the recent detailed models of emission lines quoted above seem to support the presence of a stratified BLR, with the parameters (density, column density, covering factor) varying with distance from the central source." + In Fig., In Fig. + 2 we report some examples of the spectra of the diffuse BLR. emission. plotted in the ή(0) representation]. calculated for different. values of η and Ig. assuming the values Tipe10 Ix (Gvhich fixes the peak ofthe blue bump around LO Hz. dashed lines). £ij=3107 erg/s and Hu1077 em.," 2 we report some examples of the spectra of the diffuse BLR emission [plotted in the $\nu L(\nu)$ representation], calculated for different values of $n$ and $N_H$, assuming the values $T_{BB}=10^5$ K (which fixes the peak of the blue bump around $\sim 10^{15}$ Hz, dashed lines), $L_{\rm ill}=3\times 10^{47}$ erg/s and $R_{\rm +in}=10^{18}$ cm." + The laree value of the luminosity ids suitable to haracterize the powerful quasars at mecium-hieh redshift., The large value of the luminosity is suitable to characterize the powerful quasars at medium-high redshift. + Disk luminosity £L107 erg/s have been inferred. Crom re optical-U data of. sources. recently observed. withΟΙ) (c.g.V. TVavecchio et al., Disk luminosity $L> 10^{47}$ erg/s have been inferred from the optical-UV data of sources recently observed with (e.g. Tavecchio et al. + 2007. Sambruna ct al.," 2007, Sambruna et al." + )07)., 2007). + The radius of the BLE has been fixed to a value oetween those provided by the relations found by. WKaspi et I. (, The radius of the BLR has been fixed to a value between those provided by the relations found by Kaspi et al. ( +2007) and. Bentz et al. (,2007) and Bentz et al. ( +2006).,2006). + These relations connect 1e luminosity at a given wavelength to the distance. of 1ο clouds emitting a given line. estimated. through the reverberation mapping technique.," These relations connect the luminosity at a given wavelength to the distance of the clouds emitting a given line, estimated through the reverberation mapping technique." + The relations recently lerived by Ixaspi et al., The relations recently derived by Kaspi et al. + is based on the CIV. line. and re continuum is evaluated at A=1350Α.. while the Bentz οἱ al.," is based on the CIV line and the continuum is evaluated at $\lambda = 1350$, while the Bentz et al." + relation uses the 112 line ane the continuum at A=5100 AX.," relation uses the $\beta$ line and the continuum at $\lambda = +5100$ ." + In both cases the relation has the same dependence. Rerpycx(ALP.," In both cases the relation has the same dependence, $R_{BLR}\propto (\lambda L_{\lambda})^{0.5}$." +" ""Ehe. values. of the monochromatic luminosities £555 ane Lsioy depend on the spectral shape of the illuminating continuum.", The values of the monochromatic luminosities $L_{1350}$ and $L_{5100}$ depend on the spectral shape of the illuminating continuum. + For the shape and the luminosity assumed here. the two relations provide relatively different values for erg. Rgrg—ο107 em and Rete—35107 em for Kaspi et al.," For the shape and the luminosity assumed here, the two relations provide relatively different values for $R_{BLR}$, $R_{BLR}=5\times 10^{17}$ cm and $R_{BLR}=3\times 10^{18}$ cm for Kaspi et al." + and. Bentz et aL.," and Bentz et al.," +" respectively,", respectively. + For the calculation shown in Fig., For the calculation shown in Fig. +" 2 we assume the (logarithmic) average value 8,=1077 cam.", 2 we assume the (logarithmic) average value $R_{\rm in} = 10^{18}$ cm. + ]t is worth noting that. although calculated for a specific set of. parameters. the spectra reported in Fig.," It is worth noting that, although calculated for a specific set of parameters, the spectra reported in Fig." + 2 can be easily generalized to dillerent values of Liy and BLE. radius., 2 can be easily generalized to different values of $L_{\rm ill}$ and BLR radius. +" Indeed. the normalization of the dilluse spectrum. simply scales as the luminositw Lg. while the shape (continuum ancl lines) only depends (at the first order) on the ionization parameter £=Linnli, (in terms of £. the spectra in Fig."," Indeed, the normalization of the diffuse spectrum simply scales as the luminosity $L_{\rm ill}$, while the shape (continuum and lines) only depends (at the first order) on the ionization parameter $\xi=L_{\rm ill}/nR_{\rm +in}^2$ (in terms of $\xi$ , the spectra in Fig." + 2 correspond to £=300.30 and 3. from bottom to top. respectively).," 2 correspond to $\xi=300, 30$ and 3, from bottom to top, respectively)." + Dillerent. combination of Lin. iy and à» can thus produce similar spectra.," Different combination of $L_{\rm ill}$, $R_{\rm in}$ and $n$ can thus produce similar spectra." +" Note that. if Lin ancl Ae, are linked. by a relation of the form. Ay,κLu as discussed above. the ionization parameter in different sources. would only depend on the density of the clouds (assuming similar spectra for the photoionizing continuum). since the ratio Luft, would be a fix number in cillerent sources."," Note that, if $L_{\rm ill}$ and $R_{\rm in}$ are linked by a relation of the form $R_{\rm in}\propto L_{\rm ill}^{0.5}$ as discussed above, the ionization parameter in different sources would only depend on the density of the clouds (assuming similar spectra for the photoionizing continuum), since the ratio $L_{\rm +ill}/R_{\rm in}^2$ would be a fix number in different sources." +" As expected. the total luminosity of the dilfuse emission is dominated by the optical-UV emission. and. in particular. bv few prominent lines in this band. most notably the Ly, lines of LE (1216 A)) and HolL (303 A))."," As expected, the total luminosity of the diffuse emission is dominated by the optical-UV emission, and, in particular, by few prominent lines in this band, most notably the $_{\alpha }$ lines of H (1216 ) and HeII (303 )." +" In all cases 1f underlving continuum around the peak (dominated bv recombinations and scattering. both ""Thomson and ltavleigh) contributes to few percent of the total luminosity."," In all cases the underlying continuum around the peak (dominated by recombinations and scattering, both Thomson and Rayleigh) contributes to few percent of the total luminosity." +" llowever. the continuum (mainly due to free-free emission) dominates below the peak (below ον10"" LIz). making the μα»ectrum much broader than the black body approximation."," However, the continuum (mainly due to free-free emission) dominates below the peak (below $\sim 10^{15}$ Hz), making the spectrum much broader than the black body approximation." + As we discuss later. this fact has a direct consequence on the erived EC spectrum.," As we discuss later, this fact has a direct consequence on the derived EC spectrum." + Some trends are clearly visible in Fig., Some trends are clearly visible in Fig. + 2., 2. + Increasing Na (left to right) has the cllect to increase the total emitted Luminosity and. importantly. to increase the relative contribution of the optical-UV. continuum. with respect to the emission lines.," Increasing $N_H$ (left to right) has the effect to increase the total emitted luminosity and, importantly, to increase the relative contribution of the optical-UV continuum with respect to the emission lines." + The increase of the densitv ο (bottom to top). instead. has the elfect of reducing the Ionization parameter £ and leads to increase the importance of the recombinations (as witnessed by the prominent. edges)," The increase of the density $n$ (bottom to top), instead, has the effect of reducing the ionization parameter $\xi $ and leads to increase the importance of the recombinations (as witnessed by the prominent edges)." + An interesting feature of these spectra is the presence of an important X-rav component. originating from the Compton rellection on the cloud gas (analogously to the srelleetion bump” from accretion. disks).," An interesting feature of these spectra is the presence of an important X-ray component, originating from the Compton reflection on the cloud gas (analogously to the “reflection bump” from accretion disks)." + As expected. the fraction of the N-ray continuum (and. of the overall continuum) reflected. by the BLR. increases (from left to right) with the column density Ig.," As expected, the fraction of the X-ray continuum (and of the overall continuum) reflected by the BLR increases (from left to right) with the column density $N_H$." + locreasing (from bottoni to top) the density ην instead. has the elect of reducing the rellected. X-rav. luminosity. since the ionization parameter £ (and thus. for the same value of the column density. the number of free electrons available for scattering) decreases.," Increasing (from bottom to top) the density $n$, instead, has the effect of reducing the reflected X-ray luminosity, since the ionization parameter $\xi $ (and thus, for the same value of the column density, the number of free electrons available for scattering) decreases." + The decreased ionization state of the gas is also responsible for the deepening of the depression visible in the soft. X-ray band. caused by photoelectrie absorption.," The decreased ionization state of the gas is also responsible for the deepening of the depression visible in the soft X-ray band, caused by photoelectric absorption." + “Lhe presence of an important dilluse X-ray. emission inside the DLIU could have important consequences for the propagation of 5-ravs with ££~100 MeV. produced. by the jet (Chisellini et al., The presence of an important diffuse X-ray emission inside the BLR could have important consequences for the propagation of $\gamma $ -rays with $E\sim 100$ MeV produced by the jet (Ghisellini et al. + 2008. in preparation).," 2008, in preparation)." + The basic features of the BLR emission do not strongly depend on the actual shape of the photoionizing continuum., The basic features of the BLR emission do not strongly depend on the actual shape of the photoionizing continuum. + The cleet of a dillerent temperature Lee is illustrated. by 3., The effect of a different temperature $T_{BB}$ is illustrated by Fig. + reporting the SEDs of the BLE rellection calculated for the case p=107 ?. Ng=107 em? and Tgg2.5.104 WK. The overall shape of the SEDs is similar to the hieh-temperature case (Fig.," 3, reporting the SEDs of the BLR reflection calculated for the case $n=10^{10}$ $^{-3}$, $N_H=10^{23}$ $^{-2}$ and $T_{BB}=2.5\times 10^4$ K. The overall shape of the SEDs is similar to the high-temperature case (Fig." + 2. central panel).," 2, central panel)." + However. the lower temperature has the elfect to decrease the relative Lux of the ionizing photons. leadingto decrease the luminosity of the emission lines relative to that of the continuum(whose peak. moreover. moves to lower frequencies by a factor of zm 2).," However, the lower temperature has the effect to decrease the relative flux of the ionizing photons, leadingto decrease the luminosity of the emission lines relative to that of the continuum(whose peak, moreover, moves to lower frequencies by a factor of $\approx 2$ )." + As we show later. the increasing importance of the," As we show later, the increasing importance of the" +equation of polarized radiatiou dn a plane-parallel inedium.,equation of polarized radiation in a plane-parallel medium. + The local polarization is integrated over the rotationally distorted surface., The local polarization is integrated over the rotationally distorted surface. + We briefly describe the method adopted to calculate the rotational oblateuess aud the methods of integrating the polarization over a rotationally distorted stellar disk iu section 5., We briefly describe the method adopted to calculate the rotational oblateness and the methods of integrating the polarization over a rotationally distorted stellar disk in section 5. + We discuss tle results tn section 6 followed by our conclusion iu the last section., We discuss the results in section 6 followed by our conclusion in the last section. + The known field T cwarls have effective temperatures iu the rauge 1100>Tey520Kk.," The known field T dwarfs have effective temperatures in the range $1400 > T_{\rm eff} > 550\,\rm K$." + Cloπιο» influence the observed. spectra of the warmest dwarls. but cloudess uodels generally reproduce he spectra of most T. dwarfs with T;[<120Olx. although this leuperature is likely gravity depeudeut (Step1915etal.2009).," Clouds influence the observed spectra of the warmest dwarfs, but cloudless models generally reproduce the spectra of most T dwarfs with $T_{\rm eff} < 1200\,\rm K +$, although this temperature is likely gravity dependent \citep{stephens09}." +. For the stιν reported. he' we cousidered. oily cloudless uodels appropriate for spectral types laer “ilan ibout T3 (Sepheuseal.2009)., For the study reported here we considered only cloudless models appropriate for spectral types later than about T3 \citep{stephens09}. +". For the pola‘ization study we used fou D]dia]ve-convectve edtilibrium moclels wuich give the ""uu of temperatu'e as a function of pressiye 'OUghi the atmosphere rom Ie collection employed by Saumon&Marley(2008) in their study ). ‘OWL dwarf evoltion.", For the polarization study we used four radiative-convective equilibrium models which give the run of temperature as a function of pressure through the atmosphere from the collection employed by \cite{saumon08} in their study of brown dwarf evolution. + The selectec mocles ineluce uo clotd opacity. altrough Coudensates are i1Ced iu the cheiical equilibriu1 caleulatior leyaudLockers 2008).," The selected models include no cloud opacity, although condensates are included in the chemical equilibrium calculation \citep{freedman08}." +. A more clelal sulunary of tLe Duocel alliosphieres is »esented iu Stejxheusetal.(2009)., A more detailed summary of the model atmospheres is presented in \cite{stephens09}. +.. The models sheWIL here all have ogg=E €ad solar metallicity., The models shown here all have $\log g = 5$ and solar metallicity. + ΤΙT ellect of varation in these parameters wil be explore In a uture study., The effect of variation in these parameters will be explored in a future study. +" Here we choose mocleJd. wil ilo=1100. 1200. 1000. all| 500 In. As 1oted above. the first is somewhat wari for a typle:"" cloudess [ied Τεwarl but weiiclude it as a compariso1 poiut for future studies of cloudy L dwarfW. with his T.[- "," Here we choose models with $T_{\rm eff} = 1400$, 1200, 1000, and 800 K. As noted above, the first is somewhat warm for a typical cloudless field T dwarf but we include it as a comparison point for future studies of cloudy L dwarfs with this $T_{\rm eff}$." +The forr 1uodel temperatu'e-pressure profiles descibed above were hen used as inputs for polarization radiative trausfer model., The four model temperature-pressure profiles described above were then used as inputs for the polarization radiative transfer model. + The same atmosjoherie opacities euployed in the calculati of the racliaive-couvective equilibrium models (Freedinan.Marleyaud.Lodders2008) were t in bohi caleulatious., The same atmospheric opacities employed in the calculation of the radiative-convective equilibrium models \citep{freedman08} were used in both calculations. + We note that iu the calculation of these temperaure profiles we compt [Iuxes in 180 separate spectral bins., We note that in the calculation of these temperature profiles we computed fluxes in 180 separate spectral bins. + Within each bin we computed the radiative transfer 8 tii once [or eac Lol eight k-coefficient gauss points (Marleyetal.2002).," Within each bin we computed the radiative transfer 8 times, once for each of eight k-coefficient gauss points \citep{marley02}." +. The details of the uuderlyi opacity calculation a'e presented in Freeclinan.MarleyaudLocdcers(2008)., The details of the underlying opacity calculation are presented in \cite{freedman08}. +. For the polarizati study we folowed this sane procedure aud computed monochromatic intensities at centers of same 180 fhx bius using the same opacities., For the polarization study we followed this same procedure and computed monochromatic intensities at centers of the same 180 flux bins using the same opacities. + Final computed equantities are the gauss weiglited sn ol the eight incleperent radiative trausfer calculatious at each of the 150 waveleneth points., Final computed quantities are the gauss weighted sum of the eight independent radiative transfer calculations at each of the 180 wavelength points. + We note that wule the resultiug spectrum bas somewhat low spectral resolution. polarization changes slowly with waveleugh and this resolution is adequate for our purposes.," We note that while the resulting spectrum has somewhat low spectral resolution, polarization changes slowly with wavelength and this resolution is adequate for our purposes." +nue).,. + The non-trivial solution to this Equation is ο... =b(r.Lio. which is the principal result of this paper.," The non-trivial solution to this Equation is ,L') =, which is the principal result of this paper." + This formula was found by considering initially the case of two sets of galaxies with different luminosities. so the integral is replaced by a sum over the two subsets.," This formula was found by considering initially the case of two sets of galaxies with different luminosities, so the integral is replaced by a sum over the two subsets." + The resulting equations were then solved with the aid ofMATHEMATICA., The resulting equations were then solved with the aid of. + The form of the 2-class solution suggested a conjecture for the general solution with a countable number of sets of galaxies. and thus for a set of galaxies with a continuous distribution of luminosities.," The form of the 2-class solution suggested a conjecture for the general solution with a countable number of sets of galaxies, and thus for a set of galaxies with a continuous distribution of luminosities." + The conjecture was readily verified by direct substitution., The conjecture was readily verified by direct substitution. + It is straightforward to see that this reduces to the formula of FKP (their equation 2.3.4) for a sample of galaxies at a single luminosity., It is straightforward to see that this reduces to the formula of FKP (their equation 2.3.4) for a sample of galaxies at a single luminosity. + Eq., Eq. + 28. shows that w(r.L) depends not only on the expected bias of galaxies of that luminosity b(r.L). but additionally on the bias of galaxies of all luminosities at this location through {dLn(r.LHPGr.L).," \ref{eq:w} shows that $w(\r,L)$ depends not only on the expected bias of galaxies of that luminosity $b(\r,L)$, but additionally on the bias of galaxies of all luminosities at this location through $\int +dL\,\bar{n}(\r,L)b^2(\r,L)$." + This follows because the balance between shot noise and cosmic variance. which is at the heart of the derivation of the optimal weights. depends on what we learn from all galaxies whatever their luminosity.," This follows because the balance between shot noise and cosmic variance, which is at the heart of the derivation of the optimal weights, depends on what we learn from all galaxies whatever their luminosity." + It is also interesting to note that. while the contribution of galaxies to the overdensity estimate appears to be inversely proportional to their bias (the 1/b(r.L) factor in Eq. 6)).," It is also interesting to note that, while the contribution of galaxies to the overdensity estimate appears to be inversely proportional to their bias (the $1/b(\r,L)$ factor in Eq. \ref{eq:Fr}) )," + optimizing the weight actually means that the net contribution of these galaxies is increased — they contain the most signal-to-noise because of their strong clustering., optimizing the weight actually means that the net contribution of these galaxies is increased – they contain the most signal-to-noise because of their strong clustering. + The value of à in Eq., The value of $\alpha$ in Eq. + 6 sets the expected number of galaxies for a particular survey., \ref{eq:Fr} sets the expected number of galaxies for a particular survey. +" In this Section we discuss how this can be set given no information other than the survey itself,", In this Section we discuss how this can be set given no information other than the survey itself. + Suppose that we had used an incorrect value of a in Eq. 6..," Suppose that we had used an incorrect value of $\alpha$ in Eq. \ref{eq:Fr}," + so that this Equation becamefracu(rL) (κ)2 to the right hand side of Eq. 1-4., so that this Equation became )|^2 to the right hand side of Eq. \ref{eq:expFkFk}. + Turning this argument around. we see that not knowing the true value ofa is equivalent to adding a multiple of the Fourier transformed window function to our power estimate.," Turning this argument around, we see that not knowing the true value of $\alpha$ is equivalent to adding a multiple of the Fourier transformed window function to our power estimate." + In general. the average weighted galaxy density has to be derived from the survey itself. and it is therefore impossible to know the true offset between the number of galaxies observed and that expected.," In general, the average weighted galaxy density has to be derived from the survey itself, and it is therefore impossible to know the true offset between the number of galaxies observed and that expected." + In this situation. the only sensible thing to do is to set (pL). so that the average weighted overdensity is artificially set to zero.," In this situation, the only sensible thing to do is to set = , so that the average weighted overdensity is artificially set to zero." + This self-normalization forces (0)—O and results in à deficit in the estimated power equivalent to subtracting a scaled copy of the window function. centered on fk=0 (Peacock Nicholson 1991).," This self-normalization forces $P(0)=0$ and results in a deficit in the estimated power equivalent to subtracting a scaled copy of the window function, centered on $k=0$ (Peacock Nicholson 1991)." + In the limit of no window. the effect of this self-normalization would be to remove a delta function located at kh=Osuch that (0)=0.," In the limit of no window, the effect of this self-normalization would be to remove a delta function located at $k=0$ such that $P(0)=0$." +" In effect. this procedure evades the possibility of noise in our estimate of large-scale power owing to the uncertainty in η, at the expense of systematic damping of the large-scale signal (ef."," In effect, this procedure evades the possibility of noise in our estimate of large-scale power owing to the uncertainty in $\bar n$, at the expense of systematic damping of the large-scale signal (cf." + the approach of Tadros Efstathiou 1995)., the approach of Tadros Efstathiou 1995). + Instead of allowing for a continuous distribution of galaxy luminosities and corresponding biases. an alternative approach would have been to consider a countable number of sets of galaxies with different luminosities.," Instead of allowing for a continuous distribution of galaxy luminosities and corresponding biases, an alternative approach would have been to consider a countable number of sets of galaxies with different luminosities." + In this case. Eq.," In this case, Eq." + 6 would have become where n(r.L;)=Sδηrj) now gives the density of galaxies within subset 7.p the subset containing those galaxies of luminosity £;.," \ref{eq:Fr} would have become where $n_g(\r,L_i)=\sum_j\delta(\r-\r_j)$ now gives the density of galaxies within subset $i$, the subset containing those galaxies of luminosity $L_i$." + The analysis and derivation of optimal weights described in this paper follows exactly as for the continuous case. except that we obviously need to replace the integral over luminosity with a sum over the subsets of galaxies throughout.," The analysis and derivation of optimal weights described in this paper follows exactly as for the continuous case, except that we obviously need to replace the integral over luminosity with a sum over the subsets of galaxies throughout." + Having introduced the necessary formalism. we now illustrate the revised FKP method using simple artificial surveys.," Having introduced the necessary formalism, we now illustrate the revised FKP method using simple artificial surveys." + These artiticial surveys were designed to approximate the selection function and luminosity-dependent bias of the 2dFGRS galaxies analysed by Fer., These artificial surveys were designed to approximate the selection function and luminosity-dependent bias of the 2dFGRS galaxies analysed by P01. + The selection function is approximately matched to the part-complete 2dFGRS survey (Colless et al., The selection function is approximately matched to the part-complete 2dFGRS survey (Colless et al. + 2001) as analysed in POI., 2001) as analysed in P01. + The redshift distribution used for the galaxies is given by HE and limited to0 corresponding to 2=3 gives Aui&ALLS/2., Using the value of $\gamma$ corresponding to $z=3$ gives $\lambda_{\rm mfp}\approx\lambda_{\rm LLS}/2$. + llence. there is a redshift’ dependent: numerical factor of about 2 connecting Av with the mean separation between Lyman limit svstems.," Hence, there is a redshift dependent numerical factor of about 2 connecting $\lambda_0$ with the mean separation between Lyman limit systems." + Although this model agrees well with the results of(2000)... we should be wary of the possibility of uncertainties in the normalisation arising from the ambiguity of using the Jeans! length as the characteristic size of the objects.," Although this model agrees well with the results of, we should be wary of the possibility of uncertainties in the normalisation arising from the ambiguity of using the Jeans' length as the characteristic size of the objects." + In our calculations. we will therefore allow for a normalisation olfsct 5=Awtp/Amipanedel ," In our calculations, we will therefore allow for a normalisation offset $\kappa=\lambda_{\rm mfp}/\lambda_{\rm mfp,model}$ ." +Setting out the calculation in this way facilitates comparison with observations of the number of Lyman limit systems. per unit. redshift) and the distribution of svstems of. cülferent column density2007)., Setting out the calculation in this way facilitates comparison with observations of the number of Lyman limit systems per unit redshift and the distribution of systems of different column density. +. Using this model and observational input. we may convert observations of into constraints onN," Using this model and observational input, we may convert observations of into constraints on." +oone Vhe main sources of uncertainty arise from as and Ay and from the temperaturc-density relation., The main sources of uncertainty arise from $\alpha_S$ and $\lambda_0$ and from the temperature-density relation. + Given AN. we calculate the LILLE region filling fraction Qui using where €={μηfora)? is the clumping of ionized hvdrogen.," Given $\dot{N}_{\rm ion}$, we calculate the HII region filling fraction $Q_{\rm HII}$ using where $C\equiv\langle n_{\rm HII}^2\rangle/\langle n_{\rm HII}\rangle^2$ is the clumping of ionized hydrogen." + Note that we assume case-X recombination. this is appropriate since the majority of recombinations occur on the edge of self-shielding dense clumps which will trap the ionizing photons produced. by recombination direct to the ground. state preventing them. from. contributing to ionization in the ICM.," Note that we assume case-A recombination, this is appropriate since the majority of recombinations occur on the edge of self-shielding dense clumps which will trap the ionizing photons produced by recombination direct to the ground state preventing them from contributing to ionization in the IGM." + Desides the sources. the crucial uncertainty in the evolution of the neutral fraction lies in the dependence of the recombination rate upon the clumping C'.," Besides the sources, the crucial uncertainty in the evolution of the neutral fraction lies in the dependence of the recombination rate upon the clumping $C$." + This quantity is expected to be redshift dependent and. vary significantly from €' Lat high redshifts if low density regions are ionized first. to €C'4 at low redshift. where the remaining neutral gas is located in overdense regions.," This quantity is expected to be redshift dependent and vary significantly from $C\lesssim 1$ at high redshifts if low density regions are ionized first, to $C\gtrsim 4$ at low redshift, where the remaining neutral gas is located in overdense regions." + “This variation may have significant elfect on the reionization history. since a high clumping factor maydelay the completion of reionization bv As~ 2.," This variation may have significant effect on the reionization history, since a high clumping factor maydelay the completion of reionization by $\Delta z\sim2$ ." + Bt is therefore important that we explore a range of values for the clumping and. allow for its, It is therefore important that we explore a range of values for the clumping and allow for its +toward the observer (Alexander.2008).,toward the observer \citep{alexander08}. +.. A static disk atmosphere would result in a line emission centered al the stellar velocity. clearly inconsistent. wilh our observations.," A static disk atmosphere would result in a line emission centered at the stellar velocity, clearly inconsistent with our observations." + Thus. we consider this result as the first strong evidence for a disk being photoevaporated by its central star.," Thus, we consider this result as the first strong evidence for a disk being photoevaporated by its central star." + The line profiles of CS Cha and T Cha are broadly consistent with predictions from the photoevaporative disk wind model (Fig. 4)).," The line profiles of CS Cha and T Cha are broadly consistent with predictions from the photoevaporative disk wind model (Fig. \ref{figure:Alexander}) )," + but there are also a lew discrepancies. especially for the spectroscopic binary CS Cha.," but there are also a few discrepancies, especially for the spectroscopic binary CS Cha." + For this binary the predicted line is broader (han observed., For this binary the predicted line is broader than observed. + This could result [rom a disk viewed at less (han 45° inclination. but the emission should be slightly more blue-shilted than observed.," This could result from a disk viewed at less than $^\circ$ inclination, but the emission should be slightly more blue-shifted than observed." + In the simplest assumption that neon atoms are ionizedonly by stellar EUV photons. we can use the observed line luminosities to estimate the stellar ionizing flux «P reaching the disk surface.," In the simplest assumption that neon atoms are ionized by stellar EUV photons, we can use the observed line luminosities to estimate the stellar ionizing flux $\Phi$ reaching the disk surface." +" The reason is that. line fluxes scale approximately linearly with Φ (for ?1. y is approximately constant.," When $x_0 > 1$, $y$ is approximately constant." +" When ry=ld. the typical behavior is that y for sinall c. peaks at 6=wy with a height: Cy. aud then falls+ off⋅ as ""Cyle2 (the higher: Cy. the narrower the peak aud hence the transition between the constant aud.e ? behaviors is more abrupt)."," When $x_0 \lesssim 1$, the typical behavior is that $y$ for small $x$ , peaks at $x = x_0$ with a height $C_0$, and then falls off as $ C_0^{-1} x^{-2}$ (the higher $C_0$ , the narrower the peak and hence the transition between the constant and $x^{-2}$ behaviors is more abrupt)." +" Initially. y= coustant auc the density py and pressure py for the eround state are xà.9, "," Initially, $y =$ constant and the density $\rho_0$ and pressure $p_0$ for the ground state are $\propto a^{-6}$." +"White 2ry and ifie cm1/|C,| then y=Cyly2,", When $x \gg x_0$ and if $x \gg 1/|C_0|$ then $y = C_0^{-1} x^{-2}$. + The pressure and thedensity then have two ternis where the «a6 terii doimuinates at early times., The pressure and thedensity then have two terms where the $a^{-6}$ term dominates at early times. + The density transitions to a cosmological constant with po=ο κ opp159ipo1/2> , The density transitions to a cosmological constant with $p_0 = -\rho_0$ when $a \approx H_{0r}^{1/2} C_0^{-1/3} 2^{-1/6} m^{-1/2}$. +Tr Praagthenunpa κα ©(Arbeyet αἱ.2002).., If $\rho_\Phi > \rho_{\rm rad}$ then $\rho_\Phi \propto a^{-6}$ \citep{arby}. +Tlowever.in this regine the above cerivation becomes invalid.," However, in this regime the above derivation becomes invalid." +" Iu the matter domination regime (7=3/2). ((16)) becomes where 1=Πυρά7? with Hg,2278«10.76V."," In the matter domination regime $n=3/2$ ), \ref{scalar}) ) becomes where $H = H_{0m} a^{-3/2}$ with $H_{0m} \approx 7.8 \times 10^{-34} eV$ ." + Usine ((19)) we obtain an equation for wj: For the ground state (&= 0). this equation las au exact solution where Cy. C2 aud the phase a are coustauts with the constraint ονCZ=1.," Using \ref{psibreak}) ) we obtain an equation for $\omega_k$: For the ground state $k=0$ ), this equation has an exact solution where $C_1$, $C_2$ and the phase $\alpha$ are constants with the constraint $C_2^2 - C_1^2 = 1$." + This solution is in agreement with Arbevefaf(2002)., This solution is in agreement with \cite{arby}. +. When Cy=0 the solution reduces to wy=ai., When $C_1=0$ the solution reduces to $\omega_0 = am$. + Solutions with non-zero Cy oscillate around the wy=em solution. ((31)), Solutions with non-zero $C_1$ oscillate around the $\omega_0 = am$ solution. \ref{matter_sol}) ) + can also be written in terms of f as The oscillations have a period of z/in (— a few vears for i=1075 eV)., can also be written in terms of $t$ as The oscillations have a period of $\pi / m$ $\sim$ a few years for $m = 10^{-23}$ eV). + The pressure averages to zero on cosinological timescales causing the eround state scalar field particles to behave like pressureless matter., The pressure averages to zero on cosmological timescales causing the ground state scalar field particles to behave like pressureless matter. + We also solve ((20)). numerically iucbludiug the effect of both radiation aud matter in the IIubble piriuueter. The umuerical solutious are fully specified by the valueof the field and itsfirst derivative at a given a. as well as an overall scaling of the density.," We also solve \ref{fullw}) ) numerically including the effect of both radiation and matter in the Hubble parameter, The numerical solutions are fully specified by the valueof the field and itsfirst derivative at a given $a$ , as well as an overall scaling of the density." + In both cases.the overall scaling of the density was chosen to match the observed cosinological density of cold dark matter.," In both cases,the overall scaling of the density was chosen to match the observed cosmological density of cold dark matter." +Node merger is displaved in Figure 9.,Node merger is displayed in Figure 9. + In Figure 9 we can see clearly that as the meridional flow speed is increased. node merger. first illustrated in Figures 5. 6 and 7. is accomplished topologically by the (wo counterclockwise cells increasing their Iatitudinal dimension towarel each other. until the clockwise counter-cell is completely squeezed out. aud (he two cells in effect merge to create a single cell (hat reaches all the wav to the poles.," In Figure 9 we can see clearly that as the meridional flow speed is increased, node merger, first illustrated in Figures 5, 6 and 7, is accomplished topologically by the two counterclockwise cells increasing their latitudinal dimension toward each other, until the clockwise counter-cell is completely squeezed out and the two counter-clockwise cells in effect merge to create a single cell that reaches all the way to the poles." + By contrast. a very different evolution of the pattern occurs if the boundary [low speed is fixed and the turbulent viscosity is increased.," By contrast, a very different evolution of the pattern occurs if the boundary flow speed is fixed and the turbulent viscosity is increased." + This is shown in Figure 10., This is shown in Figure 10. + IIere we see that with increasing v bv just a [actor of (wo. starting from the same case as shown in Figure 9a. the larger zunplitude primary cell and particularly the countercell migrate toward the poles. squeezing the second counterclockwise cell out of existence there.," Here we see that with increasing $\nu$ by just a factor of two, starting from the same case as shown in Figure 9a, the larger amplitude primary cell and particularly the countercell migrate toward the poles, squeezing the second counterclockwise cell out of existence there." + The result is (o retain one node. al a relatively low latitude within the polar cap.," The result is to retain one node, at a relatively low latitude within the polar cap." + rather than jumping from two nodes to zero., rather than jumping from two nodes to zero. + In this example the turbulent viscosity must be raised (wo orders of magnitude to eliminate the last node., In this example the turbulent viscosity must be raised two orders of magnitude to eliminate the last node. + We can understuxd (he physics behind this feature if we start. wilh the definition of viscositv., We can understand the physics behind this feature if we start with the definition of viscosity. + The viscous coefficient is defined by the ratio of shear lorce per unit area and the eradient of velocity perpendicular to the direction of shear., The viscous coefficient is defined by the ratio of shear force per unit area and the gradient of velocity perpendicular to the direction of shear. + It is inversely proportional to the velocity gradient., It is inversely proportional to the velocity gradient. + Therefore with the increase in viscous coefficient the velocity gradient should decrease. which means velocities will be more correlated over longer distance.," Therefore with the increase in viscous coefficient the velocity gradient should decrease, which means velocities will be more correlated over longer distance." + Thus each cell grows bigger in the latitude direction and pushes the next cell. eventually making the pobwardamost cell to vanish.," Thus each cell grows bigger in the latitude direction and pushes the next cell, eventually making the polwardmost cell to vanish." + In Figure 11 we display solutions for the differential rotation linear velocity (hat. arises from the forcing at the boundary. For the same cases for which streaanfunction node positions were plotted in Figure 4.," In Figure 11 we display solutions for the differential rotation linear velocity that arises from the forcing at the boundary, for the same cases for which streamfunction node positions were plotted in Figure 4." + We have not included in these solutions any differential rotation (hat is independent of z that we might wish to include to allow a closer comparison with solar observations. since. as we have stated earlier. this z independent differential rotation has no effect on the strezunfunctions of meridional flow.," We have not included in these solutions any differential rotation that is independent of $z$ that we might wish to include to allow a closer comparison with solar observations, since, as we have stated earlier, this $z$ independent differential rotation has no effect on the streamfunctions of meridional flow." + It is simply a linear function of ur. declining to zero at the left hand boundary of the cartesian channel from whatever value was specilied on the right boundary (black straight line).," It is simply a linear function of $x$, declining to zero at the left hand boundary of the cartesian channel from whatever value was specified on the right boundary (black straight line)." + As stated earlier. it corresponds to constant angular velocity in the evlindyrical and spherical shell cases.," As stated earlier, it corresponds to constant angular velocity in the cylindrical and spherical shell cases." + The total solution for differential rotation would be the sum of the appropriate colored curve and the black line., The total solution for differential rotation would be the sum of the appropriate colored curve and the black line. +compare them to LL observations of local spirals and. with the results of hydro simulations.,compare them to HI observations of local spirals and with the results of hydro simulations. + Lastly we close with some discussion ancl conclusions., Lastly we close with some discussion and conclusions. +" DLAS are defined as those absorption svstems that have a column censity of neutral hvdrogen in excess of 2.107"" atoms per square centimeter ((Wolle 1986). ("," DLAS are defined as those absorption systems that have a column density of neutral hydrogen in excess of $2 \times 10^{20}$ atoms per square centimeter \nocite{wolfe:86}( 1986). \nocite{pw:96,pw:97j}{ (" +1996. 1997a) found that the velocity. profiles of low ionization state metal lines (Si. Fe. Cr. ete.),"1996, 1997a) found that the velocity profiles of low ionization state metal lines $^+$, $^+$, $^+$, etc.)" + trace each other well ancl therefore presumably the kinematics of the cold gas., trace each other well and therefore presumably the kinematics of the cold gas. + They therefore undertook to obtain a large sample of the kinematic properties of DLAS as measured. by the associated metal lines and compared them to the predictions from a number of models., They therefore undertook to obtain a large sample of the kinematic properties of DLAS as measured by the associated metal lines and compared them to the predictions from a number of models. + ALL of the observations were obtained with LIES ((Vogt 1992) on the 10m Week | telescope., All of the observations were obtained with HIRES \nocite{vogt:92}( 1992) on the 10m Keck I telescope. + None of the DLAS were chosen withpriori kinematic information and the metal line profiles were selected according to strict criteria including that they not be saturated. therefore it is believed. that the sample is kinematically unbiasec," None of the DLAS were chosen with kinematic information and the metal line profiles were selected according to strict criteria including that they not be saturated, therefore it is believed that the sample is kinematically unbiased." + We have taken care that our mocel profiles match the resolution ancl signal-to-noise of the observations and that they conform to the same prolile selection Criteria. (, We have taken care that our model profiles match the resolution and signal-to-noise of the observations and that they conform to the same profile selection criteria. \nocite{pw:97}{ ( +1997b. hereafter PWO97) developed four statistics to characterize the velocity profiles of the gas. which we also use to compare our mocdels to the data set of 36 velocity. profiles in (1998) and (2000).,"1997b, hereafter PW97) developed four statistics to characterize the velocity profiles of the gas, which we also use to compare our models to the data set of 36 velocity profiles in \nocite{pw:98}{ (1998) and \nocite{wp:00}{ (2000)." + The four statistics as defined in PN97 are: The other. observational data that) ow modcling of DLAS must conform to are the cüllerential density distribution FN) (the number of absorbers per unit column density per unit absorption distance) and the distribution of metal abundances., The four statistics as defined in PW97 are: The other observational data that our modeling of DLAS must conform to are the differential density distribution $f(N)$ (the number of absorbers per unit column density per unit absorption distance) and the distribution of metal abundances. + The most recent determination of fUN) comes from (2000)., The most recent determination of $f(N)$ comes from \nocite{sw:00}{ (2000). + Phe metal abundances in camped svstems at high. redshift (2.> 2) have most recently been compiled. by (1997) and (1999. 2000).," The metal abundances in damped systems at high redshift $z>2$ ) have most recently been compiled by \nocite{pett:97}{ (1997) and \nocite{pw:99,pw:00}{ (1999, 2000)." + We use the semi-analvtie models developed by the Santa Cruz group (Somerville 1997: 1999:Somerville. 2000). which are based. on the general approach pioneered by (1991). Waullmann. (1993) ane (1994).," We use the semi-analytic models developed by the Santa Cruz group \nocite{some:97,sp:99,spf:00}( 1997; 1999;, 2000), which are based on the general approach pioneered by \nocite{wf:91}{ (1991), \nocite{kwg:93}{, (1993) and \nocite{cole:94}{ (1994)." + Our analysis is based on the fiducial ACDAL mocel presented in (2000. hereafter SPE). which was shown there to produce good. agreement with many properties of the observed. population of Lvman-break ealaxies at redshift ~2.54. and the global evolution with redshift of the star formation density. metallicity. and cold eas density of the Universe.," Our analysis is based on the fiducial $\Lambda$ CDM model presented in \nocite{spf:00}{ (2000, hereafter SPF), which was shown there to produce good agreement with many properties of the observed population of Lyman-break galaxies at redshift $\sim2.5-4$, and the global evolution with redshift of the star formation density, metallicity, and cold gas density of the Universe." + Below we describe the aspects of the SAAIS most relevant to modeling the DLAS. and refer the reader to SPE and (1999. hereafter SP). for further details.," Below we describe the aspects of the SAMs most relevant to modeling the DLAS, and refer the reader to SPF and \nocite{sp:99}{ (1999, hereafter SP), for further details." + Vhe number density of virializecl dark matter halos as a unction of mass and redshift is given by an improved. Press-Seheehter model (Sheth 1999)., The number density of virialized dark matter halos as a function of mass and redshift is given by an improved Press-Schechter model \nocite{st:99}( 1999). + The merging ustory of cach dark matter halo at a desired output redshift is then determined. according to the prescription of Somerville (1999)., The merging history of each dark matter halo at a desired output redshift is then determined according to the prescription of \nocite{sk:99}{ (1999). + As in SP. we assume that idos with velocity dispersions less than ~30knis| are Whotoionized and that the gas within them cannot cool or orm stars.," As in SP, we assume that halos with velocity dispersions less than $\sim 30 \kms$ are photoionized and that the gas within them cannot cool or form stars." + This sets the effective mass resolution of our merger trees., This sets the effective mass resolution of our merger trees. + When halos merge. the central galaxy in the argest progenitor halo becomes the new central galaxy ane all other halos become “sub-halos”.," When halos merge, the central galaxy in the largest progenitor halo becomes the new central galaxy and all other halos become “sub-halos”." + These sub-halos are daced at a distance frs Crom the centre of the new judo. where rey is the virial radius of the new halo.," These sub-halos are placed at a distance $f_{mrg} r_{\rm vir}$ from the centre of the new halo, where $r_{\rm vir}$ is the virial radius of the new halo." + We wil ake [μυ to be 0.5 as in SP. but willexamine the importance of this parameter in section 5..," We will take $f_{mrg}$ to be 0.5 as in SP, but will examine the importance of this parameter in section \ref{depend}." + After each merger event. the satellite galaxies. [al owards the centre of the halo due to dynamical friction.," After each merger event, the satellite galaxies fall towards the centre of the halo due to dynamical friction." + We caleulate the radial position of cach satellite within the ido using the cdilferential formula —ORys), We calculate the radial position of each satellite within the halo using the differential formula =-0.42. +" llere my, and m. are the masses of the halo and satellite respectively. and ο is a ""οποια parameter which cleseribes the orbit of the satellite and is drawn from a Hat clistribution between 0.02 and 1 as suggested by N-bodvy simulations ((Navarro. Frenk 1995)."," Here $m_h$ and $m_{sat}$ are the masses of the halo and satellite respectively, and $\epsilon$ is a “circularity” parameter which describes the orbit of the satellite and is drawn from a flat distribution between 0.02 and 1 as suggested by N-body simulations \nocite{nfw:95}(, 1995)." + The halos are assumed to have a singular isothermal densitv. profile aud to be tidally truncated where the density of the sub-halo is equal to that of its host at its current radius., The halos are assumed to have a singular isothermal density profile and to be tidally truncated where the density of the sub-halo is equal to that of its host at its current radius. + When a sub- reachesthe centre of the host. it is destroved and. the ealaxycontained within it is merged with the centralgalaxy.," When a sub-halo reachesthe centre of the host, it is destroyed and the galaxycontained within it is merged with the centralgalaxy." +2NLASS photometry anc show evidence that the Sh2-132 complex is a site of triggered star formation. as suggested by its hierarchical structure and age distribution of the star clusters.,"2MASS photometry and show evidence that the Sh2-132 complex is a site of triggered star formation, as suggested by its hierarchical structure and age distribution of the star clusters." + The presence of gas and dust bubbles reinforces this idea., The presence of gas and dust bubbles reinforces this idea. + We thank an anonymous referee for constructive comments ancl suggestions., We thank an anonymous referee for constructive comments and suggestions. + We acknowledge support from the Brazilian Institution CNPq., We acknowledge support from the Brazilian Institution CNPq. + This publication makes use of data products from the Two Micron. ALL Sky Survey. which is a joint project of the University of Massachusetts: aud the Infrared Processing and Analysis Centre/C'alifornia Institute of Technology. funded by the National Aeronautics anc Space Administration and the National Science Loundation.," 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 Centre/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation." + This research has mace use of the WEBDA database. operated at the Institute for Astronomy. of the University of Vienna.," This research has made use of the WEBDA database, operated at the Institute for Astronomy of the University of Vienna." +"The intrinsic source size can normally be estimated from the measured size by subtracting the scattering size in quadrature: The scattering deconvolved intrinsic size, therefore depends on the exact form of the assumed scattering power law (Oscar=ax AS).","The intrinsic source size can normally be estimated from the measured size by subtracting the scattering size in quadrature: The scattering deconvolved intrinsic size, therefore depends on the exact form of the assumed scattering power law $\theta_{scat} = a \times\lambda^{\zeta}$ )." + Recent revisions of this power law have assumed a 12 dependence of the scattering size (???)..," Recent revisions of this power law have assumed a $\lambda^{2}$ dependence of the scattering size \citep{2005Natur.438...62S,2006ApJ...648L.127B,2009A&A...496...77F}." +" Using our data and the data in the literature, we show in Fig."," Using our data and the data in the literature, we show in Fig." + 11 the ratio of the apparent major and minor axes of AA* relative to the A?-scattering model determined by ?.., \ref{fig:ratio} the ratio of the apparent major and minor axes of A* relative to the $\lambda^2$ -scattering model determined by \citet{2006ApJ...648L.127B}. +" Due to the poor constraint of the apparent size along the minor axis, it is difficult to see any difference in the broadening effect between the major and minor axes."," Due to the poor constraint of the apparent size along the minor axis, it is difficult to see any difference in the broadening effect between the major and minor axes." +" We notice, however, that both the major and minor sizes deviate from this scattering law at longer cm-wavelength."," We notice, however, that both the major and minor sizes deviate from this scattering law at longer cm-wavelength." +" This discrepancy could stem from difficulties in measuring the size when faced with confusing extended emission around AA* and in the AA complex at long cm-wavelengths, but on the other hand, a steeper power-law index than 2 for the 2 dependence of the scattering size would remove this discrepancy completely."," This discrepancy could stem from difficulties in measuring the size when faced with confusing extended emission around A* and in the A complex at long cm-wavelengths, but on the other hand, a steeper power-law index than 2 for the $\lambda$ dependence of the scattering size would remove this discrepancy completely." +" If this is the case, the intrinsic structure would begin to shine through already atsomewhat longer wavelengths than currently estimated (e.g. at > 3.6ccm, ?))."," If this is the case, the intrinsic structure would begin to shine through already atsomewhat longer wavelengths than currently estimated (e.g. at $\geq$ cm, \citet{2006ApJ...648L.127B}) )." +" A power-law fit to the major axis size at wavelengths longer than 17 cm yields for the wavelength dependence of the size the following power law: For this fit, a reduced xl of 18.9 is formally obtained, which is lower than the reduced x2 of 22.3 for the 2? scattering law proposed by ?.."," A power-law fit to the major axis size at wavelengths longer than 17 cm yields for the wavelength dependence of the size the following power law: For this fit, a reduced $\chi_{\nu}^{2}$ of 18.9 is formally obtained, which is lower than the reduced $\chi_{\nu}^{2}$ of 22.3 for the $\lambda^2$ scattering law proposed by \citet{2006ApJ...648L.127B}." +" In both cases, the relatively higher value of the reduced y? indicates additional systematic effects, which are not described well by the assumption of a simple power law."," In both cases, the relatively higher value of the reduced $\chi_{\nu}^{2}$ indicates additional systematic effects, which are not described well by the assumption of a simple power law." +" We note that a reduced x2 of only 7 was obtained by ?,, when using a much narrower wavelength range of ccm, ie. when performing a local, not a global fit."," We note that a reduced $\chi_{\nu}^{2}$ of only 7 was obtained by \citet{2006ApJ...648L.127B}, when using a much narrower wavelength range of cm, i.e. when performing a local, not a global fit." +" For the minor axis, the sizes are determined less well."," For the minor axis, the sizes are determined less well." +" A direct power-law fit, which leaves both the slope and the coefficient unconstrained, does not yield a reasonable result."," A direct power-law fit, which leaves both the slope and the coefficient unconstrained, does not yield a reasonable result." + We therefore assume the same power-law index for the minor axis as for the major axis., We therefore assume the same power-law index for the minor axis as for the major axis. +" With this restriction, we determine a normalization constant of 0.56+0.03 for the minor axis."," With this restriction, we determine a normalization constant of $\pm$ 0.03 for the minor axis." + Figure 12. shows the apparent size normalized by this scattering law., Figure \ref{fig:ratio2} shows the apparent size normalized by this scattering law. +" In comparison to the 2? dependence shown in Fig. 11,,"," In comparison to the $\lambda^2$ dependence shown in Fig. \ref{fig:ratio}," + a systematic overshooting of the data over the model above ccm wavelength is avoided., a systematic overshooting of the data over the model above cm wavelength is avoided. + The angular broadening of the size of AA* is caused by the electron density fluctuations in the interstellar medium., The angular broadening of the size of A* is caused by the electron density fluctuations in the interstellar medium. +" The wavenumber (k) power spectrum of the density fluctuations is usually written in the form of a power law «&? with cutoffs on the largest (“outer scale"", on which the fluctuations occur) and smallest (“inner scale"", on which the fluctuations dissipate) spatial scales and power-law index f."," The wavenumber (k) power spectrum of the density fluctuations is usually written in the form of a power law $\propto k^{\beta}$ with cutoffs on the largest (“outer scale"", on which the fluctuations occur) and smallest (“inner scale"", on which the fluctuations dissipate) spatial scales and power-law index $\beta$." +" The wavelength dependence of the scattering size follows Osca;&AS, with £=5 (?,andreferencetherein).."," The wavelength dependence of the scattering size follows $\theta_{scat} \varpropto \lambda^{\zeta}$, with $\zeta = \frac{\beta}{\beta-2}$ \citep[][and reference therein]{1998ApJ...508L..61L}." +" The angular broadening scales as 1 if the electron density spectrum is a power law with a Kolmogorov spectral index, B=B."," The angular broadening scales as $\lambda^{2.2}$ if the electron density spectrum is a power law with a Kolmogorov spectral index, $\beta = \frac{11}{3}$." +" When the length of the VLBI baseline becomes comparable to the inner scale, the scattering law changes and has the following form: Oc,&A? (e.g.,?).."," When the length of the VLBI baseline becomes comparable to the inner scale, the scattering law changes and has the following form: $\theta_{scat} \varpropto \lambda^{2}$ \citep[e.g.,][]{2004ApJ...613.1023L}." +" ? shows that the source was exactly Gaussian in shape (B=4.00+ 0.03), indicating that the power-law index should be 2."," \citet{2004Sci...304..704B} shows that the source was exactly Gaussian in shape $\beta=4.00\pm0.03$ ), indicating that the power-law index should be 2." +" They argue that the projected baselines are much shorter than the inner scale of scattering, and therefore ὅ=2 (??).. "," They argue that the projected baselines are much shorter than the inner scale of scattering, and therefore $\zeta=2$ \citep{1989MNRAS.238..963N,1994MNRAS.269...67W}. ." +The power-law index of Z=2.12+0.12 determined at longer, The power-law index of $\zeta = 2.12 \pm 0.12$ determined at longer +he shielding effect of stellar radiation by dust.,the shielding effect of stellar radiation by dust. + However. we fail to explain this trend quantitatively only by the effeet of dust optical depth.," However, we fail to explain this trend quantitatively only by the effect of dust optical depth." + Thus. we conclude that there is a relation between dust-ο-σας ratio and interstellar radiation field (SRF) intensity.," Thus, we conclude that there is a relation between dust-to-gas ratio and interstellar radiation field (ISRF) intensity." +" This relation is consistent with a ""constant dust optical depth"" of star-orming regions in BCDs. implying that dust extinction plays an important role in determining the condition for a burst of star 'ormation."," This relation is consistent with a “constant dust optical depth” of star-forming regions in BCDs, implying that dust extinction plays an important role in determining the condition for a burst of star formation." + The correlation between dust-fo-gas ratio and dust emperature is equivalent to. that between metallicity and dust temperature found in Engelbrachtetal.(2008).. since there is a correlation between dust-to-gas ratio and metallicity.," The correlation between dust-to-gas ratio and dust temperature is equivalent to that between metallicity and dust temperature found in \citet{engelbracht08}, since there is a correlation between dust-to-gas ratio and metallicity." + By comparing the correlation strengths. we propose that dust-to-gas ratio is more fundamental than metallicity in regulating dust temperature. although we will have to contirm this with a larger sample.," By comparing the correlation strengths, we propose that dust-to-gas ratio is more fundamental than metallicity in regulating dust temperature, although we will have to confirm this with a larger sample." + We thank the anonymous referee for useful comments which improved this paper considerably., We thank the anonymous referee for useful comments which improved this paper considerably. + We are grateful to T. Onaka. H. Kaneda. and Y. Hibi for helpful discussions.," We are grateful to T. Onaka, H. Kaneda, and Y. Hibi for helpful discussions." + We thank all members of project for their continuous help and support., We thank all members of project for their continuous help and support. + This research has made use of the NASA/IPAC Extragalactic Database (NED). which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." +galaxy with an optical radial velocity of 1787+17 kms ο. and (ο) NGC 7463. an SADb pec galaxy with an optical radial velocity of 2439+24 km |.,"galaxy with an optical radial velocity of $1787 \pm 17$ km $^{-1}$, and (c) NGC 7463, an SABb pec galaxy with an optical radial velocity of $2439 \pm 24$ km $^{-1}$." + The very broad. spectrum seen in Figure 2 suggests that in all probability we are seeing emission from all three. with that of NGC 7465 dominating.," The very broad spectrum seen in Figure 2 suggests that in all probability we are seeing emission from all three, with that of NGC 7465 dominating." + This galaxy. at 2=0.0474. is a new emission detection. but has a previously known OIL meeamaser which we also detect (Figures 1 and 4).," This galaxy, at $z=0.0474$, is a new emission detection, but has a previously known OH megamaser which we also detect (Figures 1 and 4)." +" It has a total IR luminosity of Ly,=10157-01577, making it one of the more IR luminous objects in our sample."," It has a total IR luminosity of $L_{\rm IR}=10^{11.67 +\pm 0.16} L_\odot$, making it one of the more IR luminous objects in our sample." +" The caleulated. mass from its distorted spectrum is 10571705AL: à value that is slightly lower than the median (109791, ) and the mean (109797929 44.) for objects with IR Iuminosities greater than 10!""£L, (Table 7)."," The calculated mass from its distorted spectrum is $10^{9.71\pm 0.08} M_\odot$; a value that is slightly lower than the median $10^{9.86} M_\odot$ ) and the mean $10^{9.99 \pm 0.10} +M_\odot$ ) for objects with IR luminosities greater than $10^{11.50} +L_\odot$ (Table 7)." + Also known as HI Zw 1023. this galaxy is al a redshift of 0.0560. ancl is also a new emission detection (Figure 1).," Also known as III Zw 103, this galaxy is at a redshift of $z=0.0560$ , and is also a new emission detection (Figure 1)." + With a total IR. luminosity of Lig=101975]D 36 js also one of the more IR luminous sources in our sample.," With a total IR luminosity of $L_{\rm IR}=10^{11.88 \pm 0.16} L_\odot$, it is also one of the more IR luminous sources in our sample." + We were unable to determine if (here is OIL emission/absorption in this source. because the spectra of all its main and satellite lines were severely affected bv REL," We were unable to determine if there is OH emission/absorption in this source, because the spectra of all its main and satellite lines were severely affected by RFI." + Its mass (10797071. ) is lower than (he median ancl mean of galaxies with comparable HA. Iumninosities (Table 7)., Its mass $10^{9.76\pm 0.07} M_\odot$ ) is lower than the median and mean of galaxies with comparable IR luminosities (Table 7). + Both the and OIIM emission lines (Figures 1 ancl 3) of this ULIRG ἐς= 0.1067) are new detections., Both the and OHM emission lines (Figures 1 and 3) of this ULIRG $z=0.1067$ ) are new detections. + A study. by Dinh-V-Trungetal.(2001). showed that (his object is a svstem of (wo interacting ealaxies separated by 20 κρο, A study by \citet{DVT01} showed that this object is a system of two interacting galaxies separated by 20 kpc. + Hs northern component is disturbed. while (he southern component is a normal spiral with a very thick bar structure.," Its northern component is disturbed, while the southern component is a normal spiral with a very thick bar structure." + High resolution radio interlerometric observations are needed to establish from which galaxy in this svstem the and OIIM emission lines originate., High resolution radio interferometric observations are needed to establish from which galaxy in this system the and OHM emission lines originate. + This galaxy is al a redshift of z=0.0912. which is the second hiehest redshift in our observed sample.," This galaxy is at a redshift of $z=0.0912$, which is the second highest redshift in our observed sample." + It is one of two sources with no detection. with the other source being IRAS 20210--1121 (2=0.0564: see above).," It is one of two sources with no detection, with the other source being IRAS 20210+1121 $z=0.0564$; see above)." +" Its IR luminositv is 1017572 and the derived 36 upper limit for its mass. assuming a 400 km J| velocity width. is LOM""AL."," Its IR luminosity is $10^{12.08\pm 0.17}~L_{\odot}$ and the derived $\sigma$ upper limit for its mass, assuming a 400 km $^{-1}$ velocity width, is $10^{10.30}~M_{\odot}$." +" This Timass limit is greater than the median and the mean mass values for sources with Ly,οL., which are 10""9.17, and 10929—-1""1[| yespectivelv."," This mass limit is greater than the median and the mean mass values for sources with $L_{\rm IR} > 10^{11.50}~L_{\odot}$, which are $10^{9.86}~M_{\odot}$ and $10^{9.99 \pm 0.10}~M_{\odot}$, respectively." + Therefore. the non-detection of emission [rom this source does not necessarily imply. hydrogen deficiency.," Therefore, the non-detection of emission from this source does not necessarily imply hydrogen deficiency." + This target consists of three galaxies Iving within our IIPDW at similar redshifts., This target consists of three galaxies lying within our HPBW at similar redshifts. + These are. (a) a starburst galaxy. (tvpe spiral) Iving 1H aresec from our pointing position with an optical radial velocity of 17584x69 kins I. (b) a peculiar Sv1 galaxy also 1H arcsec [rom our pointing with anoptical radial velocity of 17121218 kms ¢.and (ο) a spiralllll galaxy about. 1 arcmin from our pointing with an optical radial velocity," These are, (a) a starburst galaxy (type spiral:HII) lying 14 arcsec from our pointing position with an optical radial velocity of $17584 \pm 69$ km $^{-1}$, (b) a peculiar Sy1 galaxy also 14 arcsec from our pointing with anoptical radial velocity of $17121 \pm +18$ km $^{-1}$ ,and (c) a spiral:HII galaxy about 1 arcmin from our pointing with an optical radial velocity" +important. giving a slightly lower number of planets detected at intermediate masses 24.2V/232RPD for laree R.", $G(R)\rightarrow -V/2\pi^2R^3$ for large $R$. + Now let us consider our measurement of πο)., Now let us consider our measurement of $\wis(R)$. +" In a small radial bin from 8 to R| dR. wewould estimate 1]a(R) as the ratio of the observed counts of pairs in that radialrange to the expected ΠΟ""."," In a small radial bin from $R$ to $R+dR$ , wewould estimate $1+\wis(R)$ as the ratio of the observed counts of pairs in that radialrange to the expected number." +in tun increases the requirements for the energy in accelerated electrons and at the same lime requires verv small magnetic fields.,"in turn, increases the requirements for the energy in accelerated electrons and at the same time requires very small magnetic fields." + Thus. in such scenarios we [ace a sienilicant (bv orders of magnitude) deviation from equipartition. Wy=> (seee.g.Tavecchioetal. 2009).," Thus, in such scenarios we face a significant (by orders of magnitude) deviation from equipartition, $W_{\rm e} >> W_{\rm B}$ \citep[see e.g.][]{tavecchio09}." +". Alternatively, Aharonianetal.(2008) have suggested a scenario for the formation of VILE spectra of almostarbitrary hardness by involving additional absorption of VIIE -ravs interacting with dense radiation fields in (he vicinity of the 2-rav. production region."," Alternatively, \citet{aharonian08} have suggested a scenario for the formation of VHE spectra of almost hardness by involving additional absorption of VHE $\gamma$ -rays interacting with dense radiation fields in the vicinity of the $\gamma$ -ray production region." + The kev element in this scenario is (lie presence of a dense photon field with a narrow enerey distribution or wilh a sharp low energy cut-off around =>10eV.," The key element in this scenario is the presence of a dense photon field with a narrow energy distribution or with a sharp low energy cut-off around $>10\,\rm eV$." + In this case. 5-ravs are attenuated more ellectively at energies 100GeV than at energies ~1—10TeV. and therefore. [or large optical depths (7> 1). the emerging spectrum in the VILE band should eracdually harden towards higher energies (lordetail.seeAharonianetal.2003).," In this case, $\gamma$ -rays are attenuated more effectively at energies $\sim 100\, \rm GeV$ than at energies $\sim \rm 1-10\,TeV$, and therefore, for large optical depths $\tau\ge1$ ), the emerging spectrum in the VHE band should gradually harden towards higher energies \citep[for detail, see][]{aharonian08}." +. While the absorption of high energv 5-ravs in the inner parts of AGN jets is generally possible. or even unavoidable in some cases (AleBreen1979:Lin&Bai2006:Reimer2007:Sitarek&Beclnarek2005:Liuetal.2008:Bai2009:TaveechioMazin 2009).. the detailed modeling of this process requires additional assumptions concerning the presence ol low-Irequency radiation fields. the location and size of the y-ray production region. the Doppler factor of the jet. We note that currently there is no observational evidence excluding the photon field. properties required by Abaronianetal.(2008).. also in the case of BL Lacs.," While the absorption of high energy $\gamma$ -rays in the inner parts of AGN jets is generally possible, or even unavoidable in some cases \citep{mcbreen79,liu06,reimer07,sitarek08,liu08,bai09,tavecchio09*b}, the detailed modeling of this process requires additional assumptions concerning the presence of low-frequency radiation fields, the location and size of the $\gamma$ -ray production region, the Doppler factor of the jet, We note that currently there is no observational evidence excluding the photon field properties required by \citet{aharonian08}, also in the case of BL Lacs." + Remarkably. the internal absorption hypothesis provides an alternative explanation for the non-thermal X-ray. emission. namely as svnchrotron radiation of secondary (pair-produced) electrons (Aharonianetal.2008).. which suggests a possible solution to the problem of low acceleration efficiency. in leptonic models of high οποιον emission of blazars (Costamanteοἱal. 2009)..," Remarkably, the internal absorption hypothesis provides an alternative explanation for the non-thermal X-ray emission, namely as synchrotron radiation of secondary (pair-produced) electrons \citep{aharonian08}, which suggests a possible solution to the problem of low acceleration efficiency in leptonic models of high energy emission of blazars \citep{costamante09}. ." +et al.,et al. + 2009a) by usi& the latest of the W-D code aid an extensive g-search procedure., 2009a) by using the latest of the W-D code and an extensive $q$ -search procedure. + Tle stl‘face teiiperature of the primary star was fixed at Ty =9.120 Ix. according to its spectral type Al) and Heunmaecs (1988) tabe.," The surface temperature of the primary star was fixed at $T_{1}$ =9,420 K, according to its spectral type A0 and Harmanec's (1988) table." + We had attempted to 1uprove the spectral classification by obaluiie hieh-'esollion spectra wih the echelle spectrograp1 attached to the L.5-1n telescope at Bohytuusan Optical Astronomical Olpervatory (BOAQ) in Ixo‘ea (μα et al., We had attempted to improve the spectral classification by obtaining high-resolution spectra with the echelle spectrograph attached to the 1.8-m telescope at Bohyunsan Optical Astronomical Observatory (BOAO) in Korea (Kim et al. + 2002)., 2002). + These images we‘e not well e10lg exposed to im»xove upon the literature value |out. indicated a similar result., These images were not well enough exposed to improve upon the literature value but indicated a similar result. + Initial bolometric and monochromaic limb-darkeuing coelli‘Tents were taken from the tables of val Hamune (1993) aud were used together with the moclel atinosplie'e option., Initial bolometric and monochromatic limb-darkening coefficients were taken from the tables of van Hamme (1993) and were used together with the model atmosphere option. + The g-searcl [or inodes 2. 3. |] aud 5 of the syuthesizine code (Wilson Biernall 1976) converged aud showed acceptale photometric solutions only for mode 5 (semi-detached systeus for which tlie secondary stars [il the inner Roche lobes).," The $q$ -search for modes 2, 3, 4 and 5 of the synthesizing code (Wilson Biermann 1976) converged and showed acceptable photometric solutions only for mode 5 (semi-detached systems for which the secondary stars fill the inner Roche lobes)." + As displayed in Figure 3. tle optimal solution is around g=0.60.," As displayed in Figure 3, the optimal solution is around $q$ =0.60." + This τιdertaudiug contoaus {ο the sense of the mass tratsfer from tle secondary component to he hotter. more nnassive priuary star suggested by the pdod study," This undertanding conforms to the sense of the mass transfer from the secondary component to the hotter, more massive primary star suggested by the period study." + The q value was treaed as ai adjustable parameter 1llc il subsequelt svutheses deriving binary )aralnueers., The $q$ value was treated as an adjustable parameter in all subsequent syntheses deriving binary parameters. + The best resit or uuspotted photosplieres i isted in οςjhnus (2) and (G3) of Table 6 and the residuals [rom tl eaialysis are plotted in the left j»auels of Figure {. where plase-lockect. uuuodelled light variatiois are indicated.," The best result for unspotted photospheres is listed in columns (2) and (3) of Table 6 and the residuals from the analysis are plotted in the left panels of Figure 4, where phase-locked, unmodelled light variations are indicated." + Such features car be reasonably attributed to a Lot spot on the surface of the primary as a result of the impact of the gas stream [rom the cooler. less uassive secondary star.," Such features can be reasonably attributed to a hot spot on the surface of the primary as a result of the impact of the gas stream from the cooler, less massive secondary star." + This situation is know1 for the Aleoltype. semi-detached binary RZ Cas (Rodriguez et al.," This situation is known for the Algol-type, semi-detached binary RZ Cas (Rodriguez et al." + 22001)., 2004). + This interpretatio does not exclude the j»ossible existence of maguetic cool spots located ou the surface of the lae-Lvpe star., This interpretation does not exclude the possible existence of magnetic cool spots located on the surface of the late-type star. + We therefo'e tested two spot mocels: a hot spot ou the more lassive primary star dle LO mass Urausfer aud a cool spot ou the secordary star caused by magnetic activity., We therefore tested two spot models: a hot spot on the more massive primary star due to mass transfer and a cool spot on the secondary star caused by magnetic activity. + Iu a formal seise. as sliown by the entries on the last line o. Table 6. the hot spot mocel does improve the light-curve fit.," In a formal sense, as shown by the entries on the last line of Table 6, the hot spot model does improve the light-curve fit." + Separate tjals for a cool spot ou tle secondary star were not so successful as for the ho-spot model., Separate trials for a cool spot on the secondary star were not so successful as for the hot-spot model. + Final results for all the light eu‘ves are given in columus (1) aud (5) of Table 6 aud tie residuals from our Lot-spot model are show Lin the right panels of Figure |., Final results for all the light curves are given in columns (4) and (5) of Table 6 and the residuals from our hot-spot model are shown in the right panels of Figure 4. + As seen iu the figure. there is a slight imoxovenment iu the residuals for the spot mocel at about phase 0.57 in all j»auels compared ο the unspoted moctlel.," As seen in the figure, there is a slight improvement in the residuals for the spot model at about phase 0.87 in all panels compared to the unspotted model." + Tlls Oryal phase is almost exactly where we would expect the effects o on gas streauni o be evident., This orbital phase is almost exactly where we would expect the effects of a gas stream to be evident. + The hot spot agrees well with the concept of mass tanser [rom the secoidary to 1e primary compotent inferred [rom the period analysis aud [rom tlie relatively. large size of the ot star., The hot spot agrees well with the concept of mass transfer from the secondary to the primary component inferred from the period analysis and from the relatively large size of the hot star. + Iu acklitio1 there are small systematic differences betwee1 tlie two seasons for he light residuals. which meais that mass transfer activity may be variable. as is sometimes reportec for ligt curves of Algol jnaries.," In addition, there are small systematic differences between the two seasons for the light residuals, which means that mass transfer activity may be variable, as is sometimes reported for light curves of Algol binaries." + Iu. all tjese (rials. a possible third ligh source ((4) was Consdered but he results remained iiclistinetishale [rom 0.00 within their errors.," In all these trials, a possible third light source $\ell_{3}$ ) was considered but the results remained indistinguishable from 0.00 within their errors." + We fixed f;1 to be Q.Q cluring te final light-curve analysis., We fixed $\ell_{3}$ to be 0.0 during the final light-curve analysis. + Because of the almost complete eclipses. the light curve determinacy lor CL Aur is quite high.," Because of the almost complete eclipses, the light curve determinacy for CL Aur is quite high." +dust particles (Williamsetal.1997:Mason2001:Harker2002:1999).. branch.,"dust particles \citep{Wil97, Mas01, harker02, woo99}, ." + The lack of a negative branch in the NIB. lor C/1995 OI (IIale-Dopp) can. to first order. be explained by the added polarization of light scattered from more “Ravleigh-like’ particles coming from the jet.," The lack of a negative branch in the NIR for C/1995 O1 (Hale-Bopp) can, to first order, be explained by the added polarization of light scattered from more 'Rayleigh-like' particles coming from the jet." + The addition of these smaller parücles increases the [fractional polarization above what would otherwise be a typical polarization vs. phase curve for the rest of the coma., The addition of these smaller particles increases the fractional polarization above what would otherwise be a typical polarization vs. phase curve for the rest of the coma. + Ow ff band polarimetry of comet C/2007 N3 (Lulin) is the first observation of the polarization of a comet in the NIB. at a phase angle wilhin a few degrees of zero., Our $H$ band polarimetry of comet C/2007 N3 (Lulin) is the first observation of the polarization of a comet in the NIR at a phase angle within a few degrees of zero. + The polarimetry lor comet C/2007 N23 (Lulin) given in Table 1..is plotted vs. phase angle in Fie. 1., The polarimetry for comet C/2007 N3 (Lulin) given in Table \ref{tab:pol_tab} is plotted vs. phase angle in Fig. \ref{fig:pol-lulin}. + The solid line is the tvpical dependence of polarization on phase angle in the £2 band mentioned earlier., The solid line is the typical dependence of polarization on phase angle in the $R$ band mentioned earlier. + Our /2 band observations of comet C/2007 N3 (Lulin) are entirely consistent with the tvpical optical behavior of polarization comets., Our $R$ band observations of comet C/2007 N3 (Lulin) are entirely consistent with the typical optical behavior of polarization comets. + The NIB. polarization of comet C/2007 N3 (Lulin) is also entirely consistent with the contemporaneous visual polarization measurements. and the NIR negative polarization is clearly comparable with a lvpical oplical negative branch polarization behavior observed in most comets al small (x 25°)) phase angles.," The NIR polarization of comet C/2007 N3 (Lulin) is also entirely consistent with the contemporaneous visual polarization measurements, and the NIR negative polarization is clearly comparable with a typical optical negative branch polarization behavior observed in most comets at small $\le 25$ ) phase angles." + Within the LOpam spectral range covered by the SLI module. the observed SED of comets often are comprised of amorphous carbon grams. which produce the underlying featureless emission (continuum) in the 8—13 wavelength region. and small (S lamm)) siliceous dust grains which produce broad features and distinct resonances in excess ol the continuum," Within the $10~\micron$ spectral range covered by the SL1 module, the observed SED of comets often are comprised of amorphous carbon grains, which produce the underlying featureless emission (continuum) in the $8 - 13$ wavelength region, and small $\ltsimeq$ 1 ) siliceous dust grains which produce broad features and distinct resonances in excess of the continuum" +LAI-R was supported by a PPARC post-coctoral research erant.,LM-R was supported by a PPARC post-doctoral research grant. + Lhe Isaac Newton telescope is operated on the island of La Palma by the Isaac. Newton Group in the Spanish Observatorio del Itoque de los Muchachos of the Instituto ο Astrofissica cle Canarias., The Isaac Newton telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de sica de Canarias. + The authors would. like to potrank the Variable Star Network. VSNIZE. and the Variable tar Observers League in Japan. VSOLJ. for making their ata available as most of the light curves. presented. in lis paper were produced using their observations.," The authors would like to thank the Variable Star Network, VSNET, and the Variable Star Observers League in Japan, VSOLJ, for making their data available as most of the light curves presented in this paper were produced using their observations." + Ln this research. we have used. and acknowledge with thanks. data from the AAVSO International. Database. based. on observations submitted to the AAVSO by variable star observers worldwide.," In this research, we have used, and acknowledge with thanks, data from the AAVSO International Database, based on observations submitted to the AAVSO by variable star observers worldwide." + Phe reduction and analysis of the data was carried out on the Southampton node of the STATULINI network., The reduction and analysis of the data was carried out on the Southampton node of the STARLINK network. + We also wish to thank the referee and D. Steeghs for useful comments and L. Gonzallez Hernánndez. for computer support., We also wish to thank the referee and D. Steeghs for useful comments and L. Gonzállez Hernánndez for computer support. +necd to be observed to be competitive with the C06 field star planet frequency. the requirements are even more strict.,"need to be observed to be competitive with the G06 field star planet frequency, the requirements are even more strict." +" Surveys would need to cover ~387.000 stars at detection efficieney. before the upper Πιτ, at confidence. would be inconsistent with the confidence lower bound on the C06 frequency."," Surveys would need to cover $\sim 387,000$ stars at detection efficiency before the upper limits, at confidence, would be inconsistent with the confidence lower bound on the G06 frequency." + When we consider the upper lits on VILIS even more additional stars are required., When we consider the upper limits on VHJs even more additional stars are required. + We conclude that the current upper Limits of the Π.Ι and VILI frequencies determined using the null results of transit surveys in open clusters do uot sugecst a sjenificaut difference between the frequency of plaucts in open clusters and the field., We conclude that the current upper limits of the HJ and VHJ frequencies determined using the null results of transit surveys in open clusters do not suggest a significant difference between the frequency of planets in open clusters and the field. + Open clusters remain. to the best of our knowledge. a viable aud useful target for exoplanet transit survevs. aud we do /not vet have euough data to discern whether the cuvirouments of open clusters have any noticeable effect ou planet formation and survival.," Open clusters remain, to the best of our knowledge, a viable and useful target for exoplanet transit surveys, and we do not yet have enough data to discern whether the environments of open clusters have any noticeable effect on planet formation and survival." + We recommend that any future survevs carefully quantify any mull results. since the conibination of many such outcomes has the poteutial to better coustrain the frequency of short-period plaucts and answer interesting questions about the formation of planets in stellar clusters.," We recommend that any future surveys carefully quantify any null results, since the combination of many such outcomes has the potential to better constrain the frequency of short-period planets and answer interesting questions about the formation of planets in stellar clusters." + We would like to thank K.Z. Stauck for the initial idea to do this analysis. aud useful discussions throughout the process.," We would like to thank K.Z. Stanek for the initial idea to do this analysis, and useful discussions throughout the process." + We also thank Wenueth Janes. Thomas Beatty. Benjamin Shappee and Calen EHeuderson for useful discussions and couuncuts on the mnauuscript.," We also thank Kenneth Janes, Thomas Beatty, Benjamin Shappee and Calen Henderson for useful discussions and comments on the manuscript." + This research has made use of the WEBDA database. operated at the Tustitute for Astronomy of the University of Vienna. and the Exoplanet Orbit Database aud the Exoplanet Data Explorer at exoplaucts.ore.," This research has made use of the WEBDA database, operated at the Institute for Astronomy of the University of Vienna, and the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org." +"the emphasis in the literature on these QSO hosts, it may be that such very massive systems, being exceptional and rare, tell us little about typical star forming environments at very high redshift.","the emphasis in the literature on these QSO hosts, it may be that such very massive systems, being exceptional and rare, tell us little about typical star forming environments at very high redshift." +" And while, young star-forming galaxies at high redshift with strong nebular emission appear to be somewhat dust-obscured in spite of their blue continuua (??),, the quantities of dust are not large, consistent with the idea that in the early universe, most of the star-formation is likely to be less obscured than at later times."," And while, young star-forming galaxies at high redshift with strong nebular emission appear to be somewhat dust-obscured in spite of their blue continuua \citep{schaerer,watson10}, the quantities of dust are not large, consistent with the idea that in the early universe, most of the star-formation is likely to be less obscured than at later times." +" GRBs, associated as are with the deaths of massive stars, usually occur in theyyoung, blue and sub-luminous galaxies with a high specific and are therefore likely to be good probes of star-forming regions, especially at high redshift."," GRBs, associated as they are with the deaths of massive stars, usually occur in young, blue and sub-luminous galaxies with a high specific star formation rate \citep{lefloch,courty,christensen,prochaska,savaglio09,castro-ceron} and are therefore likely to be good probes of star-forming regions, especially at high redshift." +" In this work, we have determined that all the identified z>6 GRBs have low or negligible extinctions."," In this work, we have determined that all the identified $z>6$ GRBs have low or negligible extinctions." +" By comparing these results with the first spectroscopic GRB extinction sample of ?,, we find that at high-redshifts (z= 4), GRB sightlines appear significantly less extinguished (see Fig. )):"," By comparing these results with the first spectroscopic GRB extinction sample of \citet{zafar11}, we find that at high-redshifts $z\gtrsim4$ ), GRB sightlines appear significantly less extinguished (see Fig. \ref{zplot}) ):" + the majority of reddened low-redshift GRBs are observed with Ay~ 0.3mmag., the majority of reddened low-redshift GRBs are observed with $A_V\sim0.3$ mag. +" While the numbers are small, the absence of any GRBs at z24 with extinctions in this range is striking."," While the numbers are small, the absence of any GRBs at $z\gtrsim4$ with extinctions in this range is striking." +" The first explanation to examine is observational bias, where higher-redshift GRBs will be observed farther into the restframe UV where the extinction is likely to be more severe, possibly preventing spectra from being obtained or the afterglow from being detected."," The first explanation to examine is observational bias, where higher-redshift GRBs will be observed farther into the restframe UV where the extinction is likely to be more severe, possibly preventing spectra from being obtained or the afterglow from being detected." +" For the z>6 GRBs, a restframe Ay=0.3 corresponds to 1-1.5 magnitudes of extinction in the observed J-band and 0.5—0.8 magnitudes in the observed K, for an SMC extinction curve."," For the $z>6$ GRBs, a restframe $A_V=0.3$ corresponds to 1–1.5 magnitudes of extinction in the observed $J$ -band and 0.5–0.8 magnitudes in the observed $K$ , for an SMC extinction curve." + Considering the with Ay=0.3 the GRBs at z>6 could have been detected with relative ease and a photometric redshift obtained.," Considering the photometric observations given in \citet{ruiz07,haislip,tagliaferri,greiner,tanvir}, we found that even with $A_V=0.3$ the GRBs at $z>6$ could have been detected with relative ease and a photometric redshift obtained." +" In the case of 0050904, it seems likely that a spectroscopic redshift would have been obtained even with restframe 0.3."," In the case of 050904, it seems likely that a spectroscopic redshift would have been obtained even with restframe $A_V=0.3$ ." +" This work therefore hints at a low extinction of most z>4 bursts, since it seems that our z>6 bursts would have been found even with Ay=0.3."," This work therefore hints at a low extinction of most $z>4$ bursts, since it seems that our $z>6$ bursts would have been found even with $A_V=0.3$." + Therefore we have looked at all known z>5 GRB afterglows in the literature., Therefore we have looked at all known $z>5$ GRB afterglows in the literature. + There are four bursts with firm estimates of z>5 known., There are four bursts with firm estimates of $z>5$ known. + Three of them have estimates of their dust extinction available., Three of them have estimates of their dust extinction available. +" The four bursts are: 0050814 (?) at z~5.3, 0060522 (?) at z=5.11, 0060927 (?;; ?)) at z=5.46 and 0071025 (?)) at z~ 5."," The four bursts are: 050814 \citep{jakobsson06} at $z\sim5.3$, 060522 \citep{cenko06} at $z=5.11$, 060927 \citealt{ruiz07}; \citealt{zafar11}) ) at $z=5.46$ and 071025 \citep{perley} at $z\sim5$." +"? obtained a photometric redshift of the afterglow of 0050814 and the SED is consistent with no dust reddening (P. Jakobsson, private comm."," \citet{jakobsson06} obtained a photometric redshift of the afterglow of 050814 and the SED is consistent with no dust reddening (P. Jakobsson, private comm." + 2010)., 2010). +" (?) give a spectroscopic redshift for 0060522 based on the Lya break, however no estimate of the extinction is available so far in the literature."," \citep{cenko06} give a spectroscopic redshift for 060522 based on the $\alpha$ break, however no estimate of the extinction is available so far in the literature." + ? obtained the spectroscopic redshift of the afterglow of 0060927., \citet{ruiz07} obtained the spectroscopic redshift of the afterglow of 060927. + We have studied the SED of the afterglow of this burst in our spectroscopic sample of ? and it is consistent with Ay=0 (see Fig. Bp., We have studied the SED of the afterglow of this burst in our spectroscopic sample of \citet{zafar11} and it is consistent with $A_V=0$ (see Fig. \ref{zplot}) ). +" Moderate extinction is claimed in the case of 0071025 (?),, with extinction corresponding to Ay~0.5 (converting A39,4 to Ay using the SMC extinction curve ratio)."," Moderate extinction is claimed in the case of 071025 \citep{perley}, with extinction corresponding to $A_V\sim0.5$ (converting $A_{3000\,\AA}$ to $A_V$ using the SMC extinction curve ratio)." + A ? extinction curve is required to fit the SED., A \citet{maiolino} extinction curve is required to fit the SED. +" With this extinction, 0071025 has a high enough extinction to begin to fill in the gap at high redshift around Ay~0.3, though it is notable that it has the lowest redshift of all the bursts perhapsexamined here."," With this extinction, 071025 has a high enough extinction to begin to fill in the gap at high redshift around $A_V\sim0.3$, though it is perhaps notable that it has the lowest redshift of all the bursts examined here." + It is more anomalous in the sense that it has an apparently unique extinction curve since reanalyses have shown that no other QSO or GRB any longer require such a peculiar extinction (see ??)..," It is more anomalous in the sense that it has an apparently unique extinction curve since reanalyses have shown that no other QSO or GRB any longer require such a peculiar extinction \citep[see][]{gallerani,zafar}. ." + The issues of bias and low number statistics are clearly important and we cannot resolve them with this sample., The issues of bias and low number statistics are clearly important and we cannot resolve them with this sample. +" The fact that we infer very little dust in the afterglows studied here does not imply that dusty environments do not exist along sightlines to z>6 GRBs, but it suggests that there is less dust in highly star-forming regions at z4."," The fact that we infer very little dust in the afterglows studied here does not imply that dusty environments do not exist along sightlines to $z>6$ GRBs, but it suggests that there is less dust in highly star-forming regions at $z\gtrsim4$." +" This result is also potentially interesting in the context of dark bursts — suggesting that bursts may not exist at high redshift, and highly-extinguishedthat bright, very high redshift GRBs will be detectable as long as they are observed in the NIR."," This result is also potentially interesting in the context of dark bursts -- suggesting that highly-extinguished bursts may not exist at high redshift, and that bright, very high redshift GRBs will be detectable as long as they are observed in the NIR." +" Finally, the comparison to the column densities of metals is striking."," Finally, the comparison to the column densities of metals is striking." +" In the cases of both 0050904 and 0090423, column densities of Nyx~3x107 and 1x102 are claimed (assuming solar abundances and neutral elements, ?;; ?;; ?;; ?;; Starling et al."," In the cases of both 050904 and 090423, column densities of $N_{H,X }\sim3\times10^{22}$ and $1\times10^{23}$ are claimed (assuming solar abundances and neutral elements, \citealt{watson062}; \citealt{campana}; \citealt{gendre}; \citealt{tanvir}; Starling et al." + in prep., in prep. + 2011) from the soft X-ray absorption., 2011) from the soft X-ray absorption. + The dust-to-metals ratios in both cases are at most a few percent of the value in the local group., The dust-to-metals ratios in both cases are at most a few percent of the value in the local group. +" Given that the metals are likely to be highly-ionized (??),, the metal column must be substantially higher than found using neutral medium models."," Given that the metals are likely to be highly-ionized \citep{schady,watson07}, the metal column must be substantially higher than found using neutral medium models." + This could drive the dust-to-metals ratio down below percent of local group values., This could drive the dust-to-metals ratio down below a percent of local group values. +" While it is established that aGRB environments can have low dust-to-metals ratios (???),, these high-redshift objects are extreme."," While it is established that GRB environments can have low dust-to-metals ratios \citep{ardis, watson06, schady}, these high-redshift objects are extreme." +" Such extreme ratios could be related to the more effective destruction of dust due to the high luminosity of these bursts (e.g.2); the effects of dust destruction may be discernible not only in very early colour changes in the GRB prompt phase UV emission, but also in the extinction curve at later times (?).."," Such extreme ratios could be related to the more effective destruction of dust due to the high luminosity of these bursts \citep[e.g.][]{fruchter}; the effects of dust destruction may be discernible not only in very early colour changes in the GRB prompt phase UV emission, but also in the extinction curve at later times \citep{perna02}." +" A small dust-to-metals ratio could however, also be due to something more fundamental, such as the production of metals in SNe but delayed formation and rapidgrowth of the dust."," A small dust-to-metals ratio could however, also be due to something more fundamental, such as the rapid production of metals in SNe but delayed formation and growth of the dust." + For the metals to form before the dust suggests at least several million years between the formation of metals andthe onset of dust growth., For the metals to form before the dust suggests at least several million years between the formation of metals andthe onset of significant dust growth. + Observations of a larger sample may help tosignificantclarify this issue (see ?))., Observations of a larger sample may help toclarify this issue (see \citealt{zafar11}) ). + We have investigated cosmicdust at z>6 using the afterglows of the highest redshift GRBs known., We have investigated cosmicdust at $z>6$ using the afterglows of the highest redshift GRBs known. +" We performed multi-epoch NIR-X-ray SED analysis of 0050904,080913, and 090423."," We performed multi-epoch NIR–X-ray SED analysis of 050904,080913, and 090423." + We infer from our, We infer from our +"Computing (NIC), JAHich, Germany.","Computing (NIC), Jülich, Germany." + aacknowledges the support by the DFG Priority Programme 1177 and additional support by the DFG Cluster of Excellence ’Origin and Structure of the Universe’., acknowledges the support by the DFG Priority Programme 1177 and additional support by the DFG Cluster of Excellence 'Origin and Structure of the Universe'. + F.S. thanks for the support from DFG Research Unit 1254., F.S. thanks for the support from DFG Research Unit 1254. +"The equations for fy ancl fs are now: & = = 0. and so on for higher orders O(57)., Noticethat the function /; will be determined by the previous functions (fi.fo....f;1] onlv.","The equations for $f_{1}$ and $f_{2}$ are now: - + + - = 0, and so on for higher orders $\left.\cal{O}\right.(\gamma^{3})$ Noticethat the function $f_i$ will be determined by the previous functions $\left\{f_{1},f_{2},...f_{i-1}\right\}$ only." + So. we have a infinite set of recurrent equations.," So, we have a infinite set of recurrent equations." + The next step is (he usual one. as (he first part of this work linear case).," The next step is the usual one, as the first part of this work linear case)." + Thus. defining the new function the Eq. (27))," Thus, defining the new function (x,t) =, the Eq. \ref{ft18}) )" + can be written as 7 TE. + . pP., can be written as - + + - = 0. + Observe (hat the above equation is pretty (he sameas linearizecl equation (7)., Observe that the above equation is pretty the sameas linearized equation $(\ref{ft2.7})$. + Since € satislies (7) we can (hen use the solutions ((16)—(20)) to obtain the functions fi which are given by: = (4) ALAP.," Since $\xi$ satisfies $(\ref{ft2.7})$ we can then use the solutions $((\ref{ft10}) - (\ref{ft14}))$ to obtain the functions $f_1$, which are given by: = ( M^2." + wi- ((35)) AAP., = ( M^2. +Perhaps the most significant result from these observations is the insight they provide the origin of the moving line systems observed m nova ejecta.,Perhaps the most significant result from these observations is the insight they provide the origin of the moving line systems observed in nova ejecta. + It is unusual to have so long a plateau for a recurrent nova (although not for a classical nova) in the visible during which the UV ts optically thick in lines from neutrals and singly ionized species., It is unusual to have so long a plateau for a recurrent nova (although not for a classical nova) in the visible during which the UV is optically thick in lines from neutrals and singly ionized species. + We do not know. at this point. the ejecta from T Pyx are so massive.," We do not know, at this point, the ejecta from T Pyx are so massive." + This episode is not unusual in rise. duration. or amplitude compared with previous outbursts and suggests that the ejection is not unusually massive relative to the historical events despite the long hiatus.," This episode is not unusual in rise, duration, or amplitude compared with previous outbursts and suggests that the ejection is not unusually massive relative to the historical events despite the long hiatus." + Thus. the details provided by the OT spectra become especially significant: this is showing a generic behavior that is also seen in classical novae Gaposchkin 1957. MeLaughlin 1954. 1964).," Thus, the details provided by the NOT spectra become especially significant: this is showing a generic behavior that is also seen in classical novae (Payne-Gaposchkin 1957, McLaughlin 1954, 1964)." +" The recombination of He II following the first observation. an interval of about one week. provides an estimate of the electron density. 2,2x10° em™ for the outer part of the ejecta at -2500 km s' at a radius of 1.5x10 em."," The recombination of He II following the first observation, an interval of about one week, provides an estimate of the electron density, $n_e \approx 2\times 10^6$ $^{-3}$ for the outer part of the ejecta at -2500 km $^{-1}$ at a radius of $1.5\times 10^{15}$ cm." + Assuming a ballistic expansion with an το radial dependence and an innermost of 500 km s! based on the separation of the inner emission peaks on the Fe II profiles. the mass of a spherical. filled ejecta is =2»I0? fM... where f is the radially constant filling factor.," Assuming a ballistic expansion with an $r^{-3}$ radial dependence and an innermost of 500 km $^{-1}$ based on the separation of the inner emission peaks on the Fe II profiles, the mass of a spherical, filled ejecta is $\approx 2\times 10^{-5}f$ $_\odot$, where $f$ is the radially constant filling factor." + This is consistent with the long duration of the Fe-curtain phase. more than 50 days and of the same order as in classical novae for which such masses are normal but must be an upper limit.," This is consistent with the long duration of the Fe-curtain phase, more than 50 days and of the same order as in classical novae for which such masses are normal but must be an upper limit." + If. however. the shell is severely fragmented. as appears the case from the DACs. but every line of sight encounters at least one such optically thick filament. then the mass be lower by a large factor.," If, however, the shell is severely fragmented, as appears the case from the DACs, but every line of sight encounters at least one such optically thick filament, then the mass be lower by a large factor." + A filling factor f~0.01 would reduce the mass estimate to that normally found for recurrent novae (e.g. Anupama 2009. Schaefer 2010) but requires that the individual filaments or substructures are extremely opaque and completely covering.," A filling factor $f \sim 0.01$ would reduce the mass estimate to that normally found for recurrent novae (e.g. Anupama 2009, Schaefer 2010) but requires that the individual filaments or substructures are extremely opaque and completely covering." + A test is Whether there is a constant bolometric luminosity phase such as that found for classical novae (see e.g. Shore but that requires continued ultraviolet observations that are not yet completed., A test is whether there is a constant bolometric luminosity phase such as that found for classical novae (see e.g. Shore but that requires continued ultraviolet observations that are not yet completed. + As a proof-of-concept. we show in Fig.," As a proof-of-concept, we show in Fig." + 5 à schematic model for the absorption line evolution that applies most simply to the Na I resonance lines (Fig., 5 a schematic model for the absorption line evolution that applies most simply to the Na I resonance lines (Fig. + 4)., 4). + This assumed a recombination front moving outward in the expanding ejecta., This assumed a recombination front moving outward in the expanding ejecta. + A constant velocity gradient with απ) density variation were imposed and the recombination was integrated through the ejecta., A constant velocity gradient with an $r^{-3}$ density variation were imposed and the recombination was integrated through the ejecta. + Each profile represents one time step. the timescale being the recombination time from the disappearance of C ILI/N III aand the He II lines between the first and second NOT observation. about 5 days.," Each profile represents one time step, the timescale being the recombination time from the disappearance of C III/N III and the He II lines between the first and second NOT observation, about 5 days." + The intrinsic line. profile was assumed to be gaussian. but the details are not important for this simulation.," The intrinsic line profile was assumed to be gaussian, but the details are not important for this simulation." + The decrease in the total optical depth. scaling as (77. and the separation of the absorption component are reproduced.," The decrease in the total optical depth, scaling as $t^{-2}$, and the separation of the absorption component are reproduced." + The individual fine structure features are not included. they would be part of the absorption in any velocity interval. nor is the emissio1 (only an invariant gaussian Was used for visualization of the absorption since the ejecta are assumed to be detached from the white dwarf.," The individual fine structure features are not included, they would be part of the absorption in any velocity interval, nor is the emission (only an invariant gaussian was used for visualization of the absorption since the ejecta are assumed to be detached from the white dwarf." + The line evolution can thus be understood assuming only that the structure was frozen in the ejecta at the time of expulsion., The line evolution can thus be understood assuming only that the structure was frozen in the ejecta at the time of expulsion. + There is no need for either colliding shocks and winds (Kato Hachisu 2007) or subsequent collisions with circum-system material (e.g. Williams et al., There is no need for either colliding shocks and winds (Kato Hachisu 2007) or subsequent collisions with circum-system material (e.g. Williams et al. + 2008. Williams Mason 2010). although the latter may also occurd.," 2008, Williams Mason 2010), although the latter may also occur4." + The evolution of the different DACs can be explained the changes in the optical depth of specific transitions in the ultraviolet as the ejecta expand., The evolution of the different DACs can be explained the changes in the optical depth of specific transitions in the ultraviolet as the ejecta expand. + Finally. the last NOT spectrum shows weak emission appearing on [O I] 5577 and wwith a double peaked structure that is consistent with with the innermost part of the ejecta becoming optically thin in the ultraviolet and beginning to again display both He I and [O I] emission lines.," Finally, the last NOT spectrum shows weak emission appearing on [O I] 5577 and with a double peaked structure that is consistent with with the innermost part of the ejecta becoming optically thin in the ultraviolet and beginning to again display both He I and [O I] emission lines." +limes: MJD 52454 and MJD 52487.,times: MJD 52454 and MJD 52487. + Data Irom the former time was taken from when the primary outburst hac passed its peak but still bright relative to quiescent levels., Data from the former time was taken from when the primary outburst had passed its peak but still bright relative to quiescent levels. + It was also al (his time that we had data in all five bands., It was also at this time that we had data in all five bands. + The latter time is that near the peak of the secondary maximun flux., The latter time is that near the peak of the secondary maximum flux. + We constructed the SEDs following the method described here. sublvacting the quiescent fluxes of 4U 1543-47 trom the outburst fluxes thereby isolating the flux related to the outburst source.," We constructed the SEDs following the method described here, subtracting the quiescent fluxes of 4U 1543-47 from the outburst fluxes thereby isolating the flux related to the outburst source." + Again. fInxes were converted to mJv using (he same zeropoint [Iuxes mentioned above.," Again, fluxes were converted to mJy using the same zeropoint fluxes mentioned above." + Errors for the SED points for MJD 52454 were calculated from photometric errors., Errors for the SED points for MJD 52454 were calculated from photometric errors. + Errors for the SED of the underlving flux at ALJD 52487 were estimated] from the error in estimating the baseline connecting points either side of the secondary maxinuun., Errors for the SED of the underlying flux at MJD 52487 were estimated from the error in estimating the baseline connecting points either side of the secondary maximum. + This was found to be c 0.1 mae., This was found to be $\pm$ 0.1 mag. +" When constructing mullicolor-blackhocdy models we again fixed rj, = 3r, and M, = 5 M..", When constructing multicolor-blackbody models we again fixed $_{in}$ = $_g$ and $_1$ = 5 $_{\odot}$. + Figure 16. shows the SED at MJD 52454 and three (vpical multicolor-blackbody fils., Figure \ref{fig:sed_2454} shows the SED at MJD 52454 and three typical multicolor-blackbody fits. +" We first chose r;,; = 10?r;, which was within the primary Roche-lobe radius (~ 5 x 10H em ~ 105r,,).", We first chose $_{out}$ = $^5$ $_{in}$ which was within the primary Roche-lobe radius $\sim$ 5 x $^{11}$ cm $\sim$ $^6$ $_{in}$ ). +" The resulting fit (shown as solid line) gave M. = 19.SAT 1 and Tou = 5970""Ix. This A is somewhat higher than usually observed (see above). hence we chose M = 107 ! (dashed line) and 105"" ! (dot-dashed line) for the next (wo fits."," The resulting fit (shown as solid line) gave $\dot{M}$ = $^{19.9}$ $^{-1}$ and $_{out}$ = $^o$ K. This $\dot{M}$ is somewhat higher than usually observed (see above), hence we chose $\dot{M}$ = $^{18.0}$ $^{-1}$ (dashed line) and $^{17.0}$ $^{-1}$ (dot-dashed line) for the next two fits." +" The corresponding temperatures of the outer disk were 5632K. and 5314K. and r4; = 5r, and 10 5r;,. respectively."," The corresponding temperatures of the outer disk were $^o$ K and $^o$ K, and $_{out}$ = $^{4.4}$ $_{in}$ and $^{4.1}$ $_{in}$, respectively." + In all three cases the models could provide a good overall match to the SED. although the 4? values were never satisfactory. perhaps due to systematic errors [rom subtracting the flix due to the secondary. star.," In all three cases the models could provide a good overall match to the SED, although the $\chi^2$ values were never satisfactory, perhaps due to systematic errors from subtracting the flux due to the secondary star." + All temperatures are very reasonable eiven that the peak of the outburst has passed ancl that (he accretion disk has probably transilioned to a cooler state al this time., All temperatures are very reasonable given that the peak of the outburst has passed and that the accretion disk has probably transitioned to a cooler state at this time. + The corresponding AM. are also plausible., The corresponding $\dot{M}$ are also plausible. + The same fitting procedure was performed for the SED of the underlying flux at NJD 5248. using the same three r4; as above.," The same fitting procedure was performed for the SED of the underlying flux at MJD 52487, using the same three $_{out}$ as above." + The SED and resulting fits are shown in Figure 17.., The SED and resulting fits are shown in Figure \ref{fig:sed_under}. +" Again we see good fits with the corresponding temperatures being 1125Ix. (solid line). ΕΤ (dashed line) and 1680""IN. (dot-dashed line) and M = 1047 !. 10! ! and 105 | respectively."," Again we see good fits with the corresponding temperatures being $^o$ K (solid line), $^o$ K (dashed line) and $^o$ K (dot-dashed line) and $\dot{M}$ = $^{17}$ $^{-1}$, $^{16}$ $^{-1}$ and $^{15}$ $^{-1}$, respectively." +" Although these outer-disk temperatures seem low. fits to ellipsoidal light curves of other svstems suggest that Ty, can be < 2000""Ix. (e.g.BeerandPodsiacllowski 2002)."," Although these outer-disk temperatures seem low, fits to ellipsoidal light curves of other systems suggest that $_{out}$ can be $\le$ $^o$ K \citep[e.g.][]{bee02}." + since (he single-blackbocdwv aud multicolor-blackbocds models cannot aclequately describe the SED of the secondary maximum flix. we briefly look at non-thermal emission models.," Since the single-blackbody and multicolor-blackbody models cannot adequately describe the SED of the secondary maximum flux, we briefly look at non-thermal emission models." + We fitted the SED of the secondary maximum flux will a broken power-law in which, We fitted the SED of the secondary maximum flux with a broken power-law in which +ApJ accepted 31 December 2010.,ApJ accepted 31 December 2010. +et al.,et al. + 2007)., 2007). + This study revealed that these GC's hold a fraction of binaries ranging from to depending on the cluster., This study revealed that these GCs hold a fraction of binaries ranging from to depending on the cluster. + In. such analysis. an anti-correlation. with 1e cluster age has been also noticed.," In such analysis, an anti-correlation with the cluster age has been also noticed." + Milone et al. (, Milone et al. ( +2008) enlarged. the sample of analysed clusters and. showed. an even stronger anti-correlation between binary fraction and cluster Luminosity (mass).,2008) enlarged the sample of analysed clusters and showed an even stronger anti-correlation between binary fraction and cluster luminosity (mass). +a This last correlation is predicted I= heoretical mocels as à consequcnee of the similar dependence of the cluster mass and. of the efliceney of the binary destruction. process on the cluster density ane velocity dispersion (Sollima 2008)., This last correlation is predicted by theoretical models as a consequence of the similar dependence of the cluster mass and of the efficency of the binary destruction process on the cluster density and velocity dispersion (Sollima 2008). + Unfortunately. the sparse number of analysed. objects together with the small range of parameters covered by the sample does not allow a firm conclusion on this issue.," Unfortunately, the sparse number of analysed objects together with the small range of parameters covered by the sample does not allow a firm conclusion on this issue." + Open clusters (OC's) represents an important group of objects to study the frequeney of. binary systenis., Open clusters (OCs) represents an important group of objects to study the frequency of binary systems. + They are indeed. both less massive and vounger than GCs. covering a range of structural parameters. where homogeneous. determinations of binary fractions are. still missing.," They are indeed both less massive and younger than GCs, covering a range of structural parameters where homogeneous determinations of binary fractions are still missing." + Moreover. their proximity and. low density. makes the determination of the binary frequency in these stellar systems particularly easy.," Moreover, their proximity and low density makes the determination of the binary frequency in these stellar systems particularly easy." + Estimates of the binary fraction in individual open OC's have been provided by several authors (Sandhu. Pandey Sagar 2003: Bica Bonatto 2005 and references therein).," Estimates of the binary fraction in individual open OCs have been provided by several authors (Sandhu, Pandey Sagar 2003; Bica Bonatto 2005 and references therein)." + However. it is dillicult to interpret. the results obtained by these authors in a global picture because of the different assumption mace in these works.," However, it is difficult to interpret the results obtained by these authors in a global picture because of the different assumption made in these works." + A recent homogeneous analysis of the fraction of binaries in a sample of six OC's have been presented by Sharma et al. (, A recent homogeneous analysis of the fraction of binaries in a sample of six OCs have been presented by Sharma et al. ( +2008).,2008). + Nevertheless. a direct comparison of these last results with those obtained for GCs is not possible since these authors assume a significantly cülferent clistribution of mass-ratios andd measure the [fraction of binaries over the entire cluster extent.," Nevertheless, a direct comparison of these last results with those obtained for GCs is not possible since these authors assume a significantly different distribution of mass-ratios and measure the fraction of binaries over the entire cluster extent." + In this paper we present an estimate of the binary fraction in the core of five high-latitucle OC's., In this paper we present an estimate of the binary fraction in the core of five high-latitude OCs. + We used a set of archive images obtained. with the Wide Field Imager (at the ESO2.2m telescope). Wide Field Camera (Isaac Newton Telescope) ancl 1.5m Danish telescope cameras.," We used a set of archive images obtained with the Wide Field Imager (at the ESO2.2m telescope), Wide Field Camera (Isaac Newton Telescope) and 1.5m Danish telescope cameras." + In 82 we describe the observations and the data reduction. techniques., In 2 we describe the observations and the data reduction techniques. + In 83 the adopted. method to determine the fraction of binary svstems is presented., In 3 the adopted method to determine the fraction of binary systems is presented. + In 84 we derived. the binary fractions in our target. clusters., In 4 we derived the binary fractions in our target clusters. + 85 is devoted to the analysis of the correlations between the binary fractions measured in our sample of OC's and GCs and the main cluster’s physical parameters., 5 is devoted to the analysis of the correlations between the binary fractions measured in our sample of OCs and GCs and the main cluster's physical parameters. + Finally. we summarize and cliscuss our results in 86.," Finally, we summarize and discuss our results in 6." + The photometric data-set consists of a set. of. wide-ield images of a sample of five OC's., The photometric data-set consists of a set of wide-field images of a sample of five OCs. + The target clusters have been selected on the basis of the following criteria: Five cluster. passed. these criteria namely NCCISS. NGC2204. NGC2243. NCC2420 and NG€2516.," The target clusters have been selected on the basis of the following criteria: Five cluster passed these criteria namely NGC188, NGC2204, NGC2243, NGC2420 and NGC2516." + In Table 1 the main physical parameters of the above target clusters are listed., In Table 1 the main physical parameters of the above target clusters are listed. + The age (fo). the metallicity 1οΗ)) and the Galactic latitude (5) are from the WEBDA database (Alermilliod Paunzen 2003) while the V absolute magnitude (CM) from Lata et al.," The age $t_{9}$ ), the metallicity ([Fe/H]) and the Galactic latitude $b$ ) are from the WEBDA database (Mermilliod Paunzen 2003) while the V absolute magnitude $M_{V}$ ) from Lata et al." +(00092)1. For cach cluster we retrived all the available exposures in the B and. V. bands from the ESO and. INC: Science Archives with the WEL and WEC cameras. respectively.," For each cluster we retrived all the available exposures in the B and V bands from the ESO and ING Science Archives with the WFI and WFC cameras, respectively." + WELGIZSO2.2m frames of NCC2204 and δές20160 aux WECGINT images of NGCISS and. NOGC2420 have been retrived., WFIESO2.2m frames of NGC2204 and NGC2516 and WFCINT images of NGC188 and NGC2420 have been retrived. + Images cover an area of 34’33. around the center of these clusters., Images cover an area of $34\arcmin\times33\arcmin$ around the center of these clusters. + Each cluster has been centered in one of the chips of the camera. allowing to sample the entire cluster extent.," Each cluster has been centered in one of the chips of the camera, allowing to sample the entire cluster extent." + In addition. small field €«5) images obtained a the 1.5m Danish telescope have been used to study the core of NGC2243.," In addition, small field $3\arcmin\times5\arcmin$ ) images obtained at the 1.5m Danish telescope have been used to study the core of NGC2243." + Alter applying the stancard bias ane Lat-fick correction. the photometric analysis has been performed on the pre-reduced. images using the Slxtractor photometric package (Bertin Arnouts 1996).," After applying the standard bias and flat-field correction, the photometric analysis has been performed on the pre-reduced images using the SExtractor photometric package (Bertin Arnouts 1996)." + Given the small star density in these clusters οslarsaresee at Ye20). croweling does not allect the aperture photometry. allowing {ο properly estimate the magnitude of stars.," Given the small star density in these clusters $\leq 0.03~stars~arcsec^{-2}$ at $V<20$ ), crowding does not affect the aperture photometry, allowing to properly estimate the magnitude of stars." + For each star we measured the flux. contained within a radius re~bWLIAL from the star center., For each star we measured the flux contained within a radius $\sim$ FWHM from the star center. + After applving the correction for exposure time. airmass and nominal infinite aperture. instrumental magnitudes have been transformed into the absolute Johnson system by using à set of standard stars from the Lancolt (1992) list observed. during cach observing run.," After applying the correction for exposure time, airmass and nominal infinite aperture, instrumental magnitudes have been transformed into the absolute Johnson system by using a set of standard stars from the Landolt (1992) list observed during each observing run." + Previous photometric analysis are. present in the literature for all the clusters analysecl in this work., Previous photometric analysis are present in the literature for all the clusters analysed in this work. + Our photometry has been compared with the photometric catalog already published. (I&rusberg Chabover 2006 for Νέας158: WKassis et al., Our photometry has been compared with the photometric catalog already published (Krusberg Chaboyer 2006 for NGC188; Kassis et al. + 1997 for Νας2204: Bonifazi ct al., 1997 for NGC2204; Bonifazi et al. + 1990 for NCGC2243: Sharma et al., 1990 for NGC2243; Sharma et al. + 2006 for Νας220 and Jellries. Thurston Llambly 2001 for NGC2516).," 2006 for NGC2420 and Jeffries, Thurston Hambly 2001 for NGC2516)." + Phe mean magnitude cdillerences found are always smaller than 0.02 mag in both passbancds. consistent with no svstematic olfset.," The mean magnitude differences found are always smaller than 0.02 mag in both passbands, consistent with no systematic offset." + Optimal astrometric solutions have been obtained. through cross-correlation with a catalog suitable 2MLASS astrometric stanclarel stars., Optimal astrometric solutions have been obtained through cross-correlation with a catalog suitable 2MASS astrometric standard stars. +" Phe internal accuracy of the astrometry has been found to be «0.2"".", The internal accuracy of the astrometry has been found to be $<0.2\arcsec$. + Fig., Fig. + 1 shows the (1.5. V) CMDs of the 5 OC's in our sample.," \ref{cmd} shows the $V, B-V$ ) CMDs of the 5 OCs in our sample." + Only stars within 5' from the cluster center are shown., Only stars within $\arcmin$ from the cluster center are shown. + The CALDs sample the cluster population from the sub-giant branch down to 4-5 magnitudes below the MS turn-olf., The CMDs sample the cluster population from the sub-giant branch down to 4-5 magnitudes below the MS turn-off. + In all the target clusters the binary sequence is well defined and clistinguishable from the cluster’s MS., In all the target clusters the binary sequence is well defined and distinguishable from the cluster's MS. + Jo determine the fraction of binaries in our sample of OCS we analysed the distribution of stars in the CMD displaced above the cluster Main-Sequence (MS) following the method described in Sollima et al. (, To determine the fraction of binaries in our sample of OCs we analysed the distribution of stars in the CMD displaced above the cluster Main-Sequence (MS) following the method described in Sollima et al. ( +2007).,2007). + Any binary system is indeed seen as a single star with a flux equal to the sum of the [luxes of the two components., Any binary system is indeed seen as a single star with a flux equal to the sum of the fluxes of the two components. + This effect produces, This effect produces +The zoom in figure 5 is instructive.,The zoom in figure \ref{fig:clus} is instructive. +" We can still discern the close correspondence between the dark and baryonic structures, and most of the small structures in the upper panels are indeed detected in the lower panels."," We can still discern the close correspondence between the dark and baryonic structures, and most of the small structures in the upper panels are indeed detected in the lower panels." +" However, some remarkable features can be found: in the bottom left panel, there is a satellite (in orange, under the largest satellite in yellow) with a tidal tail (in red), which is detected by AdaptaHOP as a satellite whose tail is a ""satellite"" of this satellite."," However, some remarkable features can be found: in the bottom left panel, there is a satellite (in orange, under the largest satellite in yellow) with a tidal tail (in red), which is detected by AdaptaHOP as a satellite whose tail is a “satellite” of this satellite." + This structure finder is thus capable of detecting interesting features., This structure finder is thus capable of detecting interesting features. +" Most strikingly, the red arc near the centre of the main galaxy is an artefact: it is not a satellite, but rather an arm of the spiral galaxy."," Most strikingly, the red arc near the centre of the main galaxy is an artefact: it is not a satellite, but rather an arm of the spiral galaxy." +" In figure 5,, we can see the central galaxy of the halo, which contains a large disc of ~160 kpc (comoving) at z=0.46."," In figure \ref{fig:clus}, we can see the central galaxy of the halo, which contains a large disc of $\simeq 160$ kpc (comoving) at $z=0.46$." +" Figures 7(a) and 7(b) show, respectively, a"," Figures \ref{fig:faceon} and \ref{fig:edgeeon} show, respectively, a" +of the main survey.,of the main survey. +" The 2MASS 90009 field. of size 1?x9.3. centered at a=1692715.6"". 0——244123"" (J2000). covers part of the p Oph cloud core. and has limiting magnitudes (at (he 5 σ level) of 20.5. 20.0. and 19.0 at JJ.LF ancl AN. respectively."," The 2MASS 90009 field, of size $1^\circ \times 9.3'$, centered at $\alpha = 16^{\rm h}27^{\rm m}15.6^{\rm s}$, $\delta =-24^\circ41'23''$ (J2000), covers part of the $\rho$ Oph cloud core, and has limiting magnitudes (at the 5 $\sigma$ level) of 20.5, 20.0, and 19.0 at $J,\,H$ and $K_s$, respectively." + Some additional information on the 2\IASS Calibration Fields. and on this field in particular. is given by Plavehanetal.(2008a.b).," Some additional information on the 2MASS Calibration Fields, and on this field in particular, is given by \citet{plav08a,plav08b}." +. We supplement these images with archival data at 3.6. 4.5. 5.8. and 8.0 jn from IRAC (Fazioetal.2004) on the Space Telescope (Werneretal.2004)... based on observations made in 2004 Apr 27May 7 as part of the e2d legacy project 2003).," We supplement these images with archival data at 3.6, 4.5, 5.8, and 8.0 $\mu$ m from IRAC \citep{faz04} on the Space Telescope \citep{werner04}, based on observations made in 2004 Apr 27–May 7 as part of the c2d legacy project \citep{evans03}." +. The archival BCD images were reprocessed (o correct for artifacts (Gncluding saturation. column pulldown. muxbleed. Παρα effects. instrumental background. aud pixel-value outliers) and mosaicked using the Science Center MODPEX software.," The archival BCD images were reprocessed to correct for artifacts (including saturation, column pulldown, muxbleed, “jailbar"" effects, instrumental background and pixel-value outliers) and mosaicked using the Science Center MOPEX software." + Figure 1. shows the relationship of tlie observed [field to an extinction map of the cloud core., Figure \ref{fig1} shows the relationship of the observed field to an extinction map of the cloud core. +" For comparison purposes. the field has been divided into “cloud” and ""exterior regions."," For comparison purposes, the field has been divided into “cloud"" and “exterior"" regions." + The lower boundary ofthe “cloud” region was chosen to coincide with the ly)—5 mag contour of Cambrésv(1999).. at ὁ=—24.87.," The lower boundary ofthe “cloud"" region was chosen to coincide with the $A_V=5$ mag contour of \citet{cam99}, at $\delta=-24.8^\circ$." +" Our exterior"" region was chosen to extend southward from declination —24.9°. wherein Ay<3 mag."," Our “exterior"" region was chosen to extend southward from declination $-24.9^\circ$, wherein $A_V<3$ mag." +" The two regions are (herefore definecl as follows: The image data from all seven bands were interpolated onto a common pixel-erid wilh a sampling interval of 0.5 ""spatially coincident with the 2MAÀSS images."," The two regions are therefore defined as follows: The image data from all seven bands were interpolated onto a common pixel-grid with a sampling interval of $0.5''$, spatially coincident with the 2MASS images." +" During this procedure. the images were co-registered with the 2421ASS images by matching the positions of bright stars. achieving a band-to-band registration accuracy of ~ 0.2”, "," During this procedure, the images were co-registered with the 2MASS images by matching the positions of bright stars, achieving a band-to-band registration accuracy of $\sim0.2''$ ." +These images were then processed using our MULTIPIIOT prolile-Littàng source extraction, These images were then processed using our MULTIPHOT profile-fitting source extraction +In tho νους 1991-2000 2701. emnunuierav bursts (GRBs) were detected. by the BATSE instraucut onboard the Compton Canuna-Rav Observatory (Meceanetal. 2001)).,In the years 1991-2000 2704 gamma-ray bursts (GRBs) were detected by the BATSE instrument onboard the Compton Gamma-Ray Observatory \cite{mee01}) ). + After the launch of the Switt satellite (November 20010) the frequency of detected GRBs by this instrament is cca LOO/vear (CGolirelsetal. 20053)., After the launch of the Swift satellite (November 2004) the frequency of detected GRBs by this instrument is cca 100/year \cite{swift}) ). +" Thivially, any coniparison of different databases is highly useful."," Trivially, any comparison of different databases is highly useful." + For example. iu the BATSE database - doubtlessly - three subgroups Chort. “iutermediate” and “lone” GRBs) are seCLL (Iorváthetal.2006.Chattopadhyay2007 aud references therein).," For example, in the BATSE database - doubtlessly - three subgroups (""short"", ""intermediate"" and ""long"" GRBs) are seen \cite{ho06,cha07} and references therein)." + The short aud long subgroups are αμ different phenomena (Balazsctal. 2003))., The short and long subgroups are physically different phenomena \cite{bal03}) ). + Ilowewer. coutrary to this. it is still well possible that je intermediate suberoup is not a veal plivsically aifercut separate suberoup aud it d$ occurring in ιο DATSE database due to οςe. some observational vases arising frou the DATSE trigecringao procedure (Iorváthetal. 2006)).," However, contrary to this, it is still well possible that the intermediate subgroup is not a real physically different separate subgroup and it is occurring in the BATSE database due to e.g. some observational biases arising from the BATSE triggering procedure \cite{ho06}) )." + The best choice. to proceed iu Us “bias vs. separate suberoup” controversy. is à now study of another database gained by another instrument.," The best choice, to proceed in this ""bias vs. separate subgroup"" controversy, is a new study of another database gained by another instrument." + IIence. it is highly useful to ask: Are these subgroups also seen in the Swift data-set?," Hence, it is highly useful to ask: Are these subgroups also seen in the Swift data-set?" + The purpose of this article is the statistical analysis of the Swift database. which could auswer this question.," The purpose of this article is the statistical analysis of the Swift database, which could answer this question." + We will proceed identically to the successtul statistical analvsis done on the BATSE Catalog (Horváth 1998)) leading to the discovery of the third subgroup (Mukhlerjeeetal.19985.Bagolv1998.HTorváth1999.Ilorváthetal.2006.Chattopadhyay 2007]).," We will proceed identically to the successful statistical analysis done on the BATSE Catalog \cite{ho98}) ) leading to the discovery of the third subgroup \cite{mu98,bag98,ho99,ha00,rm02,ho02,ho03,bal03,ho06,cha07}) )." + Recently. a statistical study on the Switt database - usimg the imaxiuunu likelihood method - has already shown evidence for the third subgroup CUlorvathetal. 2008)).," Recently, a statistical study on the Swift database - using the maximum likelihood method - has already shown evidence for the third subgroup \cite{ho08}) )." + The 4? fitting was not used. “because of the sull yopulation”.," The $\chi^2$ fitting was not used, ""because of the small population""." +" However. ustorically, the first evidence or the third subgroup in the BATSE database. came just. from. the 47.n metlo (IIorváth:1998}). and also the ΠΠΡΟ of 388 need not )o ΜΗ for this testing."," However, historically, the first evidence for the third subgroup in the BATSE database came just from the $\chi^2$ method \cite{ho98}) ), and also the number of 388 need not be small for this testing." +" Ποσο, In any case. one las to probe this fitting on the Swift data sample too."," Hence, in any case, one has to probe this fitting on the Swift data sample too." + In additiou. since approximately one third of he Swift’s bursts have already well determined redshifts (contrary to the BATSE’s GRBs. where ouly a few objects iad ineasured redshifts (Ramiurez-Ruiz&Feuinnore2000.Norris2002.Bagolyetal. 2003))). sole additional tests can be also done ou the samples with aud without redshifts.," In addition, since approximately one third of the Swift's bursts have already well determined redshifts (contrary to the BATSE's GRBs, where only a few objects had measured redshifts \cite{rafe00,nor02,bag03}) )), some additional tests can be also done on the samples with and without redshifts." + The paper is organized as follows., The paper is organized as follows. + The samples are defined in Section 2 - these samples are also listed iu detail a+ the eud of the article., The samples are defined in Section 2 - these samples are also listed in detail at the end of the article. + Section 2 presents the 47 fitting of these samples., Section 3 presents the $\chi^2$ fitting of these samples. + Section L discusses the results of this paper aud Section 5 stuumarizes them., Section 4 discusses the results of this paper and Section 5 summarizes them. + We define two samples from the Swift dlata-sct (Gehrelsetal. 2005)): the sample of CRBs without measured redshifts (2) aud the sample with measured redshifts., We define two samples from the Swift data-set \cite{swift}) ): the sample of GRBs without measured redshifts $z$ ) and the sample with measured redshifts. + These two samples are collected in Tables {-8 aud Tables 9-11. respectively.," These two samples are collected in Tables 4-8 and Tables 9-11, respectively." +" We compiled these tables for the couvenieuce: cach table contains the name of CRB. its BAT duration Toy. BAT flucuce at range 15150keV, BAT l-sec peak photon flux at range 1150hel and Tables 9-11 also redshitt."," We compiled these tables for the convenience; each table contains the name of GRB, its BAT duration $T_{90}$, BAT fluence at range $15-150\; keV$, BAT 1-sec peak photon flux at range $15-150\; +keV$ and Tables 9-11 also redshift." + Oulv these bursts were taken into account. of which the CRB duration was measured.," Only these bursts were taken into account, of which the GRB duration was measured." + The samples cover the period from November 2001 to the eud of February 2009: the first (last) object is CRBOL1217 (GRDBO090205)., The samples cover the period from November 2004 to the end of February 2009; the first (last) object is GRB041217 (GRB090205). +" Tables La (9-11) contain 258 (130) GRBs. aud heuce the total iuuber of GRBs. which are studied in this paper. is 38s,"," Tables 4-8 (9-11) contain 258 (130) GRBs, and hence the total number of GRBs, which are studied in this paper, is 388." + Tu what follows. we study both samples separately ane. also together as one single set Cthe whole sample”).," In what follows, we study both samples separately and also together as one single set (""the whole sample"")." +redshift fora GRB afterglow (MeZeerοἱal.|1997).,redshift for a GRB afterglow \citep{met97}. +. The clisance scale in this cosmological scenario for GRBs lias been derived frou he observec N(>P) distribution. usually ou the assumption tliat GRBs are staudard candles (PetdletouetaL1906:Wijersal.1998:Totaui1999).," The distance scale in this cosmological scenario for GRBs has been derived from the observed $N(>P)$ distribution, usually on the assumption that GRBs are standard candles \citep{pen96,wij98,tot99}." +. ναοί».Thorsett.andHarrison(L998) |ave sliown hat relaxiig die standard caudle assumption renders a broad range of mocels cousistent witli the BATSE NV(>P) relation., \citet{kru98} have shown that relaxing the standard candle assumption renders a broad range of models consistent with the BATSE $N(>P)$ relation. + Iu thisLeller. we are reporting the resuts of setting the cosmological distauce scale of GRBs. assuming a [ull luminosity funeion and using the euclidean «Εαν7 value as a distance iudi‘ator.," In this, we are reporting the results of setting the cosmological distance scale of GRBs, assuming a full luminosity function and using the euclidean $$ value as a distance indicator." + We use the BD2 sample of GRBs ¢erived [rom 5.9 vears of BATSE DISCLA data. brielly described iu Sec.," We use the BD2 sample of GRBs derived from 5.9 years of BATSE DISCLA data, briefly described in Sec." + 2., 2. + The characerization of the luminosity function aud its evolution. aud the derivation of predicted distributis of luminosity. V/V. redshift. and flux are discussed in Sec.," The characterization of the luminosity function and its evolution, and the derivation of predicted distributions of luminosity, $V/V_{max}$, redshift, and flux are discussed in Sec." + 3., 3. + Tve results for a variety of luiinosity Functions are presented in Sec., The results for a variety of luminosity functions are presented in Sec. + { and the conclusions are SULuarized in Sec., 4 and the conclusions are summarized in Sec. + 5., 5. + We are assumiug iu this paper a Hubble coustaut Πο=10 kim “Alpe | aud zero cosmological coustant., We are assuming in this paper a Hubble constant $H_o = 70$ km $^{-1}$ $^{-1}$ and zero cosmological constant. + We use a large homogeneous sample (the BD2 sample) of 1391. GRBs derived frou. BATSE DISCLA data. cousisting of the continuous data stream from the eight BATSE detectors in four euergv chaunels ou a time scale of 102[ msec (Fishinanetal.LOSO).," We use a large homogeneous sample (the BD2 sample) of 1391 GRBs derived from BATSE DISCLA data, consisting of the continuous data stream from the eight BATSE detectors in four energy channels on a time scale of 1024 msec \citep{fis89}." +. This sample is a revision. described below. of the BDI sample wlich resulted from a search of DISCLA data over the period TJD 8365—10528 (Schunidt1999).," This sample is a revision, described below, of the BD1 sample which resulted from a search of DISCLA data over the period TJD $8365-10528$ \citep{sch99}." +. The BDI sample was based on a triMDooer algorithm that used the background both before and alter tie ouset of the burst and required an excess of at least 5o over background in at least two detecto ‘sin the euergy rauge 50—300 keV. In 11e process of classilving triggers for the creation of the BD1 sample (Sclunidt.1999).. we hacl accejxed LOLS DISCLA triigeers tLat were within 230 sec of a GRB in the BATSE catalog (Meeganοἱal.1999) as genuie GRBs.," The BD1 sample was based on a trigger algorithm that used the background both before and after the onset of the burst and required an excess of at least $5\sigma$ over background in at least two detectors in the energy range $50-300$ keV. In the process of classifying triggers for the creation of the BD1 sample \citep{sch99}, we had accepted 1018 DISCLA triggers that were within 230 sec of a GRB in the BATSE catalog \citep{mee99} as genuine GRBs." + In addition. we classified another LOL DISCLA triggers as GRBs.," In addition, we classified another 404 DISCLA triggers as GRBs." + Li a subsequent revision. we have now inspected the output of the BATSE detectors over a time inte‘val of 12.000 sec arouid each o ‘the LOL GRBs not in the BATSE catalog. as wel as those in the catalog for which times o' positious differed appreciably.," In a subsequent revision, we have now inspected the output of the BATSE detectors over a time interval of 12,000 sec around each of the 404 GRBs not in the BATSE catalog, as well as those in the catalog for which times or positions differed appreciably." + In tLe process. we rejected T triggers as caused by source fluctuations. 18 turied out to be parts of othe: GBBs of long duration. aid 6 were ideitified as the soft repeater SGIARIS06-20 aud rejeced.," In the process, we rejected 7 triggers as caused by source fluctuations, 18 turned out to be parts of other GRBs of long duration, and 6 were identified as the soft repeater SGR1806-20 and rejected." + As a consequence of the revision. the BD2 sample now contains 1391 GRBs. o. whic1 1013 are listed in tie BATSE catalog. atother 377 are Classified as GRBs. and oue as a proable CRB.," As a consequence of the revision, the BD2 sample now contains 1391 GRBs, of which 1013 are listed in the BATSE catalog, another 377 are classified as GRBs, and one as a probable GRB." + For the purpose of this paper. we can cha‘acterize the BD2 sauple as folows.," For the purpose of this paper, we can characterize the BD2 sample as follows." + The 1mber of GRBs is 1391., The number of GRBs is 1391. + The sample effectively reλε...ts 2.003 years of ful sky coverage (Schmid1999).. so the rate is GOL GRBs per year.," The sample effectively represents 2.003 years of full sky coverage \citep{sch99}, so the rate is 694 GRBs per year." + The average euclideai Vl/\TP Is 0.3310.008., The average euclidean $V/V_{max}$ is $0.334\pm0.008$. +" The limitiug flux has a distribution C'(/5,,,) that has JEELL cerived as follows.", The limiting flux has a distribution $G(P_{lim})$ that has been derived as follows. + For LOL positious of fixed celestial coordinates distributed isotropically aroμις te sky. we checked every LOO sec duriug every teutl," For 104 positions of fixed celestial coordinates distributed isotropically around the sky, we checked every 100 sec during every tenth" +Stellar initial masses are controlled by the accretion of gas through disks onto the star in the protostellar phase.,Stellar initial masses are controlled by the accretion of gas through disks onto the star in the protostellar phase. + For a binary or multiple system this. process is more complex because it potentially involves the presence of circumstellar and circumbinary gas reservoirs. that control the mass distribution (??)..," For a binary or multiple system this process is more complex because it potentially involves the presence of circumstellar and circumbinary gas reservoirs that control the mass distribution \citep{Bate:1997,Ochi:2005}." + Understanding the origin of such a distribution therefore requires the observation of multiple systems. the characterisations of their masses. and of the nature of the accretion sources.," Understanding the origin of such a distribution therefore requires the observation of multiple systems, the characterisations of their masses, and of the nature of the accretion sources." + GW Orionis ts à single-line spectroscopic binary Classical T Tauri Star with an orbital period of 242 days located at «400 pe (?)??.., GW Orionis is a single-line spectroscopic binary Classical T Tauri Star with an orbital period of 242 days located at $\approx 400$ pc \citep{Mathieu:1991}. + The primary star’s mass has been estimated to be 2.5 M. and the secondary's as 0.5 M. with an expected separation of ~1 AU (circular orbit of inclination = 277)., The primary star's mass has been estimated to be 2.5 $_{\odot}$ and the secondary's as 0.5 $_{\odot}$ with an expected separation of $\sim$ 1 AU (circular orbit of inclination $\approx 27^{\circ}$ ). + Evidence of a third companion was found based on the analysis of radial velocity residuals (confirmed period of 3850 days: Latham. priv.," Evidence of a third companion was found based on the analysis of radial velocity residuals (confirmed period of 3850 days; Latham, priv." + comm.)., comm.). + The spectral energy distribution (SED) of the unresolved complete system shows a large infrared excess compared with a photosphere from a 5662 K G5 star (?) with a strong 10-microns silicate emission feature., The spectral energy distribution (SED) of the unresolved complete system shows a large infrared excess compared with a photosphere from a 5662 K G5 star \citep{Cohen:1979} with a strong 10-microns silicate emission feature. + An important near-to-mid-infrared dip in the SED has been interpreted as the signature of a circumbinary (CB) disk. whose inner part is clearing up to 3.3 AU from the star system (?).," An important near-to-mid-infrared dip in the SED has been interpreted as the signature of a circumbinary (CB) disk, whose inner part is clearing up to 3.3 AU from the star system \citep{Mathieu:1991}." +.? have attempted to simulate the interaction of the CB disk with the central system., \citet{Artymowicz:1994} have attempted to simulate the interaction of the CB disk with the central system. + Photometric time-dimming behaviour led ? to conclude that eclipses resulted from material around GW Ori B that covers the central star., Photometric time-dimming behaviour led \citet{Shevchenko:1998} to conclude that eclipses resulted from material around GW Ori B that covers the central star. + An accurate model of the disk structure is not possible without good knowledge of the stellar components of this system., An accurate model of the disk structure is not possible without good knowledge of the stellar components of this system. + We present here the first long-baseline interferometer data on GW Ori using the [OTA interferometer and succesfully obtain the first reconstructed image of a T Tauri system with astronomical-unit resolution., We present here the first long-baseline interferometer data on GW Ori using the IOTA interferometer and succesfully obtain the first reconstructed image of a T Tauri system with astronomical-unit resolution. + IOTA was a three 45cm siderostats interferometer. located on Mt. Hopkins Arizona and operated by Smithsonian Astrophysical Observatory (2)..," IOTA was a three 45cm siderostats interferometer, located on Mt. Hopkins Arizona and operated by Smithsonian Astrophysical Observatory \citep{Schloerb:2006}." + The three telescopes (A.B.C) were movable along two perpendicular axes and could occupy 17 stations offering a way to synthetize a beam with a maximum 35x15 m aperture.," The three telescopes (A,B,C) were movable along two perpendicular axes and could occupy 17 stations offering a way to synthetize a beam with a maximum $35\times15$ m aperture." + This corresponds to a resolution of =5x I2mas in the H-band., This corresponds to a resolution of $\approx 5\times12$ mas in the $H$ -band. + Observations took place during period 2003 November - 2005 November., Observations took place during period 2003 November - 2005 November. + Pour array configurations were used to pave the UV plane., Four array configurations were used to pave the UV plane. + The observations were made in the H band using the IONIC3 instrument (2).., The observations were made in the $H$ band using the IONIC3 instrument \citep{Berger:2003}. + IONIC3 allowed each of the three baselines to be combined separately. which provided six interferograms.," IONIC3 allowed each of the three baselines to be combined separately, which provided six interferograms." + Fringe patterns were temporally encoded. detected. and locked with a PICNIC detector array (??)..," Fringe patterns were temporally encoded, detected, and locked with a PICNIC detector array \citep{Pedretti:2004p5147,Pedretti:2005}." + We used the data reduction method deseribed in? to extract squared visibilities (V) and closure phases (CP) from the interferograms., We used the data reduction method described in \cite{Monnier:2004p6916} to extract squared visibilities $V^2$ ) and closure phases (CP) from the interferograms. + Instrumental V and CP effects were, Instrumental $V^2$ and CP effects were +zones having undergone truncations (mergers) over a range of metallicity.,zones having undergone truncations (mergers) over a range of metallicity. + The model also allows for mass loss to occur at a rate proportional to the star formation rate by defining an elective vield., The model also allows for mass loss to occur at a rate proportional to the star formation rate by defining an effective yield. + Fie., Fig. + 5 is taken from (he paper of Ivezic et al. (, 5 is taken from the paper of Ivezic et al. ( +2008) (bottom right of their fig.,2008) (bottom right of their fig. + 7)., 7). + The points with error bars show the metallicity distribution of halo stars with height above the plane |Z |=5-7 kpc., The points with error bars show the metallicity distribution of halo stars with height above the plane $\mid Z\mid$ =5-7 kpc. + The blue curve shows the predicted metallicity distribution of the left over gas aller (he collisions have taken. place., The blue curve shows the predicted metallicity distribution of the left over gas after the collisions have taken place. + Because the model does not predict. either ihe metallicity distribution or the mass of the stars formed. diving the mergers we have assumed that the post-merger stellar and cluster distribution is (he same as that of the left over gas and used a gas to star formation efficiency of ~0.07 to estimate the mass of the stars ancl clusters., Because the model does not predict either the metallicity distribution or the mass of the stars formed during the mergers we have assumed that the post-merger stellar and cluster distribution is the same as that of the left over gas and used a gas to star formation efficiency of $\sim 0.07$ to estimate the mass of the stars and clusters. + The solid black line (arbitrary normalization) shows the distribution of metallicitv of the stars formed prior to the mergers., The solid black line (arbitrary normalization) shows the distribution of metallicity of the stars formed prior to the mergers. + It was calculated using exactly the sme chemical evolution model given in H04., It was calculated using exactly the same chemical evolution model given in H04. +" The model parameters are log(p,rr/Z.)=—0.3. log(Z./Z.)=—1.50. sud oy,=0.32."," The model parameters are $_{eff}/Z_{\odot}) +=-0.3$ , $Z_{c}/Z_{\odot})=-1.50$, and $\sigma_{blue}=0.32$." + Using the above star formation elliciency. (he ratio of the mass of stars formed during (he mergers to those formed prior to the collisions is ~0.8.," Using the above star formation efficiency, the ratio of the mass of stars formed during the mergers to those formed prior to the collisions is $\sim 0.8$." +" This number will also depend on the value assumed [for p,jj.", This number will also depend on the value assumed for $_{eff}$. + For illustrative purposes here and to minimize parameters we have kept the effective vield the same as the true vield (ie. 0.5Z.)., For illustrative purposes here and to minimize parameters we have kept the effective yield the same as the true yield (i.e. $_{\odot}$ ). + The stars formed prior to the merger are clearly more metal poor than the post-erger population and apparentlv do not show up in (he data in Fig., The stars formed prior to the merger are clearly more metal poor than the post-merger population and apparently do not show up in the data in Fig. + 5 although no altempt was made to fit more (han one component to the data., 5 although no attempt was made to fit more than one component to the data. + These stars are expected {ο have different kinematic properties since (hey would not have been affected in the same wav bv the collisions which produced the burst of star formation and clusters., These stars are expected to have different kinematic properties since they would not have been affected in the same way by the collisions which produced the burst of star formation and clusters. + In fact. (hese stars mav belong to the second blue halo population which is more metal poor and with different kinematics identified in a deeper survey by Carollo et al. (," In fact, these stars may belong to the second blue halo population which is more metal poor and with different kinematics identified in a deeper survey by Carollo et al. (" +2007).,2007). + Note (hat a prediction of this model is that. generally the stars enclosed by (he blue curve should have (he same kinematics and spatial distribution as the blue (halo) globular clusters since they are assumed (ο have formed at the same time., Note that a prediction of this model is that generally the stars enclosed by the blue curve should have the same kinematics and spatial distribution as the blue (halo) globular clusters since they are assumed to have formed at the same time. + Further these clusters should belong to the ‘voune halo eroup of Zinn (1993)., Further these clusters should belong to the `young' halo group of Zinn (1993). + Fie., Fig. + 6 [rom the top right of fig 7 of Ivezie et al., 6 from the top right of fig 7 of Ivezic et al. + shows a similar plot but now with stars from |Z|=1.5—2.0 kpe., shows a similar plot but now with stars from $\mid Z\mid=1.5-2.0$ kpc. + Here the red curve is the chemical model metallicity prediction asstuned for stars and red clusters formed curing (he second set of collisions., Here the red curve is the chemical model metallicity prediction assumed for stars and red clusters formed during the second set of collisions. + Instead of using a Gaussian to determine the metallicity distribution of (he stus/clusters formed during the collisions. we have used an extreme value distribution function which has the shape of an asvmmnietrical Gaussian.," Instead of using a Gaussian to determine the metallicity distribution of the stars/clusters formed during the collisions, we have used an extreme value distribution function which has the shape of an asymmetrical Gaussian." + ie. the function fofHO4 is replaced by, i.e. the function f ofH04 is replaced by +temperature. aud velocity structure.,"temperature, and velocity structure." + We use f1ο Monte-Carlo radiative rauster code RATRAN (?) to calculate equilibriun pomuatious for cach rotational level of the CO molecle and generate a sky-projeced nuage of the CO(3-2) lune enüssion at a eiven viewing ecomctry iu foreach model, We use the Monte-Carlo radiative transfer code RATRAN \citep{hog00} to calculate equilibrium populations for each rotational level of the CO molecule and generate a sky-projected image of the CO(3-2) line emission at a given viewing geometry $i$ for each model. + M ceopare these simulatedinodelsdir etluiothdjulyli, We compare these simulated models directly to the data in the Fourier domain. + (eio Rog Hhudebelow dade πα μαμα s," In order to sample the model images at the appropriate spatial frequencies for comparison with the SMA data, we use the MIRIAD task." +tatistic for cacli model compared with the «ata using he real aud 1naginary simulated visibilities., We then compute the $\chi^2$ statistic for each model compared with the data using the real and imaginary simulated visibilities. + Due to he high comp.παολα]. iuteusitv of the molecular line radiative transer. it is prohibitively tie-incusive to eenerate very aree and welbsuupled exids «X models ;or the 47» comparison.," Due to the high computational intensity of the molecular line radiative transfer, it is prohibitively time-intensive to generate very large and well-sampled grids of models for the $\chi^2$ comparison." + Dustead. we move fron coarscly-sunupled ervids that cover large regions of xuaueter space to progressively more refined (but still suwll) exids Oo avoid lucis atf a local münimuun.," Instead, we move from coarsely-sampled grids that cover large regions of parameter space to progressively more refined (but still small) grids to avoid landing at a local minimum." + Ilow«OT. this jus the result that the degeneracies of the xwanieter spatὉ are poorly οlaractorized.," However, this has the result that the degeneracies of the parameter space are poorly characterized." + A discussion of these degsneracies is meluded in Section 1.1 below., A discussion of these degeneracies is included in Section \ref{sec:degen} below. + Tje best-fit parameters for )oth. types of models are prescuted in Table , The best-fit parameters for both types of models are presented in Table \ref{tab:hires_best}. . +Their temperature and density structures are ploted in Figure 6.., Their temperature and density structures are plotted in Figure \ref{fig:temp_dens}. + Note that the nudaue temperatures for the similarity solution models are likely much lower than indicated: the power-law telerature representation paramieterizes oulv the radial depησος of temperature in the upper disk lavers from whicT the optically thick CO(3-2) cinission arises., Note that the midplane temperatures for the similarity solution models are likely much lower than indicated; the power-law temperature representation parameterizes only the radial dependence of temperature in the upper disk layers from which the optically thick CO(3-2) emission arises. + Twe A? values for the similarity solutions are lower thari for the D'Alessio et al., The $\chi^2$ values for the similarity solutions are lower than for the D'Alessio et al. + models: this may be due to eracieuts between eas and dust properties that influence the D'Alessio et al., models; this may be due to gradients between gas and dust properties that influence the D'Alessio et al. + model ft but. not the similarity solujon models., model fit but not the similarity solution models. + A sample of channel maps comparing the data with the two classes of models are preseuted in Figures { and 5.., A sample of channel maps comparing the data with the two classes of models are presented in Figures \ref{fig:model_chmap_hd} and \ref{fig:model_chmap_twh}. + From the residuals in the D'Alessio ct al., From the residuals in the D'Alessio et al. +" inodel of TW Ίνα, there is evidence of a mistach in the temperature eradieut between the model aud he data: the resimals are systematically wore positive near the disk ceuter and negative farther frou the star."," model of TW Hya, there is evidence of a mismatch in the temperature gradient between the model and the data: the residuals are systematically more positive near the disk center and negative farther from the star." + For IID 163296. the differcuce is more subtle: the resichals are small and appareutly spatially random (with he exception of sole positive enissionu seen near a velocity of but not near the corresponding positina in the mirror half of the line).," For HD 163296, the difference is more subtle: the residuals are small and apparently spatially random (with the exception of some positive emission seen near a velocity of $^{-1}$ but not near the corresponding position in the mirror half of the line)." + It should be noted that the CO abundance derived for lis source is extremely low. ne lhyee orders of nsu the staydard ," It should be noted that the CO abundance derived for this source is extremely low, nearly three orders of magnitude below the standard value of $10^{-4}$." +T logye overestimate of the teniperative in the upper disk lavers., The reason for this is most likely an overestimate of the temperature in the upper disk layers. + Iu the absence of better information. this SED model was created with a very ow turbulent linewidtli (~5Omame-ss 2) ane correspondingly little stirring of large dust erains above the inicplajc.," In the absence of better information, this SED model was created with a very low turbulent linewidth $\sim$ $^{-1}$ ) and correspondingly little stirring of large dust grains above the midplane." + The addition of turbulent linewidth comparable to the best-fit value for the CO lines would substautialv reduce settling aud lower the teniperaure of the upper disk lavers as more of the mass is placed in large dust exams., The addition of a turbulent linewidth comparable to the best-fit value for the CO lines would substantially reduce settling and lower the temperature of the upper disk layers as more of the mass is placed in large dust grains. + Such a model is under development by Qi et al. (, Such a model is under development by Qi et al. ( +in prep). and can also aid in explaining the spatial distribution of multiple €'O transitions and CO isotopologue cussion frou this disk.,"in prep), and can also aid in explaining the spatial distribution of multiple CO transitions and CO isotopologue emission from this disk." + One important outcome of the modeling process is t1ο consistency in the measurement of turbulent linewidhi in cach source for the two types of models. despite t1ο differeuces in their treatinent of temperature.," One important outcome of the modeling process is the consistency in the measurement of turbulent linewidth in each source for the two types of models, despite the differences in their treatment of temperature." + Iu bohi vpes of models for ID 163296. the best-fit model wihi urbuleuce fits the data better than a comparable nioel without turbulence at the ~36 level.," In both types of models for HD 163296, the best-fit model with turbulence fits the data better than a comparable model without turbulence at the $\sim3\sigma$ level." +" If he turbulent inewidth is fixed at Onuuss+ in the similarity solutina and the temperature allowed to vary to compcusate. t1C xumneter Tiu, luust increase to KI: even then. tle 4? or a model with higher temperature and 10 turbulence is a poorer fit than the best-fit model with turbulence at he ~30 level (the line profile for this model is plotted in Figure 1)."," If the turbulent linewidth is fixed at $^{-1}$ in the similarity solution and the temperature allowed to vary to compensate, the parameter $T_{100}$ must increase to K; even then, the $\chi^2$ for a model with higher temperature and no turbulence is a poorer fit than the best-fit model with turbulence at the $\sim3\sigma$ level (the line profile for this model is plotted in Figure \ref{fig:model_chmap_hd}) )." + The TW ναdata are consistent with uo urbuleut lineidtli whatsoever., The TW Hyadata are consistent with no turbulent linewidth whatsoever. +The Perseus Cluster is one of the nearest galaxy clusters and is the brightest. X-ray cluster in the sky.,The Perseus Cluster is one of the nearest galaxy clusters and is the brightest X-ray cluster in the sky. + The cluster and its central galaxy NGC 1275 have been the focus of intense study for many vears. at N-ray. optical. Επ. ane millimetre wavelengths.," The cluster and its central galaxy NGC 1275 have been the focus of intense study for many years, at X-ray, optical, IR and millimetre wavelengths." + The first molecular detections were of CO rotational emission. towards the centre of NGC ," The first molecular detections were of CO rotational emission towards the centre of NGC 1275 \citep{Laza89, Mira89, Reut93, Brai95, +Inou96, Brid98, Lim08}." +CO emission also extends to some tens of kpe from the central galaxy (27???) and is strongly correlated with the filamentary structure observed in Ho (2???) within the ho eas detected in N-rays at 0.5 keV. (2)...," Observations have now demonstrated that CO emission also extends to some tens of kpc from the central galaxy \citep{Salo06,Salo08a,Salo08b,Salo11} and is strongly correlated with the filamentary structure observed in $\alpha$ \citep{Hu83, +Cowi83,Cons01} within the hot gas detected in X-rays at 0.5 keV \citep{Fabi08}." + Phe Hà structure is also correlated with warm I» emission (?72)..," The $\alpha$ structure is also correlated with warm $_{2}$ emission \citep{Edge02,Wilm02}." + Some of the molecular gas towards the cluster must be at high density (e10) )," Some of the molecular gas towards the cluster must be at high density $\geqslant +10^{4}$ $^{-3}$ )." + ?/ have made the first. detection. of the high density tracer LICN(3-2) emission towards the centre of NGC 1275., \citet{Salo08a} have made the first detection of the high density tracer HCN(3-2) emission towards the centre of NGC 1275. + The nature of the filamentary structure is the subject of current discussion., The nature of the filamentary structure is the subject of current discussion. + ? note two possibilities: either that the CO filaments form far from the ealaxy’s centre [rom upliftecl warm gas. eventually falling back (τὸ. or that the molecular gas is entrained and dragged out of the galaxy by rising hot gas.," \citet{Salo11} note two possibilities: either that the CO filaments form far from the galaxy's centre from uplifted warm gas, eventually falling back \citep{Reva08}, or that the molecular gas is entrained and dragged out of the galaxy by rising hot gas." + Eviclenthy. further observations of molecular gas may help to determine its origin.," Evidently, further observations of molecular gas may help to determine its origin." + In this paper. we present observations of emission lines of CN(2-1). (3-2) and C2 11(3-2) towards the central galaxy and also towards a position 20” to the cast where there is strong CO emission in the associated filamentary structure.," In this paper, we present observations of emission lines of CN(2-1), $^{+}$ (3-2) and $_{2}$ H(3-2) towards the central galaxy and also towards a position $''$ to the east where there is strong CO emission in the associated filamentary structure." + ‘These three species were identified in a theoretical study (7) as tracers of regions inlluenced. by the dissipation of turbulence and waves. heating the gas anc accelerating cosmic ravs (see also ??7)).," These three species were identified in a theoretical study \citep{Baye10c} as tracers of regions influenced by the dissipation of turbulence and waves, heating the gas and accelerating cosmic rays (see also \citealt{Craw92, Pope08a}) )." + 7? developed: models. of the optical ancl infrared emission filamentary— regions in order to, \citet{Ferl09} developed models of the optical and infrared emission filamentary regions in order to +"would require the introduction of too many spots, which lowers the global precision of the parameters of the best fit.","would require the introduction of too many spots, which lowers the global precision of the parameters of the best fit." + This fit is obtained for an inclination of , This fit is obtained for an inclination of $40^{+20}_{-10}{}^\circ$. +"The equatorial rotation period is 4.30£0.05 days and the 40720"".differential rotation rate 5*2? We have used the wavelet technique to confirm the rotation period of the surface of the star (?)..", The equatorial rotation period is $4.30\pm 0.05$ days and the differential rotation rate $5^{+10}_{-5}$ We have used the wavelet technique to confirm the rotation period of the surface of the star \citep{1998BAMS...79...61T}. + We have used the Morlet wavelet (a moving Gaussian envelope with a varying width) to produce the wavelet power spectrum shown in Fig. 8.., We have used the Morlet wavelet (a moving Gaussian envelope with a varying width) to produce the wavelet power spectrum shown in Fig. \ref{wavelet}. + This spectrum is a representation of the correlation between the wavelet with a given frequency (y-axis) along time (x-axis)., This spectrum is a representation of the correlation between the wavelet with a given frequency (y-axis) along time (x-axis). +" As showed in ?,, the strength of this method is to see the evolution with time of the power, as well as to resolve the uncertainty between the fundamental period and the first harmonic that could happen, as in the solar case (?).."," As showed in \citet{2010A&A...511A..46M}, the strength of this method is to see the evolution with time of the power, as well as to resolve the uncertainty between the fundamental period and the first harmonic that could happen, as in the solar case \citep{2008arXiv0810.1803M}." + The left panel of the plot shows the presence of power in the wavelet spectrum for periods between 4 and 5 days., The left panel of the plot shows the presence of power in the wavelet spectrum for periods between 4 and 5 days. + This power excess is observed all along the 149 days of observation., This power excess is observed all along the 149 days of observation. + When collapsed over the observation time (right panel) we see the accumulation of power at 4.3 days well above the 9596 confidence level limit., When collapsed over the observation time (right panel) we see the accumulation of power at 4.3 days well above the $\%$ confidence level limit. +" The reliability of the result depends on two factors: the cone of influence, which is related to the fact that the periodicity has to be at least one quarter of the total length of the time- and a confidence level corresponding to a of probability that the peak observed is not due to noise."," The reliability of the result depends on two factors: the cone of influence, which is related to the fact that the periodicity has to be at least one quarter of the total length of the time-series and a confidence level corresponding to a of probability that the peak observed is not due to noise." +" Thus, using this methodology we determine that the rotation period of HD 170987 is ~4.3 days (or 2.7 wHz), which is compatible with the analysis of the low-frequency PSD described above."," Thus, using this methodology we determine that the rotation period of HD 170987 is $\sim$ 4.3 days (or 2.7 $\mu$ Hz), which is compatible with the analysis of the low-frequency PSD described above." + It is very clear that the power present around 2.7 μΗΖ is concentrated between the 30th and the 70th day (black shaded region) as well as during another small period around the 100th day., It is very clear that the power present around 2.7 $\mu$ Hz is concentrated between the 30th and the 70th day (black shaded region) as well as during another small period around the 100th day. + This agrees with the results obtained with the PSD., This agrees with the results obtained with the PSD. +" Given the value of the rotation period and the v sini, we can deduce the inclination angle i = 50°""19."," Given the value of the rotation period and the v $\sin i$, we can deduce the inclination angle $i$ = $50\degr \;^{+20}_{-13}$." +" Using different methods, we have estimated the global parameters of the acoustic modes of HD 170987, such as the location of the p-mode bump, the mean large spacing, and the maximum bolometric amplitude per radial mode."," Using different methods, we have estimated the global parameters of the acoustic modes of HD 170987, such as the location of the p-mode bump, the mean large spacing, and the maximum bolometric amplitude per radial mode." + To evaluate the possible presence of p-mode oscillations in the spectrum we start by analyzing a smoothed version of the PSD., To evaluate the possible presence of p-mode oscillations in the spectrum we start by analyzing a smoothed version of the PSD. + We smoothed the PSD in the range 200 to 8000 uHz with a Gaussian running mean with a width of 200 uHz., We smoothed the PSD in the range 200 to 8000 $\mu$ Hz with a Gaussian running mean with a width of 200 $\mu$ Hz. +" The reason not to include the low-frequency part of the spectrum is that this region of the PSD mainly bears the signatures of the slow trends in the data and of stellar activity (rotation), which is already explained in Sect. ??.."," The reason not to include the low-frequency part of the spectrum is that this region of the PSD mainly bears the signatures of the slow trends in the data and of stellar activity (rotation), which is already explained in Sect. \ref{sectrot}." + The smoothed PSD is shown in Fig. 9.., The smoothed PSD is shown in Fig. \ref{back}. +" Two clear bumps are seen in the spectrum, one around 300 and one around 1000 wHz."," Two clear bumps are seen in the spectrum, one around 300 and one around 1000 $\mu$ Hz." + The bump around 1000 Hz could originate from the p-mode oscillations (as it corresponds, The bump around 1000 $\mu$ Hz could originate from the p-mode oscillations (as it corresponds +(Fig.,(Fig. + 6cc). picking up the eastern side of the cavity and the eastern core.," \ref{pvplots}c c), picking up the eastern side of the cavity and the eastern core." +" From this plot. it seems that there are two structures. a velocity gradient associated with the eastern core. of ~L5 im a region of 7"", and à curve structure associated with the cavity."," From this plot, it seems that there are two structures, a velocity gradient associated with the eastern core, of $\sim1.5$ in a region of $''$, and a curve structure associated with the cavity." + Note that the curve structure seen in the PV-plot of Fig., Note that the curve structure seen in the PV-plot of Fig. + 6ce suggests that the cavity is expanding., \ref{pvplots}c c suggests that the cavity is expanding. + Overall it seems that both cuts. at PA.=90° and ΡΑ.Ξ140. reveal expanding motions. suggesting that these motions could be produced by a combination of stellar winds. radiation. and/or molecular outflows from the central cluster.," Overall it seems that both cuts, at $=90\degr$ and $=140\degr$, reveal expanding motions, suggesting that these motions could be produced by a combination of stellar winds, radiation, and/or molecular outflows from the central cluster." + Hence. the 55142 cluster seems to be in process of disrupting the natal cloud.," Hence, the 5142 cluster seems to be in process of disrupting the natal cloud." + However. we will not further discuss the kinematies of the region since it is not the aim of this paper.," However, we will not further discuss the kinematics of the region since it is not the aim of this paper." + We studied the chemical environment of 55142. by analyzing the column density of several molecular species., We studied the chemical environment of 5142 by analyzing the column density of several molecular species. + We used the (1-0) (this work). «οἱ. and (2.2) (from Zhangetal. 2002)). and (1-0) and A(1-0) (from Hunteretal. 1999)) data.," We used the (1–0) (this work), (1,1) and (2,2) (from \citealt{zhang2002}) ), and (1–0) and (1–0) (from \citealt{hunter1999}) ) data." + In order to properly compare the emission of all the molecules. we convolved theN-H-..NH3..HCO™.. and echannel maps to obtain a final circular beam of ~4’.," In order to properly compare the emission of all the molecules, we convolved the, and channel maps to obtain a final circular beam of $\sim4''$." +" We computed the column density maps by extracting the spectra for positions in a grid of 1”xI"".", We computed the column density maps by extracting the spectra for positions in a grid of $1''\times1''$. +" Using CLASS we fitted the hyperfine structure of each spectrum for -(1-0) and (OL.D). and a single Gaussian for the (2.2), (1-0)and (1-0)."," Using CLASS we fitted the hyperfine structure of each spectrum for (1–0) and (1,1), and a single Gaussian for the (2,2), (1–0) and (1–0)." + We fitted only those positions with an intensity greater than 5o for .((1-0) and «οὈ Ἡ order to ensure we are detecting all the hyperfine components. whereas for the other molecular species we fitted the spectra with an intensity greater than 4c.," We fitted only those positions with an intensity greater than $\sigma$ for (1–0) and (1,1) in order to ensure we are detecting all the hyperfine components, whereas for the other molecular species we fitted the spectra with an intensity greater than $\sigma$." + In the following sections we show the method used to compute the column density for each molecule., In the following sections we show the method used to compute the column density for each molecule. + The main results are summarized in Table 2.., The main results are summarized in Table \ref{coldens}. + We used the hypertine structure fitting program in CLASS (Forveille.Guilloteau.&Lucas1989) adopting the hyperfine frequencies given in Casellietal.(1995) to determine theeysp.. the intrinsic line widths. total optical depths. and excitation temperatures (7..)) in each position of the grid.," We used the hyperfine structure fitting program in CLASS \citep*{forveille1989} adopting the hyperfine frequencies given in \citet{caselli1995} to determine the, the intrinsic line widths, total optical depths, and excitation temperatures ) in each position of the grid." + The value of wwas derived assuming a filling factor of I., The value of was derived assuming a filling factor of 1. + As shown in Table |.. the excitation temperature.Τα. derived from the hyperfine fits in the eastern core. is in the range ~ 14-16 K. while hhas lower values. around - 10-15 K and -δ-θ K. for the western and central cores. respectively.," As shown in Table \ref{hfspar}, the excitation temperature, derived from the hyperfine fits in the eastern core, is in the range $\sim$ 14–16 K, while has lower values, around $\sim$ 10–12 K and $\sim$ 8–9 K, for the western and central cores, respectively." +" The results obtained from the fits indicate that the eemission is essentially optically thin for most of the region (Tyo,=0.3-0.6).", The results obtained from the fits indicate that the emission is essentially optically thin for most of the region $\tau_{\mathrm{TOT}}\simeq$ 0.3–0.6). + However the optical depth in the western core reaches higher values. around τοιz1.5-2.," However the optical depth in the western core reaches higher values, around $\tau_{\mathrm{TOT}}\simeq$ 1.5–2." +" We calculated the ccolumn density. corrected for theprimary beam response. following the expression given in Casellietal.(2002b).. and approximating the partition. function. to Οοι(AT.ΠΡ)~0.3473T4. where K is the Boltzmann constant. 7., the excitation temperature. / is the Planck constant. and B ts the rotational constant ofNH."," We calculated the column density, corrected for theprimary beam response, following the expression given in \citet{caselli2002b}, and approximating the partition function to $Q_{\mathrm{rot}}\simeq(kT_{\mathrm{ex}}/hB)\sim0.4473~T_{\mathrm{ex}}$, where $k$ is the Boltzmann constant, $T_{\mathrm{ex}}$ the excitation temperature, $h$ is the Planck constant, and $B$ is the rotational constant of." +.. Figure 7aa shows the resulting ccolumn density map., Figure \ref{fcoldens}a a shows the resulting column density map. + Clearly. we found important variation in the ccolumn density in 55142.," Clearly, we found important variation in the column density in 5142." +" The highest value of the ecolumn density. 3x10""em7. is reached in the western core."," The highest value of the column density, $3\times10^{13}$, is reached in the western core." + Toward the eastern core we found values of the ecolumn density around ~1x10!em... while the ccolum density has the lowest values. around -|-- 5x10)? em7?.. toward the millimeter condensation. ttoward the central core (see Table 2)).," Toward the eastern core we found values of the column density around $\sim1\times10^{13}$, while the column density has the lowest values, around $\sim$ $\times10^{12}$ , toward the millimeter condensation, toward the central core (see Table \ref{coldens}) )." + The values found in the western and eastern cores are in good agreement with the ccolumn densities reported by Pirogovetal.(2003.2007). and Fontanietal.(2006) for dense molecular cloud cores with massive stars and star clusters. and for a sample of high-mass protostellar candidates. respectively.," The values found in the western and eastern cores are in good agreement with the column densities reported by \citet{Pirogov2003,Pirogov2007}, and \citet{Fontani2006} for dense molecular cloud cores with massive stars and star clusters, and for a sample of high-mass protostellar candidates, respectively." + In addition. the values of the ccolumn density found in the western and eastern cores of 55142 are also consistent with those reported in recent studies conducted toward massive star-forming regions observed with interferometers citealtpalau2007.beuther2009)). but those obtained in the central core are clearly below.," In addition, the values of the column density found in the western and eastern cores of 5142 are also consistent with those reported in recent studies conducted toward massive star-forming regions observed with interferometers \\citealt{palau2007,beuther2009}) ), but those obtained in the central core are clearly below." + It is important to emphasize the difference of | order of magnitude in the ccolumn density in the central core compared to the western and eastern cores., It is important to emphasize the difference of 1 order of magnitude in the column density in the central core compared to the western and eastern cores. + The uncertainty in the ccolumn density 15 of the order of 25-50 %.. and it has been estimated taking into account the uncertainty in the output parameters of CLASS and theuncertainty in the calibration.," The uncertainty in the column density is of the order of 25–50 , and it has been estimated taking into account the uncertainty in the output parameters of CLASS and theuncertainty in the calibration." +3. we describe in detail how the evelic spectrum. can be computed for pulsar observations. and. present an example using actual data.,"\ref{sec:pulsar}, we describe in detail how the cyclic spectrum can be computed for pulsar observations, and present an example using actual data." + Finally. Section 4 shows how the pulsar evelic spectrum can be used to measure and correct for LSAL scattering. and discusses possible future applications of these methocis.," Finally, Section \ref{sec:apps} shows how the pulsar cyclic spectrum can be used to measure and correct for ISM scattering, and discusses possible future applications of these methods." + We begin with a brief overview of stochastic processes and spectral analysis. to establish. terminology.," We begin with a brief overview of stochastic processes and spectral analysis, to establish terminology." + This is followed by a introduction of the main features of evcelic spectral anlvsis., This is followed by a introduction of the main features of cyclic spectral anlysis. + Phe more rigorous treatments presented by 2 for stochastic processes and 2 for evelie spectra are useful references., The more rigorous treatments presented by \citet{papoulis} for stochastic processes and \citet{gardner:book} for cyclic spectra are useful references. + While we frame the discussion in terms of continuous-time functions. the discretization of the following equations is straightforwarel.," While we frame the discussion in terms of continuous-time functions, the discretization of the following equations is straightforward." + A general stochastic signal. .e(£). can largely be characterized by its second-order statistics.," A general stochastic signal, $x(t)$, can largely be characterized by its second-order statistics." + In the time domain. these are correlations. defined here svmmoetrically: Ilere. the expectation value represents an average over many realizations of the signal.," In the time domain, these are correlations, defined here symmetrically: Here, the expectation value represents an average over many realizations of the signal." +Sfafionary processes are those whose correlation function depends only on the time dillerence 7 between any two points and not explicitly on the time /., processes are those whose correlation function depends only on the time difference $\tau$ between any two points and not explicitly on the time $t$. + While the signals themselves have rancom variation versus time. their statistics are constant.," While the signals themselves have random variation versus time, their statistics are constant." +" The signal can alternately be characterized. by the power spectrum S,(0). which is the Fourier transform of the correlation. function C'(r)."," The signal can alternately be characterized by the power spectrum $S_x(\nu)$, which is the Fourier transform of the correlation function $C_x(\tau)$." + For ergodic signals. the correlation function can be estimated from a single realization of the signal via a time average: This forms the basis for practical spectral analysis of random signals.," For ergodic signals, the correlation function can be estimated from a single realization of the signal via a time average: This forms the basis for practical spectral analysis of random signals." + In practice. both creodicity ancl stationarity are almost always assumed. a priori. since one usually has only one realization of a signal.," In practice, both ergodicity and stationarity are almost always assumed a priori, since one usually has only one realization of a signal." + Due to the Fourier-pair uncertainty relations. the spectral resolution Av is limited to approximately Lt or larger.," Due to the Fourier-pair uncertainty relations, the spectral resolution $\Delta\nu$ is limited to approximately $T^{-1}$ or larger." + In radio astronomy. .r(/) is the bascband voltage. a quantity proportional to the incident radio wave's electric field. mixed (frequencev-shifted) to near zero frequency.," In radio astronomy, $x(t)$ is the baseband voltage, a quantity proportional to the incident radio wave's electric field, mixed (frequency-shifted) to near zero frequency." + Early digital radio spectrometers often explicitly evaluated Eqn., Early digital radio spectrometers often explicitly evaluated Eqn. + 2 using dedicated: hardware., \ref{eqn:acf} using dedicated hardware. +" ln. modern systems. S,(27) is usually computed. using a fast Fourier transform. (ΕΕΕ) of ÁO)."," In modern systems, $S_x(\nu)$ is usually computed using a fast Fourier transform (FFT) of $x(t)$." + In order for a pulse to be resolved in time. Z7 must be small compared. to the pulse width.," In order for a pulse to be resolved in time, $T$ must be small compared to the pulse width." + For pulsars. this puts a limit on the finest achievable frequency resolution of Av©(PAS)* where P is the pulse period and Ae is the pulse width in turns.," For pulsars, this puts a limit on the finest achievable frequency resolution of $\Delta \nu \gtrsim (P\Delta\phi)^{-1}$ where $P$ is the pulse period and $\Delta \phi$ is the pulse width in turns." + An interesting ¢lass of nonstationary signal are those whose statistics vary periodically with time., An interesting class of nonstationary signal are those whose statistics vary periodically with time. + These are known ascyclosiationary signals and their. correlations exhibit periodicity: Lt is important to note that although (ήν7) is periodic in /. it is not generally periodic in rz. and .r(/) itself is not necessarily a periodic function.," These are known as signals and their correlations exhibit periodicity: It is important to note that although $C_x(t,\tau)$ is periodic in $t$, it is not generally periodic in $\tau$, and $x(t)$ itself is not necessarily a periodic function." + Simple examples of evclostationary signals can be obtained: by periodically amplituce- or frequency-mocdulating a stationary noise process., Simple examples of cyclostationary signals can be obtained by periodically amplitude- or frequency-modulating a stationary noise process. +" In this paper we will sometimes use the quantity pulse phase ὦ=££P in place of fas an independent variable in expressions such as €',.(0.7)."," In this paper we will sometimes use the quantity pulse phase $\phi = t/P$ in place of $t$ as an independent variable in expressions such as $C_x(\phi,\tau)$." + The evelic analog of the power spectrum can be obtained by Fourier transforming (1τὸ) along both the | and 7 axes: This quantity is known as the ancl it is a function of two frequency variables.," The cyclic analog of the power spectrum can be obtained by Fourier transforming $C_x(t,\tau)$ along both the $t$ and $\tau$ axes: This quantity is known as the and it is a function of two frequency variables." + Phe frequency jp is conjugate to 7 exactly as in the standard. power spectrum., The frequency $\nu$ is conjugate to $\tau$ exactly as in the standard power spectrum. +" The frequency a is conjugate to £. and takes on the discrete values a,=nfl it is computed here as a Fourier series rather than a continuous Fourier. transform."," The $\alpha$ is conjugate to $t$, and takes on the discrete values $\alpha_n += n/P$ – it is computed here as a Fourier series rather than a continuous Fourier transform." +" In the stationary signal case. S,(via)—0 for a#0."," In the stationary signal case, $S_x(\nu;\alpha)=0$ for $\alpha\neq0$." + The periodic correlation can be estimated from a single signal realization similarly to Eqn., The periodic correlation can be estimated from a single signal realization similarly to Eqn. +" 2. by folding"" the correlations modulo the periodicity P: ‘This again assumes ergodicitv of the signal. over NV periods."," \ref{eqn:acf} by “folding” the correlations modulo the periodicity $P$: This again assumes ergodicity of the signal, over $N$ periods." + In this computation. the integration time 7 is given by INP. the number of periods folded.," In this computation, the integration time $T$ is given by $NP$, the number of periods folded." + The integration time sets an ultimate limit on the range of 7 that can be measured. and again the spectral resolution is limited: to AvTOTi.," The integration time sets an ultimate limit on the range of $\tau$ that can be measured, and again the spectral resolution is limited to $\Delta \nu \gtrsim T^{-1}$." + Llowever. in constrast with Eqn. 2.," However, in constrast with Eqn. \ref{eqn:acf}," + 2 is not constrained by the pulse width. as the nonstationarity has alreacly been correctly taken into account in I5qn. 5..," $T$ is not constrained by the pulse width, as the nonstationarity has already been correctly taken into account in Eqn. \ref{eqn:corrsum}. ." + This decouples the pulse phase resolution from the frequency resolution., This decouples the pulse phase resolution from the frequency resolution. + ]t is easy to see that various symmetry. relationships exist among these quantities., It is easy to see that various symmetry relationships exist among these quantities. + In our symmetric formulation. ον.vr)=οδειτ).," In our symmetric formulation, $C_x(t,-\tau)=C^*_x(t,\tau)$." + Similarly. Sov:a)=Si(eia).," Similarly, $S_x(\nu;-\alpha)=S^*_x(\nu;\alpha)$." + A useful intermediate. quantity is the SG) that is obtained by Fourier transforming C'i(f.r) with respect to 7 alone.," A useful intermediate quantity is the $S_x(\nu,t)$ that is obtained by Fourier transforming $C_x(t,\tau)$ with respect to $\tau$ alone." +" By symmetry. S,(o.£) ispurely real-valued. and therefore is straightforward to visualize."," By symmetry, $S_x(\nu,t)$ ispurely real-valued, and therefore is straightforward to visualize." +" S,(o.1) is superficially similar to signal power as a function of time ancl frequeney."," $S_x(\nu,t)$ is superficially similar to signal power as a function of time and frequency." + Llowever as discussed below. it also contains information about the signal phase. and thus is not strictly positive.," However as discussed below, it also contains information about the signal phase, and thus is not strictly positive." +Lt can be shown that the evelic spectrum also represents correlations inthe frequeney domain (??)..,"It can be shown that the cyclic spectrum also represents correlations inthe frequency domain \citep{gardner:cyc, gardner:book}. ." + Using the Fourier transform of (i). IXN (9). we have:," Using the Fourier transform of $x(t)$ , $X(\nu)$ , we have:" +"correlation is expected due to the different monochromatic radio luminosity of halos with different v, (Eq. 2)).",correlation is expected due to the different monochromatic radio luminosity of halos with different $\nu_s$ (Eq. \ref{Eq:Pnu_P1p4}) ). +" Our calculations show that the fraction of clusters hosting radio halos with v;23500 MHz is about a few percent, thus we would expect 6P/P=+1/2x(3500/1400)?—1.7 for halos with v,>1.4 GHz, which is in line with the observed scatter."," Our calculations show that the fraction of clusters hosting radio halos with $\nu_s\ge 3500$ MHz is about a few percent, thus we would expect $\delta P/P=\pm 1/2\times(3500/1400)^{1.3}\sim 1.7$ for halos with $\nu_s\ge 1.4$ GHz, which is in line with the observed scatter." +" However, we stress that there are other possible sources of scatter which are difficult to take into account in homogeneous models."," However, we stress that there are other possible sources of scatter which are difficult to take into account in homogeneous models." + These are due to differences in the cosmic rays and magnetic field content in clusters with the same mass., These are due to differences in the cosmic rays and magnetic field content in clusters with the same mass. +" Once we anchor the luminosity of halos with v,>1.4 GHz, P14(1.4,Ly), to the observed P(1.4)—Ly correlation, Monte Carlo calculations carried out by considering an observing frequency vo and Eq."," Once we anchor the luminosity of halos with $\nu_s>1.4$ GHz, $P_{1.4}(1.4,L_X)$, to the observed $P(1.4)-L_X$ correlation, Monte Carlo calculations carried out by considering an observing frequency $\nu_0$ and Eq." + 2. allow us to derive the expected radio halo luminosity functions (RHLF; see C06 C09 for details)., \ref{Eq:Pnu_P1p4} allow us to derive the expected radio halo luminosity functions (RHLF; see C06 C09 for details). +" As an example, Fig."," As an example, Fig." +" |. shows the total RHLF obtained from Monte Carlo calculations at v;=120 MHz (black line) and z=0— 0.1, together with the differential contributions to the RHLF from halos with different v; (see figure caption)."," \ref{Fig.RHLF} shows the total RHLF obtained from Monte Carlo calculations at $\nu_0=120$ MHz (black line) and $z=0-0.1$ , together with the differential contributions to the RHLF from halos with different $\nu_s$ (see figure caption)." +" As expected, radio halos with smaller v, mainly contribute to the low-power end of the total RHLF, and the peaks of the RHLF of different populations move towards low radio powers with decreasing v;."," As expected, radio halos with smaller $\nu_s$ mainly contribute to the low-power end of the total RHLF, and the peaks of the RHLF of different populations move towards low radio powers with decreasing $\nu_s$." +" This implies that, depending on their sensitivity, surveys at low radio frequency will unveil new populations of halos."," This implies that, depending on their sensitivity, surveys at low radio frequency will unveil new populations of halos." +" The aim of this section is to investigate how the presence of the new population of ultra-steep spectrum halos, predicted in deep low frequency radio surveys, may affect the radio — X-ray luminosity correlation of halos at low radio frequency."," The aim of this section is to investigate how the presence of the new population of ultra-steep spectrum halos, predicted in deep low frequency radio surveys, may affect the radio – X-ray luminosity correlation of halos at low radio frequency." + LOFAR will carry out surveys between 15 and 210 MHz in the Northern hemisphere with unprecedented sensitivity and spatial resolution., LOFAR will carry out surveys between 15 and 210 MHz in the Northern hemisphere with unprecedented sensitivity and spatial resolution. + Since LOFAR is expected to carry out the deepest large area radio surveys at νοξ 120 MHz Rótttgering et al., Since LOFAR is expected to carry out the deepest large area radio surveys at $\nu_o$ = 120 MHz Rötttgering et al. +" 2006), in this paper we focus on the P(120)—Lx correlation."," 2006), in this paper we focus on the $P(120)-L_X$ correlation." + The most crucial point in this respect is the estimate of the minimum diffuse flux of a radio halo detectable by these surveys as a function of redshift., The most crucial point in this respect is the estimate of the minimum diffuse flux of a radio halo detectable by these surveys as a function of redshift. + It is well known that the brightness profiles of radio halos smoothly decrease with distance from the cluster center Govoni et al., It is well known that the brightness profiles of radio halos smoothly decrease with distance from the cluster center Govoni et al. + 2001; Murgia et al., 2001; Murgia et al. + 2009) implying that the outermost region of the halos will be difficult to detect in radio surveys., 2009) implying that the outermost region of the halos will be difficult to detect in radio surveys. + Brunetti et al. (, Brunetti et al. ( +2007) found that the typical profiles of radio halos are such that about 5896 of their flux is contained within half radius (Ry).,2007) found that the typical profiles of radio halos are such that about $58$ of their flux is contained within half radius $R_H$ ). +" Following C09, in order to have a good sensitivity to diffuse emission, we assume a beam of 25x arcsec and estimate the minimum flux of a Mpc-sized halo detectable in a LOFAR survey, fy, by requiring that the mean brightness within half radius of a halo, Bzosr,, is € times the rms (F) of the survey, where= θµ(ς) is ‘lanathe [22]angular sizemi of radio halos, in arcseconds, at a given redshift."," Following C09, in order to have a good sensitivity to diffuse emission, we assume a beam of $25\times25$ arcsec and estimate the minimum flux of a Mpc-sized halo detectable in a LOFAR survey, $f_{H}$ , by requiring that the mean brightness within half radius of a halo, $B_{<0.5\,R_H}$, is $\xi$ times the $rms$ $F$ ) of the survey, where $\theta_{H}(z)$ is the angular size of radio halos, in arcseconds, at a given redshift." +" In the case of €5-1 this approach would guaranty the detection, at several c, of the central brightest region of halos, thus leading to the identification of candidate radio halos in the survey."," In the case of $\xi\simeq1$ this approach would guaranty the detection, at several $\sigma$, of the central brightest region of halos, thus leading to the identification of candidate radio halos in the survey." + This simple approach has been tested in Cassano et al. (, This simple approach has been tested in Cassano et al. ( +"2008) by injecting “fake” radio halos in the (u,v) plane of NVSS and GMRT observations.","2008) by injecting “fake” radio halos in the (u,v) plane of NVSS and GMRT observations." + It has been shown that radio halos become visible in the images as soon as their flux approaches that obtained by Eq., It has been shown that radio halos become visible in the images as soon as their flux approaches that obtained by Eq. +" 4 with £=1 and &=2 for the NVSS and GMRT observations, respectively (see also Brunetti et al."," \ref{fmin} with $\xi=1$ and $\xi=2$ for the NVSS and GMRT observations, respectively (see also Brunetti et al." + 2007; Venturi et al., 2007; Venturi et al. + 2008)., 2008). + The LOFAR Large Area Survey isexpected to reach an rms~0.1 mJy/beam at 120 MHz with a beam ~5x5 arcsec., The LOFAR Large Area Survey isexpected to reach an $rms\sim0.1$ mJy/beam at 120 MHz with a beam $\sim5\times$5 arcsec. + These resolution and sensitivity are obtained by assuming, These resolution and sensitivity are obtained by assuming +It is noted that. (wo results of Lemma G correspond to uniqueness and comparison principle of its associated PDE.,"It is noted that, two results of Lemma \ref{lem:dpp} correspond to uniqueness and comparison principle of its associated PDE." + However. we provide the probabilistic proof Lemma 6 since we wanl to cover potentially discontinuous hinction 4244 of(4.3).. in which uniqueness mav nol remain (rue.," However, we provide the probabilistic proof Lemma \ref{lem:dpp} , since we want to cover potentially discontinuous function $\varphi_1$ of, in which uniqueness may not remain true." +bars are sensitive to the inclusion of the supercluster: if we exclude the supercluster. then our error bars are similar to those of Jing&Borner (2004)... who assume an analytical approximation for their errors.,"bars are sensitive to the inclusion of the supercluster: if we exclude the supercluster, then our error bars are similar to those of \cite{JB2004}, who assume an analytical approximation for their errors." + In addition. Jing&Bórner(2004) used the LOOK data release of the 2HFGRS and excluded areas of the 2dFGRS with (0)«0.1 (areas with low redshift completeness).," In addition, \cite{JB2004} used the 100k data release of the 2dFGRS and excluded areas of the 2dFGRS with $R(\theta)<0.1$ (areas with low redshift completeness)." + As shown in Figure 15 of Collessetal.€2001).. the northern strip of the 2HFGRS 100kK data release has a large hole in its coverage between [2.5hrs and 13.5hrs in RA (due mainly to tilting constraints). which coincides with region 3 in Figure 2..," As shown in Figure 15 of \cite{Colless2001}, the northern strip of the 2dFGRS 100k data release has a large hole in its coverage between 12.5hrs and 13.5hrs in RA (due mainly to tilting constraints), which coincides with sub--region 3 in Figure \ref{jk}." +" Therefore. the sample used by Jing&Borner does include the main core of the ""Sloan Great Wall” and explains why our measurements of the 3PCF agree with theirs 3PCF when we exclude sub-regions 3 4. Baughetal.(2004). Crotonetal. (2004)."," Therefore, the sample used by \cite{JB2004} + does include the main core of the “Sloan Great Wall” and explains why our measurements of the 3PCF agree with theirs 3PCF when we exclude sub–regions 3 4. \cite{Baugh2004}, \cite{Croton2004}," + and Gaztanagaal.(2005). present an analysis of the higher-order correlation functions for the full 3HFGRS catalogue., and \cite{Gaz2005} present an analysis of the higher–order correlation functions for the full 2dFGRS catalogue. +" In Figure | of (2004). the ""Sloan Great Wall"" is visible in the NGP strip of the full 2dFGRS."," In Figure 1 of \cite{Baugh2004}, the “Sloan Great Wall” is visible in the NGP strip of the full 2dFGRS." + Baughetal.(2004) also found that the presence of this supercluster. and another in the 2dFGRS SGP area. signiticantly affected their measurement of the higher-order correlations on scales >4h +Mpe. consistent with our findings in Figures | and 3. (see also Gaztanagaetal. (2005))).," \cite{Baugh2004} also found that the presence of this supercluster, and another in the 2dFGRS SGP area, significantly affected their measurement of the higher–order correlations on scales $>4\,{h^{-1}}$ Mpc, consistent with our findings in Figures \ref{jingplot} and \ref{plotcorr} (see also \cite{Gaz2005}) )." +" The influence of these superclusters on the higher-order correlation functions indicates that we have not yet reached a “fair sample"" of the Universe with the 2dFGRS and SDSS samples used herein.", The influence of these superclusters on the higher–order correlation functions indicates that we have not yet reached a “fair sample” of the Universe with the 2dFGRS and SDSS samples used herein. + This was also, This was also +The situation should improve as one observes further down (he luminosity function.,The situation should improve as one observes further down the luminosity function. + By their very nature. blue stragglers tend (o produce PNs with hieh-mass central stars.," By their very nature, blue stragglers tend to produce PNs with high-mass central stars." + Their existence will therefore complicate PN-based efforts to probe a galaxys recent. (~2 (ντ) star formation history (e.g..Villaver.Stanghellini.&Shaw2004)., Their existence will therefore complicate PN-based efforts to probe a galaxy's recent $\sim 2$ Gyr) star formation history \citep[\eg][]{villaver04}. +. However. the inverse relationship between main-sequence mass and stellar lifetime. coupled with the initial mass relation. guarantees that single stars will be the dominant source of lower mass cores.," However, the inverse relationship between main-sequence mass and stellar lifetime, coupled with the initial mass-final mass relation, guarantees that single stars will be the dominant source of lower mass cores." + Spectroscopy. of objects Z2 mag down the [O III] A5007 PNLF is therefore still a viable method of probing the distant past of a stellar population., Spectroscopy of objects $\gtrsim 2$ mag down the [O III] $\lambda 5007$ PNLF is therefore still a viable method of probing the distant past of a stellar population. + Unlortunately. reaching those depths in the distant galaxies of Leo I and Virgo will be extremely difficult.," Unfortunately, reaching those depths in the distant galaxies of Leo I and Virgo will be extremely difficult." + This research made use of the NASA Extragalactic Database and was supported in part by NSF grants AST 00-71238 and AST 03-02030., This research made use of the NASA Extragalactic Database and was supported in part by NSF grants AST 00-71238 and AST 03-02030. +The remaining two ,image of tri-linear combination of three quarks (or anti-quarks). +equationsare obtained inasimilar manner.resulting inthe followi AS =—UIqdeU.," The quarks transform with matrices $U$ (or ${\bar{U}}$ for the anti-quarks), but these matrices are not unitary: their determinants are equalto $j^2$ or $j$, respectively." + AS = US[del(U)]. (12) The determinant ofthe 2 compl," So, quarks cannot be put on the same footing as classical spinors; they transform under a $Z_3$ -covering of the $SL(2, {\bf C})$ group." +ex matrix U7} evervwhere the right- side. Takingthe determinantx ofthe matrix , A similar covariance requirement can be formulated with respect to the set of $2$ -forms mapping the quadratic quark-anti-quark combinations into a four-dimensional linear real space. +A appearsgets immediately on hand one del(N) [del (U)]*.," As we already saw, the symmetry \ref{commutation2}) ) imposed on these expressions reduces their number to four." + (13) Takinginto accountthatthe whichdelines theο L(2.," Let us define two quadratic forms, $\pi{\mu}_{A {\dot{B}}}$ and its conjugate ${\bar{\pi}}^{\mu}_{{\dot{B}} A}$ with the following symmetry requirement The Greek indices $\mu, \nu...$ take on four values, and we shall label them $0,1,2,3$." + C) group. matricesU5} definedabove. The determinant of Ücan take on thevalues 1.jorj? SL(2.," It follows immediately from \ref{commutation2}) ) that Such matrices are non-hermitian, and they can be realized by the following substitution: where ${\sigma}^{\mu}_{A {\dot{B}}}$ are the unit $2 \time 2$ matrix for $\mu = 0$, and the three hermitian Pauli matrices for $\mu = 1,2,3$." +C) group. while the matrices U5} ," Again, we want to get the same form of these four matrices in another basis." +willbe defined asfollows: UL jM.UP jMue --—jM.UP λος (15.) the determinantof Ü being equalto j. Obviously. (he same reasoning leads tothe conjugatecubic representation of5L(2. C) ifwe," Knowing that thelower indices $A$ and ${\dot{B}}$ undergo the transformation with matrices $U^{A'}_B$ and ${\bar{U}}^{{\dot{A}}'}_{\dot{B}}$, we demand that there exist some $4 \times 4$ matrices $\Lambda^{{\mu}'}_{\nu}$ representing the transformation of lower indices by the matrices $U$ and ${\bar{U}}$: and this defines the vector $4 \times 4)$ representation of the Lorentz group." + require the covariance of the conjugate by imposing(he equation similar to(3)) NL Pape aot=aM Pinelc4 Uppb Ue.pe (16) ThematrixÜ is the complex conjugate arguments bv (4)): (ot," Introducing the invariant “spinorial metric"" in two complex dimensions, $\varepsilon^{AB}$ and $\varepsilon^{{\dot{A}}{\dot{B}}}$ such that $\varepsilon^{12} = - \varepsilon^{21} = 1$ and $\varepsilon^{{\dot{1}}{\dot{2}}} = - \varepsilon^{{\dot{2}}{\dot{1}}}$, we can define the contravariant components $\pi^{\nu \, \, A {\dot{B}}}$." +tgt) (gPgbgt) _— (ρ0ρερῖ) gigPgt‘) Wehave found the waytoderive thecovering group ofthe Lorentz group actingon spinors via theusual spin," It is easy to show that the Minkowskian space-time metric, invariant under the Lorentz transformations, can be defined as Together with the anti-commuting spinors ${\psi}^{\alpha}$ the four real coefficients defining a Lorentz vector, $x_{\mu} \, {\pi}^{\mu}_{A {\dot{B}}}$ , can generate now the supersymmetry via standard definitions of super-derivations." +, 6. +orial representation. Thespinorsare obtained," Consider now three generators, $Q^a , \, \, a=1,2,3$ , and their conjugates ${\bar{Q}}^{\dot{b}}$ satisfying similar cubic commutation relations as in the two-dimensional case:" +the induced electric field inside the conductive fluid is an irrotational field.,the induced electric field inside the conductive fluid is an irrotational field. +" In this case, there is neither an eddy electric field nor an eddy current in the conductive fluid."," In this case, there is neither an eddy electric field nor an eddy current in the conductive fluid." +" Sequentially, there is no magnetic force acting on the conductive fluid when it passes through the magnetic field with velocityv."," Sequentially, there is no magnetic force acting on the conductive fluid when it passes through the magnetic field with velocity." +. This case is a special solution of the frozen-in field equation (6)., This case is a special solution of the frozen-in field equation (6). +" The frozen-in field equation (6) can be expanded as: 'The first term on the right-hand side includes the divergence of the magnetic field V-B, therefore, this term is always zero."," The frozen-in field equation (6) can be expanded as: The first term on the right-hand side includes the divergence of the magnetic field $\nabla\cdot\emph{\textbf{B}}$, therefore, this term is always zero." + The factor V-v in the second term is the divergence of the velocity field., The factor $\nabla\cdot\emph{\textbf{v}}$ in the second term is the divergence of the velocity field. +" When the fluid moves without expansion or compression (i.e., the bulk has not change), this term is also zero."," When the fluid moves without expansion or compression (i.e., the bulk has not change), this term is also zero." +" When the path of each conductive fluid element follows an isomagnetic surface (i.e., constant B), the third term (v-V)B is also equal to zero."," When the path of each conductive fluid element follows an isomagnetic surface (i.e., constant B), the third term $(\textbf{\emph{v}}\cdot\nabla)\emph{\textbf{B}}$ is also equal to zero." +" If all of the fluid elements threaded by a magnetic field line have the same velocity, without differential movement, the fourth term (B-V)v is also zero."," If all of the fluid elements threaded by a magnetic field line have the same velocity, without differential movement, the fourth term $(\textbf{\emph{B}}\cdot\nabla)\emph{\textbf{v}}$ is also zero." +" If the shapes of magnetic field lines have not change and this term is not equal to zero, the shape of the fluid will change."," If the shapes of magnetic field lines have not change and this term is not equal to zero, the shape of the fluid will change." +" Therefore, providing the shape and the size of the conductive fluid remain the same, all of the situations shown in Fig."," Therefore, providing the shape and the size of the conductive fluid remain the same, all of the situations shown in Fig." +" 2, Fig."," 2, Fig." + 4 and Fig., 4 and Fig. + 5 correspond to a special solution where all four terms are zero in the right-hand side of equation (7)., 5 correspond to a special solution where all four terms are zero in the right-hand side of equation (7). +" In these cases the induced electric field inside the conductive fluid are irrotational, and the frozen-in phenomenon is not manifested."," In these cases the induced electric field inside the conductive fluid are irrotational, and the frozen-in phenomenon is not manifested." + Because the case illustrated in Fig., Because the case illustrated in Fig. +" 5 is equivalent to that in the vicinity of a pulsar's equator, the viewpoint that the plasma of a pulsar cannot cross the magnetic field lines is inaccurate."," 5 is equivalent to that in the vicinity of a pulsar's equator, the viewpoint that the plasma of a pulsar cannot cross the magnetic field lines is inaccurate." +" Another description of the frozen-in field equation is From this equation, one can see that the essence"," Another description of the frozen-in field equation is From this equation, one can see that the essence" +"Saturn, far interior to the dust source, reaches a maximum optical depth at a factor of a few less than 7=v/c, even as we turn up the dust production rate.","Saturn, far interior to the dust source, reaches a maximum optical depth at a factor of a few less than $\tau=v/c$, even as we turn up the dust production rate." +" The critical optical depth near Saturn is 7,©v/c#3x10-°.", The critical optical depth near Saturn is $\tau_r \approx v/c \approx 3\times 10^{-5}$. +" In general, if we see an exozodiacal cloud with optical depth >10, like, e.g., the dust in the central 20 AU of the e Eridani system (Moranetal.2004;Backman2009),, we can infer the presence of a second source of dust."," In general, if we see an exozodiacal cloud with optical depth $\gtrsim 10^{-4}$, like, e.g., the dust in the central 20 AU of the $\epsilon$ Eridani system \citep{mora04, back09}, we can infer the presence of a second source of dust." +" This prediction is consistent with observations for 25 yum flux in excess of the stellar photosphere withSpitzer (Hinesetal.2006;Bryden2006;Lawleretal. 2009),, which find stars with hot dust with luminositites D;g/L,>10~4 to be much rarer than stars with cold dust."," This prediction is consistent with observations for $25 \ \mu$ m flux in excess of the stellar photosphere with \citep{hine06, bryd06, lawl09}, which find stars with hot dust with luminositites $L_{IR}/L_{\star} > 10^{-4}$ to be much rarer than stars with cold dust." +" Wyattetal.(2006) offers a list of known stars with evidence for hot dust at «10 AU; we can infer all the stars on this list must have central sources of grains, perhaps asteroid-belt analogs, interior to 10 AU."," \citet{wyat06} offers a list of known stars with evidence for hot dust at $< 10$ AU; we can infer all the stars on this list must have central sources of grains, perhaps asteroid-belt analogs, interior to 10 AU." + We synthesized images from our multi-grain size collisional models to illustrate what they would look like to various telescopes., We synthesized images from our multi-grain size collisional models to illustrate what they would look like to various telescopes. +" To create these images, we illuminated the grains with solar flux appropriate to their distance from the star, and calculated the scattered light and thermal emission."," To create these images, we illuminated the grains with solar flux appropriate to their distance from the star, and calculated the scattered light and thermal emission." + We assumed simple generic emissivity laws to account for the poor ability of grains to radiate and absorb photons with wavelengths larger than the grain size: emissivity e=1 for wavelengths A<27s and e=(275/A)? for \>27s (Backman& 1993)., We assumed simple generic emissivity laws to account for the poor ability of grains to radiate and absorb photons with wavelengths larger than the grain size: emissivity $\epsilon = 1$ for wavelengths $\lambda \le 2 \pi s$ and $\epsilon = (2 \pi s/\lambda)^2 $ for $\lambda > 2 \pi s$ \citep{back93}. +". We used the tools in ZODIPIC (Moranetal.2004) to self-consistently calculate the temperatures of the grains, given solar radiation and the emissivities above."," We used the tools in ZODIPIC \citep{mora04} to self-consistently calculate the temperatures of the grains, given solar radiation and the emissivities above." +" For the Tmaxv103 images, we rebinned the simulations by a factor of two in each direction, to average down the Poission noise in the histograms, which increases for short collision times, as collisions remove the small grains."," For the $\tau_{\rm{max}} \sim 10^{-4}$ images, we rebinned the simulations by a factor of two in each direction, to average down the Poission noise in the histograms, which increases for short collision times, as collisions remove the small grains." + We blocked the region interior to 5 AU with a software mask., We blocked the region interior to 5 AU with a software mask. + We did not model the point spread function of any telescope., We did not model the point spread function of any telescope. +" Figure 7 shows the SEDs of the three collisional models, including the contribution from the stellar photosphere."," Figure \ref{fig:seds} shows the SEDs of the three collisional models, including the contribution from the stellar photosphere." +" This figure can be compared to Figure 14 in (2002),, which does not include the effect of collisions in reshaping the disk."," This figure can be compared to Figure 14 in \citet{mm1}, which does not include the effect of collisions in reshaping the disk." +" Dotted lines in the figure show a blackbody curve with the same peak wavelengths as each model, labeled according to their characteristic temperatures."," Dotted lines in the figure show a blackbody curve with the same peak wavelengths as each model, labeled according to their characteristic temperatures." +" As the optical depth increases, we find that the peak in the SED from the dust thermal emission moves from 80 jum to 40 wm as resonant trapping becomes less effective at retaining grains in the outer Solar System."," As the optical depth increases, we find that the peak in the SED from the dust thermal emission moves from $80 \ \mu$ m to $40 \ \mu$ m as resonant trapping becomes less effective at retaining grains in the outer Solar System." +" As the disk crosses the threshold into the collision-dominated regime, the model curves narrow to more closely resemble the shape of a single-temperature blackbody curve: the emission from large grains in the cold classical Kuiper Belt."," As the disk crosses the threshold into the collision-dominated regime, the model curves narrow to more closely resemble the shape of a single-temperature blackbody curve: the emission from large grains in the cold classical Kuiper Belt." +The present article is related to the more theoretical ones (?]. and [?]..,The present article is related to the more theoretical ones \cite{RTT08} and \cite{CST10}. + In the first one [?].. the authors obtained an infinite set of nonlocal boundary conditions for the 3D inviscid primitive equations by studyiug the stationary problem associated with the linearized equations.," In the first one \cite{RTT08}, the authors obtained an infinite set of nonlocal boundary conditions for the 3D inviscid primitive equations by studying the stationary problem associated with the linearized equations." + In the second one [?].. the authors gave due (ireatiment of (he special zero (barotropic) mode of the primitive equations and established (he wellposedness of the corresponding linearized problem using the linear semigroup theory.," In the second one \cite{CST10}, the authors gave due treatment of the special zero (barotropic) mode of the primitive equations and established the well–posedness of the corresponding linearized problem using the linear semi–group theory." + Various nmumnerical schemes through the projection method were also proposed. and the stability issue was studied for all of them.," Various numerical schemes through the projection method were also proposed, and the stability issue was studied for all of them." + In the present work we intend to discuss the numerical simulations of the 3D. mviscid primitive equations on a nested set. of domains., In the present work we intend to discuss the numerical simulations of the 3D inviscid primitive equations on a nested set of domains. + Alter performing the normal mode expansions of the unknowns. we are presented with an infinite sel of 2D equations.," After performing the normal mode expansions of the unknowns, we are presented with an infinite set of 2D equations." + For the zero mode we use one of the schemes proposed in [?].. which is semi.implicit. and is derived by (he pressure.correction method.," For the zero mode we use one of the schemes proposed in \cite{CST10}, which is semi–implicit, and is derived by the pressure–correction method." + For the higher modes. i.e. (he subcritical aud supercritical modes. we use (he splitiingup method for (the discretizations and advance the unknowns along the. and. y directions in separate sub-," For the higher modes, i.e. the subcritical and supercritical modes, we use the splitting–up method for the discretizations and advance the unknowns along the $x$ – and $y$ –directions in separate sub-steps." + It then seems natural to impose boundary conditions bv characteristics along ther and y directions separately., It then seems natural to impose boundary conditions by characteristics along the $x$ – and $y$ –directions separately. + In the course of the article we recall the normal mode expansion leading to the infinite svstem of 2D equations (two spatial dimensions and time)., In the course of the article we recall the normal mode expansion leading to the infinite system of 2D equations (two spatial dimensions and time). + Then we show how to cliseretize it in a form suitable for (he implementation of the boundary. conditions., Then we show how to discretize it in a form suitable for the implementation of the boundary conditions. + Two simulations are performed., Two simulations are performed. + An initial simulation is carried out on a large domain with homogeneous boundary conditions., An initial simulation is carried out on a large domain with homogeneous boundary conditions. + Using the data from (he initial simulation as boundary conditions. we perform a second simulation of the same equations on a small interior domain.," Using the data from the initial simulation as boundary conditions, we perform a second simulation of the same equations on a small interior domain." + Then we compare these two results over (he interior domain., Then we compare these two results over the interior domain. + llere the goals are twolold., Here the goals are twofold. + On the one hand we want to numerically verily whether the boundary conditions. proven suitable lor the linearized equations. are also suitable for (he nonlinear equations.," On the one hand we want to numerically verify whether the boundary conditions, proven suitable for the linearized equations, are also suitable for the nonlinear equations." + On the other haad. we want lo numerically verify the transparency property of the proposed boundary conditions.," On the other hand, we want to numerically verify the transparency property of the proposed boundary conditions." + Both goals are satisfactorily achieved., Both goals are satisfactorily achieved. + The article is organized as lollows., The article is organized as follows. + In Section. ?? we recall the 3D equations and their normal mode expansion., In Section \ref{s2} we recall the 3D equations and their normal mode expansion. + The issues of boundary conditions and wellposecluess are also discussed., The issues of boundary conditions and well–posedness are also discussed. + The numerical schemes are presented in Section ??.., The numerical schemes are presented in Section \ref{s3}. + The settings for the numerical simulations. and the results of (he simulations are discussed in Section ??..," The settings for the numerical simulations, and the results of the simulations are discussed in Section \ref{s4}. ." +llowever. systems close to the dashed line may have lost around half of their mass during the saturation period they have aleacky weathereel.,"However, systems close to the dashed line may have lost around half of their mass during the saturation period they have aleady weathered." + We know that all the planets in our sample have survived the saturation phase of their star., We know that all the planets in our sample have survived the saturation phase of their star. + However most of these systems could. have existed. closer in. since most are well outside their Roche limit.," However most of these systems could have existed closer in, since most are well outside their Roche limit." + In fact. there is a clear deficit of systems close to their Roche limits. as shown in Fig. 3..," In fact, there is a clear deficit of systems close to their Roche limits, as shown in Fig. \ref{aoveraroche}," + despite selection cllects biasing surveys towards detection of close-in svstenis., despite selection effects biasing surveys towards detection of close-in systems. + The Roche limit sets the minimum orbital separation for a planet. within which tidal forces become too strong and pull the panet apart.," The Roche limit sets the minimum orbital separation for a planet, within which tidal forces become too strong and pull the planet apart." + The Ποσο limit or à lluid body (gas giant planets are assumed to be best reesented by a [uid model rather than a rigid body). as given by 2... is where ων is the Roche limit. a is the semi major axis. and py ane p. are the density of the planet ancl star respectively.," The Roche limit for a fluid body (gas giant planets are assumed to be best represented by a fluid model rather than a rigid body), as given by \cite{rochelim}, is where $a_{roche}$ is the Roche limit, a is the semi major axis, and $\rho_{p}$ and $\rho_{*}$ are the density of the planet and star respectively." + lte-plotting Figure 2.. but moving the planets in to their Roche limit results in Figure 4..," Re-plotting Figure \ref{sat}, but moving the planets in to their Roche limit results in Figure \ref{roche}." + In this case ~50% of known systems would have absorbed enough energy to move their entire mass out to infinity., In this case $\sim$ of known systems would have absorbed enough energy to move their entire mass out to infinity. + Pherefore closer-orbiting analogs of the known planets would have sullered catastrophic evaporation., Therefore closer-orbiting analogs of the known planets would have suffered catastrophic evaporation. + The loss of such svstems may account for the eut-olf seen in Figure 1.. since they would be situated to the left of their current positions. thereby filling the sparsely populated areas of these clagrams.," The loss of such systems may account for the cut-off seen in Figure \ref{correlations}, since they would be situated to the left of their current positions, thereby filling the sparsely populated areas of these diagrams." + Planets that would have survived at their Roche limit tend to have either high clensities and surface gravities. or already exist close to their Roche limits.," Planets that would have survived at their Roche limit tend to have either high densities and surface gravities, or already exist close to their Roche limits." +(> IOkkeV) Dus on MJD 55218. with the emergence of a disk blackbody component in the N-ray. spectrum.,"$>10$ keV) flux on MJD 55218, with the emergence of a disk blackbody component in the X-ray spectrum." + This is consistent with the evidence from the X-ray timing and racio observations. sugeesting 555218 as the likely date of the initial radio ejection event.," This is consistent with the evidence from the X-ray timing and radio observations, suggesting 55218 as the likely date of the initial radio ejection event." + Yangetal.(2010) found. that uniform cleccleration of component X fitted. their measurements better. than a ballistic model with no deceleration., \citet{Yan10} found that uniform deceleration of component A fitted their measurements better than a ballistic model with no deceleration. + However. their suggested: deceleration parameters. (Fig. 3))," However, their suggested deceleration parameters (Fig. \ref{fig:angsep}) )" + imply an ejection date of 555201.8 (2010 January 5)., imply an ejection date of 55201.8 (2010 January 5). +TE was still sun-constrainecd on this date. so no PCA observations Nswe available to ascertain the X-ray state of the source. but jc. and observations (Nakahiractal.2010) yomrow that this was significantly prior to the beginning of 10 X-ray spectral softening. ancl we deem this unlikely as yo true date of ejection.," was still sun-constrained on this date, so no PCA observations are available to ascertain the X-ray state of the source, but the and observations \citep{Nak10} show that this was significantly prior to the beginning of the X-ray spectral softening, and we deem this unlikely as the true date of ejection." + Assuming an cjection cate of 555218. we are unable to Π the motion of the cjecta with a uniform cleceleration model.," Assuming an ejection date of 55218, we are unable to fit the motion of the ejecta with a uniform deceleration model." + Our best-fitting model has a v value of 230.9., Our best-fitting model has a $\chi^2$ value of 230.9. + Either our assumed ejection date is wrong or the uniform. cleccleration model does not. describe the data well., Either our assumed ejection date is wrong or the uniform deceleration model does not describe the data well. + X. plausible alternative could be the scenario outlined by Wang.Dai&Lu(2003).. whereby a shock wave propagates into the interstellar medium. sweeping up material as it moves. and decelerating such that the late-time behaviour approaches the Sedov solution. 42x.£?," A plausible alternative could be the scenario outlined by \citet*{Wan03}, whereby a shock wave propagates into the interstellar medium, sweeping up material as it moves, and decelerating such that the late-time behaviour approaches the Sedov solution, $R\propto t^{2/5}$." + Allowing the zero point to lloat and fitting the measured positions of component A with a simplistic Sedov model R=Ry|aOotfoo. where A? isM the angular separationH of the component [rom the core. we find. Ao=406d29 mmas. hk=75.7cx:6.5 mamascdd ‘and fy=MJD55232.3t1.6. with a reduced. 47. value of 0.2.," Allowing the zero point to float and fitting the measured positions of component A with a simplistic Sedov model $R=R_0+k(t-t_0)^{0.4}$, where $R$ is the angular separation of the component from the core, we find $R_0=406\pm29$ mas, $k=75.7\pm6.5$ $^{-0.4}$, and $t_0={\rm MJD\,}55232.3\pm1.6$, with a reduced $\chi^2$ value of 0.2." + Although the zero tine and position (fy and o. respectively) do not correspond to our assumed ejection date and derived core position. when coupled with an initial coasting phase where the ejecta travel purely ballistically (asproposedbyLao&Zhang2009).. this model appears to provide a plausible fit to the data (Fig. 3)).," Although the zero time and position $t_0$ and $R_0$, respectively) do not correspond to our assumed ejection date and derived core position, when coupled with an initial coasting phase where the ejecta travel purely ballistically \citep[as proposed by][]{Hao09}, this model appears to provide a plausible fit to the data (Fig. \ref{fig:angsep}) )." + The derived zero time. fg. is just consistent within error bars with an extrapolation of the expansion of component A (Yangetal.2010) to zero size. which occurs on 73:55229.1.0.," The derived zero time, $t_0$, is just consistent within error bars with an extrapolation of the expansion of component A \citep{Yan10} to zero size, which occurs on $55229.7\pm1.0$." + Ht also coincides with the rise phase of the second [lare in the integrated radio light curves. suggesting that the breadth of the second. Dare could. be due to the release of energv as component A begins to cdecelerate. possibly combined with the ejection of component D. Llowever. if component B were ejected during this second racio Hare. its non-detection in the three VEDI observations prior to 555253 is surprising.," It also coincides with the rise phase of the second flare in the integrated radio light curves, suggesting that the breadth of the second flare could be due to the release of energy as component A begins to decelerate, possibly combined with the ejection of component B. However, if component B were ejected during this second radio flare, its non-detection in the three VLBI observations prior to 55253 is surprising." + One explanation could be that the intrinsic jet speed and inclination angle to the line ol sight are both high enough for the emission to be Doppler-deboosted until the jets have decelerated by sweeping up the surrouncing gas., One explanation could be that the intrinsic jet speed and inclination angle to the line of sight are both high enough for the emission to be Doppler-deboosted until the jets have decelerated by sweeping up the surrounding gas. + Alternatively. if the observed jet ejecta are shocks. the delav in the appearance of component. B could arise from the time taken for the ejecta to either catch up with the slower-moving material ahead of them (for internal shocks) or to sweep up and interact with the surrounding eas (Lor external shocks).," Alternatively, if the observed jet ejecta are shocks, the delay in the appearance of component B could arise from the time taken for the ejecta to either catch up with the slower-moving material ahead of them (for internal shocks) or to sweep up and interact with the surrounding gas (for external shocks)." + With only the one VLBI detection of component D and the lack of any signatures in the X-rav light curves that might correspond to a second ejection event. we cannot further constrain the cjection date of component D. and do not discuss it further.," With only the one VLBI detection of component B and the lack of any signatures in the X-ray light curves that might correspond to a second ejection event, we cannot further constrain the ejection date of component B, and do not discuss it further." + In the absence of a precise ejection date for component A. constraints from the receding components. or from. X-rav lighteurves of the cjecta as they decelerate. there are too lew constraints to conduct a more meanineful fit to the full model of Hao&Zhang(2009).," In the absence of a precise ejection date for component A, constraints from the receding components, or from X-ray lightcurves of the ejecta as they decelerate, there are too few constraints to conduct a more meaningful fit to the full model of \citet{Hao09}." +. However. the measured VLDBI angular separations. the integrated radio light curves and the expansion of component A are. all consistent with the deceleration. brightening and lateral expansion of that component close to 555232. as derived from our model fitting.," However, the measured VLBI angular separations, the integrated radio light curves and the expansion of component A are all consistent with the deceleration, brightening and lateral expansion of that component close to 55232, as derived from our model fitting." + Phus. while we cannot definitivelv verily the proposed scenario. it is certainly plausible.," Thus, while we cannot definitively verify the proposed scenario, it is certainly plausible." +" Should the mocel be applicable. the angular scale for deceleration (« 0.567)) would be significantly smaller for NTE 1752-223 than those derived by Hao&Zhang(2000) for NPE 1550-564 17739) and IL11743-322 (3""))."," Should the model be applicable, the angular scale for deceleration $<0.56$ ) would be significantly smaller for XTE J1752-223 than those derived by \citet{Hao09} for XTE J1550-564 ) and 1743-322 )." + While the distance is not vet well-determined. if NPE 1752-223 is indeed. relatively nearby. as implied by the low hydrogen column towards the source (CMarkwardtetal.2000b:CurranοἱPOLL) and as derived. via α more mocdel-dependent method (3.5+0.4kpe:Shaposhnikovetal. 2010).. then the discrepancy: in the physical scale of the radius at which deceleration. begins would be greater still.," While the distance is not yet well-determined, if XTE J1752-223 is indeed relatively nearby, as implied by the low hydrogen column towards the source \citep{Mar09b,Cur11} and as derived via a more model-dependent method \citep[$3.5\pm0.4$\,kpc;][]{Sha10}, then the discrepancy in the physical scale of the radius at which deceleration begins would be greater still." + Knowing the true core position. we can constrain the quenching factor of the compact jet in the soft state.," Knowing the true core position, we can constrain the quenching factor of the compact jet in the soft state." + During the three VLBA observations of 2010 February, During the three VLBA observations of 2010 February +the advantage of using the flux data without any assumption on the distance and luminosity.,the advantage of using the flux data without any assumption on the distance and luminosity. + In fact for many of HESS sources the location and luminosity are unknown., In fact for many of HESS sources the location and luminosity are unknown. + The relation also gives information on the geometry of the volume in which the sources are contained if a uniform source distribution is assumed., The number-intensity relation also gives information on the geometry of the volume in which the sources are contained if a uniform source distribution is assumed. + Deviation from a simple power law NxS~° with slope -1 (for the case of a thin disk) means that the sources or their luminosity function are not spatially uniformly distributed., Deviation from a simple power law $N \propto S^{-\alpha}$ with slope -1 (for the case of a thin disk) means that the sources or their luminosity function are not spatially uniformly distributed. + The major difficulties in the study of the collective properties of the HESS source population consist of the limited number of sources detected and the relatively small range of flux covered by the survey., The major difficulties in the study of the collective properties of the HESS source population consist of the limited number of sources detected and the relatively small range of flux covered by the survey. +" Also, the HESS survey of the Galaxy was not performed with uniform sensitivity."," Also, the HESS survey of the Galaxy was not performed with uniform sensitivity." +" In fact, whereas the sensitivity of the survey of the Galactic Plane in Galactic latitude is rather flat in the region between -1.5 and 1.5 degrees, its effective exposure and therefore its sensitivity is not uniform in longitude."," In fact, whereas the sensitivity of the survey of the Galactic Plane in Galactic latitude is rather flat in the region between -1.5 and 1.5 degrees, its effective exposure and therefore its sensitivity is not uniform in longitude." +" Longer observation times were dedicated by HESS to locations in the Galactic plane close to where three sources, HESS J1747-218 and HESS J1745-290 (in the Galactic Center), and HESS J1713-397, were already known."," Longer observation times were dedicated by HESS to locations in the Galactic plane close to where three sources, HESS J1747-218 and HESS J1745-290 (in the Galactic Center), and HESS J1713-397, were already known." + The average sensitivity of the survey as a function of the longitude and the latitude are shown in Fig., The average sensitivity of the survey as a function of the longitude and the latitude are shown in Fig. + 2 and Fig., 2 and Fig. +" 3 of Aharonianetal.(2006a),, respectively."," 3 of \cite{Aharonian:2005kn}, respectively." + In some locations of the Galaxy the survey was done at peak sensitivity of 2 per cent of the Crab flux., In some locations of the Galaxy the survey was done at peak sensitivity of 2 per cent of the Crab flux. + From Fig., From Fig. +" 3 of Aharonianetal.(2006a) one can deduce that in order for our sample to be complete, only sources detected with more than 6 per cent the Crab flux within —2?«|<2? can be included."," 3 of \cite{Aharonian:2005kn} one can deduce that in order for our sample to be complete, only sources detected with more than 6 per cent the Crab flux within $-{2}^{o}_h, r_h, \sigma_{p,0}$ )." + Next the cluster analysis based on the mixture model method is carried out. with respect to these three parameters., Next the cluster analysis based on the mixture model method is carried out with respect to these three parameters. + The optimum number of groups is selected objectively by a widely used method. Ix-ineans clustering (AlacQueen 1967). together with the method developed bv Sugar James (2003) for finding the optimum number of clusters.," The optimum number of groups is selected objectively by a widely used method, K-means clustering (MacQueen 1967), together with the method developed by Sugar James (2003) for finding the optimum number of clusters." + The ]v-means method is necessary. (ο find the optimum number of groups which worked as input to the mixture model method., The K-means method is necessary to find the optimum number of groups which worked as input to the mixture model method. + After doing CA by Ix-means and associated optimum number method it is found that optimality occurs at IX—4 with only one GC. C156. in a eroup.," After doing CA by K-means and associated optimum number method it is found that optimality occurs at K=4 with only one GC, C156, in a group." + Then CA is performed again after removing this object anc with optimum criterion., Then CA is performed again after removing this object and with optimum criterion. + Optimality then occurs at IxX—4 with again a very small group containing two GC's. C169 and F1GC15.," Optimality then occurs at K=4 with again a very small group containing two GCs, C169 and F1GC15." + These GCs are removed and (he process is repeated with (the sample of 127 objects., These GCs are removed and the process is repeated with the sample of 127 objects. + Now the optimum number of eroups is found al IX—2 wilh GC's distributed into three evenly populated eroups., Now the optimum number of groups is found at K=3 with GCs distributed into three evenly populated groups. + We thus select this sample for study ancl perform the new method of CA taking Ix = 3., We thus select this sample for study and perform the new method of CA taking K = 3. + In order to establish the better performance of the model based CA method. we have computed the expected misclassification probabilities corresponding to some of the parameters.," In order to establish the better performance of the model based CA method, we have computed the expected misclassification probabilities corresponding to some of the parameters." +" In particular [or 2,4 under the Ix-means method it was found to be 0.4088 whereas under the new CA method it is onlv 0.14978."," In particular for $\sigma_{p,0}$ under the K-means method it was found to be 0.4088 whereas under the new CA method it is only 0.14978." +" For CA we have removed three GCs which are outliers with respect to set S7 used for CA,", For CA we have removed three GCs which are outliers with respect to set S7 used for CA. + The mean values (with standard errors) of all the parameters are listed in Table 4., The mean values (with standard errors) of all the parameters are listed in Table 4. +" The rotation amplitudes. rotation axes. projected velocity dispersions aud rotation strength (Olt/o, = x) of the (τος groups of GCs are also listed."," The rotation amplitudes, rotation axes, projected velocity dispersions and rotation strength $\Omega$ $\sigma_{v}$ = x) of the three groups of GCs are also listed." + It is to be noted (hat lor determining rotation amplitude. rotation axis. projected velocity dispersion and rotation strength.," It is to be noted that for determining rotation amplitude, rotation axis, projected velocity dispersion and rotation strength," +In Figure 13.. the diameters (D.=ab with e and b respectively the long and short axes FWHM) and Hao| Nu] Iuminosities of N33 SNR remnants ancl of the six clouds identified in FCCOLG are presented (Long (199003).,"In Figure \ref{SNR}, the diameters $D = \sqrt{ab}$ with $a$ and $b$ respectively the long and short axes FWHM) and $\alpha+$ ] luminosities of M33 SNR remnants and of the six clouds identified in FCC046 are presented (Long \cite{lon}) )." + The properties of the largest clouds are consistent with those of SNRs., The properties of the largest clouds are consistent with those of SNRs. + The luminosities of the clouds are also compatible with those of regions ionised by the light of single stars but at leastC11.C13 and seem too Large for this interpretation.," The luminosities of the clouds are also compatible with those of regions ionised by the light of single 05-B0 stars but at least, and seem too large for this interpretation." + Phough suggestive. this of course docs not mean that they necessarily are SNlis.," Though suggestive, this of course does not mean that they necessarily are SNRs." + Nebulae around Wol-Ravet stars could. be a plausible alternative ancl are found in many irregulares and have appropriate Iuminosities and diameters (Hunter Gallagher (1986).. Chu Lasker (1980))).," Nebulae around Wolf-Rayet stars could be a plausible alternative and are found in many irregulars and have appropriate luminosities and diameters (Hunter Gallagher \cite{hun}, Chu Lasker \cite{chu}) )." + Lt is striking that these emission clouds. whatever their interpretation. are not found predominantly inside the bluish nebulosity to the north of the nucleus. something that," It is striking that these emission clouds, whatever their interpretation, are not found predominantly inside the bluish nebulosity to the north of the nucleus, something that" +The various results of the IIubble-tensor calculation are shown in several following lables.,The various results of the Hubble-tensor calculation are shown in several following tables. + Calculations were done [or [our cases: anisotropic expansion using the whole seanple. anisotropic using the 35 ealaxies wilh more accurate distances. and isotropic using each sample.," Calculations were done for four cases: anisotropic expansion using the whole 98-galaxy sample, anisotropic using the 35 galaxies with more accurate distances, and isotropic using each sample." + For reference. some parallel results from the literature are included.," For reference, some parallel results from the literature are included." + Considering the reflex solar velocity (vo. shown in Table 2)) first. (aking different samples and treating them dillerent wavs leads to a speed varving over a range of GO km s! and a direction changing over a dozen degrees.," Considering the reflex solar velocity ${\bf v}_0$, shown in Table \ref{solar}) ) first, taking different samples and treating them different ways leads to a speed varying over a range of 60 km ${\rm s}^{-1}$ and a direction changing over a dozen degrees." + Comparing these results with other determinations we find a similar variation., Comparing these results with other determinations we find a similar variation. + That of INarachentsev&Makarov(2001) uses a somewhat larger but overlapping sample of galaxies going out to a similar distance., That of \cite{KM01} uses a somewhat larger but overlapping sample of galaxies going out to a similar distance. + (1977) onlv used Local Group galaxies. so their result is not necessarily comparable (though it has been used to correct the radial velocities of more distant galaxies by. [or example. Schmidt&Boller (1992))).," \citet{YTS77} only used Local Group galaxies, so their result is not necessarily comparable (though it has been used to correct the radial velocities of more distant galaxies by, for example, \citet{SB92}) )." + The expected amount of variation. given the data. will be treated quantitatively below.," The expected amount of variation, given the data, will be treated quantitatively below." + The results for the Hubble Censor (as well as the isotropic solutions) are displaved in Table 3.., The results for the Hubble tensor (as well as the isotropic solutions) are displayed in Table \ref{tensor}. + The directions U. V and W are those of the eigenvectors. in no specilic order (tha is. U is not necessarily the closest eigenvector to X. and © in one solution is not necessarily the closest eigenvector to the U in the other).," The directions U, V and W are those of the eigenvectors, in no specific order (that is, U is not necessarily the closest eigenvector to X, and U in one solution is not necessarily the closest eigenvector to the U in the other)." + Given (he amount of attention which is to be paid to the deviations from the moclels. it is important to lev to separate (he effects of observational errors [rom real velocities.," Given the amount of attention which is to be paid to the deviations from the models, it is important to try to separate the effects of observational errors from real velocities." + For the linear relation between distance and radial velocity. deviations from the models are related by so the variances are If we assume that the distance errors are. proportional todistance.. and that their distribution once the distance is factored out is independent of them.," For the linear relation between distance and radial velocity, deviations from the models are related by so the variances are If we assume that the distance errors are proportional to, and that their distribution once the distance is factored out is independent of them," +svannelry with respect to Che rotation axis (Ixrauseetal.LO89b) and both classes have been observed in other galaxies (Becketal.1996).,symmetry with respect to the rotation axis \citep{KHB89} and both classes have been observed in other galaxies \citep{B96}. +. Galactic magnetic fields are further distinguished by (heir disk svimmetry. either sviumetric (even) or antisvmmetric (odd) across (he midplane (Ixrauseetal.1989b:seeTable1inBeck1996)..," Galactic magnetic fields are further distinguished by their disk symmetry, either symmetric (even) or antisymmetric (odd) across the midplane \citetext{\citealp{KHB89}; see Table 1 in \citealp{B96}}." + Here. only ASS magnetic field models are considered: these are classified as AO (odd) or SO (even).," Here, only ASS magnetic field models are considered; these are classified as A0 (odd) or S0 (even)." + This work will also consider clisk-even. halo-ocdd (DEIO) magnetic fields which have observational (Sunetal.2008) and theoretical (Mossetal.2010). foundations.," This work will also consider disk-even, halo-odd (DEHO) magnetic fields which have observational \citep{Sun08} and theoretical \citep{M10} foundations." + The polarizing mechanism described here is sensitive not to the directional polarity of the magnetic field. but (o its orientation (Lleiles1996).," The polarizing mechanism described here is sensitive not to the directional polarity of the magnetic field, but to its orientation \citep{H96}." +. Consider the two simple magnetic fieldl geometries in Fig. 1l:, Consider the two simple magnetic field geometries in Fig. \ref{cartoon}: + one in which the magnetic field inside a spiral arm has (lie same directional polarity as the magnetic field outside (he arm (ASS magnetic field). and one in which the magnetic field inside (he arm has the opposite directional polarity of the rest of ihe Galaxy (BSS magnetic field).," one in which the magnetic field inside a spiral arm has the same directional polarity as the magnetic field outside the arm (ASS magnetic field), and one in which the magnetic field inside the arm has the opposite directional polarity of the rest of the Galaxy (BSS magnetic field)." + A distant star whose light passes through this spiral arm to an observer would eain identical polarizations in both cases because the orientation of the fields is identical even though the directional polarities may differ., A distant star whose light passes through this spiral arm to an observer would gain identical polarizations in both cases because the orientation of the fields is identical even though the directional polarities may differ. + Ergo. background starlight polarimetry is insensitive to magnetic field reversals.," Ergo, background starlight polarimetry is insensitive to magnetic field reversals." + The predicted. NIB. polarizations were generated using simple magnetic fields configurations: axisvmameteric analv(ie magnetic fields: ancl axisvinmetric dvnamo-eeneraled configurations from the literature. in particular the dvnamo simulations of Ferriere&Sehimitt(2000) and. Mossetal.(2010).," The predicted NIR polarizations were generated using simple magnetic fields configurations: axisymmeteric analytic magnetic fields; and axisymmetric dynamo-generated configurations from the literature, in particular the dynamo simulations of \citet{FS2000} and \citet{M10}." +. From Ferriere&Sehimitt.(2000).. ihe numerical outputs of three SO and three AO magnetic field models were obtained (D. Schmitt. private communication).," From \citet{FS2000}, the numerical outputs of three S0 and three A0 magnetic field models were obtained (D. Schmitt, private communication)." + These magnetic field models had magnetic pitch angles from 7.0—10.6* and are listed in Table 1.., These magnetic field models had magnetic pitch angles from $7.0-10.6\degr$ and are listed in Table \ref{model_table}. + From Mossetal.(2010).. the nmunerical outputs ol three DEIIO magnetic field models (513b. 511b. and 527b) were obtained (D. Moss. private communication). corresponding to the three models shown in Fie.," From \citet{M10}, the numerical outputs of three DEHO magnetic field models (513b, 511b, and 527b) were obtained (D. Moss, private communication), corresponding to the three models shown in Fig." + 4 of that paper., 4 of that paper. +value.,value. + The section of the evolutionary tracks for which the models have a higher effective temperature than the approximate cool edge of the classical instability strip (Saio&Gautschy are colored gray., The section of the evolutionary tracks for which the models have a higher effective temperature than the approximate cool edge of the classical instability strip \citep{Saio98} are colored gray. +" For reference, four ‘features’ in the 1998)evolutionary tracks of Figure 4 are indicated in the H-R diagram in Figure 1.."," For reference, four `features' in the evolutionary tracks of Figure \ref{fig4} are indicated in the H-R diagram in Figure \ref{fig1}." +" T'hese features relate to the onset of a convective envelope (solid line) and of a convective core (long dashes), the Hertzsprung gap towards the base of the RGB(dot-dashes) and the so-called ‘bump’ (short where the hydrogen-burning shell burns through thedashes) discontinuity in molecular weight left from the deep convective envelope (‘first dredge up’) during the early ascent of the RGB (Thomas1967;Iben 1968)."," These features relate to the onset of a convective envelope (solid line) and of a convective core (long dashes), the Hertzsprung gap towards the base of the RGB(dot-dashes) and the so-called `bump' (short dashes) where the hydrogen-burning shell burns through the discontinuity in molecular weight left from the deep convective envelope (`first dredge up') during the early ascent of the RGB \citep{Thomas67, Iben68}." +". Since we are testing the scaling relation in models, it is appropriate that we use the value of Ave from a solar model rather than the observed value in the Sun."," Since we are testing the scaling relation in models, it is appropriate that we use the value of $\Delta\nu_\odot$ from a solar model rather than the observed value in the Sun." + These values differ due to the offset between observed and computed oscillation frequencies., These values differ due to the offset between observed and computed oscillation frequencies. + This offset is known to arise from an improper modeling of near-surface layers (Christensen-Dalsgaardetal.1988;DziembowskiDalsgaard&Thompson1997) and is presumably a problem for other stars as well (Kjeldsenetal.2008).," This offset is known to arise from an improper modeling of near-surface layers \citep{C-D88b, Dziembowski88, C-D96, +C-D97} and is presumably a problem for other stars as well \citep{Kjeldsen08}." +". The offset increases with frequency, at least in the Sun, and so affects the large separation, with Av being ~1% greater in solar models than observed (Kjeldsenetal. 2008)."," The offset increases with frequency, at least in the Sun, and so affects the large separation, with $\Delta\nu$ being $\sim1$ greater in solar models than observed \citep{Kjeldsen08}." +". We therefore adopted Ave=135.99 derived from a fit to frequencies of the well-studied Hz,model S of Christensen-Dalsgaardetal.(1996)."," We therefore adopted $\Delta\nu_\odot=135.99\,\mu\mathrm{Hz}$, derived from a fit to frequencies of the well-studied model S of \citet{C-D96}." +. We note that the surface offset also has a significant effect on óvgo (Roxburgh&Vor," We note that the surface offset also has a significant effect on $\delta +\nu_{02}$ \citep{Roxburgh03}." +"ontsov From Figure 4 we can see 2003)..that the scaling relation holds quite well for lower-mass main-sequence stars, but there is a significant deviation at other masses and evolutionary states."," From Figure \ref{fig4} we can see that the scaling relation holds quite well for lower-mass main-sequence stars, but there is a significant deviation at other masses and evolutionary states." + These deviations can be as large as for low-mass red giants and are over within the instability strip., These deviations can be as large as for low-mass red giants and are over within the instability strip. +" In Figure 5 we show the ratio against effective temperature, Tog."," In Figure \ref{fig5} we show the ratio against effective temperature, $T_{\mathrm{eff}}$ ." + From this we see that the deviation, From this we see that the deviation +and Here a is the hadron-to-lepton energy density ratio.,and Here $a$ is the hadron-to-lepton energy density ratio. +" We consider a=100 as observed in cosmic rays in the solar neighborhood (Ginzburg Syrovatskii 1964), Ly is the power in the form of relativistic particles and V is the acceleration volume, i.e. the volume of the flux tube."," We consider $a = 100$ as observed in cosmic rays in the solar neighborhood (Ginzburg Syrovatskii 1964), $L_{\rm rel}$ is the power in the form of relativistic particles and $V$ is the acceleration volume, i.e. the volume of the flux tube." +" The state particle distributions N(E) are obtained solving the steadytransport equation in the homogeneous approximation, where fec=ἴσοιν."," The steady state particle distributions $N(E)$ are obtained solving the transport equation in the homogeneous approximation, where $t_{\rm esc} = t_{\rm conv}$." + This equation has an exact analytical solution (see Ginzburg Syrovatskii 1964): with Figures 5 and 4 show the steady state particle distribution for protons and electrons., This equation has an exact analytical solution (see Ginzburg Syrovatskii 1964): with Figures \ref{Pro} and \ref{Ele} show the steady state particle distribution for protons and electrons. + These distributions are valid only as as we consider intervals much shorter than the timescale of longthe flare., These distributions are valid only as long as we consider intervals much shorter than the timescale of the flare. +" In order to estimate the luminosity due to electrons we computed synchrotron, relativistic Bremsstrahlung, synchrotron self-Compton (SSC) radiation, and IC up scattering of external seed photons (X-ray and IR radiation fields)."," In order to estimate the luminosity due to electrons we computed synchrotron, relativistic Bremsstrahlung, synchrotron self-Compton (SSC) radiation, and IC up scattering of external seed photons (X-ray and IR radiation fields)." + We calculate for protons synchrotron and y-ray emission from 4? decay in pp inelastic collisions., We calculate for protons synchrotron and $\gamma$ -ray emission from $\pi^{0}$ decay in $pp$ inelastic collisions. + We consider also thesynchrotron contribution from secondary pairs injected by charged pion decay (e.g. Orellana et al., We consider also the contribution from secondary pairs injected by charged pion decay (e.g. Orellana et al. + 2007)., 2007). + The maximum particle density is ~ 5x 1011 cm?., The maximum particle density is $\sim$ $\times$ $^{11}$ $^{-3}$. + It is localized in the accretion columns., It is localized in the accretion columns. + We consider a cylindrical portion of the accretion column of radius rac ~ 10!° cm and height ~ 0.1 rac (e.g. Orlando et al., We consider a cylindrical portion of the accretion column of radius $r_{\rm AC}$ $\sim$ $10^{10}$ cm and height $\sim$ 0.1 $r_{\rm AC}$ (e.g. Orlando et al. + 2010)., 2010). + This volume is where most of the relativistic interactions with matter takeplace®., This volume is where most of the relativistic interactions with matter take. +. For more details on high-energy processes see Vila Aharonian (2009) and Vila (2010)., For more details on high-energy processes see Vila Aharonian (2009) and Vila (2010). + Attenuation of the radiation produced byphoton annihilation is expected in T Tauri stars., Attenuation of the radiation produced byphoton annihilation is expected in T Tauri stars. +" The opacity produced by a photon field with density np,(e) and photon energy e is Here ηΞcos, # is the angle between the momenta of the colliding photons, / is the photon path, and σγγ(Εγ.ει) is the cross section for photon annihilation (Gould Schrédder 1967)."," The opacity produced by a photon field with density $n_{\rm ph}(\epsilon)$ and photon energy $\epsilon$ is Here $u = \cos \vartheta$, $\vartheta$ is the angle between the momenta of the colliding photons, $l$ is the photon path, and $\sigma_{\gamma\gamma}(E_{\gamma}, \epsilon,u)$ is the cross section for photon annihilation (Gould Schrédder 1967)." +" The absorbing photon fields are those generated within the system and the strong blackbody radiation field from the the disk (IR), the star, and the X-rays from the accreting surroundings:plasma."," The absorbing photon fields are those generated within the system and the strong blackbody radiation field from the surroundings: the disk (IR), the star, and the X-rays from the accreting plasma." +"To estimate the disk infrared photon field we adopt an internal radius for the disk of Rp ~ 120 AU (see Fig. 1)),","To estimate the disk infrared photon field we adopt an internal radius for the disk of $R_{\rm D}$ $\sim$ 120 AU (see Fig. \ref{fig:magnetosphere}) )," + and a temperature of T ~ 30 K (Dutrey et al., and a temperature of $T$ $\sim$ 30 K (Dutrey et al. + 1994)., 1994). + The X-ray temperature is taken to be T ~ 107 K (e.g. Feigelson Montmerle 1999)., The X-ray temperature is taken to be $T$ $\sim$ $^{7}$ K (e.g. Feigelson Montmerle 1999). +" Regarding the star, we consider a temperature of T, ~ 4x 10? K, and a radius R, ~ 2 Ro."," Regarding the star, we consider a temperature of $T_{\star}$ $\sim$ $\times$ $^{3}$ K, and a radius $R_{\star}$ $\sim$ 2 $R_{\odot}$ ." +" The opacity 7 (attenuation e 7) as a function of E, is shown in Fig. 6..", The opacity $\tau$ (attenuation $e^{-\tau}$ ) as a function of $E_{\gamma}$ is shown in Fig. \ref{Opa}. + The absorption is almost complete above 100 GeV., The absorption is almost complete above 100 GeV. +{Mux limit aud the fraction with redshifts set. we are now in a position to derive [rom the luminosity function for a given (the predicted distributions of Iuminosity. and redshift for the ssanple.,"flux limit and the fraction with redshifts set, we are now in a position to derive from the luminosity function for a given the predicted distributions of luminosity and redshift for the sample." + As discussed at the end of Sec., As discussed at the end of Sec. + 3. the only unknown in deriving the GRD luninosity [unction. given the correlation. is the redshift dependenceG2(2).," 3, the only unknown in deriving the GRB luminosity function, given the correlation, is the redshift dependence." +. Therefore. we can view (he excercise as one in which we explore which shape of iis compatible with the observations based on cedata.," Therefore, we can view the excercise as one in which we explore which shape of is compatible with the observations based on data." + We first explore the case where iis the galaxy star formation history (SEIL)., We first explore the case where is the galaxy star formation history (SFH). + In the many published studies of star formation in the literature. the SEIL rises fast with redshift bv about an order of magnitude out to zo1.5. bevond which it levels off: it tends to decline bevond z—3.," In the many published studies of star formation in the literature, the SFH rises fast with redshift by about an order of magnitude out to $z \sim 1.5$, beyond which it levels off; it tends to decline beyond $z \sim 3$." + We use the analvtical expression. normalized to z=0. for the ΕΤΗ described by Hopkius&Beacom(2006).. based on an extensive compilation by Hopkins(2004).," We use the analytical expression, normalized to $z=0$, for the SFH described by \citet{hop06}, based on an extensive compilation by \citet{hop04}." +. The predicted distributions of luminosity and redshift are compared to the oobservations in Figures 3 and 4., The predicted distributions of luminosity and redshift are compared to the observations in Figures 3 and 4. + The predicted imunuber of GRBs (with redshifts) is 79.6. while the observed nunber is 84.," The predicted number of GRBs (with redshifts) is 79.6, while the observed number is 84." + The prediction is ~5% below the observed number., The prediction is $\sim 5\%$ below the observed number. + It is obvious that the agreement with the observations is poor. both for the Iuminosities and the redshifts.," It is obvious that the agreement with the observations is poor, both for the luminosities and the redshifts." + We have carried out Monte Carlo simulations to find the probability. that the observed number of Iuminosities above log£=51.5 can be produced lom the predicted distribution bv chance., We have carried out Monte Carlo simulations to find the probability $P(\log L > 51.5)$ that the observed number of luminosities above $\log L = 51.5$ can be produced from the predicted distribution by chance. + We find P(logL>51.5)<10°., We find $P(\log L > 51.5) < 10^{-6}$. +" Similarly. for redshifts above 3.0 the probability P(z>3.0)<10"". see Table 3."," Similarly, for redshifts above 3.0 the probability $P(z > 3.0) < 10^{-6}$, see Table 3." +" Even if we continue the SFIL bevond the peak redshilt 2=2.55 at its peak value without any downturn. (he agreement remains poor. with P(logL>51.5)<10"" and P(z>3.0)=0.007."," Even if we continue the SFH beyond the peak redshift $z = 2.55$ at its peak value without any downturn, the agreement remains poor, with $P(\log L > 51.5) < 10^{-6}$ and $P(z > 3.0) = 0.007$." + Clearly. the SEIL cannot represent.," Clearly, the SFH cannot represent." +f2(z).. With little guidauce as to what the shape of ccould be. we use a simple schematic involving a (12) power law rise. a plateau. ancl an," With little guidance as to what the shape of could be, we use a simple schematic involving a $(1+z)$ power law rise, a plateau, and an" +order to constrain the origeiu of wwe asstued a maxiuuni age of ~ 109 sr. compatible with possible cooling times of à young ueutron star with kT ~ ου (see below. Yakovlev Pethick 2001)). clistauces in the range of ppc to ppc aud radial velocities iu he range of + |.,"order to constrain the origin of we assumed a maximum age of $\sim$ $^{6}$ yr, compatible with possible cooling times of a young neutron star with kT $\sim$ eV (see below, Yakovlev Pethick \cite{yakovlev2004}) ), distances in the range of pc to pc and radial velocities in the range of $\pm$ $^{-1}$." + Considering he short flight ine. we also neglect the effects of the galactic potential.," Considering the short flight time, we also neglect the effects of the galactic potential." + The only nearby OB association overlapping with some vackward trajectories is the upper Scorpius-C'enutaurus region belonging to the Sco OD2 complex., The only nearby OB association overlapping with some backward trajectories is the upper Scorpius-Centaurus region belonging to the Sco OB2 complex. + Amazinely. Walter Lattimer (2002)) derive a similar birth place or jin the upper Scorpius while \lotch et al. (2003))," Amazingly, Walter Lattimer \cite{wl2002}) ) derive a similar birth place for in the upper Scorpius while Motch et al. \cite{motch03}) )" + speculate on a possible birth place iu the ower Contaurus-Crusx part of the same Sco OB2 complex or3, speculate on a possible birth place in the lower Centaurus-Crux part of the same Sco OB2 complex for. +"125, We show iu Fig.", We show in Fig. + the inage obtained iu 1999., \ref{halpha} the image obtained in 1999. + Au exteuded aud elongatedc» source is clearly secu at the position of3219., An extended and elongated source is clearly seen at the position of. + The enüissiou is detecte on individual nuages whose centers were shifted ly several huudreds of pixels aud is thus unlikely to be of instrumental origin or caused by the absence of fiat-&ek correction., The emission is detected on individual images whose centers were shifted by several hundreds of pixels and is thus unlikely to be of instrumental origin or caused by the absence of flat-field correction. + The direction of largest exteut of the uchula is close to that of the apparent trajectory., The direction of largest extent of the nebula is close to that of the apparent trajectory. + nuebulae have been discovered around a small wmuber of isolate ueutron stars (sce Chatterjee Cordes 2002. for a recent review)., nebulae have been discovered around a small number of isolated neutron stars (see Chatterjee Cordes \cite{cc2002} for a recent review). + They have in general a well defined are-like shape extending several tens of arcseconds on the sky which can be interpreted as due to a bow shock created by the interaction of the lugho velocity pulsar wind with the ↕∐↑↸∖↥⋅↴∖↴↑↸∖∐⋜∐⋅⋯↸∖, They have in general a well defined arc-like shape extending several tens of arcseconds on the sky which can be interpreted as due to a bow shock created by the interaction of the high velocity pulsar wind with the interstellar medium. +≺∐∏⋯∙↕∐↑∐↸∖⋯↴∖↴↸∖∪↕≯↕⊰⊸∖⊽⋅↧↽≺∖∖⋅↱⊐⊓∙⋅↱⊢∶≩⊤⋅↱⊐ ∐⋜↧↕↻↸∖∐∐↴∖↴↴∖↴↕∪∐↸⊳⋯∏≼↧⋜↧↕↴∖↴∪⋝↸∖≺⊔∐∖↑∪⊸∖⊽≓↥⋅⋜↧⋅↖⇁↕∪∐↕∑⋜↧, In the case of emission could also be due to X-ray ionization (van Kerkwijk Kulkarni \cite{vk2001b}) ). +↑↕∪∐ ≺↖↽⋜⋯↕↘⊽↸∖↥⋅↨↘↽↖↖↽↕⋅∏↘↽∙∖↽↕↘⊽∏∐↘↽⋜∐⋅∐⊔∩⊓⋝⋝⋝⋅↽∕∏∐∖ xieht cvlindrical head of the Cautar nebula produced by the radio oulsar B2221165 (Cordes et al. 1993)).," The bright cylindrical head of the Guitar nebula produced by the radio pulsar B2224+65 (Cordes et al. \cite{cordes93}) )," + although significantly larger.oO could be a scalec-up analogueoO of the nebula seen here.," although significantly larger, could be a scaled-up analogue of the nebula seen here." + However. we shall see below that this is du fact uulikely aud that the shape aud probably also the oviein of the nebula detected around. aare que.," However, we shall see below that this is in fact unlikely and that the shape and probably also the origin of the nebula detected around are unique." + We tried to coustrain the actual size aud orientation of the cemission by fitting to the observed image a model consisting of a cylinder convolved with the poiut spread fiction., We tried to constrain the actual size and orientation of the emission by fitting to the observed image a model consisting of a cylinder convolved with the point spread function. + Owing to the poor spatial resolution available. we asstuned a simple uniformly cuitting bar VAjiipe characterized by its leugth. width aud oricutation.," Owing to the poor spatial resolution available, we assumed a simple uniformly emitting bar shape characterized by its length, width and orientation." + The Caussiuir parameters of the poiut spread function were clevived from the uearby star ο which is unresolved ithe TST tuage aud is a likely dwartM star (Motel et al. mee 999)).," The Gaussian parameters of the point spread function were derived from the nearby star ""C"" which is unresolved in the HST image and is a likely dwarf M star (Motch et al. \cite{motch1999}) )." + We used a 2-d mium 47 fitting process taking oeito account CCD readout noise aud counting statistics., We used a 2-d minimum $\chi^{2}$ fitting process taking into account CCD readout noise and counting statistics. +0.49 ps half-life (Wheatonοἱal.1989).,0.49 ps half-life \citep{Wh89}. +. Unlike simple geographic or geomagnetic coordinates. however. LAN and PAN also contain a memory of the recent history of the spacecraft trajectory most usefully. how recently and how deeply the spacecralt passed through the SAA.," Unlike simple geographic or geomagnetic coordinates, however, LAN and PAN also contain a memory of the recent history of the spacecraft trajectory – most usefully, how recently and how deeply the spacecraft passed through the SAA." + Thus matching LAN and PAN also produces a good. match for the SAA-induced background lines. which have half-lives [rom minutes to hours.," Thus matching LAN and PAN also produces a good match for the SAA-induced background lines, which have half-lives from minutes to hours." + We see such a line around 1811 keV that blends with the line., We see such a line around 1811 keV that blends with the line. + The only candidate in the gamma-ray. tables of Chu.Ekstróm&Firestone(1999) is the 1810.77. keV line of °°Mn (halflife 2.6 hr). presumably created by interactions of SAA protons with iron near the detectors.," The only candidate in the gamma-ray tables of \citet{Ch99} is the 1810.77 keV line of $^{56}$ Mn (half-life 2.6 hr), presumably created by interactions of SAA protons with iron near the detectors." +" This line was suggested as a contributor to the backeround of the germanium spectrometer on (he Wind spacecralt. (Weidenspointierοἱal.2001).. ancl the published bbackground line from ZEAO 3 (Mahoney.οἱal.1934). shows an excess in the blue wing that is consistent with the ""Mn line appearing at a low level."," This line was suggested as a contributor to the background of the germanium spectrometer on the Wind spacecraft \citep{We02}, and the published background line from HEAO 3 \citep{Ma84} shows an excess in the blue wing that is consistent with the $^{56}$ Mn line appearing at a low level." + There is no very long-lived backeround line (such as the 1275 keV line from δα) nearkeV., There is no very long-lived background line (such as the 1275 keV line from $^{22}$ Na) near. +. Such a line would require a backerounc-selection svstem which is cognizant of the total lime since the start of ihe mission. rather than relving entirely on LAN and PAN.," Such a line would require a background-selection system which is cognizant of the total time since the start of the mission, rather than relying entirely on LAN and PAN." + Figure 1 (left) shows the RIIESSI background-subtracted spectrum of the Galactic lline., Figure 1 (left) shows the RHESSI background-subtracted spectrum of the Galactic line. + The smooth curve shown is of the average background for comparison., The smooth curve shown is of the average background for comparison. + Fitting the spectrum from 1790.1825 keV to a Gaussian plus a linear background. I find a center energy of (1808.51£0.18) keV. 1.20 [rom the expected rest energv of the line at 1808.65 keV 1999).," Fitting the spectrum from 1790–1825 keV to a Gaussian plus a linear background, I find a center energy of $(1808.87 \pm 0.18)$ keV, $\sigma$ from the expected rest energy of the line at 1808.65 keV \citep{Ch99}." +. The area of the line is (1.1720.11) ((11o0). which is of the background line (averaged over the entire set of background spectra interpolated from the background library).," The area of the line is $(1.17 \pm 0.11)$ $\sigma$ ), which is of the background line (averaged over the entire set of background spectra interpolated from the background library)." + Its EWIIM. which includes instrumental broadening. is (4.58+0.44) keV. The fit is good (4? = 26.7 with 30 degrees of freedom).," Its FWHM, which includes instrumental broadening, is $(4.58 \pm 0.44)$ keV. The fit is good $\chi^2$ = 26.7 with 30 degrees of freedom)." + By fitting seven narrow background lines ranging from 186 keV to 2243 keV. Linterpolate (he intrinsic instrumental resolution to its value al aand find (4.10£0.07) keV. E avoid the instrumental background line at litself because of the blend with the line al 1811 keV. which makes it much broader than the interpolation ((4.862:0.08) keV EWILIM) and raises its center energy to (1509.242370.03) keV. Subtractinge the instrumental resolution inequacdrature from the Galactic line exgives an intrinsic . ⊳∙⋅∣∣∡⋀↼↴↖⋉ ↽ i∙↽∙∙ ∙ ∖∖⇁↕≺∐∐∪↓∟≻⋅∩≡⊰⋅↽≽⋝↳↽≼↲∖⋅≺∢∪↕⋅↕⋅≼↲⋟∖⊽≻∪∐≼∐∐⋃↥∪∖↽≼↲↥∪≺∢∐↕≼↲⋟∖⊽∪↓∾−≻∪∩↳↽∐↓∕∕⋟∖⊽∪↕⋅≀↕↴∩↲∐↓↽≻≼↲↕⋅≀↧↴⊓∐⋅≼↲∪↓ 1.21 o 1.7x 10K.," By fitting seven narrow background lines ranging from 186 keV to 2243 keV, I interpolate the intrinsic instrumental resolution to its value at and find $(4.10 \pm 0.07)$ keV. I avoid the instrumental background line at itself because of the blend with the line at 1811 keV, which makes it much broader than the interpolation $(4.86 \pm 0.08)$ keV FWHM) and raises its center energy to $(1809.34 \pm 0.03)$ keV. Subtracting the instrumental resolution in quadrature from the Galactic line gives an intrinsic width of $(2.03 ^{+0.78}_{-1.21})$ keV, corresponding to velocities of $\sim$ 200 km/s or a temperature of $1.7 \times 10^{8}$ K." +"During the forced period, o; fluctuates above and below 0.","During the forced period, $\sigma_c$ fluctuates above and below 0." +" When the forcing is removed, |o,| increases, as expected from dynamic alignment theory (Dobrowolnyetal.1980)."," When the forcing is removed, $|\sigma_c|$ increases, as expected from dynamic alignment theory \citep{dobrowolny80}." +". The increase is fairly slow: |σε] changes from 0.045 at t=28 to 0.13 at t—78, which isconsistent with previous decaying simulations 1994)."," The increase is fairly slow: $|\sigma_c|$ changes from $0.045$ at $t=28$ to $0.13$ at $t=78$ , which isconsistent with previous decaying simulations \citep[e.g.][]{grappin82,matthaeus83,pouquet86,oughton94}." +". The rratio rA is shown in the fourth panel, calculated over the same range as σ.."," The ratio $r_A$ is shown in the fourth panel, calculated over the same range as $\sigma_c$." +" During the forced period 4«t<28, its mean value is rA&0.66, which is close to the solar wind observations (Table 1))."," During the forced period $4\leq t\leq 28$, its mean value is $r_A \approx 0.66$, which is close to the solar wind observations (Table \ref{tab:parameters}) )." +" As the turbulence decays, r4 grows and approaches unity; this equipartition of energy is expected for MHD turbulence 1965)."," As the turbulence decays, $r_A$ grows and approaches unity; this equipartition of energy is expected for MHD turbulence \citep{kraichnan65}." +". We note that the opposite effect is seen in simulations without a strong mean field (e.g.Oughton&Müller 1999),, in which the rratio decreases away from unity as the energy decays."," We note that the opposite effect is seen in simulations without a strong mean field \citep[e.g.][]{oughton94,biskamp99b}, in which the ratio decreases away from unity as the energy decays." +" The fact that the equipartition occurs only in the decaying period of our RMHD simulation, while solar wind observations show r4«1 (e.g.2007;Brunoetal.Salem 2009),, suggests that solar wind turbulence may be better described by a forced model."," The fact that the equipartition occurs only in the decaying period of our RMHD simulation, while solar wind observations show $r_A<1$ \citep[e.g.][]{matthaeus82a,marsch90a,podesta07a,bruno07,salem09}, suggests that solar wind turbulence may be better described by a forced model." + The perpendicular spectral indices for the velocity and magnetic field are shown in the lower panel of Fig. 4.., The perpendicular spectral indices for the velocity and magnetic field are shown in the lower panel of Fig. \ref{fig:timeseries}. + They are calculated from the gradients of the best fit lines to the perpendicular energy spectrum in log-log space over the range 7<Κι«33 every time unit., They are calculated from the gradients of the best fit lines to the perpendicular energy spectrum in log-log space over the range $7\leq k_\perp\leq 33$ every time unit. + The perpendicular spectrum is calculated as the sum of the energy in modes nearest to Κι=V&2 for integer values of Κι., The perpendicular spectrum is calculated as the sum of the energy in modes nearest to $k_\perp=\sqrt{k_x^2+k_y^2}$ for integer values of $k_\perp$. +" During the forced period, the spectral indices are closer to —3/2 than —5/3, in agreement with previous results (Maron&Goldreich2001;Mülleretal.2003;Grap- 2010)."," During the forced period, the spectral indices are closer to $-3/2$ than $-5/3$, in agreement with previous results \citep{maron01,muller03,muller05,mason08,perez08,grappin10}." +". When the forcing is removed, however, they gradually steepen and appear to reach a steady value of —5/3 from t—58 onwards."," When the forcing is removed, however, they gradually steepen and appear to reach a steady value of $-5/3$ from $t=58$ onwards." +" In the following analysis, we investigate the anisotropic scaling in the forced period 4«t28, and the decaying period 58«t<78."," In the following analysis, we investigate the anisotropic scaling in the forced period $4\leq t\leq 28$, and the decaying period $58\leq t\leq 78$." + We assume that in each of these periods the turbulence is stationary and we can perform time averages over them., We assume that in each of these periods the turbulence is stationary and we can perform time averages over them. + The averaged energy spectra are shown in Fig. 5.., The averaged energy spectra are shown in Fig. \ref{fig:spectra}. +" Before averaging, the decaying spectra are normalised so that the average energy over the range 7XΚι<33 for each is the same as that att=58."," Before averaging, the decaying spectra are normalised so that the average energy over the range $7\leq k_\perp\leq 33$ for each is the same as that at $t=58$." +" Gradients of —5/3 and —3/2 are given for reference, although it is hard to tell the difference between these visually."," Gradients of $-5/3$ and $-3/2$ are given for reference, although it is hard to tell the difference between these visually." + It can be seen that for 7€κι«33 there are well defined power laws in all of the spectra., It can be seen that for $7\leq k_\perp\leq 33$ there are well defined power laws in all of the spectra. +" It has been suggested (e.g.Perez&Boldyrev2010) that the use of hyperviscosity may increase the bottleneck effect, altering the scaling."," It has been suggested \cite[e.g.][]{perez10b} that the use of hyperviscosity may increase the bottleneck effect, altering the scaling." + The spectra in Fig., The spectra in Fig. +" 5 do not, however, display the increase of energy at small scales that is associated with the bottleneck effect and is seen in some MHD simulations (e.g.Cho&Vishniac2000;Beresnyak 2011)."," \ref{fig:spectra} do not, however, display the increase of energy at small scales that is associated with the bottleneck effect and is seen in some MHD simulations \citep[e.g.][]{cho00,beresnyak11}." +". In the next section, we measure the anisotropic scaling using structure functions, which are expected to be less susceptible to the bottleneck effect than Fourier spectra etal. 2003)."," In the next section, we measure the anisotropic scaling using structure functions, which are expected to be less susceptible to the bottleneck effect than Fourier spectra \citep{dobler03}." +". The technique we use to analyse the simulation data is similar to that used in Section 2.2,, with modifications to account for the simulation geometry."," The technique we use to analyse the simulation data is similar to that used in Section \ref{sec:swanalysistechnique}, with modifications to account for the simulation geometry." +" Firstly, the scaling factor R, which should be larger than unity for the RMHD equations to be valid, is chosen."," Firstly, the scaling factor $R$, which should be larger than unity for the RMHD equations to be valid, is chosen." +" Here, we set R—4, which is a compromise between typical solar wind wavevector anisotropies k,/kj of between 2 and 3 and typical 5B,/Bo values of 0.1 (calculated from the data in Section 2.3))."," Here, we set $R=4$, which is a compromise between typical solar wind wavevector anisotropies $k_\perp/k_\para$ of between 2 and 3 and typical $\delta\mathbf{B}_\perp/B_0$ values of 0.1 (calculated from the data in Section \ref{sec:mfa}) )." +" This means that the simulation, which was solved in a (27)? box, is now stretched to have a size (27)*x87 and the sspeed is set to 4."," This means that the simulation, which was solved in a $(2\pi)^3$ box, is now stretched to have a size $(2\pi)^2\times8\pi$ and the speed is set to 4." +" For a particular snapshot in time, many pairs of points in the simulation box are picked at random."," For a particular snapshot in time, many pairs of points in the simulation box are picked at random." +" The second-order structure function values of the local perpendicular velocity and magnetic field components are calculated and binned, as in Section 2.2.."," The second-order structure function values of the local perpendicular velocity and magnetic field components are calculated and binned, as in Section \ref{sec:swanalysistechnique}." + The structure function of the magnetic field binned with respect to J) and { at f=28 is shown in Fig. 6.., The structure function of the magnetic field binned with respect to $l_{\para}$ and $l_{\perp}$ at $t=28$ is shown in Fig. \ref{fig:s2ppsim}. + There are on average 10 structure function values in each bin., There are on average $10^4$ structure function values in each bin. + The structure function in Fig., The structure function in Fig. + 6 is representative of the general shape of the velocity and magnetic field structure functions in both the forced and decaying periods of the simulation., \ref{fig:s2ppsim} is representative of the general shape of the velocity and magnetic field structure functions in both the forced and decaying periods of the simulation. + Similarly to the solar wind (Fig. 2)), Similarly to the solar wind (Fig. \ref{fig:s2ppsw}) ) +" and previous simulations (Cho&Vishniac2000),, the contours are elongated in the parallel direction."," and previous simulations \citep{cho00}, the contours are elongated in the parallel direction." +" In the range 0.35€/<1.3, which corresponds approximately to5 r_F/\pi D$. + Just as before. we can replace cos? with 1/2.," Just as before, we can replace $\cos^2$ with $1/2$." + Unlike the case considered in Sect. 3..," Unlike the case considered in Sect. \ref{sec:zero_exp}," + the cross-Lilter is proportional to ~qt near zero and it does not provide elective suppression of the approximation error., the cross-filter is proportional to $\sim q^4$ near zero and it does not provide effective suppression of the approximation error. + Thus. the approximate integrand has an infinite derivative at ο=0. while the exact expression has Zero derivative.," Thus, the approximate integrand has an infinite derivative at $q = 0$, while the exact expression has zero derivative." + Such distinction leads to 10 percent error. which was estimated. from a comparison of the asvmptote with numerical integration of the formula (19)).," Such distinction leads to $\approx $ 10 percent error, which was estimated from a comparison of the asymptote with numerical integration of the formula \ref{eq:wddz}) )." + As a result. of these transformations. the expression reduces to the dimensionless integral Za(e.jy). where (AL/A9) 7. with the dimensions factor in [ront of it: The Z4 depends implicitly on the distance to the laver > through jy. but it is not very important for a general estimate.," As a result of these transformations, the expression reduces to the dimensionless integral ${\mathcal I_3(a,y)}$, where $a = (\lambda_1/\lambda_2)^{1/2}$ , with the dimensions factor in front of it: The ${\mathcal I_3}$ depends implicitly on the distance to the layer $z$ through $y$, but it is not very important for a general estimate." + The dependence on y can be obtained by replacing the filter 1Jy(2ryq) with its approximate expression. x7?gq which is applicable when ys 1., The dependence on $y$ can be obtained by replacing the filter $1-J_0(2\pi yq)$ with its approximate expression $\pi^2 y^2 q^2$ which is applicable when $y \la 1$ . + In this case. the integral The relative displacement y depends implicitly on the wavelength ratio e through the refractive index dillerence (18)).," In this case, the integral The relative displacement $y$ depends implicitly on the wavelength ratio $a$ through the refractive index difference \ref{eq:x-z}) )." +" As the dillerence between the wavelengths gets larger. the factor depending on e in (21)) becomes smaller. but this is compensated by the increased ""na"," As the difference between the wavelengths gets larger, the factor depending on $a$ in \ref{eq:i3appr}) ) becomes smaller, but this is compensated by the increased $y^2$." + In the case Ay=As. the integral Z4 is calculated analytically after cdillerentiation over y. but in a rather complicated way through hypergeometric functions.," In the case $\lambda_1 = \lambda_2$, the integral ${\mathcal I_3}$ is calculated analytically after differentiation over $y$, but in a rather complicated way through hypergeometric functions." + Its xhaviour is shown in Fig., Its behaviour is shown in Fig. + 5 in two scales., \ref{fig:i3_y} in two scales. + We see that [or yx0.3 the dependence is quadratic. then it. progressively oconies weaker than linear.," We see that for $y < 0.3$ the dependence is quadratic, then it progressively becomes weaker than linear." + Comparison with the formula (21)) demonstrates that the latter provides estimates with an accuracy of about 5 percent up toy=0.3., Comparison with the formula \ref{eq:i3appr}) ) demonstrates that the latter provides estimates with an accuracy of about 5 percent up to $y = 0.3$. + Consequently. or air masses AJ;X1.5. the use of quadratic dependence of AGxag! or iNxAL.(AIP1) is sullicient for practical ρώσος.," Consequently, for air masses $M_z \la 1.5$, the use of quadratic dependence of $\Delta s^2_d \propto y^2 $ or $\Delta s^2_d \propto M_z\,(M_z^2-1)$ is sufficient for practical purposes." + Comparison of the formula (20)) with the (13)) for the colour scintillation shows that their ratio depends: only on the wavelengths of the photometric channels ancl on the relative displacement y. The relative contribution of the atmosphericdispersion to colour scintillation will be, Comparison of the formula \ref{eq:qdelta}) ) with the \ref{eq:assimp}) ) for the colour scintillation shows that their ratio depends only on the wavelengths of the photometric channels and on the relative displacement $y$ The relative contribution of the atmosphericdispersion to colour scintillation will be +and construct integrated spectra.,and construct integrated spectra. + We consider the case in which bremsstrahlung radiation is the only cooling process anc ignore evelotron cooling. so to illustrate the dillerences between between it and the conventional post-shock X-ray. emission regions resulting from the Aizu (1973) formulation.," We consider the case in which bremsstrahlung radiation is the only cooling process and ignore cyclotron cooling, so to illustrate the differences between between it and the conventional post-shock X-ray emission regions resulting from the Aizu (1973) formulation." + Figure 5 illustrates the differences in the emitted spectrum with respect to the conventional formulation for M... ane 0.5-M.. white chvarls., Figure 5 illustrates the differences in the emitted spectrum with respect to the conventional formulation for $\Msun$ and $\Msun$ white dwarfs. +" Phe variable πμ(ή) is the ratio of the bremsstrahlung emissivitv for the “leaky” post-shock region πμnu) to that for the conventional region ji,(I7:0). where £ is the photon energy."," The variable $\psi_{\rm bf}(E)$ is the ratio of the bremsstrahlung emissivity for the “leaky” post-shock region $j_{\rm br}(E;\tau_{\rm m})$ to that for the conventional region $j_{\rm br}(E;0)$, where $E$ is the photon energy." +" When 7, is relatively large (~0.01). a significant fraction of accreting material is lost from the post-shock region at large height (see Fig."," When $\tau_{\rm m}$ is relatively large $\sim 0.01$ ), a significant fraction of accreting material is lost from the post-shock region at large height (see Fig." + 1)., 1). + Because we require al of the accretion energy to be liberated before the matter diffuses out of the post-shock region. the accretion energy is racliate at higher energies and the 120 keV region of the resulting spectrum is enhanced with respect to that of the spectrum from the conventional post-shock region.," Because we require all of the accretion energy to be liberated before the matter diffuses out of the post-shock region, the accretion energy is radiated at higher energies and the 1–20 keV region of the resulting spectrum is enhanced with respect to that of the spectrum from the conventional post-shock region." + For 1.0-M.. white chvarfs the spectrum below ~5 keV is harder than that from the conventional postshock region. while above this value it is softer.," For $\Msun$ white dwarfs the spectrum below $\sim 5$ keV is harder than that from the conventional post-shock region, while above this value it is softer." + This ellect is enhanced if significant heat Hux is permitted from the white dwarf (larger values of m)., This effect is enhanced if significant heat flux is permitted from the white dwarf (larger values of $\tau_{\rm h}$ ). + For lower values of my. the temperatures are already. low at the base of the region. and the main elfect is that of the increased. heating from the white chvarl at energies below 1 keV. Phe spectrum in this case is softer than that [rom the conventional formulation. but only at low energies.," For lower values of $\tau_{\rm m}$, the temperatures are already low at the base of the region, and the main effect is that of the increased heating from the white dwarf at energies below 1 keV. The spectrum in this case is softer than that from the conventional formulation, but only at low energies." +" When both τι and 7, tend to zero. the spectrumretains the conventional form."," When both $\tau_{\rm m}$ and $\tau_{\rm h}$ tend to zero, the spectrumretains the conventional form." + From Figure 5 it is clear that it is possible to obtain either a harder or softer spectrum than that from the conventional »ost-shock region. depending on leakage parameter Τι and heating parameter mj. and on the energy range considered.," From Figure 5 it is clear that it is possible to obtain either a harder or softer spectrum than that from the conventional post-shock region, depending on leakage parameter $\tau_{\rm m}$ and heating parameter $\tau_{\rm h}$, and on the energy range considered." + When itting to X-ray spectral data. a harder model spectrum will result in a lower-mass determination for the white dwarf.," When fitting to X-ray spectral data, a harder model spectrum will result in a lower-mass determination for the white dwarf." +" Lo 73, is significant. then for typical CCD or proportional counter detectors operating in the 0.220 keV range. fitting spectra from the “leaky” formulation will generally therefore result in lower masses for more massive white cwarfs than those obtained. using he Aizu (1973) or Wu ((1994) formulations."," If $\tau_{\rm m}$ is significant, then for typical CCD or proportional counter detectors operating in the 0.2–20 keV range, fitting spectra from the “leaky” formulation will generally therefore result in lower masses for more massive white dwarfs than those obtained using the Aizu (1973) or Wu (1994) formulations." + In the case of lower-mass white cwarfs the ellect is to mimic the change in spectral slope resulting from increased exclotron cooling from a strong magnetic field., In the case of lower-mass white dwarfs the effect is to mimic the change in spectral slope resulting from increased cyclotron cooling from a strong magnetic field. +" Lt should be noted that because they are parameterisations. the treatments in 82.2 and 82.3 do not provide a prescription or definite values of 7, and τν based on atomic physies and magneto-hydrodynamies."," It should be noted that because they are parameterisations, the treatments in 2.2 and 2.3 do not provide a prescription for definite values of $\tau_{\rm m}$ and $\tau_{\rm h}$ based on atomic physics and magneto-hydrodynamics." +" However. if we simply. assume certain values for the effective temperature Zr of the white-dwarl atmosphere. then we can obtain an estimate for 7, by equation (26) after the specific aceretion rates (or the specifie pre-shock mass Εαν). m and the white-cwarf mass A are specified."," However, if we simply assume certain values for the effective temperature $T_{\rm eff}$ of the white-dwarf atmosphere, then we can obtain an estimate for $\tau_{\rm h}$ by equation (26) after the specific accretion rates (or the specific pre-shock mass flux) $\dot m$ and the white-dwarf mass $M_{\rm w}$ are specified." + LU we further assume that the temperature Z(0) at the boundary wwhere z and its derivative is zero) as the unperturbed ellective temperature of the white-dwarl atmosphere. then we may also obtain an estimate for τι using equation (31).," If we further assume that the temperature $T(0)$ at the boundary where $\tau$ and its derivative is zero) as the unperturbed effective temperature of the white-dwarf atmosphere, then we may also obtain an estimate for $\tau_{\rm m}$ using equation (31)." + In, In +shapelets.,shapelets. +" This allows us to decompose the 3-dimensional eas density distribution as Using the properties of the shapelet basis functions. it is then easy to show that the shapelet coellicients for the X-ray emissivity can be written as where By"")Ad is. the ubiquitous 3-product integral defined in Equation (47)). and m=(mj.resis) in this context."," This allows us to decompose the 3-dimensional gas density distribution as Using the properties of the shapelet basis functions, it is then easy to show that the shapelet coefficients for the X-ray emissivity can be written as where $B^{(3)}_{nml}$ is the ubiquitous 3-product integral defined in Equation \ref{eq:b3}) ), and ${\mathbf m} \equiv (m_{1},m_{2},m_{3})$ in this context." + Similarly. the coelflicients for the comptonisation parameter can be written as where (m) is the integral defined in Equation (17)).," Similarly, the coefficients for the comptonisation parameter can be written as where $\langle 1 | n \rangle$ is the integral defined in Equation \ref{eq:1n}) )." + The direct. approach. which consists in solving these two equations of the desired coellicients py. is probably clillieult in practice.," The direct approach, which consists in solving these two equations of the desired coefficients $\rho_{{\mathbf n}}$, is probably difficult in practice." +" A more convenient approach is to derive an estimate for p, by ο these coclliicients to. the observables Nyp45 and 35,55 taking into account the noise in cach measurement.", A more convenient approach is to derive an estimate for $\rho_{{\mathbf n}}$ by $\chi^{2}$ -fitting these coefficients to the observables $X_{n_{1}n_{2}}$ and $Y_{n_{1}n_{2}}$ taking into account the noise in each measurement. + The 47 procedure also produces the covariance matrix for the coellicients jy. ancl thus allows us to study any clegeneracy present in the deprojection.," The $\chi^{2}$ procedure also produces the covariance matrix for the coefficients $\rho_{{\mathbf n}}$, and thus allows us to study any degeneracy present in the deprojection." + This is ercatly facilitated in practice by the analytic forms for {1[η (Eq. 11] ," This is greatly facilitated in practice by the analytic forms for $\langle 1 | n +\rangle$ (Eq. \ref{eq:1n}] ])" +and for Be (see Paper LL). ancl the Lact that the fitted model is lincar in its output. parameters fn.," and for $B^{(3)}_{nml}$ (see Paper II), and the fact that the fitted model is linear in its output parameters $\rho_{{\mathbf n}}$." + Note that our method is fully general. ancl does. not assume that the cluster distribution has any specific form., Note that our method is fully general and does not assume that the cluster distribution has any specific form. + In particular. it could be particularly useful if the SZ observations are performed. with an interlerometcr as is the case for recent measurements (see Carlstrom et al.," In particular, it could be particularly useful if the SZ observations are performed with an interferometer as is the case for recent measurements (see Carlstrom et al." + 1999. and reference therein).," 1999, and reference therein)." + In this case. the interferometer vields a measurement of the Fourier transform of Y(ar.y) and can thus make use of the dual properties. of our shapelet. functions under Fourier transforms (eq. 9].," In this case, the interferometer yields a measurement of the Fourier transform of $Y(x,y)$, and can thus make use of the dual properties of our shapelet functions under Fourier transforms (Eq. \ref{eq:B_tilde}] ])." + A more thorough study of the deprojection using shapelets is left to future work., A more thorough study of the deprojection using shapelets is left to future work. + A study of the use of shapelets for reconstructing images with interferometers will be presented in Chang Itelregier (2001)., A study of the use of shapelets for reconstructing images with interferometers will be presented in Chang Refregier (2001). + We have deseribec and developed ai new method for analysing images., We have described and developed a new method for analysing images. + It djs. based on the decomposition of the objects in the image into a series of basis functions. of different shapes. or ‘shapelets’.," It is based on the decomposition of the objects in the image into a series of basis functions of different shapes, or `shapelets'." + The method is fully linear and uses a number of powerful properties of the basis functions., The method is fully linear and uses a number of powerful properties of the basis functions. + In particular. we showed that Llermite basis functions have simple analytic properties under convolution. noise. rotations. distortions. and rescaling.," In particular, we showed that Hermite basis functions have simple analytic properties under convolution, noise, rotations, distortions, and rescaling." + Phese functions are eieenfunctions of the QUO and thus allow us to use the formalism: developed for this problem., These functions are eigenfunctions of the QHO and thus allow us to use the formalism developed for this problem. + For instance. we showed. that transformations such as. translations. rotations. shears and clilatations can be expressed as simple combinations of the raising and lowering operators.," For instance, we showed that transformations such as translations, rotations, shears and dilatations can be expressed as simple combinations of the raising and lowering operators." + Another remarkable property of these functions is that they are (up ο à rescaling) their own Fourier transforms., Another remarkable property of these functions is that they are (up to a rescaling) their own Fourier transforms. + This is à unique woperty. which stems from the special svnunetry of the QUO Lamiltonian.," This is a unique property, which stems from the special symmetry of the QHO Hamiltonian." + We derived. analytical expressions for he Hus. centroid and radius of the object. from its shapelet cocllicients.," We derived analytical expressions for the flux, centroid and radius of the object, from its shapelet coefficients." + We also constructed polar shapelets which give he explicit rotational properties of the object., We also constructed polar shapelets which give the explicit rotational properties of the object. + Lt is interesting to compare our method to the wavelet method (see review by Stark. Murtagh Bijaoui 1998).," It is interesting to compare our method to the wavelet method (see review by Stark, Murtagh Bijaoui 1998)." + In his latter method. the image is decomposed into à sum of isis functions located on a grid across the image.," In this latter method, the image is decomposed into a sum of basis functions located on a grid across the image." + Phe basis 'unctions are taken to have a range of sizes. but have all the same shape.," The basis functions are taken to have a range of sizes, but have all the same shape." + Wavelets are thus ideal to decompose an image into dillerent scales. which can then be analysed separately.," Wavelets are thus ideal to decompose an image into different scales, which can then be analysed separately." + Our method. on the other hand. models the image as a collection of discrete objects of arbitrary shapes ancl sizes.," Our method, on the other hand models the image as a collection of discrete objects of arbitrary shapes and sizes." + lt is therefore particularly well adapted to the treatment of astronomical images. which are typically composed of a superposition of compact disjoint objects.," It is therefore particularly well adapted to the treatment of astronomical images, which are typically composed of a superposition of compact disjoint objects." + The two methods can thus be thought as complementary., The two methods can thus be thought as complementary. + For instance. one can use wavelets to remove large-scale. background: variations. and to search and detect objects in the image.," For instance, one can use wavelets to remove large-scale background variations, and to search and detect objects in the image." + The resulting object catalog can then be used as the input to the shapele method. which will then characterise the shape of each object in detail.," The resulting object catalog can then be used as the input to the shapelet method, which will then characterise the shape of each object in detail." + Our method potentially has ai wide range of applications., Our method potentially has a wide range of applications. + Lt can be viewed as a new representation of images which makes object shapes easy to study and mocify., It can be viewed as a new representation of images which makes object shapes easy to study and modify. + For instance. we applied our method to galaxy images found in the LDF ancl showed. how they could be wel represented with a small number of shapelet coellicients.," For instance, we applied our method to galaxy images found in the HDF and showed how they could be well represented with a small number of shapelet coefficients." + This can be used to compress galaxy images by a factor of 40-90. and could thus have important. applications for galaxy archival.," This can be used to compress galaxy images by a factor of 40-90, and could thus have important applications for galaxy archival." + We also cliscussed several direct applications of shapelets to measurements of eravitational lensing. and the problems of de-projection ancl PSE correction.," We also discussed several direct applications of shapelets to measurements of gravitational lensing, and the problems of de-projection and PSF correction." + Other applications to be explored are that of multi-colour shapelets ancl of the study of galaxy morphology and: classification using shapelets., Other applications to be explored are that of multi-colour shapelets and of the study of galaxy morphology and classification using shapelets. + Our original motivation for developing this method was to find a robust ancl precise method to measure weak lensing distortions in the presence of a PSE., Our original motivation for developing this method was to find a robust and precise method to measure weak lensing distortions in the presence of a PSF. + The application of shapelets to this problem and to the general problem of deconvolution will be presented in detail in Paper II., The application of shapelets to this problem and to the general problem of deconvolution will be presented in detail in Paper II. + The application of shapelets to image reconstructions [rom interferometric observations will be presented in Chang Itefregier 2001., The application of shapelets to image reconstructions from interferometric observations will be presented in Chang Refregier 2001. + The author is indebted to David Bacon. Tzu-Ching Change and it. Chitra for useful and stimulating cliscussions curing the development of this method.," The author is indebted to David Bacon, Tzu-Ching Chang and R. Chitra for useful and stimulating discussions during the development of this method." + Le is supported by the ELEC 'TME network on Gravitational Lensing and by a Wolfson College Rescarch Fellowship., He is supported by the EEC TMR network on Gravitational Lensing and by a Wolfson College Research Fellowship. +The microphysics of Gamma-Ray Burst (GRB) afterglow shocks propagating through a eircumburst medium (CBM) has been theoretically predicted by (Medvedev&Loeb1999) and later extensively studied using particle-in-cell (PIC) models in the past few years (seee.g.Keshetetal.2005:2003:Gruzinov. 2001)..,"The microphysics of Gamma-Ray Burst (GRB) afterglow shocks propagating through a circumburst medium (CBM) has been theoretically predicted by \citep{bib:Medvedev1999} and later extensively studied using particle-in-cell (PIC) models in the past few years \citep[see e.g.][]{bib:Spitkovsky2008,bib:Hededal2004, +bib:Frederiksen2004,bib:Silva2003,bib:Gruzinov2001a}." + In contrast. the initial interaction between the GRB photons and the CBM plasma ts less well studied numerically. although progress has been made for coherent wakefield processes in lower-dimensional and pair plasmas (e.g.Hoshino2008:Liang&Noguchi2007).," In contrast, the initial interaction between the GRB photons and the CBM plasma is less well studied numerically, although progress has been made for coherent wakefield processes in lower-dimensional and pair plasmas \citep[e.g.][]{bib:Hoshino2008,bib:Liang2007}." +. Whereas the burst-CBM interaction has received. strong attention in. theoretical (Beloborodov2002:Thompson&Madau2000) and observational (Connaughton2002) works. the detailed microphysical plasma dynamies in the first pulse-plasma encounter lacks sufficient treatment with respect to the high degree of forcing anisotropy in the problem of photon scattering off the relatively cold tenuous CBM.," Whereas the burst-CBM interaction has received strong attention in theoretical \citep{bib:Beloborodov2002,bib:Madau2000} and observational \citep{bib:Connaughton2002} works, the detailed microphysical plasma dynamics in the first pulse-plasma encounter lacks sufficient treatment with respect to the high degree of forcing anisotropy in the problem of photon scattering off the relatively cold tenuous CBM." + Wakefield interactions between high energy photon pulses and a plasma have been extensively studied in the context of wakefield acceleration 1n. laser-plasma. systems. both experimentally (e.g.Phuoeetal.2005:Kostyukov 2003).. and numerically in the same context (e.g.Phuocetal.2005:Pukhov 2000).," Wakefield interactions between high energy photon pulses and a plasma have been extensively studied in the context of wakefield acceleration in laser-plasma systems, both experimentally \citep[e.g.][]{bib:Phuoc2005,bib:Kostyukov2003}, and numerically in the same context \citep[e.g.][]{bib:Phuoc2005,bib:Pukhov1999}." +. In the astrophysical context of particle acceleration in GRBs. waketield acceleration has been studied in the coherent regime where the forcing of the plasma is done by the electromagnetic field (Hoshino2008:Liang&Noguchi 2007).," In the astrophysical context of particle acceleration in GRBs, wakefield acceleration has been studied in the coherent regime where the forcing of the plasma is done by the electromagnetic field \citep{bib:Hoshino2008,bib:Liang2007}." +. Incoherent — or — wakefield processes have to our knowledge so far not been studied numerically. and has been considered theoretically only in a few cases (e.g.Barbi-ellinietal.2006. 2004).," Incoherent – or – wakefield processes have to our knowledge so far not been studied numerically, and has been considered theoretically only in a few cases \citep[e.g.][]{bib:Barbiellini2006,bib:Barbiellini2004}." +" Our motivation for developing a new and improved Particle-in-cell- Monte-Carlo (PIC-MC) code framework for investigating the detailed Compton interaction of an intense GRB and a quiescent cold CBM ts two-fold: First. due to the high-energy spectrum of the prompt GRB (for BATSE of order E.~ m,c) the photon wavelength is much shorter than any characteristic length scale in the CBM plasma. A.<<à, and A.«Ap. where 6, and Ap, are the electron skin-depth and Debye-length. respectively."," Our motivation for developing a new and improved Particle-in-cell- Monte-Carlo (PIC-MC) code framework for investigating the detailed Compton interaction of an ultra-intense GRB and a quiescent cold CBM is two-fold: First, due to the high-energy spectrum of the prompt GRB (for BATSE of order $E_\gamma \sim m_e c^2$ ), the photon wavelength is much shorter than any characteristic length scale in the CBM plasma, $\lambda_\gamma \ll \delta_e$ and $\lambda_\gamma \ll \lambda_D$, where $\delta_e$ and $\lambda_D$ are the electron skin-depth and Debye-length, respectively." + We therefore expect a binary approximation to work well for prompt burst photons interacting with the plasma constituent particles through Compton scattering., We therefore expect a binary approximation to work well for prompt burst photons interacting with the plasma constituent particles through Compton scattering. +" In fact. photons in a large range down towards the electron plasma frequency zc.~Wpe=ApVine (Where v4, 15 the electron thermal speed) could be treated as point particles that interact in a binary way with the plasma."," In fact, photons in a large range down towards the electron plasma frequency $\omega_\gamma \sim \omega_{pe} = \lambda_D^{-1} v_{th,e}$ (where $v_{th,e}$ is the electron thermal speed) could be treated as point particles that interact in a binary way with the plasma." + Secondly. the extreme intensity of the burst makes the GRB front opaque to the plasma electrons.," Secondly, the extreme intensity of the burst makes the GRB front opaque to the plasma electrons." +" Assume a CBM with n,7Lem. and further assume a typical BATSE GRB with an estimated (fromBarbiellinietal.2006.eqn.2) photon flux energy density of 10?eVems! at distance Ro~10!em from the progenitor."," Assume a CBM with $n_e \approx 1~\textnormal{cm}^{-3}$, and further assume a typical BATSE GRB with an estimated \citep[from][eqn.2]{bib:Barbiellini2006} + photon flux energy density of $10^{35}~\textnormal{eV}~\textnormal{cm}^{-2}~\textnormal{s}^{-1}$ at distance $R_0 \sim 10^{16}~\textnormal{cm}$ from the progenitor." + Then. Compton scattering off the CBM plasma will occur many times every second per electron during the prompt phase: most photons survive traversing the plasma without being significantly affected.," Then, Compton scattering off the CBM plasma will occur many times every second per electron during the prompt phase; most photons survive traversing the plasma without being significantly affected." + The plasma is forced predominantly by binary particle- particle encounters. everywhere locally.," The plasma is forced predominantly by binary particle- particle encounters, everywhere locally." + These considerations motivated us to develop and employ a new and unique tool in order to gain access to the sub-Debye regime., These considerations motivated us to develop and employ a new and unique tool in order to gain access to the sub-Debye regime. +" Adopting the ""random phase approximation” (Pines&Bohm1952) we may split. in a natural way. plasma processes into two different numerical schemes depending on the characteristic scale of the dynamics. here denoted ke: In this way we obtain a substantially improved description of the plasma for both the Vlasov and detailed balance cases. and capture in a natural way the details of interaction and scattering."," Adopting the ""random phase approximation"" \citep{bib:Pines1952} we may split, in a natural way, plasma processes into two different numerical schemes depending on the characteristic scale of the dynamics, here denoted $\textbf{k}_C$: In this way we obtain a substantially improved description of the plasma for both the Vlasov and detailed balance cases, and capture in a natural way the details of wave-particle interaction and scattering." + The code is parallelized with MPI and is highly scalable., The code is parallelized with MPI and is highly scalable. + Any, Any +translates into upper-limits on the field strengths of the order of 104G. and a lower-limit on their age of ~LO!ves.,"translates into upper-limits on the field strengths of the order of $10^{15}~\rm{G}$, and a lower-limit on their age of $\sim 10^{4}~\rm{yrs}$." + Although there may be an insufficient number of observed RQINSs to conclude definitely (he exact range of periods (μον are clustered into. Pons et al. (," Although there may be an insufficient number of observed RQINSs to conclude definitely the exact range of periods they are clustered into, Pons et al. (" +2005) shows Chat all the periods ol observed RQINSs so [far are between the same range as ANPs and SGRs (3-12 8).,2005) shows that all the periods of observed RQINSs so far are between the same range as AXPs and SGRs $3$ $12~\rm{s}$ ). + This concurs with our results in that. alter 105vrs. only highly compact stars will have periods which do not deviate much from the range of their progenitor ANPs/SCRs (see Figure 4)).," This concurs with our results in that, after $10^6~\rm{yrs}$, only highly compact stars will have periods which do not deviate much from the range of their progenitor AXPs/SGRs (see Figure \ref{fig:p_cluster}) )." + The standard neutron star model for ANPs/SGRs spinning down due only to dipole radiation has PxD?RR. which negates the possibility of period clustering after 105ves.," The standard neutron star model for AXPs/SGRs spinning down due only to dipole radiation has $\dot{P} \propto B^2 R^4$, which negates the possibility of period clustering after $10^6~\rm{yrs}$." + In our model. the magnetic field is expelled from the stars interior and so decays in time. which in turn decreases the spin-down rate causing anv initial clustering in periods to remain.," In our model, the magnetic field is expelled from the star's interior and so decays in time, which in turn decreases the spin-down rate causing any initial clustering in periods to remain." + Also. Eq.," Also, Eq." + 3 predicts Chat only very compact stars can retain this clustering lor timescales of the order of 109vis., \ref{eqn:pdecay} predicts that only very compact stars can retain this clustering for timescales of the order of $10^6~\rm{yrs}$. + This can be understood physically by realizing that. given a magnetic field strength and period. a more compact star will have a higher magnetic energy density in each vortex.," This can be understood physically by realizing that, given a magnetic field strength and period, a more compact star will have a higher magnetic energy density in each vortex." + This causes each vortex expulsion event to remove greater amounts of magnetic field from the svstem. making magnetic braking become increasingly more ineffective.," This causes each vortex expulsion event to remove greater amounts of magnetic field from the system, making magnetic braking become increasingly more ineffective." + The observed periods of RQUNSs are indeed clustered. however (he range of this clustering and (he mean on which it is centered is inconclusive.," The observed periods of RQINSs are indeed clustered, however the range of this clustering and the mean on which it is centered is inconclusive." + Upon detection of more RQINSs. we will be able to conclude more confidentlv whether the mean period of RQINSs is higher (han that of AXPs and SGRs. and. this in turn will allow us to predict more accurately the radius of quark stars.," Upon detection of more RQINSs, we will be able to conclude more confidently whether the mean period of RQINSs is higher than that of AXPs and SGRs, and, this in turn will allow us to predict more accurately the radius of quark stars." + We have shown in this Letter that. il CFL quark stars are born with periods ancl magnetic fields characteristic of ANPsS/SGRBs. then both period and field will remain unchanged within a [actor of two for timescales of the order of 5x10° to 5x10°vrs (Figure 1)).," We have shown in this Letter that, if CFL quark stars are born with periods and magnetic fields characteristic of AXPs/SGRs, then both period and field will remain unchanged within a factor of two for timescales of the order of $5\times 10^{5}$ to $5\times 10^{7}~\rm{yrs}$ (Figure \ref{fig:b_decay}) )." + Therefore. because AXPs/SGRs are born within a narrow period range. their periods will remain clustered [or timescales applicable to observations.," Therefore, because AXPs/SGRs are born within a narrow period range, their periods will remain clustered for timescales applicable to observations." +" Moreover. alter timescales of 10? to 10""ves their periods will be on average higher."," Moreover, after timescales of $10^{5}$ to $10^{6}~\rm{yrs}$ their periods will be on average higher." + ILowever. because only a relatively small," However, because only a relatively small" +with J)=LOO.,with $P_0 = 100$. + The density distribution is set up by the ideal gas law. namely: in computational units.," The density distribution is set up by the ideal gas law, namely: in computational units." +" For the Spitzer diffusion coefficient. we assume the diffusion is linear as in Eq.(7). and use the approximation: &|=6.772). where s, is the classical conductivity. and T5; is taken (o be the middle value of temperature across the interface. about 0.5Ti."," For the Spitzer diffusion coefficient, we assume the diffusion is linear as in Eq.(7), and use the approximation: $\kappa_{\parallel} = \kappa_c\,T_{mid}^{2.5}$ , where $\kappa_c$ is the classical conductivity, and $T_{mid}$ is taken to be the middle value of temperature across the interface, about $0.5\,T_0$." + We choose the initial field configuration: where n and A are the mode mnmunber and wavelength of the tanelec field respectively. By—10? in computational units. and By can assume various initial values that reflect the evolving elobal field as the result of reconnection.," We choose the initial field configuration: where $n$ and $\lambda$ are the mode number and wavelength of the tangled field respectively, $B_0 = 10^{-3}$ in computational units, and $B_d$ can assume various initial values that reflect the evolving global field as the result of reconnection." + This initial field configuration is therefore one of a locally tangled field surrounding the interface with one measure of the tangle given by: When &=0. there are only locally confined field lines. whereas 2=x: indicates a straight horizontal field without anv “tangline”.," This initial field configuration is therefore one of a locally tangled field surrounding the interface with one measure of the tangle given by: When $R = 0$, there are only locally confined field lines, whereas $R = \infty$ indicates a straight horizontal field without any ""tangling""." + As /? increases. the relative fraction of Ποια energv corresponding to lines which penetrate through (heinteraction region increases.," As $R$ increases, the relative fraction of field energy corresponding to lines which penetrate through theinteraction region increases." + In oursimulations. we consider cases with #2=0.0.0.2.0.4.0.6.1.2.4.o.," In oursimulations, we consider cases with $R = 0.0,\,0.2,\,0.4,\,0.6,\,1,\,2,\,4,\,\infty$." + Figure 2((a). Figure (ία) and Figure 5((a) show the magnetic field configuration for initial 2 values of 0.0. 0.4. 1.0.," Figure \ref{fig02}( (a), Figure\ref{fig04}( (a) and Figure \ref{fig05}((a) show the magnetic field configuration for initial $R$ values of $0.0$ , $0.4$ , $1.0$ ." +is that the 2-10 keV X-ray luminosities of the objects are low with respect to their mid-IR and optical ΠΠ] luminosities.,is that the 2-10 keV X-ray luminosities of the objects are low with respect to their mid-IR and optical ] luminosities. + Under normal circumstances this would be interpreted straightforwardly as being due to suppression of the X-ray flux by an absorbing column. however a naive analysis of the X-ray spectra is at odds with this interpretation.," Under normal circumstances this would be interpreted straightforwardly as being due to suppression of the X-ray flux by an absorbing column, however a naive analysis of the X-ray spectra is at odds with this interpretation." + It may be that the simplest interpretation of the spectra is misleading us: if scattered or host galaxy emission dominates the spectrum below ~5 keV. the spectrum may appear unabsorbed when in fact a harder nuclear components is present.," It may be that the simplest interpretation of the spectra is misleading us: if scattered or host galaxy emission dominates the spectrum below $\sim 5$ keV, the spectrum may appear unabsorbed when in fact a harder nuclear components is present." + We favour the latter interpretation in four objects., We favour the latter interpretation in four objects. + These show tentative evidence for a hard excess which is likely to be a hidden reflection or transmission spectrum indicative of a heavily obscured nucleus. accounting for the low hard X-ray luminosity of these objects.," These show tentative evidence for a hard excess which is likely to be a hidden reflection or transmission spectrum indicative of a heavily obscured nucleus, accounting for the low hard X-ray luminosity of these objects." + The most compelling case is NGC 4501. where the high resolution image reveals a hard source co-incident with the nucleus embedded in a number of softer emitting regions.," The most compelling case is NGC 4501, where the high resolution image reveals a hard source co-incident with the nucleus embedded in a number of softer emitting regions." + The clear conclusion in this case is that is that 2-10 keVNewton data are dominated by non-nuclear emission. accounting for the unabsorbed X-ray spectrum.," The clear conclusion in this case is that is that 2-10 keV data are dominated by non-nuclear emission, accounting for the unabsorbed X-ray spectrum." + We infer a similar conclusion for IRAS F01475-0740. NGC 3486 and NGC 3976.," We infer a similar conclusion for IRAS F01475-0740, NGC 3486 and NGC 3976." + For two of our sources (NGC 3147 and NGC 3660) we see no signs of hidden reflection or transmission in the X-ray spectra., For two of our sources (NGC 3147 and NGC 3660) we see no signs of hidden reflection or transmission in the X-ray spectra. + NGC 3147 shows a single soft X-ray source co-incident with the nucleus in the Chandra image. and both exhibit X-ray variability.," NGC 3147 shows a single soft X-ray source co-incident with the nucleus in the Chandra image, and both exhibit X-ray variability." + These observations clearly point to the idea that we are seeing the nuclei directly in these sources. so the evidence suggest that they might intrinsically lack a BLR.," These observations clearly point to the idea that we are seeing the nuclei directly in these sources, so the evidence suggest that they might intrinsically lack a BLR." + It therefore appears from our analysis that there are two yopulations of unabsorbed Seyfert 2. galaxies and that they appear unabsorbed in X-rays for different reasons entirely., It therefore appears from our analysis that there are two populations of unabsorbed Seyfert 2 galaxies and that they appear unabsorbed in X-rays for different reasons entirely. + It may be that our view of the AGN is genuinely unobseured. and that the lack of broad lines in their optical spectra is due to an intrinsic absence or weakness of the BLR.," It may be that our view of the AGN is genuinely unobscured, and that the lack of broad lines in their optical spectra is due to an intrinsic absence or weakness of the BLR." + Alternatively though. it may be that the X- spectrum is misleading. and that the unabsorbed spectra are due © scattered or galactic soft X-rays which dominate the emission Tom a much more powerful obscured nucleus.," Alternatively though, it may be that the X-ray spectrum is misleading, and that the unabsorbed spectra are due to scattered or galactic soft X-rays which dominate the emission from a much more powerful obscured nucleus." + We discuss each in urn., We discuss each in turn. + NGC 3147 has no hidden broad line region and a observations shows no discernible extra-nuclear sources., NGC 3147 has no hidden broad line region and a observations shows no discernible extra-nuclear sources. + Between observations by andXMM-Newton. the hard X-ray flux drops by a factor of —2 indicating that it is variable in. which means that we are likely to be seeing the nucleus of NGC 3147 directly.," Between observations by and, the hard X-ray flux drops by a factor of $\sim 2$ indicating that it is variable in X-rays which means that we are likely to be seeing the nucleus of NGC 3147 directly." + 2. carried out simultaneous optical/X-ray observations of NGC 3147 to show that the apparent mismatch between optical and X-ray classification was not due to differential variability., \cite{bianchi08} carried out simultaneous optical/X-ray observations of NGC 3147 to show that the apparent mismatch between optical and X-ray classification was not due to differential variability. + By noting a small equivalent width of the iron line and a large ratio between hard X-ray and [O 111] fluxes. they come to the same conclusion that the nucleus of NGC 3147 is genuinely unobscured. and that this AGN must therefore intrinsically lack a broad line region.," By noting a small equivalent width of the iron line and a large ratio between hard X-ray and [O ] fluxes, they come to the same conclusion that the nucleus of NGC 3147 is genuinely unobscured, and that this AGN must therefore intrinsically lack a broad line region." + We cannot however rule out the Compton thick nature of this source without observing it above 10 keV. where transmission from a Compton thick medium would dominate.," We cannot however rule out the Compton thick nature of this source without observing it above 10 keV, where transmission from a Compton thick medium would dominate." + The X-ray variability of this source on short time-scales and —inabsorbed profile of its X-ray spectrum leads us to the conclusion that we are genuinely viewing the nucleus of NGC 3660 directly., The X-ray variability of this source on short time-scales and unabsorbed profile of its X-ray spectrum leads us to the conclusion that we are genuinely viewing the nucleus of NGC 3660 directly. + This leads us to believe that NGC 3660 also lacks a broad line region as we believe with NGC 3147., This leads us to believe that NGC 3660 also lacks a broad line region as we believe with NGC 3147. + However. the origin of the X- variability is not necessarily nuclear as variability was recently discovered in the ultra-luminous X-ray (ULX) source. M8? X-I (Y.," However, the origin of the X-ray variability is not necessarily nuclear as variability was recently discovered in the ultra-luminous X-ray (ULX) source, M82 X-1 \citep{mucciarelli06}." + A observation of NGC 3660 should be able to resolve any ULXs as we have shown for NGC 4501., A observation of NGC 3660 should be able to resolve any ULXs as we have shown for NGC 4501. + We also cannot rule out differential variability as the cause of the mismatch. as ? did for NGC 3147.," We also cannot rule out differential variability as the cause of the mismatch, as \cite{bianchi08} did for NGC 3147." + As has been observed in other X-ray variable Seyferts (e.g. NGC 4151. 2). the broad line flux has also been seen to vary.," As has been observed in other X-ray variable Seyferts (e.g. NGC 4151, \cite{gaskell86}) ), the broad line flux has also been seen to vary." + If the broad line flux is observed in its low state. the object will be seen as type 2. despite being unobscured.," If the broad line flux is observed in its low state, the object will be seen as type 2, despite being unobscured." + NGC 3660 will also need to be observed simultaneously in the optical and in the X-rays to rule out this possibility., NGC 3660 will also need to be observed simultaneously in the optical and in the X-rays to rule out this possibility. + ? use the small size of the iron line in NGC 3147 to argue against ye Compton thick nature of that source., \cite{bianchi08} use the small size of the iron line in NGC 3147 to argue against the Compton thick nature of that source. + However. IRASFO1475-0740 also shows a small iron line. but in this object we know jit heavy nuclear obscuration is occurring as shown by ?..," However, IRASF01475-0740 also shows a small iron line, but in this object we know that heavy nuclear obscuration is occurring as shown by \cite{tran03}." + This spectropolarimetric study showed that IRASFO1475-0740 has broad lines in its polarised optical spectrum. which are missing in s normal optical spectrum. confirming that our line of sight to ye nucleus is blocked by optically thick material.," This spectropolarimetric study showed that IRASF01475-0740 has broad lines in its polarised optical spectrum, which are missing in its normal optical spectrum, confirming that our line of sight to the nucleus is blocked by optically thick material." + We show that a Compton thick source may exhibit only a moderate iron line if 1e continuum emission below 10 keV is dominated by a strong ραcattered continuum or extra-nuclear emission., We show that a Compton thick source may exhibit only a moderate iron line if the continuum emission below 10 keV is dominated by a strong scattered continuum or extra-nuclear emission. + We demonstrated us by adding a second component to the fit of the X-ray spectrum. with a much larger column density than the first component. by using the iron line as a constraint.," We demonstrated this by adding a second component to the fit of the X-ray spectrum, with a much larger column density than the first component, by using the iron line as a constraint." + The intrinsie hard. X-ray uminosity of this second component is a factor of ~10 greater han the observed luminosity., The intrinsic hard X-ray luminosity of this second component is a factor of $\sim 10$ greater than the observed luminosity. + Assuming that the observed hard X-ray spectrum is indeed dominated by scattered light. we calculate an upper limit on the scattering fraction by fixing the column density of the second component to its lower limit.," Assuming that the observed hard X-ray spectrum is indeed dominated by scattered light, we calculate an upper limit on the scattering fraction by fixing the column density of the second component to its lower limit." + The upper limit on the scattering fraction turns out to be 50%. far higher than the typical ~3'% seen in Seyfert ? galaxies (2)...," The upper limit on the scattering fraction turns out to be $50\%$, far higher than the typical $\sim 3\%$ seen in Seyfert 2 galaxies \citep{cappi06}." + ? observed a <1% scattered fraction in two Compton thick AGN. SWIFT JO601.98636 and SWIFT J0138.64001.," \cite{ueda07} observed a $<1\%$ scattered fraction in two Compton thick AGN, SWIFT J0601.98636 and SWIFT J0138.64001." + They used that fraction to suggest that these objects have a large covering fraction of the torus. or a low abundance of the gas responsible for the scattering in those objects.," They used that fraction to suggest that these objects have a large covering fraction of the torus, or a low abundance of the gas responsible for the scattering in those objects." + The inverse could be true for TRASFO!75-0740 - it may have a low covering fraction of the torus. or a high abundance of the gas responsible for the scattering.," The inverse could be true for IRASF0175-0740 - it may have a low covering fraction of the torus, or a high abundance of the gas responsible for the scattering." + Scattered components are also often seen in reflection dominated sources (eg., Scattered components are also often seen in reflection dominated sources (eg. + NGC 1068: (235)., NGC 1068; \citep{pier94}) ). + If there is an, If there is an +with a previous minimum occurring during the 1998 season. then from Fig.,"with a previous minimum occurring during the 1998 season, then from Fig." + 6 we predict that the image A light-curve should. have a subsequent minimum at a level ~1.1.5 magnitudes fainter than the November 1999 level., \ref{assym} we predict that the image A light-curve should have a subsequent minimum at a level $\sim 1-1.5$ magnitudes fainter than the November 1999 level. +" If the source is small with respect to 5, and therefore the inter-caustic spacing. and the brightening of image A is due to the imminent. disappearance of a pair of critical images. then the rise can be modelled using the near caustic approximation of Chang and Itefsdal (1979): Lhe tus { of a point source at a small time Af=faves—£ from a fold CAUSLIC Ls where fj, is the magnification of the non-critical images. ND) the Lleavisicle step function anc e, a constant describing the strength of the caustic."," If the source is small with respect to $\eta_o$ and therefore the inter-caustic spacing, and the brightening of image A is due to the imminent disappearance of a pair of critical images, then the rise can be modelled using the near caustic approximation of Chang and Refsdal (1979): The flux $f_p$ of a point source at a small time $\Delta t = t_{caust}-t$ from a fold caustic is where $f_o$ is the magnification of the non-critical images, $\theta(\Delta t)$ the Heaviside step function and $a_o$ a constant describing the strength of the caustic." + The choice of which points to use in a fit of this type is somewhat arbitrary., The choice of which points to use in a fit of this type is somewhat arbitrary. + We have chosen the data following JD 1400. which is after the apparent inflection in the light-curve.," We have chosen the data following JD 1400, which is after the apparent inflection in the light-curve." + “Phe fit is shown in Fie. Hd..," The fit is shown in Fig. \ref{fit}," +" giving parameter values of f=0.40y. (qu=3,50mgdays? and ἐν51554daygs (— llth January 2000)."," giving parameter values of $f_o=0.40\,mJy$, $a_o=3.50\,mJy\,days^{\frac{1}{2}}$ and $t_{caust}=1554\,days$ $\sim$ 11th January 2000)." + Ehe final figure is of particular value since it predicts the time of the caustic crossing., The final figure is of particular value since it predicts the time of the caustic crossing. +" /,,4,; agrees with", $t_{caust}$ agrees with +1n ?.. we identified the first. genuine. black hole candidate using our X-ray classification method. which was developed to the fullest in. 2..,"In \citet{bsh08}, we identified the first genuine black hole candidate using our X-ray classification method, which was developed to the fullest in \citet{bsh08}." + The X-rav source associated with the globular cluster Bo 45 (hereafter known as Χο 45) exhibited behaviour associated with all low mass X-ray binaries (LAINBs) in the low state: hard power law emission. and high r.nis variability (sece.g.22).," The X-ray source associated with the globular cluster Bo 45 (hereafter known as XBo 45) exhibited behaviour associated with all low mass X-ray binaries (LMXBs) in the low state: hard power law emission, and high r.m.s variability \citep[see e.g.][]{vdk94, vdk95}." + A recent survey of Galactic neutron star LAINBs has shown that the low state is observed at 0.01.1000 keV luminosities Z0.1 Lead or systems that trace a diagonal transition in colour-colour space from low state to high state. and. 0.02. Lea. for systems that exhibit a vertical transition (2): Lea is he Eddington luminosity.," A recent survey of Galactic neutron star LMXBs has shown that the low state is observed at 0.01–1000 keV luminosities $\la$ 0.1 $L_{\rm Edd}$ for systems that trace a diagonal transition in colour-colour space from low state to high state, and $\la$ 0.02 $L_{\rm Edd}$ for systems that exhibit a vertical transition \citep{glad07}; $L_{\rm Edd}$ is the Eddington luminosity." + However. XBo 45 exhibited. this rchaviour at a 0.310 keV luminosity ~120 Eddington ora L4 M. neutron star. hence we identified it as a black role candidate.," However, XBo 45 exhibited this behaviour at a 0.3–10 keV luminosity $\sim$ 120 Eddington for a 1.4 $_{\odot}$ neutron star, hence we identified it as a black hole candidate." + XDo 45 is particularly interesting because there has »en a distinct lack of black holes in globular clusters (GC's). and most. black hole. LAINBs are thought to. be ejected rom the cluster.," XBo 45 is particularly interesting because there has been a distinct lack of black holes in globular clusters (GCs), and most black hole LMXBs are thought to be ejected from the cluster." + The theoretical work of ?/ showed that one possible formation channel for black hole LAINBs is he tidal capture of a main sequence star: indeed. it is the most likely channel for dense clusters. such as those with collapsed1 cores.," The theoretical work of \citet{kal04} showed that one possible formation channel for black hole LMXBs is the tidal capture of a main sequence star; indeed, it is the most likely channel for dense clusters, such as those with collapsed cores." + ?. 1preclictecd such svstems to be 1persistently ⋡↓⋅⋠↓⋏∙≟↓∐⊳⋜⋯∠⇂⊲↓⊔∐⋅↓⋅↓⋅⋖⋅∠⇂∐⋅∪⊔↓↿↓↥⋖⋅⋜↧∣⋡≱∖⋖⋅↓⊔∙⋖⋅∪⇂∎≱∖⋯∙∐≱∖∙∖⇁≱∖↿⋖⋅⊔↓⊳∖⇂⋯↿ ⇂↥∢⋅↓≻↓⋅∪≱∖↓≻∢⋅≼∙↥⊀↓∖⇁⋖⊾∠⇂∢≱↓↕∢⋟↓⋅," \citet{kal04} predicted such systems to be persistently bright, and inferred from the absence of such systems that the prospective donor is disrupted during capture." +↕≻∠⇂⊲↓⊳∖↓⋅⊔↓≻↿⋖⋅∠⇂∠⇂⊔↓⋰↓⊔⋏∙≟≼∼⋜↧↓≻↿⊔↓⋅⋖⋅⊳⇀∖∐∪≟⋅↱≻ jas appeared in all N-rav observations covering that region of sky. spanning ~30 vears. and hence is consistent with theoretical predictions for a svstem formed by tidal capture.," XBo 45 has appeared in all X-ray observations covering that region of sky, spanning $\sim$ 30 years, and hence is consistent with theoretical predictions for a system formed by tidal capture." + In this paper. we use the same arguments to identify Χο 144 (r2-5in.7.à=00:12:59.803641:16:06.01) as another black hole candidate.," In this paper, we use the same arguments to identify XBo 144 \citep[r2-5 in ][ $\alpha$ = 00:42:59.803 $\delta$ = 41:16:06.01]{K02} as another black hole candidate." + Furthermore. Xo 1244 is located in à confirmed. M31. GC (seetherevised.BolognaCatalogueV.3.5.March2008: ??7?7).," Furthermore, XBo 144 is located in a confirmed M31 GC \citep[see the revised Bologna Catalogue V.3.5, March 2008;][]{gall04,gal05,gal06,gal07}." +. We present detailed analysis of the 2002 June NMM-Newton observation of NBo 144. the deepest. of four exposures made between 2000 anc 2002.," We present detailed analysis of the 2002 June XMM-Newton observation of XBo 144, the deepest of four exposures made between 2000 and 2002." + Results from the other observations are consistent with this one., Results from the other observations are consistent with this one. + In Section 2 we describe the observations and. cata reduction. then present the results of our analysis in Section 3...," In Section \ref{obs} we describe the observations and data reduction, then present the results of our analysis in Section \ref{res}." + We discuss our findings in Section 4.. and draw conclusions in Section 5..," We discuss our findings in Section \ref{discuss}, and draw conclusions in Section \ref{conc}." + We rebuilt the data products for the 2002 June 26 NMM-Newton observation of the central region of AIS] using version 7.1 of the Seience Analysis Software suite (SAS)., We rebuilt the data products for the 2002 June 26 XMM-Newton observation of the central region of M31 using version 7.1 of the Science Analysis Software suite (SAS). + 1n order to screen for background. Lares. we followed the recommended. procedure. finding a small fare near the start of the observation: this was removed.," In order to screen for background flares, we followed the recommended procedure, finding a small flare near the start of the observation; this was removed." + We then svachronised thepn ancl MOS lighteurves as described in ?.., We then synchronised thepn and MOS lightcurves as described in \citet{bs07}. + We extracted pn (?).. and. MOS (MOSIanclMOS2?) data rom [rom a circular source region with radius 20” with a 20” background region at a similar oll-axis angle. with no point sources and on the same CCD chip.," We extracted pn \citep{stru01}, and MOS \citep[MOS1 and MOS2][]{turn01} data from from a circular source region with radius $''$ , with a $''$ background region at a similar off-axis angle, with no point sources and on the same CCD chip." + A larger, A larger +mean value of the highest temperature is 1.0 keV (all values) or 0.8 keV if one excludes one outlier with £72=3.4 keV. If one computes the emission-measure-weighted mean temperature for each star. the mean value for the 11 Hyades members is 0.6 keV. For the Pleiades. Gagneetal.(1995). performed 2T temperature fits to the spectral data of 16 members and provides a value for the mean plasma temperature for each star.,"mean value of the highest temperature is 1.0 keV (all values) or 0.8 keV if one excludes one outlier with $kT_2=3.4$ keV. If one computes the emission-measure-weighted mean temperature for each star, the mean value for the 11 Hyades members is 0.6 keV. For the Pleiades, \cite{gcs95} performed 2T temperature fits to the spectral data of 16 members and provides a value for the mean plasma temperature for each star." + The mean of these 16 values is 0.9 keV. Por all the members of NGC 752 which have an X-ray counterpart (21 sources detected by pplus 7. outside FFOV. detected by XMM-Newron)) we provide an estimate of the source X-ray luminosity in reftab:Ix..," The mean of these 16 values is 0.9 keV. For all the members of NGC 752 which have an X-ray counterpart (21 sources detected by plus 7, outside FOV, detected by ) we provide an estimate of the source X-ray luminosity in \\ref{tab:lx}." + The estimates for a stars mass and bolometric lummosity were obtained using the isochrones by Girardi(2002) (age = 1.9 Gyr. Z = 0.01).," The estimates for a star's mass and bolometric luminosity were obtained using the isochrones by \cite{gbb+02} (age $=$ 1.9 Gyr, Z = 0.01)." + The count rate to flux conversion factor was obtained using the software atHraAsaARC. and assuming for the emitting plasma a," The count rate to flux conversion factor was obtained using the software at, and assuming for the emitting plasma a" +As the largest eravitationally bound svsteius in the Uuverse. clusters of galaxies have attracted much interest Sa.ice the pioneering works of Zwicky. who evidenced the existence of dark matter in these objects. aud later of Abell (1958). who achieved the frst large catalogue of clusters.,"As the largest gravitationally bound systems in the Universe, clusters of galaxies have attracted much interest since the pioneering works of Zwicky, who evidenced the existence of dark matter in these objects, and later of Abell (1958), who achieved the first large catalogue of clusters." + Clusters of galaxies are now studied through various complementary approaches. e.g. optical imagine and spectroscopy. which allow inu particular OQ derive the distribution and kinematical properties of tie cluster ealaxics. and to estimate the luuinosity funcion. and N-ray spectral damaging. wh‘th gives juformations ou the physical properties of the XN-rav gas embedded iji the clusOT. and with some hpotheses cau lead to estimate the otal cluster binding mass.," Clusters of galaxies are now studied through various complementary approaches, e.g. optical imaging and spectroscopy, which allow in particular to derive the distribution and kinematical properties of the cluster galaxies, and to estimate the luminosity function, and X-ray spectral imaging, which gives informations on the physical properties of the X-ray gas embedded in the cluster, and with some hypotheses can lead to estimate the total cluster binding mass." + As a complemenary approach to large cluster survevs at small redshifts πι Las the ESO Nearby Abell Cluster Survey (ENACS. Isaecrt et al.," As a complementary approach to large cluster surveys at small redshifts such as the ESO Nearby Abell Cluster Survey (ENACS, Katgert et al." + 1996). we have close to analyze in detail a few kAv-z clusters of galaxies. by colmbining optical daa (imaging aud spectroscopy of a large nuunber of galaxies) aud N-rav data from the ROSAT archive.," 1996), we have chosen to analyze in detail a few low-z clusters of galaxies, by combining optical data (imaging and spectroscopy of a large number of galaxies) and X-ray data from the ROSAT archive." +" We preseut rere Complementary results on ABCC 85, which our group has abcdy analyzed wader various aspects (soe references below|."," We present here complementary results on ABCG 85, which our group has already analyzed under various aspects (see references below)." + ADCG 85 has a redshift of 2~0.0555. corresponding to a spatial scale of 97.0 kpce/arcnün (for Tp50 ft. value that wi] be used hereafter. together with qu-0).," ABCG 85 has a redshift of $\sim$ 0.0555, corresponding to a spatial scale of 97.0 kpc/arcmin (for $_0=50$ $^{-1}$, value that will be used hereafter, together with $_0$ =0)." +" Its ceuter is defined hereafter as the ceuter Q the diffuse N-rav component: ojouuo= OP LES LO, Oqoyop= — 9718177 (Pislar e al."," Its center is defined hereafter as the center of the diffuse X-ray component: $\alpha _{\rm J2000}=$ $^{\rm +h}$ $^{\rm mn}$ $^{\rm s}$, $\delta _{\rm J2000}=$ $-$ $^{\circ}$ 18'17"" (Pislar et al." + 1997)., 1997). +" A wealth of data is now available for this cluscr: a photometric catalogue of 1232 ealaxies obtained by scamming a jud photographic plate iu a square region +1"" (5.85 pc at the cluster redshift) from the cluster center. calibrated with V and Ro baud CCD imagine taken in he verv ceuter (Slezak et a."," A wealth of data is now available for this cluster: a photometric catalogue of 4232 galaxies obtained by scanning a band photographic plate in a square region $\pm 1^\circ$ (5.83 Mpc at the cluster redshift) from the cluster center, calibrated with V and R band CCD imaging taken in the very center (Slezak et al." + 1998) aud a spectroscopic catalogue of 551 galaxies in a roughly circular region of ‘radius in the direction of ABCC: 85. among which 305 long to the cluster (Duvet et al.," 1998) and a spectroscopic catalogue of 551 galaxies in a roughly circular region of $^\circ$ radius in the direction of ABCG 85, among which 305 belong to the cluster (Durret et al." + 1998a)., 1998a). + As discussed iu mr previous papers (Pislar c Tal, As discussed in our previous papers (Pislar et al. + 1997. Lima-Neto et al.," 1997, Lima-Neto et al." + 1997. Diet et al.," 1997, Durret et al." + 1998b). there exists in fact a complex of clusters ABCC 85/a7/s9o in this direction.," 1998b), there exists in fact a complex of clusters ABCG 85/87/89 in this direction." + In N-ravs. ABCC 85 shows a homogeneous body. outo which are," In X-rays, ABCG 85 shows a homogeneous body, onto which are" +"motion Comtonization, does not specify the particular properties of the upscattering electron gas and therefore is valid for the thermal Comptonization, as well as for the case of the hybrid thermal/non-thermal Comptonization.","motion Comtonization, does not specify the particular properties of the upscattering electron gas and therefore is valid for the thermal Comptonization, as well as for the case of the hybrid thermal/non-thermal Comptonization." + It describes the outgoing spectrum as a convolution of input “seed” black body spectrum having normalization Nome and the color temperature kT with a Green function for Comptonization process., It describes the outgoing spectrum as a convolution of input “seed” black body spectrum having normalization $N_{bmc}$ and the color temperature $kT$ with a Green function for Comptonization process. +" Similarly to the ordinary BBODY XSPEC model, the normalization Nome is a ratio of the total input black body luminosity to the square distance The resulting model spectrum is also characterized by the parameter log(A) related to the Comptonized fraction f=A/(1+A) and the Green's function spectral index a—TI—1 where I' is the photon index."," Similarly to the ordinary BBODY XSPEC model, the normalization $N_{bmc}$ is a ratio of the total input black body luminosity to the square distance The resulting model spectrum is also characterized by the parameter $\log(A)$ related to the Comptonized fraction $f=A/(1+A)$ and the Green's function spectral index $\alpha=\Gamma-1$ where $\Gamma$ is the photon index." + 'There are two reasons for using the BMC model., There are two reasons for using the BMC model. +" First, the model by the nature of the model is applicable to the general case when photons gain energy not only due to thermal Comptonization but also via dynamic or bulk motion Comptonization (seeLT99,Titarchuk,2006,f"," First, the model by the nature of the model is applicable to the general case when photons gain energy not only due to thermal Comptonization but also via dynamic or bulk motion Comptonization \citep[see LT99, ][for details]{bmc, ST06}." +"or The second reason is that the BMC norm Nome is details)..tied to the normalization of the “seed” black body, presumably originated in the disk."," The second reason is that the BMC norm $N_{bmc}$ is tied to the normalization of the “seed” black body, presumably originated in the disk." + The direct correspondence of Np; to the mass accretion rate in the disk follows from the accretion disk theory e.g. 1973).., The direct correspondence of $N_{bmc}$ to the mass accretion rate in the disk follows from the accretion disk theory \citep[see e.g. ][]{ss73}. . + The adopted spectral(see model successfully describes the most spectra., The adopted spectral model successfully describes the most spectra. +" The reduced χ-- statistic value x2,;= where Nao is the number of degrees of freedom x?/Naof,for a fit, is less or around 1.0 for more than of the observations."," The reduced $\chi^2$ -statistic value $\chi^2_{red}=\chi^2/N_{dof}$, where $N_{dof}$ is the number of degrees of freedom for a fit, is less or around 1.0 for more than of the observations." +" For a small fraction (less than 396)) of spectra with high counting statistic the value of x2,, reaches 1.5.", For a small fraction (less than ) of spectra with high counting statistic the value of $\chi^2_{red}$ reaches 1.5. +" However, it never exceeds the rejection limit of 2.0."," However, it never exceeds the rejection limit of 2.0." + Evolution of the relevant spectral parameters during the 1998 and 2000 outbursts is presented in Figures 1 and 2 correspondingly., Evolution of the relevant spectral parameters during the 1998 and 2000 outbursts is presented in Figures \ref{evol_1998} and \ref{evol_2000} correspondingly. + Different spectral states are separated by color., Different spectral states are separated by color. + In Figure 3 we illustrate the spectral evolution in XTE J1550-564 for two outbursts., In Figure \ref{eeufs} we illustrate the spectral evolution in XTE J1550-564 for two outbursts. +" The top panel presents four representative unfolded spectra for the 1998 outburst, color coded according to the color legend of Figure 1,, i.e. black for the LHS, blue for the IS, red for the VHS and orange for the HSS."," The top panel presents four representative unfolded spectra for the 1998 outburst, color coded according to the color legend of Figure \ref{evol_1998}, i.e. black for the LHS, blue for the IS, red for the VHS and orange for the HSS." + The 2000 event is presented in the bottom panel by two spectra for the LHS in black and the HSS in red., The 2000 event is presented in the bottom panel by two spectra for the LHS in black and the HSS in red. + The 1998 outburst of XTE J1550-564 developed as follows., The 1998 outburst of XTE J1550-564 developed as follows. + The outburst started on MJD 51063 and went through the initial LHS and then entered the hard IS., The outburst started on MJD 51063 and went through the initial LHS and then entered the hard IS. + Energy E'foiq dropped from 100 keV to 50 keV during this LHS-IS phase., Energy $E_{fold}$ dropped from 100 keV to 50 keV during this LHS-IS phase. + In Figure 1 this stage is marked by filled black circles., In Figure \ref{evol_1998} this stage is marked by filled black circles. +"The source exhibiteda strong VHS flare on MJD 51076, when photon index peaked at 2.8 marked by","The source exhibiteda strong VHS flare on MJD 51076, when photon index peaked at 2.8 marked by" +objects: taking the flux densities inferred from the EXT+COM data. the SERz4400 Al. vr.| and z6000 AZ. yr+ for AZTECA and AzTECS respectively.,"objects: taking the flux densities inferred from the EXT+COM data, the ${\rm SFR}\approx 4400$ $M_\odot$ $^{-1}$ and $\approx 6000$ $M_\odot$ $^{-1}$ for AzTEC4 and AzTEC8 respectively." +" Both have characteristic sizes of (a5 8kpe- where the range represents uncertainty arising from a Gaussian versus disk source structure — yielding a maximal star formation rate of SFRaia,2360097200 M. 1", Both have characteristic sizes of $\ell\approx 5-8$ kpc – where the range represents uncertainty arising from a Gaussian versus disk source structure – yielding a maximal star formation rate of ${\rm SFR_{max}}\approx 3600-7200$ $M_\odot$ $^{-1}$. + Therefore. both objects appear to be forming stars at or near the Eddington limit for a starburst.," Therefore, both objects appear to be forming stars at or near the Eddington limit for a starburst." + There are. however. a number of important caveats to consider: Generally speaking. however. we find that AzTECH and AZTECS are extended on physical scales comparable to the other wo SMGs presented in ?.. and are potentially radiating at or close o the Eddington limit for a starburst.," There are, however, a number of important caveats to consider: Generally speaking, however, we find that AzTEC4 and AzTEC8 are extended on physical scales comparable to the other two SMGs presented in \citet{younger2008highres}, and are potentially radiating at or close to the Eddington limit for a starburst." + Though in general SMGs are thought to be star formation dominatec (222222222). in principle they could contain a Significant contribution from an. obscured AGN.," Though in general SMGs are thought to be star formation dominated \citep{alexander2005,alexander2005b,alexander2008,valiante2007,menendez2007,menendez2009,pope2008b,momjian2010,serjeant2010}, in principle they could contain a significant contribution from an obscured AGN." + In fact. a preliminary analysis of recent very long baseline interferometry observations provides strong evidence that the radio continuum in at least some SMGs is powered primarily by an ultracompact AGN core (??)..," In fact, a preliminary analysis of recent very long baseline interferometry observations provides strong evidence that the radio continuum in at least some SMGs is powered primarily by an ultracompact AGN core \citep{biggs2009.evn,younger2010.evnproc}." + Clearly if this was the case for either AZTECA or AZTECS it would severely compromise their interpretation as extreme starbursts at or near their Eddington limit — the Eddington limit fora —LO? AZ. supermassive black is well in excess of 1077 L.., Clearly if this was the case for either AzTEC4 or AzTEC8 it would severely compromise their interpretation as extreme starbursts at or near their Eddington limit – the Eddington limit for a $\sim 10^9$ $M_\odot$ supermassive black is well in excess of $10^{13}$ $L_\odot$. + Recent X-ray imaging of the COSMOS field (theC-COSMOSSurvey:?) provides some constraints on the AGN content of these objects: though starbursts also produce significant X-ray emission. a detection in the hard band (2.8 keV) would be strong evidence for the presence of a buried AGN — particularly at high-redshift.," Recent X-ray imaging of the COSMOS field \citep[the C-COSMOS Survey:][]{elvis2009} provides some constraints on the AGN content of these objects; though starbursts also produce significant X-ray emission, a detection in the hard band $2-8$ keV) would be strong evidence for the presence of a buried AGN – particularly at high-redshift." + Therefore. we have examined the C-COSMOS X-ray imaging data for AZTEC4 and AzTECS.," Therefore, we have examined the C-COSMOS X-ray imaging data for AzTEC4 and AzTEC8." + While AzTECS shows no evidence for a detection. AZTECS exhibits a tentative hard X-ray source.," While AzTEC8 shows no evidence for a detection, AzTEC4 exhibits a tentative hard X-ray source." + A formal source extraction (asin2). yields net counts in the hard band of 5.5rn+2.7 ets. which translates into a flux of Agy=8.043.9 erg 2> ο — a —2c detection.," A formal source extraction \citep[as in][]{puccetti2009} yields net counts in the hard band of $5.5\pm 2.7$ cts, which translates into a flux of $F_{HX} = 8.0\pm 3.9$ erg $^{-2}$ $^{-1}$ – a $\sim 2\sigma$ detection." +" If we assume the bolometric corrections of 2.. this implies an AGN with bolometric luminosity LiaAOL.—12205.3.45 L4. and 7E2.4 at z=2.3. and 4+ respectively. which translates into Mggtea101M.= 0.2. 1.0zE0.1. and 2.1+0.8 where 5,5; 18 the Eddington ratio of the AGN (typicallynearunityduringthepeakofstarburst:22)."," If we assume the bolometric corrections of \citet{hopkins2007.templateqso}, this implies an AGN with bolometric luminosity $L_{bol}/10^{11}\, L_\odot = 1.2\pm 0.5$, $3.4\pm 1.4$, and $7\pm2.4$ at $z=2$, 3, and 4 respectively, which translates into $M_{BH}\eta_{\rm edd} /10^7 \, M_\odot = 0.4\pm 0.2$ , $1.0\pm 0.4$, and $2.1 \pm 0.8$ where $\eta_{edd}$ is the Eddington ratio of the AGN \citep[typically near unity during the peak of the starburst:][]{hopkins2005d,Hopkins2005c}." + While we cannot rule out significant X-ray absorption (Compton-thick in the case of non-detections). at these redshifts and energies the optical depths are unlikely to be extreme.," While we cannot rule out significant X-ray absorption (Compton-thick in the case of non-detections), at these redshifts and energies the optical depths are unlikely to be extreme." + Therefore. the X-ray data suggests that AGN do not contribute significantly to the IR luminosity of AZTEC4 or AZTECS.," Therefore, the X-ray data suggests that AGN do not contribute significantly to the IR luminosity of AzTEC4 or AzTEC8." + The visibility functions for AZTEC4 and AzTECS show clear evidence for structure on z0.5I aresee scales (see Figure 3)). and fitting a model to the visibility data yields a statistically Significant size measurement (see Table 2)).," The visibility functions for AzTEC4 and AzTEC8 show clear evidence for structure on $\approx 0.5-1$ arcsec scales (see Figure \ref{fig:vis}) ), and fitting a model to the visibility data yields a statistically significant size measurement (see Table \ref{tab:results}) )." + However. these observations are not sufficiently high-resolution.nor do they have sufficient signal-to-noise to distinguish an extended source structure from multiple compact components separated by less than the beam size.," However, these observations are not sufficiently high-resolution,nor do they have sufficient signal-to-noise to distinguish an extended source structure from multiple compact components separated by less than the beam size." + When we fit a dual point-source model to the visibility data. both sources — especially AZTECS — yield statistically significant €; 20) measurements for the implied sub-component flux densities and separations (see Table 3)).," When we fit a dual point-source model to the visibility data, both sources – especially AzTEC8 – yield statistically significant $\gsim 2\sigma$ ) measurements for the implied sub-component flux densities and separations (see Table \ref{tab:two_points}) )." + Therefore. while the visibility functions are consistent with an extended source Palructure. the data could also indicate a multi-component source Palructure produced by either more compact starbursts or thick AGN.," Therefore, while the visibility functions are consistent with an extended source structure, the data could also indicate a multi-component source structure produced by either more compact starbursts or Compton-thick AGN." + However. the sizes listed in Table 2. can be thought of as upper limits on the physical scale of the starburst in these objects. and therefore still argue against an extended star-forming disk.," However, the sizes listed in Table \ref{tab:results} can be thought of as upper limits on the physical scale of the starburst in these objects, and therefore still argue against an extended star-forming disk." + ? have argued — using the specific case of GN20 (seealso ?2)-— that such a multi-component source structure. particular one that appears circularly supported with significant extra-nuclear star formation is inconsistent with a major merger: rather. they they find that it is indicative of clumpy star formation owing to local instabilities in turbulent. high-redshift disks (2)..," \citet{carilli2010} have argued – using the specific case of GN20 \citep[see also][]{pope2006,younger2008highres}- – that such a multi-component source structure, particular one that appears circularly supported with significant extra-nuclear star formation is inconsistent with a major merger; rather, they they find that it is indicative of clumpy star formation owing to local instabilities in turbulent, high-redshift disks \citep{elmegreen2008}." + This is. however. not the ease.," This is, however, not the case." + First. both hydrodynamical simulations €2) and analytic arguments (2). indicate that this mode of star formation is steady-state. while the specitie star formation rate (SSFR) of GN20. for example. is zz1030 Gyr (21: a long duty cycle at this high a SSER is unphysical. and furthermore is inconsistent with cold-mode aecretion rates from cosmological simulations (22)..," First, both hydrodynamical simulations \citep{cerevino2010} and analytic arguments \citep{dekel2009} indicate that this mode of star formation is steady-state, while the specific star formation rate (SSFR) of GN20, for example, is $\approx 10-30$ $^{-1}$ \citep{carilli2010}; ; a long duty cycle at this high a SSFR is unphysical, and furthermore is inconsistent with cold-mode accretion rates from cosmological simulations \citep{keres2009,keres2009b}. ." + Second. significant non-nuclear CO emission is not inconsistent," Second, significant non-nuclear CO emission is not inconsistent" +In the course of diversification. many properties of galaxies change. and they tend to statistically change in a more or less monotonous way.,"In the course of diversification, many properties of galaxies change, and they tend to statistically change in a more or less monotonous way." + For instance mass and metallicity are both bound to increase with the complexity of a galaxy assembly history. so that they appear to be statistically correlated.," For instance mass and metallicity are both bound to increase with the complexity of a galaxy assembly history, so that they appear to be statistically correlated." + It seems dithcult to avoid the evolution to act as a confounding factor., It seems difficult to avoid the evolution to act as a confounding factor. + We thus propose that the main confounding parameter is X=T with T an indicator of the level of diversification. being something like an evolutionary clock not necessarily easily related o time or redshift.," We thus propose that the main confounding parameter is $\widetilde{X}=T$ with $T$ an indicator of the level of diversification, being something like an evolutionary clock not necessarily easily related to time or redshift." + In the simple case of a single stellar population. the time since formation is naturally a good evolutionary clock for some yarameters like luminosity £L. color and metallicity.," In the simple case of a single stellar population, the time since formation is naturally a good evolutionary clock for some parameters like luminosity $L$, color and metallicity." + However this is less obvious for r. or e., However this is less obvious for $r_e$ or $\sigma$. + Time since formation can probably be as good for a homogeneous population of galaxies if they are not atfected by significant transformation events (interactions. mergers...)," Time since formation can probably be as good for a homogeneous population of galaxies if they are not affected by significant transformation events (interactions, mergers...)." + However. galaxies from the same homogeneous yopulation Cdentical properties) do not form at the same epoch in the Universe. so that the time since formation 1s not related to redshift.," However, galaxies from the same homogeneous population (identical properties) do not form at the same epoch in the Universe, so that the time since formation is not related to redshift." +" In addition. galaxies are much more complex than single stellar populations. so that the ""age"" of a galaxy unfortunately is only an average over the ditferent stellar populations and does not characterize its complete evolutionary stage."," In addition, galaxies are much more complex than single stellar populations, so that the ""age"" of a galaxy unfortunately is only an average over the different stellar populations and does not characterize its complete evolutionary stage." + Considering now X=(1 +2. we take from Sagliaetal.(2010) that p=—0.5 and s=0.4.," Considering now $\widetilde{X}=(1+z)$ , we take from \citet{Saglia2010} that $p\simeq -0.5$ and $s\simeq 0.4$." +" Note that these values are obtained at fixed mass. which probably biases significantly the derived evolutions of r, and co."," Note that these values are obtained at fixed mass, which probably biases significantly the derived evolutions of $r_e$ and $\sigma$." +" Anyhow if a tight fundamental plane correlation exists with the parameters previously used (those given in Sagliaetal. (2010). close to ours. do not change the main result here). then equation C163) yields: Our luminosity evolution is clearly weaker than the one estimated in Sagliaetal.Q010y: Low(1+ οἱ, "," Anyhow if a tight fundamental plane correlation exists with the parameters previously used (those given in \citet{Saglia2010}, , close to ours, do not change the main result here), then equation \ref{eq:condition1obs}) ) yields: Our luminosity evolution is clearly weaker than the one estimated in \citet{Saglia2010}: $L\propto (1+z)^1$ ." +This discrepancy could probably be explained by the various hypotheses they have to make to try disentangling all effects in such a multivariate and evolutionary context., This discrepancy could probably be explained by the various hypotheses they have to make to try disentangling all effects in such a multivariate and evolutionary context. + In particular. the evolution of r. and σ are computed at fixed mass.," In particular, the evolution of $r_e$ and $\sigma$ are computed at fixed mass." + possibly introducing interdependencies of variables through the 1. ratio., possibly introducing interdependencies of variables through the $M/L$ ratio. + More importantly. the cosmological clock εἰ+3) is not a good evolutionary clock for a mixture of different populations of galaxies since they do not evolve at the same time. at the same space and along the same paths.," More importantly, the cosmological clock $(1+z)$ is not a good evolutionary clock for a mixture of different populations of galaxies since they do not evolve at the same time, at the same space and along the same paths." + It is well known that the tilt of the fundamental plane depends on the sample (D'Onofrioetal.2008) or on the group considered (Fraix-Burnetetal. 2010)., It is well known that the tilt of the fundamental plane depends on the sample \citep{DOnofrio2008} or on the group considered \citep{Fraix2010}. + Anyhow. diversification cannot be summarized with only one simple property (like redshift or mass) because galaxies are too complex objects and do not evolve linearly in a unique way.," Anyhow, diversification cannot be summarized with only one simple property (like redshift or mass) because galaxies are too complex objects and do not evolve linearly in a unique way." + In some diagrams. that is for some set of variables. a particular property could crudely depict the general trend of diversitication.," In some diagrams, that is for some set of variables, a particular property could crudely depict the general trend of diversification." + In the case of r.. c and4... and to a first approximation. mass could well represent a satisfactory driving parameter for the fundamental plane correlation. but it is certainly not unique as shown in Sect. 3.3..," In the case of $r_e$, $\sigma$ and, and to a first approximation, mass could well represent a satisfactory driving parameter for the fundamental plane correlation, but it is certainly not unique as shown in Sect. \ref{novirial}." + Since it is only approximate. some dispersion is expected.," Since it is only approximate, some dispersion is expected." + A lot of observables evolve with diversification. at least statistically. so that we should not be surprised by the many sealing relations found for galaxies and the difficulty to pinpoint the driving parameters and mechanisms.," A lot of observables evolve with diversification, at least statistically, so that we should not be surprised by the many scaling relations found for galaxies and the difficulty to pinpoint the driving parameters and mechanisms." + We also better understand why several characteristic parameters (mass. luminosity. metallicity...) and also the samples themselves have been found to influence the shape of the fundamental plane without providing a clearer picture of its origin.," We also better understand why several characteristic parameters (mass, luminosity, metallicity...) and also the samples themselves have been found to influence the shape of the fundamental plane without providing a clearer picture of its origin." + This might also explain some of the observed dispersion is most seatter plots., This might also explain some of the observed dispersion is most scatter plots. + For instance. it has been found that the dispersion of the fundamental plane strongly depends on the evolutionary group. (Fraix-Burnetetal.2010).. the correlation equation (9)) even not holding in the least diversified groups.," For instance, it has been found that the dispersion of the fundamental plane strongly depends on the evolutionary group \citep{Fraix2010}, the correlation equation \ref{eq:fundplane}) ) even not holding in the least diversified groups." + Also relations several parameters like in equation (19)) are most often wrong because the evolutionary clock 7 makes most variables to be non independent., Also relations several parameters like in equation \ref{eq:relcomb}) ) are most often wrong because the evolutionary clock $T$ makes most variables to be non independent. + Hence. dispersion may be explained by the statistical (non-causal) nature of the correlation and the heterogeneity of the samples as far as diversification is concerned.," Hence, dispersion may be explained by the statistical (non-causal) nature of the correlation and the heterogeneity of the samples as far as diversification is concerned." + Indeed. the evolutionary clock. i.e. the factor X=T. cun be hidden. not understandable analytically and not directly observable.," Indeed, the evolutionary clock, i.e. the factor $\widetilde{X}=T$, can be hidden, not understandable analytically and not directly observable." + It is more directly related to an evolutionary classification. and is a well-known problem of comparative methods in phylogeny (e.g.Felsenstein 1985).," It is more directly related to an evolutionary classification, and is a well-known problem of comparative methods in phylogeny \citep[e.g.][]{Felsenstein1985}." + The fundamental plane correlation and similarly sealing relations for galaxies can be formalized as confounding correlations., The fundamental plane correlation and similarly scaling relations for galaxies can be formalized as confounding correlations. + The confounding factor X is very probably related to. the level of diversification and may be identified in some cases with some variables that trace the global evolution of galaxies., The confounding factor $\widetilde{X}$ is very probably related to the level of diversification and may be identified in some cases with some variables that trace the global evolution of galaxies. + The dependence of the variables involved in the observed correlations on X has been assumed here to be power law functions for sake of simplicity but they could be more complicated without changing the result of the present paper., The dependence of the variables involved in the observed correlations on $\widetilde{X}$ has been assumed here to be power law functions for sake of simplicity but they could be more complicated without changing the result of the present paper. + In particular. these functions can be multivariate. with several confounding factors.," In particular, these functions can be multivariate, with several confounding factors." + The physics thus should not be invoked to explain causally euch of the observed correlations. but rather to explain. the confounding or evolutionary nature of these correlations.," The physics thus should not be invoked to explain causally each of the observed correlations, but rather to explain the confounding or evolutionary nature of these correlations." + Since the galaxy assembly history and transformation processes are complex. it is quite improbable that a simple physical theory can yield X and the dependence of observables on this parameter.," Since the galaxy assembly history and transformation processes are complex, it is quite improbable that a simple physical theory can yield $\widetilde{X}$ and the dependence of observables on this parameter." + Indeed. these functions more probably come from the statistics in the course of galaxy diversification.," Indeed, these functions more probably come from the statistics in the course of galaxy diversification." + In addition. X is probably hidden. not understandable analytically and not directly observable.," In addition, $\widetilde{X}$ is probably hidden, not understandable analytically and not directly observable." + It might also be different depending on the set of variables and the group of galaxies considered., It might also be different depending on the set of variables and the group of galaxies considered. + Gaining insights on the confounding parameter X requires several complementary statistical approaches., Gaining insights on the confounding parameter $\widetilde{X}$ requires several complementary statistical approaches. + A first one is fo combine several scaling relations and several galaxy samples in order to identify some common variables that could play the role of the confounding parameter., A first one is to combine several scaling relations and several galaxy samples in order to identify some common variables that could play the role of the confounding parameter. + A second approach is to use numerical simulations to produce synthetic populations of galaxies with as many assembly configurations as possible (ikeine.g.Robertsonetal.2006:Hopkins2008. 2009).," A second approach is to use numerical simulations to produce synthetic populations of galaxies with as many assembly configurations as possible \citep[like in e.g.][]{Robertson2006, Hopkins2008, Hopkins2009}." +. The great advantage here is to play with unobservable parameters., The great advantage here is to play with unobservable parameters. + Finally. the third approach is to group galaxies according to their assembly history.," Finally, the third approach is to group galaxies according to their assembly history." + Since the confounding parameter X is probably mainly linked to the level of diversification. the scaling relations necessarily depend on the evolutionary groups.," Since the confounding parameter $\widetilde{X}$ is probably mainly linked to the level of diversification, the scaling relations necessarily depend on the evolutionary groups." + Indeed. the very nature of X and the functions characterizing the dependence of thevariables on X are expected to depend on the assembly history of galaxies.," Indeed, the very nature of $\widetilde{X}$ and the functions characterizing the dependence of thevariables on $\widetilde{X}$ are expected to depend on the assembly history of galaxies." + Combining evolutionary numerical simulations. observed scalingrelations and classitications.recognizing the latter as evolutionary correlations. will lead us toward a much better," Combining evolutionary classifications, numerical simulations, observed scalingrelations and recognizing the latter as evolutionary correlations, will lead us toward a much better" +taken from Shapiro Ἱναπο (1987).,taken from Shapiro Kang (1987). + Since this reaction is Huportant at large redshifts when the temperature is well above ~LO? K. the departure of the fit at low T is of little consequence on the final Ty abuudauces.," Since this reaction is important at large redshifts when the temperature is well above $\sim$ $^3$ K, the departure of the fit at low $T$ is of little consequence on the final $_2$ abundances." + The evolution of IT]. and. to a large extent. that of Ilo depen crucially on the rate of this reaction.," The evolution of $_2^+$, and, to a large extent, that of $_2$ depend crucially on the rate of this reaction." + Uufortunatelv. calculations of he photodissociatiou cross section are available onlv for a sparse set of vibrational levels (Dunn 1968. Árgvros 1971).," Unfortunately, calculations of the photodissociation cross section are available only for a sparse set of vibrational levels (Dunn 1968, Argyros 1974)." + Total cross sections. averaged over a LTE distribution of level populations. have been computed by Arevros (1971) for 2500I1$ are considered. + An exception is constituted by the class of BL Lacs (with 67 1). whose kinetic and BLE luminosities appear to be correlated at the 98.4 per cent level.," An exception is constituted by the class of BL Lacs (with $\delta>1$ ), whose kinetic and BLR luminosities appear to be correlated at the 98.4 per cent level." + An interesting point is that the luminosities show the same eeneral trend of the distribution reported by CT93 for the Narrow Line emission., An interesting point is that the luminosities show the same general trend of the distribution reported by CF93 for the Narrow Line emission. + However a direct comparison of these two sets of data is rather dillieult. because it would require the inclusion of different covering factors in order to srescale” the line luminosities.," However a direct comparison of these two sets of data is rather difficult because it would require the inclusion of different covering factors in order to “rescale"" the line luminosities." + As can be seen in Fig., As can be seen in Fig. + 1. the spread in the correlation is quite large. plausibly due to intrinsic dispersion. but also to the significant uncertainties of our assumptions.," 1, the spread in the correlation is quite large, plausibly due to intrinsic dispersion, but also to the significant uncertainties of our assumptions." + In order to ascertain the likely causes of this spread. we have first looked for a possible relation between the core racio luminosity (Ly core) and Leip and indeed found that the two quantities appear to be highly correlated. at the -99.9 per cent level (note however that part of this strong correlation is due to the common redshift dependence).," In order to ascertain the likely causes of this spread we have first looked for a possible relation between the core radio luminosity $\nu_{\rm r} L_{\rm r,core}$ ) and $\ll$ and indeed found that the two quantities appear to be highly correlated at the $> +99.9$ per cent level (note however that part of this strong correlation is due to the common redshift dependence)." + As shown in Fig., As shown in Fig. + 2. the two luminosities appear to be of the same order of magnitude. with the expected tendeney for the LDO to have relatively lower core radio power.," 2, the two luminosities appear to be of the same order of magnitude, with the expected tendency for the LDQ to have relatively lower core radio power." +" We therefore examined the possible spread. introduced bv the other quantities on which the estimate of Lj, is based. namely @ and. F4."," We therefore examined the possible spread introduced by the other quantities on which the estimate of $\lk$ is based, namely $\theta$ and $F_{\rm x}$." + In order to do this. we assumed that in turn these two quantities have no intrinsic spread: we found that. while the assumption of a constant 6 does not leac to a better correlation. the tentative hypothesis of an intrinsic relation of £4 with the core radio [ux {ομως ἐνκPFyosae. gives values of Lii highly correlated with Leip at the 99.9 per cent level.," In order to do this, we assumed that in turn these two quantities have no intrinsic spread: we found that, while the assumption of a constant $\theta$ does not lead to a better correlation, the tentative hypothesis of an intrinsic relation of $F_{\rm x}$ with the core radio flux $F_{\rm r,core}$, $F_{\rm x}\propto F_{\rm r,core}$, gives values of $\lk$ highly correlated with $\ll$ at the $99.9$ per cent level." + This supports the view that the large scatter plausibly rellects a scatter in the observed. Pi., This supports the view that the large scatter plausibly reflects a scatter in the observed $F_{\rm x}$. + Iaceed. we expect that the observed strong variability in the Xray band. as well as the possible contribution of emission not cue to SSC (see e.g. Sikora et al.," Indeed, we expect that the observed strong variability in the X–ray band, as well as the possible contribution of emission not due to SSC (see e.g. Sikora et al." + 1994). would introduce largeὃν uncertainties.," 1994), would introduce large uncertainties." + Jecause οἱ the. Luge scatter found. ancl the corresponding weak correlation. we instead consider the ratio between the kinetic and broad line luminosities to determine if this shows any interesting average property.," Because of the large scatter found and the corresponding weak correlation, we instead consider the ratio between the kinetic and broad line luminosities to determine if this shows any interesting average property." + In L, In Fig. + 3. the distribution of this ratio is shown for the cilferent types of objects.," 3, the distribution of this ratio is shown for the different types of objects." + Shaded areas refer. to. sources. with an estimated o«1., Shaded areas refer to sources with an estimated $\delta<1$ . + As already cliscussed. the distributions are quite broad. but the average (and median) of this ratio for quasars is z LO.," As already discussed, the distributions are quite broad, but the average (and median) of this ratio for quasars is $\approx$ 10." + The distributions for LIPQ. LPQ. and LDQ are consistently similar according to a Ixolmogorov-Smirnov (INS) test.," The distributions for HPQ, LPQ, and LDQ are consistently similar according to a Kolmogorov-Smirnov (KS) test." + Aclopting a ἱνρίσα BLIt covering factor of ~ 0.1 (e.g. Netzer 1990). this implies that LyincLieu. the ionizing racliation.," Adopting a typical BLR covering factor of $\sim$ 0.1 (e.g. Netzer 1990), this implies that $\lk \sim \li$, the ionizing radiation." + This result is certainly intriguing. given: a) the uncertainties in the estimates of Lyi ancl especially Lisa: b) the fact that they are based on completely. independent calculations (where the only. parameter in common is the red shift): c) the sample used. which does not have any characteristic of completeness or clear selection criteria.," This result is certainly intriguing, given: a) the uncertainties in the estimates of $\ll$ and especially $\lk$; b) the fact that they are based on completely independent calculations (where the only parameter in common is the red shift); c) the sample used, which does not have any characteristic of completeness or clear selection criteria." + In Table 2. we report the results on the average values (ancl medians) of los(LyLpps) with their dispersions. for the cülferent tvpes of sources.," In Table 2, we report the results on the average values (and medians) of $\log(\lk/\ll)$ with their dispersions, for the different types of sources." + It can be seen that the same result on the ratio LyinLi roughly holds separately for the three classes of quasars (the ratio is slightly higher for LDQ when all sources are considered but goes clown considerably for the objects with ὁ2 1)., It can be seen that the same result on the ratio $\lk/\li$ roughly holds separately for the three classes of quasars (the ratio is slightly higher for LDQ when all sources are considered but goes down considerably for the objects with $\delta > 1$ ). + lt is worth noticing that the choice of estimating Lyi instead of trving to directly. measure Zi; from the optical/UVYNray fluxes. is mainly due to the cifficulty in disentangling the nonthermal anisotropic radiation from the more isotropic one (the “bluc bump) in the observed Dux (as well as to the paucity ofIUIS data for these sources).," It is worth noticing that the choice of estimating $\ll$ instead of trying to directly measure $\li$ from the optical/UV/X–ray fluxes, is mainly due to the difficulty in disentangling the non–thermal anisotropic radiation from the more isotropic one (the `blue bump') in the observed flux (as well as to the paucity of IUE data for these sources)." + We would in fact expect the ratio of these two components to be strongly dependent on the observation angle. as discussed below (see also Browne Murphy. 1987: Wills et al.," We would in fact expect the ratio of these two components to be strongly dependent on the observation angle, as discussed below (see also Browne Murphy 1987; Wills et al." + 1993)., 1993). + Figures 1 and 3 and Table 2 show that Lyinνι [ου BL Lacs is much larger than for quasars., Figures 1 and 3 and Table 2 show that $\lk/\ll$ for BL Lacs is much larger than for quasars. + Moreover. a INS test shows that the μαέν distribution for BL Lacs is different from that of quasars at the 99.1. per cent level. independently of the exclusion of sources with &<1 (but is consistent with that of LDQ only. which however include only very few objects. especially if> Lis required).," Moreover, a KS test shows that the $\lk/\ll$ distribution for BL Lacs is different from that of quasars at the 99.1 per cent level, independently of the exclusion of sources with $\delta < 1$ (but is consistent with that of LDQ only, which however include only very few objects, especially if $\delta > 1$ is required)." + This difference is reinforced by the fact that for BL Lacs this ratio should be considered as a lower limit., This difference is reinforced by the fact that for BL Lacs this ratio should be considered as a lower limit. + In fact. duc to the lack of better information. Lipi has been derived using the same line ratios adopted for quasars. as if allthose lines were also present (but very. broad) in the spectrum of BL Lacs.," In fact, due to the lack of better information, $\ll$ has been derived using the same line ratios adopted for quasars, as if allthose lines were also present (but very broad) in the spectrum of BL Lacs." + Moreover. in many sources absolutely no emission lineis detected: inclusion of these objects would have increased further the mean ratio ἐν οι.," Moreover, in many sources absolutely no emission lineis detected: inclusion of these objects would have increased further the mean ratio $\lk/\ll$ ." +windows.,windows. + The ou- aud offpulse regions contained 95 and 320 phase bius. respectively.," The on- and off-pulse regions contained 95 and 320 phase bins, respectively." + For each orbit. we created a light curve of Á's pulsed flux density with nue bv averaging every 12 pulses. for an effective time resolution of ~ 0.27 s. Orbital pliases were caleulated using he modified Julian dates of pulse arrival at the Solar-System barveenter and the pulsar ephemeris.," For each orbit, we created a light curve of A's pulsed flux density with time by averaging every 12 pulses, for an effective time resolution of $\sim$ 0.27 s. Orbital phases were calculated using the modified Julian dates of pulse arrival at the Solar-System barycenter and the pulsar ephemeris." + Analysis of hese Πολ curves reveals that. for the majority of the orbit. the pulsed flax deusity of A is coustaut within neasurclent unucertainties. exlibiting no obvious orbital shase-depeucdent variations.," Analysis of these light curves reveals that, for the majority of the orbit, the pulsed flux density of A is constant within measurement uncertainties, exhibiting no obvious orbital phase-dependent variations." + Uowever. close to superior conjunction (ie. orbital phase 907. where orbital plase is defined as the longitude from the ascending node). the mused flix deusitv of A varies dramatically.," However, close to superior conjunction (i.e. orbital phase $\deg$, where orbital phase is defined as the longitude from the ascending node), the pulsed flux density of A varies dramatically." + Otruecia Figure { shows the light curves of A for all three eclipses included im the 820-MITz observation., 9truecm Figure \ref{fig:eclipse1} shows the light curves of A for all three eclipses included in the 820-MHz observation. + Iu the lower panel. we also show a composite light curve. averaged over all three eclipses aud over 100 A pulses. for an effective time resolution of ~ 2.3 s. Our icasurements of the eclipse duration and of igress and egress shapes from this conrposite elt curve are consistent with the results of Isaspi et al. (," In the lower panel, we also show a composite light curve, averaged over all three eclipses and over 100 A pulses, for an effective time resolution of $\sim$ 2.3 s. Our measurements of the eclipse duration and of ingress and egress shapes from this composite light curve are consistent with the results of Kaspi et al. (" +2001). who averaged data in 2 s intervals.,"2004), who averaged data in 2 s intervals." + They calculated an eclipse duration (defined by the full width at half iiixiuimua of the light curve) of 27 s. which was used to place a limit of 18.600 kin on the size of the eclipsing region.," They calculated an eclipse duration (defined by the full width at half maximum of the light curve) of 27 s, which was used to place a limit of 18,600 km on the size of the eclipsing region." + They also found that eclipse iugress takes roughly four times longer than egress aud that the eclipse duratiou is frequency depeudenut. lasting louger at lower frequencies.," They also found that eclipse ingress takes roughly four times longer than egress and that the eclipse duration is frequency dependent, lasting longer at lower frequencies." + Otruecia Tuspection of the top three panels of Figure 1 shows iat the rise aud fall of the fux density duiug eclipse is rot monotonic., 9truecm Inspection of the top three panels of Figure \ref{fig:eclipse1} shows that the rise and fall of the flux density during eclipse is not monotonic. + In fact. up until orbital phases approaching 907. the lieht curves of A show amplitude peaks cousisteut with pre-eclipse levels.," In fact, up until orbital phases approaching $\deg$, the light curves of A show amplitude peaks consistent with pre-eclipse levels." + Figure 2) shows au expanded view of Figure 1 covering a sinaller range of orbital phases centered on the eclipse., Figure \ref{fig:eclipse2} shows an expanded view of Figure \ref{fig:eclipse1} covering a smaller range of orbital phases centered on the eclipse. + Ou this plot. we also indicate the measured barveeutric arrival times of the pulses of the 2.8 s pulsar D. This demonstrates clearly that the pulsed fiux density of A is modulated in svuchronisui with 0.5Pp.," On this plot, we also indicate the measured barycentric arrival times of the pulses of the 2.8 s pulsar B. This demonstrates clearly that the pulsed flux density of A is modulated in synchronism with $0.5~P_B$." + Iu all three eclipses. we see negative dips in pulsed fiux density occurring first at a time about 0.5 Pp out of phase with the D pulses; aud later also at a time iu plase with the D pulses.," In all three eclipses, we see negative dips in pulsed flux density occurring first at a time about 0.5 $P_B$ out of phase with the B pulses, and later also at a time in phase with the B pulses." + Iu order to determine more scusitively how the Hux density of A depends upon the rotational phase of D. we shifted the light curves of the second aud third eclipses x up to c0.5Pp so that the phases of the D pulses were identical to those of the first eclipse.," In order to determine more sensitively how the flux density of A depends upon the rotational phase of B, we shifted the light curves of the second and third eclipses by up to $\pm~0.5~P_B$ so that the phases of the B pulses were identical to those of the first eclipse." + We then πό. the ight curves of all three eclipses to create the bottom paucl of Fieure 2.., We then summed the light curves of all three eclipses to create the bottom panel of Figure \ref{fig:eclipse2}. + Dividiug cach 2.8 s window of D's rotational phase iuto four equal regions. we can calculate an average ight curves for each region. as shown in Figure 3..," Dividing each 2.8 s window of B's rotational phase into four equal regions, we can calculate an average light curves for each region, as shown in Figure \ref{fig:eclipse3}." + The ight curves for cach of the B pulse phase windows vary smoothly., The light curves for each of the B pulse phase windows vary smoothly. + Eclipse duratious range frou 20 s to 31s for the four D pliase windows. calculated. as in I&aspi et al. (," Eclipse durations range from 20 s to 34 s for the four B phase windows, calculated, as in Kaspi et al. (" +200D). to )o the full width at half 1naxiuimua of the eclipse.,"2004), to be the full width at half maximum of the eclipse." + Iugress occurs first at D phase 0.5 aud then at 0.0. when. assuimnius D is an orthogonal rotator. the magnetic axis of D is aligned with the line of sight to A. It occurs later and nore eradually for the other two phase windows centered. on phases 0.25 aud 0.75. when the magnetic axis of D is at right aneles to the line of sight.," Ingress occurs first at B phase 0.5 and then at 0.0, when, assuming B is an orthogonal rotator, the magnetic axis of B is aligned with the line of sight to A. It occurs later and more gradually for the other two phase windows centered on phases 0.25 and 0.75, when the magnetic axis of B is at right angles to the line of sight." + The orbital phases of egress are similar for all D pulse phases., The orbital phases of egress are similar for all B pulse phases. + For light curves at D phases centered on 0.0 and 0.5. the eclipses are essentially svuuuetric. with πα. beenmning at orbital phases near 89.17 aud ending at orbital phases near 90.6°.," For light curves at B phases centered on 0.0 and 0.5, the eclipses are essentially symmetric, with minimum beginning at orbital phases near $\deg$ and ending at orbital phases near $\deg$." + The light curves for B phases centered on 0.25 and 0.75 are less svuumetric. with the flux density minium occurring briefly. around orbital phases 90.27.90.57.," The light curves for B phases centered on 0.25 and 0.75 are less symmetric, with the flux density minimum occurring briefly, around orbital phases $90.2\deg - 90.5\deg$." + Only at around orbital phase 90.57 is fux density of all phases of D consistent with οσο zero., Only at around orbital phase $\deg$ is flux density of all phases of B consistent with being zero. + It is portant to recognize that the features we see in the S20-MIIz data cannot be due to confusion with the suele pulses of D (e.g. AIcLanghlin et al., It is important to recognize that the features we see in the 820-MHz data cannot be due to confusion with the single pulses of B (e.g. McLaughlin et al. + 2001) since the pulsed features secu in Fie., 2004) since the pulsed features seen in Fig. + 2 are not in phase with the radio pulses of D. aud. in addition. the latter. which have width of 50 12s. would be removed by the on-pulse/ott-pulse subtraction procedure used to determine Αν flux deusitv.," 2 are not in phase with the radio pulses of B, and, in addition, the latter, which have width of $\sim 50$ ms, would be removed by the on-pulse/off-pulse subtraction procedure used to determine A's flux density." + Otruecni Our analysis of these data differs from that of Kaspi et al. (, 9truecm Our analysis of these data differs from that of Kaspi et al. ( +2001) in one significant respect.,2004) in one significant respect. + While EKaspi ct al. (, While Kaspi et al. ( +2001) caleulated light curves with 2 s time resolution. we lave iuteerated over oulv 12 A pulses. affording us ~ 7 times better time resolution.,"2004) calculated light curves with 2 s time resolution, we have integrated over only 12 A pulses, affording us $\sim$ 7 times better time resolution." + Ikaspi et al. (, Kaspi et al. ( +2001) did etect sole enuission from A on short time scales during clipse. but their 2 s integratiou time was not sufficient to etect the D iiodulatioun.,"2004) did detect some emission from A on short time scales during eclipse, but their 2 s integration time was not sufficient to detect the B modulation." + We have shown that the eclipse uration varies considerably with B phase aud. heuce. that +he properties of the occulting πουπια are in fact different oe1 different regions of B’s maeuetosphere.," We have shown that the eclipse duration varies considerably with B phase and, hence, that the properties of the occulting medium are in fact different in different regions of B's magnetosphere." + The observed eclipse phenomenology can be uuderstood oe1i the context of a model invoking svuchrotron absorption, The observed eclipse phenomenology can be understood in the context of a model invoking synchrotron absorption +the fixed auc moveable stharray. cifferent baselines are obtained aud the we-coverage improves. viclding au iuproved svutliesisec antenua pattern.,"the fixed and moveable subarray, different baselines are obtained and the $uv$ -coverage improves, yielding an improved synthesised antenna pattern." + The Westerbork Northern Sky Survev (WENSS) in a 325 ΑΠ coutimmun survey of the sky above declination (Rengelink et 11997. de Bruyn ct lin preparation).," The Westerbork Northern Sky Survey (WENSS) is a 325 MHz continuum survey of the sky above declination (Rengelink et 1997, de Bruyn et in preparation)." + This area was surveved usimeg a nosaicing echuique., This area was surveyed using a mosaicing technique. + Each field was observed 18 times for 20 seconds spread over 12 hours., Each field was observed 18 times for 20 seconds spread over 12 hours. + Each mosaic was observed ou six davs with a different spacing between the fixed aud uoveable subarrav to get a uniform spatial distribution., Each mosaic was observed on six days with a different spacing between the fixed and moveable subarray to get a uniform spatial distribution. + These observations were spread over periods of weeks to vears., These observations were spread over periods of weeks to years. + The resulting flux densitics are averaged over all hese observations., The resulting flux densities are averaged over all these observations. + The WENSS beam size is « cosecà (EFWIM).," \nocite{rtb+97} + The WENSS beam size is $\times$ $\cosec ~\delta$ (FWHM)." + The final maps ave pixel sizes of21., The final maps have pixel sizes of. +097.. When a pixel was found with a fux density above five times the οσαι noise level. a two-dimecusional Gaussian was fitted to its surroundings.," When a pixel was found with a flux density above five times the local noise level, a two-dimensional Gaussian was fitted to its surroundings." + The coordinates of the ceutroid of the fit. the αμα (peal) flux deusitv and the flux density integrated. over the fit were added to the source list.," The coordinates of the centroid of the fit, the maximum (peak) flux density and the flux density integrated over the fit were added to the source list." + Extra flags iu the catalog mark multiple aud exteuded sources., Extra flags in the catalog mark multiple and extended sources. + For a point source the peak flux deusitv equals the flux density integrated over the beam., For a point source the peak flux density equals the flux density integrated over the beam. + Ouly the peal flux deusitics are used iu this analysis. since pulsars are oeitrinsically point sources.," Only the peak flux densities are used in this analysis, since pulsars are intrinsically point sources." +" Bright sources have positional errors of1.5"". weaker sources a lower declinatious have errors up to about10."," Bright sources have positional errors of, weaker sources at lower declinations have errors up to about." +" On average the uncertaiuty is5"".", On average the uncertainty is. +. The total bandwidth was 5 MIIz., The total bandwidth was 5 MHz. + For most reeious of the skv the detection lait was between 15 aud 25 indy (five times the local noise level)., For most regions of the sky the detection limit was between 15 and 25 mJy (five times the local noise level). + The polar cap (declination > 75°)) was surveved with a larger bandwidth aud the detection lint for this area was about 10 12 nh., The polar cap (declination $>$ ) was surveyed with a larger bandwidth and the detection limit for this area was about 10 – 12 mJy. + The WENSS source catalog contains 229120 sources (deDruvaetal..1998)., The WENSS source catalog contains 229420 sources \cite{b+98}. +.. A total of 181586 of these are located in the polar cap area., A total of 18186 of these are located in the polar cap area. + reffig:pos shows the deusitv of sources in the WENSS area., \\ref{fig:pos} shows the density of sources in the WENSS area. + The radio pulsar catalog (Tavlor et al.," The radio pulsar catalog (Taylor et al.," + 1993. Tavlor et al..," 1993, Taylor et al.," + 1995) contains 8I cuties iu the part of the sky that was covered by the WENSS area., 1995) contains 84 entries in the part of the sky that was covered by the WENSS area. + The typical positional uncertaintv for a pulsar with a flux density greater than 10 andy is or less., The typical positional uncertainty for a pulsar with a flux density greater than 10 mJy is or less. + In most cases the mucertainty iu the pulsar position is neeheible compared to the positional uucertaiutv of WENSS sources., In most cases the uncertainty in the pulsar position is negligible compared to the positional uncertainty of WENSS sources. + The pulsar proper motions are neglected. since for cach pulsar the change in position between the epoch of discovery aud the epoch of the WENSS is less than in rieht ascension auc less than in declination for all these pulsars.," \nocite{tml93} + \nocite{tmlc95} + The pulsar proper motions are neglected, since for each pulsar the change in position between the epoch of discovery and the epoch of the WENSS is less than in right ascension and less than in declination for all these pulsars." + This is mich simaller than the uncertainties in the WENSS positions., This is much smaller than the uncertainties in the WENSS positions. + Seven pulsars iu the WENSS area have large positional errors of aboutΕ, Seven pulsars in the WENSS area have large positional errors of about. +ν The probability that a WENSS source is located by chance within a circle of three iues this positional error is more than 90 percent. if it asstuued that the WENSS sources are undfornilv distributed over the skv.," The probability that a WENSS source is located by chance within a circle of three times this positional error is more than 90 percent, if it assumed that the WENSS sources are uniformly distributed over the sky." + Therefore. I have exchidec hese 7 pulsars (PSRs JOLIT135. D1639|36D. J1758|30. J19001230. ου1230. 2002|30 aud J2301|GO) fro trther analysis.," Therefore, I have excluded these 7 pulsars (PSRs J0417+35, B1639+36B, J1758+30, J1900+30, J1931+30, J2002+30 and J2304+60) from further analysis." + PSR B2000|LO was also excluded. since it is located in the Cyvguus A region. where uo. WENSS nap could ο mado.," PSR B2000+40 was also excluded, since it is located in the Cygnus A region, where no WENSS map could be made." + I have taken the J2000 positious of the remaimine £6 pulsus and compared them with the positious of the sources in the WENSS catalog., I have taken the J2000 positions of the remaining 76 pulsars and compared them with the positions of the sources in the WENSS catalog. + Tweutv-five pulsars have a WENSS source located wiun three times their combined positional uncertainty o. with where Ao iud Ad are the positional differcuces in right ascension and declination. respectively. aud," Twenty-five pulsars have a WENSS source located within three times their combined positional uncertainty $\sigma$, with where $\Delta\alpha$ and $\Delta\delta$ are the positional differences in right ascension and declination, respectively, and" +evolution during the spherical homologous phase. was studied by many authors (e.g..Grass-Weinberg2010:Rabinak&WaxmanNakarSari 2010).. where all use the assumption (hat in Nakar&Sari2010. we prove to be adequate) of thermal equilibrium.,"evolution during the spherical homologous phase, was studied by many authors \citep[e.g.,][]{Grassberg71,Chevalier76,Chevalier92,Chevalier08,Piro10,Rabinak10,Nakar10}, where all use the assumption (that in \citealt{Nakar10} we prove to be adequate) of thermal equilibrium." + All these studies considered only explosions where the shock breakout velocities are Newtonian and pairs are not significantly produced in the transition laver. 1e... %9=64/6<0.5 where c is (he speed of light.," All these studies considered only explosions where the shock breakout velocities are Newtonian and pairs are not significantly produced in the transition layer, i.e., $\beta_0=v_0/c<0.5$ where $c$ is the speed of light." + A large range of cosmic explosions are expected to produce breakout velocities (hat are either mildlv relativistic or ultra relativistic., A large range of cosmic explosions are expected to produce breakout velocities that are either mildly relativistic or ultra relativistic. + A [ew examples are a range of white dwarf explosions such as Ia SN (Piro.Chang&Weinberg2010).. Ja SN (Shenefal2010). and possibly accretion induced collapse (Dessartefaf2006:Piro.Quataert&Metzger2010)..," A few examples are a range of white dwarf explosions such as Ia SN \citep{Piro10}, .Ia SN \citep{Shen10} and possibly accretion induced collapse \citep{Dessart06,Piro2010AIC}." + The energy involved in most of these explosions is <10°! ere. but the compact progenitor and relatively low ejecta mass results in relativistic breakouts.," The energy involved in most of these explosions is $\lesssim 10^{51}$ erg, but the compact progenitor and relatively low ejecta mass results in relativistic breakouts." + Another example is extremely energelic explosions of massive stars. with explosion energies in the range 10?—1003 erg.," Another example is extremely energetic explosions of massive stars, with explosion energies in the range $10^{52}-10^{53}$ erg." + These were recently observed in growing nmunbers. e.g.. $N2005ap and SN2007b1 (Gal-Yam2000:Quimbyefαἱ.2009. eg.).. and are believed (o be the outcomes of various progenitor svstenmis.," These were recently observed in growing numbers, e.g., SN2005ap and SN2007bi \citep[e.g.,]{Gal-Yam09,Quimby09}, and are believed to be the outcomes of various progenitor systems." + Yel another example is massive star explosions that are associated with long gamma-ray bursts. where the breakout is ultra-relativistie.," Yet another example is massive star explosions that are associated with long gamma-ray bursts, where the breakout is ultra-relativistic." + Relativistie breakouts may also take place in choked GRBs. where the relativisüc jets [ail to penetrate through the stellar envelope. and no regular long GRB is produced.," Relativistic breakouts may also take place in choked GRBs, where the relativistic jets fail to penetrate through the stellar envelope, and no regular long GRB is produced." +" As we show here. (his mechanism is a promising source of all the observed low-luminosity GRBs,"," As we show here, this mechanism is a promising source of all the observed low-luminosity GRBs." + The physical processes involved in producing the observed signature of a relativistic shock breakout is different [rom the Newtonian case in two fundamental wavs., The physical processes involved in producing the observed signature of a relativistic shock breakout is different from the Newtonian case in two fundamental ways. +" First. once the velocily of a radiation mediated shock becomes large enough. 9,>0.5. and the temperature behind the shock exceeds 50 keV. pair production becomes the dominant source of leptons. which in turn are (he main source of photons via [ree-Iree emission."," First, once the velocity of a radiation mediated shock becomes large enough, $\beta_s > 0.5$, and the temperature behind the shock exceeds $50$ keV, pair production becomes the dominant source of leptons, which in turn are the main source of photons via free-free emission." + The exponential sensitivity of the number of pairs to the temperature regulates the rest frame temperature in the shock immediate downstream to an almost constant value of 100—200 keV. independent ol the shock Lorentz factor (Ixatz.Dudnik&Waxman2010:efal.2010).," The exponential sensitivity of the number of pairs to the temperature regulates the rest frame temperature in the shock immediate downstream to an almost constant value of $100-200$ keV, independent of the shock Lorentz factor \citep{Katz10,Budnik10}." +. The eas becomes loaded with pairs that dominate its optical depth. resulting in a temperature dependent opacity per unit of mass.," The gas becomes loaded with pairs that dominate its optical depth, resulting in a temperature dependent opacity per unit of mass." + This is in sharp contrast to Newtonian shocks. especially when 0.05«9.<0.5. where the temperature of the shocked fluid depends strongly on the shock velocity but the opacity per unit of mass is constant.," This is in sharp contrast to Newtonian shocks, especially when $0.05<\beta_s<0.5$, where the temperature of the shocked fluid depends strongly on the shock velocity but the opacity per unit of mass is constant." + The second major dillerence of relativistic explosions is (he hydrodynamics both before and after the breakout., The second major difference of relativistic explosions is the hydrodynamics both before and after the breakout. + A Newtonian shock that propagates in a power-law decreasing density. assumes (he sell similar solution of Sakurai(1960). before breakout. and the gas velocity is roughly constant after the breakout (it doubles by about a factor of (wo).," A Newtonian shock that propagates in a power-law decreasing density assumes the self similar solution of \cite{Sakurai60} before breakout, and the gas velocity is roughly constant after the breakout (it doubles by about a factor of two)." + Once the shock becomes relativistic it follows the, Once the shock becomes relativistic it follows the +We use aimodified version of the uunerical code of CSTI and CST2 to construct models of differentially rotating ueutron stars.,We use a modified version of the numerical code of CST1 and CST2 to construct models of differentially rotating neutron stars. + The code is based on similar algorithius developed by IHachisu (1986) and Ixomatszu. Exieuchi aud IIachisu (1989). aud we refer to CST for details.," The code is based on similar algorithms developed by Hachisu (1986) and Komatsu, Eriguchi and Hachisu (1989), and we refer to CST1 for details." + We adopt a polvtropic equation of state where py is the restanass density and where equatiou (19)) reduces to equation (5)) iu the Newtonian lanit., We adopt a polytropic equation of state where ${\rho_0}$ is the rest-mass density and where equation \ref{eos2}) ) reduces to equation \ref{eos1}) ) in the Newtonian limit. + We take the polvtropic coustaut A to be unity without loss of generalitv., We take the polytropic constant $K$ to be unity without loss of generality. +" Since IV""? has units of length. all solutions scale according to Af=AN""AJ. pj=Αρ cte."," Since $K^{n/2}$ has units of length, all solutions scale according to $\bar M = K^{-n/2} M$, $\bar \rho_0 = K^n \rho_0$, etc.," + where the barred quantities are dimensionless quantities correspouding to A=1. aud the unbarrec quautities are physical quautities (compare CSTI).," where the barred quantities are dimensionless quantities corresponding to $K = 1$, and the unbarred quantities are physical quantities (compare CST1)." +" Constructing differcutially rotating neutron star models requires Choosing a rotating law F(Q)= ufu. where af and d, are components of the fom-velocity 07 and © is the angular velocity.", Constructing differentially rotating neutron star models requires choosing a rotating law $F(\Omega) = u^t u_{\phi}$ where $u^t$ and $u_{\phi}$ are components of the four-velocity $u^{\alpha}$ and $\Omega$ is the angular velocity. +" We follow CST aud assume the rotation law F(Q)=(9,Q), where the parameter οἱ has units of length."," We follow CST1 and assume the rotation law $F(\Omega) = A^2(\Omega_c - \Omega)$, where the parameter $A$ has units of length." +" Expressing uf and i, iu terms O aud metric potentials vields equation (12) in CSTI. or. in the Nowtonuian lait. Tere we have rescaled A aud i din teris of the equatorial radius Πω “AL—AYR, aud s=r/h,."," Expressing $u^t$ and $u_{\phi}$ in terms $\Omega$ and metric potentials yields equation (42) in CST1, or, in the Newtonian limit, Here we have rescaled $A$ and $r$ in terms of the equatorial radius $R_e$ : $\hat A \equiv A/R_e$ and $\hat r \equiv r/R_e$." + The parameter Lis a measure of the degree of differential rotation and determines the leugth scale over which O chauges., The parameter $\hat A$ is a measure of the degree of differential rotation and determines the length scale over which $\Omega$ changes. + Since uniformi rotation is recovered iu the limit 4A>x. it is convenient to parametrize sequences by At.," Since uniform rotation is recovered in the limit $\hat A \rightarrow +\infty$, it is convenient to parametrize sequences by $\hat A^{-1}$." +" In the Newtoman huit. the ratio Q./Q. that appears in the estimate (17)) is related to A3 by οο,=1)A3. but for relativistic configurations this relation holds oulv approximately,"," In the Newtonian limit, the ratio $\Omega_c/\Omega_e$ that appears in the estimate \ref{dM4}) ) is related to $\hat A^{-1}$ by $\Omega_c/\Omega_e = 1 + \hat A^{-2}$, but for relativistic configurations this relation holds only approximately." + We adopt this particular rotation law for couvenicuce and for easy comparison with many other authors who have assunied the same law., We adopt this particular rotation law for convenience and for easy comparison with many other authors who have assumed the same law. + We also compared with the ronunants aneular momentum distribution iu the fully relativistic dvnamical merecr simulations of Shibata iux Urvu (2000) and to the post-Newtoman simulations of Faber. Rasio aud Manor (2001).," We also compared with the remnants' angular momentum distribution in the fully relativistic dynamical merger simulations of Shibata and Uryu (2000) and to the post-Newtonian simulations of Faber, Rasio and Manor (2001)." + We have found that them πιοΊσα results cau be fit reasonably well by our adopte differcutial rotation law., We have found that their numerical results can be fit reasonably well by our adopted differential rotation law. + We modify the mmuerical aleorithin of CSTI bv fing he mnaxiuuu interior density instead of the ceutra density for cach model., We modify the numerical algorithm of CST1 by fixing the maximum interior density instead of the central density for each model. + This chauge allows us to coustruct Heher mass models in some cases. since the central density does not always coincide with the παπα deusitv ai rence max Lot specify a model uniquely.," This change allows us to construct higher mass models in some cases, since the central density does not always coincide with the maximum density and hence may not specify a model uniquely." + For a given a value of η and A. we construct a sequence of models for each value of the maxima deusitv bw starting with a static. spherically sauetzie star and then decreasing the ratio of the polar to equatorial radius. Rye=Byf£BS dn decremeuts of 0.025.," For a given a value of $n$ and $\hat A$ , we construct a sequence of models for each value of the maximum density by starting with a static, spherically symmetric star and then decreasing the ratio of the polar to equatorial radius, $R_{pe} = R_p/R_e$, in decrements of 0.025." +" This sequence euds when we reach mass shedding (for large values of A). or when the code fails to converge (ποπιο the termination of equilibrium solutions) or when I,ισα=0 (bevoud which the star would become a toroid)."," This sequence ends when we reach mass shedding (for large values of $\hat A$ ), or when the code fails to converge (indicating the termination of equilibrium solutions) or when $R_{pe} = 0$ (beyond which the star would become a toroid)." + For each oue of these sequences the masini achieved mass is recorded., For each one of these sequences the maximum achieved mass is recorded. + We repeat this procedure for different values of the maximal density. covering about a decade below the ceutral density of the non-rotating miaxinmn mass model. which viclds the masimaiun allowed mass for the chosen values of 5 aud A.," We repeat this procedure for different values of the maximum density, covering about a decade below the central density of the non-rotating maximum mass model, which yields the maximum allowed mass for the chosen values of $n$ and $\hat A$." + Our ununercal results are tabulated in Appendix A.., Our numerical results are tabulated in Appendix \ref{appA}. . + Our niaxinmuui ass increases are lower limits in the scuse that even higher mass models may exist. but that we lave not been able to coustruct them muuericallv.," Our maximum mass increases are lower limits in the sense that even higher mass models may exist, but that we have not been able to construct them numerically." + Our mumerical results are tabulated in Tables A2. to ll in Appendix A..," Our numerical results are tabulated in Tables \ref{0.5} to \ref{2.9} + in Appendix \ref{appA}. ." + We also compare the increases in the muaxinuinm allowed mass with the estimate (17)). and fud surprisingly good agreement for soft equations of state aud moderate degrees of differential rotation.," We also compare the increases in the maximum allowed mass with the estimate \ref{dM4}) ), and find surprisingly good agreement for soft equations of state and moderate degrees of differential rotation." + Iu particular.we find that the fractional παται rest mass increase OAL/AL for uniformlyrotating stars is well approximated bv the inverseof the central concentration (seealso Table 11).," In particular,we find that the fractional maximum rest mass increase $\delta M/M$ for uniformlyrotating stars is well approximated by the inverseof the central concentration (seealso Table \ref{table1}) )." + For moderate degreesof differcutial, For moderate degreesof differential +ccontinues to evolve. future Chandra--LETGS observations may be able to constrain the spectral model further.,"continues to evolve, future -LETGS observations may be able to constrain the spectral model further." + Long term monitoring is necessary to test the precession idea. since it implies a cyclic spectral evolution.," Long term monitoring is necessary to test the precession idea, since it implies a cyclic spectral evolution." + Kaplanetal.(2003) suggested that iis an off-beam radio pulsar., \citet{kaplan03b} suggested that is an off-beam radio pulsar. + If it is indeed precessing. there is a possibility that at some point during its cycle the radio beam will be directed toward the earth.," If it is indeed precessing, there is a possibility that at some point during its cycle the radio beam will be directed toward the earth." + Finally. we point out that other isolated neutron stars may show similar behavior. indicative of precession.," Finally, we point out that other isolated neutron stars may show similar behavior, indicative of precession." + Further observations of those sources is therefore important. for increasing our understanding of both the hot surface of neutron stars and for probing their internal structure., Further observations of those sources is therefore important for increasing our understanding of both the hot surface of neutron stars and for probing their internal structure. + We thank Dr. Harvey Tananbaum for allowing tto be observed as part of the DDT program. and for his continued interest in the results.," We thank Dr. Harvey Tananbaum for allowing to be observed as part of the DDT program, and for his continued interest in the results." + We thank Rob van der Meer for his assistance with the LETGS data analysts., We thank Rob van der Meer for his assistance with the LETGS data analysis. +the peculiar outbursts acconipauied by infrared flares were observed on 1997 Aueust 11-15 (Eikeuberry et al.,the peculiar outbursts accompanied by infrared flares were observed on 1997 August 14-15 (Eikenberry et al. + 1998)., 1998). + The source was rolativelv quiet. thereafter for about 10 days and then went iuto a flaring state., The source was relatively quiet thereafter for about 10 days and then went into a flaring state. + Ou September 9 1ο peculiar “outburst” was secu again (Markwiudt et al., On September 9 the peculiar “outburst” was seen again (Markwardt et al. + 1999)., 1999). + For a given accretiug svsteui it is reasonable to assume iat the long term changes in the X-ray. cuission is due o chiauges iu the accretion rate.," For a given accreting system, it is reasonable to assume that the long term changes in the X-ray emission is due to changes in the accretion rate." + Unlike Cyveuus N-l where ie source transition typically takes place in a few days. je state transition in GRS 19151105 took about three uouths.," Unlike Cygnus X-1 where the source transition typically takes place in a few days, the state transition in GRS 1915+105 took about three months." + If we attribute the state trausition ax due to a change in the accretion rate near some critical accretion rate (as has been done in Chakrabarti Titarchuk 1995). je slow state transition can boe used to study the οἱ in detail at this critical rate.," If we attribute the state transition as due to a change in the accretion rate near some critical accretion rate (as has been done in Chakrabarti Titarchuk 1995), the slow state transition can be used to study the system in detail at this critical rate." + Iu this scenario the varicty of bursts and variability seen in GRS 1915)105 cau be attributed to phenomena near this critical state., In this scenario the variety of bursts and variability seen in GRS 1915+105 can be attributed to phenomena near this critical state. + Here we address the question of the fast state transition that las occurred in 1997 June 18., Here we address the question of the fast state transition that has occurred in 1997 June 18. + From Figure 1 we cau sec that the bursting properties svstematically changed during the transition., From Figure 1 we can see that the bursting properties systematically changed during the transition. + In Yadav et al. (, In Yadav et al. ( +1999) (see their Figure 2) it was shown that for about a month the source was in a burst mode with a slow transition from regular bursts to nreenlar bursts aud then again toa regular burst of shorter duration.,1999) (see their Figure 2) it was shown that for about a month the source was in a burst mode with a slow transition from regular bursts to irregular bursts and then again to a regular burst of shorter duration. + In Yadav et al. (, In Yadav et al. ( +1999) it was postulated that the ireeular bursts are manifestations of rapid state changes.,1999) it was postulated that the irregular bursts are manifestations of rapid state changes. + To quautifv the properties of the spectral states we lave taken two RXTE observations cach in the low-hard aud ligh-soft states., To quantify the properties of the spectral states we have taken two RXTE observations each in the low-hard and high-soft states. + Iu the low-hard state the observation carried out on 1997 Alarch 26 (towards the cud of the low- state) and another on 1997 May δ Gin the beeiuniug of state transition) were selected., In the low-hard state the observation carried out on 1997 March 26 (towards the end of the low-hard state) and another on 1997 May 8 (in the beginning of state transition) were selected. + In the high-soft state observations carried out on 1997 July 20 aud 1997 August 19 were chosen., In the high-soft state observations carried out on 1997 July 20 and 1997 August 19 were chosen. + The 1997 May 8 and 1907 August 19 observations are the same that are used in Yadaw et al. (, The 1997 May 8 and 1997 August 19 observations are the same that are used in Yadav et al. ( +1999).,1999). + The N-vay cuuission properties of the source iu the spectral states as deduced from these observations are compared with that obtained during the nmregular bursts observed ou 1997 June 18., The X-ray emission properties of the source in the spectral states as deduced from these observations are compared with that obtained during the irregular bursts observed on 1997 June 18. + Some salieut features of the selected: observations are giveu in Table 1., Some salient features of the selected observations are given in Table 1. + We use the standard 2 mode data which gives 128 channel euergv spectra every 16 s (used for the spectral analysis) aud 2 channel binned data below 13 keV every 0.125 is (used for the tiniug analysis)., We use the standard 2 mode data which gives 128 channel energy spectra every 16 s (used for the spectral analysis) and 2 channel binned data below 13 keV every 0.125 ms (used for the timing analysis). + The light curves of the selected low-lard aud high-soft states of the source are shown in Figure 2. with a time resolution of 1l s. The data is for all the five Proportional Counter Units (PCUs) and the energzv range 182. 13 keV. The average count rate during the low-hard state of Marchi 26 is 318I + and it increased to 5600 s:+ for the May δ data.," The light curves of the selected low-hard and high-soft states of the source are shown in Figure 2, with a time resolution of 1 s. The data is for all the five Proportional Counter Units (PCUs) and the energy range is 2 $-$ 13 keV. The average count rate during the low-hard state of March 26 is 3484 $^{-1}$ and it increased to 5600 $^{-1}$ for the May 8 data." +" During the hieli-soft states of July 20 and August 19. the observed count rates were 18330 | aud 21669 !. respectively,"," During the high-soft states of July 20 and August 19, the observed count rates were 18330 $^{-1}$ and 21669 $^{-1}$, respectively." + Several features of the state changes in black hole candidates are discernible from the light curve itself., Several features of the state changes in black hole candidates are discernible from the light curve itself. + Ou Alarch 26 (οι the count rate was low) there was higher variability in the 1 10 s time scale but the source was stable at longer time scales;, On March 26 (when the count rate was low) there was higher variability in the 1 $-$ 10 s time scale but the source was stable at longer time scales. + The situation was opposite in the high state of August. 19: there is large variability at longer time scale., The situation was opposite in the high state of August 19: there is large variability at longer time scale. + On May. 8 the count rate increased bv about50%.. but the variability characteristics were essentially the same.," On May 8 the count rate increased by about, but the variability characteristics were essentially the same." + On July 20. though the count rate was similar to that of August 19. the light curve appears siuilar to that seen during the low state. with several additional spikes at a few tens of seconds.," On July 20, though the count rate was similar to that of August 19, the light curve appears similar to that seen during the low state, with several additional spikes at a few tens of seconds." + The behavior of the source is similar to the Galactic black hole candidate source Cyvenus N-1 (see Rao et al 1998) when the source showed essentially similar pattern of changes., The behavior of the source is similar to the Galactic black hole candidate source Cygnus X-1 (see Rao et al 1998) when the source showed essentially similar pattern of changes. + To quantify the timing characteristics. we lave obtained the power density spectrum (PDS) for these four observations and these are displaved in Figure 3.," To quantify the timing characteristics, we have obtained the power density spectrum (PDS) for these four observations and these are displayed in Figure 3." + The low-hard state PDS displays all the characteristics of PDS generally observed for other Galactic black hole sources during the low-hard state (see Rao et al., The low-hard state PDS displays all the characteristics of PDS generally observed for other Galactic black hole sources during the low-hard state (see Rao et al.