source,target The flux density of 22004et is too low compared to the rms of the visibility amplitudes (20 mmdJy) for obtaining a good result with the test of the closure phase distribution., The flux density of 2004et is too low compared to the rms of the visibility amplitudes $\sim$ mJy) for obtaining a good result with the test of the closure phase distribution. The average value of the cosines of all the closure phases considered in these observations is equal to 0.005+0.002., The average value of the cosines of all the closure phases considered in these observations is equal to $0.005\pm0.002$. This average value is slightly higher than 0., This average value is slightly higher than 0. The average of the absolute values of the closure phases ts 0.0065+0.0020., The average of the absolute values of the closure phases is $0.0065\pm0.0020$. From Fig., From Fig. 2. we estimate a flux density of the supernova of 0.18£0.08 times the rms of the visibility amplitudes. o. used in our computations. which. as said above. is ~20 mmJy.," \ref{RelaTeo} we estimate a flux density of the supernova of $0.18\pm0.08$ times the rms of the visibility amplitudes, $\rho$, used in our computations, which, as said above, is $\sim20$ mJy." Hence. the estimated flux density of the (real) source in the data ts. then. 3.8+ 1.6mmJy.," Hence, the estimated flux density of the (real) source in the data is, then, $3.8\pm1.6$ mJy." This value is too high. but compatible (at a 2-sigma level) with the flux density estimated from the," This value is too high, but compatible (at a 2–sigma level) with the flux density estimated from the" test our FOR output data. Subhonenko Ciramann (2003) investigated the mass function of clusters.,"test our FOF output data, Suhhonenko Gramann (2003) investigated the mass function of clusters." The cluster mass function in the Virgo simulations has been studied in detail bv Jenkins et al. (, The cluster mass function in the Virgo simulations has been studied in detail by Jenkins et al. ( 2001).,2001). Suhhonenko Cramann (2003) found that the agreement between our results and. these obtained by Jenkins et al. (, Suhhonenko Gramann (2003) found that the agreement between our results and these obtained by Jenkins et al. ( 2001) is very good.,2001) is very good. " The FOP cluster finder depends on one parameter b. which defines the linking length as 6A,."," The FOF cluster finder depends on one parameter $b$, which defines the linking length as $b\lambda_p$." The conventional choice for this parameter is 6=0.2 (see e.g. Góttz. Lluchra Drandenberger 1998: Jenkins et al.," The conventional choice for this parameter is $b=0.2$ (see e.g. Göttz, Huchra Brandenberger 1998; Jenkins et al." 2001)., 2001). In this paper we also define clusters by using the value 6=0.2., In this paper we also define clusters by using the value $b=0.2$. We also study. velocities of the clusters defined. by the parameters b=0.15., We also study velocities of the clusters defined by the parameters $b=0.15$. In the limit of very large numbers of particles per object. FOR approximately selects the matter enclosed. by an Isodensity contour at. ορ.," In the limit of very large numbers of particles per object, FOF approximately selects the matter enclosed by an isodensity contour at $\rho_b/b^3$." We studied FOF clusters that contained at least. ten particles., We studied FOF clusters that contained at least ten particles. Phe three-dimensional peculiar velocity. of each cluster was defined as where Ny is the number of particles in the cluster and Fis the peculiar velocity of the particle # in the cluster.," The three-dimensional peculiar velocity of each cluster was defined as where $N_{f}$ is the number of particles in the cluster and $\vec v_i$ is the peculiar velocity of the particle $i$ in the cluster." We also selected DALAN clusters using the following method. (, We also selected DMAX clusters using the following method. ( 1) We calculated the density contrast on a eric.,1) We calculated the density contrast on a grid. " For each grid point. the density contrast was determined as where AN ds the number of particles in the sphere of raciius £2, around the grid. point. and is the mean number of particles in the sphere of radius ("," For each grid point, the density contrast was determined as where $N$ is the number of particles in the sphere of radius $R_s$ around the grid point, and is the mean number of particles in the sphere of radius $R_s$. (" 2) We found the density maxima on the grid.,2) We found the density maxima on the grid. The erid point was considered. as a density. maximum. if its clensity contrast. was higher than the density contrast. in all 26 neighbouring erid points.," The grid point was considered as a density maximum, if its density contrast was higher than the density contrast in all 26 neighbouring grid points." The location of the eric point. where the density contrast had a maximum. value. was identified as the candidate eluster centre. (," The location of the grid point, where the density contrast had a maximum value, was identified as the candidate cluster centre. (" 3) The final cluster list was obtained by deleting the candidate clusters with lower density contrast in all. pairs separated by less than the radius /?..,3) The final cluster list was obtained by deleting the candidate clusters with lower density contrast in all pairs separated by less than the radius $R_s$. In this wav we define the clusters as maxima of the density. field smoothecl by a top-hat window: with a radius Hus, In this way we define the clusters as maxima of the density field smoothed by a top-hat window with a radius $R_s$. Vhe smoothing length sets a lower limit on the size of detected structures in the simulations., The smoothing length sets a lower limit on the size of detected structures in the simulations. " We used the smoothing radii 2,=1.5h Alpe and R=1.0h !Mpe.", We used the smoothing radii $R_s=1.5h^{-1}$ Mpc and $R_s=1.0h^{-1}$ Mpc. The mean number of particles in spheres of Ry=15h* Mpe and By=1.057 Alpe is N=17.26 and N= 5.12. respectively.," The mean number of particles in spheres of $R_s=1.5h^{-1}$ Mpc and $R_s=1.0h^{-1}$ Mpc is $\bar N=17.26$ and $\bar N=5.12$ , respectively." To select the Ry=1.55.+ Alpe clusters. we used a 256% grid (the cell size /=0.920 Alpe).," To select the $R_s=1.5h^{-1}$ Mpc clusters, we used a $256^3$ grid (the cell size $l=0.936 h^{-1}$ Mpc)." For ἐς=1.0ht Alpe. we used a 350° grid (/=0.68401 Alpe).," For $R_s=1.0h^{-1}$ Mpc, we used a $350^3$ grid $l=0.684 h^{-1}$ Mpc)." " For comparison. for the 2.=1.05.1 Alpe clusters we used alsoa 256""RH &rid."," For comparison, for the $R_s=1.0h^{-1}$ Mpc clusters we used alsoa $256^3$ grid." We studied. the rms density contrast and. the rms peculiar velocity on the 256° eric., We studied the rms density contrast and the rms peculiar velocity on the $256^3$ grid. Phe rms density contrast on the grid. was 5.05 and [29 for the radii R=15h+ Alpe and A;=L.0f* Alpe. respectively.," The rms density contrast on the grid was $5.05$ and $7.29$ for the radii $R_s=1.5h^{-1}$ Mpc and $R_s=1.0h^{-1}$ Mpc, respectively." The ris peculiar velocity. σοι was determined for the fraction of grid points. P. where the number of particles ΑΝ1l.," The rms peculiar velocity, $\sigma_v$, was determined for the fraction of grid points, $F$, where the number of particles $N>1$." Uf there are no particles in the neighbourhood of a grid point. the velocity field is undetermined.," If there are no particles in the neighbourhood of a grid point, the velocity field is undetermined." " For R,=L.5h+ Alpe. we found that f=0.96 and σι=473kms5."," For $R_s=1.5h^{-1}$ Mpc, we found that $F=0.96$ and $\sigma_v=473 \kms$." For Ry=LOb+ Alpe. f=0.69 and σι=481kms1 respectively.," For $R_s=1.0 h^{-1}$ Mpc, $F=0.69$ and $\sigma_v=481 \kms$, respectively." Here we took into account the finite size of the simulation box (sec next section)., Here we took into account the finite size of the simulation box (see next section). We also studied the rms density contrast ane the rms peculiu velocity on the 350% eric anc found. similar results., We also studied the rms density contrast and the rms peculiar velocity on the $350^3$ grid and found similar results. For each DALAN cluster. we investigated the cluster mass. AM. and the peculiar velocity. ey. at the radius. f.," For each DMAX cluster, we investigated the cluster mass, $M$, and the peculiar velocity, $v_{cl}$, at the radius $R_s$." " The mass in the cluster was determined as Al=Nyni). where IN, is the number of particles in a sphere of radius AR. around the centre of the cluster."," The mass in the cluster was determined as $M=N_d \,m_p$, where $N_d$ is the number of particles in a sphere of radius $R_s$ around the centre of the cluster." The peculiar velocity of each cluster was defined as where ο is the peculiar velocity of the particle 7 in the DAIAN cluster., The peculiar velocity of each cluster was defined as where $\vec v_i$ is the peculiar velocity of the particle $i$ in the DMAX cluster. Suhhonenko Cramann (2003) compared the cluster peculiar velocities defined by dillerent methocls (i.e. the FOL method versus the DALAN method) for massive clusters., Suhhonenko Gramann (2003) compared the cluster peculiar velocities defined by different methods (i.e. the FOF method versus the DMAX method) for massive clusters. By using dillerent. methods to identify the clusters. we select almost the same objects in the simulation.," By using different methods to identify the clusters, we select almost the same objects in the simulation." But we assign cillerent velocities to the same clusters., But we assign different velocities to the same clusters. To determine the rms peculiar velocities of clusters. we used the equation where the parameter ος describes the dispersion. of cluster velocities. Όρη derived from the simulations ancl the parameter ej is the linear contribution from the velocity Iluctuations on scales greater than the size of the simulation box L.," To determine the rms peculiar velocities of clusters, we used the equation where the parameter $v_s$ describes the dispersion of cluster velocities, $v_{cli}$, derived from the simulations and the parameter $v_L$ is the linear contribution from the velocity fluctuations on scales greater than the size of the simulation box $L$ ." Ht is given by Ny is the number of clusters studied., It is given by $N_{cl}$ is the number of clusters studied. Using eq. (, Using eq. ( 4). the linear rms peculiar velocity of peaks can be written as The second term in this expression is not sensitive to the amplitude of large-scale[uctuations at wavenumbers &.< 2x/L.,"4), the linear rms peculiar velocity of peaks can be written as The second term in this expression is not sensitive to the amplitude of large-scalefluctuations at wavenumbers $k<2\pi/L$ ." " Vherefore. the linear rms velocity of peaks can be expressed. approximately. as where m,CH)' is. determined. by the power spectruni at the wavenumbers &2x/L andej is given by eq. ("," Therefore, the linear rms velocity of peaks can be expressed, approximately, as where $\sigma_p^{\prime} (R)$ is determined by the power spectrum at the wavenumbers $k>2\pi/L$ and$v_L$ is given by eq. (" 11).,11). Figure & shows the normalized average power spectra of LOS velocity of the two chromospheric aand ID)) and two of the plotospheric aud À 3969.3) lines inside the uubra of the suuspot.,Figure \ref{fig:power_spectra} shows the normalized average power spectra of LOS velocity of the two chromospheric and ) and two of the photospheric and $\lambda$ 3969.3) lines inside the umbra of the sunspot. We chose lis iron line because it has better signal to noise aud its ormation height is distant from the laver where iis formed., We chose this iron line because it has better signal to noise and its formation height is distant from the layer where is formed. In the photosphere (bottom panel). the power is concentrated between 2 and { πα]. correspouding to he 5 minute baud. with a maxinuun peak at 3.5 1uIIEz.," In the photosphere (bottom panel), the power is concentrated between 2 and 4 mHz, corresponding to the 5 minute band, with a maximum peak at 3.5 mHz." Both spectral lines peak at the same frequency. although he power of the lue is slightlv higher.," Both spectral lines peak at the same frequency, although the power of the line is slightly higher." The increase of the power at requeucies above 1.5 mllz is more important than the oue for frequencies below this value., The increase of the power at frequencies above 4.5 mHz is more important than the one for frequencies below this value. The velocity power spectra of both chromospheric mes (top panel) have a broad distribution of frequencies. with he largest power beiug in the baud from 5 to 10 112.," The velocity power spectra of both chromospheric lines (top panel) have a broad distribution of frequencies, with the largest power being in the band from 5 to 10 mHz." The chromospheric power spectra has a maxi at 6.2 inllz aud several secondary peaks around it (sceforconrparisouLites1986)., The chromospheric power spectrum has a maximum at 6.2 mHz and several secondary peaks around it \citep[see for comparison][]{Lites1986}. . These frequency. peaks correspond to the chromospheric 3 minutes oscillatious., These frequency peaks correspond to the chromospheric 3 minutes oscillations. At the highest peak of the power spectra. both aan thave almost the sane power. but for those frequeucies with lower power. the power of the lis ducreased comparing to theΕΠ.," At the highest peak of the power spectra, both and have almost the same power, but for those frequencies with lower power, the power of the is increased comparing to the." .. Note that at weights sampled by our spectral lines we do not find a continuous transition from the peak at 23.5 illz o the oue at 6.2 mllz. but rather a cdiscontinuous vchavior between the photospherie aud chromospleric oower spectra.," Note that at heights sampled by our spectral lines we do not find a continuous transition from the peak at 3.5 mHz to the one at 6.2 mHz, but rather a discontinuous behavior between the photospheric and chromospheric power spectra." However. the promincut secondary. peak around 5.5 iilIz in the power spectra of the line is wich more obvious than the corresponding iu the ypower spectra. which could indicate some transition owards higher frequencics in the power spectra as the waves propagate upward from the formation height of he lime to the lines.," However, the prominent secondary peak around 5.5 mHz in the power spectra of the line is much more obvious than the corresponding in the power spectra, which could indicate some transition towards higher frequencies in the power spectra as the waves propagate upward from the formation height of the line to the lines." A phase diagram gives the phase difference (Ao) between two signals., A phase diagram gives the phase difference $\Delta \phi$ ) between two signals. Di our study; we use Ao to nieasure the time delay between the oscillatory velocity signals frou. two spectral lines aud assume that the difference between them is mainly due to the difference of the formation height of the two lines.," In our study, we use $\Delta \phi$ to measure the time delay between the oscillatory velocity signals from two spectral lines and assume that the difference between them is mainly due to the difference of the formation height of the two lines." In the following. we will show the phase difference spectra between differeut combinations of pairs of spectral lines used in this work.," In the following, we will show the phase difference spectra between different combinations of pairs of spectral lines used in this work." To obtain the phase spectra. we treated cach spatial point separately and calculated the Fourier-transtorm of the temporal evolution of the respective velocities.," To obtain the phase spectra, we treated each spatial point separately and calculated the Fourier-transform of the temporal evolution of the respective velocities." We derived the phases. aud from them the phase difference of the two signals as a function of the frequency.," We derived the phases, and from them the phase difference of the two signals as a function of the frequency." There is a 2z ambiguity in the computation of the pliase value. so all phase differences have been projected in the range cz.," There is a $\pi$ ambiguity in the computation of the phase value, so all phase differences have been projected in the range $\pm \pi$." Then we calculated listograms of the relative occurrence of a given value of the plase differences at cach frequency takiug into account all the corresponding spatial points (seealsoKvijgeretal.2001.andreferences thereiu).., Then we calculated histograms of the relative occurrence of a given value of the phase differences at each frequency taking into account all the corresponding spatial points \citep[see also][ and references therein]{Krijger+etal2001}. . " We obtained the data displaved in Έπος, 9- 15..", We obtained the data displayed in Figs. \ref{fig:dfase_SiHe}- \ref{fig:dfase_FeSi_quiet}. Iun addition. to the phase difference spectra. we calculated the coherence spectra.," In addition to the phase difference spectra, we calculated the coherence spectra." They provide au estimate of the statistical validity of the phase aud power spectra., They provide an estimate of the statistical validity of the phase and power spectra. Consideriug » pairs of signals ο) aud gilt). whose Fourier transforius are IX(uw) aud ία). respectively. the coherence is defined as where Aople)=οί) hi," Considering $n$ pairs of signals $x_k(t)$ and $y_k(t)$, whose Fourier transforms are $\bar{X}_k(\omega)$ and $\bar{Y}_k(\omega)$, respectively, the coherence is defined as where $\Delta\phi_k(\omega)=\phi_{xk}(\omega)-\phi_{yk}(\omega)$." our case. the sub-index Á& covers the spatial Oye(e).position.," In our case, the sub-index $k$ covers the spatial position." " The colerence evaluates statistically for every frequency w the relation of the Ao,(e) for the » A-siguals.", The coherence evaluates statistically for every frequency $\omega$ the relation of the $\Delta\phi_k(\omega)$ for the $n$ $k$ -signals. It takes the value 1 when Δωρίω) is the same for all the &., It takes the value 1 when $\Delta\phi_k(\omega)$ is the same for all the $k$. If the phase difference of the different À is arbitrary. the coherence takes very low values.," If the phase difference of the different $k$ is arbitrary, the coherence takes very low values." We selected a confidence limut at 0.7. and for frequencies with coherence above this value we consider the pliase spectra to be reliable.," We selected a confidence limit at 0.7, and for frequencies with coherence above this value we consider the phase spectra to be reliable." We also analyzed the increase of the amplitude of the oscillations., We also analyzed the increase of the amplitude of the oscillations. We calculated the amplification spectra as the ratio between the power at two lavers. both of them averaged all over the mubra: Following Centeneetal.(2006).. the observations were compared with a amodel of linear vertical propagation of slow magucto-acoustic wave in an isothermal atmosphere that iuchudes radiative losses described by Newtous cooling law.," We calculated the amplification spectra as the ratio between the power at two layers, both of them averaged all over the umbra: Following \citet{Centeno+etal2006}, the observations were compared with a model of linear vertical propagation of slow magneto-acoustic wave in an isothermal atmosphere that includes radiative losses described by Newton's cooling law." Assuming that the iuuplitude of the vertical velocity changeswith height by, Assuming that the amplitude of the vertical velocity changeswith height by isetal.,s et al. with the allowed transitions listed in the compilation of Verner et al..," with the allowed transitions listed in the compilation of Verner et al.," " making a total of 48 transitions involving the ground 7 P"" levels ancl upper levels.", making a total of 48 transitions involving the ground $^2$ $^o$ levels and upper levels. Phe indirect excitation rate by the UV radiation field of the Galaxy could then be determined: Piz=9.310Haul, The indirect excitation rate by the UV radiation field of the Galaxy could then be determined: $\Gamma_{\frac{1}{2}\frac{3}{2}}=9.3\ 10^{-11}\ \mathrm{s}^{-1}$. In order to assess the relevance of the ὃς δρ configuration upper levels in the relative population of the eround “Pom4 levels. we have performed. test. caleulations comparing 2:2our LO-level model ion with the 2-Ievel ion.," In order to assess the relevance of the 2s $^2$ configuration upper levels in the relative population of the ground $^2\mathrm{P}^o_{\frac{1}{2},\frac{3}{2}}$ levels, we have performed test calculations comparing our 10-level model ion with the 2-level ion." At high. temperatures the 2s 2p2 configuration⋅. levels may be excited. by collisions with hot electrons in the medium., At high temperatures the 2s $^2$ configuration levels may be excited by collisions with hot electrons in the medium. " llowever. the testeases have shown that this elfect does not contribute significantly to the excitation of the 7"" levels for temperatures 2<<30000 Ix. where the discrepancies reach about 5 percent."," However, the testcases have shown that this effect does not contribute significantly to the excitation of the $^2\mathrm{P}^o$ levels for temperatures $T\leq 30000$ K, where the discrepancies reach about 5 percent." Therefore. for temperatures lower than 30000 Ix. only two levels can be taken into account.," Therefore, for temperatures lower than 30000 K, only two levels can be taken into account." The population ratio of the excited. [ine-structure level relatively to the ground level is then expressed by:, The population ratio of the excited fine-structure level relatively to the ground level is then expressed by: thines these are hampered by uucertainties concerning the plivsies of the mnerinost disk regiois.,things these are hampered by uncertainties concerning the physics of the innermost disk regions. Yot woe note that in the hydrodvuamical approach explored by Psaltis Norma1 (2000). the test particle frequencies (the same as in the RPAL plus an adclitiona freqicacy at νο|14.) are selected by the response of an annulus in the disk. whe1 this is subject to a wide-band input noise.," Yet we note that in the hydrodynamical approach explored by Psaltis Norman (2000), the test particle frequencies (the same as in the RPM plus an additional frequency at $\nu_\phi+\nu_r$ ) are selected by the response of an annulus in the disk, when this is subject to a wide-band input noise." If confirmed. the RPAL will provide an uuprecedeuted opportunity to micasure CR effect E he strong field regime. such as the periastrou precession in the vicidtv of the mareinally stable orbit and the racial dependence of the Lense- jodal precession frequency.," If confirmed, the RPM will provide an unprecedented opportunity to measure GR effects in the strong field regime, such as the periastron precession in the vicinity of the marginally stable orbit and the radial dependence of the Lense-Thirring nodal precession frequency." Iu. principle. accurately measured kHz QPO and TBO freqiencies would vield crucial information ou the compact object sucli as its lass al angular moment by solving Eqs.," In principle, accurately measured kHz QPO and HBO frequencies would yield crucial information on the compact object such as its mass and angular momentum by solving Eqs." 1-3 for ii. afAL aud r).," 1-3 for $m$, $a/M$ and $r$ )." " Should suitable. additional observables be found. it might become possible to obtain a scelfconsistencey check of the RPM. toseether with tests of GB iu the strong field reele,"," Should suitable, additional observables be found, it might become possible to obtain a self-consistency check of the RPM, together with tests of GR in the strong field regime." , computed the Anderson-Darling statistic. as described by ?.. for each group.,"computed the Anderson-Darling statistic, as described by \citet{Hou09}, for each group." Only group 15 shows significant non-Gaussianity in the velocity distribution. at 795 per cent contidence.," Only group 15 shows significant non-Gaussianity in the velocity distribution, at $>95$ per cent confidence." Other indications of a relaxed cluster. could. be the presence of a dominant galaxy near the X-ray centre (e.g.2).. and an approximately spherical. centrally-concentrated galaxy distribution.," Other indications of a relaxed cluster could be the presence of a dominant galaxy near the X-ray centre \citep[e.g.][]{D+10}, and an approximately spherical, centrally–concentrated galaxy distribution." In many of the clusters. there is an obvious dominant galaxy. large and luminous. near the centre of the X-ray image.," In many of the clusters, there is an obvious dominant galaxy, large and luminous, near the centre of the X-ray image." To quantify this. we have selected all cluster members within 700 km/s Xf the mean redshift and 500 Κρο of the recomputed centre. and identified the most luminous (in A) as the BCG.," To quantify this, we have selected all cluster members within 700 km/s of the mean redshift and 500 kpc of the recomputed centre, and identified the most luminous (in $K$ ) as the BCG." Figure 14. shows the luminosity of each of these BCGs. as a function of the host cluster £Lx.," Figure \ref{fig-bcg_mag} shows the luminosity of each of these BCGs, as a function of the host cluster $L_X$." There is little correlation here. although we note that tree of the X-ray undetected clusters have BCGs that are among t1ο least luminous in the sample (unfortunately. all three have only shallow 2MASS imaging. and thus the total luminosities may be significantly underestimated).," There is little correlation here, although we note that three of the X-ray undetected clusters have BCGs that are among the least luminous in the sample (unfortunately, all three have only shallow 2MASS imaging, and thus the total luminosities may be significantly underestimated)." It is also interesting that group 15. which has a high stellar mass given its Zy. has one of the mos massive BCOs in the sample.," It is also interesting that group 15, which has a high stellar mass given its $L_X$, has one of the most massive BCGs in the sample." Next we calculated the luminosity ratio between the first- anc third-ranked galaxy. Lj45.," Next we calculated the luminosity ratio between the first- and third-ranked galaxy, $L_{K,13}$." In Figure 15 we show this as a function of AZ. which is the distance in Mpc between the brightest cluster galaxy (BCG) and the geometric centre of the cluster. recomputed as above.," In Figure \ref{fig-bcgs} we show this as a function of $\Delta R$, which is the distance in Mpc between the brightest cluster galaxy (BCG) and the geometric centre of the cluster, recomputed as above." Interestingly. the distribution of the X-ray undetected clusters (and also the outlier group 15) is distinet from most of the “normal” systems. in the sense that their BCG is at least 250 Κρο from the centre.," Interestingly, the distribution of the X-ray undetected clusters (and also the outlier group 15) is distinct from most of the “normal” systems, in the sense that their BCG is at least 250 kpc from the centre." " However. we note that. of the 12 otherwise ""normal"" systems. only about half have a dominant CLis> 3). centrally located (AR«250 κο BCG,"," However, we note that, of the 12 otherwise “normal” systems, only about half have a dominant $L_{K,13}>3$ ), centrally located $\Delta R<250$ kpc) BCG." We now attempt to quantify the spatial distribution ofthe most luminous galaxies. i.e. those that are at most 0.6 mag fainter than Aly. so that we are equally deep in all clusters.," We now attempt to quantify the spatial distribution of the most luminous galaxies, i.e. those that are at most 0.6 mag fainter than $M_K^\ast$, so that we are equally deep in all clusters." The undetected cluster 18 only has three galaxies above this limit. so we omit it from the following analysis.," The undetected cluster 18 only has three galaxies above this limit, so we omit it from the following analysis." " We calculate the concentration as he fraction of such cluster members within 0.5/2,,,.", We calculate the concentration as the fraction of such cluster members within $0.5R_{\rm rms}$. For the elongation. we first perform a least-squares regression analysis to tind the principle axis of each cluster on the sky: then we calculate he dispersion perpendicular to and parallel to this axis.," For the elongation, we first perform a least-squares regression analysis to find the principle axis of each cluster on the sky; then we calculate the dispersion perpendicular to and parallel to this axis." The elongation is the ratio of the two values. always defined as the arger divided by the smaller so the ratio is greater than unity.," The elongation is the ratio of the two values, always defined as the larger divided by the smaller so the ratio is greater than unity." The results are shown in Figure 16.. where the points are colour-coded as before.," The results are shown in Figure \ref{fig-shapes}, where the points are colour-coded as before." Error bars are computed using a jackknife resampling., Error bars are computed using a jackknife resampling. Interestingly. most of the X-ray underluminous systems again appear separated from the majority of the population. as either low-concentration or highly elongated clusters.," Interestingly, most of the X-ray underluminous systems again appear separated from the majority of the population, as either low-concentration or highly elongated clusters." Only cluster 17 lies in a region of the plane occupied by the majority of normal clusters., Only cluster 17 lies in a region of the plane occupied by the majority of normal clusters. Note that cluster 16 is highly elongated: from Figure 15 we see that it has a distinctly dominated galaxy. but located 350 kpe from the centre.," Note that cluster 16 is highly elongated; from Figure \ref{fig-bcgs} we see that it has a distinctly dominated galaxy, but located 350 kpc from the centre." This may indicate a merging or otherwise unrelaxed system., This may indicate a merging or otherwise unrelaxed system. Cluster 18. which is the only other X-ray undetected system with a dominant. centrally-located galaxy. has too few members to measure either quantity shown here with adequate precision.," Cluster 18, which is the only other X–ray undetected system with a dominant, centrally-located galaxy, has too few members to measure either quantity shown here with adequate precision." Again. however. there are examples of clusters (3 and 9) with normal X-ray properties and equally low concentrations.," Again, however, there are examples of clusters (3 and 9) with normal X-ray properties and equally low concentrations." This result needs to be approached with some caution. as there are multiple parameters at work here. related to the magnitude and velocity selections. the choice of centre. and the definition of concentration.," This result needs to be approached with some caution, as there are multiple parameters at work here, related to the magnitude and velocity selections, the choice of centre, and the definition of concentration." Nonetheless. we tentatively conclude that it seems likely dynamical age plays some role in the X-ray luminosity of a given cluster.," Nonetheless, we tentatively conclude that it seems likely dynamical age plays some role in the X-ray luminosity of a given cluster." All the clusters that appear relaxed in the optical — with a dominant central galaxy Qvithin 250kpe of the cluster centre. and at least three times brighter than the third-ranked galaxy). a centrally concentrated (> 0.25) galaxy population. and a spatial axis ratio of less than two — show normal X-ray," All the clusters that appear relaxed in the optical – with a dominant central galaxy (within 250kpc of the cluster centre, and at least three times brighter than the third–ranked galaxy), a centrally concentrated $>0.25$ ) galaxy population, and a spatial axis ratio of less than two – show normal X-ray" interstellar column density.,interstellar column density. Several qualitative conclusions can be drawn from. the observations: First. in all cases. there is a deficit of emission expected from lower temperatures.," Several qualitative conclusions can be drawn from the observations: First, in all cases, there is a deficit of emission expected from lower temperatures." Second. in most cases. a continuous distribution of temperatures is nevertheless required.," Second, in most cases, a continuous distribution of temperatures is nevertheless required." Finally. absorption by intervening cool gas at the redshift of the cluster cannot explain the dearth of soft X-ray emission.," Finally, absorption by intervening cool gas at the redshift of the cluster cannot explain the dearth of soft X-ray emission." In $6 below. we perform quantitive spectral fits to further explore the departures from the cooling-flow model.," In 6 below, we perform quantitive spectral fits to further explore the departures from the cooling-flow model." In this section. we set quantitative limits on emission from various parts of the temperature distribution.," In this section, we set quantitative limits on emission from various parts of the temperature distribution." To derive these limits. we use the Monte Carlo methods presented by Jernigan&Kahn (2002).. and implicitly used by Petersonetal.(2001) and Xuetal.(2002).," To derive these limits, we use the Monte Carlo methods presented by \cite{peterson3}, and implicitly used by \cite{peterson1} and \cite{xu}." . The basic procedure is based on an astrophysical model for the spatial and spectral dependence of the emission., The basic procedure is based on an astrophysical model for the spatial and spectral dependence of the emission. The Monte Carlo approach ts required because a different spectrum at each projected spatial position is required to test the cooling-flow model in detail., The Monte Carlo approach is required because a different spectrum at each projected spatial position is required to test the cooling-flow model in detail. We randomly generate photons with an associated dispersion angle. cross-dispersion angle. and CCD pulseheight value.," We randomly generate photons with an associated dispersion angle, cross-dispersion angle, and CCD pulseheight value." The resulting count distributions are then compared with the raw data. after the various data selection cuts and transformations.," The resulting count distributions are then compared with the raw data, after the various data selection cuts and transformations." In fitting for global parameters. such as the background normalization. we find the best fitting solution by using multivariate methods. as described in Peterson.Jernigan&Kahn(2002).," In fitting for global parameters, such as the background normalization, we find the best fitting solution by using multivariate methods, as described in \cite{peterson3}." . For the abundances and temperatures. we use a X statistic of the combined extracted first and second order spectra for both instruments and we iteratively adjust the surface brightness distribution to match the cross-dispersion profile.," For the abundances and temperatures, we use a $\chi^2$ statistic of the combined extracted first and second order spectra for both instruments and we iteratively adjust the surface brightness distribution to match the cross-dispersion profile." Por the cluster emission we adopt a relatively simple model. so as to reduce sensitivity to fitting biases.," For the cluster emission we adopt a relatively simple model, so as to reduce sensitivity to fitting biases." For the surface brightness. we use a spherical } profile where the core radius is left free and the ./ parameter is fixed to the value determined from EPIC spectral fits (Kaastraetal. 2002)).," For the surface brightness, we use a spherical $\beta$ profile where the core radius is left free and the $\beta$ parameter is fixed to the value determined from EPIC spectral fits \citealt{kaastra2}) )." " Additionally. we allow the normalization of the emission inside of a three-dimensional radius. 7,4. to be larger than the normalization outside of the radius."," Additionally, we allow the normalization of the emission inside of a three-dimensional radius, $r_{cool}$, to be larger than the normalization outside of the radius." In this way. the spatial profile can be much more peaked than the standard / profile.," In this way, the spatial profile can be much more peaked than the standard $\beta$ profile." This three dimensional distribution is then projected on the sky., This three dimensional distribution is then projected on the sky. The precise shape of the spatial distribution is not eritically important for determining the cooling luminosity limits as long as it reproduces the rough behavior of the emission profile., The precise shape of the spatial distribution is not critically important for determining the cooling luminosity limits as long as it reproduces the rough behavior of the emission profile. Outside of 7544. the emission is set to an isothermal temperature.," Outside of $r_{cool}$, the emission is set to an isothermal temperature." Inside that radius. we fit for the normalization of the differential emissionmeasure distribution below the upper temperature. 75.," Inside that radius, we fit for the normalization of the differential emissionmeasure distribution below the upper temperature, $T_0$ ." The emission measure is divided into several temperature bins between 175 and Tp. JT; and io. io and and isTo and T," The emission measure is divided into several temperature bins between $\case{1}{2} T_0$ and $T_0$, $\case{1}{4} T_0$ and $\case{1}{2} T_0$, $\case{1}{8} T_0$ and $\case{1}{4} T_0$, and $\case{1}{16} T_0$ and $\case{1}{8} T_0$." his choice is arbitrary. but it providesiT. robust fitting i.solutions since the fractional ionization curves are roughly equally spaced in the logarithm of the temperature.," This choice is arbitrary, but it provides robust fitting solutions since the fractional ionization curves are roughly equally spaced in the logarithm of the temperature." Preliminary fits indicate that only negligible hot ambient plasma coexists mside the cooling radius. so additional isothermal emission inside this radius ts ignored.," Preliminary fits indicate that only negligible hot ambient plasma coexists inside the cooling radius, so additional isothermal emission inside this radius is ignored." Within each temperature bin. we use the isobaric radiative cooling-flow model to predict the shape of the emission measure distribution. but this is not critically important since we do not have the spectral sensitivity to sample the emission measure distribution m very fine intervals.," Within each temperature bin, we use the isobaric radiative cooling-flow model to predict the shape of the emission measure distribution, but this is not critically important since we do not have the spectral sensitivity to sample the emission measure distribution in very fine intervals." This approach clearly forces the coolest emission to conform to a specified spatial distribution., This approach clearly forces the coolest emission to conform to a specified spatial distribution. Further detailed analyses are required to pinpoint its exact spatial location., Further detailed analyses are required to pinpoint its exact spatial location. Our spatial model. however. seems to be compatible qualitatively with the relatively small differences in the observed emission lines spatial profiles of M$7 (Sakelliouetal.2002)).," Our spatial model, however, seems to be compatible qualitatively with the relatively small differences in the observed emission lines spatial profiles of M87 \citealt{sakelliou}) )." We assume uniform spatial abundances throughout the cluster. emission., We assume uniform spatial abundances throughout the cluster emission. This considerably simplifies. the. fitting procedure. and makes the limits on the coolest emission conservative.," This considerably simplifies the fitting procedure, and makes the limits on the coolest emission conservative." It is known that abundance gradients exist in clusters. but they are generally flat within the cooling-flow region and weaken whenever more freedom is given to the temperature distribution (Molendi&Pizzolato2001).," It is known that abundance gradients exist in clusters, but they are generally flat within the cooling-flow region and weaken whenever more freedom is given to the temperature distribution \citep{molendi}." .. The iron. neon. oxygen. magnesium. and silicon abundances are left as free parameters.," The iron, neon, oxygen, magnesium, and silicon abundances are left as free parameters." All other elements are tied to tron since they contribute few counts., All other elements are tied to iron since they contribute few counts. In Abell 1835 and Abell 665. the magnesium. neon. and silicon abundances are tied to iron since the emission is from very high temperatures.," In Abell 1835 and Abell 665, the magnesium, neon, and silicon abundances are tied to iron since the emission is from very high temperatures." The absorption column density is left as a free parameter to account for variations along the line of sight to the cluster., The absorption column density is left as a free parameter to account for variations along the line of sight to the cluster. In NGC 533 the absorption is set to the galactic value since it has little low energy continuum emission., In NGC 533 the absorption is set to the galactic value since it has little low energy continuum emission. We also ignore the effects of resonant scattering (cf. Xuetal.2002)).," We also ignore the effects of resonant scattering (cf. \citealt{xu}) )," which redistribes emission line photons within our aperture. but otherwise results in the same detected emission line flux.," which redistribes emission line photons within our aperture, but otherwise results in the same detected emission line flux." For the background. we use a semi-empirical model calibrated on blank sky Lockman Hole observations (XMM Revolutions 0070/0073).," For the background, we use a semi-empirical model calibrated on blank sky Lockman Hole observations (XMM Revolutions 0070/0073)." The model includes a spatial model for soft protons. low energy detector readout noise. and characterizations of the in-flight Al K and F K calibration sources.," The model includes a spatial model for soft protons, low energy detector readout noise, and characterizations of the in-flight Al K and F K calibration sources." All parameters are frozen in this model except the relative normalization of the particle component. and the overall normalization which can vary by factors of 10 from observation to observation.," All parameters are frozen in this model except the relative normalization of the particle component, and the overall normalization which can vary by factors of 10 from observation to observation." The background is relatively flat in wavelength., The background is relatively flat in wavelength. The model has the following free parameters: local column density. normalization of each part of the cooling flow emission measure distribution. abundances of magnesium. neon. silicon. oxygen. and iron. background temperature (75). particle background normalization. position of the source in the cross-dispersion direction. core radius. cooling radius. and overall normalization.," The model has the following free parameters: local column density, normalization of each part of the cooling flow emission measure distribution, abundances of magnesium, neon, silicon, oxygen, and iron, background temperature $T_0$ ), particle background normalization, position of the source in the cross-dispersion direction, core radius, cooling radius, and overall normalization." For each spectrum. we apply selection cuts discussed in $44.," For each spectrum, we apply selection cuts discussed in 4." However. the background model parameters and position of the source are determined before applying any data selection cuts.," However, the background model parameters and position of the source are determined before applying any data selection cuts." In addition to the model described above. we also set limits on a model wherein an intrinsic absorber embedded in the cooling-flow volume ts invoked to suppress the expected soft emission.," In addition to the model described above, we also set limits on a model wherein an intrinsic absorber embedded in the cooling-flow volume is invoked to suppress the expected soft emission." If the absorber is evenly embedded. the transmission function is given by. (1—e7'£)/z(E). where 7(E) is the photoelectric optical depth as a function of energy. as opposed to the usual exponential form.," If the absorber is evenly embedded, the transmission function is given by, $\left( 1 - e^{-\tau(E)} \right) /\tau(E)$, where $\tau(E)$ is the photoelectric optical depth as a function of energy, as opposed to the usual exponential form." For this case. we otherwise take the isobaric cooling-flow emission measure distribution. without allowing any variation from one temperature bin to the next.," For this case, we otherwise take the isobaric cooling-flow emission measure distribution, without allowing any variation from one temperature bin to the next." The errors are quoted at the 90% statistical confidence level for setting limits on the parameters., The errors are quoted at the $\%$ statistical confidence level for setting limits on the parameters. The uncertainty in the wavelength scale of 8 mA and the characteristic line spread function uncertainty of 5 mA make negligible contributions to these errors for extended sources like clusters., The uncertainty in the wavelength scale of 8 ${\mbox{m\AA}}$ and the characteristic line spread function uncertainty of 5 ${\mbox{m\AA}}$ make negligible contributions to these errors for extended sources like clusters. The effective area uncertainty is of order 10%., The effective area uncertainty is of order $\%$ . Additionally. there is known to benon-statistical noise at the 5% level of the source flux in the RGS spectra. caused by systematic dark current variations which can sometimes produce false," Additionally, there is known to benon-statistical noise at the $\%$ level of the source flux in the RGS spectra, caused by systematic dark current variations which can sometimes produce false" distribution of z>0.5 quasars in AGES ,distribution of $z>0.5$ quasars in AGES ). "These quasars are primarily mid-IR and X-ray 2011)).selected, like much of the present sample, but with a much deeper optical spectroscopic limit."," These quasars are primarily mid-IR and X-ray selected, like much of the present sample, but with a much deeper optical spectroscopic limit." " We have adjusted the AGES magnitudes for the AE(B—V)~0.14 mag extinction difference between AGES and a typical LMC site line although this may underestimate the (Udalskicorrection 1999)),necessary for a true background population."," We have adjusted the AGES magnitudes for the $\Delta E(B-V)\simeq 0.14$ mag extinction difference between AGES and a typical LMC site line ), although this may underestimate the correction necessary for a true background population." The completeness of our present sample relative to AGES is roughly (30%)) at 18.6 mag (19.3 mag)., The completeness of our present sample relative to AGES is roughly ) at 18.6 mag (19.3 mag). Figure 8 also shows the cumulative distribution of the SDSS quasars with 0.3«z2.2 from(2006)., Figure \ref{fig:cumul} also shows the cumulative distribution of the SDSS quasars with $0.3 < z < 2.2$ from. ". Given the change in bandpass (i—I)~0.5 mag color term varies significantly (thewith redshift, see Figure 9)) and the additional line width and luminosity selection criteria in it is harder to make a direct comparison, but (2006)after matching as best possible, we obtain similar completeness estimates."," Given the change in bandpass (the $(i-I) \simeq 0.5$ mag color term varies significantly with redshift, see Figure \ref{fig:AGNcolor}) ) and the additional line width and luminosity selection criteria in it is harder to make a direct comparison, but after matching as best possible, we obtain similar completeness estimates." " As expected from filling the fibers with targets, most targets are peculiar stars of various types, particularly at the brighter magnitudes."," As expected from filling the fibers with targets, most targets are peculiar stars of various types, particularly at the brighter magnitudes." " Unclassifiable spectra dominate at the fainter magnitudes, and with the weather-limited integration times, there was an effective magnitude limit of roughly 19.5-20 mag."," Unclassifiable spectra dominate at the fainter magnitudes, and with the weather-limited integration times, there was an effective magnitude limit of roughly $19.5$ $20$ mag." are difficulties with formation of the planet Fom b because the time-scales for core accretion are so long: recall that the self-stirring time-scale gives the time required to form Plito--sized objeetssitu.. while the mass of Fom b may be as high as that of Jupiter.,"are difficulties with formation of the planet Fom b because the time-scales for core accretion are so long: recall that the self-stirring time-scale gives the time required to form -sized objects, while the mass of Fom b may be as high as that of Jupiter." " The time to form a Pluto-sized body at Fomalhaut b's orbit is aroundMMyr for ry,=1.", The time to form a Pluto-sized body at Fomalhaut b's orbit is aroundMyr for $x_{\mathrm{m}}=1$. The planet most likely formed closer to the star and later moved to its current location. for example by outwards migration (e.g..2) or being scattered by another planet (e.g.. 2»).," The planet most likely formed closer to the star and later moved to its current location, for example by outwards migration \citep[e.g.,][]{2007MNRAS.378.1589M} or being scattered by another planet (e.g., \citealt*{2009arXiv0902.2779V}) )." Both of these processes would however likely disturb the dise as well., Both of these processes would however likely disturb the disc as well. Secondly. we note that. although c;z0.1. the material in the Fomalhaut dise appears to have very low proper eccentricities (22). as evidenced by the sharp inner edge to the disc.," Secondly, we note that, although $e_{\mathrm{f}}\approx 0.1$, the material in the Fomalhaut disc appears to have very low proper eccentricities \citep{2006MNRAS.372L..14Q,2009ApJ...693..734C}, as evidenced by the sharp inner edge to the disc." If the proper eccentricity of Fomalhaut's dise is only 10 per cent of the forced eccentricity then this increases the time-scale for orbit crossing to MMyr (see Equation 1-2). still much less than the system's age.," If the proper eccentricity of Fomalhaut's disc is only 10 per cent of the forced eccentricity then this increases the time-scale for orbit crossing to Myr (see Equation \ref{eq:tcross}) ), still much less than the system's age." Reducing proper eccentricities also reduces the relative velocities amongst planetesimals in direct proportion. although given the large value of e this will not prevent Fom b from causing erosive collisions.," Reducing proper eccentricities also reduces the relative velocities amongst planetesimals in direct proportion, although given the large value of $a^*$ this will not prevent Fom b from causing erosive collisions." For the Solar System's Neptune we find αἲ= 130AAU. making the Kuiper Belt able to be stirred by Neptune.," For the Solar System's Neptune we find $a^*=730$ AU, making the Kuiper Belt able to be stirred by Neptune." However. when we compare with self-stirring we find that planet-stirring acts more quickly only out to «b.=33 AAU. so Neptune's secular perturbations would not have stirred the belt before Pluto formed. assuming that the planets formed at their current semi-major.," However, when we compare with self-stirring we find that planet-stirring acts more quickly only out to $\Phi = 33$ AU, so Neptune's secular perturbations would not have stirred the belt before Pluto formed, assuming that the planets formed at their current semi-major." . So this simple model is consistent with the outer Solar System. although we note that the dynamical evolution of the early Kuiper Belt and outer planets may have been more complicated than formation of Neptune followed by growth of Kuiper Belt Objects (?)..," So this simple model is consistent with the outer Solar System, although we note that the dynamical evolution of the early Kuiper Belt and outer planets may have been more complicated than formation of Neptune followed by growth of Kuiper Belt Objects \citep{2005Natur.435..459T}." We also note that highly excited eccentricities and inclinations of KBOs may have been required to explain the details of the capture of Neptune's Trojans (2).. and capture of KBOs into high order mean motion resonances (e.g.. 2)).," We also note that highly excited eccentricities and inclinations of KBOs may have been required to explain the details of the capture of Neptune's Trojans \citep{2009AJ....137.5003N}, and capture of KBOs into high order mean motion resonances (e.g., \citealt{2003AJ....126..430C}) )." Such high inclinations might be achievable through self-stirring but not planet-stirring., Such high inclinations might be achievable through self-stirring but not planet-stirring. When dealing with multiple planets previously we treated the disc as being stirred by the planet with the lowest {ώμος assuming that the other planets had no effect on the dise.," When dealing with multiple planets previously we treated the disc as being stirred by the planet with the lowest $t_{\mathrm{cross}}$, assuming that the other planets had no effect on the disc." Such an approach is unrealistic because it neglects not only the effects of other planets on the disc. but also the mutual interactions of the planets amongst themselves.," Such an approach is unrealistic because it neglects not only the effects of other planets on the disc, but also the mutual interactions of the planets amongst themselves." We plot the precession rate 1 for planetesimals orbiting in the Sun-Jupiter-Saturn system in Figure (123)., We plot the precession rate $A$ for planetesimals orbiting in the Sun-Jupiter-Saturn system in Figure \ref{fig:A-jupsat}) ). This also shows the location of secular resonances. where the planetesimal's precession rate equals one of the system's eigenfrequencies and the forced eccentricity is formally infinite.," This also shows the location of secular resonances, where the planetesimal's precession rate equals one of the system's eigenfrequencies and the forced eccentricity is formally infinite." Figure (123) also shows the effect of reducing Saturn's mass to that of Earth: the precession rate approaches that in the planet case of Jupiter alone. and the width of the region strongly affected by the outer planets perturbations decreases.," Figure \ref{fig:A-jupsat}) ) also shows the effect of reducing Saturn's mass to that of Earth: the precession rate approaches that in the single-planet case of Jupiter alone, and the width of the region strongly affected by the outer planet's perturbations decreases." So as far as the precession rate is concerned. the behaviour is similar to the single-planet case.," So as far as the precession rate is concerned, the behaviour is similar to the single-planet case." Performing a similar analysis to that in refs:timescale.. we find that. for planetesimals on initially circular orbits. the time-scale for orbit crossing in the multi-planet case is given by," Performing a similar analysis to that in \\ref{s:timescale}, , we find that, for planetesimals on initially circular orbits, the time-scale for orbit crossing in the multi-planet case is given by" sodium fills the volume between the cylinders and the end walls.,sodium fills the volume between the cylinders and the end walls. " Solid plates attached to and co-rotating with the outer cylinder with an angular velocity, Q5 define the end walls. ("," Solid plates attached to and co-rotating with the outer cylinder with an angular velocity, $\Omega_2$ define the end walls. (" "In addition, for the dynamo experiment, an external source of helicity is supplied, driven plumes, but this is not part of the MRI experiment.)","In addition, for the dynamo experiment, an external source of helicity is supplied, driven plumes, but this is not part of the MRI experiment.)" " The schematic of the flow field, (Fig. 1)),"," The schematic of the flow field, (Fig. \ref{fig1}) )," " places particular emphasis on the primary diagnostic of multiple, 3-axis, magnetic field Hall effect detectors (sensitivity: 0.1 to 10kG) located in aerodynamically shaped probes within the rotating conducting fluid."," places particular emphasis on the primary diagnostic of multiple, 3-axis, magnetic field Hall effect detectors (sensitivity: $0.1$ to $10\,\mbox{kG}$ ) located in aerodynamically shaped probes within the rotating conducting fluid." " We expect that the radial perturbations from the MRI and their azimuthally sheared result will produce a fluctuating B, and Bg field from an original imposed static B, field through MRI growth.", We expect that the radial perturbations from the MRI and their azimuthally sheared result will produce a fluctuating $B_r$ and $B_{\theta}$ field from an original imposed static $B_z$ field through MRI growth. " These fluctuating fields are the result of the linear and non-linear growth of the various MRI modes transformed by the difference of the sheared Couette flow at a given radius and the probe angular velocity, £25, of the outer cylinder."," These fluctuating fields are the result of the linear and non-linear growth of the various MRI modes transformed by the difference of the sheared Couette flow at a given radius and the probe angular velocity, $\Omega_2$, of the outer cylinder." " A significant difficulty will be the observation of the linear growth of any particular MRI mode because the time constant for establishing the initial axial field within the conducting liquid sodiumwill be long, ~30/Q2, compared to the expected growth rate, ~Qe, of the instabilities as derived in this paper."," A significant difficulty will be the observation of the linear growth of any particular MRI mode because the time constant for establishing the initial axial field within the conducting liquid sodiumwill be long, $\sim 30/\Omega_2$, compared to the expected growth rate, $\sim \Omega_2$, of the instabilities as derived in this paper." " We therefore expect to observe primarily the near steady state of the non-linear limit of various modes, but the sequential linear phases may be observed during the comparatively slow rise of the field."," We therefore expect to observe primarily the near steady state of the non-linear limit of various modes, but the sequential linear phases may be observed during the comparatively slow rise of the field." " If the applied field or flux is amplified by the MRI such as a dynamo, then we expect to see fluctuating fields significantly greater than the applied field."," If the applied field or flux is amplified by the MRI such as a dynamo, then we expect to see fluctuating fields significantly greater than the applied field." " In addition since the inner and outer cylinders are driven separately, the relative torque as a function of the applied magnetic field becomes an integral diagnostic of the non-linear limits of the instability growth."," In addition since the inner and outer cylinders are driven separately, the relative torque as a function of the applied magnetic field becomes an integral diagnostic of the non-linear limits of the instability growth." By driving the inner cylinder and applying a variable brake with a corresponding torque measurement to the outer cylinder one can explore the full range of Couette velocity profiles including the marginal Couette flow hydrodynamic stability condition discussed next., By driving the inner cylinder and applying a variable brake with a corresponding torque measurement to the outer cylinder one can explore the full range of Couette velocity profiles including the marginal Couette flow hydrodynamic stability condition discussed next. This condition of maximum or marginal stable Couette profile can be established in the experiment precisely by gear ratios and so the degree of turbulence measured by the torque can be explored at the stability boundary., This condition of maximum or marginal stable Couette profile can be established in the experiment precisely by gear ratios and so the degree of turbulence measured by the torque can be explored at the stability boundary. In addition the pressure will be measured at five radii and compared to the pressure distributions expected of the various Couette profiles., In addition the pressure will be measured at five radii and compared to the pressure distributions expected of the various Couette profiles. A finite torque measurement can be interpreted in terms of turbulence existing between the two cylinders., A finite torque measurement can be interpreted in terms of turbulence existing between the two cylinders. " No turbulence or perfectly laminar flow will exert a torque of the order 1/R., R. the fluid Reynolds number where Re~107, compared to a turbulent torque, 1/Re'/?, if the Ekman layer circulation leads to the weak turbulence that we discuss later."," No turbulence or perfectly laminar flow will exert a torque of the order $1/R_e$, $R_e$ the fluid Reynolds number where $Re \simeq 10^7$, compared to a turbulent torque, $\sim 1/Re^{1/2}$, if the Ekman layer circulation leads to the weak turbulence that we discuss later." " This same possible weak turbulence can also be measured by introducing a very weak field, Bmin1G, small enough so as not to cause the growth of MRI in resistive liquid but large enough so that an unstable flow or weakly turbulent flow can be measured as fluctuations in B, and Bg with the Hall effect probes."," This same possible weak turbulence can also be measured by introducing a very weak field, $B_{min} \simeq 1\,\mbox{G}$, small enough so as not to cause the growth of MRI in resistive liquid but large enough so that an unstable flow or weakly turbulent flow can be measured as fluctuations in $B_r$ and $B_{\theta}$ with the Hall effect probes." Therefore the fluid flow conditions can be fully explored before the application of magnetic fields designed to create the MRI., Therefore the fluid flow conditions can be fully explored before the application of magnetic fields designed to create the MRI. " When the MRI does take place, then the instability can be recognized as a departure from the previously measured initial fluid state."," When the MRI does take place, then the instability can be recognized as a departure from the previously measured initial fluid state." It is critical to have large shear rates in order to observe the maximum growth rates of the MRI., It is critical to have large shear rates in order to observe the maximum growth rates of the MRI. " However, excessive shear will hydrodynamically destabilize the flow by the Kelvin-Helmholtz instability."," However, excessive shear will hydrodynamically destabilize the flow by the Kelvin-Helmholtz instability." Let us consider a Couette flow profile in cylindrical coordinates., Let us consider a Couette flow profile in cylindrical coordinates. " Take r,0,z as the radial, azimuthal and axial directions respectively."," Take $r, \theta, z$ as the radial, azimuthal and axial directions respectively." " The radial distribution of angular velocity of the flow, Q(r), is given by (Landau&Lifshitz1959) where Γή(10) and Ω](Ως) are the inner(outer) radii and angular velocities."," The radial distribution of angular velocity of the flow, $\Omega ( r )$ , is given by \citep{lan59} where $R_1(R_2)$ and $\Omega_1( \Omega_2)$ are the inner(outer) radii and angular velocities." system).,system). They also noted that a wide variety of planetary paratjeters can produce the twin-lobed structure seen in Vega., They also noted that a wide variety of planetary parameters can produce the twin-lobed structure seen in Vega. " Whilst our code was able to reproduce the results of Wilreretal.(2002).. their syuthetic observatious (al ilje. resolution of the Hollaudetal.(1998) Vega obse""valions show nearly svlninetrical emissio. whereas the Hollaudetal.(1998) Observatllous show a significa1| asyininetry. ("," Whilst our code was able to reproduce the results of \citet{whk02}, their synthetic observations (at the resolution of the \citet{holland98} Vega observations) show nearly symmetrical emission, whereas the \citet{holland98} observations show a significant asymmetry. (" It should be noted. however. that here are uucertaluties in the Hollandeta.(1995 observations.,"It should be noted, however, that there are uncertainties in the \citet{holland98} observations." In the moclel we are about to present. we are assuming that he observed. asyiuijetry is real.)," In the model we are about to present, we are assuming that the observed asymmetry is real.)" Based on results [rom our syuthetic catalogue. we have modelled Vega. usiu: an eutirely different plauetary configuration in au atteupt to better match these observations.," Based on results from our synthetic catalogue, we have modelled Vega using an entirely different planetary configuration in an attempt to better match these observations." αι Our jodel. a more distant. (app=73.7 AU). less eccentric (ej= 0.1) 3 Jupier inass plauet rep'oduces the observed disk structure. with no constraints on the iniial test. particle perilielia (since we a'e modelliug a lower eccenricity planet).," In our model, a more distant $a_{pl} = 73.7$ AU), less eccentric $e_{pl} = 0.1$ ) 3 Jupiter mass planet reproduces the observed disk structure, with no constraints on the initial test particle perihelia (since we are modelling a lower eccentricity planet)." " We use 5000 test pa‘icles released from parent bocdies With initial orbital elements in the range 90$ 10 kpc, so the correction from relative to absolute parallaxes must be small." Because the parallax is small — a fraction of a pixel in size — we need to (take great care with the reductions., Because the parallax is small – a fraction of a pixel in size – we need to take great care with the reductions. Therefore. we decided that each of the investigators would analvze the data independently. using different fitting techniques.," Therefore, we decided that each of the investigators would analyze the data independently, using different fitting techniques." We started [rom a common set of processed images., We started from a common set of processed images. The initial data processing consists of cleaning the images of cosmic rays. and correcting the pixel positions for distortions in (he detector.," The initial data processing consists of cleaning the images of cosmic rays, and correcting the pixel positions for distortions in the detector." Cosmic rays are a problem with all CCD detectors., Cosmic rays are a problem with all CCD detectors. " While largely cosmetic. occasionally a cosmic rav does hit within the point spread Ποιος of a source. and will affect both the astrometrv and the photometry,"," While largely cosmetic, occasionally a cosmic ray does hit within the point spread function of a source, and will affect both the astrometry and the photometry." We begin with the flat-fiekled ΠΠ images., We begin with the flat-fielded flt.fits images. We reject all pixels with a data quality Πας set to 2048 or greater (those identified as saturated pixels and cosmic ravs) by setting the data value equal to the median of the surrounding 8 pixels., We reject all pixels with a data quality flag set to 2048 or greater (those identified as saturated pixels and cosmic rays) by setting the data value equal to the median of the surrounding 8 pixels. About of the pixels in each image are so-alfected., About of the pixels in each image are so-affected. This is mostly done to simplify the data reduction code. where large data values can craw olf a mean or median.," This is mostly done to simplify the data reduction code, where large data values can draw off a mean or median." But in the end (his is of little consequence., But in the end this is of little consequence. We save (his cosmeticallv-corrected image as a fits file., We save this cosmetically-corrected image as a fits file. The ACS is aracial bay instrument on the LIST. hence there is significant and asvimimetric distortion in the images (Anderson&Ning2004).," The ACS is a radial bay instrument on the HST, hence there is significant and asymmetric distortion in the images \citep{AK04}." . We use Anderson's #ng2rym_Fortran code to find the stars in the cosmetically-corrected images and to correct for the instrumental distortion., We use Anderson's Fortran code to find the stars in the cosmetically-corrected images and to correct for the instrumental distortion. This code determines positions bv doing a P5E-fit using the liller-specilic point spread function., This code determines positions by doing a PSF-fit using the filter-specific point spread function. According to Anderson&Wing(2004).. the distortion correction corrects to better Chan 0.01 pixel in each coordinate lor sufficiently. bright stars.," According to \citet{AK04}, the distortion correction corrects to better than 0.01 pixel in each coordinate for sufficiently bright stars." The output of this code is a list of raw and corrected X and Y positions in the instrumental frame. along with an instrumental magnitude.," The output of this code is a list of raw and corrected X and Y positions in the instrumental frame, along with an instrumental magnitude." The code does not return any estimate of the uncertainty in the »osition., The code does not return any estimate of the uncertainty in the position. We adopt the mean pixel scale of 0.02827 arcsecf/pin., We adopt the mean pixel scale of 0.02827 arcsec/pix. Using the thresholds we selected (IIMUIN=5. FAHN=150). we iclentily 21 stars in the field that are common to at least five of the visits. in additional to the neutron star.," Using the thresholds we selected (HMIN=5, FMIN=150), we identify 21 stars in the field that are common to at least five of the visits, in additional to the neutron star." Thirteen of these stars are recovered in all visits. and five are seen in seven of the visits.," Thirteen of these stars are recovered in all visits, and five are seen in seven of the visits." The others lie, The others lie "The maximum change in Y, is therefore = A similar limit pertains at lower densities.",The maximum change in $Y_e$ is therefore = A similar limit pertains at lower densities. One way to exceed this limit in the high density case is if additional reaction chains occur (see 32.2)., One way to exceed this limit in the high density case is if additional reaction chains occur (see 2.2). " We show AY,4, as a dashed line in Figure 4. in comparison to the AY,’s that result from X(C7Ne)20.007 and 0.02 lines)."," We show $\Delta Y_{e,\rm max}$ as a dot-dashed line in Figure 4, in comparison to the $\Delta Y_e$ 's that result from $X(^{22}$ $)=0.007$ and $0.02$ )." " By coincidence. the maximum effect of neutronization during simmering is comparable to that associated with a solar metallicity,"," By coincidence, the maximum effect of neutronization during simmering is comparable to that associated with a solar metallicity." The other possible limiter of neutronization is the onset of the explosion., The other possible limiter of neutronization is the onset of the explosion. " The reactions in Table 1 show that Q~16 MeV is released as thermal energy when six carbon nuclei are If we let E, be the total thermal content that is within the convective core with respect to the initial isothermal WD. this implies a change AY,=—jE,/QM. in a convective core of mass M... AY, = δις For this to compete with the --Ne contribution. a total energy E. = or 71015ergsg! must be released prior to the explosion."," The reactions in Table 1 show that $Q\approx 16$ MeV is released as thermal energy when six carbon nuclei are If we let $E_c$ be the total thermal content that is within the convective core with respect to the initial isothermal WD, this implies a change $\Delta Y_e=-\eta E_cm_p/QM_c$ in a convective core of mass $M_{c}$, Y_e = -6.5 For this to compete with the $^{22}$ Ne contribution, a total energy E_c = or $7\times10^{15}\ {\rm ergs \ g^{-1}}$, must be released prior to the explosion." Simmering ends when dynamical burning is triggered. requiring 7.~8«105K (Woosleyetal.2004).," Simmering ends when dynamical burning is triggered, requiring $T_c\approx8\times 10^8\ {\rm K}$ \citep{woo04}." . If the burning occurred within a single zone with the specific heat of 32. then reaching this 7. would require z1.31010ergsel. in excess of that implied by equation (10)).," If the burning occurred within a single zone with the specific heat of 2, then reaching this $T_c$ would require $\approx1.3\times10^{16}\ {\rm ergs \ g^{-1}}$, in excess of that implied by equation \ref{eq:ec}) )." Of course. in reality the convective zone extends outward. so that little mass is at 7..," Of course, in reality the convective zone extends outward, so that little mass is at $T_c$." To accurately determine the resulting neutronization. we construct hydrostatic WD models consisting of fully convective cores as described at the beginning of $2..," To accurately determine the resulting neutronization, we construct hydrostatic WD models consisting of fully convective cores as described at the beginning of \ref{sec:rates}." We consider isothermal temperatures of either 10°K or 2«105K., We consider isothermal temperatures of either $10^8\ {\rm K}$ or $2\times 10^8\ {\rm K}$. At any given moment there is a well defined M. (Lesaffreetal.2006:Piro 2007).. and we evaluate the current thermal content by integrating the specific heat relative to the initially isothermal WD. where 7; is the isothermal WD temperature.," At any given moment there is a well defined $M_c$ \citep{les06,pir07}, and we evaluate the current thermal content by integrating the specific heat relative to the initially isothermal WD, where $T_i$ is the isothermal WD temperature." " In this way we use our time independent models to find the fraction of carbon that must have burned. f. and the associated AY, as T, and M. increase with time."," In this way we use our time independent models to find the fraction of carbon that must have burned, $f$, and the associated $\Delta Y_e$ as $T_c$ and $M_c$ increase with time." We assume no neutrino losses and thus all ee16MeV of thermal energy contributes to heating., We assume no neutrino losses and thus all $\approx16\ {\rm MeV}$ of thermal energy contributes to heating. In Figure 4. we summarize the results of these calculations., In Figure \ref{fig:ye} we summarize the results of these calculations. " —1 each case. the slope of AY, shows a break at the transition from 42 (fg>fo o3) to. =1."," In each case, the slope of $\Delta Y_e$ shows a break at the transition from $\eta=2$ $t_h>t_{\rm ec,23}$ ) to $\eta=1$." This break occurs later for more massive WDs (Fig. 1) ," This break occurs later for more massive WDs (Fig. \ref{fig:simmering}) )," thus these have more neutronization during simmering., thus these have more neutronization during simmering. " Increasing the isothermal temperature decreases M,. so that it takes less burning to reach a given 7..."," Increasing the isothermal temperature decreases $M_c$, so that it takes less burning to reach a given $T_c$." These fully integrated models make it clear that substantial neutronization occurs prior to the explosion., These fully integrated models make it clear that substantial neutronization occurs prior to the explosion. " In comparison to the AY, from Ne. simmering effects dominate if X Ne)«0.013 orZ/Z ..X2/3."," In comparison to the $\Delta Y_e$ from $^{22}$ Ne, simmering effects dominate if $X(^{22}$ $)<0.013$ or $Z/Z_\odot\lesssim2/3$." " This thwarts the occurrence of high Y, SNe la in low metallicity progenitors.", This thwarts the occurrence of high $Y_e$ SNe Ia in low metallicity progenitors. We have found that significant neutronization of the WD core occurs throughout the simmering stage of carbon burning until the onset of the explosion., We have found that significant neutronization of the WD core occurs throughout the simmering stage of carbon burning until the onset of the explosion. If substantial energy is lost to the convective Urea process (Lesaffreetal.2005.andrefer-ences therein). then the neutronization is truncated by proton captures onto freshly synthesized heavy elements (resulting in eq. [6].," If substantial energy is lost to the convective Urca process \citep[][and references therein]{les05}, then the neutronization is truncated by proton captures onto freshly synthesized heavy elements (resulting in eq. \ref{eq:yemax}] ])." " The main consequence is a uniform ""floor"" to the amount of neutronization that dominates over the metallicity dependent contribution for all progenitors with Z/Z..=2/3.", The main consequence is a uniform “floor” to the amount of neutronization that dominates over the metallicity dependent contribution for all progenitors with $Z/Z_\odot\lesssim2/3$. Given the likely significance this has for SNe Ia. more work needs to be done.," Given the likely significance this has for SNe Ia, more work needs to be done." In particular. at high ignition densities. heavy element electron captures and a full reaction network are needed to follow the resulting diverse collection of elements (see the discussion in $2.2).," In particular, at high ignition densities, heavy element electron captures and a full reaction network are needed to follow the resulting diverse collection of elements (see the discussion in 2.2)." The convective Urea process is another complication we have not addressed., The convective Urca process is another complication we have not addressed. In principle. if more energy is lost to neutrinos then more burning (and thus more neutronization) is required to make the burning dynamical.," In principle, if more energy is lost to neutrinos then more burning (and thus more neutronization) is required to make the burning dynamical." Assessing this will necessitate coupling a full nuclear network (Chamulaketal.2007b) to convective calculations.," Assessing this will necessitate coupling a full nuclear network \citep{cha07b} to convective calculations." Such models would accurately determine jj rather than simply setting it to | or 2., Such models would accurately determine $\eta$ rather than simply setting it to 1 or 2. In closing. we highlight some important features exhibited by recent observations of SNe Ia. It is clear that the amount of ?*Ni produced in SNe la has a dynamic range (0.1-1M.) larger than can be explained by metallicity or simmering neutronization.," In closing, we highlight some important features exhibited by recent observations of SNe Ia. It is clear that the amount of $^{56}$ Ni produced in SNe Ia has a dynamic range $0.1-1M_\odot$ ) larger than can be explained by metallicity or simmering neutronization." However. since an intriguing trend is the," However, since an intriguing trend is the" Figure Rellectivily spectrum of comet 9P/Tempel 1 after the impact. near the time of maximum brightness in à 2.4 aperture.,"Figure Reflectivity spectrum of comet 9P/Tempel 1 after the impact, near the time of maximum brightness in a $\arcsec$ aperture." The spectrum is the ratio of the comet spectrum and (hat of solar analog star DO41C and is displaved here in arbitrary linear [Iux units., The spectrum is the ratio of the comet spectrum and that of solar analog star P041C and is displayed here in arbitrary linear flux units. The blue ancl red channel of the instrument were individually photometrically calibrated. and the data match very well without further adjustment., The blue and red channel of the instrument were individually photometrically calibrated and the data match very well without further adjustment. The emission lines of CN and ΟΕ are Clearly visible. and the C band is faintly indicated.," The emission lines of CN and [OI] are clearly visible, and the $_3$ band is faintly indicated." The feature at 763 nm is an artifact from thestrong telluric Os absorption., The feature at 763 nm is an artifact from thestrong telluric $_2$ absorption. Filled circles represent the data that are considered reliable., Filled circles represent the data that are considered reliable. We also show the data at the ends of the spectral ranges of the blue spectrograph arm (small open circles) and of the red spectrograph arm (small plus signs) to illustrate that at the ends of each spectrum. the calibration was not reliable and why these data have not been included in the analvsis.," We also show the data at the ends of the spectral ranges of the blue spectrograph arm (small open circles) and of the red spectrograph arm (small plus signs) to illustrate that at the ends of each spectrum, the calibration was not reliable and why these data have not been included in the analysis." The boundary between where the blue vs. red data were used is at 520 nm and this boundary is indicated in the Figure., The boundary between where the blue vs. red data were used is at 520 nm and this boundary is indicated in the Figure. This boundary does not coincide with the change in slope of the spectrum., This boundary does not coincide with the change in slope of the spectrum. Below 580 nm. (he normalized slope between 350 nm and 580 nm is22.65... between 580 nm and 940 nm. the normalized slope," Below 580 nm, the normalized slope between 350 nm and 580 nm is, between 580 nm and 940 nm, the normalized slope is ." surrounding clusters.,surrounding clusters. It is superimposed. on a probable bow-shock -—33' to the southwest of 1127. and Wltll53ab., It is superimposed on a probable bow-shock $\sim$ $'$ to the southwest of 127 and 153ab. Llowever. this bow-shock seems to have been generated in 22.," However, this bow-shock seems to have been generated in 2." We may be witnessing sequential elfects of star formation., We may be witnessing sequential effects of star formation. The presence of the trapezium system in the center of 1127 will certainlv have an important9900. role in the cluster evolution., The presence of the trapezium system 900 in the center of 127 will certainly have an important role in the cluster evolution. Trapezium systems evolve into hierarchical svstems (with a much larger separation among its components) or even disperse in a few million. vears producing runaway stars., Trapezium systems evolve into hierarchical systems (with a much larger separation among its components) or even disperse in a few million years producing runaway stars. The oldest one identified so far has ~ 550Myr (Abt&Corbally 20003)., The oldest one identified so far has $\sim$ Myr \citealt{abtcor00}) ). 1127. is close to WlIC1I53ab that djs a spectroscopic binary with a primary WNG6o and an OGL (Smith.Shara&Alotlat 1996))., 127 is close to 153ab that is a spectroscopic binary with a primary WN6o and an O6I \citealt*{ssm96}) ). Evolution of this WR. to spectral type WC and its subsequent explosion as supernova will certainly have an impact on the dynamical evolution of neighbouring clusters 1127. SBDB11 and 22). by means of gas removal.," Evolution of this WR to spectral type WC and its subsequent explosion as supernova will certainly have an impact on the dynamical evolution of neighbouring clusters 127, 1 and 2), by means of gas removal." SBBIL is the vounges cluster in the sample and remains embedded., 1 is the youngest cluster in the sample and remains embedded. Ehe residual gas expulsion aud. stellar evolution may cause an increase of core radius., The residual gas expulsion and stellar evolution may cause an increase of core radius. Since 22 expulsed its residual gas. star formation must have stopped and its survival as à bound OC depends on the dvnamies and evolution of neighbouring clusters and specially of the WIUIIS3ab star.," Since 2 expulsed its residual gas, star formation must have stopped and its survival as a bound OC depends on the dynamics and evolution of neighbouring clusters and specially of the 153ab star." SBB33 hosts the 1152 star of type WN3(h)-w. a mass of MM. and mass loss rate log MM. ==--5.5 (Hamann.Grafener&Liermann 2006)).," 3 hosts the 152 star of type WN3(h)-w, a mass of $_{\odot}$ and mass loss rate $\log \dot{M}$ $_{\odot}$ -5.5 \citealt*{hgl06}) )." Since 1152 has a relatively low mass for a WR. star (the minimum initial mass for a star to become a WR. at Solar-metallicity is MM.) it can explode as supernova without evolving through the WC type. expulsing σας and dissolving the star cluster very carly.," Since 152 has a relatively low mass for a WR star (the minimum initial mass for a star to become a WR at Solar-metallicity is $_{\odot}$ ) it can explode as supernova without evolving through the WC type, expulsing gas and dissolving the star cluster very early." Two possible destinations are sugeested for the central clusters of 5h2-132:, Two possible destinations are suggested for the central clusters of Sh2-132: 7? azz120 (72)...," \citet{kalas08} $a \approx 120$ $a = \{24,38,68\}$ \citep{marois08}." >>1.5 =3 20120 uieht at fixst seem unlikely. given that A stars uake up less than the stellar population iu he Solar neighborhood aud because the stir-plauet contrast ratios are unfavorable compared to svsteiis witli autor. less massive central stars.," $> 1.5$ $\lesssim 3$ $20-120$ might at first seem unlikely, given that A stars make up less than of the stellar population in the Solar neighborhood and because the star-planet contrast ratios are unfavorable compared to systems with fainter, less massive central stars." However. in light of recent discoveries οι Doppler-based planet searches of nassive stars it is becomine appareut that A cavarfs be ideal target stars for direct imacing survers (7777777)..," However, in light of recent discoveries from Doppler-based planet searches of massive stars it is becoming apparent that A dwarfs may in fact be ideal target stars for direct imaging surveys \citep{hatzes03, setiawan05, reffert06, sato07, nied07, liu08, dollinger09}." " Measurements of the frequency of eiut plancts around the vretired” counterparts of A-ype cawarts (subgiauts aud giauts) have found that the occurence of Jovian plancts scales with stellar mass: A-ype stars CM,z1.5 MJ) are at least 5 times ore ikely than Mo dwarfs to harbor a giant planet (22?).."," Measurements of the frequency of giant planets around the “retired” counterparts of A-type dwarfs (subgiants and giants) have found that the occurrence of Jovian planets scales with stellar mass: A-type stars $M_\star \gtrsim 1.5$ ) are at least 5 times more likely than M dwarfs to harbor a giant planet \citep{johnson07b,bowler10,johnson10a}." Aud just like the current sample of imaged planets. Doppler-detected plauets around retired A stars are ore massive (7) ancl orbit farther from their stars than do planets ound around Sun-like. F. € and Is (FCI) dwarfs (?7?)..," And just like the current sample of imaged planets, Doppler-detected planets around retired A stars are more massive \citep[][]{lovis07} and orbit farther from their stars than do planets found around Sun-like, F, G and K (FGK) dwarfs \citep{johnson07, sato08b}." Tudeed. there is stroug evidence that the orbita characteristics of planets around A stars are drawn from a statistical parcut population that is distinct from those of planets around FOS dwarts.," Indeed, there is strong evidence that the orbital characteristics of planets around A stars are drawn from a statistical parent population that is distinct from those of planets around FGK dwarfs." " ? performicc a statistical analysis of planets detected im the Lick Subeiauts Survey, which comprises 31 massive stars (QU.z1.5 Αι} monitored for the past 5 vem"," \citet{bowler10} performed a statistical analysis of planets detected in the Lick Subgiants Survey, which comprises 31 massive stars $M_\star \gtrsim 1.5$ ) monitored for the past 5 years." The imass-period distribution of exoplauets arouik FCS chwarts ids typically described by a double-power-law relationship. with the frequeney of planets rising toward lower masses and remaining flat i losarithiuic seiiniajor-axis bins from ~0.05 AU to ~5 AU (????)..," The mass-period distribution of exoplanets around FGK dwarfs is typically described by a double-power-law relationship, with the frequency of planets rising toward lower masses and remaining flat in logarithmic semimajor-axis bins from $\sim 0.05$ AU to $\sim5$ AU \citep{tab02,lineweaver03, cumming08, johnson09rev}." Based ou the 7 planet detections from the Lick survey. Bowler et al.," Based on the 7 planet detections from the Lick survey, Bowler et al." concluded that the power-law indices of the distribution of planets around A stars and Sun-like stis differ at the Lo level: the planets in their sample all have >1.5 , concluded that the power-law indices of the distribution of planets around A stars and Sun-like stars differ at the $\sigma$ level; the planets in their sample all have $ > 1.5$ o (Shakura Suuvaev 1973). this timescale can be written approximately as.1.(2-1) where {1 is the local diskκοΠοιους aud O the local aneular velocity.,"$\alpha$ (Shakura Sunyaev 1973), this timescale can be written approximately as, where $H$ is the local disksemi-thickness and $\Omega$ the local angular velocity." It was originally assumed (Barcdecn Petterson 1975: Rees 1978) that the component of the disk aneular momentum ling in the pluie of the disk (that is. the warp) is transterred racially on a similar timescale.," It was originally assumed (Bardeen Petterson 1975; Rees 1978) that the component of the disk angular momentum lying in the plane of the disk (that is, the warp) is transferred radially on a similar timescale." However. if was discovered by Papaloizou Pringle (1983) hat consideration of the propagation of disk warp mist recessarily take uto account the internal lvdrodvuauiucs of the disk itself.," However, it was discovered by Papaloizou Pringle (1983) that consideration of the propagation of disk warp must necessarily take into account the internal hydrodynamics of the disk itself." In the regime in which Z//R«6<<1. and in which the disk is close to beime Keplerian. thev ound (see also Kamar Pringle 1985) that the disk schaviowr is somewhat complicated. but that to a first approximation the component of angular monmentuun ia he disk plane is transferred within the disk on a timescale of order A/15. where νο=1/207 (assunüng that a<< 1)," In the regime in which ${H/R}\,<\,{\alpha} \,<<1$, and in which the disk is close to being Keplerian, they found (see also Kumar Pringle 1985) that the disk behaviour is somewhat complicated, but that to a first approximation the component of angular momentum in the disk plane is transferred within the disk on a timescale of order $R^2/\nu_2$, where $\nu_2/\nu_1 = 1/2 \alpha^2$ (assuming that $\alpha\,<<\,1$ )." Thus. the relevant timescale for commmication of the disk warp is. Hg The original calculations by Papaloizou Pringle (1983) were carried out using Enlerian linear perturbation theory about an initially flat disk. and so were formally oulv valid for disk warp augles. 2. uch less than the disk opening auele ΠΠ.," Thus, the relevant timescale for communication of the disk warp is, t_R. The original calculations by Papaloizou Pringle (1983) were carried out using Eulerian linear perturbation theory about an initially flat disk, and so were formally only valid for disk warp angles, $\beta$ , much less than the disk opening angle $H/R$." For ACN disks for which ΠΠ~103? (see below). this is somewla Iunitiug.," For AGN disks for which $H/R\,\sim\, 10^{-2} -- 10^{-3}$ (see below), this is somewhat limiting." Recent work by Ogilvie (1998w.b) however. has shown that simular conchisious remain valid for warps of significant auplitude.," Recent work by Ogilvie (1998a,b) however, has shown that similar conclusions remain valid for warps of significant amplitude." These results have a considerable effect on the so-called Bardecu-Petterson radius. Rpp. the radius out to which the disk is aligned with the spin of the hole. as well as ou the hole/disk aligniueut timescale.," These results have a considerable effect on the so-called Bardeen-Petterson radius, $R_{\rm BP}$, the radius out to which the disk is aligned with the spin of the hole, as well as on the hole/disk alignment timescale." Since the disk turus out to be far more cficicnt at transferre warp in the radial direction than the initial estimates. which had ignored the iuterual disk liavcdvodvuaimics. it follows that both Rpp (παν Pringle 1985) aud the aliguimeut timescale are wach smaller than was originally thought.," Since the disk turns out to be far more efficient at transferring warp in the radial direction than the initial estimates, which had ignored the internal disk hydrodynamics, it follows that both $R_{\rm BP}$ (Kumar Pringle 1985) and the alignment timescale are much smaller than was originally thought." The timescale ou which a nmüsaligned. black hole aligus with its disk and the radius out to which the aliguimicut occurs have been calculated by Scheucr Feiler (1996)., The timescale on which a misaligned black hole aligns with its disk and the radius out to which the alignment occurs have been calculated by Scheuer Feiler (1996). Writing the Lense-Thirringe precession rate iu the disk as Opp=uyD. thev find that the radius out to which the disk is aligned with the spin of the hole is eiven simply as the radius at which the timescale for radial diffusion of the warp. Ap. is ofthe order of the local Leuse-Thirring precession. timescale Oil.," Writing the Lense-Thirring precession rate in the disk as $\Omega_{\rm LT}\,=\,\omega_p/R^3$, they find that the radius out to which the disk is aligned with the spin of the hole is given simply as the radius at which the timescale for radial diffusion of the warp, $t_{\rm warp}$, is ofthe order of the local Lense-Thirring precession timescale $\Omega_{\rm LT}^{-1}$." Equating these we obtain.fo.," Equating these we obtain,." where wy=2607ο. the angular momentiun of the hole. J. is given bv J=aeAl(GAL/e7). AL is the mass of the hole. aud α (099\%$. To esnuate the error. we fitted he light curve witLa sine function usi18o he IDL taskcurvefit.. ke«ping the trial periods fixed.," To estimate the error, we fitted the light curve with a sine function using the IDL task, keeping the trial periods fixed." The method has been described in more detail i1 Carpanoctal. (2007)., The method has been described in more detail in \cite{Carpano2007}. . The 36 error «X the 1.158 pulse period iρα 25s. The NMM light curve folde« at shown iu Fig. 3.., The $\sigma$ error of the s pulse period is s. The XMM light curve folded at s is shown in Fig. \ref{fig:fold}. To get more information aout TRANS JI80131.1-273932 and to address some hypotheses on its nature. we searched for possible optical couuterp:uts (within a few arcsecouds frou the nominal positio l0 the N-rayv source) m available catalogues.," To get more information about 1RXS J180431.1-273932 and to address some hypotheses on its nature, we searched for possible optical counterparts (within a few arcseconds from the nominal position of the X-ray source) in available catalogues." Amoug over 200000 Galactic bulee variable stars contained in the o»iblie domain OGLE catalogue (Wrayetal. 2001)). we ‘Ouid that a source exists within =[8 areseconds of IRNS J180131.1-273932 aud has been identified as a variable red giant aud labeled as OGLE II," Among over 200,000 Galactic bulge variable stars contained in the public domain OGLE catalogue \citealt{wep03}) ), we found that a source exists within $\simeq 4.8$ arcseconds of 1RXS J180431.1-273932 and has been identified as a variable red giant and labeled as OGLE II" which is valid when Zy « Z..,which is valid when $_{0}$ $\ll$ $_{c}$. Note that for computing purposes the right hand side of (4) is one half of the complementary error function ie. f(>/ogZ)=0.5xerfe(UogZ logZ.)) ," Note that for computing purposes the right hand side of (4) is one half of the complementary error function i.e. $f~(> log Z)=0.5\times erfc~\left(\frac{(log Z-log Z_{c})}{\sqrt{2}\sigma} \right)$ ." "By replacing M; with M,x EF. equations (1) and (2) can be written as Note (that equations (1) (2) remain the same. ("," By replacing $_{t}$ with $_{t}\times$ f, equations (1) and (2) can be written as Note that equations (1) (3) remain the same. (" Equation (1) remains the same because the nelallicily of the gas lost by collisions is the same as (hat in the clamps at the time of the collision).,Equation (1) remains the same because the metallicity of the gas lost by collisions is the same as that in the clumps at the time of the collision). " Because we now have an additional mass loss component. we define a new variable AL,;. Which represents the gas lost when the clumps collide."," Because we now have an additional mass loss component, we define a new variable $_{ml}$, which represents the gas lost when the clumps collide." Whereas Εμ is considered here to be lost to the warm hot intergalactic medium. the new Αμ component. having lost enerev in the collision. is assumed to fall to the center of the proto-galaxyv to be recycle.," Whereas $_{WHIM}$ is considered here to be lost to the `warm hot intergalactic medium', the new $_{ml}$ component, having lost energy in the collision, is assumed to fall to the center of the proto-galaxy to be recycled." Figurativelv. an individual classical chemical evolution ‘box’ is totally purged by having gas drop oul of the bottom on collision as well as having been blown continuously out of the lop as a result of previous ongoing star lormation!," Figuratively, an individual classical chemical evolution `box' is totally purged by having gas drop out of the bottom on collision as well as having been blown continuously out of the top as a result of previous ongoing star formation!" The equations governing (he evolution of these (wo mass loss components are and We limit the imumber of parameters by letting Z. define the effective vield. i.e. Equation (5) represents (he MDE of all stars formed (including those in globular clusters}.," The equations governing the evolution of these two mass loss components are and We limit the number of parameters by letting $_{c}$ define the effective yield, i.e. Equation (5) represents the MDF of all stars formed (including those in globular clusters)." We have not attempted to model globular cluster formation., We have not attempted to model globular cluster formation. It is assumed (hat the clusters are formed in bursts during collisions between clumps., It is assumed that the clusters are formed in bursts during collisions between clumps. We do attempt to make the chemical evolution consistent by ensuring that stars are formed. which. if assembled into a cluster svstem. would have the requisite mass aud (bv design) the appropriate Gaussian abundance distribution.," We do attempt to make the chemical evolution consistent by ensuring that stars are formed which, if assembled into a cluster system, would have the requisite mass and (by design) the appropriate Gaussian abundance distribution." To this end we express the amplitude of the cluster MDE as the product of the folal barvonic mass (Mj) (e.g. McLaughlin. 1999)and an efficiency. factor 7 πο that," To this end we express the amplitude of the cluster MDF as the product of the $total$ baryonic mass $_{t}$ ) (e.g. McLaughlin, 1999)and an efficiency factor $\eta$ so that" allow us to obtain high cadence mouitoring observations i N-rav aud {Yptical/UV wavelengths quickly after initial detection. allowing the study of the earliest stages of BOB outbursts with new clarity.,"allow us to obtain high cadence monitoring observations in X-ray and Optical/UV wavelengths quickly after initial detection, allowing the study of the earliest stages of BHB outbursts with new clarity." MAXI 152 was first reported after detection by the DBurst Alert Telescope (BAT: Barthehuyetal.20053) at 08:05 UT. 2010 September 25 (ALTD 5561.337. all times from this poit are quoted using MJD onuat iu UTC).," MAXI $-$ 152 was first reported after detection by the Burst Alert Telescope (BAT; \citealt{Barthelmy05}) ) at 08:05 UT, 2010 September 25 (MJD 55464.337, all times from this point are quoted using MJD format in UTC)." Follow up observations performed by the ANaav Telescope (XRT: Burrowsotal. 2005a)) aud UV/Optical Telescope (UVOT: Romiicetal. 20053) 3l imunutes later localized the transicut (Mauganoctal. 2010).. although it was initially uusidentified as a Canuna-Rav Burst aud named CRB 10925A. Based ou its detection by the NNova Alert System (Negoro2009) at MJD 5516L101 (02:530lLT. ~SA hhours before the BAT trigecr). ALANI 152 was determined to be a previously: uukuown Galactic X-ray transicut (Negoroctal.2010).," Follow up observations performed by the X-ray Telescope (XRT; \citealt{Burrows05}) ) and UV/Optical Telescope (UVOT; \citealt{Roming05}) ) 31 minutes later localized the transient \citep{Mangano10}, although it was initially misidentified as a Gamma-Ray Burst and named GRB 100925A. Based on its detection by the Nova Alert System \citep{Negoro09} at MJD 55464.104 (02:30UT, $\sim5.5$ hours before the BAT trigger), MAXI $-$ 152 was determined to be a previously unknown Galactic X-ray transient \citep{Negoro10}." . IR spectroscopy was obtained which coufirmed that the optical counterpartshowed emission ues consistent with that of an N-rav Binary (deUgartePostigo 2010)., IR spectroscopy was obtained which confirmed that the optical counterpartshowed emission lines consistent with that of an X-ray Binary \citep{deUP10}. . The transient was also detected in radio (vanHorstetal. 2010).. by citepvovkl0.. citepluulkerslü0a αμα RATE. which detected a 1.6 Iz tvpe-C ΟΡΟ iu the powerspectrum. iudicatiug that ATANI 152 is a BUB (salaiikaretal.," The transient was also detected in radio \citep{vdH10}, by \\citep{vovk10}, , \\citep{Kuulkers10a} and , which detected a 1.6 Hz type-C QPO in the power-spectrum, indicating that MAXI $-$ 152 is a BHB \citep{Kalamkar11}." 2011).. Ikuulkersetal.(2010b) reported evidence for periodicity in the hour rauge from ddata. sugecsting that2.5 this is the shortest period DIID vet known.," \cite{Kuulkers10b} reported evidence for periodicity in the hour range from data, suggesting that this is the shortest period BHB yet known." Bellonietal.(2010) reported a refined the perio measurement from ddata of 2.1112 hhowrs., \cite{Belloni10} reported a refined the period measurement from data of $2.4142$ hours. The light-curve revealed irregular structure dips lasting ο10 iniu. aux sugeest that dips analogous to those often seen in Low Alass X-ray Binaries (LAINBs) are the source of the —2. hour period. rather than eclipses frou the companion star (I&uulkersetal.2010b).," The light-curve revealed irregular structure dips lasting $5-40$ min, and suggest that dips analogous to those often seen in Low Mass X-ray Binaries (LMXBs) are the source of the $\sim2.4$ hour period, rather than eclipses from the companion star \citep{Kuulkers10b}." . We report here on broadband. observations of ALANI 152 utilizing/ all three instruments ou dauiug the first ddays of the outbirst after its initia detection., We report here on broadband observations of MAXI $-$ 152 utilizing all three instruments on during the first days of the outburst after its initial detection. We preseut spectral aud temporal analysis. iucluding the broadband UV/optical. X-ray aud had X-rav light-curves. analysis of QPOs. time resolved spectra evolution utilizing broadband spectral fits across the NRT aud BAT cucrev ranges. aud search for periodicities in the A-ray data.," We present spectral and temporal analysis, including the broadband UV/optical, X-ray and hard X-ray light-curves, analysis of QPOs, time resolved spectral evolution utilizing broadband spectral fits across the XRT and BAT energy ranges, and search for periodicities in the X-ray data." Observations with bheean after the rius lard XN-rav brightuess οἳ ALANI 152 trigecred the BAT. at MJD. 5516L337., Observations with began after the rising hard X-ray brightness of MAXI $-$ 152 triggered the BAT at MJD 55464.337. This prompted the standard CRB follow-up mode (e.g. Gehrelsetal. 2001)) 1n which the trausient was observed as an “Automated Tarect™ (AT) every z96 nuuiuute orbit with exposures of kks per orbit., This prompted the standard GRB follow-up mode (e.g. \citealt{Gehrels04}) ) in which the transient was observed as an “Automated Target” (AT) every $\approx96$ minute orbit with exposures of ks per orbit. From MJD 54168 onwards the observation cadence was lowered two 2kks observations a day. approximately spaced bv 12hhours," From MJD 55468 onwards the observation cadence was lowered two ks observations a day, approximately spaced by hours." Observations of the source continued with this cadence uutil the final observation ended at ΑΠΟ 55191.259. —27 ddavs after the initial BAT detection. after which MAXI J1659 152 became too close to the Sun for tto. observe.," Observations of the source continued with this cadence until the final observation ended at MJD 55491.259, $\sim27$ days after the initial BAT detection, after which MAXI $-$ 152 became too close to the Sun for to observe." Between MJD. 55180. and MJD 55182 ALANI 152 was not observable by NRT or |UVOT due to the proximity of the Moon., Between MJD 55480 and MJD 55482 MAXI $-$ 152 was not observable by XRT or UVOT due to the proximity of the Moon. XRT observed in Windowed Timing (WT) mode for all observations except for à Ls observation taken ou MJD 55106 in Photon Counting (PC) node. which was performed to obtain an accurate localization.," XRT observed in Windowed Timing (WT) mode for all observations except for a ks observation taken on MJD 55466 in Photon Counting (PC) mode, which was performed to obtain an accurate localization." UVOT data were typically collected utilizing all 6 UVOT filters. apart from a period between NJD 55168 aud NOD 55179 when observatious were taken utiliziug a dailv rotation of the 3 UV filters aud 4.," UVOT data were typically collected utilizing all 6 UVOT filters, apart from a period between MJD 55468 and MJD 55479 when observations were taken utilizing a daily rotation of the 3 UV filters and $u$." NANI 152 was observed by ffor Lkks on MJD 55508. 107 davs after the initial mouitoring observations euded. with NRT data collected iu PC mode. aud UVOT utilizine all 6 filters.," MAXI $-$ 152 was observed by for ks on MJD 55598, 107 days after the initial monitoring observations ended, with XRT data collected in PC mode, and UVOT utilizing all 6 filters." BAT data from the observations durime which wwas pointed at NANI 1995 were processed using the IIEASOFT script to produce cight-channel Που curves which were then converted to spectra covering the euergv range 14b.195 kkeV. BAT lieht-curves were produced automatically by the BAT Transicut Monitor web page (ταιetal.2006)., BAT data from the observations during which was pointed at MAXI $-$ 152 were processed using the HEASOFT script to produce eight-channel light curves which were then converted to spectra covering the energy range $14-195$ keV. BAT light-curves were produced automatically by the BAT Transient Monitor web page \citep{Krimm06}. . NRT light-curves aud spectra were extracted utilizing the methods deseribed by Evansetal.(2009).. with full corrections for pile-up and hot coluunus applied to the data based ona PSF fitted position of MAXI 152 obtained frou PC mode observations.," XRT light-curves and spectra were extracted utilizing the methods described by \cite{Evans09}, with full corrections for pile-up and hot columns applied to the data based on a PSF fitted position of MAXI $-$ 152 obtained from PC mode observations." NRT spectra were extracted over time mtervals strictly simultaneous with the BAT survey spectra. and binned to a minima of 20 counts per cuerey bin.," XRT spectra were extracted over time intervals strictly simultaneous with the BAT survey spectra, and binned to a minimum of 20 counts per energy bin." UVOT photometry was derived from) images viauvotmaghist. using an extraction region of radius," UVOT photometry was derived from images via, using an extraction region of radius." "Magnuitudes are based on the UVOT photometric svsteni (Pooleetal.2008) ind were uncorrectedfor the Galactic extinction in the direction of MANI 152 of Epy,=0.606 (Schlegeletal.1998)..","Magnitudes are based on the UVOT photometric system \citep{poole2008:MNRAS383} and were uncorrectedfor the Galactic extinction in the direction of MAXI $-$ 152 of $E_{(B-V)} = 0.606$ \citep{schlegel1998:ApJ500}." " Taking this value as an upper limit to the extinction of the counterpart and using the effective wavelengths of the filters (Pooleetal.2005) aud the parameterization of Pei(1992).. the extinctions iu the bbauds are: el.x Lah. ely,<2.36. 4,<2.96. usuX LIO. AyeXLas. «ο and Aims,> are known experimentallv. the values of mass ratios (p.c) from Eq. (","The magnitude of the two mass ratios is given as while the CP- violating Majorana phases $\alpha$ and $\beta$ are given by Since, $\Delta m_{12}^{2}$ and $\Delta m_{23}^{2}$ are known experimentally, the values of mass ratios $(\rho,\sigma)$ from Eq. (" 18) and (19) can be used to calculate 2.,18) and (19) can be used to calculate $m_1$. This can be done by inverting Eqs. (, This can be done by inverting Eqs. ( 14) ancl (15) to obtain (hie two values of nmi. viz.,"14) and (15) to obtain the two values of $m_1$, viz." and We vary the oscilation parameters within their known experimental ranges., and We vary the oscillation parameters within their known experimental ranges. However. the Dirac type CP- violating phase 9 is varied within its full range and 844 is varied 11 ils 30 range given bv the CIIOOZ |sound.," However, the Dirac type CP- violating phase $\delta$ is varied within its full range and $\theta_{13}$ is varied in its $\sigma$ range given by the CHOOZ bound." The two values of mq obtained from the nass ralios p alc Lo. respectively mus{ be equal to within the errors of the oscillation parameters for the simultaneous existence of a texture zero and a vanishing minor.," The two values of $m_1$ obtained from the mass ratios $\rho$ and $\sigma$, respectively must be equal to within the errors of the oscillation parameters for the simultaneous existence of a texture zero and a vanishing minor." There are in total thirty six possible slructures of neutrino mass matrix [Table 1.), There are in total thirty six possible structures of neutrino mass matrix [Table 1.] with a single texture zero and a vanishing minor., with a single texture zero and a vanishing minor. As can be seen from Table 1..," As can be seen from Table 1.," ". (wenly one structures Corrosponds to two texture zero cases which have. already. been studied extensively,"," twenty one structures corrosponds to two texture zero cases which have, already, been studied extensively." We examine the phenomenological viability of all (he remaining texture structures ancl also present «letailed phenomenological implications for the viable structures., We examine the phenomenological viability of all the remaining texture structures and also present detailed phenomenological implications for the viable structures. current is J4(0)zmJon which matches the constant current. 74i(0)=joy.,"current is $j_\parallel(0)\approx-\beta_{-0}n_-$, which matches the constant current $j_\parallel(0)=j_{0\parallel}$." Phe electrons momentum is derived as As for (50)). for electrons to be accelerated: outward one must have dyz-0.," The electron's momentum is derived as As for \ref{eq:E1}) ), for electrons to be accelerated outward one must have $\delta\eta>0$." That the same condition (37)20) is required. in. both cases is hardly surprising., That the same condition $\delta\eta>0$ ) is required in both cases is hardly surprising. In. (50)). one has d£~educ0 and xO. while in (50))r one has d&~ditz-0 but x«," In \ref{eq:E1}) ), one has $d\xi\sim -\beta_V du<0$ and $\chi>0$, while in \ref{eq:E1}) ) one has $d\xi\sim du>0$ but $\chi<0$." " OM Ly~O0. the electron's momentum increases with Z quackatically, οτνδη/2."," If $\tilde{E}_0\sim0$, the electron's momentum increases with $\tilde{z}$ quadratically, $u_-\sim \delta\eta\tilde{z}^2/2$." " In the conventional SCLE models CXrons&Scharle-mann1979:Harding&Muslimov L998)... £24«0 is obtained with dy«0. bv imposing an upper boundary. usually located at the. PEE. where £(=0. and à conducting surface of the side wall of the open field line region: in these models jo, is then determined. locally by these boundary conditions."," In the conventional SCLF models \citep{as79,hm98}, , $E_\parallel<0$ is obtained with $\delta\eta<0$, by imposing an upper boundary, usually located at the PFF, where $E_\parallel=0$, and a conducting surface of the side wall of the open field line region; in these models $j_{0\parallel}$ is then determined locally by these boundary conditions." The basic assumption in the SCLE models is the nonconstaney of 07g along How., The basic assumption in the SCLF models is the nonconstancy of $\delta\eta$ along flow. This means that if one sets oj=O initially. a nonzero δησὲ0 develops along the How inducing a parallel electric field.," This means that if one sets $\delta\eta=0$ initially, a nonzero $\delta\eta\neq0$ develops along the flow inducing a parallel electric field." Pwo cllects that Lead to on«0 have been considered in the literature. including field line curvature. corresponding to the field lines curving toward the rotation axis. and frame dragging. (Muslimov&Tsvgan 1902).," Two effects that lead to $\delta\eta<0$ have been considered in the literature, including field line curvature, corresponding to the field lines curving toward the rotation axis, and frame dragging \citep{mt92}." ". The latter dominates near the star: the elfective angular velocity. so is the €] density. is reduced by aactor (1.Aj(7ry?)« Las compared to that observed in a [at space at infinity. where A,=26(COT)υπο ο«οR=10'm. and 444=£/(1077kem) is the moment of inertia of the star (Alustimoyv&Psvean1992)."," The latter dominates near the star; the effective angular velocity, so is the GJ density, is reduced by a factor $(1-k_g(R/r)^3)<1$ as compared to that observed in a flat space at infinity, where $k_g=2GI/(c^2R^3)\approx0.15I_{38}$, $z0 is required to produce £)«0.," When $j_{0\parallel}$ is treated as a free parameter, for initially $\delta\eta=0$ , $\delta\eta>0$ is required to produce $E_\parallel<0$." This can occur only on the curvingeawavy (from the rotation axis) field lines along which [Q-B| decreases (Shibata1997:Mestel.1999).," This can occur only on the curving-away (from the rotation axis) field lines along which $|\bOmega\cdot\bB|$ decreases \citep{s97,m99}." .. A. major problem with this scenario in the context of the state limit is that the growth in [£4 is unstoppable (Shibata1997:Moestel 1999).," A major problem with this scenario in the context of the steady-state limit is that the growth in $|E_\parallel|$ is unstoppable \citep{s97,m99}." .. Llowever. such run-away growth does nol occur in our oscillatory model becausepair. creation ultimately leacs the system to switch to an oscillatory phase. as discussed in Sec.," However, such run-away growth does not occur in our oscillatory model becausepair creation ultimately leads the system to switch to an oscillatory phase, as discussed in Sec." 3., 3. For 95«0. Eq (54)) implies an oscillatory (in space) solution similar to that. found previously (Alestel&Shibata1994:1997).," For $\delta\eta<0$, Eq \ref{eq:u2}) ) implies an oscillatory (in space) solution similar to that found previously \citep{ms94,s97}." ". When the acceleration. region extends to ROR""PEE ""the ellect of the conducting side wall. at which £=0. becomes important."," When the acceleration region extends to $>R(R/R_{LC})^{1/2}$, the effect of the conducting side wall, at which $E_\parallel=0$, becomes important." When such cllect is included: acceleration of outllowing electrons is possible at BGBue)? even when oy«0 (provided that an electric field arising from such elect. dominates over that. from δή« 0) (Shibata 1991)., When such effect is included acceleration of outflowing electrons is possible at $>R(R/R_{LC})^{1/2}$ even when $\delta\eta<0$ (provided that an electric field arising from such effect dominates over that from $\delta\eta<0$ ) \citep{s97}. . We present an oscillatory polar gap model. in which the system initially undergoes a low-clensity phase. involving rapid acceleration of particles to ultra high energy. initiating a pair cascade.," We present an oscillatory polar gap model, in which the system initially undergoes a low-density phase, involving rapid acceleration of particles to ultra high energy, initiating a pair cascade." The system evolves to απ oscillatory phase., The system evolves to an oscillatory phase. The oscillations are treated as a superluminal. large amplitude clectrostatic wave that propagates along the magnetic field.," The oscillations are treated as a superluminal, large amplitude electrostatic wave that propagates along the magnetic field." The charge continuity equation implies a current-charge invariant (Jj=const) ) that ds independent of pair creation., The charge continuity equation implies a current-charge invariant $j_\parallel-\beta_V\eta={\rm const}$ ) that is independent of pair creation. As a result. the phase velocity is no longer a free parameter and can be written in terms of the initial velocity and density of the plasma.," As a result, the phase velocity $\beta_V$ is no longer a free parameter and can be written in terms of the initial velocity and density of the plasma." ]t is shown that only the superluminal case y291 is relevant here., It is shown that only the superluminal case $\beta_V>1$ is relevant here. An analytical formalism for LEAWs is derived in the hieh-density regime in which the pair density is uigher than the GJ density., An analytical formalism for LEAWs is derived in the high-density regime in which the pair density is higher than the GJ density. We ignore wave damping in our analvtical solution., We ignore wave damping in our analytical solution. Neglecting damping is justified. as the vpical damping time due to energy losses through radiation is much longer than the wave period., Neglecting damping is justified as the typical damping time due to energy losses through radiation is much longer than the wave period. In most. cases. the damping time is also longer than the light-crossing time over he gap.," In most cases, the damping time is also longer than the light-crossing time over the gap." The model predicts an outflow of relativistic pairs due o particles being dragged along in LALA., The model predicts an outflow of relativistic pairs due to particles being dragged along in LAEW. Such feature is needed: to avoid. overheating of the polar cap., Such feature is needed to avoid overheating of the polar cap. Outflowing ours would contribute to the pulsar wind., Outflowing pairs would contribute to the pulsar wind. Pairs oscillate with a net drift velocity directed along the magnetic field. »oducing a current that oscillates about the global constant current jo.," Pairs oscillate with a net drift velocity directed along the magnetic field, producing a current that oscillates about the global constant current $j_0$." Phe amplitude. of the oscillating current. is arger than the global current by a large [actor that. ds of order of magnitude the ratio of the pair censity to he C.J density., The amplitude of the oscillating current is larger than the global current by a large factor that is of order of magnitude the ratio of the pair density to the GJ density. The wave form of an inductive electric ield is characterized by a triangular shape. which can be unclerstoocl as the current being nearly constant except for a ie period during which it switches sign.," The wave form of an inductive electric field is characterized by a triangular shape, which can be understood as the current being nearly constant except for a brief period during which it switches sign." Lhe basic features of the oscillations are not sensitive to the initial conditions including the electron's or positron’s initial velocity., The basic features of the oscillations are not sensitive to the initial conditions including the electron's or positron's initial velocity. There are two possiblities for. particle acceleration. in the initial phase that leads to oscillations: (1) a vacuum-like initial electric field. which may. be applicable for the polar cap where charges are tightly. bound to the surface. and (2) SCLE. in which there is an ample supply of charges.," There are two possiblities for particle acceleration in the initial phase that leads to oscillations: (1) a vacuum-like initial electric field, which may be applicable for the polar cap where charges are tightly bound to the surface, and (2) SCLF, in which there is an ample supply of charges." Vhe first case was discussed. in Levinsonetal.(2005)., The first case was discussed in \citet{letal05}. . Lere we consider specifically. the SCLE case where an initial electric. field: appears as a result. of an imbalance oween the charge density ancl the GJ density with the atter mimicking the positive background charges., Here we consider specifically the SCLF case where an initial electric field appears as a result of an imbalance between the charge density and the GJ density with the latter mimicking the positive background charges. Electrons are accelerated. monotonically in the electric field. that increases lincarly with the phase xy., Electrons are accelerated monotonically in the electric field that increases linearly with the phase $\chi$. Since X comprises both emporal and spatial variables. such particle acceleration arises [rom a mixture of inductive and non-inductive ellects.," Since $\chi$ comprises both temporal and spatial variables, such particle acceleration arises from a mixture of inductive and non-inductive effects." An interesting limit is Vsox. in which the electric field comes. purely inductive.," An interesting limit is $V\to \infty$, in which the electric field becomes purely inductive." Qualitativelv. the usual steady-state theory can be reproduced in the limit of a zero phase speed.," Qualitatively, the usual steady-state theory can be reproduced in the limit of a zero phase speed." Ln this limit. the svstem is time independent ancl the acceleration occurs at a specific spatial location.," In this limit, the system is time independent and the acceleration occurs at a specific spatial location." By contrast. acceleration due to an inductive field can occur everywhere in the region concerned.," By contrast, acceleration due to an inductive field can occur everywhere in the region concerned." An implication of the oscillatory mocel is the prediction of plasma instability arising from. counterstreaming of electrons and. positrons: in cach oscillation electrons. and positrons are accelerated in opposite direction. and.such counterstreaming provides an ideal condition for two-stream instability which may be directly. relevant for. pulsar. raclioemission (Verdon&Alelrose 2007).., An implication of the oscillatory model is the prediction of plasma instability arising from counterstreaming of electrons and positrons; in each oscillation electrons and positrons are accelerated in opposite direction andsuch counterstreaming provides an ideal condition for two-stream instability which may be directly relevant for pulsar radioemission \citep{vm07}. . Although various formis of streaming instability have been discussed in connection with the radio emission in conventional models. the growth rate is generally too low to be ellective. requiring sonie separate assumption to enhance it.," Although various forms of streaming instability have been discussed in connection with the radio emission in conventional models, the growth rate is generally too low to be effective, requiring some separate assumption to enhance it." In the oscillatory, In the oscillatory With these points in mind. we can now explain what controls the distinctions in [lux and power spectrin between the different quadrants.,"With these points in mind, we can now explain what controls the distinctions in flux and power spectrum between the different quadrants." For lace-on views. thev all contribute identically to the light curve; as (he viewing angle moves off-axis. special relativisiic beaming and boosting enhances the approaching sides. while general relativistic light. bending and frame-clrageine enhance the back sides.," For face-on views, they all contribute identically to the light curve; as the viewing angle moves off-axis, special relativistic beaming and boosting enhances the approaching sides, while general relativistic light bending and frame-dragging enhance the back sides." The result is Chat over most of i». 0 parameter space. quadrant ais (he brightest (both approaching and in back of the black hole). d is the faintest (both receding and in front). and b and © are similar to one another (b is receding but in back: ¢ is approaching but in front).," The result is that over most of $\dot m$ $\vartheta$ parameter space, quadrant a is the brightest (both approaching and in back of the black hole), d is the faintest (both receding and in front), and b and c are similar to one another (b is receding but in back; c is approaching but in front)." The maximum flix contrast between the brightest and cimunest quadrants never exceeds a [actor of 5., The maximum flux contrast between the brightest and dimmest quadrants never exceeds a factor of $\sim 5$. " The slopes of their power spectra Iollow (he same (rend seen in flux: a,>cay on average. wilh no spectral slope falling outside (he range —2.4 \alpha_d $ on average, with no spectral slope falling outside the range $-2.4 \le \alpha \le -1.8$." However. relative to quadrant e. (he quadrant b becomes brighter and its PDS flatter as Vv increases.," However, relative to quadrant c, the quadrant b becomes brighter and its PDS flatter as $\vartheta$ increases." In the summed light curve. the contrasting effects largely cancel one another. so that the spectral slope of the composite PDS can be described bv a simple average of the euadrants: individual power-law exponents.," In the summed light curve, the contrasting effects largely cancel one another, so that the spectral slope of the composite PDS can be described by a simple average of the quadrants' individual power-law exponents." In our calculation. the «uadrants are precisely coherent at all frequencies when viewed exactly [ace-on.," In our calculation, the quadrants are precisely coherent at all frequencies when viewed exactly face-on." As the inclination angle grows. they begin to become incoherent at the hiehest frequencies. bul even lor J=7/2. the range of incoherent Irequencies is still (quite limited.," As the inclination angle grows, they begin to become incoherent at the highest frequencies, but even for $\vartheta = \pi/2$, the range of incoherent frequencies is still quite limited." The reason for this behavior is that our svmmetry condition makes their emissivity precisely coherent. so such incoherence as exists is entirely due to (inme-delav. effects: as just discussed. they are small except al the highest frequencies.," The reason for this behavior is that our symmetry condition makes their emissivity precisely coherent, so such incoherence as exists is entirely due to time-delay effects; as just discussed, they are small except at the highest frequencies." Thus. if the absolute power spectrum from a single «quadrant (before Doppler adjustments and obscuration effects) is Vv). our total power spectrum is 16.1(7) when viewed on-axis. and when viewed off-axis has essentially identical power at low frequencies. but slightly less at high.," Thus, if the absolute power spectrum from a single quadrant (before Doppler adjustments and obscuration effects) is $A^2(\nu)$, our total power spectrum is $16A^2(\nu)$ when viewed on-axis, and when viewed off-axis has essentially identical power at low frequencies, but slightly less at high." By contrast. in a full 2z simulation we expect that the emissiviües of the equadrants would have verv similar power spectra to the emissivilv we calculate. but. be completely incoherent if azimuthal correlations extend only over angles 0.42.," By contrast, in a full $2\pi$ simulation we expect that the emissivities of the quadrants would have very similar power spectra to the emissivity we calculate, but be completely incoherent if azimuthal correlations extend only over angles $\simeq 0.4\pi$." The same repertory of relativistic elfects. both special ancl general. will sGll apply. but we expect that they. will similarly cancel in sum.," The same repertory of relativistic effects, both special and general, will still apply, but we expect that they will similarly cancel in sum." " Thus. a total flux power spectrum c£:17(v) should result. as only the 5, term contributes."," Thus, a total flux power spectrum $\simeq 4A^2(\nu)$ should result, as only the $S_a$ term contributes." In other words. if (his reasoning holds. the shape of the power spectrum observed from a full 2a disk would be quite similar to what we compute. but its amplitude would be lower by about a [actor of 4.," In other words, if this reasoning holds, the shape of the power spectrum observed from a full $2\pi$ disk would be quite similar to what we compute, but its amplitude would be lower by about a factor of 4." " In this paper. we have presented a new. more plivsical method for estimating the temporal variability of radiation rom the oplically thin (""coronal) regions of 3D GRMIID"," In this paper, we have presented a new, more physical method for estimating the temporal variability of radiation from the optically thin (“coronal"") regions of 3D GRMHD" slowly over the last 25 years. including observational issues such as the frequency coverage of radio telecopes and widespread radio frequency interference (RFI) at the low frequencies (1 GHz) of the redshifted 21 em line.,"slowly over the last 25 years, including observational issues such as the frequency coverage of radio telecopes and widespread radio frequency interference (RFI) at the low frequencies $\lesssim 1$ GHz) of the redshifted 21 cm line." However. an additional important reason for the relatively-small present 21 em absorption sample is simply the dearth of known DLAs towards radio-loud QSOs suitable for 21 em absorption follow-up.," However, an additional important reason for the relatively-small present 21 cm absorption sample is simply the dearth of known DLAs towards radio-loud QSOs suitable for 21 cm absorption follow-up." We have hence been conducting an optical survey of low-frequency-selected radio-loud quasars. specitically designed to increase the numberof 7; estimates in the redshift range 2«z<4.," We have hence been conducting an optical survey of low-frequency-selected radio-loud quasars, specifically designed to increase the numberof $\ts$ estimates in the redshift range $2[κουωςcBNLOMAL, The change of the direction in the brighter part of the tail remains unexplainable aud there is also the problem iu explaining the coustaney of the spectra and the surface brightuess along the radio rug."," To sustain such a helical orbit of NGC 1265 over $360\degr$, this model would require an undetected dark object of mass $M\gtrsim M_\rmn{NGC~1265}\simeq 3\times10^{12}M_\odot$ orbiting the The change of the direction in the brighter part of the tail remains unexplainable and there is also the problem in explaining the constancy of the spectrum and the surface brightness along the radio ring." Caven these difficultics. it is attractive to consider alternative possibilities that may explore the interaction between a radio galaxy with the outskirts of the Perseus ICAL.," Given these difficulties, it is attractive to consider alternative possibilities that may explore the interaction between a radio galaxy with the outskirts of the Perseus ICM." This has been foreshadowed in a remark bv 7/— who speculate whether the large scale polarized structure that arches around the steep spectrmu tail of NGC 1265 is indeed the remains of an earlier phase of feedback., This has been foreshadowed in a remark by \citet{2005A&A...441..931D} who speculate whether the large scale polarized structure that arches around the steep spectrum tail of NGC 1265 is indeed the remains of an earlier phase of feedback. Our work will demonstrate that this picture is uot only the simplest consisteut explanation for the radio morphology and spectruni but we also use it to indirectly inter the presence of a cluster shock wave and measure its properties.," Our work will demonstrate that this picture is not only the simplest consistent explanation for the radio morphology and spectrum, but we also use it to indirectly infer the presence of a cluster shock wave and measure its properties." Previously. the morphology of a eiut radio galaxy has already: been used to iudirectly detect a large scale shock at an intersecting fhuneut of galaxies (7)— bv usine the radio galaxy as a giant cluster weather station (?)..," Previously, the morphology of a giant radio galaxy has already been used to indirectly detect a large scale shock at an intersecting filament of galaxies \citep{2001ApJ...549L..39E} by using the radio galaxy as a giant cluster weather station \citep{1998Sci...280..400B}." Caavitationallv driven. supersouic flows of intergalactic eas follow these flaments toward estes B ealaxies that represent the knots of the cosmüc web a(?7)..," Gravitationally driven, supersonic flows of intergalactic gas follow these filaments toward clusters of galaxies that represent the knots of the cosmic web \citep{1996Natur.380..603B}." The flows will inevitably collide aud. form Iaree-se shock waves (QU277)..," The flows will inevitably collide and form large-scale shock waves \citep{1998ApJ...502..518Q, 2000ApJ...542..608M, 2003ApJ...593..599R, 2006MNRAS.367..113P}." OF exeat. interest is the subclass of accretion shocks that are thought to heat the barvous of the warnrot iuterealactie iiedium (IGAL) when they are accreted outo a ealaxy cluster., Of great interest is the subclass of accretion shocks that are thought to heat the baryons of the warm-hot intergalactic medium (IGM) when they are accreted onto a galaxy cluster. Formation shocks have also beeu xoposed. as possible geueration sites of intergalactic naenetic fields (2??)..," Formation shocks have also been proposed as possible generation sites of intergalactic magnetic fields \citep{1997ApJ...480..481K, 1998A&A...335...19R, 2008Sci...320..909R}." Prior to this work. ouly discrete ucreer shock waves have been detected im the N-ravs (es.T) and there was no characterization possible of he detailed flow properties iu the post-shock regime as ο test whether shear flowsthe necessary condition for eoncrating magnetic fieldsare preseut.," Prior to this work, only discrete merger shock waves have been detected in the X-rays \citep[e.g.,][]{2002ApJ...567L..27M} and there was no characterization possible of the detailed flow properties in the post-shock regime as to test whether shear flows—the necessary condition for generating magnetic fields—are present." The structure of the paper is as follows., The structure of the paper is as follows. In Section 2.. we prescut the basic picture of our model in a nutshell while we derive the detailed three-dimensional (3D) ecolctry of NGC 1265 within our model in Section 3..," In Section \ref{sec:idea}, we present the basic picture of our model in a nutshell while we derive the detailed three-dimensional (3D) geometry of NGC 1265 within our model in Section \ref{sec:geometry}." Tn Section L. we work out the properties of the accretion shock onto the Perseus cluster iucludiug those of the post-shock flow aud preseut the implications for the παπιο warm-hot IGAL.," In Section \ref{sec:shock}, we work out the properties of the accretion shock onto the Perseus cluster including those of the post-shock flow and present the implications for the infalling warm-hot IGM." Iu Section 5.. we carefully examine the wnderling plivsics as well as the lvcdvodvuamic stability. of our model aud discuss our findings in Section 6..," In Section \ref{sec:model}, we carefully examine the underlying physics as well as the hydrodynamic stability of our model and discuss our findings in Section \ref{sec:conclusions}." Throughout this work. we use a IIubble constant of ff)=rüXkms‘AIpe," Throughout this work, we use a Hubble constant of $H_{0} = 70\,\rmn{km~s}^{-1}\rmn{Mpc}^{-1}$." " For the currently favored ACDAL cosmology with the prescut dav deusitv of total matter. O,,=0.28. aud the cosmological constant. O4=0.72. we obtain an angular diameter distance to Perseus (2=0.0179) of Daye=T5Mp: at this distance. 1 corresponds to 21.5kpc."," For the currently favored $\Lambda$ CDM cosmology with the present day density of total matter, $\Omega_m=0.28$, and the cosmological constant, $\Omega_\Lambda=0.72$, we obtain an angular diameter distance to Perseus $z=0.0179$ ) of $D_\rmn{ang}=75\,\rmn{Mpc}$; at this distance, $1\arcmin$ corresponds to $21.8\,\rmn{kpc}$." N-vav data estimates a virial radius and mass for of LOMpe and Moy)=7.7«101A. (2).," X-ray data estimates a virial radius and mass for of $R_{200}=1.9\,\rmn{Mpc}$ and $M_{200}=7.7\times10^{14}M_\odot$ \citep{2002ApJ...567..716R}." " Before we preseut the idea of our model. we poiut out the main morphological aud Spectral properties of the ejut radio galaxy NGC 1265hrotronthat every model would have to explain: (1) The syuc surface brielituess. 5,. aud the spectral ides. a. between 19 aud 92 cm along the tail of NCC 1265uas (starting at the ealaxys head) show a characteristic jour (as shown in Fieure 2 of ?))."," Before we present the idea of our model, we point out the main morphological and spectral properties of the giant radio galaxy NGC 1265 that every model would have to explain: (1) The synchrotron surface brightness, $S_\nu$, and the spectral index, $\alpha$, between 49 and 92 cm along the tail of NGC 1265 (starting at the galaxy's head) show a characteristic behaviour (as shown in Figure 2 of \citealt{1998A&A...331..901S}) )." In the first part ]of the tail. both quantities decline moderately mi a wav that is consistent with svuchrotron and inverse Compton cooling of a relativistic electron population that eot accelerated at the base or tle ier reeions of the jet. (," In the first part of the tail, both quantities decline moderately in a way that is consistent with synchrotron and inverse Compton cooling of a relativistic electron population that got accelerated at the base or the inner regions of the jet. (" "2) At the point of the tail where the twist changes in projection frou left- to right-hauced. both quantities experience a sudden dropwhile 4), changes by a factor of 10. à declines from 11 το 2.1. (","2) At the point of the tail where the twist changes in projection from left- to right-handed, both quantities experience a sudden drop—while $S_\nu$ changes by a factor of 10, $\alpha$ declines from $-1.1$ to $-2.1$ . (" "3) Finally. along the remaimime curved arc. 5, and a stay approximately constant on a total are leneth of lave=22ROL1zoTOOkpe. where R5150Xpe is the radius of m arc. &£&3/1 the projected arc leneth in uuits of 27 radius. iud &=Ph/(2zR)0. where h is the height of the 3D helix.","3) Finally, along the remaining curved arc, $S_\nu$ and $\alpha$ stay approximately constant on a total arc length of $l_\rmn{arc} = 2\pi R \xi \sqrt{1 + k^2}\gtrsim 700 \,\rmn{kpc}$, where $R\simeq150\,\rmn{kpc}$ is the radius of the arc, $\xi\simeq 3/4$ the projected arc length in units of $2\pi$ radians, and $k=h/(2\pi R)\geq0$, where $h$ is the height of the 3D helix." This property is iu particular puzzlug. as there is no visible svuchrotrou cooling or fanning out of the dilute part of the tail visible.," This property is in particular puzzling, as there is no visible synchrotron cooling or fanning out of the dilute part of the tail visible." These fiudiugs taken together sugeest the presence of two separate populations of relativistic clectrous eiviug vise to the bright aud the dim part of the tail. respectively. where the latter ιτ lave expericuced a coherent cucrectization over a length scale of 27~300kpe aud on a timescale that is shorter than the cooling time of the radio emittiug clectrous ofTancie$2.9«105vr.," These findings taken together suggest the presence of two separate populations of relativistic electrons giving rise to the bright and the dim part of the tail, respectively, where the latter must have experienced a coherent energetization over a length scale of $2 R\simeq 300\,\rmn{kpc}$ and on a timescale that is shorter than the cooling time of the radio emitting electrons of $\tau_\rmn{sync,\,ic} \lesssim 2.9\times 10^8\,\rmn{yr}$." The presence of one radio tail that counects the two electron populations iu projection poiuts to a causally counected origin of the svuchrotron racdiatiug structure., The presence of one radio tail that connects the two electron populations in projection points to a causally connected origin of the synchrotron radiating structure. The most natural explanation that combines these observational requirements are the reminders of two distinct epochs of active ealactic nucleus outbursts where the ost recent oue is still visible as a head-tail radio jet aud the older oue experienced a recent coliercut enereetization eveut., The most natural explanation that combines these observational requirements are the reminders of two distinct epochs of active galactic nucleus outbursts where the most recent one is still visible as a head-tail radio jet and the older one experienced a recent coherent energetization event. Tu we propose that such an cuereizing event couldbe partienlay.provided |* the passage of a detached radio plasmabubble from a previous outburst throueh a shock wave.," In particular, we propose that such an energizing event could be provided by the passage of a detached radio plasma bubble from a previous outburst through a shock wave." This passage transforms the plasiuabubble iuto a torus (vortex ring) and αλανασαν compresses and euereizes the agedelectron population to eut low surface brightness and steep-spectrunn radio ciussiow (as we detail below)., This passage transforms the plasma bubble into a torus (vortex ring) and adiabatically compresses and energizes the agedelectron population to emit low surface brightness and steep-spectrum radio emission (as we detail below). If the shock crossing is oblique.," If the shock crossing is oblique," northern rim.,northern rim. Therefore. the CIE condition is justified and we will not further consider the VNEI model. (," Therefore, the CIE condition is justified and we will not further consider the VNEI model. (" (source #111) ts the brightest one among the four point sources near to the remnant center.,source 11) is the brightest one among the four point sources near to the remnant center. We extracted its spectrum from a circular region with a radius of 10 aresec centered at the source position (cf., We extracted its spectrum from a circular region with a radius of 10 arcsec centered at the source position (cf. Table 1)., Table 1). " The background spectrum was extracted from a nearby region from a circle of 10 aresec radius centered at RA=19""54'""23.234>, Dec=31°29/22.75"" (02000)."," The background spectrum was extracted from a nearby region from a circle of 10 arcsec radius centered at $19^{\rm h}54^{\rm m}23.234^{\rm s}$ , $31^{\circ}29'22.75""$ (J2000)." After background subtraction. 54 net counts were avaliable for the spectral analysis of the source.," After background subtraction, 54 net counts were avaliable for the spectral analysis of the source." Since the location of iis close to the edge of ACIS-I3 CCD. we computed the response files manually with the CIAO tools MKARF and MKRME.," Since the location of is close to the edge of ACIS-I3 CCD, we computed the response files manually with the CIAO tools MKARF and MKRMF." The spectrum was binned dynamically so as to have at least 5 counts per bin., The spectrum was binned dynamically so as to have at least 5 counts per bin. In view of the small photon statistic of these sources. we adopted the C—-statistic (Cash 1979) for all the fittings.," In view of the small photon statistic of these sources, we adopted the $C-$ statistic (Cash 1979) for all the fittings." To better constrain the parameters. we fixed the hydrogen column density at the optical extinction inferred value (i.e. 4x107! em™).," To better constrain the parameters, we fixed the hydrogen column density at the optical extinction inferred value (i.e. $4\times10^{21}$ $^{-2}$ )." Fitting with a power-law model results in a reasonable fit that yields a photon index of [22.7+0.4 and a normalization at 1 keV of 14701»107 photons keV! em™ s!., Fitting with a power-law model results in a reasonable fit that yields a photon index of $\Gamma=2.7\pm0.4$ and a normalization at 1 keV of $1.4^{+0.4}_{-0.3}\times10^{-5}$ photons $^{-1}$ $^{-2}$ $^{-1}$. The best-fit column density is consistent with the values inferred from the spectra of the supernova remnant emission within the Io error bound., The best-fit column density is consistent with the values inferred from the spectra of the supernova remnant emission within the $1\sigma$ error bound. " The unabsorbed flux deduced for the best-fit power-law model parameters is f£,=4.5x107 ergs em s! in 0.5--8 keV. A blackbody model can describe the spectrum of this source equally well.", The unabsorbed flux deduced for the best-fit power-law model parameters is $f_{x}=4.5\times10^{-14}$ ergs $^{-2}$ $^{-1}$ in $0.5-8$ keV. A blackbody model can describe the spectrum of this source equally well. The best-fit model implies a temperature of T=467x10°K., The best-fit model implies a temperature of $T=4.6^{+0.7}_{-0.6}\times10^{6}~K$. The radius of the projected blackbody emitting area is in the range ~170—310 m and ~410—750 m for the adopted distances of 7 kpe and 17 kpe. respectively (see $33 for the discussion of the remnant distance).," The radius of the projected blackbody emitting area is in the range $\sim170-310$ m and $\sim410-750$ m for the adopted distances of 7 kpc and 17 kpc, respectively (see 3 for the discussion of the remnant distance)." " The unabsorbed flux deduced for the best-fit blackbody model is f,=2.6x107 ergs em™ s! in 0.5—8 keV. For the other three fainter central X-ray sources it Is interesting to compare their brightness and hardness with those ofCXOU195422.", The unabsorbed flux deduced for the best-fit blackbody model is $f_{x}=2.6\times10^{-14}$ ergs $^{-2}$ $^{-1}$ in $0.5-8$ keV. For the other three fainter central X-ray sources it is interesting to compare their brightness and hardness with those of. 97+312902.1.. To do so. we have prepared their spectra and the response files in the same way as we did forCXOU195422.," To do so, we have prepared their spectra and the response files in the same way as we did for." 97+312902.1.. Fixing the column density at ny=4x107 cm we obtained the photon indices by fitting a power-law model to their spectra., Fixing the column density at $n_{H}=4\times10^{21}$ $^{-2}$ we obtained the photon indices by fitting a power-law model to their spectra. The fitted parameters are summarised in Table 3., The fitted parameters are summarised in Table 3. The photon index provides a measure of the hardness of these X-ray sources., The photon index provides a measure of the hardness of these X-ray sources. Whereas sources #99 and ((source #110) are as soft asCXOU195422.97+312902.1.. ((source #335) appears to show harder X-ray emission.," Whereas sources 9 and (source 10) are as soft as, (source 35) appears to show harder X-ray emission." We have also computed the absorption-corrected fluxes from the inferred power-law parameters which are given in Table 3., We have also computed the absorption-corrected fluxes from the inferred power-law parameters which are given in Table 3. Given the limited photon statistics of the central point sources. the spectral analysis is not very constraining.," Given the limited photon statistics of the central point sources, the spectral analysis is not very constraining." Even for the brightest object195422.97+4312902.1.. we cannot distinguish its emission nature between the thermal and the non-thermal scenarios.," Even for the brightest object, we cannot distinguish its emission nature between the thermal and the non-thermal scenarios." To investigate if these sources are promising neutron star candidates we proceeded to search for their optical counterparts by utilizing the USNO-BI.O catalogue (Monet et al., To investigate if these sources are promising neutron star candidates we proceeded to search for their optical counterparts by utilizing the USNO-B1.0 catalogue (Monet et al. 2003)., 2003). For the search regions. we combine the positional errors of each source with the pointing uncertainty of the spacecraft.," For the search regions, we combine the positional errors of each source with the pointing uncertainty of the spacecraft." The uncertainty can be estimated from the distribution of aspect offset for a sample of point sources with accurately known celestialpositions’., The uncertainty can be estimated from the distribution of aspect offset for a sample of point sources with accurately known celestial. There is 68% of 70 sources imaged on ACIS-I have offsets smaller than ~0.4 aresec., There is $68\%$ of 70 sources imaged on ACIS-I have offsets smaller than $\sim0.4$ arcsec. We adopted this value as the astrometric uncertainty and added to the quoted positional errors (cf., We adopted this value as the astrometric uncertainty and added to the quoted positional errors (cf. Table 1) in quadrature for each coordinate., Table 1) in quadrature for each coordinate. For source #99. we have identified an optical counterpart at 0.39 arcsec away from its X-ray position.," For source 9, we have identified an optical counterpart at 0.39 arcsec away from its X-ray position." It has a magnitude of B=15.93 and R=14.69 which implies an X-ray-to-optical flux ratio to be fx/foy~107., It has a magnitude of $B=15.93$ and $R=14.69$ which implies an X-ray-to-optical flux ratio to be $f_{X}/f_{\rm opt}\sim10^{-3}$ . This ratio suggests source #99 is likely to be a field star which typically has a ratio fx/fo«0.3 (Maceacaro et al., This ratio suggests source 9 is likely to be a field star which typically has a ratio $f_{X}/f_{\rm opt}<0.3$ (Maccacaro et al. 1988)., 1988). ForCXOU195422.97-312902.1.. an optical counterpart with B=15.92 and R=14.43 ts consistent with its X-ray position.," For, an optical counterpart with $B=15.92$ and $R=14.43$ is consistent with its X-ray position." For this source the X-ray-to-optical flux ratio is at the level of ~107 which is in agreement with what is expected for a field star., For this source the X-ray-to-optical flux ratio is at the level of $\sim10^{-3}$ which is in agreement with what is expected for a field star. Wedo not find any optical counterpart for παπάCXOU195429., Wedo not find any optical counterpart for and. 824+312834.1.. Adopting the limiting magnitude in the USNO-B1.0 catalogue to be 21 (cf., Adopting the limiting magnitude in the USNO-B1.0 catalogue to be 21 (cf. Monet et al., Monet et al. 2003). the upper limit of. fy/fop Is found to be >0.1.," 2003), the upper limit of $f_{X}/f_{\rm opt}$ is found to be $>0.1$." This upper limit ts not particular constraining., This upper limit is not particular constraining. A deep optical observation is required to differentiate the nature of these two sources from the star with fy/fon<0.3 and active galactic nuclei with fy/fo<50 (Maccacaro et al., A deep optical observation is required to differentiate the nature of these two sources from the star with $f_{X}/f_{\rm opt}<0.3$ and active galactic nuclei with $f_{X}/f_{\rm opt}<50$ (Maccacaro et al. 1988: Stocke et al., 1988; Stocke et al. 1991)., 1991). We have performed a detailed spectro-imaging X-ray study of the supernova remnant wwith Chandra., We have performed a detailed spectro-imaging X-ray study of the supernova remnant with Chandra. Various properties ofG67.74+1.8.. including distance. age and explosion energy. are still poorly constrained.," Various properties of, including distance, age and explosion energy, are still poorly constrained." The type of the supernova and the nature of the progenitor are also unknown., The type of the supernova and the nature of the progenitor are also unknown. With the Chandra observation 1t became possible for the first time to shed some more detailed light on the X-ray emission nature of aand its centralpoint sources., With the Chandra observation it became possible for the first time to shed some more detailed light on the X-ray emission nature of and its centralpoint sources. The spectra of the remnants northern and southern rims can be described with a single temperature CIE model plus additional Gaussian components., The spectra of the remnants northern and southern rims can be described with a single temperature CIE model plus additional Gaussian components. Our analysis suggests a plasma temperatureof ~7x10° K., Our analysis suggests a plasma temperatureof $\sim7\times10^{6}~K$ . Assuming that the, Assuming that the "perturbations vary as eJ(*t-*). one can obtain (after some calculations) the following set of equations where I is the identity tensor, G-eyex— and ey is the unit wave vector assumed to be in the exeyXZ plane Bo=Boe, Wes=eD/m;, Ving and Va, are the background magnetic field, the gyropulsation, the thermal and the Alfvénn speeds of the particle 6, respectively.","perturbations vary as $e^{-j(\omega t-{\bf k\cdot r})}$, one can obtain (after some calculations) the following set of equations where where $\tens{I}$ is the identity tensor, $\tens{G}={\bf e_ye_x}-{\bf e_xe_y}$ and ${\bf e_k}$ is the unit wave vector assumed to be in the $XZ$ plane ${\bf B_0}=B_0{\bf e_z}$, ${\omega_c}_s=eB/m_s$, ${V_{th}}_s$ and ${V_A}_s$ are the background magnetic field, the gyropulsation, the thermal and the Alfvénn speeds of the particle $s$, respectively." " Regrouping equations (9--11)) we obtain the final equation which admits solutions only if Equation 12 yields the final dispersion equation of the reduced-two-fluid model where X—kpi, Y=ω/ωσι, pi—Vin;[Weis Di=>Vin,2 C= cosÜkp, Mei= and y=ye4-; is the total /VA?,polytropic index."," Regrouping equations \ref{eq9}- \ref{eq11}) ) we obtain the final equation which admits solutions only if Equation \ref{eq12} yields the final dispersion equation of the reduced-two-fluid model where $X=k\rho_i$, $Y=\omega/\omega_{ci}$, $\rho_i=V_{th_{i}}/\omega_{ci}$, $\beta_i={V_{th_{i}}}^2/{V_A}^2$ , $c=\cos \theta_{\bf k B}$ , $\mu_{ei}=m_e/m_i$ and $\gamma=\gamma_e+\gamma_i$ is the total polytropic index." The Me/m;solutions of equations are plotted in Figs. 1-, The solutions of equations \ref{eqdisp} are plotted in Figs. \ref{bif_apj}- -2 in low and high 5; plasmas for the given angles of propagation and SW parameters., \ref{bif_log_apj} in low and high $\beta_i$ plasmas for the given angles of propagation and SW parameters. " At low frequencies (w« we found that the slow magnetosonic mode in both wi)low and high ϐ has an asymptotic frequency At high frequencies (w> both hot and cold plasmas have two modes with differentw,;) asymptotes.", At low frequencies $\omega<\omega_{ci}$ ) we found that the slow magnetosonic mode in both low and high $\beta$ has an asymptotic frequency At high frequencies $\omega>\omega_{ci}$ ) both hot and cold plasmas have two modes with different asymptotes. Fig., Fig. 2 shows a similar dispersion curve inlog-log scale., \ref{bif_log_apj} shows a similar dispersion curve inlog-log scale. One can see that the first mode is connected at low frequency, One can see that the first mode is connected at low frequency <10IAL.yy| for aa;=Od.,$\lesssim 10^{-4} \msunyr$ for $\alpha_M = 0.1$. Outbursts are trigeere at rc9110 AU for protostelhu iufall rates —10OALvr b, Outbursts are triggered at $r \sim 1-10$ AU for protostellar infall rates $\sim 10^{-5} - 10^{-6} \msunyr$ . " The outbursts are stronger ik shorter with larger aa, or Έλι", The outbursts are stronger and shorter with larger $\alpha_{M}$ or $_{M}$. The total mass accretec during one outburst mainly depends ou Tay., The total mass accreted during one outburst mainly depends on $_{M}$. " While the outbursts are sliehtlv shorter for more massive centra stars. the outburst M is nearly iudepeudoeut of centra star πάσα,"," While the outbursts are slightly shorter for more massive central stars, the outburst $\dot{M}$ is nearly independent of central star mass." The active laver surface deusitv ouly affects the mass accretion rate inthe low state: it has little effect ou the outhurst., The active layer surface density only affects the mass accretion rate the low state; it has little effect on the outburst. " By comparing with the mass accretion rate aud duration ofobserved FU Orionis events. we cau coustrain a combination of aa, aud Taj."," By comparing with the mass accretion rate and duration observed FU Orionis events, we can constrain a combination of $\alpha_{M}$ and $_{M}$." If aay is low (0.01). Ta; needs to be high (1800 Is. hieher than the dust sublimation temperature): if oa; is high (0.1) then Pay needs to be low (<1 100 Ts).," If $\alpha_{M}$ is low (0.01), $_{M}$ needs to be high (1800 K, higher than the dust sublimation temperature); if $\alpha_M$ is high (0.1) then $T_M$ needs to be low $\lesssim$ 1400 K)." Our results show that 1-D. two zone models can capture the basic features of disk evolution. given our assunptious about the action of the MBRI aud GI.," Our results show that 1-D, two zone models can capture the basic features of disk evolution, given our assumptions about the action of the MRI and GI." Iu a later paper we will address disk evolution over a much longer timescale. explicitly taking iuto account lass infall from a rotating protostellar cloud.," In a later paper we will address disk evolution over a much longer timescale, explicitly taking into account mass infall from a rotating protostellar cloud." This work was supported iu part by NASA erant NNNUOSAT139€. bv the Univerütv of Michigan. by a Sony Faculty Fellowship. a Richard aud Margaret Romano Professorial Scholarship. aud ai University Scholar appointment to Charles Camu.," This work was supported in part by NASA grant NNX08A139G, by the University of Michigan, by a Sony Faculty Fellowship, a Richard and Margaret Romano Professorial Scholarship, and a University Scholar appointment to Charles Gammie." By assundug a mareinally eravitationally stable (Q=1.5) disk. the disks structure is determined with a eiven AL. aud thus the radius where the outburst is triggered (Bo iu Fig.," By assuming a marginally gravitationally stable (Q=1.5) disk, the disk's structure is determined with a given $\dot{M}$, and thus the radius where the outburst is triggered $_{Q}$ in Fig." aud Z2009a) cau be derived., and Z2009a) can be derived. Uulike Z2009awhere the detailed vertical structure is calculated umuerically to give Bo. here we give simple analytical results for Rey by asstune the disk is vertically isothermal with coustant opacity at a given radius.," Unlike Z2009awhere the detailed vertical structure is calculated numerically to give $_{Q}$, here we give simple analytical results for $_{Q}$ by assuming the disk is vertically isothermal with constant opacity at a given radius." " First. if h=CTη) the relationship between X aud the ceutral (uidplauc) teiiperature T. is given by Using the form for & aud usiugp,—X/2/I. where Lis the disk scale height. or equivalently where © is the augular velocity at B. & is the Doltzinuaun constant and my is the unit molecular mass."," First, if $\kappa$ $^{\alpha}$ $^{\beta}$, the relationship between $\Sigma$ and the central (midplane) temperature $_{c}$ is given by Using the form for $\kappa$ and $\rho_{c}$ $\Sigma/2H$, where H is the disk scale height, or equivalently where $\Omega$ is the angular velocity at R, $k$ is the Boltzmann constant and $_{H}$ is the unit molecular mass." " Then with Q-2c,0/2zGYX. and inserting equation (3)) iuto Q to derive the relationship between R aud T; at a e¢iven © and AL The dust opacity fitting from Z2009a suggests. at TX1100 IX, a 0.738. 3—0 and C=0.053."," Then with $_{s}$$\Omega$ $\pi$ $\Sigma$, and inserting equation ) into Q to derive the relationship between R and $T_{c}$ at a given Q and $\dot{M}$ The dust opacity fitting from Z2009a suggests, at $\lesssim 1400$ K, $\alpha$ =0.738, $\beta$ =0 and C=0.053." If we plot the relationship between R aud AL by eiven T2 T3; 21100 IK aud Q-1.5. we find which correspouds well with the Ro calculated in Figure δ.," If we plot the relationship between R and $\dot{M}$ by given $_{c}$ $_{M}$ =1400 K and Q=1.5, we find which corresponds well with the $_{Q}$ calculated in Figure ." ", Since Πωλ”9 for Τη =1LOO TS case. the outburst timescale is roughly ↖↖⇁↕∐∖↥⋅↸∖↗∕↕↴∖↴↸⊳⋜↧↕↸⊳∏↕⋜↧↑↸∖≺↧↕≯∪↥⋅⊺↙∶⊺↼∖∣∶⊔∩∩↕↘⊽∙↕≻↿∐⋅↕∐∶↴∙⊾⋯↕⊓∏∐∷∖↴↑∙∐∪↖↖⇁↸∖↖↽↸∖↥⋅∙⊺↙≼⊳≺∏∏≺∏⋝↸∖↕∐∶↴⋁∐↸∖↥⋅↑∐⋜⋯↑↕∐∖⋀∖↕↕⊰↕⊓⋅↕∶↴⋁∶↴⋁↸∖↥⋅ ↑↸∖∐∏⋉∖↥⋅⋜↧⊓∐⋅↸∖⊺↼∖∣∙↸∖↴∖↴↻↸∖↸⊳↕⋜↧∐⋅↖↽↕∐↑∐↸∖↕∐∐↸∖↥"," Since $_{Q}$$\propto$$\dot{M}^{2/9}$ for $T_{M}$ =1400 K case, the outburst timescale is roughly where $\nu$ is calculated for $_{c}$ $_{M}$ =1400 K. During outburst, however, $_{c}$ could be higher than the MRI trigger temperature $_{M}$ , especially in the inner part of the disk." ⋅↻⋜∐⋅↑∪↕≯↑∐↸∖≼∐∖↴↘↽∙ ↕↕≯↖↖⇁↸∖↕≯↿∐⋅↑∐↸∖↥⋅⋜↧↴∖↴↴∖↴⋯⊔↸∖↑∐↸∖∪∏⊓∏∐⋅↴∖↴↑⋀∐∿⊼∕∑∪⊽↿⋟≺↘≻⋝⇈∐↕↴∖↴↕↴∖↴↑∐↸∖↴∖↴↑↸∖⋜∥↧⋅↖↽⋜↧↸⊳↸⊳↥⋅↸∖↑↕∪∐≺∐∖↴↘↽↴∖↴∪↕∏↑↕∪∐↖↖↽↕∐↸⊳∐⋯⋜↧⋅↖↽∐∪↑↴⋝↸∖⊓⋅⋯∖↕∐ the time-dependent case).we find," If we further assume the outburst $\dot{M}\sim\nu\Sigma(R_{Q})$ (this is the steady accretion disk solution which may not be true in the time-dependent case),we find" large. probably close to IKeplerianu.,"large, probably close to Keplerian." " Since (subject to the above caveats) we do not fiud lear perturbations to condeise out of hot galactic eas, we turn to the question of why the sunulatious of Ikaufinaun (2006) ane Sonuucr-Larsen (2006) did."," Since (subject to the above caveats) we do not find linear perturbations to condense out of hot galactic gas, we turn to the question of why the simulations of Kaufmann (2006) and Sommer-Larsen (2006) did." The eutropx profiles of these ΤΗ caleulatious are nof eivon. so it is cifficuIt to know if they are sienificautly flatter than we adoot here. but cosmological collapse simulations ecucrally produce reasonably steep eutropv profiles.," The entropy profiles of these SPH calculations are not given, so it is difficult to know if they are significantly flatter than we adopt here, but cosmological collapse simulations generally produce reasonably steep entropy profiles." " The Sonuuer-Larseun siuulation was cosmological, and so did inclue filamentary flows. aud so the perturbations might be seeded by these fows (awe address this possibility iu more detail iu the next section}: however. both sets of authors argue that the condensation is coming from the hot eas. aud Ikaufiuauu (2006) in particular sugeest that the seeds are relatively small fluctuations arising frou particle noise."," The Sommer-Larsen simulation was cosmological, and so did include filamentary flows, and so the perturbations might be seeded by these flows (we address this possibility in more detail in the next section); however, both sets of authors argue that the condensation is coming from the hot gas, and Kaufmann (2006) in particular suggest that the seeds are relatively small fluctuations arising from particle noise." Based on the simulations here. we do not expect such fluctuations to cool.," Based on the simulations here, we do not expect such fluctuations to cool." One other possible reason for this discrepancy is resolution the sunulatious iu this paper have significantly better resolution (several pc) than that in the cosmological ruus (typically several huudred pe)., One other possible reason for this discrepancy is resolution – the simulations in this paper have significantly better resolution (several pc) than that in the cosmological runs (typically several hundred pc). Another possible explanation is the difficulty that SPI codes have resolving Welvin IHehuholtz iustabiltiües Aecertz (2007) found that dense clumps moving through a diffuse background were artificially stabilized bv particle effects at the boundary., Another possible explanation is the difficulty that SPH codes have resolving Kelvin Helmholtz instabiltiies -- Agertz (2007) found that dense clumps moving through a diffuse background were artificially stabilized by particle effects at the boundary. This prestunably could help explain why slishtlv overdense clouds were uot disrupted. aud may act to suppress the oscillations that stabilize Lucar overdeusitics.," This presumably could help explain why slightly overdense clouds were not disrupted, and may act to suppress the oscillations that stabilize linear overdensities." We tuu now to the evolution of nonlinear clouds initial perturbations which are well out of the linear reginae., We turn now to the evolution of nonlinear clouds – initial perturbations which are well out of the linear regime. These might be due to particularly large perturbations from dark matter halos. or. more likely. from iuflowiug fibuneutarv eas.," These might be due to particularly large perturbations from dark matter halos, or, more likely, from inflowing filamentary gas." In particular. the low-teiiperature cud of the Wari Tot Lonized Medium at ~10 K (WILL eg Davé et al.," In particular, the low-temperature end of the Warm Hot Ionized Medium at $\sim10^5$ K (WHIM; e.g. Davé et al." 2001) will have overdeusities of order 5-30 when flowing iuto the hot halo., 2001) will have overdensities of order 5-30 when flowing into the hot halo. This material is sufficiently overdeuse that it escapes sieuificaut heating by the virial accretion shock., This material is sufficiently overdense that it escapes significant heating by the virial accretion shock. Clips of this eas might then cool and accrete onto the disk. providing fuel for star formation.," Clumps of this gas might then cool and accrete onto the disk, providing fuel for star formation." We find that overdensitics can cool significantly. provided they meet the criteria that the ratio of the cooling to acceleration time is below about 1 (see Fig. 9)).," We find that overdensities can cool significantly, provided they meet the criteria that the ratio of the cooling to acceleration time is below about 1 (see Fig. \ref{time_ratio}) )." This generally cutails substautial overdeusities aud/or low initial cloud heights (siuce the cooling time drops faster than the acceleration time with decreasing height)., This generally entails substantial overdensities and/or low initial cloud heights (since the cooling time drops faster than the acceleration time with decreasing height). For accretion of WIITM-like eas in filameuts at distances around LO kpc. as suggested by dFEeres ILleruquis (2009). Figures 3. and 9 indicate that overdeusities of about 10 are required.," For accretion of WHIM-like gas in filaments at distances around 40 kpc, as suggested by Kereš Hernquist (2009), Figures \ref{timescale} and \ref{time_ratio} indicate that overdensities of about 10 are required." The overdeusities iu the fliuneu in that paper appear to be similar to this value. therefore we conclude that this mechanisin for nonlinear seceding of cooling instabilities may be a viable wav to produce cok halo gas.," The overdensities in the filament in that paper appear to be similar to this value, therefore we conclude that this mechanism for nonlinear seeding of cooling instabilities may be a viable way to produce cold halo gas." This is oue ofthe key results of this paper., This is one of the key results of this paper. We also note that we monitored the material cooling anc find that the suvouucdiue hot halo medinu docs not coo along with the overdensity., We also note that we monitored the material cooling and find that the surrounding hot halo medium does not cool along with the overdensity. The clouds modeled here are initially nost similar in temperature to the absorbers detected with ultraviolet spectrograplis (~10° K: Thom Chen 200s: Tripp et al., The clouds modeled here are initially most similar in temperature to the absorbers detected with ultraviolet spectrographs $\sim$ $^5$ K; Thom Chen 2008; Tripp et al. 2008: Prochaska et al., 2008; Prochaska et al. 2011: Naravanan ct al., 2011; Narayanan et al. 2011)., 2011). The sample of absorbers remains somewhat nuited. with detections thus far largely bevoud. 100 spc (in projection) fro the nearest galaxy.," The sample of absorbers remains somewhat limited, with detections thus far largely beyond 100 kpc (in projection) from the nearest galaxy." For most svstenis it remains somewhat unclear if the absorbers are arising roni collisional or photo-ionization., For most systems it remains somewhat unclear if the absorbers are arising from collisional or photo-ionization. Receutly there has οσο a detection of an absorber at 2=0.35 only S5 κής aud 95 kpe in projection from a galaxy that is ound to be a plotoionized structure with a leneth scale £01 L2AIpeandlog ay=Lito L9 (Thom ct al., Recently there has been a detection of an absorber at $z=0.35$ only 85 km/s and 95 kpc in projection from a galaxy that is found to be a photoionized structure with a length scale $L \approx$ 0.1–1.2 Mpc and log $n_{\rm H} = -4.4$ to $-4.9$ (Thom et al. 2011)., 2011). Thisdensity is typical of the densities estimated ‘or other potentially photoiouized absorbers (log mp=τος S: Thom Chen 2008: Prochaska et. al., Thisdensity is typical of the densities estimated for other potentially photoionized absorbers (log $n_{\rm H} = -4$ to $< -5$; Thom Chen 2008; Prochaska et al. 2011)., 2011). Based ou our results. these types of low deusity structures may have difficulty being able to cool.," Based on our results, these types of low density structures may have difficulty being able to cool." For M10 IS dows from the IGM to play a substantial role in feeding galaxy halos cold gas. we would expect the future absorbers detected by COS to be fouud closer to galaxies and with somewhat higher overdeusities.," For $\sim$ $^5$ K flows from the IGM to play a substantial role in feeding galaxy halos cold gas, we would expect the future absorbers detected by COS to be found closer to galaxies and with somewhat higher overdensities." Our results may also have implications on the cooling of warmer clouds traced by Lyra aud absorption line systems. but further simulations with initial cloud conditions more siuiar to these should be completed before definitive statements can be mado.," Our results may also have implications on the cooling of warmer clouds traced by $\alpha$ and absorption line systems, but further simulations with initial cloud conditions more similar to these should be completed before definitive statements can be made." " For those clouds that do cool before disrupting. they usually reach a ininiuun temperature around 101 K (although iu some cases Z,,5,<107 K) and continue to accelerate."," For those clouds that do cool before disrupting, they usually reach a minimum temperature around $10^4$ K (although in some cases $T_{min} < 10^3$ K) and continue to accelerate." They eventually reach large velocities. and are subject to dynamical instabilitics which. in our sinulations. quickly shred the clouds.," They eventually reach large velocities, and are subject to dynamical instabilities which, in our simulations, quickly shred the clouds." This cau be secu in the las wanel in Fie. 5..," This can be seen in the last panel in Fig. \ref{seq_cool}," where the cloud has been dispersed aud the averaged specific eutropv starts to erow with time., where the cloud has been dispersed and the averaged specific entropy starts to grow with time. This occurs after the cloud has travelled ouly about 10 kpe. and so occurs before it hits the disk.," This occurs after the cloud has travelled only about 10 kpc, and so occurs before it hits the disk." This is in agreement with ITeitsch Putian (2009). who also find (for sinular cloud masses). a nuiaxinmua distauce vefore disruption of about 10 kpc.," This is in agreement with Heitsch Putman (2009), who also find (for similar cloud masses), a maximum distance before disruption of about 10 kpc." This secs to imply hat even if the cloud cools. it will not be able to fuel the disk with cold eas. aud will mstead simply add to the rot halo.," This seems to imply that even if the cloud cools, it will not be able to fuel the disk with cold gas, and will instead simply add to the hot halo." The cloud mass determines whether or not the cloud will be disrupted before it reaches the midplane. which akes roughly a dynamical time.," The cloud mass determines whether or not the cloud will be disrupted before it reaches the midplane, which takes roughly a dynamical time." The lager the mass. he longer the disruption leneth. aud so we suspect that clouds with even larger masses (than the maxima value of 2.07«LO? AL. in our models) will travel further. although this has not specifically been tested.," The larger the mass, the longer the disruption length, and so we suspect that clouds with even larger masses (than the maximum value of $2.07 \times 10^5$ $_\odot$ in our models) will travel further, although this has not specifically been tested." In heres Ieruquist. the typical cloud masses were about 10 AL... however this may be largely due to their resolution limitations.," In Kereš Hernquist, the typical cloud masses were about $10^6$ $_\odot$, however this may be largely due to their resolution limitations." In auy case. it would be interesting to further investigate the survival of such huge clouds im future work as our results indicate the direct accretion of gas to the disk from cold flows or stripped satellite eas at large radii may be dificult despite the initial ability for chuups to cool.," In any case, it would be interesting to further investigate the survival of such large clouds in future work as our results indicate the direct accretion of gas to the disk from cold flows or stripped satellite gas at large radii may be difficult despite the initial ability for clumps to cool." " Finally, we note that there is au interesting regine where the cooling time is shorter than the D-V or the acceleration time but longer than the dvuamical time."," Finally, we note that there is an interesting regime where the cooling time is shorter than the B-V or the acceleration time but longer than the dynamical time." Tn this case. the gas will start to cool but will impact the disk before it can cool siguificautlv. aud so will be accreted as war eas.," In this case, the gas will start to cool but will impact the disk before it can cool significantly, and so will be accreted as warm gas." Such inflowing gas will escape observations aud instead appear as au ionized coumponcut with uceative velocities (c.¢.. HTaffuer et al.," Such inflowing gas will escape observations and instead appear as an ionized component with negative velocities (e.g., Haffner et al." 2003)., 2003). For au, For an electron density. caleulated from the II660. line in NGC7538-IBSI.,electron density calculated from the $\alpha$ line in NGC7538-IRS1. This line is very much wider and out of character with the other measurements in our sample., This line is very much wider and out of character with the other measurements in our sample. Aside from this one exception. (he correlation of density. wilh observing frequency indicates that the higher frequency lines are associated wilh higher density gas.," Aside from this one exception, the correlation of density with observing frequency indicates that the higher frequency lines are associated with higher density gas." The line center velocities also increase (redshift) with Irequency. except for the lines of NGC7538-IRS1.," The line center velocities also increase (redshift) with frequency, except for the lines of NGC7538-IRS1." The combination of the (wo correlations. line center velocity with frequency. ancl line width with frequency was first noticed in W3(OII) by Berulis&Ershov(1983)...," The combination of the two correlations, line center velocity with frequency and line width with frequency was first noticed in W3(OH) by \citet{BerulisErshov1983}. ." Welch&(1987) and Wetoetal.(1995). interpreted the dual correlation as evidence for an accelerating flow within a densitv gradient (Guilloteattetal.1983)., \citet{WelchMarr1987} and \citet{Keto1995} interpreted the dual correlation as evidence for an accelerating flow within a density gradient \citep{Guilloteau1983}. .. A full explanation is given in Ketoetal.(1995) (see also Brocklehurst&Seaton (1972))jand can be summarized as follows: The peak intensitv of RRLs is proportional to the densitv. squared and inversely proportional to the line width., A full explanation is given in \citet{Keto1995} (see also \citet{BrocklehurstSeaton1972}) )and can be summarized as follows: The peak intensity of RRLs is proportional to the density squared and inversely proportional to the line width. Thus the peak intensity of optically thin high lrequency lines with negligible pressure broadening is proportional to the density. squared., Thus the peak intensity of optically thin high frequency lines with negligible pressure broadening is proportional to the density squared. The peak intensity of lower frequency lines is proportional to the first power of the density since the pressure broadened line width is itself proportional to density., The peak intensity of lower frequency lines is proportional to the first power of the density since the pressure broadened line width is itself proportional to density. Thus in spatially unresolved observations of gas with a density gradient. the higher frequeney RRLs are dominated by enussion from (he higher density gas while the lower frequency. RIVLs include contributions from both high and low density gas.," Thus in spatially unresolved observations of gas with a density gradient, the higher frequency RRLs are dominated by emission from the higher density gas while the lower frequency RRLs include contributions from both high and low density gas." An observed difference in velocity between the high and low lrequency lines thus indicates a difference in velocity between the high and low density gas., An observed difference in velocity between the high and low frequency lines thus indicates a difference in velocity between the high and low density gas. The correlation of velocities and width with frequency therefore indicates (hat in these IU] regions there is both a flow and a density gradient., The correlation of velocities and width with frequency therefore indicates that in these HII regions there is both a flow and a density gradient. The (wo are naturally related by the conservation of mass and the geometry of the flow., The two are naturally related by the conservation of mass and the geometry of the flow. In general. if the flow is either outward and divereing or inward and converging (hen conservation of mass requires (hal there be a clensily eradient except in the unique circumstance (hat (he variation of the flow speed exactly cancels the geometric divergence or convergence.," In general, if the flow is either outward and diverging or inward and converging then conservation of mass requires that there be a density gradient except in the unique circumstance that the variation of the flow speed exactly cancels the geometric divergence or convergence." We determined the spectral energy distirubutions (SEDs) of (he ILLI regions in our sample using our own millimeter and centimeter observations and data collected [rom the literature., We determined the spectral energy distrubutions (SEDs) of the HII regions in our sample using our own millimeter and centimeter observations and data collected from the literature. " We selected only those data with angular resolutions close to 1"" specifically excluding single dish observations.", We selected only those data with angular resolutions close to $^{\prime\prime}$ specifically excluding single dish observations. Most of the data for NGC7538-IRS1 and G45.074-0.14 are from Pratapet and Garayetal.(1986.table3).. respectively.," Most of the data for NGC7538-IRS1 and G45.07+0.14 are from \citet[][table 1]{Pratap1992} and \citet[][table 3]{Garay1986}, respectively." The rest of the observations are listed in table 6.., The rest of the observations are listed in table \ref{fluxdata}. Most of these data do not include estimated uncertainties., Most of these data do not include estimated uncertainties. However. the calibration of radio data is fairlystandard.," However, the calibration of radio data is fairlystandard." Maiy of the reported observations were made, Many of the reported observations were made al.,al. 1998)., 1998). " Thus, a more realistic disk should probably have a warmer outer disk."," Thus, a more realistic disk should probably have a warmer outer disk." It is unclear if this would encourage outward migration by reducing the likelihood of instability or discourage outward migration by overly puffing up the disk., It is unclear if this would encourage outward migration by reducing the likelihood of instability or discourage outward migration by overly puffing up the disk. This is an area for future study., This is an area for future study. Fig., Fig. 19 show the evolution of radiative run R2 in which Jupiter and Saturn start to accrete gas at the same time., \ref{fig:model_rad2} show the evolution of radiative run R2 in which Jupiter and Saturn start to accrete gas at the same time. " As it grows, Jupiter's outward migration due to the entropy-related corotation torque makes the planets converge, until their orbital period ratio reaches a minimum of ~1.25 at t~800 orbits (i.e., Saturn is interior to the 3:2 resonance)."," As it grows, Jupiter's outward migration due to the entropy-related corotation torque makes the planets converge, until their orbital period ratio reaches a minimum of $\sim 1.25$ at $t\sim 800$ orbits (i.e., Saturn is interior to the 3:2 resonance)." " Once it has accreted enough gas to cancel the effect of the corotation torque, Jupiter migrates inward again, resulting in a divergent migration which continues until the planets become locked in the 3:2 resonance."," Once it has accreted enough gas to cancel the effect of the corotation torque, Jupiter migrates inward again, resulting in a divergent migration which continues until the planets become locked in the 3:2 resonance." Outward migration of Jupiter and Saturn is then triggered and appears to be maintained until the simulation was stopped after 10 orbits., Outward migration of Jupiter and Saturn is then triggered and appears to be maintained until the simulation was stopped after $10^4$ orbits. " Compared with the isothermal disk, Saturn's eccentricity is significantly higher although its behavior is steady and not obviously chaotic as in run R1."," Compared with the isothermal disk, Saturn's eccentricity is significantly higher although its behavior is steady and not obviously chaotic as in run R1." We do not know if this outward migration will continue indefinitely or whether the system might be subject to an instability similar to run R1., We do not know if this outward migration will continue indefinitely or whether the system might be subject to an instability similar to run R1. " Thus, simulations R1 and R2 demonstrate that periods of outward migration of Jupiter and Saturn in radiative disks are viable."," Thus, simulations R1 and R2 demonstrate that periods of outward migration of Jupiter and Saturn in radiative disks are viable." " However, only one of two simulations produced clear two-phase migration."," However, only one of two simulations produced a clear two-phase migration." " Given the limitations in our simulationsa (especially with regards to the thermal state of the outer disk), we do not know whether a two-phase migration of Jupiter and Saturn is a likely outcome in radiative disks."," Given the limitations in our simulations (especially with regards to the thermal state of the outer disk), we do not know whether a two-phase migration of Jupiter and Saturn is a likely outcome in radiative disks." " Indeed, these radiative simulations were performed assuming that the radius R=1 in the computational domain corresponds to 5 AU."," Indeed, these radiative simulations were performed assuming that the radius $R=1$ in the computational domain corresponds to $5$ AU." " Contrary to isothermal runs, it is worth to note that results from radiative simulations can not be scaled to apply to different parameters."," Contrary to isothermal runs, it is worth to note that results from radiative simulations can not be scaled to apply to different parameters." " Unless the Grand Tack occured in the last stages of the disk's lifetime, our radiative calculations therefore probably underestimate the disk temperature at the location where Jupiter's migration reversed."," Unless the Grand Tack occured in the last stages of the disk's lifetime, our radiative calculations therefore probably underestimate the disk temperature at the location where Jupiter's migration reversed." We are currently working to test the outward migration mechanism of Masset Snellgrove (2001) in more realistic radiative disks under a range of physical conditions., We are currently working to test the outward migration mechanism of Masset Snellgrove (2001) in more realistic radiative disks under a range of physical conditions. Our results thus far show that a two-phase migration of Jupiter and Saturn is extremely robust in isothermal disks but is as-yet uncertain in radiative disks., Our results thus far show that a two-phase migration of Jupiter and Saturn is extremely robust in isothermal disks but is as-yet uncertain in radiative disks. " Protoplanetary disks can be considered to be isothermal if they are optically thin (i.e., if the optical depth r< 1) and radiative if they are optically thick (r> 1)."," Protoplanetary disks can be considered to be isothermal if they are optically thin (i.e., if the optical depth $\tau < 1$ ) and radiative if they are optically thick $\tau > 1$ )." But when in the Solar Nebula's history was it isothermal or radiative?, But when in the Solar Nebula's history was it isothermal or radiative? " To address this question we constructed a simple, 1- model of the viscously-evolving Solar Nebula."," To address this question we constructed a simple, 1-D model of the viscously-evolving Solar Nebula." The disk extended from 0.1 to 40 AU and initially contained 40 M; following an R! surface density profile., The disk extended from 0.1 to 40 AU and initially contained $40$ $M_J$ following an $R^{-1/2}$ surface density profile. " We adopted an α prescription for the disk's viscosity (Shakura Sunyaev 1973) and used the same value as in most of the hydro simulations, a=2x102."," We adopted an $\alpha$ prescription for the disk's viscosity (Shakura Sunyaev 1973) and used the same value as in most of the hydro simulations, $\alpha = 2\times 10^{-3}$." We solved the viscous diffusion for the surface density: and calculated the temperature using a simple radiative balance between the disk’s viscous heating and radiative cooling (as in Lyra et al 2010): where σ is the Stephan-Boltzmann constant and Q is the orbital frequency., We solved the viscous diffusion for the surface density: and calculated the temperature using a simple radiative balance between the disk's viscous heating and radiative cooling (as in Lyra et al 2010): where $\sigma$ is the Stephan-Boltzmann constant and $\Omega$ is the orbital frequency. " The effective optical depth to the disk midplane is represented by tf, which is defined as The optical depth is τ=κΣ/2."," The effective optical depth to the disk midplane is represented by $\tau_{eff}$, which is defined as The optical depth is $\tau = \kappa \Sigma /2$." We assume that the opacity κ is dominated by small grains and use the values from Bell Lin (1994)., We assume that the opacity $\kappa$ is dominated by small grains and use the values from Bell Lin (1994). Fig., Fig. 20 shows 8 Myr in the evolution of a representative Solar Nebula., \ref{fig:1dmodel} shows 8 Myr in the evolution of a representative Solar Nebula. As the disk viscously spreads its surface density decreases uniformly and the disk cools., As the disk viscously spreads its surface density decreases uniformly and the disk cools. The cooling is not uniform due to the large variations in opacity between different temperature regimes., The cooling is not uniform due to the large variations in opacity between different temperature regimes. " Similarly, the disk is initially optically thick in its inner 20 AU and optically thin farther out."," Similarly, the disk is initially optically thick in its inner 20 AU and optically thin farther out." " In time, the boundary between optically thick and thin moves inward but interior to 1 AU the disk remains optically thick throughout."," In time, the boundary between optically thick and thin moves inward but interior to 1 AU the disk remains optically thick throughout." " Because we have not included photo-evaporation, the disk's density continues to decrease but never to zero."," Because we have not included photo-evaporation, the disk's density continues to decrease but never to zero." " In reality, at some point we expect the disk to be completely removed by either photo-evaporation (Hollenbach et al 1994; Adams et al."," In reality, at some point we expect the disk to be completely removed by either photo-evaporation (Hollenbach et al 1994; Adams et al." was discovered in the carly 119808 by Seward. Hlarnden Lelfanc (1984) using data from the Einstein X-rav Observatory.,"was discovered in the early 1980s by Seward, Harnden Helfand (1984) using data from the Einstein X-ray Observatory." The pulsar is located inside the supernova renmunant SNR 0540.693 in the Large. Magellanic Cloud., The pulsar is located inside the supernova remnant SNR 0540–693 in the Large Magellanic Cloud. Lt has a short rotation period (~50 ms) and a rapid spindown with a characteristic age of only 1500. vr., It has a short rotation period $\sim$ 50 ms) and a rapid spindown with a characteristic age of only 1500 yr. The X-ray profile of the )ulsar consists of a single broad. profile which covers about half the pulse phase (2).., The X-ray profile of the pulsar consists of a single broad profile which covers about half the pulse phase \cite{pkh03}. Phe profile is not Gaussian in shape but appears to be double peaked and also contains structure on the rising and trailing edges., The profile is not Gaussian in shape but appears to be double peaked and also contains structure on the rising and trailing edges. The profile does not appear to evolve significantly [rom optical to hard. X-ravs., The profile does not appear to evolve significantly from optical to hard X-rays. This pulse shape is in contrast t¢» the high-cnerey emission from the Crab pulsar., This pulse shape is in contrast to the high-energy emission from the Crab pulsar. In the Cra» two sharp peaks with a separation of 0.4 pulse phase are sen at all energies.," In the Crab, two sharp peaks with a separation of 0.4 pulse phase are seen at all energies." The radio emission [roni went undetected: for a decade until Mancheser et al., The radio emission from went undetected for a decade until Manchester et al. discovered a broad. weak radio pulse at 064 Giz.," \nocite{mml+93} discovered a broad, weak radio pulse at 0.64 GHz." The lux density at that frequency is 0:4 mi)v and t1¢ pulse duty evcle is more than with the hint of a doude profile. similar to the profile seen at high energies.," The flux density at that frequency is 0.4 mJy and the pulse duty cycle is more than with the hint of a double profile, similar to the profile seen at high energies." Mancjester et al., Manchester et al. failed to detect the pulsar at either 1.4 or 0.44 Cillz.," \nocite{mml+93} failed to detect the pulsar at either 1.4 or 0.44 GHz." The pulsar was observed with the Parkes racio telescope in 2001 as part of a survey to detect. giant. pulses. from voung ancl millisecond pulsus., The pulsar was observed with the Parkes radio telescope in 2001 as part of a survey to detect giant pulses from young and millisecond pulsars. Single puses were detected with energy more than 1000 times that of the average pulse energy CJlohnston Romani 2003:: hereafter Paper D)., Single pulses were detected with energy more than 1000 times that of the average pulse energy (Johnston Romani \nocite{jr03}; hereafter Paper I). Such strong pulses. first seen in the Crab pulsar. are called “giant oulses and this wews their first. detection. from an extra-galactic pulsar.," Such strong pulses, first seen in the Crab pulsar, are called `giant pulses' and this was their first detection from an extra-galactic pulsar." “The' giant. pulses are scatter. broacdened. at 1.4 Cllz with an exponentia scattering time of 0.4 ms and lave an emission. bandwidth of at least 256 Mllz., The giant pulses are scatter broadened at 1.4 GHz with an exponential scattering time of 0.4 ms and have an emission bandwidth of at least 256 MHz. There is some evidence that the [lux density clistribution of the giant pulses is a power-law with a shallower index than seen or the Crab and 1SB 31937|21 (Paper D., There is some evidence that the flux density distribution of the giant pulses is a power-law with a shallower index than seen for the Crab and PSR B1937+21 (Paper I). In the Crab oulsar. PSR. 190212] and SR DIS21I24 the giant pulses are exactly in phase with the high energy. emission. which wovicles evidence tjw their emission may have a common origin (7)...," In the Crab pulsar, PSR B1937+21 and PSR B1821–24 the giant pulses are exactly in phase with the high energy emission which provides evidence that their emission may have a common origin \cite{rj01}." Anatempt was made o match the phases of the radio giant pulses with the X-ray profile for obtained with the tossi X-ray ‘Timine Explorer (RN’TE). however this was suject to Caveats concerning the absolute timine between the X-ray and the radio. and. as is shown later in tlis paper. was incorrect in Paper L In S hr of integration Johnston Romani (2003) failed to detect any integrale Hux density from the pulsar to a level of 18 pry. assuming a duty evele of1054.," An attempt was made to match the phases of the radio giant pulses with the X-ray profile for obtained with the Rossi X-ray Timing Explorer (RXTE), however this was subject to caveats concerning the absolute timing between the X-ray and the radio, and, as is shown later in this paper, was incorrect in Paper I. In 8 hr of integration Johnston Romani (2003) failed to detect any integrated flux density from the pulsar to a level of 13 $\mu$ Jy, assuming a duty cycle of." .. Phis implies the spectral index between 0.64 and 1.38 CGllz must be steeper than 14., This implies the spectral index between 0.64 and 1.38 GHz must be steeper than --4.4. ‘Timing of the |oulsar has been carried out in the X-ray band since its discoycory., Timing of the pulsar has been carried out in the X-ray band since its discovery. The two most recent papers dealing, The two most recent papers dealing with the observations. Hana Wlamer for supplying her unpublished 2dF data of ÀA3101. aud Bruce Peterson for the use of Mathams thesis data.,"with the observations, Ilana Klamer for supplying her unpublished 2dF data of A3104, and Bruce Peterson for the use of Mathams' thesis data." M. C.F. acknowledges the support of a NASA Space Grant Craduate Fellowship at the University of North Carolina-Chapel Wall., M. C. F. acknowledges the support of a NASA Space Grant Graduate Fellowship at the University of North Carolina-Chapel Hill. R. W. IT. acknowledges erant support from the Australian Research Council., R. W. H. acknowledges grant support from the Australian Research Council. M. J. IT. acknowledecs support through πας Cirant JOOL[369 aciuiulstered by the University of Tasmania., M. J. H. acknowledges support through IRGS Grant J0014369 administered by the University of Tasmania. A portion of this work was supported by NSF erants AST-9900720 aud AST-0106113 to the Universitv of North Carolina-Chapel Till., A portion of this work was supported by NSF grants AST-9900720 and AST-0406443 to the University of North Carolina-Chapel Hill. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Tustitute of Technology. under coutract with the National Aeronautics and Space Acuuinistration.," 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." oecause of broad. line. emission. from. polvevclic aromatic ivcdrocarbon (PAID) molecules (Dale et 22001).,because of broad line emission from polycyclic aromatic hydrocarbon (PAH) molecules (Dale et 2001). AX variety of models have been used. to describe the a-LR SEDs of clusty galaxies., A variety of models have been used to describe the far-IR SEDs of dusty galaxies. We compare four well-constrained descriptions with data for a variety of types of galaxy. and highlight the importance both of degeneracies »ween the parameters anc the need. to avoid baroque descriptions that require a greater number of paranictors han can be justified and [fixed bv existing data.," We compare four well-constrained descriptions with data for a variety of types of galaxy, and highlight the importance both of degeneracies between the parameters and the need to avoid baroque descriptions that require a greater number of parameters than can be justified and fixed by existing data." Using one uniform. self-consistent description. of the SED we discuss the accuracy of photometric redshifts that can be derived for high-redshift. galaxies based. on their observed colours. making assumptions concerning their SEDs.," Using one uniform, self-consistent description of the SED we discuss the accuracy of photometric redshifts that can be derived for high-redshift galaxies based on their observed colours, making assumptions concerning their SEDs." We describe in detail the cegeneracy between redshift and dust temperature when fitting photometric data for high-redshift ealaxies (Blain 1999b: Blain ct 22002). ancl cliscuss the prospects for breaking this degeneracy using information about absolute luminosity. obtained. from a luminositytemperature (L7). relation for clusty galaxies.," We describe in detail the degeneracy between redshift and dust temperature when fitting photometric data for high-redshift galaxies (Blain 1999b; Blain et 2002), and discuss the prospects for breaking this degeneracy using information about absolute luminosity, obtained from a luminosity--temperature ) relation for dusty galaxies." ;X narrow range of SEDs was included implicitly in recent. discussions of the prospects for determining mni photometric redshilts (LIughes et 22002: Arctxaga et wave:22003: Dunlop et 22003). which leads to encouraging results.," A narrow range of SEDs was included implicitly in recent discussions of the prospects for determining mm-wave photometric redshifts (Hughes et 2002; Aretxaga et 2003; Dunlop et 2003), which leads to encouraging results." We discuss existing. data on theLT relation (Dunne et 22000: Stanford et 22000: Dale ct al., We discuss existing data on the relation (Dunne et 2000; Stanford et 2000; Dale et al. 2001: Dale Lelou 2002: 22002: Aanard Blain 2003: Chapman ct al., 2001; Dale Helou 2002; 2002; Barnard Blain 2003; Chapman et al. 2003). which leads to a much less optimistic outlook for far-It/submim photometric redshifts.," 2003), which leads to a much less optimistic outlook for far-IR/submm photometric redshifts." Lhe observed. dispersion in theLT relation is the kev quantity that limits. the ellectiveness of the technique., The observed dispersion in the relation is the key quantity that limits the effectiveness of the technique. In Section 2 we describe four SED mioclels. and compare rem with a range of observed. galaxy SEDs.," In Section 2 we describe four SED models, and compare them with a range of observed galaxy SEDs." We highlight 16 consequences of errors in the fitted SEDs and theLY relation for determining photometric redshilts in Section L., We highlight the consequences of errors in the fitted SEDs and the relation for determining photometric redshifts in Section 3. Finally. in Section 4. we describe the requirements. for spectroscopic observations that will remove this uncertainty. and cleseribe the opportunities that much more detailed far-IR SEDs measured using from 2003 will provide for better understanding theLY relation and for determining [ar-Hi-based. photometric redshilts.," Finally, in Section 4, we describe the requirements for spectroscopic observations that will remove this uncertainty, and describe the opportunities that much more detailed far-IR SEDs measured using from 2003 will provide for better understanding the relation and for determining far-IR-based photometric redshifts." Various functions have been used to describe the quasi-blackbody far-HIt/submm: of the SEDs of cust. galaxies., Various functions have been used to describe the quasi-blackbody far-IR/submm of the SEDs of dusty galaxies. The parameters that define the SED generally disguise the inevitably complex &eometrical mix of dust. grains at different temperatures in the interstellar medium of these galaxies. which are often disturbed: anc interacting. and sometimes very Luminous.," The parameters that define the SED generally disguise the inevitably complex geometrical mix of dust grains at different temperatures in the interstellar medium of these galaxies, which are often disturbed and interacting, and sometimes very luminous." The [αὐ-11. emission is visible at different optical depths in both emitted and scattered raciation., The far-IR emission is visible at different optical depths in both emitted and scattered radiation. " The simplest SED description. is based on a. blackbocdvy spectrum D,xUuexptheKk)1] at a single temperature T. às a Function of frequency. v. modified by a frequencydependent emissivity funetion e»x£. where 3 is in the range |.2 (Llilelebrancl 1983)."," The simplest SED description is based on a blackbody spectrum $B_\nu \propto \nu^3 / [ \exp(h\nu/kT) - 1 ]$ at a single temperature $T$ , as a function of frequency $\nu$, modified by a frequency-dependent emissivity function $\epsilon_\nu \propto \nu^\beta$, where $\beta$ is in the range 1–2 (Hildebrand 1983)." This vields an SED function is Note that this function. has an exponential Wien dependence when vXALyh., This yields an SED function is Note that this function has an exponential Wien dependence when $\nu \gg kT/h$. Ht is necessary to modify this o à shallower form in order to agree with observed. SEDs (sce 11)., It is necessary to modify this to a shallower form in order to agree with observed SEDs (see 1). A straightforward way to counteract the mid-IR. Wien tail is to substitute à power-Iaw SED. f;xvmm at high frequencies. matching the power-law and. thermal unction (equation 1) with a smooth gradient at a frequency vo which requires the condition οαναν)=a to » salistieck.," A straightforward way to counteract the mid-IR Wien tail is to substitute a power-law SED, $f_\nu \propto \nu^{-\alpha}$ at high frequencies, matching the power-law and thermal function (equation 1) with a smooth gradient at a frequency $\nu'$ which requires the condition ${\rm d\,ln}f_\nu(\nu')/{\rm d\,ln}\nu' = -\alpha$ to be satisfied." Three parameters are requiredλα to describe the SED: T. 3 and a.," Three parameters are required to describe the SED: $T$, $\beta$ and $\alpha$ ." The dust temperature 7 determines the requeney of the SED peak. the emissivity index 2 fixes the xower-Imw. index of the SED in the RavleighJeans regime. and à sets the slope of the mid-Hi SED.," The dust temperature $T$ determines the frequency of the SED peak, the emissivity index $\beta$ fixes the power-law index of the SED in the Rayleigh–Jeans regime, and $\alpha$ sets the slope of the mid-IR SED." TFhis SED was used in the context of studving submim-wave galaxy evolution by Blain et ((19992). ancl has been used without the Wien correction to fit low-redshift SEDs by Dunne et ((2000).," This SED was used in the context of studying submm-wave galaxy evolution by Blain et (1999a), and has been used without the Wien correction to fit low-redshift SEDs by Dunne et (2000)." " An alternative ""optically thick’ functional form substitutes a more complex emissivity function. ενx1οκρ(νμα) ]. to describe the expected increase in the optical depth of cust emission at higher frequencies. leading to an SED function. This SED has been used by several authors. especially those dealing with the SEDs of galaxies and AGN at the highest redshifts (e.g. Benford et 11999: Isaak οἱ 22002) where the SED is probed close to its rest-frame peak."," An alternative `optically thick' functional form substitutes a more complex emissivity function, $\epsilon_\nu \propto [1 - \exp({\nu/\nu_0})^\beta]$ , to describe the expected increase in the optical depth of dust emission at higher frequencies, leading to an SED function, This SED has been used by several authors, especially those dealing with the SEDs of galaxies and AGN at the highest redshifts (e.g. Benford et 1999; Isaak et 2002) where the SED is probed close to its rest-frame peak." This SIED is identical to the Z a 3 form at long wavelengths. but tends to a pure blaekbody at frequencies ereater than Áo. as expected from an optically thick source.," This SED is identical to the $T$ $\alpha$ $\beta$ form at long wavelengths, but tends to a pure blackbody at frequencies greater than $\nu_0$ , as expected from an optically thick source." This function also requires a power-law to. temper the SED on the Wien tail. using the parameter a.," This function also requires a power-law to temper the SED on the Wien tail, using the parameter $\alpha$." Four SED parameters are thus required in this model: 7. 6 and 3 as before. plus vo.," Four SED parameters are thus required in this model: $T$ , $\alpha$ and $\beta$ as before, plus $\nu_0$." There is a strong clegeneracy between the value of vy and the values of Z7 and 3 (see 22.4)., There is a strong degeneracy between the value of $\nu_{\rm 0}$ and the values of $T$ and $\beta$ (see 2.4). llence. a reasonable value of vy that. corresponds. to a frequeney close to the 60- and 100-7; bands is usually assumed.," Hence, a reasonable value of $\nu_{\rm 0}$ that corresponds to a frequency close to the 60- and $\mu$ m bands is usually assumed." Including this frequenev-dependent opacity allows a more physical description of the SED. but the parameter vy ds cüllicult to determine unambiguously [rom available observed data.," Including this frequency-dependent opacity allows a more physical description of the SED, but the parameter $\nu_{\rm 0}$ is difficult to determine unambiguously from available observed data." Descriptions of the SED can include more than one dust emperature., Descriptions of the SED can include more than one dust temperature. Most. notably. these. include: models. based on radiative transfer caleulations. in which a continuous distribution of sources is assumed in some geometry. and he temperature distribution of the dust as a function of »osition is calculated self-consistently to build up an SED (Granato. Danese Franceschini 1996: Devriendtοἱ al.," Most notably, these include models based on radiative transfer calculations, in which a continuous distribution of sources is assumed in some geometry, and the temperature distribution of the dust as a function of position is calculated self-consistently to build up an SED (Granato, Danese Franceschini 1996; Devriendtet al." 1999: Efstathiou. Rowan-Robinson Siebenmorgen 2000).," 1999; Efstathiou, Rowan-Robinson Siebenmorgen 2000)." ote. however.that evenfor nearby. galaxies the spatial andspectral resolution available is insullicient to constrain the10 parameters required to describe this (ype of model even in the simplest spherical ecometry.," Note, however,that evenfor nearby galaxies the spatial andspectral resolution available is insufficient to constrain the$\sim 10$ parameters required to describe this type of model even in the simplest spherical geometry." When the sub-aresec, When the sub-arcsec function of mass in the four quartiles of environment.,function of mass in the four quartiles of environment. Figure 6 presents our results., Figure \ref{fig:fig5} presents our results. " From these plots, it is possible to see that for the sample ofred galaxies there is a mean reddening of (A(U—V)rest)=0.093+0.007 mag between the lowest (9.5 10.6), while for the the difference is smaller ((A(U—V),est)=0.047 40.009)."," From these plots, it is possible to see that for the sample of galaxies there is a mean reddening of $\left<\Delta(U-V)_{rest}\right>=0.093\pm0.007$ mag between the lowest $9.510.6$ ), while for the the difference is smaller $\left<\Delta(U-V)_{rest}\right>=0.047\pm0.009$ )." " Furthermore, in Fig."," Furthermore, in Fig." " 6 the mean of the color distribution shown in black, evaluated for the whole sample, shows that the slopes of the relation are similar in different The slopes Su of the relation found in the mass range of our sample, with mean values in the range 10«logio(M/Mo)<10.8, are reported in Table 4.."," \ref{fig:fig5} the mean of the color distribution shown in black, evaluated for the whole sample, shows that the slopes of the relation are similar in different The slopes $S_{M}$ of the relation found in the mass range of our sample, with mean values in the range $10=0.126\pm0.005$ for the sample. " The slopes found for the sample are a little shallower ((S.)=0.066+ 0.007), probably because the stricter color selection applied to obtain the sample reduces the range of variation in the (U—V)rest color."," The slopes found for the sample are a little shallower $\left=0.066\pm0.007$ ), probably because the stricter color selection applied to obtain the sample reduces the range of variation in the $(U-V)_{rest}$ color." " In the present study, we didn't correct our colors for redshift evolution."," In the present study, we didn't correct our colors for redshift evolution." " To verify that our results are not biased by this effect, we studied thered galaxies, since they are the most numerous sample, dividing them into four redshift bins, 0.1«z0.35, 0.95«z0.5, 0.5«z0.7, and 0.78.5$ kpc and half at $R<8.5$ kpc. (" c£.,cf. Fig., Fig. 5. and Fig. 1))., \ref{fig:colden} and Fig. \ref{fig:tomo}) ). In this section. we illustrate the differences among the results obtained with our reference mocel and those taking cilferent parameters. the aim being to understand the role plaved by these parameters in the evolution of a galactic fountain.," In this section, we illustrate the differences among the results obtained with our reference model and those taking different parameters, the aim being to understand the role played by these parameters in the evolution of a galactic fountain." In order to obtain a relatively large number of models. we have run them adopting a spatial resolution for the finest. eric (26 pc) which was worse than that adopted for the reference model (13 pc).," In order to obtain a relatively large number of models, we have run them adopting a spatial resolution for the finest grid (26 pc) which was worse than that adopted for the reference model (13 pc)." This latter model was also run with this coarser grid in order to make homogeneous comparisons., This latter model was also run with this coarser grid in order to make homogeneous comparisons. Although the results depend. on the adopted: spatial, Although the results depend on the adopted spatial (unpublished).,(unpublished). We illustrate this in Figure 3.. together with the allowed distance ranges from Walter (2001) and Kaplan et ((2002).," We illustrate this in Figure \ref{f:ism}, together with the allowed distance ranges from Walter (2001) and Kaplan et (2002)." " The value of Ny, estimated in this way at a distance of GOpe is an order of magnitude lower (han the X-ray measurement. but is in good agreement with the distance of 140pe derived by the latter authors."," The value of $N_H$ estimated in this way at a distance of 60pc is an order of magnitude lower than the X-ray measurement, but is in good agreement with the distance of 140pc derived by the latter authors." This distance would place oon the outskirts of the R CrA cloud using the cloud distance of Ixnude [log (1998) of e» 17Ope and within the cloud using the canonical cloud distance of ~130 pe., This distance would place on the outskirts of the R CrA cloud using the cloud distance of Knude g (1998) of $\sim 170$ pc and within the cloud using the canonical cloud distance of $\sim 130$ pc. In either case. wwotld likely lie in a region of relatively hieh ISM density (~1-10 *).," In either case, would likely lie in a region of relatively high ISM density $\sim 1$ -10 $^{-3}$ )." " While these estimates of Ny, are crucle and will smooth out. any small-scale ISAT inhomogeneities. the larger distance is easier to reconcile with the measured column."," While these estimates of $N_H$ are crude and will smooth out any small-scale ISM inhomogeneities, the larger distance is easier to reconcile with the measured column." The cloud distauce of Inude Hog (1993) then represents an upper Iimit to the distance ofJ1356., The cloud distance of Knude g (1998) then represents an upper limit to the distance of. 5—3154. Our results. combined with the recent analvsis of Ransom et ((2002). demonstrate a lack of pulsed features above a level of 2.7 unaccelerated search: {from the accelerated search of Ransom et al.)," Our results, combined with the recent analysis of Ransom et (2002), demonstrate a lack of pulsed features above a level of 2.7 (unaccelerated search; from the accelerated search of Ransom et al.)" ancl no unequivocal detection of spectral features., and no unequivocal detection of spectral features. This dearth of indices with which to restrict parameter space precludes an obvious answer to the problem of (he nature and origin ofJ1356., This dearth of indices with which to restrict parameter space precludes an obvious answer to the problem of the nature and origin of. "5—3754. The apparent lack of electron or proton resonance cvclotron. absorption suggests that magnetic field strengths in the ranges (1-7)xLO! and (0.2-1.3)x10!4 G are less likely. as discussed by Paerels οἱ ""n(2001) nfor RAJ 0720.4—3125 and by Burwily et ((2001). but. as emphasised by the nol ""excluded owing to possible difficulties in detecting the absorption features."," The apparent lack of electron or proton resonance cyclotron absorption suggests that magnetic field strengths in the ranges $7)\times 10^{10}$ and $1.3)\times 10^{14}$ G are less likely, as discussed by Paerels et (2001) for RXJ $-$ 3125 and by Burwitz et (2001), but, as emphasised by the latter, should not be excluded owing to possible difficulties in detecting the absorption features." Iideed. neutron stars with different levels of magnetic field up to LOY G have now been observed with high resolution X-ray. spectrometers and none have so [ar shown absorption features (hat are intrinsic to the stellar photosphere RRAJ 0720.4—3125.Paerels et al.," Indeed, neutron stars with different levels of magnetic field up to $10^{15}$ G have now been observed with high resolution X-ray spectrometers and none have so far shown absorption features that are intrinsic to the stellar photosphere RXJ $-$ 3125—Paerels et al." 2001: PSR OGS6+14Marshall Schulz 2002: VelaPavlov et 22001: and 4U 0142461.Juett et al., 2001; PSR 0656+14—Marshall Schulz 2002; Vela—Pavlov et 2001; and 4U 0142+61—Juett et al. 2002)., 2002). " Our derived angular size based on modelling of the LETGS spectra. km/100pc. is consistent. with that of Durwitz et ((2001). though the revised allowed distance range of 111-200 pe (kaplan et 22002). together with the distance upper limit constraint based on the Ro CraA cloud. Dij,<1.70. now implies a radiation radius in the range Ry= 3.8-8.2 km."," Our derived angular size based on modelling of the LETGS spectra, $R_\infty/D_{100}=4.12\pm 0.68$ km/100pc, is consistent with that of Burwitz et (2001), though the revised allowed distance range of 111-200 pc (Kaplan et 2002), together with the distance upper limit constraint based on the R CrA cloud, $D_{100}\leq 1.70$, now implies a radiation radius in the range $R_\infty=3.8$ -8.2 km." The hieh end of this range. corresponding to (the largest allowed," The high end of this range, corresponding to the largest allowed" of a possible differential effect which is sensitive to t1e observer line-of-sight and which would appear in observed distributions superimposed upon other effects whose origins may lie in the underlying distributions of SN Iu explosion properties.,of a possible differential effect which is sensitive to the observer line-of-sight and which would appear in observed distributions superimposed upon other effects whose origins may lie in the underlying distributions of SN Ia explosion properties. " As mentioned in Section 3.1.. the range of A, obained from the grid of models is very wide. spanning more than 1.55 mag."," As mentioned in Section \ref{sect:toy-models}, the range of $M_{\mbox{\scriptsize p}}$ obtained from the grid of models is very wide, spanning more than 1.5 mag." This illustrates that the effects. of a lop-sided Ni distribution could. in principle. be very significant at the precision level se by contemyorary observational data (e.g. in a sample of SNe for which bolcymetric peak magnitudes are available. as presented by 2.. the erro estimates typically correspond to 10 — [5 per cen in flux).," This illustrates that the effects of a lop-sided Ni distribution could, in principle, be very significant at the precision level set by contemporary observational data (e.g. in a sample of SNe for which bolometric peak magnitudes are available, as presented by \citealt{stritzinger05}, the error estimates typically correspond to 10 – 15 per cent in flux)." Tye scale of the effects is broadly comparable to those established for other models involving departures from sphericity., The scale of the effects is broadly comparable to those established for other models involving departures from sphericity. For exampe. 9? investigated some observational consequences of ellipsoidal SN ejecta and showed that for quite modest departures from spjericity (axis ratios in the range 0.9 to 1.2). one finds a viewing angle dependence of the peak brightness on the scale of tenths o a magnitude (see also ? and 1? for motivation of such a model in the context of spectropolarimetrie observations).," For example, \citet{hoeflich91} investigated some observational consequences of ellipsoidal SN ejecta and showed that for quite modest departures from sphericity (axis ratios in the range 0.9 to 1.2), one finds a viewing angle dependence of the peak brightness on the scale of tenths of a magnitude (see also \citealt{howell01} and \citealt{wang03} for motivation of such a model in the context of spectropolarimetric observations)." As one wouId expect. even greater angular variations — comparable to those obained here — can be obtained from ellipsoidal models with more exreme axis ratios (2)..," As one would expect, even greater angular variations – comparable to those obtained here – can be obtained from ellipsoidal models with more extreme axis ratios \citep{sim07}." " Similar scales of light curve angular dependence (up to ~0.25 mag) were also found by ? in a study of a SN model with a geometric ""hole"" in the ejecta and by 9 ina very recent study of a 2D GCD model."," Similar scales of light curve angular dependence (up to $\sim 0.25$ mag) were also found by \citet{kasen04} in a study of a SN model with a geometric “hole” in the ejecta and by \citet{kasen06c} in a very recent study of a 2D GCD model." " We note that the angular variation is so large that one can ikely rule out the more extreme models (models C. D and E) as being representative of typical SNe conditions — this follows rom the observed tightness of the correlation in the plot of bolometric flux versus recession velocity for nearby SNe Ia (the ""Hubble diagram: see e.g. 2))."," We note that the angular variation is so large that one can likely rule out the more extreme models (models C, D and E) as being representative of typical SNe conditions – this follows from the observed tightness of the correlation in the plot of bolometric flux versus recession velocity for nearby SNe Ia (the “Hubble diagram”; see e.g. \citealt{stritzinger05}) )." However. these models do show hat it is possible to arrange extreme geometries that could prodin substantial deviations from the mean and provide one possiple explanation for some apparently anomalous events (2).," However, these models do show that it is possible to arrange extreme geometries that could produce substantial deviations from the mean and provide one possible explanation for some apparently anomalous events \citep{hillebrandt07}." " Since both Ad, and /,, are simple funcions of he viewing angle (equations | and 2). it follows that there is an equally simdle relationship between these two quantities for a given model. as ean be seen in Figure 4.."," Since both $M_{\rm p}$ and $t_{\rm p}$ are simple functions of the viewing angle (equations 1 and 2), it follows that there is an equally simple relationship between these two quantities for a given model, as can be seen in Figure \ref{fig:toy-arnett}." " For the models with moderate to arge values of f (Models B — E». the points are all fairly close to ftdllowing he same line in the A7,.-/, plane."," For the models with moderate to large values of $f$ (Models B – E), the points are all fairly close to following the same line in the $M_{\rm p}$ $t_{\rm p}$ plane." " Thus. from these modes alone one might hope that combined measurements of both A, and ἐν could be used to extract the true luminosity despite the effect of viewing"," Thus, from these models alone one might hope that combined measurements of both $M_{\rm p}$ and $t_{\rm p}$ could be used to extract the true luminosity despite the effect of viewing" In Fie.,In Fig. 5 we show the heal capacity per unit volume as a [function οἱ temperature for various choices of {ει, 5 we show the heat capacity per unit volume as a function of temperature for various choices of $T_c$. For /«0 it depends on whether one approaches (he phase coexistence curve [rom (he low density side or (he high density side., For $t < 0$ it depends on whether one approaches the phase coexistence curve from the low density side or the high density side. For /20 it is computed at the critical density., For $t > 0$ it is computed at the critical density. When scaled by (he entropy density al the critical point. the result for />0 is independent of the choice of Z;.. whereas for /«0 it is almost but not «quite independent.," When scaled by the entropy density at the critical point, the result for $t > 0$ is independent of the choice of $T_c$, whereas for $t < 0$ it is almost but not quite independent." For reference. (he entropy density al the critical point is 1.741. 3.416. and 5.861 * for T. = GO. 100. ancl 140 MeV. respectively.," For reference, the entropy density at the critical point is 1.741, 3.416, and 5.861 $^{-3}$ for $T_c$ = 60, 100, and 140 MeV, respectively." similar mass already observed in the Pleiades. the Hyades (e.g. Sternetal.. 1995:; Micelaetal.. 1996)) and in thesample by Ng&Bertelli(1998). studied by Micela(2002a).,"similar mass already observed in the Pleiades, the Hyades (e.g. \citealp{ssk95}; ; \citealp{msk+96}) ) and in thesample by \cite{nb98} studied by \cite{micela02}." . The observed spread in Lx at a fixed age Is associated to the spread in rotational periods (Pizzolatoetal.. 2003)). which appears to depend on the coupling between the circumstellar disc and the star in the pre-main sequence phase: in some objects this coupling prevents a young star from spinning up during its PMS contraction. yielding a large spread in the initial angular momentum distribution (e.g. Bouvier.1994:: Chor&Herbst. 1996)).," The observed spread in $L_{\rm X}$ at a fixed age is associated to the spread in rotational periods \citealp{pmm+03}) ), which appears to depend on the coupling between the circumstellar disc and the star in the pre-main sequence phase; in some objects this coupling prevents a young star from spinning up during its PMS contraction, yielding a large spread in the initial angular momentum distribution (e.g. \citealp{bouvier94}; \citealp{ch96}) )." The analysis of ~ 500 pre-main sequence and recently arrived main-sequence stars by Herbst(2005) supports this view., The analysis of $\sim$ 500 pre-main sequence and recently arrived main-sequence stars by \cite{hm05} supports this view. The median X-ray luminosity of 1.3 «10°Serg for type stars in NGC 752 is in good agreement with the decayingisi trend of X-ray luminosity from the Hyades to the field stars., The median X-ray luminosity of 1.3 $ \times 10^{28}$ for solar-type stars in NGC 752 is in good agreement with the decaying trend of X-ray luminosity from the Hyades to the field stars. The value is about 6 times lower than the median value for the Hyades and 6.5 times higher than the median value from field stars. consistent with a steepening of the X-ray luminosity scaling law after the age of the Hyades.," The value is about 6 times lower than the median value for the Hyades and 6.5 times higher than the median value from field stars, consistent with a steepening of the X-ray luminosity scaling law after the age of the Hyades." In a study of nine solar-like G-stars with ages ranging from 70 Myr to 9 Gyr. Guedeletal.(1997) found Ly«£7 with 1.5. for stars with ages beyond afew 100 Myr. in agreement with the earlier results by Maggioetal.(1987).," In a study of nine solar-like G-stars with ages ranging from 70 Myr to 9 Gyr, \cite{ggs97} found $L_{\rm X} \propto t^{-\beta}$ with $\beta \sim 1.5$ , for stars with ages beyond a few 100 Myr, in agreement with the earlier results by \cite{msv+87}." . The study of a sample of 11 late-type stars 11 the Chandra Deep Field-North by Feigelsonetal.(2004) is also consistent with this scalingσι law. for 1«f11 Gyr. althotgh an excellent fit to their data is found forB=2.0.," The study of a sample of 11 late-type stars in the Chandra Deep Field-North by \cite{fhm+04} is also consistent with this scaling law, for $ 1 < t < 11$ Gyr, although an excellent fit to their data is found for $\beta=2.0$." Pace&Pasquint(2004) find evidence for avery steep decay of the chronospherie activity between 0.5 and 2 Gyr. their sample at ~2 Gyr consistingof seven stars.," \cite{pp04} find evidence for a very steep decay of the chromospheric activity between 0.5 and 2 Gyr, their sample at $\sim 2$ Gyr consistingof seven stars." Comparison of the median X-ray luminosity of NGC 752 with that of the Hyades is fully consistent with a sealing law with 6~1.5.," Comparison of the median X-ray luminosity of NGC 752 with that of the Hyades is fully consistent with a scaling law with $\beta \sim 1.5$." This scaling law is also consistent with the decay in X-ray luminosity from NGC 752 to the field stars. given the age uncertainties of the field stars.," This scaling law is also consistent with the decay in X-ray luminosity from NGC 752 to the field stars, given the age uncertainties of the field stars." " Since Lx=17, (e.g. Pallavicintetαἱ...1981: Pizzolatoetal.. 2003)). this result implies @~0.75 for the scaling law of rotational velocities. fort21 Gyr."," Since $L_{\rm X} \approx v_{\rm rot}^{2}$ (e.g. \citealp{pgr+81}; \citealp{pmm+03}) ), this result implies $\alpha \sim 0.75$ for the scaling law of rotational velocities, for $t \ga 1$ Gyr." This ts significantly steeper than found by Skumanich(1972) and would require a nearly-dipolar magnetic configuration to be explained in terms of magnetic breaking (Kawaler. 1988))., This is significantly steeper than found by \cite{skuma72} and would require a nearly-dipolar magnetic configuration to be explained in terms of magnetic breaking \citealp{kawaler88}) ). The effect of differential rotation in the stellar interior and the onset of magnetic saturation. however. may also play a role (Krishnamurthietal... 1997)) and it is possible that the coupling efficiency between outer and inner layers of stars weakens with age or that it 15 mass dependent (Barnes. 2003)).," The effect of differential rotation in the stellar interior and the onset of magnetic saturation, however, may also play a role \citealp{kpb+97}) ) and it is possible that the coupling efficiency between outer and inner layers of stars weakens with age or that it is mass dependent \citealp{barnes03}) )." Comparison of rotational velocities in the Pleiades with those in older clusters such as M34 and the Hyades shows that. within the age interval of the Pleiades and Hyades. a star’s rotational rate typically decreases less steeply than predicted by a pure magnetic braking law. that Is @<0.3 (Queloz 1998)).," Comparison of rotational velocities in the Pleiades with those in older clusters such as M34 and the Hyades shows that, within the age interval of the Pleiades and Hyades, a star's rotational rate typically decreases less steeply than predicted by a pure magnetic braking law, that is $\alpha < 0.3$ \citealp{qam+98}) )." The decay of the median Lx of stars with mass M=0.5--1.2Me from the Pleiades to the Hyades reported by Micela(2002a) (the points shown in reffig:Ixvage)) and that reported by for stars with M=0.9—1.2Mo for the same clusters. confirm this result (o« 0.25).," The decay of the median $L_{\rm X}$ of stars with mass $M=0.8-1.2~M_{\sun}$ from the Pleiades to the Hyades reported by \cite{micela02} (the points shown in \\ref{fig:lxvage}) ) and that reported by for stars with $M=0.9-1.2~M_{\sun}$ for the same clusters, confirm this result $\alpha < 0.25$ )." As discussed by Quelozetal.(1998).. a value of a<0.3 could be an indicatior that angular momentum tapped in the radiative core of slow rotators on the zero age main sequence resurfaces into the convective envelope betwee! the Pleiades and Hyades ages.," As discussed by \cite{qam+98}, a value of $\alpha < 0.3$ could be an indication that angular momentum tapped in the radiative core of slow rotators on the zero age main sequence resurfaces into the convective envelope between the Pleiades and Hyades ages." We know from helioseismology that there is no gradient between the angular velocities of the core and the envelope in the Sun. thus our data suggest a change in rotation regimes of the stellar interior at f~ | Gyr.," We know from helioseismology that there is no gradient between the angular velocities of the core and the envelope in the Sun, thus our data suggest a change in rotation regimes of the stellar interior at $t\sim $ 1 Gyr." The shape of the temporal evolution of the X-ray luminosity ο solar-mass stars also. has an important consequence in the evolution of close-in exoplanets — within 0.5 AU., The shape of the temporal evolution of the X-ray luminosity of solar-mass stars also has an important consequence in the evolution of close-in exoplanets $-$ within 0.5 AU. As shown by Penzetal.(2008 ).. the later the timing of the transition between the two scaling laws of Lx. the smaller the fraction of gaseous planets which at 4.5 Gyr retain most of their initial mass.," As shown by \cite{pml08}, , the later the timing of the transition between the two scaling laws of $L_{\rm X}$, the smaller the fraction of gaseous planets which at 4.5 Gyr retain most of their initial mass." Our result indicates this transition to be at around | Gyr., Our result indicates this transition to be at around 1 Gyr. evidence for a standard amount of energy release in GRBs. E~Were.,"evidence for a standard amount of energy release in GRBs, $E\sim 10^{51}{\rm \,erg}$." Making the simplest assuuptiou of a constant energv for all loue-diuration bursts (which are the only oues with measured redshifts so far). one can easily derive the buuiuositv functiou from the iufriusic distribution of burst durations.," Making the simplest assumption of a constant energy for all long-duration bursts (which are the only ones with measured redshifts so far), one can easily derive the luminosity function from the intrinsic distribution of burst durations." The luminosity of à burst is then siiply zET. aud the resulting luminosity function is obtained by inverting the horizontal axis in Figure [aud changing TZ to E/T.," The luminosity of a burst is then simply $\approx E/T$, and the resulting luminosity function is obtained by inverting the horizontal axis in Figure 4 and changing $T$ to $E/T$." The lone-duration bursts would thou narrowly cluster around a luuninosity of ~l0? re st., The long-duration bursts would then narrowly cluster around a luminosity of $\sim 10^{50}$ erg $^{-1}$. We have derived the redshift distribution of CRBs out to :z20 under the asstuption that the CRB eveut rate traces the cosmic star formation rate., We have derived the redshift distribution of GRBs out to $z\ga 20$ under the assumption that the GRB event rate traces the cosmic star formation rate. We find that z50% of all GRBs ou the sky originate from a redshift of 5 or higher., We find that $\ga 50$ of all GRBs on the sky originate from a redshift of 5 or higher. Ou the other haud. the fraction of barvous that have been incorporated iuto stars by 2~5 is much smaller. courprising only ~15% of the stellar lass formed by today.," On the other hand, the fraction of baryons that have been incorporated into stars by $z\sim 5$ is much smaller, comprising only $\sim 15$ of the stellar mass formed by today." The difference hetween the two fractious follows from the differcut cosmological factors in the redshift inteeratious for the statistics of transient events on the sky as compared to the ceusus of fossil objects iu the local universe., The difference between the two fractions follows from the different cosmological factors in the redshift integrations for the statistics of transient events on the sky as compared to the census of fossil objects in the local universe. The favorable statistical bias towards high-redshift events on the sky is expected to apply also to Type II supernova explosions which are related to the formation of massive stars in a similar wav as GRBs., The favorable statistical bias towards high-redshift events on the sky is expected to apply also to Type II supernova explosions which are related to the formation of massive stars in a similar way as GRBs. Despite their cdinmnunug with increasing redshift. highredshift supernovae will be detectable with sufficiently seusitive telescopes such as the (NGST: Miralda-Escudé Rees 1997: Woods Loeb 1998).," Despite their dimming with increasing redshift, high–redshift supernovae will be detectable with sufficiently sensitive telescopes such as the (NGST; Miralda-Escudé Rees 1997; Woods Loeb 1998)." Iu fact. our calculation implies that without auv additional bias (such as redshitt-dependent dust extinction) approximately half of all Type II supernovae detected by NOST will originate at iz5.," In fact, our calculation implies that without any additional bias (such as redshift-dependent dust extinction) approximately half of all Type II supernovae detected by NGST will originate at $z\ga 5$." Deep observations of high.redshift CRBs aud superuovae offer an ideal window into the earliest epoch of cosmic structure formation., Deep observations of high–redshift GRBs and supernovae offer an ideal window into the earliest epoch of cosmic structure formation. The lenethening of the duration of these transieuts bv a factor (1|2) niakes it casier for observers to monitor their lehtciurves., The lengthening of the duration of these transients by a factor $(1+z)$ makes it easier for observers to monitor their lightcurves. Differcut iustrmucuts mav find GRBs up to different redshifts. depending on their detection scusitivity aud the Helly uncertain CRB huninosity function (Schaefer et al.," Different instruments may find GRBs up to different redshifts, depending on their detection sensitivity and the highly uncertain GRB luminosity function (Schaefer et al." 2001: Schinidt 2001: Norris 2002)., 2001; Schmidt 2001; Norris 2002). A trigecr-biased way o imfer the redshift evolution of the CRB event rate is o colnpare the nuuber counts of CRBs with the same absolute (iutrinsic) Iunuinositv iu different redshift bius., A trigger-unbiased way to infer the redshift evolution of the GRB event rate is to compare the number counts of GRBs with the same absolute (intrinsic) luminosity in different redshift bins. " If ""ture observations of this type were to determine a mean redshift for the CRB distribution siguificautlv lower than he one predicted in this paper. then this would iucicate either that CRB formation at high + is substantially suppressed. or that GRBs originate from the coalescence of binaries with a time delav of a few Cir between the formation of a massive star aud the CRB event."," If future observations of this type were to determine a mean redshift for the GRB distribution significantly lower than the one predicted in this paper, then this would indicate either that GRB formation at high $z$ is substantially suppressed, or that GRBs originate from the coalescence of binaries with a time delay of a few Gyr between the formation of a massive star and the GRB event." " Recent observations indicate that a large fraction. —DU. of all well-localized GRBs lave no associated optical afterglow. and are classified as ""(opticallv) dark GRBs” (es Piro et al."," Recent observations indicate that a large fraction, $\sim 50$, of all well-localized GRBs have no associated optical afterglow, and are classified as “(optically) dark GRBs” (e.g., Piro et al." 2002)., 2002). According to our model. a substantial fraction of these dark bursts could originate from 2z6.," According to our model, a substantial fraction of these dark bursts could originate from $z\ga 6$." The intervening. partially neutral GAL would cficiently absorb the rest-frame UV afterglow that would otherwise have been redshifted iuto the optical baud.," The intervening, partially neutral IGM would efficiently absorb the rest-frame UV afterglow that would otherwise have been redshifted into the optical band." We thank Rennan Barkana. Jeremy Πο. Jonathan Mackey. Bolan Paczvisski aud Martin Rees for helpful discussious.," We thank Rennan Barkana, Jeremy Heyl, Jonathan Mackey, Bohdan Paczyńsski and Martin Rees for helpful discussions." " This work was supported in part bv NASA erants NAC οτος, 5-768. aud by NSF erants T.AST-0071019."," This work was supported in part by NASA grants NAG 5-7039, 5-7768, and by NSF grants AST-9900877, AST-0071019." of the peak-like reionization is very clear. in particular at 10«(200 from Fig. S..,"of the peak-like reionization is very clear, in particular at $10 < \ell <200$ from Fig. \ref{log1}. ." Figure 9 shows how important he peak-like reionization at των=500 could be for he distortion at higher multipole range of the polarization »ower spectrum., Figure \ref{log2} shows how important the peak-like reionization at $\zreio=500$ could be for the distortion at higher multipole range of the polarization power spectrum. In Fig., In Fig. LO we plot the Oy. function. the comparison between the model 4 and the standard. single reionization model at ziic6.," \ref{pldiff1} we plot the $D_{4,{\rm s}}$ function, the comparison between the model 4 and the standard single reionization model at $\zreio \simeq 6$." Fig., Fig. LL is the comparison ovtween the model 5 and the standard. single reionization model at τμ26., \ref{pldiff2} is the comparison between the model 5 and the standard single reionization model at $\zreio \simeq 6$. In. Table 2. we show the calculated ikelihood for the anisotropy and PLO correlation power spectra from the model 5 against those from. results (llinshawetal.2003:Ixogutct2003).," In Table 2, we show the calculated likelihood for the anisotropy and $TE$ correlation power spectra from the model 5 against those from results \cite{wmapdata1,wmapdata2}." .. They are close to he parameters from the moclel 4., They are close to the parameters from the model 4. Once again we would like to point out that all the »eculiarities. induced. by the extra. peak-like reionization rave localized. structure which appears at some fixed multipole range., Once again we would like to point out that all the peculiarities induced by the extra peak-like reionization have localized structure which appears at some fixed multipole range. These features can by tested by the »olarization measurements., These features can by tested by the polarization measurements. We have investigated the two-epochecl reionization models of the Universe., We have investigated the two-epoched reionization models of the Universe. The two-cpoched reionization can be induced. by the structure formation as described. in. Cen model (2002).. or caused by unknown sources of the energy injection (peak-like reionization) at relatively high redshifts 2oBO.," The two-epoched reionization can be induced by the structure formation as described in Cen model \shortcite{cen}, or caused by unknown sources of the energy injection (peak-like reionization) at relatively high redshifts $z>30$." We have shown that for the Cen model (2002). the and the mission would be able to detect the general shape of the ionization history for the two-epoched reionized plasma. which cdillers from the single reionization models at z213.6 or z26.," We have shown that for the Cen model \shortcite{cen} the and the mission would be able to detect the general shape of the ionization history for the two-epoched reionized plasma, which differs from the single reionization models at $z \simeq 13.6$ or $z \simeq 6$." However. any peculiarities of the ionization fraction of the matter inside the range 6<2 13.6. such as the decreasing of ionization. do not observed by the experiment due to the statistical significance from the cosmic variance ellect.," However, any peculiarities of the ionization fraction of the matter inside the range $6 < z <13.6$ , such as the decreasing of ionization, do not observed by the experiment due to the statistical significance from the cosmic variance effect." Phe peak-like reionization model. on the other hand. has some distinct features in the shape of ionization fraction. and of the polarization power spectrum. as well.," The peak-like reionization model, on the other hand, has some distinct features in the shape of ionization fraction, and of the polarization power spectrum as well." The most. pronounced. manifestation of the peak-like reionization model is the localized features in the polarization power spectrum which differs from the stancarcl single reionization mioclel., The most pronounced manifestation of the peak-like reionization model is the localized features in the polarization power spectrum which differs from the standard single reionization model. We reckon that. such kind of deviation from the standard. reionization model. in case of confirmation by the data. will be significant for investigation of unstable particles or any relic decaving during the ‘dark age’ of the Universe.," We reckon that such kind of deviation from the standard reionization model, in case of confirmation by the data, will be significant for investigation of unstable particles or any relic decaying during the `dark age' of the Universe." Note that in this paper we clo not consider the secondary anisotropies ancl polarization produced by the peak-like relonization at high redshifts., Note that in this paper we do not consider the secondary anisotropies and polarization produced by the peak-like reionization at high redshifts. These effects seem to. be important if we take into account the [act that the relaxation of the peculiar velocity of barvonic matter and dark matter ab loc200 is completed and we can have the analog of the Ostriker-Vishniak effect and the Doppler effect. but for specific shape of the ionization fraction.," These effects seem to be important if we take into account the fact that the relaxation of the peculiar velocity of baryonic matter and dark matter at $z \simeq 200$ is completed and we can have the analog of the Ostriker-Vishniak effect and the Doppler effect, but for specific shape of the ionization fraction." These ellects will be investigated in the next paper., These effects will be investigated in the next paper. This paper. is. supported in part by Danmarks CGrundforskningsfond through its support forthe establishment of the Theoretical Astrophysics Center., This paper is supported in part by Danmarks Grundforskningsfond through its support forthe establishment of the Theoretical Astrophysics Center. pressure. defined by equilibrium at 39.1 K (Fig.,"pressure, defined by equilibrium at 39.1 K (Fig." 6)., 6). Because it may be as thin as a few molecular layers. the surface film may not be visible in the near-IR spectra.," Because it may be as thin as a few molecular layers, the surface film may not be visible in the near-IR spectra." " The case for CH, is more complex.", The case for $_4$ is more complex. As previously realized (Cruikshank et al., As previously realized (Cruikshank et al. 1993. Yelle et al.," 1993, Yelle et al." 1995. Strobel and Summers 1995. Strobel et al.," 1995, Strobel and Summers 1995, Strobel et al." " 1996). the CH, atmospheric mixing ratio at the surface measured by Voyager (1.81077) is at least three orders of magnitude larger than expected for ideal mixture."," 1996), the $_4$ atmospheric mixing ratio at the surface measured by Voyager $\sim$ $\times$ $^{-4}$ ) is at least three orders of magnitude larger than expected for ideal mixture." " However. we note that it is also smaller. by a factor of ~6. than the ice CH,/N> mixing ratio. and as such does not agree with the detailed balancing model in its simplest form."," However, we note that it is also smaller, by a factor of $\sim$ 6, than the ice $_4$ $_2$ mixing ratio, and as such does not agree with the detailed balancing model in its simplest form." " Unlike CO. CH, is subject to atmospheric photolysis and mass separation. and its vapor pressure is more temperature-dependent."," Unlike CO, $_4$ is subject to atmospheric photolysis and mass separation, and its vapor pressure is more temperature-dependent." " This probably makes the surface/atmosphere abundance relationship for CH, complex and seasonally variable.", This probably makes the surface/atmosphere abundance relationship for $_4$ complex and seasonally variable. " In any case. the phase diagram of N»-CH, is not obviously consistent with the formation of a CH-rich solid solution veneer (Stansberry et al.."," In any case, the phase diagram of $_2$ $_4$ is not obviously consistent with the formation of a $_4$ -rich solid solution veneer (Stansberry et al.," 1996)., 1996). " In fact. explaining the range of observed CH, atmospheric abundance would require a CH, mole fraction in the surface film as high as 50-80 (Fig."," In fact, explaining the range of observed $_4$ atmospheric abundance would require a $_4$ mole fraction in the surface film as high as 50-80 (Fig." " 6). well beyond the solubility limit of CH, in No (Prokhvatilov and Yantsevich The formation of pure CH, ice grains. decoupled from the mixture and not influencing its sublimation (Stansberry et al."," 6), well beyond the solubility limit of $_4$ in $_2$ (Prokhvatilov and Yantsevich The formation of pure $_4$ ice grains, decoupled from the mixture and not influencing its sublimation (Stansberry et al." 1996. Spencer et al.," 1996, Spencer et al." 1997). further evolving into a lag deposit. may be a more plausible outcome.," 1997), further evolving into a lag deposit, may be a more plausible outcome." Using a Bond albedo of 0.85 (Triton’s polar cap) and an emissivity of 0.7-1. à reasonable subsolar temperature for these pure methane patches is 45-48 K. Applying the Stansberry et al. (," Using a Bond albedo of 0.85 (Triton's polar cap) and an emissivity of 0.7-1, a reasonable subsolar temperature for these pure methane patches is 45-48 K. Applying the Stansberry et al. (" 1996) Pluto model then indicates that methane patches covering 0.5-1 of Triton’s surface are sufficient to maintain à «ΧΙΟ atmospheric mixing ratio.,1996) Pluto model then indicates that methane patches covering 0.5-1 of Triton's surface are sufficient to maintain a $\sim$ $\times$ $^{-4}$ atmospheric mixing ratio. " Although there is no evidence for such patches in Triton’s near-IR spectrum. the methane longitudinal distribution of CH, ice is different from that of to and small areas of CH4-dominated ice. notably near 300° longitude. are not inconsistent with observations (Grundy et al."," Although there is no evidence for such patches in Triton's near-IR spectrum, the methane longitudinal distribution of $_4$ ice is different from that of $_2$, and small areas of $_4$ -dominated ice, notably near $^{\circ}$ longitude, are not inconsistent with observations (Grundy et al." 2010)., 2010). " In contrast. the existence of widespead pure methane ice is ruled out: therefore the emphasized fact that the Voyager-measured methane partial pressure was consistent with vapor pressure equilibrium of pure CH, ice at 38 K is probably coincidental."," In contrast, the existence of widespead pure methane ice is ruled out; therefore the emphasized fact that the Voyager-measured methane partial pressure was consistent with vapor pressure equilibrium of pure $_4$ ice at 38 K is probably coincidental." After the Voyager encounter. a variety of seasonal N» cycle models (see review in Yelle et al.," After the Voyager encounter, a variety of seasonal $_2$ cycle models (see review in Yelle et al." 1995) were explored to attempt explaining Triton’s visual appearance and the then measured surface pressure., 1995) were explored to attempt explaining Triton's visual appearance and the then measured surface pressure. These models. which essentially differed in the assumed ice and substrate albedos and thermal inertia. had limited success. leaving unanswered the simple question of where the ice is on Triton.," These models, which essentially differed in the assumed ice and substrate albedos and thermal inertia, had limited success, leaving unanswered the simple question of where the ice is on Triton." Yet. they made distinctive predictions as to the short-term evolution of Triton's atmosphere.," Yet, they made distinctive predictions as to the short-term evolution of Triton's atmosphere." High thermal inertia models predicted a pressure increase as Triton approached and passed Southern summer solstice in 2000 (Triton subsolar latitude moved from 45.5 S in 1989 to à maximum 50 S in 2000 and 47 S in 2009)., High thermal inertia models predicted a pressure increase as Triton approached and passed Southern summer solstice in 2000 (Triton subsolar latitude moved from 45.5 S in 1989 to a maximum 50 S in 2000 and 47 S in 2009). " This is a consequence of increased insolation on. and attendant sublimation of. the Southern polar cap (Spencer and Moore 1992, Forget et al."," This is a consequence of increased insolation on, and attendant sublimation of, the Southern polar cap (Spencer and Moore 1992, Forget et al." 2000)., 2000). " In contrast. ""dark frost models (Hansen and Paige 1992) or low thermal inertia models predicted a pressure decrease from ~1980 on. due to the exhaustion of the seasonal southern cap and re-condensation of N» on the invisible winter pole."," In contrast, “dark frost"" models (Hansen and Paige 1992) or low thermal inertia models predicted a pressure decrease from $\sim$ 1980 on, due to the exhaustion of the seasonal southern cap and re-condensation of $_2$ on the invisible winter pole." The discovery, The discovery From (he many observations of the two-point correlation function. both in its angular (e.g. Lidiman anc Peterson 1996. Maddox οἱ al.,"From the many observations of the two-point correlation function, both in its angular (e.g. Lidman and Peterson 1996, Maddox et al." 1990) and spatial (e.g. Ratcliffe et al., 1990) and spatial (e.g. Ratcliffe et al. 1998. Qiuriei et al.," 1998, Giuricin et al." 2001) form. it is now well established Chat galaxies are clustered out. to distances of at least 10. Alpe.," 2001) form, it is now well established that galaxies are clustered out to distances of at least 10 Mpc." In addition. numerous studies of the distribution of bright ealaxies (e.g. Dressler 1980) show that elliptical galaxies preferentially occur in regions of hieh ealaclic densitv whilst spiral galaxies dominate in the field.," In addition, numerous studies of the distribution of bright galaxies (e.g. Dressler 1980) show that elliptical galaxies preferentially occur in regions of high galactic density whilst spiral galaxies dominate in the field." These basic observations have led to a multitude of theoretical simulations to explain the observed clustering properties and morphological segregation (e.g. Daugh οἱ al., These basic observations have led to a multitude of theoretical simulations to explain the observed clustering properties and morphological segregation (e.g. Baugh et al. 1996)., 1996). A major implication of the majority of these models is that elliptical galaxies are lormecd from (he merger of many sub-chumps luring the early stages of the evolution of the Universe., A major implication of the majority of these models is that elliptical galaxies are formed from the merger of many sub-clumps during the early stages of the evolution of the Universe. Although not ruling out the presence X elliptical galaxies in low densitv environments. the hierarchical models suggest that on average {μον are very different. from the cluster ellipticals. with likely evidence of recent star-Iormation and/or merger events.," Although not ruling out the presence of elliptical galaxies in low density environments, the hierarchical models suggest that on average they are very different from the cluster ellipticals, with likely evidence of recent star-formation and/or merger events." There have been many studies of elliptical galaxies in low-density environments with somewhat inconclusive results. with some studies suggesting only minor star formation at low reclshilts (e.g. Silva and Bothun 1993. Bernardi οἱ al.," There have been many studies of elliptical galaxies in low-density environments with somewhat inconclusive results, with some studies suggesting only minor star formation at low redshifts (e.g. Silva and Bothun 1998, Bernardi et al." 1998) whilst other studies have shown strong evidence for recent merger/star formation activity (e.g. Treu et al..," 1998) whilst other studies have shown strong evidence for recent merger/star formation activity (e.g. Treu et al.," 1999. 2001. IXuntschner et al.," 1999, 2001, Kuntschner et al." 2002)., 2002). A major problem with the current comparisons between theory and observation is the lack of a consistent definition of a field galaxy., A major problem with the current comparisons between theory and observation is the lack of a consistent definition of a field galaxy. Several of the studies (e.g. Tren et al., Several of the studies (e.g. Treu et al. 1999. 2001. 2002. Aars et al.," 1999, 2001, 2002, Aars et al." 2001) use redshift survevs of the brighter galaxies to derive a sample of isolated. ellipticals., 2001) use redshift surveys of the brighter galaxies to derive a sample of isolated ellipticals. However. the incompleteness of the recdshilt catalogues may lead {ο (he inclusion of several ellipticals (hat have close neighbours.," However, the incompleteness of the redshift catalogues may lead to the inclusion of several ellipticals that have close neighbours." This has led many (o a final visual inspection to confirm (heir isolated nature. destroving the objectiveness of tlie selection criteria.," This has led many to a final visual inspection to confirm their isolated nature, destroying the objectiveness of the selection criteria." Only using an extensive redshift survey can an objective sample be constructed (e.g. ]xuntschiner οἱ al., Only using an extensive redshift survey can an objective sample be constructed (e.g. Kuntschner et al. 2002) but even then incompleteness in the catalogue can lead {ο erroneous selection of non-fiekl galaxies., 2002) but even then incompleteness in the catalogue can lead to erroneous selection of non-field galaxies. The studies have also concentrated on the properties of the ealaxies (themselves. with little. if anv. analvsis of the local environment of the elliptical which. from the morpholoey-density relationship. is likely to also have a very significant effect on the properties of the elliptical galaxy.," The studies have also concentrated on the properties of the galaxies themselves, with little, if any, analysis of the local environment of the elliptical which, from the morphology-density relationship, is likely to also have a very significant effect on the properties of the elliptical galaxy." In this paper. we use an objective definition of a [ied galaxy applied to an all-sky galaxy cabalogue that can also be applied to the theoretical simulations.," In this paper, we use an objective definition of a field galaxy applied to an all-sky galaxy catalogue that can also be applied to the theoretical simulations." We also investigate the variation of the number of field ellipticals with selection criteria., We also investigate the variation of the number of field ellipticals with selection criteria. Using all-sky photographic survevs we have made a preliminary study of the environment of these galaxies in a search for a surrounding faint dwarf galaxy. population., Using all-sky photographic surveys we have made a preliminary study of the environment of these galaxies in a search for a surrounding faint dwarf galaxy population. population states (in particular. N(/)=0.2) should be mitigated.,"population states (in particular, $N(i)=0, 2$ ) should be mitigated." " The incorporation of equation (25) into the model is labelled ""Method C"".", The incorporation of equation (25) into the model is labelled “Method C”. Tables 4 and 5 show that in the low- and intermediate-density cases. the change has only marginal. though beneficial. effects.," Tables 4 and 5 show that in the low- and intermediate-density cases, the change has only marginal, though beneficial, effects." However. the high-density results of Table 6 are much improved.," However, the high-density results of Table 6 are much improved." The abundances of many important species. such asCO. CO» and HCO. show a very good level of agreement. whilst H2O and CH:OH are a perfect match to the exact results. within computational errors.," The abundances of many important species, such asCO, $_2$ and $_2$ CO, show a very good level of agreement, whilst $_2$ O and $_3$ OH are a perfect match to the exact results, within computational errors." The match for species with abundances less than | is also much improved. although not perfect.," The match for species with abundances less than 1 is also much improved, although not perfect." For high density. the results for all species are within of the exact results. and the majority are within10%.," For high density, the results for all species are within of the exact results, and the majority are within." Although method C produces an acceptable match to the exact methods in each density regime. certain species. most notably CO» and O:. are not so well reproduced. particularly at low and intermediate densities.," Although method C produces an acceptable match to the exact methods in each density regime, certain species, most notably $_2$ and $_2$, are not so well reproduced, particularly at low and intermediate densities." In fact. one further competition process must be considered to improve these results.," In fact, one further competition process must be considered to improve these results." The formation of CO. and O» depend on the mobility of the oxygen atom on the grain surface., The formation of $_2$ and $_2$ depend on the mobility of the oxygen atom on the grain surface. In comparison to atomic hydrogen. oxygen is very slow to diffuse between binding sites. due to its greater diffusion barrier. and its being much more massive than H. making tunnelling ineffective (although efficient tunnelling of hydrogen is also questionable. see Section 6).," In comparison to atomic hydrogen, oxygen is very slow to diffuse between binding sites, due to its greater diffusion barrier, and its being much more massive than H, making tunnelling ineffective (although efficient tunnelling of hydrogen is also questionable, see Section 6)." The consideration of competition up to now has concentrated solely on the case of two reactive species on a grain at any one time., The consideration of competition up to now has concentrated solely on the case of two reactive species on a grain at any one time. However. the reaction rate for O-dependent reactions is so slow. at ~4+κ102 s! (using values from Table 3). that a hydrogen atom may acerete before reaction occurs; 1t may then react with one or other of the reactants considered in the oxygen reaction.," However, the reaction rate for O-dependent reactions is so slow, at $\sim 4 \times 10^{-5}$ $^{-1}$ (using values from Table 3), that a hydrogen atom may accrete before reaction occurs; it may then react with one or other of the reactants considered in the oxygen reaction." To test the influence of this competition process. terms equal to the aceretion rate of hydrogen are inserted into equations (17). (20) and (21). for all reactions involving atomic oxygen.," To test the influence of this competition process, terms equal to the accretion rate of hydrogen are inserted into equations (17), (20) and (21), for all reactions involving atomic oxygen." Reaction of atomic hydrogen with oxygen (or the other reactant. where applicable) is assumed to be instantaneous. if H-aceretion takes place before the oxygen-dependent reaction can oceur.," Reaction of atomic hydrogen with oxygen (or the other reactant, where applicable) is assumed to be instantaneous, if H-accretion takes place before the oxygen-dependent reaction can occur." " Tables 4 — 6 show the results of this approach. labelled ""Method D""."," Tables 4 – 6 show the results of this approach, labelled “Method D”." In the low-density regime. the reproduction of the exact results is now perfect. within computational accuracy.," In the low-density regime, the reproduction of the exact results is now perfect, within computational accuracy." In the intermediate density regime. the abundances of a number of species are now an exact match. or very close. e.g. Η. H». Π.Ο. CO. HCO. H:CO. CH30 and CH3OH. whilst O2 is slightly less accurate than with method C. Even the worst match. CO». is much improved. falling within 10% of the exact result.," In the intermediate density regime, the abundances of a number of species are now an exact match, or very close, e.g. H, $_2$, $_2$ O, CO, HCO, $_2$ CO, $_3$ O and $_3$ OH, whilst $_2$ is slightly less accurate than with method C. Even the worst match, $_2$, is much improved, falling within $10$ of the exact result." But in the high-density case. whilst some species such as CO show improved accuracy. many others diverge from the exact results. including formaldehyde (H»CO) and methanol (CH;OH).," But in the high-density case, whilst some species such as CO show improved accuracy, many others diverge from the exact results, including formaldehyde $_2$ CO) and methanol $_3$ OH)." The level of agreement is generally worse than that achieved with method C. This may be explained by the fact that in this density regime. the accretion rate of oxygen itself is very fast.," The level of agreement is generally worse than that achieved with method C. This may be explained by the fact that in this density regime, the accretion rate of oxygen itself is very fast." The accretion of hydrogen atoms interferes with certain reactions. but the further accretion of oxygen acts to mitigate this effect. as it may itself react with the newly accreted hydrogen.," The accretion of hydrogen atoms interferes with certain reactions, but the further accretion of oxygen acts to mitigate this effect, as it may itself react with the newly accreted hydrogen." It becomes clear that in order to devise a generalised system to deal with accretion-competition effects. it would be necessary to consider not only the accretion of every reactive species. but also the probability that each might react with any other acereting species. in the context of a reaction between two entirely different reactants.," It becomes clear that in order to devise a generalised system to deal with accretion-competition effects, it would be necessary to consider not only the accretion of every reactive species, but also the probability that each might react with any other accreting species, in the context of a reaction between two entirely different reactants." Such a scheme could certainly be devised. but it would be extremely complex. both to implement and to fully understand.," Such a scheme could certainly be devised, but it would be extremely complex, both to implement and to fully understand." It would also. in all likelihood. be far more computationally expensive than. for example. Method C. Under those circumstances. the value of choosing such an approach over exact methods like the master equation would be questionable.," It would also, in all likelihood, be far more computationally expensive than, for example, Method C. Under those circumstances, the value of choosing such an approach over exact methods like the master equation would be questionable." " In. addition to. the parameter set shown in Table 3. Stantchevaetal.(2002) implemented the ""slow"" (M2) surface rates of Ruffle Herbst (2000)."," In addition to the parameter set shown in Table 3, \cite{stant2} implemented the “slow” (M2) surface rates of Ruffle Herbst (2000)." These are defined by diffusion barriers in line with the values suggested by Katz for the H + H H» reaction., These are defined by diffusion barriers in line with the values suggested by \cite{katz} for the H + H $\rightarrow$ $_2$ reaction. Implicit in. these rates is the assumption that hydrogen-atom tunnelling through the diffusion barrier is inefficient; they represent a purely thermal hopping mechanism., Implicit in these rates is the assumption that hydrogen-atom tunnelling through the diffusion barrier is inefficient; they represent a purely thermal hopping mechanism. Using these values. rate equations produce a perfectly acceptable match to the results of the Monte Carlo technique. in all regimes.," Using these values, rate equations produce a perfectly acceptable match to the results of the Monte Carlo technique, in all regimes." Those same results are reproduced by even the simplest of the modified-rate methods presented here., Those same results are reproduced by even the simplest of the modified-rate methods presented here. The slower rates ensure either that the rate limit of equation (13) 1s reached. or that populations are high enough to place each reaction in the deterministic limit.," The slower rates ensure either that the rate limit of equation (13) is reached, or that populations are high enough to place each reaction in the deterministic limit." This would not necessarily be the case in regimes with higher temperatures or smaller grains., This would not necessarily be the case in regimes with higher temperatures or smaller grains. It is clear that even a basic rate-modification scheme. such as applied here to the hydrogen system of Barzel&Biham (2007b).. is capable of achieving accurate results.," It is clear that even a basic rate-modification scheme, such as applied here to the hydrogen system of \cite{barzel2}, , is capable of achieving accurate results." However. application to the more complex water- and methanol-producing systems of Barzel Biham demonstrates the need to consider competition between," However, application to the more complex water- and methanol-producing systems of Barzel Biham demonstrates the need to consider competition between" high-velocity SN blast. respectively. and is the SN rate (McKee 1989).,"high-velocity SN blast, respectively, and $\gamma$ is the SN rate \citep{mckee89}." . Since we are interested in objects whose time-scale of star formation is much longer than 10*τ vr. it is assumed that the SN rate is proportional to the star formation rate (equation À7)).," Since we are interested in objects whose time-scale of star formation is much longer than $10^7$ yr, it is assumed that the SN rate is proportional to the star formation rate (equation \ref{eq:snr}) )." " We adopt €,A.=1300 M.; (McKee 1989)..", We adopt $\epsilon_\mathrm{s}M_\mathrm{s}=1300$ $_{\sun}$ \citep{mckee89}. . Then we obtain where Jw—«Alonft:&9.65.," Then we obtain where $\beta_\mathrm{SN}\equiv\epsilon_\mathrm{s}M_\mathrm{s} \gamma /\psi\simeq 9.65$." Equations (39))4 412) are converted to the time evolution of the metallicity Z=Adz/Ad.... and the dust-to-gas ratio D.= as where we should evaluate Adu)Idi]; according to Method IL or IL in Section 4.3.., Equations \ref{eq:dMgdt}) \ref{eq:dMddt}) ) are converted to the time evolution of the metallicity $Z=M_\mathrm{Z}/M_\mathrm{gas}$ and the dust-to-gas ratio $\mathcal{D}=M_\mathrm{dust}/M_\mathrm{gas}$ as where we should evaluate $[\mathrm{d}M_\mathrm{dust}/\mathrm{d}t]_\mathrm{acc}$ according to Method I or II in Section \ref{subsec:recipe}. It is convenient to combine the above two equations to obtain the relation between D and Z: In. Method L dAZiafdaccfe=oD£cupine.) (equation 30)) where/ 7pNoAdon.fer is the star formation time-scale.," It is convenient to combine the above two equations to obtain the relation between $\mathcal{D}$ and $Z$: In Method I, $[\mathrm{d}M_\mathrm{dust}/\mathrm{d}t]_\mathrm{acc}/ \psi=\mathcal{D}\xi (\tau_\mathrm{SF}/ \tau_\mathrm{grow})$ (equation \ref{eq:dMdt1}) ), where $\tau_\mathrm{SF}\equiv X_\mathrm{cl}M_\mathrm{gas} /\psi$ is the star formation time-scale." In Method IL. clausfdacest=Dc (equation 38).," In Method II, $[\mathrm{d}M_\mathrm{dust}/\mathrm{d}t]_\mathrm{acc}/ \psi=\beta\mathcal{D}/\epsilon$ (equation \ref{eq:dMdt3}) )." A large rap in Method I is equivalent with a small ο in Methods II: that is. a small star formation efficiency means a long star formation time-scale.," A large $\tau_\mathrm{SF}$ in Method I is equivalent with a small $\epsilon$ in Methods II; that is, a small star formation efficiency means a long star formation time-scale." Because of this simple equivalence. we hereafter concentrate on Method Π.," Because of this simple equivalence, we hereafter concentrate on Method II." Adopting Method II eequation 38)). equation (473) is reduced to Lada.Lombardi.&Alves(2010) show that the star formation efficiency in molecular clouds is roughly 0.1.," Adopting Method II equation \ref{eq:dMdt3}) ), equation \ref{eq:dDdZ}) ) is reduced to \citet{lada10} show that the star formation efficiency in molecular clouds is roughly 0.1." They also mention that molecular clouds survive after the star formation activity over the last 2 Myr., They also mention that molecular clouds survive after the star formation activity over the last 2 Myr. The comparison with the age of stellar clusters associated with molecular clouds indicates that the lifetime of clouds is ~10 Myr(Leisawitz.Bash.&Thaddeus1989:Fukui&Kawamura 2010)..," The comparison with the age of stellar clusters associated with molecular clouds indicates that the lifetime of clouds is $\sim 10$ Myr\citep{leisawitz89,fukui10}. ." Thus. we hereafter assume ο=0.1 and Tu)=10 Myr as standard values.," Thus, we hereafter assume $\epsilon =0.1$ and $\tau_\mathrm{mol}=10$ Myr as standard values." For the initial condition. we assume D=0 and Z=0.," For the initial condition, we assume $\mathcal{D}=0$ and $Z=0$." " The relations between dust-to-gas ratio and metallicity are shown in reftig:dy,,cfal forfi,=0.1 and in etelpin. 01 reftig:dg,,forfi,=0.01."," The relations between dust-to-gas ratio and metallicity are shown in \\ref{fig:dg_metal} for $f_\mathrm{in}=0.1$ and in \\ref{fig:dg_metal_fin0.01} for $f_\mathrm{in}=0.01$." " At low metallicity levels. the solution of equation (485) is approximated by D~fi,"," At low metallicity levels, the solution of equation \ref{eq:dDdZ_final}) ) is approximated by $\mathcal{D}\sim f_\mathrm{in}Z$." " This is why the dust-to-gas ratio in the low-metallicity regime is Z.lower in etel reftig:dg,,0ltheaninfig. reffig:dau", This is why the dust-to-gas ratio in the low-metallicity regime is lower in \\ref{fig:dg_metal_fin0.01} than in \\ref{fig:dg_metal}. etat. pin. I gasraliooceursbecauscoflhegraingrowlhincloudsο," Above a certain metallicity level, a rapid increase of dust-to-gas ratio occurs because of the grain growth in clouds." ς αμ ο acdeeseasiagetunéfiogrofi nsi zedislribulio, The metallicity level at which this growth occurs is very sensitive to the grain size distribution. The observational data of nearby galaxies are also shown for comparison., The observational data of nearby galaxies are also shown for comparison. For the uniformity of data. we select the samples observed byAKARI:: blue compact dwarf galaxies in &Ichikawa(2009) and spiral galaxies 881 from Sun&Hi-rashita2011 and IIOI from Suzukietal.2007)).," For the uniformity of data, we select the samples observed by: blue compact dwarf galaxies in \citet{hirashita09b} and spiral galaxies 81 from \citealt{sun11} and 101 from \citealt{suzuki07}) )." The dust masses are estimated from 90 Lum and 140 pum data by using the mass absorption coefficient in Hirashita&Ichikawa(2009).., The dust masses are estimated from 90 $\micron$ and 140 $\micron$ data by using the mass absorption coefficient in \citet{hirashita09b}. . For the gas mass of the dwarf galaxies and M881. we adopt the H mass. since the molecular mass is negligible or not detected.," For the gas mass of the dwarf galaxies and 81, we adopt the H mass, since the molecular mass is negligible or not detected." The H masses of 881 and of the dwarf galaxies are taken from Walter and in Hirashita&Ichikawa(2009).. respectively.," The H masses of 81 and of the dwarf galaxies are taken from \citet{walter08} and in \citet{hirashita09b}, , respectively." For L101. we adopt the sum of neutral and molecular gas masses compiled in Suzukietal.(2007).," For 101, we adopt the sum of neutral and molecular gas masses compiled in \citet{suzuki07}." . The oxygen abundance is adopted for the indicator of the metallicity. and the solar abundance is assumed to be2003).," The oxygen abundance is adopted for the indicator of the metallicity, and the solar abundance is assumed to be." The oxygen abundances of the dwarf galaxies are compiled in Hirashita&Ichikawa(2009)... and those of the spiral galaxies at the half- radius are taken from Garnett(2002)...," The oxygen abundances of the dwarf galaxies are compiled in \citet{hirashita09b}, and those of the spiral galaxies at the half-light radius are taken from \citet{garnett02}. ." Typical errors of the observational quantities are comparable to the size of symbols in the figures., Typical errors of the observational quantities are comparable to the size of symbols in the figures. To ensure that the results are not systematically different from other results. we add the data in Issa.MacLaren.&Wolfendale (1990)..who estimated the dust mass from the extinction.," To ensure that the results are not systematically different from other results, we add the data in \citet*{issa90}, ,who estimated the dust mass from the extinction." The overall trend of the data is reproduced by the models., The overall trend of the data is reproduced by the models. Asanoetal.(2011). also include a sample whose dust mass is derived from observations by Engelbrachtetal.(2008) and show that the relation between dust-to-gas ratio and metallicity does not significantly change., \citet{asano11} also include a sample whose dust mass is derived from observations by \citet{engelbracht08} and show that the relation between dust-to-gas ratio and metallicity does not significantly change. The inclusion of data may boost the dust abundance because of the possible contribution from very cold dust especially in dwarf galaxies (Grossietal, The inclusion of data may boost the dust abundance because of the possible contribution from very cold dust especially in dwarf galaxies \citep{grossi10}. .2010). Gallianoetal.(2005). also. find a large contribution from very cold dust in the submillimetre for some dwarf galaxies., \citet{galliano05} also find a large contribution from very cold dust in the submillimetre for some dwarf galaxies. However. since the modeling of submillimetre emission may be significantly affected by the assumed emissivity index of large grains. we do not use the submillimetre data in this paper.," However, since the modeling of submillimetre emission may be significantly affected by the assumed emissivity index of large grains, we do not use the submillimetre data in this paper." We should Keep in mind that that inclusion of submillimetre data ean rather the dust mass especially for dust-rich galaxies because the dust temperature estimate becomes. better (Galametzetal.2011)., We should keep in mind that that inclusion of submillimetre data can rather the dust mass especially for dust-rich galaxies because the dust temperature estimate becomes better \citep{galametz11}. In their models. the 160 jum data are used: thus. it is not still unclear if there is a discrepancy between the dust temperatures estimated by and those estimated by including submillimetre data.," In their models, the 160 $\micron$ data are used; thus, it is not still unclear if there is a discrepancy between the dust temperatures estimated by and those estimated by including submillimetre data." The dust mass in M881 derived by the observation (3.4.10* M.: Bendoetal. 2010)) is similar to that estimated by the observation adopted in this paper (3.2.10* M.:Sun&Hirashita201 L9)., The dust mass in 81 derived by the observation $3.4\times 10^7$ $_\odot$; \citealt{bendo10}) ) is similar to that estimated by the observation adopted in this paper $3.2\times 10^7$ $_\odot$; \citealt{sun11}) ). We have shown that the grain size distribution significantly affects the evolution of dust mass above a certain metallicity level where the grain growth in clouds is activated., We have shown that the grain size distribution significantly affects the evolution of dust mass above a certain metallicity level where the grain growth in clouds is activated. In fact. as shown in Figs.,"In fact, as shown in Figs." and 9. the difference in the grain size distribution makes a significant imprint in the relation between dust-to-gasratio and metallicity.," \ref{fig:dg_metal} and \ref{fig:dg_metal_fin0.01}, , the difference in the grain size distribution makes a significant imprint in the relation between dust-to-gasratio and metallicity." This comes from the dependence of 9«2 on metallicity., This comes from the dependence of $\beta$ on metallicity. Movceacertainmeltallicityglevel.arapidiner," As shown in equation\ref{eq:taugrow_taucl}) ),$\beta\propto(\tau_\mathrm{grow} /\tau_\mathrm{cl})^{-1}$." eascoxsisbuiln in equation (313.5:9X(ras/Το)1 metallicity., \\ref{fig:taugrow} shows that $\tau_\mathrm{grow}/\tau_\mathrm{cl}$ is a decreasing function of metallicity. Thus.«2 increases as the system is enriched with metals. and if the last term in equation (48)) becomes positive at a certain," Thus,$\beta$ increases as the system is enriched with metals, and if the last term in equation \ref{eq:dDdZ_final}) ) becomes positive at a certain" canomeal or with a mild convective core overshooting. (μον concluded that all evolutionary computations predict masses which are svstematically larger for a fixed Iuminosity. especially toward the longest periods.,"canonical or with a mild convective core overshooting, they concluded that all evolutionary computations predict masses which are systematically larger for a fixed luminosity, especially toward the longest periods." Ii this context. let us also quote Dono et al. (," In this context, let us also quote Bono et al. (" 2002) ancl Ixeller Wood (2002). who studied LAIC bump Cepheids and found that the Cepheids are ~ less massive (or e more luminous) for their Iuminositv (or mass) predicted by canonical (no overshooting) evolutionary models.,"2002) and Keller Wood (2002), who studied LMC bump Cepheids and found that the Cepheids are $\sim$ less massive (or $\sim$ more luminous) for their luminosity (or mass) predicted by canonical (no overshooting) evolutionary models." Finally. Brocato et al. (," Finally, Brocato et al. (" 2004) investigated a selected sample of short-period Cepheids in the LMC cluster NGC 1506 and showed that. under reasonable assumptions for NGC! 1866 reddening anc distance modulus. it appears ciffieull to escape the evidence for pulsation masses smaller (han the evolutionary ones. either using canonical or mild convective core overshootüng computations.,"2004) investigated a selected sample of short-period Cepheids in the LMC cluster NGC 1866 and showed that, under reasonable assumptions for NGC 1866 reddening and distance modulus, it appears difficult to escape the evidence for pulsation masses smaller than the evolutionary ones, either using canonical or mild convective core overshooting computations." In this investigation. we shall take advantage of the sample of 34 Galactic Cepheids presented by Storm et al. (," In this investigation, we shall take advantage of the sample of 34 Galactic Cepheids presented by Storm et al. (" "2004. herealter SO4) to push forward the BOL result bv. using accurate PLC relations from updated nonlinear pulsating models. together with evolutionary relations which account for the difference between ""static and “mean” magnitudes of the pulsating stars.","2004, hereafter S04) to push forward the B01 result by using accurate $PLC$ relations from updated nonlinear pulsating models, together with evolutionary relations which account for the difference between “static” and “mean"" magnitudes of the pulsating stars." Actually. previous theoretical studies for classical Cephlieids (Caputo et al.," Actually, previous theoretical studies for classical Cepheids (Caputo et al." 1999. Paper IV: Caputo et al.," 1999, Paper IV; Caputo et al." 2000. Paper V). RR. Lyrae stars (Bono et al.," 2000, Paper V), RR Lyrae stars (Bono et al." 1995; Marconi et al., 1995; Marconi et al. 2003). and anomalous Cepheids (Marconi et al.," 2003), and anomalous Cepheids (Marconi et al." 2004) disclosed that the discrepancy between (he mean magnitude. i.e. the tine average along (he pulsation cvele. and the static magnitude (the value the variable would have in case it were a static star) is not negligible. and increases together with the pulsation amplitude.," 2004) disclosed that the discrepancy between the mean magnitude, i.e. the time average along the pulsation cycle, and the static magnitude (the value the variable would have in case it were a static star) is not negligible, and increases together with the pulsation amplitude." We present in 82 the pulsation models which have been used to predict suitable analytical relations connecting the period to the pulsator mass. mean magnitude. and color.," We present in 2 the pulsation models which have been used to predict suitable analytical relations connecting the period to the pulsator mass, mean magnitude, and color." In Section 3. the evolutionary constraints are discussed. while 84 deals with mass estimates of the observed sample of Galactic Cepheids.," In Section 3, the evolutionary constraints are discussed, while 4 deals with mass estimates of the observed sample of Galactic Cepheids." These results are discussed in 85 taking also into account (he uncertainties due to Cepheil chemical composition. absolute distance. and reddening.," These results are discussed in 5 taking also into account the uncertainties due to Cepheid chemical composition, absolute distance, and reddening." The conclusions of this investigation are briefly outlined in 86., The conclusions of this investigation are briefly outlined in 6. During the last lew vears. we provided theoretical predictions for classical C'epheids as based on a wide erid of nonlinear. nonlocal. and time-dependent. convective pulsational models.," During the last few years, we provided theoretical predictions for classical Cepheids as based on a wide grid of nonlinear, nonlocal, and time-dependent convective pulsational models." The first series of computations (Dono et al., The first series of computations (Bono et al. 1999b. Paper IL) includes the pulsational properties (e.e.. period and light curve) of stellar structures. covering a wide range of effeclive temperatures. stellar masses ranging trom 5 (o l1LV.. and a solar-like chemical composition (Z—0.02. Y 20.28).," 1999b, Paper II) includes the pulsational properties (e.g., period and light curve) of stellar structures, covering a wide range of effective temperatures, stellar masses ranging from 5 to $M_{\odot}$, and a solar-like chemical composition (Z=0.02, $Y$ =0.28)." For each mass. the luminosity level was fixed according to," For each mass, the luminosity level was fixed according to" has been studied in [?]..,has been studied in \cite{CST10}. It is a standing conjecture that the boundary conditions are also suitable for the nonlinear svstem(2.9).. at least [or a certain period of time.," It is a standing conjecture that the boundary conditions are also suitable for the nonlinear system, at least for a certain period of time." For the modes »>1. we rewrite equation (2.6)) in the matrix form as follows: IIere and We write and We celine ο as the positive integer satisDving the following relations:," For the modes $n \ge 1$, we rewrite equation \ref{e1.5}) ) in the matrix form as follows: Here and We write and We define $n_c$ as the positive integer satisfying the following relations:" The main reason lor studying supernovae magnilied by gravitational lensing is to investigate the chance of observing supernovae too faint to be observed in the absence of lensing. which is usually (he case for cosmologically distant supernovae. specilically (wpe la’s.,"The main reason for studying supernovae magnified by gravitational lensing is to investigate the chance of observing supernovae too faint to be observed in the absence of lensing, which is usually the case for cosmologically distant supernovae, specifically type Ia's." To calculate the observed rate of type Ia supernovae we use the result of predicted rates by Dahlén lor a hierarchical star formation rate model with a charactristic time of 7=1 Gvr (Fig., To calculate the observed rate of type Ia supernovae we use the result of predicted rates by \citet{DahFra99} for a hierarchical star formation rate model with a charactristic time of $\tau=1$ Gyr (Fig. " 3). which limits our caleulation to the redshilt depth of zaj4,=5."," 3), which limits our calculation to the redshift depth of $z_{Max} = 5$." In order lor a supernova to be detected. its apparent magnitude m should not exceed (he limiting magnitude of (he survey μμ.," In order for a supernova to be detected, its apparent magnitude $m$ should not exceed the limiting magnitude of the survey $m_{limit}$." " Using the definitions of the apparent magnitude and aamplilieation. we get: in which. mi, is he observed magnitude. and m, is the apparent magnitude of the supernova in (he absence of the lensing."," Using the definitions of the apparent magnitude and amplification, we get: in which, $m_{amp}$ is the observed magnitude, and $m_{o}$ is the apparent magnitude of the supernova in the absence of the lensing." " We can further write i, in terms of the absolute magnitude A, of the supernova and rewrite (he detection criterion as where D,(z.) is the luminosity distance of (he supernova at redshilt z..", We can further write $m_{o}$ in terms of the absolute magnitude $M_{abs}$ of the supernova and rewrite the detection criterion as where $D_{L}(z_{s})$ is the luminosity distance of the supernova at redshift $z_{s}$. " The absolute nagnitude of twpe la SNe has a very narrow Gaussian distribution around M4,=—19.16 at a conticence level of (Iichardsonetal.2002).", The absolute magnitude of type Ia SNe has a very narrow Gaussian distribution around $M_{abs}=-19.16$ at a confidence level of \citep{Rich02} . Here. we assume that the supernova. is detected as soon as ils absolute magnitude becomes brighter (han M;=—183.," Here, we assume that the supernova is detected as soon as its absolute magnitude becomes brighter than $M_{abs}=-18$." We take the deflecting halo to be at redshifts ος = 0.2. 0.5. and 1.0. and with virial uasses of mg=1.0οTAL. and mus=1.0x101M.ft.," We take the deflecting halo to be at redshifts $z_{s}$ = 0.2, 0.5, and 1.0, and with virial masses of $m_{d1}=1.0 \times 10^{12} h^{-1} M_{\odot}$ and $m_{d2}=1.0 \times 10^{14}M_{\odot} h^{-1}$." " Concentration parameter c. overdensitv 9,. ancl virial radius rag; (1n units of Apef "") for each case are given in Table 1."," Concentration parameter c, overdensity $\delta_{c}$, and virial radius $r_{200}$ (in units of $Kpc h^{-1}$ ) for each case are given in Table 1." The field of view is taken to be the spatial angle subtending the virial area of the halo., The field of view is taken to be the spatial angle subtending the virial area of the halo. By breaking the projected halo into pixels with the angular size of Ory and 0.9. (which are, By breaking the projected halo into pixels with the angular size of $\delta x_{1}$ and $\delta x_{2}$ (which are of the cross-sectional temperature structure. the prime focus of this paper. is therefore a crucial method to distinguish between these two opposite scenarios of microscopic or macroscopic plasma heating processes iu the solar corona.,"of the cross-sectional temperature structure, the prime focus of this paper, is therefore a crucial method to distinguish between these two opposite scenarios of microscopic or macroscopic plasma heating processes in the solar corona." " The cross-sectional temperature structure of coronal loops has been studied carly ou οι EUV and soft N-rav images with Skvlab. Yolikoh. SMM. SolIO/EIT. aud CDS. but the spatial resolution of these instruments was Hmnited to a range of z2.5""—10"" (2:2.7 Nin)."," The cross-sectional temperature structure of coronal loops has been studied early on from EUV and soft X-ray images with Skylab, Yohkoh, SMM, SoHO/EIT, and CDS, but the spatial resolution of these instruments was limited to a range of $\approx 2.5\arcsec-10\arcsec$ $\approx 2-7$ Mm)." " This is a typical spatial scale of loop buudles that consist of euseiubles of many unresolved loop strands. which are resolved when inspected with hieli-resolutiou nuages. such as with TRACE with a pixel size of 0.5"". (corresponding to an effective spatial resolution of ~1.257. 1.6. 220.9 Ma: Gburek et al."," This is a typical spatial scale of multi-thermal loop bundles that consist of ensembles of many unresolved loop strands, which are resolved when inspected with high-resolution images, such as with TRACE with a pixel size of $0.5\arcsec$ (corresponding to an effective spatial resolution of $\approx 1.25\arcsec$, i.e., $\approx 0.9$ Mm; Gburek et al." 2006)., 2006). Analysis of high-resolution TRACE nuages with three temperature filters in the range of Tz(0.72.7 AUS has giveu support for near-isothermal loops (Del Zamna and Mason 2003: Aschwanden aud Nightingale 2005: Warren ct al., Analysis of high-resolution TRACE images with three temperature filters in the range of $T \approx 0.7-2.7$ MK has given support for near-isothermal loops (Del Zanna and Mason 2003; Aschwanden and Nightingale 2005; Warren et al. 2008. or Tripathi et al.," 2008, or Tripathi et al." 2009. usine also Winode/EIS data). but noiuti-thermality iu loops have also been claimed (Schinelz ct al.," 2009, using also Hinode/EIS data), but multi-thermality in loops have also been claimed (Schmelz et al." 2009)., 2009). Each applied method has been criticized for differeut reasons: (d) Loop-associated fluxes can be heavily contaminated by the umltithermal backeround of other loops along a Lue-ofsight it the background is not measured cospatially to the target loop. which unavoidibly leads to a imulti-therual bias: (41) triple-filter analysis has a limited temperature rauge and thus may not reveal the full temperature width of a differential enuission measure (DEAL) distribution. leading to an isothermal bias: or (ii) the inversion of a DEM from triple-filter data is uuderconstramed aud biased towards the teiiperature rauge with the highest instrmuental sensitivity.," Each applied method has been criticized for different reasons: (i) Loop-associated fluxes can be heavily contaminated by the multi-thermal background of other loops along a line-of-sight if the background is not measured cospatially to the target loop, which unavoidibly leads to a multi-thermal bias; (ii) triple-filter analysis has a limited temperature range and thus may not reveal the full temperature width of a differential emission measure (DEM) distribution, leading to an isothermal bias; or (iii) the inversion of a DEM from triple-filter data is underconstrained and biased towards the temperature range with the highest instrumental sensitivity." All three problems can now be siguificautly mitieated with data from the new (Leen et al., All three problems can now be significantly mitigated with data from the new (Lemen et al. 2001: Boerner et al., 2011; Boerner et al. " 2011) onboard the(SDOJ. which observes the Sun with 8 different temperature filters. with an uninterrupted cadence of 12 s. and a pixel size of 0.6"" (corresponding to a spatial resolution of z1.6"" or zz1.2 Mii: Boerner ct al."," 2011) onboard the, which observes the Sun with 8 different temperature filters, with an uninterrupted cadence of 12 s, and a pixel size of $0.6\arcsec$ (corresponding to a spatial resolution of $\approx 1.6\arcsec$ or $\approx 1.2$ Mm; Boerner et al." 2001)., 2001). Iu this Paper we present a unilticttempcrature analysis of LOO loop segnieuts observed at 10 different spatial locations aud 10 different times., In this Paper we present a multi-temperature analysis of 100 loop segments observed at 10 different spatial locations and 10 different times. Section 2 contains the description of the data analysis aud results in terms of differcutial emission measure (DEAL) distribution modeling. while Section 3 contains a discussion of the results aud theoretical cousequences. followed by couclusious iu Section £.," Section 2 contains the description of the data analysis and results in terms of differential emission measure (DEM) distribution modeling, while Section 3 contains a discussion of the results and theoretical consequences, followed by conclusions in Section 4." " ATA saw first light on 2010 March 29 and produced since then continuous data of the full Sun with a 1096« detector with a pixel size of 0.6"", corresponding to au effective spatial resolution of zz1.6""."," AIA saw first light on 2010 March 29 and produced since then continuous data of the full Sun with a $4096 \times 4096$ detector with a pixel size of $0.6\arcsec$, corresponding to an effective spatial resolution of $\approx 1.6\arcsec$." ATA contains 10 differcut waveleneth chaunels. three in white lieht and UV. and seven EUV chaunels. whereof six are centered on stroug iron lines. covering the coronal range from T220.6 MIN to 216 MEI.," AIA contains 10 different wavelength channels, three in white light and UV, and seven EUV channels, whereof six are centered on strong iron lines, covering the coronal range from $T\approx 0.6$ MK to $\gapprox 16$ MK." " ATA records a set of 8 near-siniultaueous miages in each filter every 12 s. The umuber of temperature channels was chosen to be compatible with the achievable temperature resolution. which is approximately a Gaussian half width of OxyTi©OL (corresponding to a full width of half peak of Alog(T,.)z 0.25)."," AIA records a set of 8 near-simultaneous images in each filter every 12 s. The number of temperature channels was chosen to be compatible with the achievable temperature resolution, which is approximately a Gaussian half width of $\sigma_{\Delta log(T_e)} \approx 0.1$ (corresponding to a full width of half peak of $\Delta log(T_e) \approx 0.25$ )." The lines were chosen to be emitted by ious of a single clement. 3.0... irou. to avoid a dependence on the relative abundances in the coronal plasma.," The lines were chosen to be emitted by ions of a single element, i.e., iron, to avoid a dependence on the relative abundances in the coronal plasma." A list of the ATA tempcrature channels is given in Table 1., A list of the AIA temperature channels is given in Table 1. The coutributious of differeut coronal regions (coronal holes. quiet Sun. active regions. flare plasma) to the differeut ATA EUV channels was studied in Boerner et al. (," The contributions of different coronal regions (coronal holes, quiet Sun, active regions, flare plasma) to the different AIA EUV channels was studied in Boerner et al. (" 2001) and O'Dwyer ct al. (,2001) and O'Dwyer et al. ( 2010). predicting count rates of tot10 DN | for the 6 coronal ALA chauncls,"2010), predicting count rates of $10^1-10^5$ DN $^{-1}$ for the 6 coronal AIA channels." The teiiperatire resolution is fundamentally limited due to svstematic, The temperature resolution is fundamentally limited due to systematic "Experiments such as the Dark Energy Survey (Frieman 2005) ancl WigeleZ (Blake 2011) ave aimed αἱ determination of the equation of state P = pw. Measurement of QO, and O, are also within their scope (Ixomatsu 2009: equation 80).",Experiments such as the Dark Energy Survey (Frieman 2005) and WiggleZ (Blake 2011) are aimed at determination of the equation of state P = $\rho$ w. Measurement of $\Omega_1$ and $\Omega_0$ are also within their scope (Komatsu 2009; equation 80). For small z ΠΠ. where w=dida.," For small z and $w_{eff} \approx$ –1, where $w^\prime~=~dw/da$." Coeflicient(s in the Friedinanu equation are related to w by equation (4) and are identified in Table I., Coefficients in the Friedmann equation are related to w by equation (4) and are identified in Table 1. " 0.5 true Our primary conclusion is that introducing O4 or Q, does not change WAIAP values of Hy or O,,.", 0.5 truein Our primary conclusion is that introducing $\Omega_1$ or $\Omega_{-1}$ does not change WMAP values of $_0$ or $\Omega_m$. " His easy to show that (his conclusion extends to phantom energy. generally [or w « 1l with Ma""O,-a""OQ,=[? and x <0."," It is easy to show that this conclusion extends to phantom energy generally for w $<$ –1 with $\Sigma a^{-n}\Omega_n~+~a^{-x}\Omega_x~ = ~h^2$ and x $<$ 0." Using the supernova data alone. 1 is not possible to determine all the £s because of degeneracies.," Using the supernova data alone, it is not possible to determine all the $\Omega$ 's because of degeneracies." ABut in combination with CMB data. the degeneracies are broken.,"  But in combination with CMB data, the degeneracies are broken." Second. we find that O4 < 0.2 and οαν < 0.1 with," Second, we find that $\Omega_1$ $<$ 0.2 and $\Omega_{-1}$ $<$ 0.1 with" As Williamsοἱal.(1996) found a change in the (12) slope at a magnitude of around 26. n(m) has been fitted to their data in the (wo magnitude intervals |23. 260) ancl 260. 29].,"As \citet{W96} found a change in the $n(m)$ slope at a magnitude of around 26, $n(m)$ has been fitted to their data in the two magnitude intervals [23, 26] and [26, 29]." The fitted Gm) functions have been used in eq., The fitted $n(m)$ functions have been used in eq. 8 to compute the n(n)-estimated ej., \ref{sigma_bg} to compute the $n(m)$ -estimated $\sigma_{\rm BG}^2$. Rests are listed in table 3.., Results are listed in table \ref{t-sigma}. " These n(m)-estimated oj, values will be later on compared with those directly. derived [rom the SBF measurements (whieh we will call the SDE-measured Oc).", These $n(m)$ -estimated $\sigma_{\rm BG}^2$ values will be later on compared with those directly derived from the SBF measurements (which we will call the SBF-measured $\sigma_{\rm BG}^2$ ). This comparison will allow us to evaluate the validity of the differential number counts of both Williamsetal.(1996) and Metcealfeetal.(2001) ancl. as a result. a final nin) will be proposed.," This comparison will allow us to evaluate the validity of the differential number counts of both \citet{W96} and \citet{Met01} and, as a result, a final $n(m)$ will be proposed." Belore describing5 the details of the SBF measurements in ILDF images. note that the SBF techuique is valid only if faint galaxies have a stellar appearance.," Before describing the details of the SBF measurements in HDF images, note that the SBF technique is valid only if faint galaxies have a stellar appearance." In Ferguson.(1998) the radiusmagnitude relation lor galaxies in the Williamsetal.(1996). HIDE catalogue has been analvzed., In \citet{Fer98} the radius–magnitude relation for galaxies in the \citet{W96} HDF catalogue has been analyzed. " For magnitudes fainter than Vig;=28.8. all the galaxies have a raclius smaller that 0.16"". elose to the EWIIM of the WF chips."," For magnitudes fainter than $V_{606}=28.8$, all the galaxies have a radius smaller that $0.16 \arcsec$, close to the FWHM of the WF chips." So very faint galaxies. in the magnitude range where SBF will be measured. can be assumed to have a stellar appearance.," So very faint galaxies, in the magnitude range where SBF will be measured, can be assumed to have a stellar appearance." ]lere. the practical procedure for obtaining the SBF signal in IIDE-N images is described in detail.," Here, the practical procedure for obtaining the SBF signal in HDF-N images is described in detail." First of all. it should be noted that cosmic ravs awe diffieult to discriminate from stars in frames.," First of all, it should be noted that cosmic rays are difficult to discriminate from stars in frames." In order (o estimate and eliminate the cosmic-ray contribution to the SBF signal. J). a procedure based on the random nature of cosmic-ray events Las been used for each filler and chip.," In order to estimate and eliminate the cosmic-ray contribution to the SBF signal, $P_0$, a procedure based on the random nature of cosmic-ray events has been used for each filter and chip." The SBF signal has be measured not only on the final combined images. but on all the individual images listed in Table 1. as well.," The SBF signal has be measured not only on the final combined images, but on all the individual images listed in Table \ref{t-data} as well." " Belore computing (he power specirum of an image. objects brighter (han m, must be masked out."," Before computing the power spectrum of an image, objects brighter than $m_{\rm c}$ must be masked out." In this study. the window functions have been created using the photometrie catalogue. which is the only one available to us.," In this study, the window functions have been created using the \citet{W96} photometric catalogue, which is the only one available to us." As isophotal magnitudes were considered while creating the window functions. in order to convert them to (he total magnitude scale an isophotal-to-total magnitude correction of 0.2 mae 1996) was applied.," As isophotal magnitudes were considered while creating the window functions, in order to convert them to the total magnitude scale an isophotal-to-total magnitude correction of 0.2 mag \citep{W96} was applied." The SBF analvsis have been be performed considering (wo clilferent values of m: 27.8 and 28.8., The SBF analysis have been be performed considering two different values of $m_{\rm c}$: 27.8 and 28.8. " All objects brighter than my, have been masked out using a window function whose pixel values are zero in a circle centered on the location of the bright objects and unity in the rest of the image.", All objects brighter than $m_{\rm c}$ have been masked out using a window function whose pixel values are zero in a circle centered on the location of the bright objects and unity in the rest of the image. The window [unction has been created. using a patch radius large enough to completely mask bright galaxies. including their external haloes and therefore merged galaxies where these exist.," The window function has been created using a patch radius large enough to completely mask bright galaxies, including their external haloes and therefore merged galaxies where these exist." The procedure creating (he mask has been the following: first. the brightest galaxies have been masked one by one manually.," The procedure creating the mask has been the following: first, the brightest galaxies have been masked one by one manually." "ratio and therefore the dust parameter Τα, we kept all other parameters of the model fixed, in particular, the radiation pressure mean efficiency and the stellar luminosity, were kept constant.","ratio and therefore the dust parameter $\Gamma_d$, we kept all other parameters of the model fixed, in particular, the radiation pressure mean efficiency and the stellar luminosity, were kept constant." " Now, if the average dust-to-gas ratio is increased by an order of magnitude then accordingly, the dust parameter Τα must also correspondingly increase by an order of magnitude."," Now, if the average dust-to-gas ratio is increased by an order of magnitude then accordingly, the dust parameter $\Gamma_d$ must also correspondingly increase by an order of magnitude." " Thus, for the second model’s results shown in Figure 1,, we took Τα=5 and (6)=1/200; Scenario 1b."," Thus, for the second model's results shown in Figure \ref{fig:figure1}, , we took $\Gamma_d=5$ and $\langle \delta \rangle = 1/200$; Scenario 1b." " For this latter model, the dust velocity profile is shown with the green solid line that lies below the red solid line."," For this latter model, the dust velocity profile is shown with the green solid line that lies below the red solid line." " This range of the dust-to-gas ratio of 1/2000<(6)< 1/200, represents a reasonable bound for the amountof dust in the atmosphere of Betelgeuse (e.g. ?).."," This range of the dust-to-gas ratio of $1/2000 \leq \langle \delta \rangle \leq1/200$ , represents a reasonable bound for the amountof dust in the atmosphere of Betelgeuse \citep[e.g.][]{Harper2001}. ." It was seen in our earlier work (c.f.Figure6of?) that changing the dust parameter shifted the location of the critical points., It was seen in our earlier work \citep[c.f. Figure 6 of][]{Thirumalai2010} that changing the dust parameter shifted the location of the critical points. " In general, increasing the value of the dust parameter Τα results in moving the location of the sonic point and fast point towards the surface of the star; this is the case should dust formation occur inside the sonic point in the hybrid wind model."," In general, increasing the value of the dust parameter $\Gamma_d$ results in moving the location of the sonic point and fast point towards the surface of the star; this is the case should dust formation occur inside the sonic point in the hybrid wind model." " However, it was shown earlier (seeFigure9of?,anddiscussionthereof) that formation of dust beyond the fast point does not influence the location of the critical points."," However, it was shown earlier \cite[see Figure 9 of][and discussion thereof]{Thirumalai2010} that formation of dust beyond the fast point does not influence the location of the critical points." " Then, Eq. (1))"," Then, Eq. \ref{eq:1}) )" can simply be integrated with the presence of the Heaviside function from r=rq to r=oo for a given value of Τα., can simply be integrated with the presence of the Heaviside function from $r=r_d$ to $r=\infty$ for a given value of $\Gamma_d$. " Thus in this case, the wind has already successfully passed through the critical points and emerged super-Alfvénnic prior to dust condensation."," Thus in this case, the wind has already successfully passed through the critical points and emerged super-Alfvénnic prior to dust condensation." " Beyond about rzr4=25Ro, the acceleration of the gas in the wind due to dust drag in the second model 5, Scenario 1b) starts to decline more steeply than in the case of a hybrid model with a smaller value of 4=0.5 (Scenario la)."," Beyond about $r \approx r_A=25R_0$ , the acceleration of the gas in the wind due to dust drag in the second model $\Gamma_d=5$ , Scenario 1b) starts to decline more steeply than in the case of a hybrid model with a smaller value of $\Gamma_d=0.5$ (Scenario 1a)." " Thus, the gas in the wind in the first model (Ta= 0.5, Scenario 1a) at this distance, is still getting accelerated, therefore it’s terminal velocity is slightly larger and the red long-dashed line lies above the green long-dashed line."," Thus, the gas in the wind in the first model $\Gamma_d=0.5$ , Scenario 1a) at this distance, is still getting accelerated, therefore it's terminal velocity is slightly larger and the red long-dashed line lies above the green long-dashed line." " Thus, when Ig is smaller, acceleration due to radiation pressure continues to have an effect, out to larger distances from the star."," Thus, when $\Gamma_d$ is smaller, acceleration due to radiation pressure continues to have an effect, out to larger distances from the star." The effect on the dust grains is a little counter-intuitive and can be understood by examining Eq. (4))., The effect on the dust grains is a little counter-intuitive and can be understood by examining Eq. \ref{eq:4}) ). We can re-write Eq. (4)), We can re-write Eq. \ref{eq:4}) ) " by replacing the dust grain number density with an expression employing the dust-to-gas ratio as, Upon examining the second term under the square-root; the radiation pressure term, we can see that the smaller the value of the average dust-to-gas ratio, the larger this term will be and therefore the larger the value of the dust grain velocity, v(r)."," by replacing the dust grain number density with an expression employing the dust-to-gas ratio as, Upon examining the second term under the square-root; the radiation pressure term, we can see that the smaller the value of the average dust-to-gas ratio, the larger this term will be and therefore the larger the value of the dust grain velocity, $v(r)$." " Thus, when the radiation pressure mean efficiency and the stellar luminosity are kept constant, then naturally, the dust grain velocity is larger for smaller to-gas ratios; this is the effect seen in Figure 1.."," Thus, when the radiation pressure mean efficiency and the stellar luminosity are kept constant, then naturally, the dust grain velocity is larger for smaller dust-to-gas ratios; this is the effect seen in Figure \ref{fig:figure1}." " For the calculations carried out above, we assumed that the dust grains were spherical and were assumed to be on average (see7?) about 0.005um in size with a density of about 4 g/cm?."," For the calculations carried out above, we assumed that the dust grains were spherical and were assumed to be on average \citep[see][]{Perrin2007} about $\mu$ m in size with a density of about 4 $^3$." " With regard to scattering of radiation by the dust grains, in the current study this was assumed to be absent, thus precluding the complications that arise upon including this effect."," With regard to scattering of radiation by the dust grains, in the current study this was assumed to be absent, thus precluding the complications that arise upon including this effect." " Briefly, the inclusion of isotropic scattering would have the effect, for the simple theory described here, of altering the radiation pressure mean efficiency as, Qrp—Q+ Q?, where Q and Q? represent the efficiencies of absorption and isotropic scattering, respectively."," Briefly, the inclusion of isotropic scattering would have the effect, for the simple theory described here, of altering the radiation pressure mean efficiency as, $Q_{rp} \mapsto Q^A + Q^S$ , where $Q^A$ and $Q^S$ represent the efficiencies of absorption and isotropic scattering, respectively." " In a more rigorous model, these could be calculated for a particular type of dust grain and used in the equations, thus incorporating scattering of photons by dust grains."," In a more rigorous model, these could be calculated for a particular type of dust grain and used in the equations, thus incorporating scattering of photons by dust grains." " Moreover, in the framework of the current theory, the dust grains do not possess azimuthal velocity with respect to the gas."," Moreover, in the framework of the current theory, the dust grains do not possess azimuthal velocity with respect to the gas." " That being said, Poynting-Robertson drag due to scattering of radiation by dust grains would inevitably decelerate the grains in the azimuthal direction, thereby altering the momentum equations further."," That being said, Poynting-Robertson drag due to scattering of radiation by dust grains would inevitably decelerate the grains in the azimuthal direction, thereby altering the momentum equations further." " In reality however, it is to be acknowledged that scattering is probably anisotropic since the dust grains may well align themselves along field lines."," In reality however, it is to be acknowledged that scattering is probably anisotropic since the dust grains may well align themselves along field lines." " Such a detailed analysis involving the complex phenomena touched upon above, while being extremely pertinent and closer to a realistic picture, was considered to be outside the scope of the current study, where the aim is to portray a simple picture."," Such a detailed analysis involving the complex phenomena touched upon above, while being extremely pertinent and closer to a realistic picture, was considered to be outside the scope of the current study, where the aim is to portray a simple picture." " It is implicitly assumed in our model thatdust condensation occurs abruptly at a distance where the gas temperature (Tyas) falls below the dust condensation temperature Ty,,,4.", It is implicitly assumed in our model thatdust condensation occurs abruptly at a distance where the gas temperature $T_{gas}$ ) falls below the dust condensation temperature $T_{dust}^{c}$ . " Inaddition, we assume that that the conditions areconducive for grain growth."," Inaddition, we assume that that the conditions areconducive for grain growth." " In the current,"," In the current," bv the standard deviations.,by the standard deviations. The results are insensitive to whether we take the logarithm or not. but. stancarcizine is crucial because otherwise the result. would. depend. on the choice of mass unit (note that all other parameters are dimensionless).," The results are insensitive to whether we take the logarithm or not, but standardizing is crucial because otherwise the result would depend on the choice of mass unit (note that all other parameters are dimensionless)." Figure 2. shows the results of the PCA., Figure \ref{pcdp1} shows the results of the PCA. Each panel shows the correlation between the halo property plotted along the vertical axis anc the PC€ plotted along. the rorizontal axis., Each panel shows the correlation between the halo property plotted along the vertical axis and the PC plotted along the horizontal axis. As in Figure 1. the values of the Spearman rank correlation coellicients are shown and the colour scale indicates the distribution of haloes.," As in Figure \ref{ccdp1}, the values of the Spearman rank correlation coefficients are shown and the colour scale indicates the distribution of haloes." The eigenvalue of each C is shown along the horizontal axis., The eigenvalue of each PC is shown along the horizontal axis. PC] clearly stands out as most important. accounting or no less than of the total variance. compared to or PC2.," PC1 clearly stands out as most important, accounting for no less than of the total variance, compared to for PC2." PCs 3 and 4 also account for z1054 of the variance. out the remaining PCs are not that significant.," PCs 3 and 4 also account for $>10$ of the variance, but the remaining PCs are not that significant." However. to account for of the total variance. we require no less than 6 PCs. a suprisingly large number.," However, to account for of the total variance, we require no less than 6 PCs, a suprisingly large number." Even the least important C still accounts for more than of the variance., Even the least important PC still accounts for more than of the variance. Clearly. dark matter haloes are complicated objects whose structure cannot be described using a small number of parameters.," Clearly, dark matter haloes are complicated objects whose structure cannot be described using a small number of parameters." PCI correlates very strongly with concentration (As= 0.86). which indicates that this parameter is most fundamental.," PC1 correlates very strongly with concentration $\rank=-0.86$ ), which indicates that this parameter is most fundamental." Environment. spin. and particularly triaxiality also correlate significantly with PCL. but they correlate more stronely with other PCs.," Environment, spin, and particularly triaxiality also correlate significantly with PC1, but they correlate more strongly with other PCs." All other parameters correlate most strongly with PCT., All other parameters correlate most strongly with PC1. This is consistent. with the fact that its eigenvalue. is by far the greatest., This is consistent with the fact that its eigenvalue is by far the greatest. This confirms what Figure 1. suggested: of the parameters that we consider. concentration is most fundamental.," This confirms what Figure \ref{ccdp1} suggested: of the parameters that we consider, concentration is most fundamental." PC? correlates very strongly with spin (2s= 0.72). stronely with mass (fs= 0.56). but not at all with concentration.," PC2 correlates very strongly with spin $\rank=0.72$ ), strongly with mass $\rank=-0.56$ ), but not at all with concentration." PC3 only correlates. strongly with environment (fs= 0.68)., PC3 only correlates strongly with environment $\rank=0.68$ ). PCA correlates most stronglv with triaxiality (As= 0.64). but is also stronely correlated with environment (2s= 0.55).," PC4 correlates most strongly with triaxiality $\rank=0.64$ ), but is also strongly correlated with environment $\rank=-0.55$ )." llence. concentration. age. relaxedness. mass. and substructure all belong to a single family of parameters. which however. still contains a Large amount of scatter.," Hence, concentration, age, relaxedness, mass, and substructure all belong to a single family of parameters, which however, still contains a large amount of scatter." PC's 2-1 together account for the variance that is not linked with concentration., PCs 2-4 together account for the variance that is not linked with concentration. “Phat part. of the variance is mostly due to the scatter in spin. environment. and triaxialitv. the three parameters that are most independent of the main family of halo properties.," That part of the variance is mostly due to the scatter in spin, environment, and triaxiality, the three parameters that are most independent of the main family of halo properties." As this paper was in the final stages of. preparation. Skibba& Macció.(2011) posted a preprint of an independent. related. studs.," As this paper was in the final stages of preparation, \cite{Skibba2011} posted a preprint of an independent, related study." While they also carried. out a PCA. albeit with a somewhat different set of parameters. they dic not present a correlation study.," While they also carried out a PCA, albeit with a somewhat different set of parameters, they did not present a correlation study." In. agreement with our PCA results. they fined that concentration is more fundamental than mass.," In agreement with our PCA results, they find that concentration is more fundamental than mass." However. they also find that relaxecdness is about as important as concentration. whereas we find that the variation with relaxedness that does. not trace concentration only features stronglv in PCS. which accounts for only of the total variance.," However, they also find that relaxedness is about as important as concentration, whereas we find that the variation with relaxedness that does not trace concentration only features strongly in PC5, which accounts for only of the total variance." This dilference may be due to the fact that their PCA includes multiple measures of relaxedness and that they did not consider ago. which is closelv related. to concentration.," This difference may be due to the fact that their PCA includes multiple measures of relaxedness and that they did not consider age, which is closely related to concentration." Another cause of discrepancy ds the use of dillerent definitions for environment., Another cause of discrepancy is the use of different definitions for environment. Thev use the overdensity in a fixed aperture (of S Mpc/h). which has been shown to correlate very stronely with mass (Llaasetal.2011).. whereas our environmental parameter is insensitive to mass.," They use the overdensity in a fixed aperture (of 8 $/h$ ), which has been shown to correlate very strongly with mass \citep{Haas2011}, whereas our environmental parameter is insensitive to mass." To conclude. both the correlation analysis and the PCA demonstrate that concentration. age. substructure. mass. sphericity. and relaxecdness are closely related. with concentration being most. fundamental.," To conclude, both the correlation analysis and the PCA demonstrate that concentration, age, substructure, mass, sphericity, and relaxedness are closely related, with concentration being most fundamental." Friaxialitv. spin. and (mass-independent) environment are more independent. although spin correlates. strongly with substructure aud both spin and triaxiality are substantially correlated: with concentration.," Triaxiality, spin, and (mass-independent) environment are more independent, although spin correlates strongly with substructure and both spin and triaxiality are substantially correlated with concentration." While the scale of a halo is set by its mass. all other properties are more closely related to concentration.," While the scale of a halo is set by its mass, all other properties are more closely related to concentration." We thank Alan Dully for. providing us with the halo concentrations ancl Volker Springel for allowing us to use and GADGET-8., We thank Alan Duffy for providing us with the halo concentrations and Volker Springel for allowing us to use and -3. The simulations were run on the Cosmology Machine at the LOC in. Durham as part. of the Virgo Consortium research. programme., The simulations were run on the Cosmology Machine at the ICC in Durham as part of the Virgo Consortium research programme. This work was supported by a Marie Curic reintegration grant and by the Initial Training Network CosmoConip., This work was supported by a Marie Curie reintegration grant and by the Initial Training Network CosmoComp. and parallel).,and parallel). " The LL spectral maps cover an area of 493""x474” (376""x395"" for N 76).", The LL spectral maps cover an area of $493\arcsec \times 474\arcsec$ $376\arcsec \times 395\arcsec$ for N 76). The SL maps are constructed similarly except that we use full slit width steps parallel to the slit to increase the mapped area at the expense of some pixel redundancy., The SL maps are constructed similarly except that we use full slit width steps parallel to the slit to increase the mapped area at the expense of some pixel redundancy. " All of the SL maps, aside from the map of SMC Bl, have 120 perpendicular by 5 parallel pointings (220""x 208"") with integration times of 14 seconds per position."," All of the SL maps, aside from the map of SMC B1, have 120 perpendicular by 5 parallel pointings $220\arcsec \times 208\arcsec$ ) with integration times of 14 seconds per position." " We have made a deeper map of SMC B1, the location where PAH emission was first detected from the SMC (Reachetal. using 60 by 4 slit positions (109""x 156"") with 60 2000)second integration times."," We have made a deeper map of SMC B1, the location where PAH emission was first detected from the SMC \citep{reach00} using 60 by 4 slit positions $109\arcsec \times 156\arcsec$ ) with 60 second integration times." The spectral coverage of the low-resolution orders extends between 5.2 and 38.5 wwith spectral resolving power ranging between 120., The spectral coverage of the low-resolution orders extends between 5.2 and 38.5 with spectral resolving power ranging between $\sim 60-120$ . "Besides achieving an ‘acceleration’ (u$*<—1/3). our kev result is (hat when perturbations exist (Le. Z(1)> 0). one has HIP 0$ ), one has $H^\mathrm{FRW}_{0} < H^\mathrm{Obs}_{0}$, which is astrophysically interesting \citep[e.g.,][]{BlanchardAltConcord} and solves a number of problems with matter-only cosmologies." First. since (RWPOPS)ο a low HER can solve the classic Age Problem/Crisis in cosmology (e.g..Wolb&Turner1990). by increasing /9' [rom the ~9—LO GYr expected from decelerating flat. οςΔΙ cosmologies. to values of ~13—14 GYr for our stronglv-perturbed models.," First, since $(t^\mathrm{FRW}_{0} , t^\mathrm{Obs}_{0}) \propto 1 / H^\mathrm{FRW}_{0}$, a low $H^\mathrm{FRW}_{0}$ can solve the classic Age Problem/Crisis in cosmology \citep[e.g.,][]{KolbTurner} by increasing $t^\mathrm{Obs}_{0}$ from the $\sim$$9-10$ GYr expected from always-decelerating flat SCDM cosmologies, to values of $\sim$$13-14$ GYr for our strongly-perturbed models." " Secondly. since Oy=ρωXpy/Hg. a universe that to have insullicient density for closure due to OU""xpy/(187)?~0.3. may very well be spatially flat (in a sense) for the same physical matter density py. with OXExoΗμ8)?LE. ("," Secondly, since $\Omega _\mathrm{M} = \rho _\mathrm{M} / \rho _\mathrm{crit} \propto \rho _\mathrm{M} / H^{2}_{0}$, a universe that to have insufficient density for closure due to $\Omega^\mathrm{Obs}_\mathrm{M} \propto \rho _\mathrm{M} / (H^\mathrm{Obs}_{0})^{2} \sim 0.3$, may very well be spatially flat (in a pre-perturbed sense) for the physical matter density $\rho _\mathrm{M}$, with $\Omega^\mathrm{FRW}_\mathrm{M} \propto \rho _\mathrm{M} / (H^\mathrm{FRW}_{0})^{2} \simeq 1$. (" And note that CMD-related tests of cosmic flatness e.¢.. Larsonetal.(2011). primarily measure (he pre-perturbed era.),"And note that CMB-related tests of cosmic flatness – e.g., \citet{WMAP7yrLikeliParams} – primarily measure the pre-perturbed era.)" " Thus we can reconcile the apparent contradiction between the CMB measurements of /Q' indicating flatness. and our seemingly low-natter-density universe (as indicated bythe growth of structure). requiring the addition of any non-clustering Dark Energy species to fill the apparent gap between QQ""~0.3 and Qy,=I."," Thus we can reconcile the apparent contradiction between the CMB measurements of $l^\mathrm{Obs}_{\mathrm{A}}$ indicating flatness, and our seemingly low-matter-density universe (as indicated bythe growth of structure), requiring the addition of any non-clustering Dark Energy species to fill the apparent gap between $\Omega^\mathrm{Obs}_\mathrm{M} \sim 0.3$ and $\Omega_\mathrm{Tot} \equiv 1$." " Examining our 60 simulated cosmological models quantitatively, we informally choose a sel ol best runs — six Wy; models and six Yyyy models which provide very good SNe data fits. while simultaneously producing good cosmological parameters."," Examining our 60 simulated cosmological models quantitatively, we informally choose a set of `best' runs – six $\Psi _{\mathrm{Lin}}$ models and six $\Psi _{\mathrm{MD}}$ models – which provide very good SNe data fits, while simultaneously producing good cosmological parameters." " A truly optimized search over (he (Wy.zii) parameter space is not really called for at this (ov-moclel stage of our formalism: but a quick effort at optimization reveals an extensive ‘trench’ in parameter space for the Vj runs withquite low (and highly degenerate) \j4, values. vet offering a wide variation {ο choose from regarding their output cosmological parameters."," A truly optimized search over the $(\Psi _{0},z_\mathrm{init})$ parameter space is not really called for at this toy-model stage of our formalism; but a quick effort at optimization reveals an extensive `trench' in parameter space for the $\Psi _{\mathrm{MD}}$ runs withquite low (and highly degenerate) $\chi ^{2} _{\mathrm{Fit}}$ values, yet offering a wide variation to choose from regarding their output cosmological parameters." " So for illustration purposes. we arbitrarily select one low-\74, case. (Wa.zii)=(0.768.14). as a so-called. run. giving us a total of thirteen “best runs” for more in-depth study."," So for illustration purposes, we arbitrarily select one $\chi ^{2} _{\mathrm{Fit}}$ case, $(\Psi _{0},z_\mathrm{init}) = (0.768,14)$, as a so-called ``semi-optimized"" run, giving us a total of thirteen “best runs"" for more in-depth study." Residual Hubble diagrams of these best runs are shown in Figure 4.., Residual Hubble diagrams of these best runs are shown in Figure \ref{FigBestCosmSims}. These thirteen cosmological models clearly produce good Hubble curves. being visually almost indistinguishable from one another (and fom the now best-fit. O4=0.713. Concordance ACDM model) in the SN-cata-rich region of 2PSOL=IL. ," These thirteen cosmological models clearly produce good Hubble curves, being visually almost indistinguishable from one another (and from the now best-fit, $\Omega _{\Lambda} = 0.713$, Concordance $\Lambda$ CDM model) in the SN-data-rich region of $z^{\mathrm{Obs}} \sim 0.1 - 1$." "The causal backreaction formalism has therefore succeeded in reproducing the apparent cosmic acceleration as il is actually measured. via SNe standard candles,"," The causal backreaction formalism has therefore succeeded in reproducing the apparent cosmic acceleration as it is actually measured, via SNe standard candles." " More quantitatively, (he comprehensive output data from these thirteen best runs (and from best-lit ACDM and SCDAL. for comparison) are given in Table 1.. eSum"," More quantitatively, the comprehensive output data from these thirteen best runs (and from best-fit $\Lambda$ CDM and SCDM, for comparison) are given in Table \ref{TableSimRunsCosParamsABBREV}." marizing the results: these runs fit the SNe data essentially as well as ACIDM in terms of xp4. and are comparable in Pry.," Summarizing the results: these runs fit the SNe data essentially as well as $\Lambda$ CDM in terms of $\chi^{2}_{\mathrm{Fit}}$ , and are comparable in $P_{\mathrm{Fit}}$ ." The mid-range values of {0 indicate a strong enough backreaction effect to explain(he apparent acceleration. without being so large (1.e..," The mid-range values of $I_{0}$ indicate a strong enough backreaction effect to explainthe apparent acceleration, without being so large (i.e.," The evolution along the RGB ends when the thermal conditions for igniting helium burning are attained in the electron degenerate core.,The evolution along the RGB ends when the thermal conditions for igniting helium burning are attained in the electron degenerate core. " A runaway nuclear burning of He in the core occurs, the so-called He-flash, after which the star contracts and starts quiescent core helium burning along the HB."," A runaway nuclear burning of He in the core occurs, the so-called He-flash, after which the star contracts and starts quiescent core helium burning along the HB." " The value of the He-core mass at the He-flash (M.g.) controls the brightness of both the TRGB and the HB, two of the most important primary standard candles for old stellar populations (see, e.g., Lee, Freedman Madore 1993, Salaris Cassisi 1997, Caputo 1998, Catelan 2009, and references therein)."," The value of the He-core mass at the He-flash $M_{cHe}$ ) controls the brightness of both the TRGB and the HB, two of the most important primary standard candles for old stellar populations (see, e.g., Lee, Freedman Madore 1993, Salaris Cassisi 1997, Caputo 1998, Catelan 2009, and references therein)." Table 1 lists some relevant evolutionary properties at the TRGB for selected models computed with either the LUNA or the NACRE rate., Table \ref{tab1} lists some relevant evolutionary properties at the TRGB for selected models computed with either the LUNA or the NACRE rate. " The LUNA reaction rate causes an increase of the He-core mass at the He-flash of the order of ~0.002—0.003Ms, compared to the results with the NACRE rate."," The LUNA reaction rate causes an increase of the He-core mass at the He-flash of the order of $\sim0.002-0.003M_\odot$, compared to the results with the NACRE rate." The size of this difference is only slightly larger than the change due to the use of different sets of conductive opacities (Salaris et al., The size of this difference is only slightly larger than the change due to the use of different sets of conductive opacities (Salaris et al. " 2002, Cassisi et al."," 2002, Cassisi et al." 2007)., 2007). " Although the He-core mass is larger in the LUNA models, the surface luminosity at the TRGB is lower, the difference being Alog(L/Lo)z0.02 dex."," Although the He-core mass is larger in the LUNA models, the surface luminosity at the TRGB is lower, the difference being $\Delta\log(L/L_\odot)\approx 0.02$ dex." " This is due to the lower efficiency of the CNO cycle in the H-burning shell, that offsets the luminosity increase expected from the higher core mass (see, e.g., the discussion in Weiss et al."," This is due to the lower efficiency of the CNO cycle in the H-burning shell, that offsets the luminosity increase expected from the higher core mass (see, e.g., the discussion in Weiss et al." 2005)., 2005). Weiss et al. (, Weiss et al. ( "2005) obtained qualitatively similar results in terms of variation of M.g, and luminosity at the TRGB when updating their 'N(p,y)'°O reaction rate to the LUNA value and using the NACRE 3a reaction rate.","2005) obtained qualitatively similar results in terms of variation of $M_{cHe}$ and luminosity at the TRGB when updating their $^{14}N(p,\gamma)^{15}O$ reaction rate to the LUNA value and using the NACRE $\alpha$ reaction rate." " Quantitatively, however, both the increase of M. and decrease of the RGB tip luminosity are (at least for the Z=0.0001 case tabulated in their Table 1) about factor of 2 larger."," Quantitatively, however, both the increase of $M_{cHe}$ and decrease of the RGB tip luminosity are (at least for the Z=0.0001 case tabulated in their Table 1) about factor of 2 larger." " This may be due to the fact their reference !'N(p,y)?O reaction rate was the Adelberger et al. ("," This may be due to the fact their reference $^{14}N(p,\gamma)^{15}O$ reaction rate was the Adelberger et al. (" "1998) one, that is even larger than our reference NACRE rate.","1998) one, that is even larger than our reference NACRE rate." " Before closing this section, we comment briefly on the results obtained with the"," Before closing this section, we comment briefly on the results obtained with the" and ?.. that Alfvénn waves emitted by nearby collapsing protostars cause transient removal of ice mantles from the surrounding dust. resulting in the liberation of methanol into the gas phase at a distance from the protostellar core on the order of the MHD-wave damping length (~10 AU).,"and \citet{buc06}, that Alfvénn waves emitted by nearby collapsing protostars cause transient removal of ice mantles from the surrounding dust, resulting in the liberation of methanol into the gas phase at a distance from the protostellar core on the order of the MHD-wave damping length $\sim10^4$ AU)." ? used this theory to successfully explain the origin of the abundance gradients of various species observed along the ridge of TMC-I., \citet{mar00} used this theory to successfully explain the origin of the abundance gradients of various species observed along the ridge of TMC-1. The young age of Cha-MMS1 implies that protostellar collapse is currently in progress. resulting in the production of Alfvénn waves that could be responsible for desorption of the observed methanol.," The young age of Cha-MMS1 implies that protostellar collapse is currently in progress, resulting in the production of Alfvénn waves that could be responsible for desorption of the observed methanol." From the ratios of our observed CH:OH lines with those of ?.. differing temperatures were calculated for the A and E methanol nuclear spin species of 7.]+0.9 K and 4.7+0.6 K. respectively.," From the ratios of our observed $_3$ OH lines with those of \citet{kon00}, differing temperatures were calculated for the A and E methanol nuclear spin species of $7.1\pm0.9$ K and $4.7\pm0.6$ K, respectively." The column densities of A and E methanol (given in Table 2)) also differ. but within the error. bars.," The column densities of A and E methanol (given in Table \ref{tab:colds}) ) also differ, but within the error bars." The ratio of the sums over the statistical weights of the quantum states of A and E methanol approaches unity. so in the limit of high temperature (in. thermodynamic and chemical equilibrium). the abundances of A and E methanol should be approximately equal.," The ratio of the sums over the statistical weights of the quantum states of A and E methanol approaches unity, so in the limit of high temperature (in thermodynamic and chemical equilibrium), the abundances of A and E methanol should be approximately equal." Convergence of the A and E abundances ts calculated to oceur for temperatures above about 30 K (see??)..," Convergence of the A and E abundances is calculated to occur for temperatures above about 30 K \citep[see][]{wir09,wir11}." At lower temperatures. A-methanol is the more abundant species because its ground state is 7.9 K lower in energy than that of E-methanol.," At lower temperatures, A-methanol is the more abundant species because its ground state is 7.9 K lower in energy than that of E-methanol." Given that both spin species are likely to have the same spatial distribution in the ISM. their relative column densities in Cha-MMSI may be more accurately compared by assuming a common excitation temperature.," Given that both spin species are likely to have the same spatial distribution in the ISM, their relative column densities in Cha-MMS1 may be more accurately compared by assuming a common excitation temperature." In LTE at 6.1 K. the column densities of A and E methanol calculated from our observations are (7.2+0.7)x10 em and (6.6+0.7)xI0 em.," In LTE at 6.1 K, the column densities of A and E methanol calculated from our observations are $(7.2\pm0.7)\times10^{12}$ $^{-2}$ and $(6.6\pm0.7)\times10^{12}$ $^{-2}$." Using only the higher-frequency lines observed by ?.. we calculate the respective column densities to be (7.540.7)xLO em? and (7.9+0.8)x10? em-7.," Using only the higher-frequency lines observed by \citet{kon00}, we calculate the respective column densities to be $(7.5\pm0.7)\times10^{12}$ $^{-2}$ and $(7.9\pm0.8)\times10^{12}$ $^{-2}$." These results are consistent with equal abundances of A and E methanol. implying formation at close to statistical equilibrium.," These results are consistent with equal abundances of A and E methanol, implying formation at close to statistical equilibrium." In cold interstellar clouds. molecular tons become enriched in deuterium as a result of exothermic gas-phase fractionation reactions involving HD (?)..," In cold interstellar clouds, molecular ions become enriched in deuterium as a result of exothermic gas-phase fractionation reactions involving HD \citep{mil89}." ? found a deuterated N2»H7 fraction in Cha-MMSI of [N:D]/[N:H =11%.. which is typical for prestellar cores and young protostars| observed in the nearby Galaxy.," \citet{bel06} found a deuterated $_2$ $^+$ fraction in Cha-MMS1 of $_2$ $^+$ $_2$ $^+$ ] =, which is typical for prestellar cores and young protostars observed in the nearby Galaxy." The cyanoacetylene deuteration fraction [DC3N]/[HC3N] = 3.6+ 1s within the range of values previously observed in TMC-1 (1—6596: ??)). and is similar to the carbon-chain-rich prestellar core L1544(6%:: ?)). and the protostar L1527(366: 2)).," The cyanoacetylene deuteration fraction $_3$ $_3$ N] = $3.6\pm1.5$ is within the range of values previously observed in TMC-1 $1-6$; \citealt{tur01,sai02}) ), and is similar to the carbon-chain-rich prestellar core L1544; \citealt{how94}) ), and the protostar L1527; \citealt{sak09b}) )." A emislargec-C;HDcolumndensityof4.515x107 found in Cha-MMS1. which ts about 5 times greater than in L1527 and an order of magnitude greater than in TMC-1I (??)..," A large $c$ $_3$ HD column density of } is found in Cha-MMS1, which is about 5 times greater than in L1527 and an order of magnitude greater than in TMC-1 \citep{sak09b,tur01}." Accounting for the rather large uncertainty in the c-C3H> column density (see Section 3.2.0). we calculate that the cyclopropenylidene deuteration fraction [c-Ci3HD]/[e-CsH;] is between and34%.," Accounting for the rather large uncertainty in the $c$ $_3$ $_2$ column density (see Section \ref{sec:radex}) ), we calculate that the cyclopropenylidene deuteration fraction $c$ $_3$ $c$ $_3$ $_2$ ] is between and." . This is not significantly different from the range of values (5— 15%)) reported in a sample of twelve dark clouds by ?.. and the value of reported in L1527 by ?.. but is consistent with previous results which show the c-C3H> deuteration fraction ts larger than that of HC3N (e.g.??)..," This is not significantly different from the range of values $5-15$ ) reported in a sample of twelve dark clouds by \citet{bel88}, and the value of reported in L1527 by \citet{sak09b}, but is consistent with previous results which show the $c$ $_3$ $_2$ deuteration fraction is larger than that of $_3$ N \citep[\eg][]{tur01,sak09b}." Chemical models predict comparable levels of deuteration for ο ΗΒ and HC3N: deuterium enrichment in both these species is considered to originate predominantly from the CH:D ion (eg.??).," Chemical models predict comparable levels of deuteration for $c$ $_3$ HD and $_3$ N; deuterium enrichment in both these species is considered to originate predominantly from the $_2$ $^+$ ion \citep[\eg][]{rob00,tur01}." Deuteration may also occur by deuteron transfer as a result of collisions. with H;D'. followed by dehydrogenation upon recombination.," Deuteration may also occur by deuteron transfer as a result of collisions with $_2$ $^+$, followed by dehydrogenation upon recombination." Discrepancy between the deuteration fractions of c-CiHD and HC3N is indicative of an incomplete understanding of the deuterium chemistry of these two species., Discrepancy between the deuteration fractions of $c$ $_3$ HD and $_3$ N is indicative of an incomplete understanding of the deuterium chemistry of these two species. The fact that c- C3H> can become doubly deuterated may partly explain why c-CiHD is so abundant: if sufficient c-CiD» forms. it woulc act as a buffer for c-C;HD in subsequent proton-deuteror exchange processes.," The fact that $c$ $_3$ $_2$ can become doubly deuterated may partly explain why $c$ $_3$ HD is so abundant: if sufficient $c$ $_3$ $_2$ forms, it would act as a buffer for $c$ $_3$ HD in subsequent proton-deuteron exchange processes." It may thus be of interest to search for c-CiD»s in Cha-MMS1] and similar environments., It may thus be of interest to search for $c$ $_3$ $_2$ in Cha-MMS1 and similar environments. However. we are not aware of any published laboratory studies οἱ the rotational spectrum of c-CiD»: such a study would be warranted.," However, we are not aware of any published laboratory studies on the rotational spectrum of $c$ $_3$ $_2$; such a study would be warranted." The c-C3H> molecule exists in. two nuclear spit configurations: ortho and para. and it has been suggested that the ortho-to-para ratio (OPR) may be used as a probe of interstellar cloud ages (?)..," The $c$ $_3$ $_2$ molecule exists in two nuclear spin configurations: ortho and para, and it has been suggested that the ortho-to-para ratio (OPR) may be used as a probe of interstellar cloud ages \citep{mor06}. ." However. our present data are insufficient to usefully constrain the OPR.," However, our present data are insufficient to usefully constrain the OPR." Additional observations of c-CiH» and c-C;HD lines from a range of energy energy levels and with a range of optical depths will be required in order to better constrain the column densities of these species and derive more reliable values for the c-C3;H> OPR and deuteration fraction., Additional observations of $c$ $_3$ $_2$ and $c$ $_3$ HD lines from a range of energy energy levels and with a range of optical depths will be required in order to better constrain the column densities of these species and derive more reliable values for the $c$ $_3$ $_2$ OPR and deuteration fraction. " We observed large abundances ofthe sulphur-bearing carbon chains C,S (à=|— 3). on the same order of magnitude as found in various parts of the Taurus molecular cloud complex (e.g.2).."," We observed large abundances ofthe sulphur-bearing carbon chains $_n$ S $n=1-3$ ), on the same order of magnitude as found in various parts of the Taurus molecular cloud complex \citep[\eg][]{hir04}." Our [CCS]/[C3S] column density ratio (5.7+ 2.1) is greater than the values observed by ?.. of 2.1. 2.3. 2.0 in the dense cores LI495B. L1521B and L1521E. respectively. and ts more similar to the value of 5.1 found in TMC-1.," Our $_3$ S] column density ratio $5.7\pm2.1$ ) is greater than the values observed by \citeauthor{hir04}, , of 2.1, 2.3, 2.0 in the dense cores L1495B, L1521B and L1521E, respectively, and is more similar to the value of 5.1 found in TMC-1." The relatively large value in Chà-MMSI is primarily attributable to a relativelylow C3S column density. which is more consistent with the lower C3S column densities observed in the carbon-chain-rich cloud cores LI512. and LI251A by ?..," The relatively large value in Cha-MMS1 is primarily attributable to a relativelylow $_3$ S column density, which is more consistent with the lower $_3$ S column densities observed in the carbon-chain-rich cloud cores L1512 and L1251A by \citet{cor11}." Sulphur is believed to be incorporated into gas-phase hydrocarbon molecules in the ISM mainly by ton-neutral chemistry involving S (?).., Sulphur is believed to be incorporated into gas-phase hydrocarbon molecules in the ISM mainly by ion-neutral chemistry involving $^+$ \citep{mil90}. " Recombination of HC,S species then produces sulphuretted carbon chains.", Recombination of $_n$ $^+$ species then produces sulphuretted carbon chains. " The main source of Ην is from the reaction S + c-CiH» ——HC;S” + H. followed by recombination of HC3S~ to produce C3S. Thus. the relatively low C3S abundance in Cha-MMSI could be explained by a relative underabundance of c-C3H» compared with LI495B. LI521B and LI521E. An alternative method for the synthesis of C3S is by the neutral-neutral reaction C,H + CS — CSS + H(?).. However. this reaction is relatively slow (two orders of magnitude slower than the ton-neutral reaction). and is therefore expected to be less important in the production of C3S. The [N;:H ΟΡ] ratio may be used as a measure of chemical age in interstellar clouds on the basisthat carbon chains are most abundant at early times. whereas N.H becomes more abundant lateron as CO freezes out (e.g. ?). "," The main source of $_3$ $^+$ is from the reaction $^+$ + $c$ $_3$ $_2$ $\longrightarrow$$_3$ $^+$ + H, followed by recombination of $_3$ $^+$ to produce $_3$ S. Thus, the relatively low $_3$ S abundance in Cha-MMS1 could be explained by a relative underabundance of $c$ $_3$ $_2$ compared with L1495B, L1521B and L1521E. An alternative method for the synthesis of $_3$ S is by the neutral-neutral reaction $_2$ H + CS $\longrightarrow$ $_3$ S + H\citep{smi04}. However, this reaction is relatively slow (two orders of magnitude slower than the ion-neutral reaction), and is therefore expected to be less important in the production of $_3$ S. The $_2$ $^+$ ]/[CCS] ratio may be used as a measure of chemical age in interstellar clouds on the basisthat carbon chains are most abundant at early times, whereas $_2$ $^+$ becomes more abundant lateron as CO freezes out \citep[\eg][]{tak11}. ." Using the N:H abundance from ?.. we derive |N-H7|/[CCS] = 0.5+0.3 in Chi-MMS which is similar to the value of 0.52+0.07 found in the young.HI. carbon-chain- VeLLO L1521F (2).. indicating a comparable chemical age. but less than the value 1.18+0.21 in the more evolved," Using the $_2$ $^+$ abundance from \citet{bel06}, , we derive $_2$ $^+$ ]/[CCS] = $0.5\pm0.3$ in Cha-MMS1, which is similar to the value of $0.52\pm0.07$ found in the young, carbon-chain-rich VeLLO L1521F \citep{tak11}, , indicating a comparable chemical age, but less than the value $1.18\pm0.21$ in the more evolved" aand ool 10.200 Ix. and. 9.950 Ix. 10.600. Ix. ancl 10.600. Ix. and 10.200 Ix ancl 10.100 Ix. for rim. knots and NEB. respectively.,"and of 10,200 K and 9,950 K, 10,600 K and 10,600 K, and 10,200 K and 10,100 K, for rim, knots and NEB, respectively." And the aare automatically matched with the empirical values. since they are constraining the model as input. parameters.," And the are automatically matched with the empirical values, since they are constraining the model as input parameters." The corresponding ionisation structure is shown in ‘Table 8. from which we obtain the | and ratios of the dillerent zones in the nebula. as being: 1.64 component). 1.33 (I-component) and 1.56 (NEB). that. as above. are in contradiction with the ratios adopted in the empiricalef scheme.," The corresponding ionisation structure is shown in Table 8, from which we obtain the $^+$ and $^+$ ratios of the different zones in the nebula, as being: 1.64 ), 1.33 ) and 1.56 (NEB), that, as above, are in contradiction with the ratios adopted in the empirical scheme." We chose to include Table S in the paper. although qualitatively similar to Table 5. to allow for moclel zefs to be derived at a later time should one wish to do so.," We chose to include Table 8 in the paper, although qualitatively similar to Table 5, to allow for model s to be derived at a later time should one wish to do so." Finally. the projected emission maps obtained from this model are not shown here as they are qualitatively identical to those of our original model (right panels of Figure 2).," Finally, the projected emission maps obtained from this model are not shown here as they are qualitatively identical to those of our original model (right panels of Figure 2)." This work focused on the study of the apparent N overabundance in the outer knots of NGC 7000 with respect to the main nebular rim and shell., This work focused on the study of the apparent N overabundance in the outer knots of NGC 7009 with respect to the main nebular rim and shell. Alexander&Balick(1997). and Gruenwald&Χίοeas(1998) showed that long-slit data may give spurious overabuncdances of N ancl other elements in the outer regions of model PNe., \citet{b01} and \citet{b020} showed that long-slit data may give spurious overabundances of N and other elements in the outer regions of model PNe. TFhese authors have identified the cillerent charge-exchange reaction rates of N and O as the main responsible for the effect in the low-ionization regions of the nebulae. therefore allecting the /O) ratio. that as cliscussed in Section 3.4. is commonly. used to obtain the gef for nitrogen.," These authors have identified the different charge-exchange reaction rates of N and O as the main responsible for the effect in the low-ionization regions of the nebulae, therefore affecting the $^+$ $^+$ /O) ratio, that as discussed in Section 3.4, is commonly used to obtain the for nitrogen." However. as shown by. Mampaso(2004) charec-exchange reactions can. in this case. account at most by of the nitrogen overabundance of the knots of NGC 7009.," However, as shown by \citet{b030} charge-exchange reactions can, in this case, account at most by of the nitrogen overabundance of the knots of NGC 7009." In this paper we have presented a model that was able to reproduce the main spectroscopic characteristics of the various spatial regions of NGC 7009. without the need of assuming an inhomogencous set of abuncances., In this paper we have presented a model that was able to reproduce the main spectroscopic characteristics of the various spatial regions of NGC 7009 without the need of assuming an inhomogeneous set of abundances. We investigated the importance of taking into account the ellects of a narrow slit. and our results in Table 3 and 7 show ju the convolution of the model results with the profile of 10 narrow slit used. for the observations presented in rresults in the Nu] emission being enhanced respect to iin all regions of the nebula. with the effect being slightly more pronounced in the knots.," We investigated the importance of taking into account the effects of a narrow slit, and our results in Table 3 and 7 show that the convolution of the model results with the profile of the narrow slit used for the observations presented in results in the [N ] emission being enhanced respect to in all regions of the nebula, with the effect being slightly more pronounced in the knots." The /O) predicted by our models are 0.60. 0.72 and 0.62 (or alternatively.|. 0.61. 0.75 and 0.64) for the rim. knots ancl the whole nebula. respectively. all at variance with thezef assumption of unitv for this ratio.," The $^+$ $^+$ /O) predicted by our models are 0.60, 0.72 and 0.62 (or alternatively, 0.61, 0.75 and 0.64) for the rim, knots and the whole nebula, respectively, all at variance with the assumption of unity for this ratio." The 1ο will therefore be underestimated. by the empiricalscheme.," The s will therefore be underestimated by the empiricalscheme," "time-step is overestimated, the integration could lead to unphysically too strong feedback effects.","time-step is overestimated, the integration could lead to unphysically too strong feedback effects." We also want to warn the reader against any feedback implementation that would inject the energy as a rate to be applied over a given length of time., We also want to warn the reader against any feedback implementation that would inject the energy as a rate to be applied over a given length of time. Modifying either the rate of entropy change or the hydrodynamical acceleration would not conserve the input energy if the kick operator (from the leap-frog integration scheme) is applied on two successive steps of different length., Modifying either the rate of entropy change or the hydrodynamical acceleration would not conserve the input energy if the kick operator (from the leap-frog integration scheme) is applied on two successive steps of different length. " Considering the problems mentioned above, we recommend injecting instantaneously the feedback energy just before the computation of the next time-step, whilst, taking into account the following two actions to preserve the accuracy of the time integration."," Considering the problems mentioned above, we recommend injecting instantaneously the feedback energy just before the computation of the next time-step, whilst, taking into account the following two actions to preserve the accuracy of the time integration." " Firstly, to ensure the fast information transfer of the change of energy in the medium, we use the time-step limiter proposed by SM09."," Firstly, to ensure the fast information transfer of the change of energy in the medium, we use the time-step limiter proposed by SM09." In Appendix C we describe an implementation of this limiter in which preserve the time-step synchronisation., In Appendix \ref{app:timelimiter} we describe an implementation of this limiter in which preserve the time-step synchronisation. " Secondly, to ensure that the computation of the time-step following the explosion takes properly into account the local hydrodynamical change, we impose that the particles which receive the energy update their signal velocity and hydrodynamical acceleration."," Secondly, to ensure that the computation of the time-step following the explosion takes properly into account the local hydrodynamical change, we impose that the particles which receive the energy update their signal velocity and hydrodynamical acceleration." " Doing so, we impose for these particles an update of the computation of their next time-step that will lead to an update of their hydrodynamical properties right after the explosion time (see Appendix D for the detail about this time-step update)."," Doing so, we impose for these particles an update of the computation of their next time-step that will lead to an update of their hydrodynamical properties right after the explosion time (see Appendix \ref{app:timeupdate} for the detail about this time-step update)." We will now show that these actions are essential to be considered altogether in order to preserve the concordance of feedback methods when using individual time-steps., We will now show that these actions are essential to be considered altogether in order to preserve the concordance of feedback methods when using individual time-steps. In this section we describe the Sedov’s blast wave tests performed with an individual time-step scheme., In this section we describe the Sedov's blast wave tests performed with an individual time-step scheme. " Before showing the results of our simulations, we mention the differences with the setup used in Sec. 2.1.."," Before showing the results of our simulations, we mention the differences with the setup used in Sec. \ref{subsec:globalsedovsetup}." " Starting with the same glass-like uniform conditions presented in Sec. 2.1,,"," Starting with the same glass-like uniform conditions presented in Sec. \ref{subsec:globalsedovsetup}," " all particles are evolved over global, background time-steps that are of the order of Atpack~107%."," all particles are evolved over global, background time-steps that are of the order of $\Delta t_{\rm back} \sim 10^{-3}$ ." " Since all particles are synchronised from the beginning of the simulation, the issues about an explosion occurring in the middle of active steps or about neighbouring particles being initially on different time-bin levels, will not be addressed in this section."," Since all particles are synchronised from the beginning of the simulation, the issues about an explosion occurring in the middle of active steps or about neighbouring particles being initially on different time-bin levels, will not be addressed in this section." We refer to Sec., We refer to Sec. 3.3 for an analysis of these effects on the long-term evolution of the medium., \ref{sec:evrard} for an analysis of these effects on the long-term evolution of the medium. " 'To avoid a pre-defined population of the time-bin levels in these Sedov’s test simulations, the injection of a total energy of E,—1 (either in thermal or kinetic form), is delayed by a few of the background steps."," To avoid a pre-defined population of the time-bin levels in these Sedov's test simulations, the injection of a total energy of $E_\star=1$ (either in thermal or kinetic form), is delayed by a few of the background steps." " In order to focus on feedback processes similar to SN explosions or BH activity, we have set the total initial internal energy of the system to Eg=1."," In order to focus on feedback processes similar to SN explosions or BH activity, we have set the total initial internal energy of the system to $E_0=1$." " Given the resolution N=128? of the simulations, the initial energy contrast between the heated/kicked particles and the background ones is of the order of ~10°."," Given the resolution $N=128^3$ of the simulations, the initial energy contrast between the heated/kicked particles and the background ones is of the order of $\sim 10^6$." All tests presented in this section have been run until t=0.04 after the explosion time., All tests presented in this section have been run until $t=0.04$ after the explosion time. It is interesting to remind here that the amount of injected energy constrains the time-steps that follow the explosion., It is interesting to remind here that the amount of injected energy constrains the time-steps that follow the explosion. " Since the signal velocity (seeMonaghan1997) at the explosion location is related to the energy injection as Usigος./Ux, we can already anticipate through the Courant criterion that, for the energy contrast considered here, the step of the heated/kicked particles will be ~10? times smaller than the background step."," Since the signal velocity \citep[see][]{Monaghan1997} at the explosion location is related to the energy injection as $v_{\rm sig} \propto \sqrt{u_\star}$, we can already anticipate through the Courant criterion that, for the energy contrast considered here, the step of the heated/kicked particles will be $\sim 10^3$ times smaller than the background step." This will correspond to an abrupt drop of about 10 levels in the hierarchy of time-bins., This will correspond to an abrupt drop of about 10 levels in the hierarchy of time-bins. " 'To analyse the behaviour of our time-step scheme, we use a set of simulations (see Table 2)) where combinations of the integration techniques and numerical parameters are investigated."," To analyse the behaviour of our time-step scheme, we use a set of simulations (see Table \ref{table:sedovstat}) ) where combinations of the integration techniques and numerical parameters are investigated." Here we use again a simulation with a global time-stepping scheme as reference., Here we use again a simulation with a global time-stepping scheme as reference. " Then, we test the limiter technique without the time-step update."," Then, we test the limiter technique without the time-step update." " Finally, we enforce the time-step update, as describe in Appendix D.."," Finally, we enforce the time-step update, as describe in Appendix \ref{app:timeupdate}." " With the latter setup, we estimate the impact of the limiter parameter fstep, as well as the time integration efficiency parameter η (from Eq. B3)),"," With the latter setup, we estimate the impact of the limiter parameter $f_{\rm step}$, as well as the time integration efficiency parameter $\eta$ (from Eq. \ref{eq:accdtnew}) )," for both the thermal and kinetic feedback methods., for both the thermal and kinetic feedback methods. " With the aim of studying two different initial energy distributions, we also compare simulations where the energy is injected over a different number of particles."," With the aim of studying two different initial energy distributions, we also compare simulations where the energy is injected over a different number of particles." " In order to quantify the accuracy of the different methods, we estimate the input energy conservation error"," In order to quantify the accuracy of the different methods, we estimate the input energy conservation error" and the double scattering parameter is a m—R-00 = The distance parameter d is d= I5) where (he equality in (he second relation holds when the two lenses ave at the distance.,and the double scattering parameter is a = = The distance parameter $d$ is d 1 where the equality in the second relation holds when the two lenses are at the distance. The effective mass ratio e is Luo τετef fale doe The effective mass ratio is smaller (han the mass ratio., The effective mass ratio $\epsilon$ is = = = d The effective mass ratio is smaller than the mass ratio. The weight is shifted to the last scatterer in double scattering lensing., The weight is shifted to the last scatterer in double scattering lensing. Note that we have chosen the last scatterer for the reference mass., Note that we have chosen the last scatterer for the reference mass. It should be worth pointing out that the double scattering parameter « is essentially the (square of the) Einstein radius that is easily measurable in an (almost) axisvuunetric svslem as in 5D59J0946-4-1006. (Gavazzietal2008).., It should be worth pointing out that the double scattering parameter $a$ is essentially the (square of the) Einstein radius that is easily measurable in an (almost) axisymmetric system as in SDSSJ0946+1006 \citep{double-ring-first}. In an axisvaumetric DSTP lens three ring images are formed. even though the innermost ring is “unstable” to break into a and y/a measures the middle ring radius in units of the Einstein ring radius of the total effective mass rp.," In an axisymmetric DSTP lens three ring images are formed, even though the innermost ring is “unstable"" to break into a half-circle, and $\sqrt{a}$ measures the middle ring radius in units of the Einstein ring radius of the total effective mass $r_E$." The DSTP lens svstem can be considered to have two characteristic parameters rp and να., The DSTP lens system can be considered to have two characteristic parameters $r_E$ and $\sqrt{a}$. llere the focus is in the main lens and the interest is on what happens to the Einsteing rng of the main lens under (he perturbation of a perturbing mass., Here the focus is in the main lens and the interest is on what happens to the Einsteing ring of the main lens under the perturbation of a perturbing mass. So it is useful to renormalize the lens equation bx the Einstein ring radius of the main lens., So it is useful to renormalize the lens equation by the Einstein ring radius of the main lens. There are two cases: 1) object Lis the perturbing mass: 2) object 2 is the perturbing mass., There are two cases: 1) object 1 is the perturbing mass; 2) object 2 is the perturbing mass. Case 1): Renormaltize (hie lens equation (2)) so that the unit distance is rps., Case 1): Renormalize the lens equation \ref{eqLeq}) ) so that the unit distance is $r_{E2}$ . "In hydrostatic equilibrium, the gas pressure P(r) balances the gravitational acceleration g(r) where P= and is the gas density.","In hydrostatic equilibrium, the gas pressure $P(r)$ balances the gravitational acceleration $g(r)$ where $P = {\rho k_b T}/{\mu m_H}$ and $\rho(r)$ is the gas density." " This by itself is not pkyT/umgsufficient to p(r)determine the density and temperature profiles uniquely; however, if we also use the fact, as suggested by Figure 7,, that compressional heating balances cooling, we can make more progress."," This by itself is not sufficient to determine the density and temperature profiles uniquely; however, if we also use the fact, as suggested by Figure \ref{fig_compress}, that compressional heating balances cooling, we can make more progress." " We write this as, where A(T) is the cooling rate and v, is the radial velocity."," We write this as, where $\Lambda(T)$ is the cooling rate and $v_r$ is the radial velocity." We have assumed the work done on a fluid, We have assumed the work done on a fluid saluples containing the highest redshift SACs selected at these wavelengths (albeit these samples contain contanunation from lower redshift objects).,samples containing the highest redshift SMGs selected at these wavelengths (albeit these samples contain contamination from lower redshift objects). Without further imultiwaveleugth data. it is impossible to tell individually which of the 8 candidates are at :>d. and which are just peaking at ga because they have cooler dust temperatures.," Without further multi-wavelength data, it is impossible to tell individually which of the 8 candidates are at $z>4$, and which are just peaking at $\,\mu$ m because they have cooler dust temperatures." One wav to test the reality of these high redshift candidates is to further coustrain their SEDs with data at longer subi wavelengths such ax those from the 8704540 LABOCA siuvey of ECDFS (Weiss et al.," One way to test the reality of these high redshift candidates is to further constrain their SEDs with data at longer submm wavelengths such as those from the $\,\mu$ m LABOCA survey of ECDFS (Weiss et al." 2009)., 2009). In order to do a robust comparison between the LABOC'A and BLAST fluxes. a correction for flux boosting necds to be applied to both surveys using the same method (ee. Coppin et al.," In order to do a robust comparison between the LABOCA and BLAST fluxes, a correction for flux boosting needs to be applied to both surveys using the same method (e.g. Coppin et al." 2006)., 2006). This is bevond the scope of this paper but should be possible with full access to the signal aud noise maps from both survers., This is beyond the scope of this paper but should be possible with full access to the signal and noise maps from both surveys. Another poteutial way to break the degeneracy between redshift aud temperature for these candidates is with the radio aud/or far-IR (e.g. Ἰθ0 μι) flux: we discuss this further in the next section.," Another potential way to break the degeneracy between redshift and temperature for these candidates is with the radio and/or far-IR (e.g. $100\,\mu$ m) flux; we discuss this further in the next section." Photometry- frou 500 µια alone can provide au accurate nieasure of (1|Maqua.," Photometry from $\,\mu$ m alone can provide an accurate measure of $(1+z)/T_{\rm{dust}}$." Fig., Fig. 3) shows a simulation ofHerschel SPIRE photometry for a source that peaks at 500 jan. Fitting modified blackbody models to this data we fiud the pairs of T and z that fit these data (panel b of Fig. 3))," \ref{fig:sim} shows a simulation of SPIRE photometry for a source that peaks at $\,\mu$ m. Fitting modified blackbody models to this data we find the pairs of T and z that fit these data (panel b of Fig. \ref{fig:sim}) )" " aud the resulting Ley (panel c of Fig. 21),", and the resulting $L_{\rm{FIR}}$ (panel c of Fig. \ref{fig:sim}) ). The radio onüssion from e@alaxics is known to correlate well with the infrared cinission iu the local Universe (Coudon 1992)., The radio emission from galaxies is known to correlate well with the infrared emission in the local Universe (Condon 1992). Because of this racdio-intrared correlation. radio data is often used to help ideutifv counterparts to SMCs (e.g. Ivison et al.," Because of this radio-infrared correlation, radio data is often used to help identify counterparts to SMGs (e.g. Ivison et al." 2002). aud to constrain the redshift (e.g. Carilli Yun 1999: Isles et al.," 2002), and to constrain the redshift (e.g. Carilli Yun 1999; Hughes et al." 2002: Arctxaga ct al., 2002; Aretxaga et al. 2007)., 2007). We demonstrate the latter vont iu panel d of Fie. 3.., We demonstrate the latter point in panel d of Fig. \ref{fig:sim}. Here we assume the average value and scatter in the gq parameter from fitting local ealaxies (Yun. Reddy Condon 2001).," Here we assume the average value and scatter in the $q$ parameter from fitting local galaxies (Yun, Reddy Condon 2001)." The radio fux is rot degenerate with the redshift: however. unfortunately. he large scatter in the local racio-IR correlation provides arly loose coustraiuts on the redshift of iudividual objects from the racio flux.," The radio flux is not degenerate with the redshift; however, unfortunately, the large scatter in the local radio-IR correlation provides fairly loose constraints on the redshift of individual objects from the radio flux." Nevertheless. a laree fraction of the bright SAIGs detected with SPIRE will be above he flax limits of deep (tras< 543v) 1.1 Giz radio survevss," Nevertheless, a large fraction of the bright SMGs detected with SPIRE will be above the flux limits of deep $\sigma_{\rm{radio}}<5\,\mu$ Jy) 1.4 GHz radio surveys." With laree statistical samples. the redshift distribution inferred from) includius radio observations should be robust. assuming the radio-IR correlation holds out to high redshift.," With large statistical samples, the redshift distribution inferred from including radio observations should be robust, assuming the radio-IR correlation holds out to high redshift." Below ~ 504au rest-frame. the SED of galaxies is uo ongcr donuuated by the single temperature modified dackbody but iustead by warmer dust compoucuts.," Below $\sim50\,\mu$ m rest-frame, the SED of galaxies is no longer dominated by the single temperature modified blackbody but instead by warmer dust components." This can be seen in panel a of Fie., This can be seen in panel a of Fig. 3. where the dash-dot curve isa Chary Elbaz (CEOL) teiiplate represcutative of ocal star foriung galaxies., \ref{fig:sim} where the dash-dot curve is a Chary Elbaz (CE01) template representative of local star forming galaxies. Fitting the CEOL templates (allowing the luminosity aud temperature to varv) to the simulated SPIRE photometry we estimate the 1004421 Hux as a function of redshift (ραπ ο of Fig. 3)).," Fitting the CE01 templates (allowing the luminosity and temperature to vary) to the simulated SPIRE photometry we estimate the $\,\mu$ m flux as a function of redshift (panel e of Fig. \ref{fig:sim}) )." While he curve is not smooth (due to discrete templates within the CEOL brary). overall the far-IR flux can constrain the redshift for this simulated galaxy with uo xior assunrptiou on its dust temperature.," While the curve is not smooth (due to discrete templates within the CE01 library), overall the far-IR flux can constrain the redshift for this simulated galaxy with no prior assumption on its dust temperature." The dotted ine in panel e of Fig., The dotted line in panel e of Fig. 3. shows the scusitivity of the deepest.Herschel PACS extragalactie survey. (GOODSIHoerschel. PI: D. Elbaz): this deep survey should detect bright SMCs bevoud 2~3 by measuring the redshitted cussion from wari dust that is heated in O&BB star-forming regions aud appears to correlate well with ongoing star-formation (Calzetti et al.," \ref{fig:sim} shows the sensitivity of the deepest PACS extragalactic survey (GOODS, PI: D. Elbaz); this deep survey should detect bright SMGs beyond $z\sim3$ by measuring the redshifted emission from warm dust that is heated in B star-forming regions and appears to correlate well with ongoing star-formation (Calzetti et al." 2005)., 2005). From the BLAST ECDFS data we estimate a space deusity of Lindy at zo|: this is «35% (8/23) of all sources selected down to these depths in the BLAST data.," From the BLAST ECDFS data we estimate a space density of $<17\,$ $^{-2}$ for sources with $_{500}>45\,$ mJy at $z>4$; this is $<35\,$ (8/23) of all sources selected down to these depths in the BLAST data." These bright 500 prueselected SALCs at 2>Lb coutribute «1%( of the total background emission at jan (Fixsen et al.," These bright $\,\mu$ m-selected SMGs at $z>4$ contribute $<1\%$ of the total background emission at $\,\mu$ m (Fixsen et al." 1998)., 1998). Coustrained by a recent analysis of the infrared extragalactic backerouncd light (EBL). galaxies evolution models predict the source deusity of galaxies with S390>2T11J& at 2o>L to be 5deg 7 (Chary Pope 2010).," Constrained by a recent analysis of the infrared extragalactic background light (EBL), galaxies evolution models predict the source density of galaxies with $_{500}>27\,$ at $z>4$ to be $\,$ $^{-2}$ (Chary Pope 2010)." The range of predicted umber density comes from considering two evolutious of the inodels both of which fit the observed EBL., The range of predicted number density comes from considering two evolutions of the models both of which fit the observed EBL. We Bud that our cuxreut observational constraint is consistent with both evolutionary scenarios., We find that our current observational constraint is consistent with both evolutionary scenarios. Future subuui surveys with much larger telescopes such as JOAMT. LAIT and CCAT will reach πιο. deeper flux limits before litting the confusion Lut.," Future submm surveys with much larger telescopes such as JCMT, LMT and CCAT will reach much deeper flux limits before hitting the confusion limit." " With these sHurvevs. woe can expect to detect mamy more dusty ealaxies at :2Lt: the models in Chary Pope (2010) predict a umber density of des7 at :>1 for ealaxies down to Sindy at μαι, Tn the past two wears the tally of :>1 spectroscopically confirmed SMCSs has erown frou zero to (Capak et al."," With these surveys, we can expect to detect many more dusty galaxies at $z>4$; the models in Chary Pope (2010) predict a number density of $\,$ $^{-2}$ at $z>4$ for galaxies down to $\,$ mJy at $\,\mu$ m. In the past two years, the tally of $z>4$ spectroscopically confirmed SMGs has grown from zero to (Capak et al." 2008: Coppin et al., 2008; Coppin et al. 2009: Daddi et al., 2009; Daddi et al. 2009a.b).," 2009a,b)." Coppin et al. (, Coppin et al. ( "2009) estimate the umuber deusitv of SAICs at 2>1 by combining these 5 sources frou, 3. independent submillimeter surveys and find a ↕∪↖↖⇁↸∖↥⋅∐∐∐↑∪↕∣≼∐∖∶↴∙⊾−∙↖↖↕∐↕","2009) estimate the number density of SMGs at $z>4$ by combining these 5 sources from 3 independent submillimeter surveys and find a lower limit of $>7\,$ $^{-2}$." ↸∖↑↕∐↴∖↴↕↴∖↴↸⊳∪∐↴∖↴↕↴∖↴↑↸∖∐↑↖↖↽↕↑∐ ⋅≻⇁⋅ ⋅⋅ ⋅ ⋅ ≺∏∐⋅↻↥⋅↸∖≼∐↸⊳↑↕∪∐↴∖↴↕⋟∪↥⋅⋅↱⊐∩∩∕∣↕⊔≒∖↴↸∖↕↸∖↸⊳↑↸∖≼↧∶↴∙⊾⋜↧↕⋜↧⊼↕↸∖↴∖↴↖↖⇁↸∖∐∪↑↸∖↑∐⋜↧↑ ↑↕∐∖↴∖↴↸∖∐↴∖↴↕↑↕↖↽↕↑↕↸∖↴∖↴∪↕⋟↑∐↸∖↕≧∫⇀⊀≚≋⊺⋜⋯≼↧↴∖↴∏↴⋝∐↓∐∐⋯↸∖↑↸∖↥⋅↴∖↴↿∐⋅↖⇁↸∖∙↖⇁↴∖↴ ⋜⋯∖∐∪↑↑↕∐∖↴∖↴⋜⋯∐∖⋜↕↑−∙∶↓∶∪∐↕⋅↖↽↕⋅↱⊐∪↕⋟↑↕∐∖∶↓ spectroscopically confirmed SAICs might be detected down to the BLAST ECDFS survey depths (assuming a typical SAIC dust temperature).," While this is consistent with our predictions for $\,\mu$ m-selected galaxies we note that the sensitivities of the BLAST and submillimeter surveys are not the same at $z=4$; only $1/5$ of the $z>4$ spectroscopically confirmed SMGs might be detected down to the BLAST ECDFS survey depths (assuming a typical SMG dust temperature)." Folding this in. the Coppin ct al. (," Folding this in, the Coppin et al. (" 2009) estimate down to Suy720 ταν scales to > L.ldee7 at 2>f.,"2009) estimate down to $_{850}>20\,$ mJy scales to $>1.4\,$ $^{-2}$ at $z>4$." There is some evidence that large numbers of very niassive ealaxics af 2[| pose a substantial challeuge to standard ealaxy formation theorv (e.g. Baugh ot al., There is some evidence that large numbers of very massive galaxies at $z>4$ pose a substantial challenge to standard galaxy formation theory (e.g. Baugh et al. 2005)., 2005). Fig., Fig. Lo sunuuarizes the current observational constraints on the nuuber deusitv of bright SMCs as a function of redshift., \ref{fig:num} summarizes the current observational constraints on the number density of bright SMGs as a function of redshift. Blue and green bars are for 4na-selected. SMCsS using values from the literature (Chapman et al.," Blue and green bars are for $\,\mu$ m-selected SMGs using values from the literature (Chapman et al." 2005: Coppin et al., 2005; Coppin et al. 2009: Pope et al., 2009; Pope et al. 2006) aud the red bar is our new upper nit frou the analvsis in this paper of the BLAST pau-selected sources.," 2006) and the red bar is our new upper limit from the analysis in this paper of the BLAST $\,\mu$ m-selected sources." Overall. there does not appear to be roo for a large fraction of the SAIC population to be above 2=1 down to these flix limits.," Overall, there does not appear to be room for a large fraction of the SMG population to be above $z=4$ down to these flux limits." "where gp, is the radiation transfer function. which can be computed with a Boltzmann code. j; are the spherical Jessel functions. and PG)xfeo 1.is the primordial. power spectrum. with a spectral index my.","where $g_{T,\ell}$ is the radiation transfer function, which can be computed with a Boltzmann code, $j_{\ell}$ are the spherical Bessel functions, and $P(k)\propto k^{n_s-4}$ is the primordial power spectrum, with a spectral index $n_s$." OOn large angular scales. the Sachs-Wolfe (SW) elect is the dominant contribution to the CAIB signal.," On large angular scales, the Sachs-Wolfe (SW) effect is the dominant contribution to the CMB signal." " In this regime. the CAMB bispectrum takes the following analytical form: This bispectrum is maximal when one of the multipoles is minimal (£4,«f2= £5) whieh is called. the squeezed configuration."," In this regime, the CMB bispectrum takes the following analytical form: This bispectrum is maximal when one of the multipoles is minimal $\ell_1 \ll \ell_2 \simeq \ell_3$ ) which is called the squeezed configuration." A commonly usec cubie estimator of {κι has been developed: by 2..., A commonly used cubic estimator of $f_{\mathrm{NL}}$ has been developed by \cite{Komatsu2005}. He is much faster than performing. the whole bispectrum analysis and fitting the local bispectrum., It is much faster than performing the whole bispectrum analysis and fitting the local bispectrum. ln its original version. the estimator takes into account beam profile and homogeneous noise. and has been used on WALAP data to vield the current constraint 10«fxy74 (?)..," In its original version, the estimator takes into account beam profile and homogeneous noise, and has been used on WMAP data to yield the current constraint $-10 < f_\mathrm{NL} < 74$ \citep{Komatsu2011}." The estimator was then further developed by several authors by adding a linear term accounting for masking and inhomogeneous noise (2).., The estimator was then further developed by several authors by adding a linear term accounting for masking and inhomogeneous noise \citep{Creminelli2006}. Here. we will only consider noiseless full-sky maps without beam smoothing so that we can apply the estimator in its original form.," Here, we will only consider noiseless full-sky maps without beam smoothing so that we can apply the estimator in its original form." " To build the [νι estimator we first. define the filtered maps at comoving distance r and direction n: where C, is the CMD power spectrum.", To build the $f_{\mathrm{NL}}$ estimator we first define the filtered maps at comoving distance $r$ and direction $\mathbf{n}$: where $C_\ell$ is the CMB power spectrum. D(r.n) is then an estimated map of the primordial potential luctuations Φα) via Wiener filtering.," $B(r,\mathbf{n})$ is then an estimated map of the primordial potential fluctuations $\Phi(r\;\!\mathbf{n})$ via Wiener filtering." The integral of LB permits us to estimate [κι as: where DS.ES is the local bispectrum for fixe=1. to be compared VERONwith the observed value Bhs 111 can be," The integral of $A B^2$ permits us to estimate $f_\mathrm{NL}$ as: where $B^{\mathrm{loc}}_{\ell_1 \ell_2 \ell_3}=\sqrt{N_{\ell_1 \ell_2 \ell_3}} \, b^{\mathrm{loc}}_{\ell_1 \ell_2 \ell_3}$ is the local bispectrum for $f_\mathrm{NL}=1$, to be compared with the observed value $B^{\mathrm{obs}}_{\ell_1 \ell_2 \ell_3}$." Pyfataeshown that this estimator takes analytically the form: Lt is near-optimal in the sense that it minimizes the 47 for weak NC (under some assumptionson isosceles and equilateral triangles)., It can be shown that this estimator takes analytically the form: It is near-optimal in the sense that it minimizes the $\chi^2$ for weak NG (under some assumptionson isosceles and equilateral triangles). The estimator becomes sub-optimal (e.g. 2)) for large enough. fee. when the variance of the hispectrum ects O(fg) correction compared to the weak NG computation with Wick's theorem (see Appendix. ??))," The estimator becomes sub-optimal (e.g. \cite{Elsner2009}) ) for large enough $f_\mathrm{NL}$, when the variance of the bispectrum gets $\mathrm{O}\!\left(f_\mathrm{NL}^2\right)$ correction compared to the weak NG computation with Wick's theorem (see Appendix \ref{appendix:wngvar}) )." " Several wavs of visualising the angular bispectrum have been proposed in the literature. e.g. isosurfaces in the (61.65.65). 3D space by 2.. or slices of constant perimeter in the orthogonal transverse coordinate (£41,545) space by T. "," Several ways of visualising the angular bispectrum have been proposed in the literature, e.g. isosurfaces in the $\ell_1,\ell_2,\ell_3$ ) 3D space by \cite{Fergusson2010}, , or slices of constant perimeter in the orthogonal transverse coordinate $\ell _{\perp a},\ell _{\perp b}$ ) space by \cite{Bucher2010}. ." "Under the assumption of statistical isotropy. the bispectrunm b,jy. is invariant under permutations of £4. f£» ancl £5. ie."," Under the assumption of statistical isotropy, the bispectrum $b_{\ell_1 \ell_2 \ell_3}$ is invariant under permutations of $\ell_1$ , $\ell_2$ and $\ell_3$, ie." it is a function of the shape and size of the triangle (C1{ον(ο) only. ic. independent of its orientation.," it is a function of the shape and size of the triangle $(\ell_1, \ell_2, \ell_3)$ only, i.e. independent of its orientation." Pherefore. we can find a parametrisation invariant under permutation of £41. (S. and £5. which avoids reclundaney of information and allows convenient. visualisation and interpretation of data.," Therefore, we can find a parametrisation invariant under permutation of $\ell_1$, $\ell_2$, and $\ell_3$, which avoids redundancy of information and allows convenient visualisation and interpretation of data." Let us denote as (£1.f2.45) the equivalence class of the triplet under permutations.," Let us denote as $\overline{(\ell_1,\ell_2,\ell_3)}$ the equivalence class of the triplet under permutations." " The elementary symmetric polvnoniuals ensure. the invariance under permutations: Vhrough Carcdan’s formula. there is à. one-to-one correspondence between (£41.£5.£5). defined by the roots of the polynomial X?aN?|oXση. and the triplet (m,05.05)."," The elementary symmetric polynomials ensure the invariance under permutations: Through Cardan's formula, there is a one-to-one correspondence between $\overline{(\ell_1,\ell_2,\ell_3)}$, defined by the roots of the polynomial $X^3 - \sigma_1 X^2 + \sigma_2 X - \sigma_3$, and the triplet $(\sigma_1,\sigma_2,\sigma_3)$." We Further define the scale-invariant parameters 65—]12e./o]j3 and ὃν=2a3/o} with coellicient chosen so that συ and es vary in the range 0.1].," We further define the scale-invariant parameters $\tilde{\sigma}_2=12\sigma_2/\sigma_1^2-3$ and $\tilde{\sigma}_3=27\sigma_3/\sigma_1^3$ with coefficient chosen so that $\tilde{\sigma}_2$ and $\tilde{\sigma}_3$ vary in the range [0,1]." As illustrated in the upper panel of Fig. L..," As illustrated in the upper panel of Fig. \ref{triparam}," this parametrisation does not allow us to discriminate ellicientIy between the dillerent triangles., this parametrisation does not allow us to discriminate efficiently between the different triangles. We find that the parameters noted (P.£8) and defined provide a clearer distinction. of the triangles as is illustrated in the bottom panel of Pig. 1..," We find that the parameters noted $(P,F,S)$ and defined as: provide a clearer distinction of the triangles as is illustrated in the bottom panel of Fig. \ref{triparam}." To illustrate the use of our (P.£F.S)-parametrisation. we plot in Fig. 2," To illustrate the use of our $(P,F,S)$ -parametrisation, we plot in Fig. \ref{fig:cmbparam}" the theoretical CMD bispectrum produced by the local NC model [κι computed through σα. 10...," the theoretical CMB bispectrum produced by the local NG model $f_\mathrm{NL}$, computed through Eq. \ref{eq:cmbispth}." " The triangle perimeters. 2. vary between μαι=30 (equilateral configuration with fi,= 10) and μις=6120 (equilateral configuration with fuss,= 2040)."," The triangle perimeters, $P$, vary between $P_\mathrm{min}=30$ (equilateral configuration with $\ell_\mathrm{min}=10$ ) and $P_\mathrm{max}=6120$ (equilateral configuration with $\ell_\mathrm{max}=2040$ )." We plot representative perimeters tracing the building up of the bispectrum with scale. giving 2/3 on cach panel.," We plot representative perimeters tracing the building up of the bispectrum with scale, giving $P/3$ on each panel." The color code scales from deep purple/black (most negative) to red/dark erey (positive)., The color code scales from deep purple/black (most negative) to red/dark grey (positive). In the first. panels for the smallest. perimeters. Low riangles are present.," In the first panels for the smallest perimeters, few triangles are present." As the perimeter increases the (£5) space is populated starting with equilateral configurations (upper right corner) first to reach squeezed configuration (upper left corner) later.," As the perimeter increases the $(F,S)$ space is populated starting with equilateral configurations (upper right corner) first to reach squeezed configuration (upper left corner) later." Conversely in the last panels for the areest perimeters. the resolution limit (uss=2048 limits he possible configurations. leaving only the equilateral riangles in the end.," Conversely in the last panels for the largest perimeters, the resolution limit $\ell_\mathrm{max}=2048$ limits the possible configurations, leaving only the equilateral triangles in the end." The Saehs-Wolle shape (see Iq. 13)), The Sachs-Wolfe shape (see Eq. \ref{eq:cmbispsw}) ) is visible at. low »erimeters. with the colors (value of the bispectrum) varving 1orizontally with S but not vertically with £.," is visible at low perimeters, with the colors (value of the bispectrum) varying horizontally with $S$ but not vertically with $F$ ." We note that hestrong negative values(deeppurple/black) are located in the near-squeezed configuration (upper Ieft corner)., We note that thestrong negative values(deeppurple/black) are located in the near-squeezed configuration (upper left corner). The sign of the radiation transfer function can be traced. via he equilateral triangles which are positive for 2/3~200 (first acoustic peak) and become negative for 2/3~500 ," The sign of the radiation transfer function can be traced via the equilateral triangles which are positive for $P/3 \sim 200$ (first acoustic peak) and become negative for $P/3 \sim 500$ " "viscous timescale A4, close to the inner radius of the disk. and not the dynamical timescale r/c.","viscous timescale $t_{\rm visc}$ close to the inner radius of the disk, and not the dynamical timescale $r_g/c$." In terms of the a parameter and the disk scale height to radius ratio (/1/7). this timescale can be expressed asSpine. L(G)rLM where « is the viscosity coefficient.," In terms of the $\alpha$ parameter and the disk scale height to radius ratio $(h/r)$, this timescale can be expressed as = )^2, where $\alpha$ is the viscosity coefficient." Consequently. the inner disk needs to be sufficiently thick and viscous (ήτα20.1) in order to minimize the variability timescale without violating the luminosity constraint eq. (22)).," Consequently, the inner disk needs to be sufficiently thick and viscous $(h/r)^2\alpha \gppr 0.1$ ) in order to minimize the variability timescale without violating the luminosity constraint eq. \ref{m_l}) )." Similar conditions seem to be required to account for the X-ray spectral-timing properties of both AGNs and BH X-ray binaries (Arevalo Uttley 2006)., Similar conditions seem to be required to account for the X-ray spectral-timing properties of both AGNs and BH X-ray binaries (Arevalo Uttley 2006). Suppose therefore that in its innermost parts the disk is geometrically thick (as. e.g.. for an ADAF).," Suppose therefore that in its innermost parts the disk is geometrically thick (as, e.g., for an ADAF)." Within a more global scenario. one may then naturally expect a transition to a standard cooling-dominated (geometrically-thin) disk to occur at some radius ry.," Within a more global scenario, one may then naturally expect a transition to a standard cooling-dominated (geometrically-thin) disk to occur at some radius $r_{\rm tr}$." These transition regions are known to be prone to dynamical instabilities (e.g.. Gracia et al.," These transition regions are known to be prone to dynamical instabilities (e.g., Gracia et al." 2003)., 2003). " Interestingly. on longer timescales the X-ray (RXTE) PSD of PKS 2155-304 seems to show a characteristic rollover-timescale of t,~| day (Kataoka et al."," Interestingly, on longer timescales the X-ray (RXTE) PSD of PKS 2155-304 seems to show a characteristic rollover-timescale of $t_c \sim 1$ day (Kataoka et al." 2001)., 2001). " If this is indicative of the location of the transition region. Le. fau)~ .a reasonable transition radius ry~507, might be inferred (note that for ADAFs (1/r)~1 In order to account for the observed VHE variability characteristics. suppose therefore that fluctuations in the disk accretion rate on timescales às short as 5, are efficiently transmitted to the jet. leading to red notse-type fluctuations in the injection. rate for Fermi-type particle acceleration."," If this is indicative of the location of the transition region, i.e., $t_{\rm visc}(r_{\rm tr}) \sim t_c$ , a reasonable transition radius $r_{\rm tr} \sim 50~r_g$ might be inferred (note that for ADAFs $(h/r) \sim 1$ In order to account for the observed VHE variability characteristics, suppose therefore that fluctuations in the disk accretion rate on timescales as short as $t_v$ are efficiently transmitted to the jet, leading to red noise-type fluctuations in the injection rate for Fermi-type particle acceleration." Obviously we will only be able to observe emission with red notse-characteristics if these signatures do not get blurred by processes occurring on a longer timescale within. the source: For an observer. flux changes will always appear to be convolved and thus dominated by the longest timescales (Salvati et al.," Obviously we will only be able to observe emission with red noise-characteristics if these signatures do not get blurred by processes occurring on a longer timescale within the source: For an observer, flux changes will always appear to be convolved and thus dominated by the longest timescales (Salvati et al." " 1998), Le. tt... At,. where f.. Ar, and Δίμμ>face are the timescales (as seen by an observer) for injection. for photons traveling across the radial width of the source. and for the relevant radiative. processes. respectively."," 1998), i.e., t_v, t_r, where $t_v$, $\Delta t_r$ and $\Delta t_{\rm rad} \geq t_{\rm acc}$ are the timescales (as seen by an observer) for injection, for photons traveling across the radial width of the source, and for the relevant radiative processes, respectively." " For the radial travel time across the source one has At-- where [,>10 denotes the characteristic bulk Lorentz factor and r the radial source dimension in the rest frame of the galaxy (note that length contraction only affects the dimension along the direction of motion)."," For the radial travel time across the source one has t_r, where $\Gamma_b \geq 10$ denotes the characteristic bulk Lorentz factor and $r$ the radial source dimension in the rest frame of the galaxy (note that length contraction only affects the dimension along the direction of motion)." Typical bulk Lorentz factors inferred for the VHE emission region(s) in PKS 2155-305 during the 2006 high state are in the range of L5~(30—50) and perhaps even higher (e.g.. Begelman et al.," Typical bulk Lorentz factors inferred for the VHE emission region(s) in PKS 2155-305 during the 2006 high state are in the range of $\Gamma_b \sim (30-50)$ and perhaps even higher (e.g., Begelman et al." 2008)., 2008). " For the model to be consistent. one thus requires a radial source dimension that satisfies r<2x104(5/200secXE5,/30) em."," For the model to be consistent, one thus requires a radial source dimension that satisfies $r < 2 \times 10^{14}~(t_v/200~\mathrm{sec}) (\Gamma_b/30)$ cm." Either the VHE region is thus located very close to the BH. or the jet exhibits an internal velocity stratification of the (fast) spine - (slow) shear-type where the VHE emission is e.g. produced by Compton up-scattering within a fast moving similar to the needle-in-jet model recently proposed (Ghisellini Tavecchio 2008).," Either the VHE region is thus located very close to the BH, or the jet exhibits an internal velocity stratification of the (fast) spine - (slow) shear-type where the VHE emission is e.g. produced by Compton up-scattering within a fast moving spine, similar to the needle-in-jet model recently proposed (Ghisellini Tavecchio 2008)." Consider next the radiative timescale and üssume synchrotron losses to dominate the high-energy branch of the energetic particle distribution (γ΄) that is responsible for the up-scattering of soft photons to the VHE regime., Consider next the radiative timescale and assume synchrotron losses to dominate the high-energy branch of the energetic particle distribution $n_e(\gamma')$ that is responsible for the up-scattering of soft photons to the VHE regime. The radiative timescale thus 1s (Pm) en , The radiative timescale thus is 40 ) )^2 ). Hence. in order to work successfully. the proposed scenario requires co-moving magnetic field strengths that are sufficiently high (5.~| G) and electrons responsible for up-scattering that are sufficiently energetic (y'210°).," Hence, in order to work successfully, the proposed scenario requires co-moving magnetic field strengths that are sufficiently high $B' \sim 1$ G) and electrons responsible for up-scattering that are sufficiently energetic $\gamma' \gppr 10^5$ )." These parameters are again consistent with recent model fits to the observed spectral energy distribution of PKS 2155-304 within the needle-in-jet framework (Ghisellini Tavecchio 2008)., These parameters are again consistent with recent model fits to the observed spectral energy distribution of PKS 2155-304 within the needle-in-jet framework (Ghisellini Tavecchio 2008). Obviously. extreme short-term. variability may. for these (and other) reasons not necessarily show up at lower energies.," Obviously, extreme short-term variability may for these (and other) reasons not necessarily show up at lower energies." " As a consequence: If synchrotron radiation. from the fast ""needle"" component would dominate the emission in the optical domain. then the detectable minimum variability timescales are expected to be correspondingly longer. e.g.. on the order of a few to several tens of minutes for the above noted parameters."," As a consequence: If synchrotron radiation from the fast ""needle"" component would dominate the emission in the optical domain, then the detectable minimum variability timescales are expected to be correspondingly longer, e.g., on the order of a few to several tens of minutes for the above noted parameters." This might be compared with theminimum variability timescale of ~15 min during an optical observational campaign on PKS 2155-304 in 1995 (Paltani et al., This might be compared with theminimum variability timescale of $\sim 15$ min during an optical observational campaign on PKS 2155-304 in 1995 (Paltani et al. 1997)., 1997). " KoHowing the above analysis. let us suppose that PKS 2155-304 harbors a close binary system consisting of a primary BH with mass my,~5x10M. ana à secondary one with mass no-107M (mass ratio g~ 0.02)."," Following the above analysis, let us suppose that PKS 2155-304 harbors a close binary system consisting of a primary BH with mass $m_1 \sim 5 \times 10^8 M_{\odot}$ and a secondary one with mass $m_2\sim10^7 M_{\odot}$ (mass ratio $q \sim0.02$ )." Evidence for a possible longterm period of ~(4—7) yr in the optical V band (Fan Lin 2000: cf., Evidence for a possible longterm period of $\sim(4-7)$ yr in the optical V band (Fan Lin 2000; cf. also Brinkmann et al., also Brinkmann et al. " 2000 for soft-X-ray hints) might possibly fit well into such a framework: If one requires the secondary to be on an orbit that could intersect the accretion disk around the primary with a typical (maximum) disk size of 1037 with x~ Land r,=2Gain/c (Goodmat 72003). possible Keplerian periods P;=2z:/O, are constrained to be smaller than Pj=451+q)y7(9m/5xLOSMi) yr. a condition that seems well satisfied for PKS 2155-304."," 2000 for soft-X-ray hints) might possibly fit well into such a framework: If one requires the secondary to be on an orbit that could intersect the accretion disk around the primary with a typical (maximum) disk size of $10^3 x~r_s$, with $x \sim 1$ and $r_s=2~G m_1/c^2$ (Goodman 2003), possible Keplerian periods $P_k=2\pi/\Omega_k$ are constrained to be smaller than $P_k \simeq 45 \,(1+q)^{-1/2} x^{3/2} (m_1/5 \times 10^8 M_{\odot})$ yr, a condition that seems well satisfied for PKS 2155-304." This suggests that binary disk interactions could indeed result i optical QPOs on the timescale of several vears (see Rieger 2007 for more details)., This suggests that binary disk interactions could indeed result in optical QPOs on the timescale of several years (see Rieger 2007 for more details). " Accordingly. we may derive an upper limit oi the intrinsic Keplerian orbital period of the binary labelkeplerP, ο H"," Accordingly, we may derive an upper limit on the intrinsic Keplerian orbital period of the binary P_k 13 ) ," " Accordingly. we may derive an upper limit oi the intrinsic Keplerian orbital period of the binary labelkeplerP, ο HE"," Accordingly, we may derive an upper limit on the intrinsic Keplerian orbital period of the binary P_k 13 ) ," " Accordingly. we may derive an upper limit oi the intrinsic Keplerian orbital period of the binary labelkeplerP, ο HES"," Accordingly, we may derive an upper limit on the intrinsic Keplerian orbital period of the binary P_k 13 ) ," " Accordingly. we may derive an upper limit oi the intrinsic Keplerian orbital period of the binary labelkeplerP, ο HESS"," Accordingly, we may derive an upper limit on the intrinsic Keplerian orbital period of the binary P_k 13 ) ," " Accordingly. we may derive an upper limit oi the intrinsic Keplerian orbital period of the binary labelkeplerP, ο HESSy"," Accordingly, we may derive an upper limit on the intrinsic Keplerian orbital period of the binary P_k 13 ) ," " Accordingly. we may derive an upper limit oi the intrinsic Keplerian orbital period of the binary labelkeplerP, ο HESSyn"," Accordingly, we may derive an upper limit on the intrinsic Keplerian orbital period of the binary P_k 13 ) ," "origin, it is customary to compare the results obtained with those of surrogate data (Theileretal.1992).","origin, it is customary to compare the results obtained with those of surrogate data \citep{The92}." ". Here surrogate data are generated which have practically the same power spectrum and distribution as the original time series, but are of stochastic origin."," Here surrogate data are generated which have practically the same power spectrum and distribution as the original time series, but are of stochastic origin." " The essential idea is to formulate a null hypothesis that the data has been created by stationary linear stochastic process, and then to attempt ato reject this hypothesis by comparing results for the data with appropriate realizations of surrogate data."," The essential idea is to formulate a null hypothesis that the data has been created by a stationary linear stochastic process, and then to attempt to reject this hypothesis by comparing results for the data with appropriate realizations of surrogate data." " Schreiber&Schmitz(1996) have proposed a scheme, known as Iterative Fourier Transform (IAAFT), which generates Amplitudesurrogate Adjusteddata that are more consistent in representing the null hypothesis (Kugiumtzis1999)."," \cite{Sch96} have proposed a scheme, known as Iterative Amplitude Adjusted Fourier Transform (IAAFT), which generates surrogate data that are more consistent in representing the null hypothesis \citep{Kug99}." ". In this work, the software which uses tha above technique to generate dresden.mpg.de/tisean/TISEAN_22.1/index.html)surrogates has (http://www.mpipks-been used."," In this work, the software which uses tha above technique to generate surrogates 2.1/index.html) has been used." " The bottom panel of Figure 4,, shows the SVD decomposition for surrogate data of the Lorenz system."," The bottom panel of Figure \ref{svdlor}, shows the SVD decomposition for surrogate data of the Lorenz system." " As expected, the dynamical phase picture is qualitatively different for the surrogate as compared to the original time series."," As expected, the dynamical phase picture is qualitatively different for the surrogate as compared to the original time series." " It should be emphasized that a qualitative or quantitative difference between a particular kind of surrogate and original data, although highly suggestive, does not necessarily imply that the original time series has a non stochastic origin."," It should be emphasized that a qualitative or quantitative difference between a particular kind of surrogate and original data, although highly suggestive, does not necessarily imply that the original time series has a non stochastic origin." " Ideally, the null hypothesis should be tested several different kinds of surrogate data, before a usingconcrete conclusion can be reached."," Ideally, the null hypothesis should be tested using several different kinds of surrogate data, before a concrete conclusion can be reached." " Data from a natural deterministic non-linear system may have contamination from stochastic noise, either inherently or due to the detection process."," Data from a natural deterministic non-linear system may have contamination from stochastic noise, either inherently or due to the detection process." Such contamination generally makes it difficult to identify the non-linear behavior of the system., Such contamination generally makes it difficult to identify the non-linear behavior of the system. " Apart from the level of contamination, the effect on the analysis also depends on the nature of the noise."," Apart from the level of contamination, the effect on the analysis also depends on the nature of the noise." " At the same level of contamination (i.e. at the same percentage of noise addition) the effect of white noise ( i.e. when the power spectrum of the noise signal is a constant) is more than that of red noise ( i.e. when the power spectrum, P(f)ος f-?)."," At the same level of contamination (i.e. at the same percentage of noise addition) the effect of white noise ( i.e. when the power spectrum of the noise signal is a constant) is more than that of red noise ( i.e. when the power spectrum, $P(f) \propto f^{-2}$ )." " This is illustrated in Figure 5,, where SVD plots of the Lorenz system with red and white noise addition are shown."," This is illustrated in Figure \ref{svd_noise}, where SVD plots of the Lorenz system with red and white noise addition are shown." " While the effect of noise on the limit cycle is to broaden the original one dimensional curve, its effect on the complex chaotic behavior can be more pronounced."," While the effect of noise on the limit cycle is to broaden the original one dimensional curve, its effect on the complex chaotic behavior can be more pronounced." Note that a white noise contamination does not allow the dynamics to be effectively reconstructed for the Lorenz with R=28., Note that a white noise contamination does not allow the dynamics to be effectively reconstructed for the Lorenz system with $R = 28$. It is often desirable to have a quantitative systemmeasure apart from a qualitative picture of the reconstructed dynamics., It is often desirable to have a quantitative measure apart from a qualitative picture of the reconstructed dynamics. Such a quantitative measure is the computation of the correlation dimension., Such a quantitative measure is the computation of the correlation dimension. " Briefly, the computation procedure is to choose a large number of points in the reconstructed dynamics as centers."," Briefly, the computation procedure is to choose a large number of points in the reconstructed dynamics as centers." " The correlation function is the number of points which are within a distance R from a center, averaged over all the centers, and may be formally written as where xj are the reconstructed vectors (Eqn 2), N is the number of vectors, N. is the number of centers and H is"," The correlation function is the number of points which are within a distance R from a center, averaged over all the centers, and may be formally written as where $\vec{x}_j$ are the reconstructed vectors (Eqn 2), $N$ is the number of vectors, $N_c$ is the number of centers and H is" In this paper we investigate the hypothesis that activity in galactic nuclei is induced by the acquisition and disruption of a small gas-rich companion galaxy.,In this paper we investigate the hypothesis that activity in galactic nuclei is induced by the acquisition and disruption of a small gas-rich companion galaxy. " There has been considerable discussion. of this ""minor merger hypothesis in the literature (see. for example. recent. discussions in ‘Taniguchi. 1999: Chatzichristou. 2000.a.b: 2001 a.b. and papers therein)"," There has been considerable discussion of this `minor merger' hypothesis in the literature (see, for example, recent discussions in Taniguchi, 1999; Chatzichristou, 2000,a,b; 2001 a,b, and papers therein)." In elliptical galaxies. a study of the effects of minor merecrs is motivated. by the observational evidence (van Dokkum Lranx. 1995) that dust. discs are present in the cores of a high fraction of ellipticals. with a higher detection rate in radio galaxies (Verdoes IxIeijn et al.," In elliptical galaxies, a study of the effects of minor mergers is motivated by the observational evidence (van Dokkum Franx, 1995) that dust discs are present in the cores of a high fraction of ellipticals, with a higher detection rate in radio galaxies (Verdoes Kleijn et al.," 2000)., 2000). ‘This result is consistent with the results of surveys of 3€CH radio galaxies by de Koll ct al. (, This result is consistent with the results of surveys of 3CR radio galaxies by de Koff et al. ( 2000) and by Martel et al. (,2000) and by Martel et al. ( 1999).,1999). “Phe simplest interpretation of these is that the dust structure seen in these galaxies is the debris trail of a small merger incident., The simplest interpretation of these is that the dust structure seen in these galaxies is the debris trail of a small merger incident. The analysis of de Wolf et al. (, The analysis of de Koff et al. ( 2000). and the finding by Sparks ct al. (,"2000), and the finding by Sparks et al. (" 2000) that galaxies with optical jets tend to display face-on (1.0. round) dust. disces. both suggest that the radio jets in radio galaxies show a tendency to be aligned. perpendicular to the observed. dust disc structure.,"2000) that galaxies with optical jets tend to display face-on (i.e. round) dust discs, both suggest that the radio jets in radio galaxies show a tendency to be aligned perpendicular to the observed dust disc structure." In this picture a recent merger would have stimulated the current nuclear activity., In this picture a recent merger would have stimulated the current nuclear activity. Phe surrounding dust. structure would. indicate the plane of the orbit. of the disrupted satellite. and the resulting radio jets would naturally be expected to be perpencicular to this plane.," The surrounding dust structure would indicate the plane of the orbit of the disrupted satellite, and the resulting radio jets would naturally be expected to be perpendicular to this plane." In view of this. we investigate first the conditions required for a small gas-rich satellite galaxy to be accreted bv a larger galaxy in such a wav that it gives rise the a dust. clise similar to those observed.," In view of this, we investigate first the conditions required for a small gas-rich satellite galaxy to be accreted by a larger galaxy in such a way that it gives rise the a dust disc similar to those observed." To focus the discussion we concentrate on modelling 1e formation of the cust disc in the otherwise unremarkixe El galaxy NGC 3379., To focus the discussion we concentrate on modelling the formation of the dust disc in the otherwise unremarkable E1 galaxy NGC 3379. Our results ave straightforwardly applicable to other gas-poor ellipticals., Our results are straightforwardly applicable to other gas-poor ellipticals. “Phe cust disc in NGC 3379 (van Dokkum Frans. 1995: Ferrari ct al..," The dust disc in NGC 3379 (van Dokkum Franx, 1995; Ferrari et al.," 1999) has a radius LOOpe. and a miss estimated to be around 150ΔΕΟ.," 1999) has a radius $\sim 100\pc$, and a mass estimated to be around $150\msun$." In addition Ferrari et al. (, In addition Ferrari et al. ( 1999) show that there is more patchy dust extending out to about Lkpe from the nucleus.,1999) show that there is more patchy dust extending out to about $1\kpc$ from the nucleus. We adopt a simplified »ocedure to model the interaction., We adopt a simplified procedure to model the interaction. We use spherical models or both the major galaxy and the minor merece and model the motion of the orbit of the satellite using simple dynamical friction. along with a straightforward. model for he tidal disruption of the satellite (Section 2).," We use spherical models for both the major galaxy and the minor mergee and model the motion of the orbit of the satellite using simple dynamical friction, along with a straightforward model for the tidal disruption of the satellite (Section 2)." We use a simple model for the subsequent. evolution of the stripped eas (Section 3)., We use a simple model for the subsequent evolution of the stripped gas (Section 3). Our basic conclusion (Sections 5.1 and 6) is hat in order to generate a cust disc of the kind observed it is necessary for the initial trajectory of the merging satellite o be accurately directed: towards the nucleus of the major ealaxy., Our basic conclusion (Sections 5.1 and 6) is that in order to generate a dust disc of the kind observed it is necessary for the initial trajectory of the merging satellite to be accurately directed towards the nucleus of the major galaxy. Llowever. reality turns out to be more complicated than," However, reality turns out to be more complicated than" vector. (J;). is proportional to the anti-syiunetric product of the (wo tensors. the inertial momentum tensor (7;;) and the local tidal shear tensor. (7;;). as Here the defintions of ἐν and Tj; are given as where q is the Lagrangian position of the particles that reside in the proto-halo regions. V and p(q) ave the Lagrangian volume and the density of the proto-halo region. respectively. and &(q) is the velocity perturbation potential.,"vector, $J_{i}$ ), is proportional to the anti-symmetric product of the two tensors, the inertial momentum tensor $(I_{ij})$ and the local tidal shear tensor, $(T_{ij})$, as Here the defintions of $I_{ij}$ and $T_{ij}$ are given as where ${\bf q}$ is the Lagrangian position of the particles that reside in the proto-halo regions, $V$ and $\rho({\bf q})$ are the Lagrangian volume and the density of the proto-halo region, respectively, and $\Phi({\bf q})$ is the velocity perturbation potential." Given the property of the perfectly. anti-svmmetric tensor e;; in equation (1)). an additional condition has to be satisfied [or the first-order generation of the proto-halo angular momenta: the principal axes of Z;; and 7;; have to be misaligned with each other (Catelan&Theuns1996).," Given the property of the perfectly anti-symmetric tensor $\epsilon_{ijk}$ in equation \ref{eqn:ang}) ), an additional condition has to be satisfied for the first-order generation of the proto-halo angular momentum: the principal axes of $I_{ij}$ and $T_{ij}$ have to be misaligned with each other \citep{cat-the96}." . Furthermore. a crucial implication of equation (1)) is that if this additional condition is satisfied and (hus (he angular momentum of a proto-halo is generated al first order. (hen the direction of the proto-halo angular momentum is not random bul preferentially aligned with the principal axes of the local tidal tensor (Lee&Pen2000)..," Furthermore, a crucial implication of equation \ref{eqn:ang}) ) is that if this additional condition is satisfied and thus the angular momentum of a proto-halo is generated at first order, then the direction of the proto-halo angular momentum is not random but preferentially aligned with the principal axes of the local tidal tensor \citep{lee-pen00}." Numerical experiments have revealed that the principal axes of (7;;) and (1) ave correlated strongly but not perfectly (Lee&Pen2000:Porcianietal.2002).. which indicates that the first-order generation of the proto-halo angular momentum is not so efficient. aud the degree of the alienments between the proto-halo spin directions and the principal axes ol the local tidal shear tensors would not be so high.," Numerical experiments have revealed that the principal axes of $(I_{ij})$ and $(T_{ij})$ are correlated strongly but not perfectly \citep{lee-pen00,por-etal02}, which indicates that the first-order generation of the proto-halo angular momentum is not so efficient and the degree of the alignments between the proto-halo spin directions and the principal axes of the local tidal shear tensors would not be so high." " Motivated by this numerical clue. Lee&Pen(2000) suggested the following «quadratic formula to quantify the expected degree of the alignments between the halo spins and the local tidal shears. generalizing the linear tidal torque theory: where (L;) is (he unit spin vector of a halo. (T;,) is the unit traceless tidal tensor smoothed on the halo mass scale. and à is a correlation parameter in the range of [0.3/5] which measures the strength of the correlation between (Lj) and (Τι )."," Motivated by this numerical clue, \citet{lee-pen00} suggested the following quadratic formula to quantify the expected degree of the alignments between the halo spins and the local tidal shears, generalizing the linear tidal torque theory: where $(\hat{L}_{i})$ is the unit spin vector of a halo, $(\hat{T}_{ij})$ is the unit traceless tidal tensor smoothed on the halo mass scale, and $a$ is a correlation parameter in the range of $[0,3/5]$ which measures the strength of the correlation between $(\hat{L}_{i})$ and $(\hat{T}_{ij})$ ." " It is worth recalling the fact that the ensemble average ΙΙ) in the left hand side of equation (3)) is obtained by (aking the average of LiL; from the sample halos having all different mass. while the tidal shear field in the right hand side of equation "" (3))is smoothed on the single mass scale which"," It is worth recalling the fact that the ensemble average $\langle\hat{L}_{i}\hat{L}_{j}\rangle$ in the left hand side of equation \ref{eqn:stc}) ) is obtained by taking the average of $\hat{L}_{i}\hat{L}_{j}$ from the sample halos having all different mass, while the tidal shear field in the right hand side of equation \ref{eqn:stc}) )is smoothed on the single mass scale which" realization of the initial linear densitv Ποιά defined on a cubical lattice. (,realization of the initial linear density field defined on a cubical lattice. ( Phis constitutes part of the initial conditions for a cosmological simulations. which can therefore be used to test our method.),"This constitutes part of the initial conditions for a cosmological simulations, which can therefore be used to test our method.)" Secondly we smooth the density [field in cubical blocks on a range of scales. using for cach scale of refinement a set of eight. displaced. grids.," Secondly we smooth the density field in cubical blocks on a range of scales, using for each scale of refinement a set of eight displaced grids." Phe blocks are then ordered in decreasing overdensity. increasing collapse time)., The blocks are then ordered in decreasing overdensity increasing collapse time). We then run down this list creating a merger tree for halos. (, We then run down this list creating a merger tree for halos. ( Lhe decision whether to merge two sub-halos together into a larger one is crucial for preventing the growth of unphysically-large structures.),The decision whether to merge two sub-halos together into a larger one is crucial for preventing the growth of unphysically-large structures.) As a bonus our technique retains spatial information about the relative location of halos a measure of their separation. not just the merging topology).," As a bonus our technique retains spatial information about the relative location of halos a measure of their separation, not just the merging topology)." In the next section we deseribe our merger algorithm in more detail., In the next section we describe our merger algorithm in more detail. Tests on simple power-law spectra of density perturbations are presented. in Section 3. and the relative success. benefits and disadvantages of our method. are contrasted with others in Section 4.," Tests on simple power-law spectra of density perturbations are presented in Section 3, and the relative success, benefits and disadvantages of our method are contrasted with others in Section 4." We begin. with a realization of the chosen density field in a periodic cubical box of side £—2. where f is a positive integer.," We begin with a realization of the chosen density field in a periodic cubical box of side $L\equiv2^l$, where $l$ is a positive integer." A standard initial condition generator is used which populates the box with waves of random phase and amplitude drawn from a gaussian of mean zero and variance equal to the chosen input. power-spectrun., A standard initial condition generator is used which populates the box with waves of random phase and amplitude drawn from a gaussian of mean zero and variance equal to the chosen input power-spectrum. Neither the fact that £L is a power of two. nor the periodi boundary conditions are strictly necessary but are chosen for simplicity.," Neither the fact that $L$ is a power of two, nor the periodic boundary conditions are strictly necessary but are chosen for simplicity." Next we average the density Huctuations within cubical of side 2. 4. .... L.," Next we average the density fluctuations within cubical of side 2, 4, $\ldots$, $L$." At each smoothing level we use eight. sets of overlapping erids. displaced by half a block-length in cach co-ordinate direction relative to one another (sce 1))," At each smoothing level we use eight sets of overlapping grids, displaced by half a block-length in each co-ordinate direction relative to one another (see \ref{figblock}) )." This ensures that density peaks will always be approximately centred within one of the blocks and is a major advantage over other methods., This ensures that density peaks will always be approximately centred within one of the blocks and is a major advantage over other methods. The density fluctuations within blocks ancl base-cells are now ordered in decreasing densitv. which is the same order in which they would collapse as the universe ages (under the natyvve assumption that they. all have the same morphology at all times: we will test the accuracy of this assumption later).," The density fluctuations within blocks and base-cells are now ordered in decreasing density, which is the same order in which they would collapse as the universe ages (under the ve assumption that they all have the same morphology at all times: we will test the accuracy of this assumption later)." The final step is to build up à merger tree to express the collapse history of blocks., The final step is to build up a merger tree to express the collapse history of blocks. This is a much harder problem than in the simple bbecause the blocks we use are not always nested. inside one another but may overlap., This is a much harder problem than in the simple because the blocks we use are not always nested inside one another but may overlap. Our initial guess was to merge together all collapsed blocks which overlap with one another. but this leads to very elongated: structures which can stretch across a large fraction of the box.," Our initial guess was to merge together all collapsed blocks which overlap with one another, but this leads to very elongated structures which can stretch across a large fraction of the box." While these may represent large-scale pancakes or filaments. they are clearly. not the kind of simple virialized halos which we are trving to identify.," While these may represent large-scale pancakes or filaments, they are clearly not the kind of simple virialized halos which we are trying to identify." In practice they would probably break up into smaller objects and so we need to find some way to limit their growth., In practice they would probably break up into smaller objects and so we need to find some way to limit their growth. The procedure we use to do this is as follows:, The procedure we use to do this is as follows: produced only by photodissociation.,produced only by photodissociation. " The main conclusion that we can draw from this is that at the point at which star formation begins, the clouds have not yet reached chemical equilibrium throughout their volume."," The main conclusion that we can draw from this is that at the point at which star formation begins, the clouds have not yet reached chemical equilibrium throughout their volume." " In run A, on the other hand, the situation is very different."," In run A, on the other hand, the situation is very different." " In the absence of Ho selfshielding and dust shielding, the He fractional abundance is much smaller: the peak value at the displayed output time of 2.3Myr is tu,c2x10-3, implying that even in the densest gas, less than of the hydrogen is in molecular form."," In the absence of $_{2}$ self-shielding and dust shielding, the $_{2}$ fractional abundance is much smaller: the peak value at the displayed output time of $2.3 \: {\rm Myr}$ is $x_{\rm H_{2}} \simeq 2 \times 10^{-3}$, implying that even in the densest gas, less than of the hydrogen is in molecular form." " In addition, the very small degree of scatter in the relationship between TH, and n implies that the gas is in chemical equilibrium, as we would expect given that in the absence of shielding, the Ha photodissociation timescale tpa~600yr, which is very much shorter than the age of the cloud."," In addition, the very small degree of scatter in the relationship between $x_{\rm H_{2}}$ and $n$ implies that the gas is in chemical equilibrium, as we would expect given that in the absence of shielding, the $_{2}$ photodissociation timescale $t_{\rm pd} \simeq 600 \: {\rm yr}$, which is very much shorter than the age of the cloud." " In Figure 5,, we show how the fractional abundance of CO, xco=nco/n, varies as a function of n in runs A, D1 and D2."," In Figure \ref{rhoco}, , we show how the fractional abundance of CO, $x_{\rm CO} \equiv n_{\rm CO} / n$, varies as a function of $n$ in runs A, D1 and D2." Results are shown at the same output times as in Figure 4.., Results are shown at the same output times as in Figure \ref{rhoh2}. " No results are plotted for runs B or C, because Zco=0 by design in these runs."," No results are plotted for runs B or C, because $x_{\rm CO} = 0$ by design in these runs." Several points should be noted., Several points should be noted. " First, the CO abundance in run A is tiny, as is to be expected given the low Hz abundance and the absence of dust shielding."," First, the CO abundance in run A is tiny, as is to be expected given the low $_{2}$ abundance and the absence of dust shielding." " Second, the distribution of CO abundances in runs D1 and D2 are very similar, despite the difference in the initial conditions for these two runs."," Second, the distribution of CO abundances in runs D1 and D2 are very similar, despite the difference in the initial conditions for these two runs." This suggests that the CO content of the gas is primarily sensitive to itscurrent H» content and density structure., This suggests that the CO content of the gas is primarily sensitive to its $_{2}$ content and density structure. " Any sensitivity to the chemical history of the gas, which is very different in runs D1 and D2, must be small."," Any sensitivity to the chemical history of the gas, which is very different in runs D1 and D2, must be small." " Additional support for this point is provided by Figure 6,, which shows a CO column density projection of the clouds in runs D1 and D2 at t—2.2Myr."," Additional support for this point is provided by Figure \ref{fig:cocol}, which shows a CO column density projection of the clouds in runs D1 and D2 at $t = 2.2 \: {\rm Myr}$." " Although there appears to be somewhat more structure at low CO column densities in run D2 than in run D1, the main features of the cloud are very similar in both simulations, and there is no clear observational signature of the different chemical histories that one could point to in these runs."," Although there appears to be somewhat more structure at low CO column densities in run D2 than in run D1, the main features of the cloud are very similar in both simulations, and there is no clear observational signature of the different chemical histories that one could point to in these runs." To help us to understand why the presence or absence of molecules appearsto have such a limited effect on the, To help us to understand why the presence or absence of molecules appearsto have such a limited effect on the lies in finding a mechanism that can cause a substantial fraction of stars to migrate several kiloparsees while retaining the observed approximately circular orbits.,lies in finding a mechanism that can cause a substantial fraction of stars to migrate several kiloparsecs while retaining the observed approximately circular orbits. In a seminal paper. Sellwood&Bin-ney(2002.hereafterSBO2). investigated the relationship between changes in stellar angular momentum and disk heating.," In a seminal paper, \citet[][hereafter SB02]{Sellwood02} investigated the relationship between changes in stellar angular momentum and disk heating." They found that radial migration is a ubiquitous process in spiral galaxies: stars naturally migrate (change angular momentum) as they resonantly interact with transient spiral waves., They found that radial migration is a ubiquitous process in spiral galaxies; stars naturally migrate (change angular momentum) as they resonantly interact with transient spiral waves. Stars in corotational resonance (CR) with said waves are scattered without heating the disk and maintain their nearly circular orbits (unlike Lindblad resonance (LR) scattering)., Stars in corotational resonance (CR) with said waves are scattered without heating the disk and maintain their nearly circular orbits (unlike Lindblad resonance (LR) scattering). In the present paper. we examine radial migration in simulations of disk galaxies.," In the present paper, we examine radial migration in simulations of disk galaxies." Our experiments include galactic disks evolved both in isolation and under the action of infalling satellites of the type expected in the currently favored. cold dark matter (CDM) paradigm of hierarchical structure formation (e.g.Peebles1982:Blumenthaletal.1984).," Our experiments include galactic disks evolved both in isolation and under the action of infalling satellites of the type expected in the currently favored cold dark matter (CDM) paradigm of hierarchical structure formation \citep[\eg,][]{Peebles82,Blumenthal_etal84}." . The latter set of eXperiments were presented in the studies of Kazantzidisetal.(2008.hereafterKOS) and Kazantzidisetal.(2009) and were utilized to investigate the dynamical and morphologica signatures of galactic disks subject to bombardment by CDM substructure.," The latter set of experiments were presented in the studies of \citet[][hereafter K08]{Kazantzidis08} and \citet{Kazantzidis09} and were utilized to investigate the dynamical and morphological signatures of galactic disks subject to bombardment by CDM substructure." Inspired by SBO2. several groups have recently investigatec —1e. potential role of radial mixing in the chemical and dynamica σπαvolution of disk galaxies.," Inspired by SB02, several groups have recently investigated the potential role of radial mixing in the chemical and dynamical evolution of disk galaxies." Schónrich&Binney(2009). presented de first chemical evolution model to incorporate radial migration., \citet{Schonrich09} presented the first chemical evolution model to incorporate radial migration. The rate at which stars migrate via the SBO2 mechanism is left as a free parameter constrained by the metallicity distribution function IDF) of solar neighborhood stars in the GCS (Nordstrómetal.ly O043., The rate at which stars migrate via the SB02 mechanism is left as a free parameter constrained by the metallicity distribution function (MDF) of solar neighborhood stars in the GCS \citep{Nordstrom04}. . Their model successfully reproduced. within systematic uncertainties. the observed age-metallicity distribution of stars in ye GCS (Holmbergetal.2007) and the observed correlation --between tangential velocity and abundance pattern described by Haywood(2008).," Their model successfully reproduced, within systematic uncertainties, the observed age-metallicity distribution of stars in the GCS \citep{Holmberg07} and the observed correlation between tangential velocity and abundance pattern described by \citet{Haywood08}." .. However. there is partial degeneracy between —je magnitude of radial migration and other parameters in the model such as star-formation raes and gas inflow characteristics.," However, there is partial degeneracy between the magnitude of radial migration and other parameters in the model such as star-formation rates and gas inflow characteristics." Furthermore. it is unclear whether the level of migration required to fit the data is consistent with tjeoretical expectations.," Furthermore, it is unclear whether the level of migration required to fit the data is consistent with theoretical expectations." Numerical simulations have confirmed. the occurrence of radial migration under a variey of conditions., Numerical simulations have confirmed the occurrence of radial migration under a variety of conditions. Roskaretal.(2008a.b) studied the migration of stars in a simulation of an isolated Milky Way (MW)-sized stellar disk formed from the cooling of a pressure-supported gas cloud in a 1072A7. dark matter halo.," \citet{Roskar08a, Roskar08b} studied the migration of stars in a simulation of an isolated Milky Way (MW)-sized stellar disk formed from the cooling of a pressure-supported gas cloud in a $10^{12} \msun$ dark matter halo." In their simulations. some older stars radially migrated to the outskirts of the disk wile maintaining nearly circular orbits. forming a population akin to that observed in M31 and M33 (Ferguson&Johnson200>Fergusonetal.," In their simulations, some older stars radially migrated to the outskirts of the disk while maintaining nearly circular orbits, forming a population akin to that observed in M31 and M33 \citep{Ferguson01, Ferguson07}." 2007).. RoSkaretal.(2008b) found that —50% of all stars in the solar neighborhood were9 not bornος this is a natural explanation for the observed dispersion in the AMR and solar neighborhood metallicity distribution function (MDF).," \citet{Roskar08b} found that $\sim 50\%$ of all stars in the solar neighborhood were not born; this is a natural explanation for the observed dispersion in the AMR and solar neighborhood metallicity distribution function (MDF)." " More recently. Quillenetal.(2009) investigated. radial migration in a stellar disk perturbed by a low-mass (~5.LO"" AZ.) orbiting satellite."," More recently, \citet{Quillen09} investigated radial migration in a stellar disk perturbed by a low-mass $\sim 5\times10^9\ \msun$ ) orbiting satellite." Their numerical simulations integrated fest particle orbits in a static galactic potential and highlighted the fact that mergers and perturbations from satellite galaxies and subhalos can induce stellar radial mixing., Their numerical simulations integrated test particle orbits in a static galactic potential and highlighted the fact that mergers and perturbations from satellite galaxies and subhalos can induce stellar radial mixing. Although informative. test particle simulations in a static isothermal potential will not capture all the relevant physics of the process of stellar radial migration in disk galaxies: the interactions between the gravitational perturbations and the self-gravity of the disk are essential to a detailed analysis of the phenomenon.," Although informative, test particle simulations in a static isothermal potential will not capture all the relevant physics of the process of stellar radial migration in disk galaxies; the interactions between the gravitational perturbations and the self-gravity of the disk are essential to a detailed analysis of the phenomenon." In our paper. we expand on the analysis of Quillenal.(2009). by investigating radial migration using fully numerical simulations both with and without satellite bombardment.," In our paper, we expand on the analysis of \citet{Quillen09} by investigating radial migration using fully numerical simulations both with and without satellite bombardment." There are now several established phenomena that can cause a star to populate a region of the disk different from its birth radit., There are now several established phenomena that can cause a star to populate a region of the disk different from its birth radii. Stars on elliptical orbits maintain their guiding center and angular momentum (modulo asymmetries in the potential) but can be found over the range in galacto-centric radius detined by their pericenter and apocenter., Stars on elliptical orbits maintain their guiding center and angular momentum (modulo asymmetries in the potential) but can be found over the range in galacto-centric radius defined by their pericenter and apocenter. Changing a star's angular momentum. and hence its guiding center. requires direct scattering or a resonant interaction with transient patterns in the disk.," Changing a star's angular momentum, and hence its guiding center, requires direct scattering or a resonant interaction with transient patterns in the disk." The local encounters of stars with molecular clouds (e.g.Spitzer&Sehwarzsehild1953). or Lindblad resonance (LR) scattering between stars and spiral waves SSBO2) both change stellar guiding centers (albeit to a relatively small degree) and increase the random motions of stars over time. “blurring” the disk.," The local encounters of stars with molecular clouds \citep[\eg][]{Spitzer53} or Lindblad resonance (LR) scattering between stars and spiral waves SB02) both change stellar guiding centers (albeit to a relatively small degree) and increase the random motions of stars over time, “blurring” the disk." Stars scattered at CR with spiral waves can change their guiding centers by several kiloparsees without increasing the amplitude of their radial motion., Stars scattered at CR with spiral waves can change their guiding centers by several kiloparsecs without increasing the amplitude of their radial motion. For any single spiral wave. SBO? predict that stars are scattered on each side of the CR. “churning” the contents of thedisk’.," For any single spiral wave, SB02 predict that stars are scattered on each side of the CR, “churning” the contents of the." Stars may undergo several encounters with transient spiral waves throughout their lifetimes., Stars may undergo several encounters with transient spiral waves throughout their lifetimes. While SBO2 investigate all resonant interactions between spiral waves and stars. we will refer to this special case of CR as the “SBO2mechanism’=.," While SB02 investigate all resonant interactions between spiral waves and stars, we will refer to this special case of CR as the “SB02." . As SBO2 note. migration due to spiral waves can be described by blurring and churning regardless of how the waves arise (satellites.e.g... could induce spiral structure that would lead to migration described by SBO2).," As SB02 note, migration due to spiral waves can be described by blurring and churning regardless of how the waves arise (satellites, could induce spiral structure that would lead to migration described by SB02)." Simulations have shown that other transient wave patterns internal to a galaxy. such as those resulting from bar propagation. can produce resonance overlap with existing spiral patterns and induce radial migration (Minchev&Famaey2010:Minchevetal.2011).," Simulations have shown that other transient wave patterns internal to a galaxy, such as those resulting from bar propagation, can produce resonance overlap with existing spiral patterns and induce radial migration \citep{Minchev10, Minchev11}." Orbiting satellites. external to the galaxy and discussed above. will have a complex interaction with the disk as they provide a means of direct scattering over a large area and also induce spiral modes in the disk.," Orbiting satellites, external to the galaxy and discussed above, will have a complex interaction with the disk as they provide a means of direct scattering over a large area and also induce spiral modes in the disk." In this work. we aim to characterize radial migration induced by satellite bombardment and compare its effects on the stellar disk with those observed in secularly evolved galaxies.," In this work, we aim to characterize radial migration induced by satellite bombardment and compare its effects on the stellar disk with those observed in secularly evolved galaxies." Our investigation complements earlier and ongoing radial migration studies., Our investigation complements earlier and ongoing radial migration studies. We perform a simulation campaign. including numerical experiments of isolated disk galaxies with different scale heights and gas fractions. which in turn lead to different levels of spiral structure.," We perform a simulation campaign, including numerical experiments of isolated disk galaxies with different scale heights and gas fractions, which in turn lead to different levels of spiral structure." For the first time. we examine the effect of satellite bombardment on radial migration utilizing simulations where galactic disks are subjected to a cosmologically motivated satellite accretion history.," For the first time, we examine the effect of satellite bombardment on radial migration utilizing simulations where galactic disks are subjected to a cosmologically motivated satellite accretion history." " Via a comparative approach. we determine how the magnitude and efficiency of radial migration depend on input physies. establish correlations between orbital parameters and migration, and present evidence that each of the three migration mechanisms is distinct in the examined parameter space."," Via a comparative approach, we determine how the magnitude and efficiency of radial migration depend on input physics, establish correlations between orbital parameters and migration, and present evidence that each of the three migration mechanisms is distinct in the examined parameter space." These characteristics lead to possible observational signatures that may constrain the relative importance of each migration mechanism in the Milky Way., These characteristics lead to possible observational signatures that may constrain the relative importance of each migration mechanism in the Milky Way. hard X-ray continuum (rather than as soft thermal emission from the optically-thick part of the accretion disk).,hard X-ray continuum (rather than as soft thermal emission from the optically-thick part of the accretion disk). Lf the corona is geometrically-thin then. with the exception. of returning radiation. we need not consider light bending ellects. when deducing the X-ray [lux that iraciates the optically-thick accretion clisk (and hence gives rise to the observed. rellection spectrum).," If the corona is geometrically-thin then, with the exception of returning radiation, we need not consider light bending effects when deducing the X-ray flux that irradiates the optically-thick accretion disk (and hence gives rise to the observed reflection spectrum)." Assuming that the corona is geomectrically-thin and emits isotropically. the optically-thick clisk will be irracliatecl by N-ravs with an intensity. where f is an appropriate averaging of f(r) over the inner radii of the disk that contributes to the returning raciation.," Assuming that the corona is geometrically-thin and emits isotropically, the optically-thick disk will be irradiated by X-rays with an intensity, where $\bar{f}$ is an appropriate averaging of $f(r)$ over the inner radii of the disk that contributes to the returning radiation." Given a functional form for ftr). this irradiation profile can be used to construct the appropriately weighted relativistic smearing kernel that can then be convolved with the rest-frame reflectionspectrum!.. thereby producing a full spectral mocel of smeared reflection from the disk.," Given a functional form for $f(r)$, this irradiation profile can be used to construct the appropriately weighted relativistic smearing kernel that can then be convolved with the rest-frame reflection, thereby producing a full spectral model of smeared reflection from the disk." We now compare the EPLC pn data for MC6-30-15 with spectral models constructed from this generalized standard model of thin-disk accretion., We now compare the EPIC pn data for MCG–6-30-15 with spectral models constructed from this generalized standard model of thin-disk accretion. However. we must first choose a functional form for f(r). the fraction of the dissipated energy released in the irradiating X-ray continuum.," However, we must first choose a functional form for $f(r)$, the fraction of the dissipated energy released in the irradiating X-ray continuum." Here. we choose the function form: where Mar can be considered as a “coronal truncation racdius.," Here, we choose the function form: where $r_{\rm out}$ can be considered as a “coronal truncation radius”." We also examine the situation in which f(r) is a powerlaw in radius (see below)., We also examine the situation in which $f(r)$ is a powerlaw in radius (see below). Using this form for f(r) in eqn. L1..," Using this form for $f(r)$ in eqn. \ref{eq:dissipation_law}," we construct new relativistic smearing functions and hence a spectral. mocel that can be compared with the data., we construct new relativistic smearing functions and hence a spectral model that can be compared with the data. Phis model (and indeed all moclels presented. in the rest of this paper) assume a near-extremal Werr black hole (with spin @= 0.998) and employ the Laor (1991) relativistic transferfunction?., This model (and indeed all models presented in the rest of this paper) assume a near-extremal Kerr black hole (with spin $a=0.998$ ) and employ the Laor (1991) relativistic transfer. . We shall refer to the most general form of our model. where Ay and rou are [ree parameters. as VPORQULED (shorthand for runcated-PORQUED clisk).," We shall refer to the most general form of our model, where $\Delta\eta$ and $r_{\rm out}$ are free parameters, as tTORQUED (shorthand for truncated-TORQUED disk)." The results of fitting model CPORQUED to the EPIC on data are reported in Fig., The results of fitting model tTORQUED to the EPIC pn data are reported in Fig. daa. Fig.," \ref{fig:phys_fits}a a, Fig." 5. and Table 2.., \ref{fig:rout_deta_cont} and Table \ref{tab:fits3}. Examination of the confidence contours in the (Gru.zNp)- shows that. within the context of this model. the data require the disk to be both torqued (νο. Ay70) and »ossess a finite coronal truncation radius at better than the confidence level for two interesting parameters.," Examination of the confidence contours in the $(r_{\rm out},\Delta\eta)$ -plane shows that, within the context of this model, the data require the disk to be both torqued (i.e., $\Delta\eta>0$ ) and possess a finite coronal truncation radius at better than the confidence level for two interesting parameters." In fact. he data require a very strongly torqued disk. with Ay222 (1.c.. )) at the confidence level for one interesting xwameter.," In fact, the data require a very strongly torqued disk, with $\Delta\eta>22$ (i.e., ) at the confidence level for one interesting parameter." In the language of Agol Werolik (2000). the data argue for an “inlinite-cllicieney disk”. in which the dominant energy source is the black hole spin as opposed o gravitational potential energy of the accretion flow.," In the language of Agol Krolik (2000), the data argue for an “infinite-efficiency disk”, in which the dominant energy source is the black hole spin as opposed to gravitational potential energy of the accretion flow." We explore the constraints imposed by these data urther by restricting parameters of the CPORQUED mocel and examining the clleet on the eoodness-of-t., We explore the constraints imposed by these data further by restricting parameters of the tTORQUED model and examining the effect on the goodness-of-fit. Firstly. we consider the case in which the disk is subject to à torque atr —ny but the corona is not truncated (Le. rau0cX« we refer to this as the PORQUIED model).," Firstly, we consider the case in which the disk is subject to a torque at $r=r_{\rm ms}$ but the corona is not truncated (i.e., $r_{\rm out}\rightarrow \infty$; we refer to this as the TORQUED model)." From Table 2.. it can be seen that the goodness-of-fit parameter increases slightly GAYS=7 for one less degree of freedom. in. both he kkeV and kkeV. fits).," From Table \ref{tab:fits3}, it can be seen that the goodness-of-fit parameter increases slightly $\Delta\chi^2=7$ for one less degree of freedom in both the keV and keV fits)." An application of the F-test suggests that this is a significantly worse description of these data at the level., An application of the F-test suggests that this is a significantly worse description of these data at the level. However. Protassov et al. (," However, Protassov et al. (" 2002) have pointed out that it is formally incorrect to use he F-test in this case: the PORQUED model lies on one »indary of the parameter space describing ΕΟΟ (the Trou=O boundary). ancl this fact can skew the srobability. distribution of the goodness of fit. parameter.,"2002) have pointed out that it is formally incorrect to use the F-test in this case; the TORQUED model lies on one boundary of the parameter space describing tTORQUED (the $1/r_{\rm out}=0$ boundary), and this fact can skew the probability distribution of the goodness of fit parameter." Due to this caveat. we consider that the evidence for coronal runcation is marginal.," Due to this caveat, we consider that the evidence for coronal truncation is marginal." secondly. we assess the evidence for the presence of he inner torque at =ry ," Secondly, we assess the evidence for the presence of the inner torque at $r=r_{\rm ms}$." Lowe impose the restriction hat Ay=0. we have an irradiation profile that follows a PP dissipation profile. albeit with an outer truncation radius.," If we impose the restriction that $\Delta\eta=0$, we have an irradiation profile that follows a PT dissipation profile, albeit with an outer truncation radius." We refer to this model as (UPPDISK., We refer to this model as tPTDISK. As reported in ‘Table 20 (also see Fig., As reported in Table \ref{tab:fits3} (also see Fig. 4bb). the goodness-of-Iit. parameter increases hy AY?=13 upon the removal of this one degree of freedom from the models.," \ref{fig:phys_fits}b b), the goodness-of-fit parameter increases by $\Delta\chi^2=13$ upon the removal of this one degree of freedom from the models." Phe F-test implies that this is a significantly worse description of the data at 1e level., The F-test implies that this is a significantly worse description of the data at the level. Note that we doοἱ impose the restriction that «δη20 in ow CPORQUED fits and. hence. the restricted: mocel *PDISK does.20/ lie on the boundary of the parameter space describing ΕΟΟο».," Note that we do impose the restriction that $\Delta\eta>0$ in our tTORQUED fits and, hence, the restricted model tPTDISK does lie on the boundary of the parameter space describing tTORQUED." Thus. the restriction on the pplication of the E-test. raised by Protassoy et al. (," Thus, the restriction on the application of the F-test raised by Protassov et al. (" 2002) oes not apply here and we have no reason to distrust the Petest results.,2002) does not apply here and we have no reason to distrust the F-test results. Hence. these data provide strong evidence for 10 presence of an inner clisk torque.," Hence, these data provide strong evidence for the presence of an inner disk torque." We note that the best-fitting parameters of tPEDISIN Uso might be inconsistent with the overall spectral energy istribution of AIC6-30-15., We note that the best-fitting parameters of tPTDISK also might be inconsistent with the overall spectral energy distribution of MCG–6-30-15. The coronal truncation rackius in these fits is constrained to be ra=5.0oyhy. Che same as the half-light. radius of the accretion disk (rye&Sra: Aeol Ixrolik. 2000).," The coronal truncation radius in these fits is constrained to be $r_{\rm out}=5.0^{+1.0}_{-0.7}\,r_{\mathrm g}$, the same as the half-light radius of the accretion disk $r_{1/2}\approx 5r_{\mathrm g}$; Agol Krolik 2000)." Since of the total radiative luminosity of this AGN is observed to emerge in the X- band (Iteynolds et al., Since of the total radiative luminosity of this AGN is observed to emerge in the X-ray band (Reynolds et al. " 1997). this result would imply an extremely high value of f(r) (νου, almost unity) in the inner clisk."," 1997), this result would imply an extremely high value of $f(r)$ (i.e., almost unity) in the inner disk." We can also use this chain of reasoning to eliminate, We can also use this chain of reasoning to eliminate "Lin,~l2<10%ees tin redshift :~26. which is close to the observed Zip, of LAEs in this redshift span (es.Cawiseretal.2007:CronmwallOuchietal.2008:Ciudullo 2011).","$\La \sim 1- 2 \times 10^{42}~\ergs$ in redshift $z \sim 2 - 6$, which is close to the observed $L^{*}_{\lya}$ of LAEs in this redshift span \citep[e.g.,][]{Gawiser07, Gronwall07, Ouchi08, Ciardullo11}." . This main progenitor has a halo mass of —104M. at τον6. and ~NM1012.AZ. at 2~2. NEin good agreciuent with. suggestions: from clustering analvsis bv Ouchietal. (2010)...," This main progenitor has a halo mass of $\sim 10^{11}~\Msun$ at $z \sim 6$, and $\sim 10^{12}~\Msun$ at $z \sim 2$, in good agreement with suggestions from clustering analysis by \citet{Ouchi10}. ." " These results sugecst that some the observed LAEs at :~2)6 may be similar to the main progenitors of MW-like 1, ealaxies at high redshifts.", These results suggest that some the observed LAEs at $z \sim 2 - 6$ may be similar to the main progenitors of MW-like $L^*$ galaxies at high redshifts. The calculated escape fractious of Lyra photons (foe) are shown in the middle panel of Figure 7.., The calculated escape fractions of $\lya$ photons $\fesc$ ) are shown in the middle panel of Figure \ref{fig:La}. Tere. the fl is estimated by correcting all escaped photons over whole solid angle and dividiug bv iutrinsically enütted photon mmber.," Here, the $\fesc$ is estimated by correcting all escaped photons over whole solid angle and dividing by intrinsically emitted photon number." Uulike the SER. the fi has higher values at ower redshift +<2. then decreases gradually to ~ 20/4.," Unlike the SFR, the $\fesc$ has higher values at lower redshift $z \lesssim 2$, then decreases gradually to $\sim 20~\%$ ." At.2 [the fi increases again., At $z \gtrsim 4$ the $\fesc$ increases again. The fi. of the main xogenitor fluctuates in the range of ~20604., The $\fesc$ of the main progenitor fluctuates in the range of $\sim 20 - 60 ~\%$. The nedian fo at 2<2.8 bis ~30%. which is consistent with the recent observation by the TETDEN pilot survey (Blancetal.2011).," The median $\fesc$ at $2 \lesssim z \lesssim 4$ is $\sim 30~\%$, which is consistent with the recent observation by the HETDEX pilot survey \citep{Blanc11}." . At lower redshift :=1. there is a aree dispersion in f. παπα to the recent observation w Ateketal.(2009).," At lower redshift $z \lesssim 1$, there is a large dispersion in $\fesc$, similar to the recent observation by \cite{Atek09}." . This large scattering may be caused by. variation iu a muuber of physical properties such as SER. inetallicitv. aud disk orieutation.," This large scattering may be caused by variation in a number of physical properties such as SFR, metallicity, and disk orientation." We will discuss the depeudeuce of fie on these propertics iu detail iu Section 5.1.., We will discuss the dependence of $\fesc$ on these properties in detail in Section \ref{sec:fesc}. We note that the Lya RTcaleulatious in our work. which take iuto account local ionization structure aud iuhonmnogeneous deusity distribution of gas and dust. produce a smaller escape fraction (fic~20080% at Doce6) than that in previous scii-analyvtical work of Salvadorictal.(2010). (fice280%) and Dayal&Libe- (fa~6090 3. in which a uuifonu slab niodel was assumed.," We note that the $\lya$ RTcalculations in our work, which take into account local ionization structure and inhomogeneous density distribution of gas and dust, produce a smaller escape fraction $\fesc \sim 20 - 80~\%$ at $z \sim 6$ ) than that in previous semi-analytical work of \citet[]{Salvadori10} $\fesc \gtrsim 80 \%$ ) and \citet[]{Dayal11b} $\fesc \sim 60 - 90~\%$ ), in which a uniform slab model was assumed." We fiud that more than half of Lya phliotous can be absorbed. because dense gas aud dust around the star-forming aud Lyo-enüttius resions absorb the photous effectively.," We find that more than half of $\lya$ photons can be absorbed, because dense gas and dust around the star-forming and $\lya$ -emitting regions absorb the photons effectively." The EW of Lya line is defined by the ratio between the Lvo fiux and the UV Πας density fiy dm rest frame. where the mean flux density of A=0001600 iu rest frame is used.," The EW of $\lya$ line is defined by the ratio between the $\lya$ flux and the UV flux density $f_{\rm UV}$ in rest frame, where the mean flux density of $\lambda = 1300 - {1600} \; \A$ in rest frame is used." The resulting Lya EWs are shown in the bottom panel of Figure 7.., The resulting $\lya$ EWs are shown in the bottom panel of Figure \ref{fig:La}. Most of the galaxies have EWz20A. they are therefore classified as LAEs (c.g.," Most of the galaxies have $\EW \gtrsim 20\; \A$ , they are therefore classified as LAEs \citep[e.g.,][]{Gronwall07}." The mecian EW increases with redshift. from 30A at redshift :=Oto ~820A at. ~," The median EW increases with redshift, from $\sim 30\; \A$ at redshift $z =0$ to $\sim 820\, \A$ at $z \sim 8.5$ ." This trend is iu broad agreement with observations that galaxies at higher redshifts appear to have higher EW than their counterparts at lower redshifts (6.8...Crouwalletal.2007:Ouchi 2008).," This trend is in broad agreement with observations that galaxies at higher redshifts appear to have higher EW than their counterparts at lower redshifts \citep[e.g.,][]{Gronwall07, Ouchi08}." . The high EW at 26 is produced by excitation cooling. which culances the Lyra cmussion at high redshift. but at low redshift it reduces the EW as the stellar population ages (6.8.Finkelsteinetal. 2009).," The high EW at $z \gtrsim 6$ is produced by excitation cooling, which enhances the $\lya$ emission at high redshift, but at low redshift it reduces the EW as the stellar population ages \citep[e.g.,][]{Finkelstein09}." . Recent observations of LAEs at ~0.2.0.E shows that most local LAEs. uulike those at 2m have EWs less than 100A (Deharvengctal.2008:Cowieetal. 2011)... consistent with the trend seeu in our model.," Recent observations of LAEs at $z \sim 0.2 - 0.4$ shows that most local LAEs, unlike those at $z \gtrsim 3$, have EWs less than $100~\A$ \citep{Deharveng08, Cowie11}, , consistent with the trend seen in our model." We should point out that the results preseuted iu Figure 7 are “unfiltered” bv detection limit. and that we caution against taking these umubers too literally when compared with a particular survey. because the observed properties depeud strongly on the observational threshold.," We should point out that the results presented in Figure \ref{fig:La} are “unfiltered” by detection limit, and that we caution against taking these numbers too literally when compared with a particular survey, because the observed properties depend strongly on the observational threshold." Note also in the current work. we did nof include the transiuissiou in intergalactic medina (IGM).," Note also in the current work, we did not include the transmission in intergalactic medium (IGM)." The Lya properties can be changed by ICM extinction., The $\lya$ properties can be changed by IGM extinction. " The neutral bydrogen in IGM at high redshift can scatter a part of Lvo. photons. aud decrease the Zip, aud EW."," The neutral hydrogen in IGM at high redshift can scatter a part of $\lya$ photons, and decrease the $\La$ and EW." For example. Laursenctal.(2011) suggested that the IGAL trausmussion could be ~20% at :=6.5.," For example, \citet{Laursen11} suggested that the IGM transmission could be $\sim 20~\%$ at $z=6.5$." The transiission depends scusitively on the viewing augle and the cuvirouments of a galaxy. as it is affected by the inhomogeneous flamentary structure of ICAL," The transmission depends sensitively on the viewing angle and the environments of a galaxy, as it is affected by the inhomogeneous filamentary structure of IGM." The emergent Lye euission line of the main progenitor is shown in Figure 8.., The emergent $\lya$ emission line of the main progenitor is shown in Figure \ref{fig:profile}. The frequency of the iutrinsic Lva photon is suupled from a Maxwollian distribution with the eas temperature at the cussion location iu the rest flame of the gas., The frequency of the intrinsic $\lya$ photon is sampled from a Maxwellian distribution with the gas temperature at the emission location in the rest flame of the gas. Our sample Lyo lines show mostly sinele peak. commnou profiles of LAEs observed both at high redshift (2~ 6) (e.g.Ouchietal.2010) and iu the nearby universe (6.g..Cowieetal.2010).," Our sample $\lya$ lines show mostly single peak, common profiles of LAEs observed both at high redshift $z \sim 6$ ) \citep[e.g.,][]{Ouchi10} and in the nearby universe \citep[e.g.,][]{Cowie10}." . Tn a static aud optically thick medimu. the Lvo profile can be double peaked. but when the effective opticaldepth is small due to high relative eas speed or ionization state. therenueht be only a single peak (Zheng& 2002)..," In a static and optically thick medium, the $\lya$ profile can be double peaked, but when the effective opticaldepth is small due to high relative gas speed or ionization state, theremight be only a single peak \citep{Zheng02}. ." Tn our case. the flow speed of eas is up to ~300Em/s. aud the gas ishighly ionized by stellar and ACN radiation. which result iu à single peak.," In our case, the flow speed of gas is up to $\sim 300$km/s, and the gas ishighly ionized by stellar and AGN radiation, which result in a single peak." Iu the case at high redshift :.2 6. the gas is liehlv concentrated around the ealaxvcenter. hence they become optically thick aud cause the Lya photous," In the case at high redshift $z \gtrsim 6$ , the gas is highly concentrated around the galaxycenter, hence they become optically thick and cause the $\lya$ photons" Barred ealaxies constitute a major fraction of all disc ealaxies classified in the optical. more than iucludiug strong bars aud intermediate morphologies (Sellwood Wilkiuson 1993)).," Barred galaxies constitute a major fraction of all disc galaxies classified in the optical, more than including strong bars and intermediate morphologies (Sellwood Wilkinson \cite{sel93}) )." " This fraction increases when also neu-infrared images are used for classification. thus πιάΠλιο the importance for the seucral understanding of the evolution of galaxies,"," This fraction increases when also near-infrared images are used for classification, thus underlining the importance for the general understanding of the evolution of galaxies." The non-axisviunetic potential has a strougc» nupact ou the Ooeas dynamics aud the y.ar formation in barred systems., The non-axisymmetric potential has a strong impact on the gas dynamics and the star formation in barred systems. Observations reveal a correlation between the radial abundance eradient and the strength of the bar (Martin Rov 1991: Friedl et al. 1991:, Observations reveal a correlation between the radial abundance gradient and the strength of the bar (Martin Roy \cite{mar94}; ; Friedli et al. \cite{fri94}; Martinet Friedl 19973)., Martinet Friedli \cite{mar97}) ). This is interpreted as the result of two effects caused by the bar: a stronger radial gas flow aud hence a strouger racial musing of metals aud the efficiency of star formation., This is interpreted as the result of two effects caused by the bar: a stronger radial gas flow and hence a stronger radial mixing of metals and the efficiency of star formation. The racial lnass transfer concentrates eas near the ealactic center and at the ends of the bar at corotation., The radial mass transfer concentrates gas near the galactic center and at the ends of the bar at corotation. Enhanced star formation is the consequence of gas acctuilation., Enhanced star formation is the consequence of gas accumulation. The rotating bar poteutial also heats up the outer disk parts which leads to larger stellar velocity dispersions aud a radial diffusion of stars. (, The rotating bar potential also heats up the outer disk parts which leads to larger stellar velocity dispersions and a radial diffusion of stars. ( Sellwood Wilkiusou 1993)).,Sellwood Wilkinson \cite{sel93}) ). Calactie bars have also been considered to support the central iutall of gas to feed a ceutral “ouster(e.g.," Galactic bars have also been considered to support the central infall of gas to feed a central ""monster""(e.g." Beck et al. 1999))., Beck et al. \cite{bec99}) ). Several authors have claimed that active galactic nuclei (ACN) are ore likely iu barred ealaxies than iu non-barred ones (0.5. Simlsin et al. 195011, Several authors have claimed that active galactic nuclei (AGN) are more likely in barred galaxies than in non-barred ones (e.g. Simkin et al. \cite{sim80}; Arsenault 19893)., Arsenault \cite{ars89}) ). Πιο] et al. (1990)), Hummel et al. \cite{hum90}) ) note that the fraction of central radio sources in barred spirals is hy a factor of 5 higher than iu non-harred spirals., note that the fraction of central radio sources in barred spirals is by a factor of 5 higher than in non-barred spirals. Other authors doubt that there is a significautlv ligher umber of bars in galaxies harboring an AGN (eg. Balick Ileckiiun 1982: Πο et al. 1997))., Other authors doubt that there is a significantly higher number of bars in galaxies harboring an AGN (e.g. Balick Heckman \cite{bal82}; Ho et al. \cite{ho97}) ). It appears that the concentration of gas on a scale of —1 kpe at he ealactic center required to enhance the central star formation can casily be achieved by a bar poteutial., It appears that the concentration of gas on a scale of $\sim$ 1 kpc at the galactic center required to enhance the central star formation can easily be achieved by a bar potential. It secius much more dificult. however. to acctunulate enough eas on a scale of a few pc to tens of pc in order to produce an AGN.," It seems much more difficult, however, to accumulate enough gas on a scale of a few pc to tens of pc in order to produce an AGN ." Other effects depending on the environment of tle ealaxies (iuteraction: Elucercen et al. 1990::, Other effects depending on the environment of the galaxies (interaction: Elmegreen et al. \cite{elm90}; contents: Cavatte ct al. 19903) , contents: Cayatte et al. \cite{cay90}) ) play au important role in mass distribution. gas flow. and therefore iu the formation and evolution of bars aud the star formation history in these svstenis.," play an important role in mass distribution, gas flow, and therefore in the formation and evolution of bars and the star formation history in these systems." One of the most famous. closest aud most widely studied xuvred ealaxies is NGC 1303 (M61). mienmber of the Virgo Cluster. which is observed at au inclination of (Cubathalkurta et al. 1988))," One of the most famous, closest and most widely studied barred galaxies is NGC 4303 (M61), member of the Virgo Cluster, which is observed at an inclination of (Guhathakurta et al. \cite{guh88}) )" .Optical spectra of this ealaxy indicate that it consistsof a nuclear starburst,.Optical spectra of this galaxy indicate that it consistsof a nuclear starburst "mass contained in the outer convective envelope: Rey. the radius fraction of the base of the convective envelope: log13. the base ten logarithm of the central pressure: logT... the base ten logarithm of the central temperature: logp.. the base ten logarithim of the central densitv: X,.. the central mass fraction of heavy elements: Z.. the central mass fraction of heavy elements.","mass contained in the outer convective envelope; $_{\mathrm {env}}$, the radius fraction of the base of the convective envelope; $\log{P_c}$, the base ten logarithm of the central pressure; $\log{T_c}$, the base ten logarithm of the central temperature; $\log{\rho_c}$, the base ten logarithm of the central density; $_c$, the central mass fraction of heavy elements; $_c$, the central mass fraction of heavy elements." The nuclear energy generation properties of both the stancdarcl (4117-20) ancl nonstancdarel (4411-16) solar models are listed in Table 2., The nuclear energy generation properties of both the standard 17-20) and nonstandard 1-16) solar models are listed in Table 2. Table 2 lists the fraction of total photon huminosityv coming from the PP I. PP II. and PP III branches of the PP network and from ihe CNO evele.," Table 2 lists the fraction of total photon luminosity coming from the PP I, PP II, and PP III branches of the PP network and from the CNO cycle." Also listed are the individual neutrino fluxes from the neutrino producing reactions that occur in the sun (see Figure 1 of GD97)., Also listed are the individual neutrino fluxes from the neutrino producing reactions that occur in the sun (see Figure 1 of GD97). Note that in GD9T the neutrino fluxes are listed in units of LOMem 7s +., Note that in GD97 the neutrino fluxes are listed in units of $^{10}$ $^{-2}$ $^{-1}$. " Finally. Table 2 lists P(* CI). the total neutrino flux. in SNU. for the ""CI detector: and (* Ga). the total neutrino flux. in SNU. for the ""1a detector."," Finally, Table 2 lists ${\Phi}$ $^{37}$ Cl), the total neutrino flux, in SNU, for the $^{37}$ Cl detector; and ${\Phi}$ $^{71}$ Ga), the total neutrino flux, in SNU, for the $^{71}$ Ga detector." Asatest on the validity of a moclel. the expected oscillation frequencies can be compared with observations Irom the Sun.," As a test on the validity of a model, the expected oscillation frequencies can be compared with observations from the Sun." Guenthers non-radial. non-adiabatic pulsation program (Guenther 1994) was used to calculate the oscillation frequencies of the models produced wilh YREC.," Guenther's non-radial, non-adiabatic pulsation program (Guenther 1994) was used to calculate the oscillation frequencies of the models produced with YREC." The model output was then compared with data obtained by the Michelson Doppler Imager (MDI) instrument on board the during the first. νου of its operation (Rhodes et al., The model output was then compared with data obtained by the Michelson Doppler Imager (MDI) instrument on board the during the first year of its operation (Rhodes et al. 1997)., 1997). This data set was chosen as il comprises one of the longest time-series of data. 360 days.," This data set was chosen as it comprises one of the longest time-series of data, 360 days." More recent MDI-SOIIO data include only 144-day. or 72-day data sets. aud therefore restrict the number of data points. wilh most sets having very few [20.1.2 modes.," More recent MDI-SOHO data include only 144-day or 72-day data sets, and therefore restrict the number of data points, with most sets having very few =0,1,2 modes." Data from the GOLF experiment (see Bertello et al., Data from the GOLF experiment (see Bertello et al. 2000 and ia οἱ al., 2000 and a et al. 2001 for the latest results) were not considered here despite the low-degree modes., 2001 for the latest results) were not considered here despite the low-degree low-frequency modes. While these modes can tell us a lot about the structure of the core (see Turck-Chiézze et al., While these modes can tell us a lot about the structure of the core (see Turck-Chièzze et al. 2001). for our purposes here. it requires mixing one set of low degree modes with intermediate and high degree modes [rom another instrument. which can give rise to artifacts in (he solar core unless the data are contemporaneous (see Basu et al.," 2001), for our purposes here, it requires mixing one set of low degree modes with intermediate and high degree modes from another instrument, which can give rise to artifacts in the solar core unless the data are contemporaneous (see Basu et al." 1996. 1997).," 1996, 1997)." Hence. in au attempt to avoid such artifacts. we have opted for a homogeneous set of data.," Hence, in an attempt to avoid such artifacts, we have opted for a homogeneous set of data." For comparison. BISON+LOWL (Basu οἱ al.," For comparison, BiSON+LOWL (Basu et al." 1997) data were also used., 1997) data were also used. This cata set had been specially constructed by obtaining frequencies [rom contemporaneous DiSON and LOWL time series., This data set had been specially constructed by obtaining frequencies from contemporaneous BiSON and LOWL time series. This set gave results verv similar to those obtained by the MDI-SOIIO dala set used. here., This set gave results very similar to those obtained by the MDI-SOHO data set used here. llow does our theoretical estimate for the population of the scattered. disk. compare with estimates [rom direct observations of the SDOs?,How does our theoretical estimate for the population of the scattered disk compare with estimates from direct observations of the SDOs? To make (his comparison we need to consider the population of JFC-size SDOs., To make this comparison we need to consider the population of JFC-size SDOs. The JFC population has been determined to be dominated by objects of 110 kim in diameter (2?):: such objects in the heliocentric distance range 3050 AU would have magnitude mr~30 and fainter (assuming the average albedo of 0.04 [or cometary nuclei).," The JFC population has been determined to be dominated by objects of 1–10 km in diameter \citep{tancredi06,lowry08}; such objects in the heliocentric distance range 30–50 AU would have magnitude $m\sim30$ and fainter (assuming the average albedo of $0.04$ for cometary nuclei)." Surveys for faint objects in the outer solar svstem have vet to achieve limiting magnitudes in this range. but the size distributions determined from detections of brighter objects can be extrapolated (to give an estimate of how many objects exist in the scattered disk.," Surveys for faint objects in the outer solar system have yet to achieve limiting magnitudes in this range, but the size distributions determined from detections of brighter objects can be extrapolated to give an estimate of how many comet--sized objects exist in the scattered disk." At present. the size distribution determined by probes deepest into the small end of the trans-Neptunian population in the 30 to 50 AU distance range.," At present, the size distribution determined by \citet{bernstein04} probes deepest into the small end of the trans-Neptunian population in the 30 to 50 AU distance range." The limiting magnitude of (his survev is mr=29. which just approaches the range of interest [or JFC-size objects.," The limiting magnitude of this survey is $m=29$, which just approaches the range of interest for JFC-size objects." The authors find a turnover in the scattered disk size distribution near mc25. which implies far fewer small objects (han estimated from an extrapolation of the single power law that describes the larger objects.," The authors find a turnover in the scattered disk size distribution near $m\simeq25$, which implies far fewer small objects than estimated from an extrapolation of the single power law that describes the larger objects." To compare the results of our simulations to the ? size distribution. we must account for the heliocentric distance and eclipGic latitude range of (he observations.," To compare the results of our simulations to the \citet{bernstein04} size distribution, we must account for the heliocentric distance and ecliptic latitude range of the observations." The reported size distribution is for objects in the 30.50 AU zone observed close to the ecliptic. so it is necessary (o know what percentage of our simulated SDO population is in (his range al any given lime.," The reported size distribution is for objects in the 30–50 AU zone observed close to the ecliptic, so it is necessary to know what percentage of our simulated SDO population is in this range at any given time." To do this. we calculated the test particles. heliocentric distance distiibution averaged over the last LOO Myr of the integration: the result is shown in Figure 55: on average. of our particles can be found in the 3050 AU heliocentric distance range.," To do this, we calculated the test particles' heliocentric distance distribution averaged over the last 100 Myr of the integration; the result is shown in Figure \ref{f:helio}: on average, of our particles can be found in the 30–50 AU heliocentric distance range." This corresponds (ο a population of (0.8—1.7)x103., This corresponds to a population of $(0.8-1.7)\times10^{8}$. The ecliptic latitudes of the objects were also caleulated over the last LOO Myr. ancl on average of the simulated SDOs are within +3° of the ecliptic. which corresponds to (he latitude range of most ABO survevs.," The ecliptic latitudes of the objects were also calculated over the last 100 Myr, and on average of the simulated SDOs are within $\pm3^\circ$ of the ecliptic, which corresponds to the latitude range of most KBO surveys." Figure 6 shows (he resulting ecliptie skv density for the simulated SDOs compared to the 72. cumulative size distribution., Figure \ref{f:size_dist} shows the resulting ecliptic sky density for the simulated SDOs compared to the \citet{bernstein04} cumulative size distribution. The objects in the source population lor the JECs must be at least as large as the JECs theniselves. so the observed distribution needs to overlap the theoretical population estimate in (he 110 km diameter range. i.e. in the magnitude range 3035.," The objects in the source population for the JFCs must be at least as large as the JFCs themselves, so the observed distribution needs to overlap the theoretical population estimate in the 1–10 km diameter range, i.e. in the magnitude range 30–35." From Figure 6.. we see that even for the most favorable extrapolation of the observations. the theoretical estimate from our simulation just barely agrees in this range.," From Figure \ref{f:size_dist}, we see that even for the most favorable extrapolation of the observations, the theoretical estimate from our simulation just barely agrees in this range." For the best.fit size distribution the discrepancy wilh theory is more than (wo orders of magnitude., For the best–fit size distribution the discrepancy with theory is more than two orders of magnitude. is that we see the period spacing between successive overtones.,is that we see the period spacing between successive overtones. Iu this case the period spacings. equal to 18.5 (1-1) and 10.1 (1-2) s. would imply a stellar lass of 0.67 (1-1) and 0.70 AL. (122) using the interpolation formmla of Wiuget et al. (," In this case the period spacings, equal to 18.8 (l=1) and 10.4 (l=2) s, would imply a stellar mass of 0.67 (l=1) and 0.70 $M_{\odot}$ (l=2) using the interpolation formula of Winget et al. (" 1991).,1991). This asteroseianologicale mass would be higher than the 0.59 AL. value. found from spectroscopy plus evolutionary tracks (Dreizler et al.," This asteroseismological mass would be higher than the 0.59 $M_{\odot}$ value, found from spectroscopy plus evolutionary tracks (Dreizler et al." 1996)., 1996). But this discrepancy would not be very siguificaut as itis possible that the interpolation formmla of Winect et al. (, But this discrepancy would not be very significant as it is possible that the interpolation formula of Winget et al. ( 1991) needs some adjustinent because of the CCT composition of 22321.,1991) needs some adjustment because of the peculiar composition of 2324. Tn au alternative interpretation we assumed that the DFT instability was real aud we applied the Linear State Space model (IXóunig Tinuner 1997) to investiga| the quasi-periodic nature of these variations., In an alternative interpretation we assumed that the DFT instability was real and we applied the Linear State Space model (Könnig Timmer 1997) to investigate the quasi-periodic nature of these variations. As discussed i- Section 5. this approach is also partially successful. but it also requires new lonecr observations to be coufirmiect.," As discussed in Section 5, this approach is also partially successful, but it also requires new longer observations to be confirmed." At the moment we can only speculate about the physical interpretation., At the moment we can only speculate about the physical interpretation. Do we see the coupling time between different e-31nodes or the damping of a single mod:?, Do we see the coupling time between different g-modes or the damping of a single mode? lun principle. the quasi-periodic nature of 2232| couk evel chdaneger the interpretation as e-anode pulsations.," In principle, the quasi-periodic nature of 2324 could even endanger the interpretation as g-mode pulsations." Iu conclusion both possible interpretations of the apparent DET instability need a new bigger observational effort. which could be realized only with a larger number of telescopes in à WET-like campaign.," In conclusion both possible interpretations of the apparent DFT instability need a new bigger observational effort, which could be realized only with a larger number of telescopes in a WET-like campaign." " If we adopt the ivpothesis that the DFT instability is only apparent. --- is also possible to estimate the duration needed for PAuch a campaign in order to be able to separate all the requencies,"," If we adopt the hypothesis that the DFT instability is only apparent, it is also possible to estimate the duration needed for such a campaign in order to be able to separate all the frequencies." Tf all the l=1 aud 122 frequencies were excited oe ithe region between 150 and 500 yz. where most power is concentrated. the average frequency separation would c about O.L fz.," If all the l=1 and l=2 frequencies were excited in the region between 450 and 500 $\mu$ Hz, where most power is concentrated, the average frequency separation would be about 0.4 $\mu$ Hz." Tn a more realistic case. if ouly of 1e frequencies were excited (as i 11159. which is the CAV Vir star with the largest number of detected modes). a frequeney resolution of about 0.5 gz would be enough.," In a more realistic case, if only of the frequencies were excited (as in 1159, which is the GW Vir star with the largest number of detected modes), a frequency resolution of about 0.8 $\mu$ Hz would be enough." Therefore we would require a data set with a time base of about 1.7 times the data set analvzed in this paper., Therefore we would require a data set with a time base of about 1.7 times the data set analyzed in this paper. becomes dominant for intermediate inclinations.,becomes dominant for intermediate inclinations. " The exact outcome of the polarisation depends on the relative Stokes fluxes coming from the polar outflows, on the one hand side, and from the accretion disc and torus, on the other hand side."," The exact outcome of the polarisation depends on the relative Stokes fluxes coming from the polar outflows, on the one hand side, and from the accretion disc and torus, on the other hand side." When viewed strictly edge-on the absorption effects in the torus are too strong and the polarisation angle is always determined by the polar outflows., When viewed strictly edge-on the absorption effects in the torus are too strong and the polarisation angle is always determined by the polar outflows. But a rotation of the polarisation angle between the soft and the hard X-ray band is observed and could be used to measure the misalignment between the symmetry axes of the torus and the outflows., But a rotation of the polarisation angle between the soft and the hard X-ray band is observed and could be used to measure the misalignment between the symmetry axes of the torus and the outflows. " In the first and second column of Table 2,, we quantify the difference Av in the polarisation angles between 20 keV and 2 keV for different obscured viewing angles."," In the first and second column of Table \ref{tab:dpsi}, we quantify the difference $\Delta \psi$ in the polarisation angles between 20 keV and 2 keV for different obscured viewing angles." The values of Aw vary strongly with the inclination but even at edge-on view and for a high optical depth of the ionisation cone a small rotation of the polarisation angle is noted., The values of $\Delta \psi$ vary strongly with the inclination but even at edge-on view and for a high optical depth of the ionisation cone a small rotation of the polarisation angle is noted. " For contrast, we show in Fig."," For contrast, we show in Fig." 6 the results for the X-ray polarisation of a model including polar outflows with rcone= but being aligned to the z-axis., \ref{fig:torus_cones003_noinc} the results for the X-ray polarisation of a model including polar outflows with $\tau_{\rm cone} = 0.03$ but being aligned to the $z$ -axis. " Without inclining the double-cone, ~ can only adopt the two possible values that correspond to the perpendicular polarisation caused by the polar scattering in the soft X-ray band and the aligned polarisation vector due to the disc/torus at higher photon energies."," Without inclining the double-cone, $\psi$ can only adopt the two possible values that correspond to the perpendicular polarisation caused by the polar scattering in the soft X-ray band and the aligned polarisation vector due to the disc/torus at higher photon energies." This bimodal distribution of the polarisation vector is related to the symmetry of the model with respect to the z-axis., This bimodal distribution of the polarisation vector is related to the symmetry of the model with respect to the $z$ -axis. " The comparison shows that the gradual change of w with photon energy, as it is apparent in the modelling case of Fig."," The comparison shows that the gradual change of $\psi$ with photon energy, as it is apparent in the modelling case of Fig." " 5 (left), is characteristic for a misalignment of the outflows with respect to the torus."," \ref{fig:torus_cones003_03}~ (left), is characteristic for a misalignment of the outflows with respect to the torus." The third and fourth column of Table 2 show some exemplary results for a scenario that includes equatorial scattering., The third and fourth column of Table \ref{tab:dpsi} show some exemplary results for a scenario that includes equatorial scattering. The corresponding models are based on the cases of Sect., The corresponding models are based on the cases of Sect. 4.3 but additionally include an equatorial wedge as described in Table 1.., \ref{sec:disc_tor_cones} but additionally include an equatorial wedge as described in Table \ref{tab:models}. The additional scattering region has an impact at all viewing directions., The additional scattering region has an impact at all viewing directions. " For polar outflows with low optical depth Tcone, the rotation Aw of the polarisation angle can either rise or fall with respect to the models of Sect. 4.3;;"," For polar outflows with low optical depth $\tau_{\rm cone}$, the rotation $\Delta \psi$ of the polarisation angle can either rise or fall with respect to the models of Sect. \ref{sec:disc_tor_cones};" " for a high Tone, the value of Aw always diminishes."," for a high $\tau_{\rm cone}$, the value of $\Delta \psi$ always diminishes." " At edge-on inclination, the polarised flux escaping from the torus funnel is too small to efficiently counterbalance the effect of polar scattering."," At edge-on inclination, the polarised flux escaping from the torus funnel is too small to efficiently counterbalance the effect of polar scattering." " Therefore, the resulting Aw is very low."," Therefore, the resulting $\Delta \psi$ is very low." 'The results illustrate that the wavelength-dependence of the scattering efficiency and the radiative coupling between the different reprocessing regions are important to understand the net polarisation., The results illustrate that the wavelength-dependence of the scattering efficiency and the radiative coupling between the different reprocessing regions are important to understand the net polarisation. " The equatorial electron scattering competes with the polar electron scattering in the outflows, independently of spectral energy."," The equatorial electron scattering competes with the polar electron scattering in the outflows, independently of spectral energy." " Therefore, the polarisation position angles are systematically higher when equatorial scattering is included."," Therefore, the polarisation position angles are systematically higher when equatorial scattering is included." The rise in v is more, The rise in $\psi$ is more At low burst fluxes. the observed normalizatious show a simall albcit statistically significaif trend towards lower values.,"At low burst fluxes, the observed normalizations show a small albeit statistically significant trend towards lower values." In the case of IU 3L where the potential decrease is the largest. the uoriualizajon changed from 133.7£16.1 dan/l0 kpc)? to 1110d+⋅ ∣↽ U ∶↓⋅↱⊐∙∩∐↘↽⋯∐⊔↘↴⋉⊳⋝−⋜↧↴∖↴↑∐↸∖↕−⊓↕⊼≼∐∖↸⊳↕∐∐∖≼↧↕↥⋅∪⋯∩∖ H J ⋅10N cre sYan to 0.5«10 σος tom 2.," In the case of 4U $-$ 34, where the potential decrease is the largest, the normalization changed from $133.7\pm 16.4$ (km/10 $^2$ to $114.0\pm 15.6$ (km/10 $^2$ as the flux declined from $6\times 10^{-8}$ erg $^{-1}$ $^{-2}$ to $0.5\times 10^{-8}$ erg $^{-1}$ $^{-2}$." This corresponds to a <15 ↥⋅↸∖≼↧⋯⊳↑↕∪∐↕∐↑↕∐∖∐∪↥⋅↕⊔⋜↧∐∑⋜↧↑↕∪∐∙↕∐∪," This corresponds to a $\lesssim 15$ reduction in the normalization." ↑∐↸∖↥⋅↴∖⋯ rees. the decline is even smaller.," In other sources, the decline is even smaller." This weak cepeudence seen in the data argues against he models with solar couposition. as shown in Figure 2," This weak dependence seen in the data argues against the models with solar composition, as shown in Figure \ref{fig:fcolor}." The decline in the normalization can. in principle. be accounted for with a =| Increase int1e color correction actor (see eq. [3]])," The decline in the normalization can, in principle, be accounted for with a $\lesssim 4$ increase in the color correction factor (see eq. \ref{eq:rapp}] ])" towards low temperatures., towards low temperatures. As can be secu in Figure 2. current atinosphere 1uoclels do not predict such an evolution.," As can be seen in Figure \ref{fig:fcolor}, current atmosphere models do not predict such an evolution." IIowever. as we discussed in the beginning of &1 a nuniber of effects reatec to the plivsies of musts on the neutron star surface (uneven cooling and burst oscillalous). as well as the recTeo sensitivity of the PCA at low energies. are capable of causing the observed trend in tl1ο normalization.," However, as we discussed in the beginning of 4, a number of effects related to the physics of bursts on the neutron star surface (uneven cooling and burst oscillations), as well as the reduced sensitivity of the PCA at low energies, are capable of causing the observed trend in the normalization." Moreover. he ta cect iu he data we would aiii to model is comparable to the uncertaimtyv iniifeyiue theoretically the color correction factor ron the atmosphere models and is also comparable to the deviatio1 of the observed. and theoretical spectra from dackbodies.," Moreover, the $\lesssim 4\%$ effect in the data we would aim to model is comparable to the uncertainty in inferring theoretically the color correction factor from the atmosphere models and is also comparable to the deviation of the observed and theoretical spectra from blackbodies." The latter couceri can be remedied by fitting directly theoretical model spectra to the data. but reducimg he theoretical uucertaimties present iu the models to less than ~ few percent is significantly more challeugiug.," The latter concern can be remedied by fitting directly theoretical model spectra to the data, but reducing the theoretical uncertainties present in the models to less than $\sim$ few percent is significantly more challenging." An alternative approach is to allow for a range of values for the color correction factor that span the spread of, An alternative approach is to allow for a range of values for the color correction factor that span the spread of present im the data will set the difficulty in automatically selecting which light curve contaius a true transit.,present in the data will set the difficulty in automatically selecting which light curve contains a true transit. " To find this siguature the method developed in. Ἱόροπ]οSoro""CC» andὶ Roca"" Cortésstéss (200: (2002)). hasas beenΌσοι applied."," To find this signature the method developed in Réggulo and Roca Cortéss \cite{regulo1}) ), has been applied." :n What the method detects is the spacing among the equidistant set of Tn brief. the method works as follows.," What the method detects is the spacing among the equidistant set of In brief, the method works as follows." The starting out is the square of selected scale from the previous stop. coutaining the equally spaced peaks we intend to fud.," The starting point is the square of selected scale from the previous step, containing the equally spaced peaks we intend to find." The next step is to obtain the power spectrum of Us signal by perforiiuug a EFT., The next step is to obtain the power spectrum of this signal by performing a FFT. This spectu is again a series of equally spaced peaks. but now the first peak is at zero frequency. iudepeudeut of the epoch or phase of je transits (see Fig.," This spectrum is again a series of equally spaced peaks, but now the first peak is at zero frequency, independent of the epoch or phase of the transits (see Fig." 6. for the FFT of the light curves shown in Fig. 5))., \ref{figFFT} for the FFT of the light curves shown in Fig. \ref{figselscale}) ). Fiudiug the spacing among the peaks 1s now unuch easier. knowing the position ofthe first one.," Finding the spacing among the peaks is now much easier, knowing the position of the first one." The search for the spacing (7) is done iteratively trying a range of values that im our case covers from 1 day to 60 days in steps of 512 s. which corresponds to the temporal resolution of CoRoT data.," The search for the spacing $T$ ) is done iteratively trying a range of values that in our case covers from 1 day to 60 days in steps of 512 s, which corresponds to the temporal resolution of CoRoT data." We try to fud if there is a signal 1.5 times above the rius of the power spectrum at any of the bins spaced ry = T. apart., We try to find if there is a signal 1.5 times above the rms of the power spectrum at any of the bins spaced $\nu_{0}$ = $T^{-1}$ apart. " To evaluate""valuate the! significanceSjeuificauce of the found peaks peaksaudand to toavoidavo binwng effects. this procedure is repeated 50 times on the selected scale. but coutiuuously shortening its length. uutil it is shortened for about 10:4."," To evaluate the significance of the found peaks and to avoid binning effects, this procedure is repeated 50 times on the selected scale, but continuously shortening its length, until it is shortened for about $\%$." The coincidence of periods mong peaks found in the 50 trials is then registered., The coincidence of periods among peaks found in the 50 trials is then registered. This lwethod searching for the period also finds the auultiples 20d snbuniltiplesof of any periodicity present in the data., This method of searching for the period also finds the multiples and submultiples of any periodicity present in the data. TRUFAS was applied to the 999 svuthetic Lelt curves of DTI. aud Fie.," TRUFAS was applied to the 999 synthetic light curves of BT1, and Fig." 7 shows typical results of the trausit search., \ref{figspacing} shows typical results of the transit search. Iu the example in Fie. 5..," In the example in Fig. \ref{figselscale}," light curve 533 has a very clear planctary transit. aud the period found by TRUFAS is 6.3985 davs with a level of coincidence of 91.," light curve 533 has a very clear planetary transit, and the period found by TRUFAS is 6.3985 days with a level of coincidence of 94." Light curve 168 has a weak trausit signal that was found by only 3 of the 5 algorithms compared in DTI., Light curve 168 has a weak transit signal that was found by only 3 of the 5 algorithms compared in BT1. Tere TRUFAS found a signal at a level of coincidence of 86% among the 50 trials. with a periodicity of 11.5125 days.," Here TRUFAS found a signal at a level of coincidence of 86 among the 50 trials, with a periodicity of 11.5125 days." The other peaks that appear in Fig., The other peaks that appear in Fig. 7. are the multiples aud subinultiples of the found period., \ref{figspacing} are the multiples and submultiples of the found period. he stellar mass of the ceutral galaxy (dashed lines) with he SAMSsx exact predictions (solid lines).,the stellar mass of the central galaxy (dashed lines) with the SAMs exact predictions (solid lines). The! estimation is computed iu the same halo mass rauge used i1i ZCZUür. ο facilitate the comparison.," The estimation is computed in the same halo mass range used in ZCZ07, to facilitate the comparison." Iu this case. we see that the approxinatioun underestimates the merger ccontribution of satellites to the final stellar mass. especlally at the Hehest halo masses probed.," In this case, we see that the approximation underestimates the merger contribution of satellites to the final stellar mass, especially at the highest halo masses probed." This may arise due to he aereine of additional satellites to the brightest oue iu each progenitor halo. and iav agai cad to a stronger dowusizing effect.," This may arise due to the merging of additional satellites to the brightest one in each progenitor halo, and may again lead to a stronger downsizing effect." We note tha the behavior of he estimated satellite merger coutrilition goes in the opposite direction than that of smaller central ealaxics., We note that the behavior of the estimated satellite merger contribution goes in the opposite direction than that of smaller central galaxies. This leads to a partial cancellation such hat the estimate of the toal merger contribution is reasonable. which also iuplies that the iuferred coutzibution TOM recent star ornation is not stronglv affected bv he approximate ature of the above method.," This leads to a partial cancellation such that the estimate of the total merger contribution is reasonable, which also implies that the inferred contribution from recent star formation is not strongly affected by the approximate nature of the above method." It is hard to draw definitive concuxjous from all hese tests eiven the iutrinsic uncertainties in both the SANs aid the ZCZUÜT estinmatious., It is hard to draw definitive conclusions from all these tests given the intrinsic uncertainties in both the SAMs and the ZCZ07 estimations. We clarity that the atter assuniptions investigated here have to do with ransforumüus the ZCZÜT measurement of tlie growth of stellar iuass iu central galaxies as a function of halo uass (them Fie., We clarify that the latter assumptions investigated here have to do with transforming the ZCZ07 measurement of the growth of stellar mass in central galaxies as a function of halo mass (their Fig. 8). which is robust. to he overall contribution of mergers a star formation to the stellar nass assciubly (their Fig.," 8), which is robust, to the overall contribution of mergers and star formation to the stellar mass assembly (their Fig." 9)., 9). More care should certainly © elven to these assunrptions. taking iuto account sincoth accretion aud incorporating better froatiuent of central aud satellite «vuanudes determined from analytic uodels (ee... Zeutueretal. 20051) or from siuulations (oe. Waneetal2006:Whiteal.2007:Wakeetal. 2008)).," More care should certainly be given to these assumptions, taking into account smooth accretion and incorporating better treatment of central and satellite dynamics determined from analytic models (e.g., \citealt{Zentner05}) ) or from simulations (e.g., \citealt{wang06,White07,Wake08}) )." Nonetheless. we expect the qualitative results of ZCZÜT to still be valid (or even somewlhat strenethcued with these corrections. as discussed above). and believe that such phenomenological methods can proviο powerful coustraiuts ou theories of galaxy formaion and evolution.," Nonetheless, we expect the qualitative results of ZCZ07 to still be valid (or even somewhat strengthened with these corrections, as discussed above), and believe that such phenomenological methods can provide powerful constraints on theories of galaxy formation and evolution." m lis paper we studv theoretical predictions for the evolution of stellar mass in galaxies as a functiou of their host halo mass using senud-analvtie galaxy formation models based ou the Milleuniuuu simulation.," In this paper we study theoretical predictions for the evolution of stellar mass in galaxies as a function of their host halo mass, using semi-analytic galaxy formation models based on the Millennium simulation." We utilize two differeut SAM implemenations. the AIPA (Crotonetal.2006:DeLucia&Blaizo2007) aud Durham (Bowerctal.2006) models.," We utilize two different SAM implementations, the MPA \citep{Croton06,DeLucia07} and Durham \citep{Bower06} models." " We investigate the differeut contributions to the erowth o stellar nass. and the role of mergers and star formajon in the stellar mass asseniblv frou, 2~1 to the present;"," We investigate the different contributions to the growth of stellar mass, and the role of mergers and star formation in the stellar mass assembly from $z\sim1$ to the present." Such an investigation with SAAS is timely iux nuportaut as several recent studies lave started to explore the ealaxy-halo connection aud related iuferences on galaxy evolution (e.g. ZCZOT: Whiteetal20E:Conroy2011:Noisteimetal. 2011b)).," Such an investigation with SAMs is timely and important as several recent studies have started to explore the galaxy-halo connection and related inferences on galaxy evolution (e.g., ZCZ07; \citealt{White07,Conroy09,Wake10,wang09,Behroozi10,Firmani10,Guo10,Leauthaud11,Neistein11}) )." These stu1ος enmplov different plienomenological approaches utiliziie observed statistical properties of galaxies. such as correlation functions. abundances of salaxies and sell lias functions.," These studies employ different phenomenological approaches utilizing observed statistical properties of galaxies, such as correlation functions, abundances of galaxies and stellar mass functions." Iu our study. we particularly compare the SAM predictions to the methodology and results presented in ZCZÜT. to assess the poteutial of such studies to constrain galaxy formation models and to guide future efforts of modeling galaxy. evolution.," In our study, we particularly compare the SAM predictions to the methodology and results presented in ZCZ07, to assess the potential of such studies to constrain galaxy formation models and to guide future efforts of modeling galaxy evolution." We find that the SEE. the fraction of hbarvou mass hat has converted iuto stars in the central eaANION. as πιοΊο of halo mass has a peaked distribtion. with a niaxiual value of ~23% at 5~0 and ~[NU a Dod].," We find that the SFE, the fraction of baryon mass that has converted into stars in the central galaxies, as a function of halo mass has a peaked distribution, with a maximal value of $\sim 23\%$ at $z\sim0$ and $\sim18\%$ at $z\sim1$." " The location of the peak shifts toward lower halo nass with time. reflecting ""halo dowusizimg."," The location of the peak shifts toward lower halo mass with time, reflecting “halo downsizing”." Both SAN uodels produce simular results for the erowtl1 of stellar uass iu central ealaxies from. ~1 to 0 asa πλοίο of he present-day halo mass., Both SAM models produce similar results for the growth of stellar mass in central galaxies from $z\sim1$ to 0 as a function of the present-day halo mass. At both redshifts. he ceutra ealaxy stellar mass mereases rapidly with halο lnass for relatively low-mass halos (below 2«1022/5.FAL.) iux at a lower rate for more massive halos.," At both redshifts, the central galaxy stellar mass increases rapidly with halo mass for relatively low-mass halos (below $\sim 2 \times 10^{12} \Msunh$ ) and at a lower rate for more massive halos." The fraction of stellar nass already in place at 2~1 also varies with fina halo mass: it is about 50% CIOUC) for the \IPA (Durham) model at the owW-lnass cad. increasing with halo mass to about 65% for halos with mass ~ a few «1tWebTALL. and decreases somewhat at the highest halo mass probed.," The fraction of stellar mass already in place at $z\sim1$ also varies with final halo mass: it is about $50\%$ $40\%$ ) for the MPA (Durham) model at the low-mass end, increasing with halo mass to about $65\%$ for halos with mass $\sim$ a few $\times 10^{12} \Msunh$, and decreases somewhat at the highest halo mass probed." The SAAL predictions for the «iffereut coitributions to the stellar mass assembly since | incicate that star formation is more nuportaut in low mass halos (~ a few «10175IAL.) while accreion through merecrs dominates at the high-anass eud (~1057h1M.) where star formation is negligible.," The SAM predictions for the different contributions to the stellar mass assembly since $z\sim1$ indicate that star formation is more important in low mass halos $\sim$ a few $\times 10^{11} \Msunh$ ), while accretion through mergers dominates at the high-mass end $\sim 10^{13} \Msunh$ ), where star formation is negligible." Iu the iutenediate reeine both these processes contrimte., In the intermediate regime both these processes contribute. This trend with iio nass is another manifestation of cowsizine., This trend with halo mass is another manifestation of downsizing. The wo SAMs provide similar results. differing mostly iu heir predictions for the coutribution of snaller ceutral ealaxies inergiue with the main ceutral ealixv.," The two SAMs provide similar results, differing mostly in their predictions for the contribution of smaller central galaxies merging with the main central galaxy." This ikelv arises frou differences in the galaxy formation wescriptions and in the merecr trees of these models., This likely arises from differences in the galaxy formation prescriptions and in the merger trees of these models. We also stidy the predictions of the MPA SAM or the stellar mass erowth since 2—2., We also study the predictions of the MPA SAM for the stellar mass growth since $z \sim 2$. The rends ‘oud are very smaülu to those for :~d. including he presence of the “downsizing” pattern.," The trends found are very similar to those for $z \sim 1$, including the presence of the “downsizing” pattern." As expected. uuch less stellar mass is already iu place iu the mad xogenitors compared to z1 aud the coutribution from ucreiue of smaller ceutral galaxies is considerably arecr.," As expected, much less stellar mass is already in place in the main progenitors compared to $z\sim 1$ and the contribution from merging of smaller central galaxies is considerably larger." Furthermore. he contribution frou. star formation is nuportaut at z] halo masses. even at the hieh-mass cud.," Furthermore, the contribution from star formation is important at all halo masses, even at the high-mass end." Qur study is motivated by ZCZüT who deveop a novel phenomenological approach to study galaxy evolution bv connecting galaxy clustering results a cüffereut epochs through the growth of the hosting inlo lass., Our study is motivated by ZCZ07 who develop a novel phenomenological approach to study galaxy evolution by connecting galaxy clustering results at different epochs through the growth of the hosting halo mass. " Such applications can poteutially provide nuportaut constraints for galaxy formation models as a ""unction of he host halo mass. which is a fundamental parameter in such models."," Such applications can potentially provide important constraints for galaxy formation models as a function of the host halo mass, which is a fundamental parameter in such models." We compare our finding to those X ZCZüT., We compare our finding to those of ZCZ07. We find that the SAMs and ZCZO07. prodiὉ snadar rens for the stellar mass asseniblv in halos. 10Wever. here are siguificaut quantitative differences.," We find that the SAMs and ZCZ07 produce similar trends for the stellar mass assembly in halos, however, there are significant quantitative differences." The SEE of ceutral galaxies as à function of halo mass at bot1 epoclis iu the SAMS and ZCZÜT are qualitatively similar. with he same overall peaked shape aud halo downsizing.," The SFE of central galaxies as a function of halo mass at both epochs in the SAMs and ZCZ07 are qualitatively similar, with the same overall peaked shape and halo downsizing." The nain discrepancy appears at 2~lL where the MPA SAM xedicts a ~5056 higher SFE than ZCZO07., The main discrepancy appears at $z \sim 1$ where the MPA SAM predicts a $\sim 50\%$ higher SFE than ZCZ07. The differences are also apparent when οςntrastiue. or these two approaches. the stellar mass content of iilos at the two epochs as à function of prescut-day halo nass (Fie.," The differences are also apparent when contrasting, for these two approaches, the stellar mass content of halos at the two epochs as a function of present-day halo mass (Fig." 5)., 5). While the overall trends are in qualitative agreement. there are striking differences.," While the overall trends are in qualitative agreement, there are striking differences." Aga1. the most significant difference is that the SAAIs predict a larecr stellar miass content at 2~1 for all halo masses (with a bigecrao discrepancy for loweranass halos).," Again, the most significant difference is that the SAMs predict a larger stellar mass content at $z \sim1$ for all halo masses (with a bigger discrepancy for lower-mass halos)." The results, The results second post-Nowtoniu order iav be needed. (, post-Newtonian order may be needed. ( i) Auy distribution of mass (such as dark matter or gas) within the orbit. even if it is spherically svuuuetric. will generally contribute to the periceuter advance. (,"ii) Any distribution of mass (such as dark matter or gas) within the orbit, even if it is spherically symmetric, will generally contribute to the pericenter advance. (" "ii) Tidal distortions of the stars are likely to occur near the periceuters of the highly ecceutric orbits. leading to additional contributions to the pericenter advance of the foin 30Min)Ray!kat|3627/2etfs)jtl 2), where m. R aud ζω are the mass. radius and “apsidal constant”. or Love number of the star. respectively,","iii) Tidal distortions of the stars are likely to occur near the pericenters of the highly eccentric orbits, leading to additional contributions to the pericenter advance of the form $30\pi (M/m)(R/a)^5 k_2 (1+3e^2/2+e^4/8)/(1-e^2)^5$ , where $m$, $R$ and $k_2$ are the mass, radius and “apsidal constant”, or Love number of the star, respectively." Tidal coutributious could be sienificant for suffücientlv close ancl eccentric orbits., Tidal contributions could be significant for sufficiently close and eccentric orbits. Of course. if a star ects too close to the black hole. it could be tidally disrupted.," Of course, if a star gets too close to the black hole, it could be tidally disrupted." " This possibility sets a lower bound on the orbital period Prinοm)e) 972, sot by veqnivine that the periceuter distance exceed the Roche radius of the star."," This possibility sets a lower bound on the orbital period $P_{\rm min} \sim 2\sqrt{3}\pi (R^3/m)^{1/2}(1-e)^{-3/2}$ , set by requiring that the pericenter distance exceed the Roche radius of the star." This is illustrated by the dotted. curves in Fig. 1.., This is illustrated by the dotted curves in Fig. \ref{fig1}. By contrast. the precessious of the node aud inclination‘ ‘are relatively‘ inmune frou such effects.," By contrast, the precessions of the node and inclination are relatively immune from such effects." " vo ⊀≚∐↖⇁↴∖↴≻↕∐∖↥⋅↕↸⋈↧∐↖↽↴∖↴↖⇁∐⊔⊔↸∖⊓⋅↕↸⊳≼∐∖↴↑↥⋅∏∏↑↕∪∐∪↕≯↕⊔⋪↧↴∖↴↴∖↴↙⋅⋅ ‘ has no effect on these orbit elements,", Any spherically symmetric distribution of mass has no effect on these orbit elements. As long as any tidal. distortion.⋅ of. the star is: quasi-equilibriu:∙∙∙ neelieible⋅⋅ tidal⋅ lag.. the resulting perturbing. of forces. are purely radial.. aud thus lave no effect⋅ ou the node or inclination.," As long as any tidal distortion of the star is quasi-equilibrium with negligible tidal lag, the resulting perturbing forces are purely radial, and thus have no effect on the node or inclination." ⋅⋅⋅ ⊟⋅∪⋯↑∐↸∖⋯↸∖⋜↧↴∖↴↿∐⋅↸∖≺↧∪↥⋅↴⋝↕↑↸∖↕↸∖⊔↸∖↓↑↴∖↴⋜⋯≼↧↑∐∖∐⋅ ≼⊔⋅↕↕⋟↑↴∖↴↕≯∪↥⋅⋜↧∶↴∙⊾↕↖⇁↸∖∐↴∖↴⋜∐⋅∙⊏≺∣∙," From the measured orbit elements and their drifts for a given star, Eq. \ref{tanbeta}) )" ≺⊔⋝∶↴∙⊾↕↖⇁↸∖↴∖↴↑∐∖⋜⊔∶↴⋁↕↸∖ j). oeGopence1lout MEC. assumH ⊽fiona7Q utoano 1&e theorems.," gives the angle $\beta$, independently of any assumption about the no-hair theorems." utisThisPAIN measurement then fixes ! the spin axis of the black hole to lie ou a plane perpendicular to the stars orbital plane that makes an anele ο) relativo to the line of nodes., This measurement then fixes the spin axis of the black hole to lie on a plane perpendicular to the star's orbital plane that makes an angle $\beta$ relative to the line of nodes. The equivalent determination for another stellar orbit fixes another plane: as long as the two planes are not degenerate. their intersection determines the direction of the spin axis. modulo a reflection through the origin.," The equivalent determination for another stellar orbit fixes another plane; as long as the two planes are not degenerate, their intersection determines the direction of the spin axis, modulo a reflection through the origin." This information is then sufficient to determine the angles à aud? for cach star., This information is then sufficient to determine the angles $\alpha$ and $\beta$ for each star. Then. frou the πιος deteriuued. for. each star. toecther with. the orbit. clemenuts. one can solve for. J aud .Qo.," Then, from the magnitude determined for each star, together with the orbit elements, one can solve for $J$ and $Q_2$." Iu practice. of course. the analysis of the astrometric data will be carried out im a nore sophisticated. if less transparcut manner.," In practice, of course, the analysis of the astrometric data will be carried out in a more sophisticated, if less transparent manner." Using data from all detected stars. one carries out a inulti»paranieter least-squares fit. standard iu solu-svsteii celestial iuechiues. to στοπιο their orbit clements.," Using data from all detected stars, one carries out a multi-parameter least-squares fit, standard in solar-system celestial mechanics, to determine their orbit elements." Their motions would be based on Eq. (1)), Their motions would be based on Eq. \ref{eom}) ) but with AY. J aud Q» treated as parameters to be fit along with the orbit elements of each star.," but with $M$, ${\bf J}$ and $Q_2$ treated as parameters to be fit along with the orbit elements of each star." If necessary. the model cau be extended to include effects of an additional matter distribution. tidal effects. aud so on.," If necessary, the model can be extended to include effects of an additional matter distribution, tidal effects, and so on." " We lave shown that a class of stars orbiting a rotating central black hole iu our galaxy in short period. high eccentricity orbits. will experience precessious of their orbital planes induced by both fune drageiug and the quadrupolar eravity of the hole. at levels that could be as large as 10 parcseconds per vear,"," We have shown that a class of stars orbiting a rotating central black hole in our galaxy in short period, high eccentricity orbits, will experience precessions of their orbital planes induced by both frame dragging and the quadrupolar gravity of the hole, at levels that could be as large as 10 $\mu$ arcseconds per year." Observatious of the orbits of at least two such stars can im principle lead. to ⋜↧≼∐∖↑↸∖↥⋅∐∐∐⋜↧⊓∪∐∪↕↑↕∐∖⋜⋯∶↴∙∏↕⋜∐⋅⋯∪∐∐∖∐⊓∐⊔↖↽↸∖↸⊳↑∪↥⋅⋅⋅ : . J and quadrupole moment Qo: of: the black hole. and could provide a test of the no-hair theorenis eeucral ⋅⋅relativity.," Observations of the orbits of at least two such stars can in principle lead to a determination of the angular momentum vector ${\bf J}$ and quadrupole moment $Q_2$ of the black hole, and could provide a test of the no-hair theorems of general relativity." " with Alternative possibilities for no-haix tests involve ↑↕∐∐∐∶↴⋁↕⊔↸∖⋜↧↴∖↴↿∐⋅↸∖⋯↸∖∐↑↴∖↴∪↕≯↻∏↕↴∖↴⋜∐⋅↴∖↴∪↥⋅↴⋝↕↑↕∐∶↴⋁↴⋝↕⋜∪↘↽≓ ∐∪↕↸∖↸⊳∪∐∏≻⋜∐∐∪↕↴∖↴∩↖↸∖⊼∙∖↽↕↘∪↻↸∖∐↘↽⋯⊥∩∩≝⊔∙∙∶↴∙⊾↥⋅⋜↧↖⇁↕↑⋜↧↑↕∪∐⋜↧↕≓. -↽⋅⋅↽ ⋅⋅wave nmnieasurements of compact objects spiralling iuto massive black holes (Ryan1997:Clanipedakis or detection of∙ no-hair↓∙↻⊔ quasi-nornial ""ringdown eravitational radiation of perturbed black holes (Drever.etal.2001:Berti.etal."," Alternative possibilities for no-hair tests involve timing measurements of pulsars orbiting black-hole companions \citep{kopeikin}, gravitational-wave measurements of compact objects spiralling into massive black holes \citep{ryan,glampedakis,hughes}, or detection of quasi-normal “ringdown” gravitational radiation of perturbed black holes \citep{dreyer,bcw}." 2006).. Detecting such stars so close to the black hole. and carving out infrared astrometry to 10 pavesecond accuracy will be a challenge.," Detecting such stars so close to the black hole, and carrying out infrared astrometry to $10 \, \mu$ arcsecond accuracy will be a challenge." However. if this challenge can be met with future improved adaptive. optics: svstenis currently under studs. such as CRAVITY (Eisenhaueretal.2008).. it could lead to a powerful test of the black-hole paracdigi.," However, if this challenge can be met with future improved adaptive optics systems currently under study, such as GRAVITY \citep{eisenhauer}, it could lead to a powerful test of the black-hole paradigm." Iu future work. we plan to study in detailsuch colplicating effects as secoud-post-Newtoniau (2PN) corrections to the Sclivarzsclüld part of the pericenter advance. tidal effects; effects of nuuseen nnss distributions within the observed stellar orbits. and lightD deflection and Shapiro," In future work, we plan to study in detailsuch complicating effects as second-post-Newtonian (2PN) corrections to the Schwarzschild part of the pericenter advance, tidal effects, effects of unseen mass distributions within the observed stellar orbits, and light deflection and Shapiro" Iu future work. we plan to study in detailsuch colplicating effects as secoud-post-Newtoniau (2PN) corrections to the Sclivarzsclüld part of the pericenter advance. tidal effects; effects of nuuseen nnss distributions within the observed stellar orbits. and lightD deflection and Shapiro!," In future work, we plan to study in detailsuch complicating effects as second-post-Newtonian (2PN) corrections to the Schwarzschild part of the pericenter advance, tidal effects, effects of unseen mass distributions within the observed stellar orbits, and light deflection and Shapiro" "Now. [sin(ler.|?0)]l. and it will attain its maximum for some 6. so Note that this has no explicit dependence on c;. but can have a dependence on ci if e, depends on c;.","Now, $|\sin\left(At_{\mathrm{cross}}+\beta-\theta\right)|\le 1$, and it will attain its maximum for some $\theta$, so Note that this has no explicit dependence on $e_{\mathrm{f}}$, but can have a dependence on $e_{\mathrm{f}}$ if $e_{\mathrm{p}}$ depends on $e_{\mathrm{f}}$." " In the remainder of this paper. unless otherwise stated. we assume the orbits are initially circular: this means that e;=¢),."," In the remainder of this paper, unless otherwise stated, we assume the orbits are initially circular; this means that $e_{\mathrm{f}}=e_{\mathrm{p}}$." Then. for an internal perturber. we have while for an external perturber. we have Orbit crossing begins more quickly if the perturbing planet is more massive or eccentric. and the time-scale is a strong function of planetesimal semi-major axis.," Then, for an internal perturber, we have while for an external perturber, we have Orbit crossing begins more quickly if the perturbing planet is more massive or eccentric, and the time-scale is a strong function of planetesimal semi-major axis." Equation (16)) is in good agreement with equation (14) of ?.. which was derived as an empirical law based on a slightly moditied secular theory and N-body simulations. for test particles on circumprimary orbits in a binary system (i.e.. external. very massive perturber).," Equation \ref{eq:tcrossext}) ) is in good agreement with equation (14) of \cite{2006Icar..183..193T}, which was derived as an empirical law based on a slightly modified secular theory and N-body simulations, for test particles on circumprimary orbits in a binary system (i.e., external very massive perturber)." The chief difference between their result and ours is for high eccentricity., The chief difference between their result and ours is for high eccentricity. Now that we have established the time-scale on which orbits cross. We proceed to eXamine the relative velocities of planetesimals undergoing collisions.," Now that we have established the time-scale on which orbits cross, we proceed to examine the relative velocities of planetesimals undergoing collisions." We shall examine how the distribution of relative velocities evolves with time., We shall examine how the distribution of relative velocities evolves with time. For planetesimals with randomised. uniformly distributed apsides. we might expect the mean relative velocity in a collision to be given by wherec is a constant of orderunity~.," For planetesimals with randomised, uniformly distributed apsides, we might expect the mean relative velocity in a collision to be given by where$c$ is a constant of order." . The value of c depends on the specitic definition of relative velocity being used. and the underlying eccentricity distribution (see 2)): in our case we wish to know the mean velocity of a planetesimal relative o others in the swarm. for which ὁ=\/5/4 when the dlanetesimals” eccentricity follows a Rayleigh distribution. which arises from the mutual gravitational scattering of planetesimals (e...2).," The value of $c$ depends on the specific definition of relative velocity being used, and the underlying eccentricity distribution (see \citealt{1993prpl.conf.1061L}) ); in our case we wish to know the mean velocity of a planetesimal relative to others in the swarm, for which $c=\sqrt{5/4}$ when the planetesimals' eccentricity follows a Rayleigh distribution, which arises from the mutual gravitational scattering of planetesimals \citep[e.g.,][]{1992Icar...96..107I}." However. the eccentricity distribution arising from a dlanet’s secular perturbations cannot be assumed to be Rayleigh. because the physical process exciting the eccentricities is very different (long-range secular perturbations vs. mutual gravitational scattering).," However, the eccentricity distribution arising from a planet's secular perturbations cannot be assumed to be Rayleigh, because the physical process exciting the eccentricities is very different (long-range secular perturbations vs. mutual gravitational scattering)." Furthermore. the apsides are constrained by =(zc5m.=p| ix).," Furthermore, the apsides are constrained by $\varpi \in (\varpi_{\mathrm{pl}}-\frac{1}{2}\pi,\varpi_{\mathrm{pl}}+\frac{1}{2}\pi)$ ." This is because. with the orbits initially circular. the complex eccentricity starts at the origin of the complex plane and precesses in a circle around z;.," This is because, with the orbits initially circular, the complex eccentricity starts at the origin of the complex plane and precesses in a circle around $z_{\mathrm{f}}$." Thus it is restricted to the half-plane containing z;., Thus it is restricted to the half-plane containing $z_{\mathrm{f}}$. Finally. Equation ¢17)) only applies locally.whereas in reality a planetesimal on an eccentric orbit can collide with others over a range of semi-major axes (see2.foradiscussion).," Finally, Equation \ref{eq:evkep}) ) only applies locally,whereas in reality a planetesimal on an eccentric orbit can collide with others over a range of semi-major axes \citep[see][ for a discussion]{2003Icar..162...27T}." In this section. we therefore examine the velocity distribution imposed by planetary secular perturbations. beginning with an estimate for the range of semi-major axes over which collisions can occur.," In this section, we therefore examine the velocity distribution imposed by planetary secular perturbations, beginning with an estimate for the range of semi-major axes over which collisions can occur." First. we estimate the maximum radial excursions of planetesimals evolving under secular perturbations.," First, we estimate the maximum radial excursions of planetesimals evolving under secular perturbations." Consider Planetesimal | located at semi-major axis αι. with eccentricity CQ)=Jey)(1. the maximum attainable under the planet's secular perurbations starting from an initially circular orbit.," Consider Planetesimal 1 located at semi-major axis $a_1$, with eccentricity $e_1=\frac{5}{2}a_1e_{\mathrm{pl}}/a_{\mathrm{pl}}$, the maximum attainable under the planet's secular perturbations starting from an initially circular orbit." We wish to find the greatest semi-major axis of an exterior planetesimal. Planetesimal 2. such that Planetesimal 2s orbit can intersect that of Planetesimal |.," We wish to find the greatest semi-major axis of an exterior planetesimal, Planetesimal 2, such that Planetesimal 2's orbit can intersect that of Planetesimal 1." If longitudes of periapse could take any angle. this would occur when Planetesimal | was at apapse and Planetesimal 2 at periapse. with the orbits tangent. and the apsides antialigned.," If longitudes of periapse could take any angle, this would occur when Planetesimal 1 was at apapse and Planetesimal 2 at periapse, with the orbits tangent, and the apsides antialigned." However. the secular solution also imposes a restriction on the longitude of periapse zc. restricting it to the range x0(maπλ.w/2),"However, the secular solution also imposes a restriction on the longitude of periapse $\varpi$, restricting it to the range $\varpi \in \left(\varpi_{\mathrm{pl}}-\pi/2, \varpi_{\mathrm{pl}}+\pi/2 \right)$." Because of this. the maximum semi-major axis for Planetesimal 2 must come when Planetesimal 2's orbit is at its lowest eccentricity. Le. c».=0.," Because of this, the maximum semi-major axis for Planetesimal 2 must come when Planetesimal 2's orbit is at its lowest eccentricity, i.e., $e_2=0$." " Denoting the difference between the semi-major axes of the orbits by Ad. we find. to lowest order in c, and a. that the maximum separation of intersecting orbits is which is simply the maximum radial excursion of Planetesimal |."," Denoting the difference between the semi-major axes of the orbits by $\Delta a$, we find, to lowest order in $e_{\mathrm{pl}}$ and $\alpha$, that the maximum separation of intersecting orbits is which is simply the maximum radial excursion of Planetesimal 1." We now numerically calculate the distribution of relative velocities which a planetesimal at αι experiences. as a function of time. assuming that all the planetesimals evolve deterministically under the Laplace-Lagrange secular solution described in refsec:dynamics.. starting on initially eireular orbits.," We now numerically calculate the distribution of relative velocities which a planetesimal at $a_1$ experiences, as a function of time, assuming that all the planetesimals evolve deterministically under the Laplace–Lagrange secular solution described in \\ref{sec:dynamics}, , starting on initially circular orbits." For interactions with planetesimals at different semi-major axes. the relative velocity is calculated using formulae in ?..," For interactions with planetesimals at different semi-major axes, the relative velocity is calculated using formulae in \cite{1998Icar..132..196W}. ." Note, Note -The radio source VLSS J1431.8+1331 is located in the cluster MaxBCG J217.958694-13.53470 (z= 0.16) and associated with the central cD galaxy.,-The radio source VLSS J1431.8+1331 is located in the cluster MaxBCG J217.95869+13.53470 $z=0.16$ ) and associated with the central cD galaxy. A second radio source is located 175 kpc to the east., A second radio source is located 175 kpc to the east. This source is connected by a faint radio bridge to the central radio source., This source is connected by a faint radio bridge to the central radio source. This source probably traces an old bubble of radio plasma from a previous episode of AGN activity of the central source., This source probably traces an old bubble of radio plasma from a previous episode of AGN activity of the central source. " The spectral curvature of this source is large, indicating the radio plasma is old, which is consistent with the above scenario."," The spectral curvature of this source is large, indicating the radio plasma is old, which is consistent with the above scenario." " -VLSS J1133.7+2324 is an elongated filamentary steep spectrum source, the nature of the source is unclear."," -VLSS J1133.7+2324 is an elongated filamentary steep spectrum source, the nature of the source is unclear." It might be a radio relic located in a galaxy cluster at z~0.6., It might be a radio relic located in a galaxy cluster at $z \sim 0.6$. " -The relic in Abell 2048 and the source 24P73 are both classified as radio phoenices, which consist of compressed fossil radio plasma from AGNs."," -The relic in Abell 2048 and the source 24P73 are both classified as radio phoenices, which consist of compressed fossil radio plasma from AGNs." " We detect several galaxies close to 24P73, probably belonging to the cluster hosting the radio phoenix."," We detect several galaxies close to 24P73, probably belonging to the cluster hosting the radio phoenix." -VLSS J0004.9—3457 is a diffuse radio source with emission surrounding the central elliptical galaxy of a small cluster or galaxy group., -VLSS $-$ 3457 is a diffuse radio source with emission surrounding the central elliptical galaxy of a small cluster or galaxy group. The source could be a radio mini-halo (or core-halo system)., The source could be a radio mini-halo (or core-halo system). An arc-like structure is located to the east of the source which has a high polarization fraction of about at 1.4 GHz indicative of ordered magnetic fields., An arc-like structure is located to the east of the source which has a high polarization fraction of about at 1.4 GHz indicative of ordered magnetic fields. " This is probably a relic, where either particles are accelerated by the DSA mechanism or radio plasma from the central AGN is compressed."," This is probably a relic, where either particles are accelerated by the DSA mechanism or radio plasma from the central AGN is compressed." " -The origin of VLSS J0915.7--2511, a diffuse radio source in MaxBCG J138.91895+25.19876, is somewhat unclear."," -The origin of VLSS J0915.7+2511, a diffuse radio source in MaxBCG J138.91895+25.19876, is somewhat unclear." The source is most likely an AGN relic or radio phoenix., The source is most likely an AGN relic or radio phoenix. We also presented optical images around five other diffuse radio source from the sample., We also presented optical images around five other diffuse radio source from the sample. " For these sources, we could not find optical counterparts in POSS-II and 2MASS images."," For these sources, we could not find optical counterparts in POSS-II and 2MASS images." We detected candidate counterparts for all of these sources with redshifts in the range 0.5. that is matched in NUV—r colour in addition to stellar mass and redshift.," We have constructed a second control sample, $C_{M*,NUV-r}$, that is matched in $NUV-r$ colour in addition to stellar mass and redshift." For each galaxy with an HI measurement. we search within a distance of 0.18 dex in log M.. 0.31 mag in NUV—r colour and 0.005 in z for the nearest neighbor in the stellar mass-redshift-colour plane.," For each galaxy with an HI measurement, we search within a distance of 0.18 dex in $\log $ $_*$, 0.31 mag in $NUV-r$ colour and 0.005 in $z$ for the nearest neighbor in the stellar mass-redshift-colour plane." Note that the chosen tolerances in log and NUV —rcolour are comparable to the errors in these quantities., Note that the chosen tolerances in $\log $ $_*$ and $NUV-r$ colour are comparable to the errors in these quantities. We repeat the above process again. with the log distance increased to 0.25 and the (NUV—r) distance increased to 0.43 mag.," We repeat the above process again, with the log $_*$ distance increased to 0.25 and the $NUV-r$ ) distance increased to 0.43 mag." In the end each HI galaxy has 2 control galaxies matched in stellar mass and (NUV—r) colour., In the end each HI galaxy has 2 control galaxies matched in stellar mass and $NUV-r$ ) colour. The νονε; control sample (examples are shown in the right-top panel of Figure 23) allows us to investigate the extent to which the NUV—r colour can serve as a “proxy” for the HI content of a galaxy.," The $C_{M*,NUV-r}$ control sample (examples are shown in the right-top panel of Figure \ref{fig:gallery}) ) allows us to investigate the extent to which the $NUV-r$ colour can serve as a “proxy” for the HI content of a galaxy." " Note that this is the underlying assumption of many photometric gas fraction techniques — if HI fraction and colour are exactly equivalent. then the HI sample and the Ον, control sample should have identical properties."," Note that this is the underlying assumption of many photometric gas fraction techniques – if HI fraction and colour are exactly equivalent, then the HI sample and the $C_{M*,NUV-r}$ control sample should have identical properties." Figure + presents histograms of the properties of these two samples., Figure \ref{fig:quality_lgm_nuvr} presents histograms of the properties of these two samples. As can be seen. there is no longer any significant ditference in concentration index between the sample with HI masses and the Cis; control sample. but the size ditferences do persist.," As can be seen, there is no longer any significant difference in concentration index between the sample with HI masses and the $C_{M*,NUV-r}$ control sample, but the size differences do persist." The ditferences in the distribution of local environment parameters and colour gradients decrease significantly. but are still significant.," The differences in the distribution of local environment parameters and colour gradients decrease significantly, but are still significant." " Finally. we have constructed a third. control sample. Cystsae that is matched in half-light radius measured from the SDSS i-band image (As,GM) in addition to stellar mass. ΝΟ—r colour and redshift."," Finally, we have constructed a third control sample, $C_{M*,NUV-r, \mu*}$, that is matched in half-light radius measured from the SDSS $i$ -band image $R_{50}(i)$ ) in addition to stellar mass, $NUV-r$ colour and redshift." For each galaxy with an HI measurement. we search within a distance of 0.3 dex in log M.. 0.52 mag in VUV—-r colour. 1.9 Κρο in AsoG3. and 0.005 in z for the nearest neighbor in the stellar mass-redshift-colour-size plane.," For each galaxy with an HI measurement, we search within a distance of 0.3 dex in $\log $ $_*$, 0.52 mag in $NUV-r$ colour, 1.9 kpc in $R_{50}(i)$, and 0.005 in $z$ for the nearest neighbor in the stellar mass-redshift-colour-size plane." In this case. there is only one control galaxy matehed to each HI galaxy.," In this case, there is only one control galaxy matched to each HI galaxy." " Catinella et al (2010) showed that a HI mass could be most accurately ""predicted"" using a linear combination of NUV—r colour and logd.", Catinella et al (2010) showed that a HI mass could be most accurately “predicted” using a linear combination of $-r$ colour and $\log \mu_*$. Figure 5 shows that very few apparent differences between the HI sample and the the Cysscvpy. control sample now remain.," Figure 5 shows that very few apparent differences between the HI sample and the the $C_{M*,NUV-r,\mu_*}$ control sample now remain." There is no longer any significant ditference in the distributions of local environment parameters., There is no longer any significant difference in the distributions of local environment parameters. " There does appear to be a difference between the distribution of e—i colour gradients. which we will investigate in more detail in the nextsection""."," There does appear to be a difference between the distribution of $g-i$ colour gradients, which we will investigate in more detail in the next." .. In this section. we analyze how the sizes and colour gradients of galaxies of fixed stellar mass depend on atomic gas fraction.," In this section, we analyze how the sizes and colour gradients of galaxies of fixed stellar mass depend on atomic gas fraction." We have generated two different sets of aperture-matched photometry for galaxies with HI measurements and also for the galaxies in our control samples., We have generated two different sets of aperture-matched photometry for galaxies with HI measurements and also for the galaxies in our control samples. The first set of measurements is generated from GALEX FUV and NUV images. and SDSS images in the ie.r.d and z-bands.," The first set of measurements is generated from GALEX FUV and NUV images, and SDSS images in the $u,g,r,i$ and $z$ -bands." Images in the ΕΙΝ 5.9.7.i. and z bands are registered so that they have the same geometry as the ΝΟΥ image. and are then convolved to the same ettective resolution as he NUV image.," Images in the FUV, $u, g, r, i$, and $z$ bands are registered so that they have the same geometry as the NUV image, and are then convolved to the same effective resolution as the NUV image." All neighboring objects are masked and the r- band image is used as the reference for flux measurements in all other bands (see Wangetal.(2009) for details)., All neighboring objects are masked and the $r$ -band image is used as the reference for flux measurements in all other bands (see \citet{wang09} for details). We use this set of shotometric measurements in our analysis of UV/optical colours and colour gradients. and for self-consistent SED fitting using all 7 shotometric bands (FUV.NUY. i.9. rio).," We use this set of photometric measurements in our analysis of UV/optical colours and colour gradients, and for self-consistent SED fitting using all 7 photometric bands (FUV,NUV, $u,g,r,i,z$ )." " The second set of measurements is generated from the SDSS e and i band images. which have significantly higher resolution han the GALEX images (~ |” instead of 5 "")."," The second set of measurements is generated from the SDSS $g$ and $i$ band images, which have significantly higher resolution than the GALEX images $\sim 1$ $''$ instead of 5 $''$ )." The band image is registered to match the geometry of the e band image. and," The $i$ -band image is registered to match the geometry of the $g$ band image, and" The signal-to-noise ratio distribution of pixels shown in Fig.,The signal-to-noise ratio distribution of pixels shown in Fig. 3 has the expected Gaussian shape., \ref{fig:snr} has the expected Gaussian shape. " However, one notices some systematic excess at the negative side."," However, one notices some systematic excess at the negative side." " Nevertheless, the source detection threshold of 5c, estimated above, separates the noise and source dominated pixel domains."," Nevertheless, the source detection threshold of $5\sigma$, estimated above, separates the noise and source dominated pixel domains." 'The list of point sources is presented in Table 2.., The list of point sources is presented in Table \ref{tab:sources}. " We attribute two marginally detected, previously unknown sources to the systematic noise."," We attribute two marginally detected, previously unknown sources to the systematic noise." " IGR. J08135+5655 is not detected in the sky mosaic of the slightly broader energy band 20—60 keV, and the region around IGR. J015324-2612 is affected by systematic noise at the edge of the sky mosaic."," IGR J08135+5655 is not detected in the sky mosaic of the slightly broader energy band $20-60$ keV, and the region around IGR J01532+2612 is affected by systematic noise at the edge of the sky mosaic." " The listof sources in Table 2,, except for two IGR’s mentioned above, was used in the iterative source removal (IROS) procedure that we applied to every ISGRI detector shadowgram (e.g.Krivonosetal.2010a)."," The listof sources in Table \ref{tab:sources}, except for two IGR's mentioned above, was used in the iterative source removal (IROS) procedure that we applied to every ISGRI detector shadowgram \citep[e.g.][]{krietal10a}." ". 'This procedure introduces additional uncertainty to the background model (Appendix Appendix C:)), but allows one to trace source variability."," This procedure introduces additional uncertainty to the background model (Appendix \ref{section:accuracy}) ), but allows one to trace source variability." " For example, the known Be/X-ray binary RX J0440.9+4431 (LS V +44 17) was in a strong outburst during the observations (Krivonosetal. 2011).."," For example, the known Be/X-ray binary RX J0440.9+4431 (LS V +44 17) was in a strong outburst during the observations \citep{atel2828,sst11}. ." Fig., Fig. 4 shows 25—60 keV," \ref{fig:data} shows $25-60$ keV" The duty evele (DC) for variability of a class of objects can be roughly taken to be the fraction of them showing significant variations on particular timescales.,The duty cycle (DC) for variability of a class of objects can be roughly taken to be the fraction of them showing significant variations on particular timescales. Η No denotes the total number of sources observed in a search for STV. and η denotes the number of sources that are found to be variable. then the duty evele. as a per centage (Gupta οἱ 22000b). is defined as We detected STV in Ll out of 12 LDLs. so the DC of Hux variation on STV timescales is 2 per We searched for variations inallofthe V. It 1 and 1 colour indices of cach source.," If $N$ denotes the total number of sources observed in a search for STV and $n$ denotes the number of sources that are found to be variable, then the duty cycle, as a per centage (Gupta et 2009b), is defined as We detected STV in 11 out of 12 LBLs, so the DC of flux variation on STV timescales is $\sim$ 92 per We searched for variations in all of the $-$ V, $-$ R, $-$ I and $-$ I colour indices of each source." In our sample of a dozen blazars we found strong short-term colour variability (STCV) in most of them. using a 0.99. probability definition for the presence of such variations (€c 2.51).," In our sample of a dozen blazars we found strong short-term colour variability (STCV) in most of them, using a $>$ 0.99 probability definition for the presence of such variations $C > 2.57$ )." Dased on our results here. we can categorize the colour variations into three classes: strong STOV: partial SPCY: and non-STC€ or no variation of colour with time.," Based on our results here, we can categorize the colour variations into three classes: strong STCV; partial STCV; and non-STCV, or no variation of colour with time." The sources that we V.find to have strong STOV are AO | 164. WS 014. 4€ 29.45 and 3€ 454.3. as they show significant variations in all the four colour indices.," The sources that we find to have strong STCV are AO $+$ 164, PKS $-$ 014, 4C 29.45 and 3C 454.3, as they show significant variations in all the four colour indices." The ormally non-ST€V. sources during our observations were 3€ 66A. OJ 287. 3C 273 and BL Lac.," The formally non-STCV sources during our observations were 3C 66A, OJ 287, 3C 273 and BL Lac." The remainder of he blazars showed one to three nominally significant colour variations and thus could be fairly said to have exhibited γατα STC€V., The remainder of the blazars showed one to three nominally significant colour variations and thus could be fairly said to have exhibited partial STCV. LIÉ we are conservative and only consider he four blazars with strong STCV then the DC of colour variation on STV timescales is 33 per cent., If we are conservative and only consider the four blazars with strong STCV then the DC of colour variation on STV timescales is $\sim$ 33 per cent. During the period 2008 September to 2009 June we carried out multiband photometric observations of 12. LBLs, During the period 2008 September to 2009 June we carried out multiband photometric observations of 12 LBLs. Comparisons of our observations with carlicr measurements of the same sources indicated. that the blazars: PINS 014. 4€ 29.45 and PINS 0S9 were in relatively mint states: AQ | 164. BL Lac and 3€ 454.3 were »ossiblv. in post-oulburst states: 85 | 714 and 3C 66V were more Likely to be in. pre-outburst. states: while the wo sources PIS | 178 and OJ 287 were in sonic intermediate state during our observing run. and none of hem appeared to be in outburst.," Comparisons of our observations with earlier measurements of the same sources indicated that the blazars: PKS $-$ 014, 4C 29.45 and PKS $-$ 089 were in relatively faint states; AO $+$ 164, BL Lac and 3C 454.3 were possibly in post-outburst states; S5 $+$ 714 and 3C 66A were more likely to be in pre-outburst states; while the two sources PKS $+$ 178 and OJ 287 were in some intermediate state during our observing run, and none of them appeared to be in outburst." We cannot even attempt ο Classify 3€ 273 in this fashion because it never has shown a large amount of optical activity: the observed total AB is a modest ~2 mag between LSST and 2000 (Courvolsier et 11998: Dai et al., We cannot even attempt to classify 3C 273 in this fashion because it never has shown a large amount of optical activity: the observed total $\Delta$ B is a modest $\sim$ 2 mag between 1887 and 2000 (Courvoisier et 1998; Dai et al. 2006b)., 2006b). We observed large [lux variations in all the sources except ὃς 23 during our observing span., We observed large flux variations in all the sources except 3C 273 during our observing span. The substantial flux variations we and others have observed. in these LBLs can be reasonably explained: by nmocels that involve relativistic shocks propagating outward (c.g... Alarscher Gear 1985: Wagner Witzel 1995: Alarseher 1996).," The substantial flux variations we and others have observed in these LBLs can be reasonably explained by models that involve relativistic shocks propagating outward (e.g., Marscher Gear 1985; Wagner Witzel 1995; Marscher 1996)." The larger Hares are expected to be produced. by the emergence. and motion of a new shock triggered by some strong variation in a physical quantity such as velocity. electron density or magnetic field moving into and through the relativistic jet.," The larger flares are expected to be produced by the emergence and motion of a new shock triggered by some strong variation in a physical quantity such as velocity, electron density or magnetic field moving into and through the relativistic jet." Smaller variations may be nicely explained. by turbulence behind. ᾱ- shock propagating down the jet (Marscher et 11992)., Smaller variations may be nicely explained by turbulence behind a shock propagating down the jet (Marscher et 1992). In a minority of blazars. gravitational micro-lensing (e.g... Cropal- Subramanian 1991) might be important.," In a minority of blazars, gravitational micro-lensing (e.g., Gopal-Krishna Subramanian 1991) might be important." The one such case among our sample where micro-lensing may play a role is AO | 164 which is known to have two galaxies (al z—0.524 and z=0.851) along our line-ol-sight to it., The one such case among our sample where micro-lensing may play a role is AO $+$ 164 which is known to have two galaxies (at $z = 0.524$ and $z=0.851$ ) along our line-of-sight to it. The variability of blazars has been extensively studied over the past two decades., The variability of blazars has been extensively studied over the past two decades. Still. to the best of our knowledge. we are reporting the most extensive scarch for optical short term colour variations (S'TC'V). ie. variations in colour with time for time periods corresponding to SLY. in a sample of LBLs.," Still, to the best of our knowledge, we are reporting the most extensive search for optical short term colour variations (STCV), i.e., variations in colour with time for time periods corresponding to STV, in a sample of LBLs." Gu et ((2006) presented monitoring of eight LBLs. seven of which are also in our sample of 12. for about. six months curing 2003 and 2004: their observations were only in the V. It and LI bands for six of their sources. though they did also have B band coverage for two of them.," Gu et (2006) presented monitoring of eight LBLs, seven of which are also in our sample of 12, for about six months during 2003 and 2004; their observations were only in the V, R and I bands for six of their sources, though they did also have B band coverage for two of them." Three phenomena that could. lead. to colour variations with time were cliscussect by Llawkins et ((2002): the effect of the underlving host galaxy: colour changes in accretion disks: ancl colour changes from. micro-lensing anc we now consider cach of these., Three phenomena that could lead to colour variations with time were discussed by Hawkins et (2002): the effect of the underlying host galaxy; colour changes in accretion disks; and colour changes from micro-lensing and we now consider each of these. The cllect of the underlying host ealaxy on colour variations of the source is usually seen in he case of low luminosity AGNs such as Sevfert. galaxies (Mg2 22) where variable seeing would include more or ess of the galaxys light along with that of the Sevfert., The effect of the underlying host galaxy on colour variations of the source is usually seen in the case of low luminosity AGNs such as Seyfert galaxies $_{B} > -22$ ) where variable seeing would include more or less of the galaxy's light along with that of the Seyfert. Since he FSROs are among the most luminous AGNs (Mg< 23). any colour variation in these sources is most unlikely o arise from the underlving host galaxy.," Since the FSRQs are among the most luminous AGNs $_{B} < -23$ ), any colour variation in these sources is most unlikely to arise from the underlying host galaxy." This is true for DL Laes as well. in that the Doppler boosted jet. emission almost invariably swamps the light from the host. galaxy. wereby often. making the determination of redshifts. very illieult. as noted above.," This is true for BL Lacs as well, in that the Doppler boosted jet emission almost invariably swamps the light from the host galaxy, thereby often making the determination of redshifts very difficult, as noted above." The STCY observed in blazar LCs might conceivably come from colour changes arising in the accretion clisc itself. particularly for the FSRQ class. where accretion disc emission may be significant ο... Malkan 1983: Pian et 11999). although the BL Lacs seem to have much weaker disc emission.," The STCV observed in blazar LCs might conceivably come from colour changes arising in the accretion disc itself, particularly for the FSRQ class, where accretion disc emission may be significant (e.g., Malkan 1983; Pian et 1999), although the BL Lacs seem to have much weaker disc emission." The standard model of a geometrically and optically thick accretion disc (e.g. Shakura Sunvaev 1973) vields a negative temperature gradient. i.e. the dise is cooler and. redder with increasing racial distance from the central black hole.," The standard model of a geometrically and optically thick accretion disc (e.g., Shakura Sunyaev 1973) yields a negative temperature gradient, i.e., the disc is cooler and redder with increasing radial distance from the central black hole." Hence any non-linear oscillations of such a cisc lead to temperature. and hence colour. changes (Hawkins ot 22002).," Hence any non-linear oscillations of such a disc lead to temperature, and hence colour, changes (Hawkins et 2002)." Microlensing of radiation from an accretion disc having the expected radial temperature eradient can also produce variations in colour., Microlensing of radiation from an accretion disc having the expected radial temperature gradient can also produce variations in colour. Yonehara et ((1999) carried out numerical simulations of the microlensing of accretion discs by a compact body ancl showed that for an optically thick accretion disk with a radial temperature eracdient colour variations are seen. while for optically thin accretion disces such induced. colour variations are unlikely. to be observable.," Yonehara et (1999) carried out numerical simulations of the microlensing of accretion discs by a compact body and showed that for an optically thick accretion disk with a radial temperature gradient colour variations are seen, while for optically thin accretion discs such induced colour variations are unlikely to be observable." The blazar AO | 164 showed strong STCV during our observing run and is known to have two [oreeround. galaxies at 2=0.524 and z=0.851 (Nilsson ct 11996)., The blazar AO $+$ 164 showed strong STCV during our observing run and is known to have two foreground galaxies at $z = 0.524$ and $z = 0.851$ (Nilsson et 1996). So at least some ofthe strong variations seen in this source could arise from microlensing of dillerent regions within a relativistic jet (e.g. Gopal-INrishna Subramanian 1991).," So at least some of the strong variations seen in this source could arise from microlensing of different regions within a relativistic jet (e.g., Gopal-Krishna Subramanian 1991)." Since there are no microlenses known to be in front, Since there are no microlenses known to be in front (822),2) ietallicitv vardstick leads to a correspoudiug chauge iu the metallicity of all stars.,metallicity yardstick leads to a corresponding change in the metallicity of all stars. " This is iu particular true for stars with z0. since their metallicity is often deteriuued |Fo/II|in a strictly differential aud therefore quite accurate way,"," This is in particular true for stars with $\mathrm{[Fe/H]}\approx 0$, since their metallicity is often determined in a strictly differential and therefore quite accurate way." Alecianctal.(2007). fouud that with the lower ACSOS solu composition they could reproduce the properties of the preauain sequence binary svsteni RS Cha. while it was inipossible to ΠΠ all observational constraints with the higher GN93 abundances.," \citet{algdc:2007} found that with the lower AGS05 solar composition they could reproduce the properties of the pre-main sequence binary system RS Cha, while it was impossible to fulfill all observational constraints with the higher GN93 abundances." Another obvious test was performed by VandenBereal.(2007. VCGOT).. using the CAID morphology of the open cluster. M67. which has a metallicity of |Fo/II|=0.00+0.03 (Randichetal.2006) and a turn-off (TO) age around | Cyr (e.g.Pietriuferuietal.200L).," Another obvious test was performed by \citet[VG07]{vgeef:2007}, using the CMD morphology of the open cluster M67, which has a metallicity of $\mathrm{[Fe/H]}= 0.00\pm0.03$ \citep{rsppp:2006} and a turn-off (TO) age around 4 Gyr \citep[e.g.\ ][]{pietr:04}." . At this age the turn-off mass is sheltly higher than 1AS. and close to the critical mass at which a convective core on the maim-sequence appears due to the dominauce of the CNO-cvele over the pp-chain (Kippeulaliu. 1990)., At this age the turn-off mass is slightly higher than $1\msun$ and close to the critical mass at which a convective core on the main-sequence appears due to the dominance of the CNO-cycle over the pp-chain \citep{kw:90}. . The CAID of M67 (Montgomeryetal.1993:Sandquist2001). shows a clear hook-like structure at the uru-off. indicative of a convective core for the turn-off stars.," The CMD of M67 \citep{mmm67:93,esm67:2004} shows a clear hook-like structure at the turn-off, indicative of a convective core for the turn-off stars." " Since the eficiency of the CNO-cvele is directly xoportioual to the abundance of these elements. the reduced solar aluudances of ACSO5 could possibly result iu a radiative core for stars at the TO. although in the fitting process the chauge iu Iuninositv (at eiven mass. i1uninositv is lower for the ACS05 mixture) aud effective cluperature complicates simple predictions about the ""TO-Anass iud core structure."," Since the efficiency of the CNO-cycle is directly proportional to the abundance of these elements, the reduced solar abundances of AGS05 could possibly result in a radiative core for stars at the TO, although in the fitting process the change in luminosity (at given mass, luminosity is lower for the AGS05 mixture) and effective temperature complicates simple predictions about the TO-mass and core structure." " Tudeed. VGOT. fouud that he TO-hook disappeared for the new abundances. hereby strenethening the case for the GSO9S metallicity scale,"," Indeed, VG07 found that the TO-hook disappeared for the new abundances, thereby strengthening the case for the GS98 metallicity scale." " However, VGOF did uot fail to mention some caveats: Their models were calculated without atomic diffusion taken into account. a physical process that at least for solar models irrespective of the metallicity scale used is esseutial for the best possible agreement with scisuic inferences."," However, VG07 did not fail to mention some caveats: Their models were calculated without atomic diffusion taken into account, a physical process that at least for solar models – irrespective of the metallicity scale used – is essential for the best possible agreement with seismic inferences." They correctly pointed out that diffusion helps to support a convective core at a stellar mass lower than iu models ieuoriug this effect (Michaudetal. 2001). mainly due to the increase of CNO abuudauces in the stellar core by eravitational settling.," They correctly pointed out that diffusion helps to support a convective core at a stellar mass lower than in models ignoring this effect \citep{mrrv:2004}, mainly due to the increase of CNO abundances in the stellar core by gravitational settling." The different ages of M67 aud the Sun. but identical prescut-day abuudances could also imply differeut initial abundances. an effect that should be taken iuto account in careful and precise studies.," The different ages of M67 and the Sun, but identical present-day abundances could also imply different initial abundances, an effect that should be taken into account in careful and precise studies." Apart from these points. one should keep in mind that with the occurrence of a convective core the question about the amount of overshooting arises.," Apart from these points, one should keep in mind that with the occurrence of a convective core the question about the amount of overshooting arises." " Its troatinent. and in particular the value of αν free parameter in its practical implementation. cannot simply be taken for granted. as usually such ""calibration was based on stellar models resting on the higher solar metallicity scale."," Its treatment, and in particular the value of any free parameter in its practical implementation, cannot simply be taken for granted, as usually such “calibration” was based on stellar models resting on the higher solar metallicity scale." Finally. the occurrence of a convective core mav also depend on other aspects and therefore any conclusion concerning the metallicity is valid only nuder the asstuuption that all other iuflueuces are uuder control.," Finally, the occurrence of a convective core may also depend on other aspects and therefore any conclusion concerning the metallicity is valid only under the assumption that all other influences are under control." Given the result bv VOOT aud the open questions raised above. we revisited M67. trving to complete aud extend the pioucering study of WOOT.," Given the result by VG07 and the open questions raised above, we revisited M67, trying to complete and extend the pioneering study of VG07." In 2 we will introduce briefly the stellar evolution code we have used for most of the calculations iu tle preseut work. aud those aspects of the iuput plivsies. besides the solar iietallicity. we will also investigate.," In \ref{s:moddat} we will introduce briefly the stellar evolution code we have used for most of the calculations in the present work, and those aspects of the input physics, besides the solar metallicity, we will also investigate." Iu 3 woe demonstrate that we can recover the results of VGUOT. a fact that is uot relevant in the lisht of the following section.," In \ref{s:fits} we demonstrate that we can recover the results of VG07, a fact that is not irrelevant in the light of the following section." We then present our preferred model. showine that iu this case the CMD morphology of M67 cau be reproduced for both solar abuudance scales.," We then present our preferred model, showing that in this case the CMD morphology of M67 can be reproduced for both solar abundance scales." Iu E we investigate. how other approaches and variations of the input plivsies may also influence the quality of isochroue fits. and also possible systematic differences arising from the use of different stellar evolution codes.," In \ref{s:fitn} we investigate, how other approaches and variations of the input physics may also influence the quality of isochrone fits, and also possible systematic differences arising from the use of different stellar evolution codes." Our conclusions will follow in 5., Our conclusions will follow in \ref{s:conc}. Most of the stellar model caleulatiouns presented iu this paper were done with the GARSTEC (Weiss&Schlatt]2008) program., Most of the stellar model calculations presented in this paper were done with the GARSTEC \citep{wsch:2008} program. Were. we briefly preseut aspects or mnocifications of the code. which are relevaut for this work.," Here, we briefly present aspects or modifications of the code, which are relevant for this work." The standard assumptions and scttings can be found iu the quoted reference., The standard assumptions and settings can be found in the quoted reference. Convective overshooting is treated as a diffusive process according to the approach described by Frevtagetal(1996)., Convective overshooting is treated as a diffusive process according to the approach described by \citet{freyt:96}. .. The exact implementation can be fouud in Πανιοctal.(1997)., The exact implementation can be found in \citet{bloe:97}. .. Based on hwdrodyuauical s«unuulatious. the diffusive constant therein (Do) is asstuned to decay exponentially bevoud the formal Sclovarzschild-border as This is equivalent to exponcutially declining velocities of convective elements.," Based on hydrodynamical simulations, the diffusive constant therein $D_\mathrm{os}$ ) is assumed to decay exponentially beyond the formal Schwarzschild-border as This is equivalent to exponentially declining velocities of convective elements." In (1)) 2 is the radial distance from the Sclavarzschild border and £7p the pressure scale height taken there., In \ref{eqn:ove}) ) $z$ is the radial distance from the Schwarzschild border and $H_P$ the pressure scale height taken there. The constant Dy sets the scale of diffuxive speed. and depends on the convective velocity ey Inside of the couvective border.," The constant $D_0$ sets the scale of diffusive speed, and depends on the convective velocity $v_0$ inside of the convective border." f is a free parameter definine the scale of the overshooting., $f$ is a free parameter defining the scale of the overshooting. It is known that fitting the CMD of vouug open clusters usually leads to an overshooting region extending for about 0.2 Πρ in the classical local prescription., It is known that fitting the CMD of young open clusters usually leads to an overshooting region extending for about 0.2 $H_P$ in the classical local prescription. We have computed some test mmodels for stars between 2 and 6 A. aud found that this overshooting value is well reproduced by the diffusive approach. during the hydrogen core burning phase. witli a value of about f=0.018. a confirmation of previous results by Herwigetal.(1997).," We have computed some test models for stars between 2 and 6 $\msun$ and found that this overshooting value is well reproduced by the diffusive approach, during the hydrogen core burning phase, with a value of about $f=0.018$, a confirmation of previous results by \citet{bloe:97}." . For :iiall convective cores. the amount of overshooting has to be limited.," For small convective cores, the amount of overshooting has to be limited." In the local description this is done. for example. by a uniltiplicative factor. which increases luearly with mass iu the range of 1 to 2AL. (seePictrin-fermietal.2001.foran example)...," In the local description this is done, for example, by a multiplicative factor, which increases linearly with mass in the range of 1 to $2\, M_\odot$ \citep[see][for an example]{pietr:04}." " In our code this is achieved by a geometrical cutoff. where fp in Equation is replaced by where AR, is the thickness of the convective zone."," In our code this is achieved by a geometrical cutoff, where $H_P$ in Equation \ref{eqn:ove} is replaced by where $\Delta R_\mathrm{cz}$ is the thickness of the convective zone." Iu this way. the ecometric cutoff has the advantage that the overshooting region is always linited to a fraction of the extension of the convective region.," In this way, the geometric cutoff has the advantage that the overshooting region is always limited to a fraction of the extension of the convective region." It is our standard limiting procedure for overshooting.,It is our standard limiting procedure for overshooting. A similar cut is used in Venturaetal.(2005. 1905]..," A similar cut is used in \citet{vcs:2005,vzmd:98}." An alternative approach. namely the use of a ramp function for the f parameter. is also applied for some of our calculations.," An alternative approach, namely the use of a ramp function for the $f$ parameter, is also applied for some of our calculations." For masses lower or equal than 1.1M. ," For masses lower or equal than $1.1\, M_\odot$ " slightly toward the zenith and nadir of L1.,slightly toward the zenith and nadir of L1. Figure 13. shows the dependence of detection efficiency i.e.. the fraction of binaries detected on declination for galaxies at the distance of the Virgo cluster.," Figure \ref{fig:f_dec} shows the dependence of detection efficiency — i.e., the fraction of binaries detected — on declination for galaxies at the distance of the Virgo cluster." Note that this dependence on declination will change if the ground-based detectors are located differently., Note that this dependence on declination will change if the ground-based detectors are located differently. In particular. the sensitivitv of detectors to inspirals from (he Virgo cluster improves [or detectors with Iattitudes corresponding to declinations near that of Virgo.," In particular, the sensitivity of detectors to inspirals from the Virgo cluster improves for detectors with lattitudes corresponding to declinations near that of Virgo." Indeed. Livingston and VIRGO. due to the relative proximity of their latitude and the Virgo cluster’s declination. are more optimally placed relative to the Virgo cluster than the HLanlord or GEO detectors.," Indeed, Livingston and VIRGO, due to the relative proximity of their latitude and the Virgo cluster's declination, are more optimally placed relative to the Virgo cluster than the Hanford or GEO detectors." Interestingly. had. Il and II2 been constructed exactly as thev are. but instead. with the present lattitude of the VIRGO detector. the LIGO network would detect about. more NS-NS inspirals (at design sensitivitv) from the Virgo cluster.," Interestingly, had H1 and H2 been constructed exactly as they are, but instead with the present lattitude of the VIRGO detector, the LIGO network would detect about more NS-NS inspirals (at design sensitivity) from the Virgo cluster." Note that the maximum detection efficiency at this distance in Figure 13. occurs [or ealaxies located at the celestial poles., Note that the maximum detection efficiency at this distance in Figure \ref{fig:f_dec} occurs for galaxies located at the celestial poles. This might be surprising since the detectors are most seusilive (o sources at (heir zenith or nadir., This might be surprising since the detectors are most sensitive to sources at their zenith or nadir. The reason for this apparently paracdoxical result is (hat a galaxy. at a declination corresponding to the detector latitude is only at the detectors zenith for a short. fraction of a sidereal day. while the efficieney. [or galaxies ad a celestial pole ave independent of sidereal time.," The reason for this apparently paradoxical result is that a galaxy at a declination corresponding to the detector latitude is only at the detector's zenith for a short fraction of a sidereal day, while the efficiency for galaxies at a celestial pole are independent of sidereal time." " Despite the shorter duty evcle for sources ad the detector zenith or nadir. it is still the case that galaxies at these locations will be seen io greater clistances,"," Despite the shorter duty cycle for sources at the detector zenith or nadir, it is still the case that galaxies at these locations will be seen to greater distances." Fieure 14. shows the detection efficiency of every galaxy in our catalog. plotted as a function of galaxy. distance.," Figure \ref{fig:4_panel} shows the detection efficiency of every galaxy in our catalog, plotted as a function of galaxy distance." The top panel shows the total elliciency lor the complete population of binaries., The top panel shows the total efficiency for the complete population of binaries. Subsequent panels shows the efficiencies for the DII-BII.. NS-DII and NS-NS sub-populations for initial LIGO.," Subsequent panels shows the efficiencies for the BH-BH, NS-BH and NS-NS sub-populations for initial LIGO." Galaxies al a given distance have a range of efficiencies owing to their different declinations., Galaxies at a given distance have a range of efficiencies owing to their different declinations. This may amount to as much as a varialion., This may amount to as much as a variation. Previous studies adopted a detection efliaency for initial LIGO of unity up to distauces of 20 Alpe for NS-NS. 40 Mpc for NS-DII. 100 Mpc for BII-DII. and 46 Mpc for the entire population. ancl zero bevond.," Previous studies adopted a detection efficiency for initial LIGO of unity up to distances of 20 Mpc for NS-NS, 40 Mpc for NS-BH, 100 Mpc for BH-BH, and 46 Mpc for the entire population, and zero beyond." These cut-olfs are shown as vertical dashed lines., These cut-offs are shown as vertical dashed lines. In our more realistic approach one sees non-zero efficiencies to much greater distances., In our more realistic approach one sees non-zero efficiencies to much greater distances. For example binaries are observed with efficiency even at distances of 130 Mpc., For example BH-BH binaries are observed with efficiency even at distances of 130 Mpc. On the other hand. inside (he previously adopted," On the other hand, inside the previously adopted" We have constructed stellar atmosphere models in spherical geometry for the observed stars using the MARCS code and the stellar parameters quoted in Table [6].,We have constructed stellar atmosphere models in spherical geometry for the observed stars using the MARCS code\citep{Gustafsson2008} and the stellar parameters quoted in Table \ref{tab:stellarparams}. In all models we use an [a/Fe] value of +0.4., In all models we use an $\left[\mathrm{\alpha}/\mathrm{Fe}\right]$ value of +0.4. " The MARCS code computes hydrostatic model photospheres under the assumption of LTE (Local Thermodynamic Equilibrium), chemical equilibrium, homogeneity and the conservation of the total flux."," The MARCS code computes hydrostatic model photospheres under the assumption of LTE (Local Thermodynamic Equilibrium), chemical equilibrium, homogeneity and the conservation of the total flux." We used these models and the Uppsala Eqwi code (ver., We used these models and the Uppsala Eqwi code (ver. 7.06) together with our measured equivalent widths (see Sect.[2.3)), 7.06) together with our measured equivalent widths (see Sect. \ref{eqwi}) ) to find two sulphur abundances for every star; one mean value based on the 11045 nm triplet and one based on the [51] 1082 nm line., to find two sulphur abundances for every star; one mean value based on the 1045 nm triplet and one based on the ] 1082 nm line. The observed and synthetic spectra with sulphur abundances determined in the way described can be seen in Fig. B]., The observed and synthetic spectra with sulphur abundances determined in the way described can be seen in Fig. \ref{fig:allspectra}. The synthetic spectra are calculated with the Bsyn code (ver., The synthetic spectra are calculated with the Bsyn code (ver. " 7.09), which is based on the same routines as the MARCS code."," 7.09), which is based on the same routines as the MARCS code." The continuous opacities are taken from the model atmospheres., The continuous opacities are taken from the model atmospheres. " Subsequently the spectra were broadened by convolving with a rad-tan function with a FWHM given in Table [6], in order to fit the data taking into account the macroturbulence of the stellar atmosphere and instrumental broadening."," Subsequently the spectra were broadened by convolving with a rad-tan function with a FWHM given in Table \ref{tab:stellarparams}, in order to fit the data taking into account the macroturbulence of the stellar atmosphere and instrumental broadening." " The atomic data for the line list used in the model calculations are taken from the VALD database (?),, except the data for the triplet and [Si] line which are taken from other sources, see Table Bl."," The atomic data for the line list used in the model calculations are taken from the VALD database \citep{Kupka1999}, except the data for the triplet and ] line which are taken from other sources, see Table \ref{tab:atomicdata}." The i] line is a M1 intercombination transition between the triplet ground state and the first excited singlet state., The ] line is a M1 intercombination transition between the triplet ground state and the first excited singlet state. The 1045 nm triplet is three relatively highly exited transitions in the triplet system., The 1045 nm triplet is three relatively highly exited transitions in the triplet system. " We note that the log(g f)-value of the i] line is debated (??),, and the derived [S/Fe] values would typically be 0.08 dex lower using the older log(gf)-value used in ? (they use log(gf)= —8.617)."," We note that the $\log (gf)$ -value of the ] line is debated \citep{Asplund2009,Caffau2010a}, and the derived $\left[\mathrm{S}/\mathrm{Fe}\right]$ values would typically be 0.08 dex lower using the older $\log (gf)$ -value used in \cite{Caffau2010a} (they use $\log (gf)=-8.617$ )." " The observed stars all have Hipparcos parallaxes, but unfortunately the uncertainties for most of our observed stars are very large, see Table [i]."," The observed stars all have Hipparcos parallaxes, but unfortunately the uncertainties for most of our observed stars are very large, see Table \ref{tab:starinfo}." " This, in combination with the narrow wavelength coverage of CRIRES makes it impossible to determine the stellar parameters based on our observations alone, sowe are forced to use stellar parameters from the literature."," This, in combination with the narrow wavelength coverage of CRIRES makes it impossible to determine the stellar parameters based on our observations alone, sowe are forced to use stellar parameters from the literature." " The stellar parameters were taken from ?,, ?,, and"," The stellar parameters were taken from \citet{Fulbright2003}, , \citet{Gratton2000}, , and" "We compared the results of our models with the blue straggler populations in four galactic globular clusters: NGC 2808, NGC 1851, 5634 and NGC 6093 (M80), see Table 5..","We compared the results of our models with the blue straggler populations in four galactic globular clusters: NGC 2808, NGC 1851, 5634 and NGC 6093 (M80), see Table \ref{tab:clusters}." The latter cluster was also studied by?., The latter cluster was also studied by. . Observations were taken from the HST WFPC2 database by and blue stragglers were selected using the procedure of These clusters were chosen because they all show different indications for multiple populations., Observations were taken from the HST WFPC2 database by and blue stragglers were selected using the procedure of These clusters were chosen because they all show different indications for multiple populations. " In the case of NGC 2808, there is an observed splitting of the main sequence in at least three sequences(?),, which is attributed to the cluster population consisting of distinct sub-populations with a different helium abundance."," In the case of NGC 2808, there is an observed splitting of the main sequence in at least three sequences, which is attributed to the cluster population consisting of distinct sub-populations with a different helium abundance." " It has become common to refer to these as “first generation"" and “second generation"" (or “third generation""), where the ""first generation"" refers to stars with a normal (low) helium abundance and ""second generation"" refers to the helium enriched population that (supposedly) formed later than the “first generation"" out of polluted material."," It has become common to refer to these as “first generation” and “second generation” (or “third generation”), where the “first generation” refers to stars with a normal (low) helium abundance and “second generation” refers to the helium enriched population that (supposedly) formed later than the “first generation” out of polluted material." " For NGC 1851, the sub-giant branch is known to be split in at least two distinct populations(??),, which can be explained if there are two populations with different total CNO abundances but with the same helium abundance."," For NGC 1851, the sub-giant branch is known to be split in at least two distinct populations, which can be explained if there are two populations with different total CNO abundances but with the same helium abundance." " Recently, have presented evidence for a split giant branch in U—J colours."," Recently, have presented evidence for a split giant branch in $U - I$ colours." Their interpretation of this is that there a Helium enhanced population in NGC 1851 (with Y= 0.28) that also has a slightly higher metallicity and they show that this would only show up as a split horizontal branch in V—J colours., Their interpretation of this is that there a Helium enhanced population in NGC 1851 (with $Y = 0.28$ ) that also has a slightly higher metallicity and they show that this would only show up as a split horizontal branch in $V - I$ colours. " Apart from the usual globular cluster abundance anomalies there is no photometric indication for a “second generation"" in NGC 6093 or NGC 5634.", Apart from the usual globular cluster abundance anomalies there is no photometric indication for a “second generation” in NGC 6093 or NGC 5634. The scenario where some blue stragglers are formed through collisions between stars of different helium content should therefore apply only to the case of NGC 2808., The scenario where some blue stragglers are formed through collisions between stars of different helium content should therefore apply only to the case of NGC 2808. " Comparing the photometry from to that of?,, there appears to be a systematic colour shift A(B—V)«0.1 to the blue in the data (before applying reddening corrections)."," Comparing the photometry from to that of, there appears to be a systematic colour shift $\Delta (B-V) \approx 0.1$ to the blue in the data (before applying reddening corrections)." " The origin of this offset is unclear, but unless we correct for it we are unable to properly fit an isochrone to the data."," The origin of this offset is unclear, but unless we correct for it we are unable to properly fit an isochrone to the data." " In practice, we adopted the data as it is available and determined an effective value of E(B—V)=0.07 for our isochrone."," In practice, we adopted the data as it is available and determined an effective value of $E(B-V) = 0.07$ for our isochrone." We use this value when comparing our models to the Piotto data., We use this value when comparing our models to the Piotto data. The reddening for NGC 2808 is somewhat uncertain., The reddening for NGC 2808 is somewhat uncertain. " finds an overall value E(B—V)=0.20+0.02, but notes that extinction maps indicate differential reddening across the cluster."," finds an overall value $E(B-V) = 0.20 \pm 0.02$, but notes that extinction maps indicate differential reddening across the cluster." " Given the offset between the and the photometry and the error bars on the reddening, our effective value E(B—V)=0.07 for the Piotto data appears to be reasonable."," Given the offset between the and the photometry and the error bars on the reddening, our effective value $E(B-V) = 0.07$ for the Piotto data appears to be reasonable." In order to compare our models with observations we calculate the colour and luminosity functions predicted by our models at an age of 12Gyr.," In order to compare our models with observations we calculate the colour and luminosity functions predicted by our models at an age of $12 \mathrm{Gyr}$." The mass spacing of our model grid is not very fine and this results in very clear discrete jumps and gaps in the theoretical colour and luminosity distributions., The mass spacing of our model grid is not very fine and this results in very clear discrete jumps and gaps in the theoretical colour and luminosity distributions. " To produce smoother distributions, we computed evolution sequences for collisions between stars with 31 distinct masses between 0.4 and 0.8 (inclusive)."," To produce smoother distributions, we computed evolution sequences for collisions between stars with $31$ distinct masses between $0.4$ and $0.8$ (inclusive)." For the masses that fall between those in our grid we interpolate between the neighbouring evolution tracks in a similar way to?., For the masses that fall between those in our grid we interpolate between the neighbouring evolution tracks in a similar way to. . In our model sets collisions only happen at discrete time intervals., In our model sets collisions only happen at discrete time intervals. " In reality, collisions may happen at any time and for our simulated population we should generate collision models at intermediate times."," In reality, collisions may happen at any time and for our simulated population we should generate collision models at intermediate times." We account for this by selecting for each evolution sequence the portion of the evolution track that falls within an age range of 12Gyr+500 Myr.," We account for this by selecting for each evolution sequence the portion of the evolution track that falls within an age range of $12\,\mathrm{Gyr} \pm 500\,\mathrm{Myr}$ ." " Every point along the evolution track is then assigned a weight weightW; At; dm O(n) PC, Mg, con). where At; is the amount of time spent in the vicinity of the current point, $(m)ο.m'* is the initial mass function of and Ym,M2,feo.) is the collision probability for star 1 and star 2 at the time of collision f,.1, which we take to be constant for simplicity."," Every point along the evolution track is then assigned a weight W_i = t_i (m_1) (m_2) (m_1, m_2, ), where $\Delta t_i$ is the amount of time spent in the vicinity of the current point, $\phi(m) \propto m^{-\alpha}$ is the initial mass function of and $\Psi(m_1, m_2, t_\mathrm{coll})$ is the collision probability for star 1 and star 2 at the time of collision $t_\mathrm{coll}$, which we take to be constant for simplicity." For model sets D and E the relative abundance of the different populations is important., For model sets D and E the relative abundance of the different populations is important. " We have taken all populations to be equally abundant, so that for model set D mixed Y,=0.24 and Yo=0.32 collisions are as likely as collisions between stars with the same helium content."," We have taken all populations to be equally abundant, so that for model set D mixed $Y_0=0.24$ and $Y_0=0.32$ collisions are as likely as collisions between stars with the same helium content." The evolution tracks are then binned in the B—V vs. My plane with the value of each bin being the sum of the weights W; of evolution tracks that pass through it., The evolution tracks are then binned in the $B - V$ vs. $M_\mathrm{V}$ plane with the value of each bin being the sum of the weights $W_i$ of evolution tracks that pass through it. The width of our bins is 0.1 in My and 0.089 in B— V., The width of our bins is $0.1$ in $M_\mathrm{V}$ and $0.089$ in $B-V$ . " To convert between theoretical logg, logL and Τεῃ to observational My and B—V we made use of the spectral library by??."," To convert between theoretical $\log g$, $\log L$ and $T_\mathrm{eff}$ to observational $M_\mathrm{V}$ and $B-V$ we made use of the spectral library by." . The resulting colour-magnitude diagram for Yo=0.24 is shown in Figure 5 along with a Yo=0.24 isochrone., The resulting colour-magnitude diagram for $Y_0 = 0.24$ is shown in Figure \ref{fig:theo_cmd} along with a $Y_0 = 0.24$ isochrone. There are some gaps in the shading in the Hertzsprung gap between the main sequence and the giant branch where our binning method misses the stars as the evolve quickly through this region., There are some gaps in the shading in the Hertzsprung gap between the main sequence and the giant branch where our binning method misses the stars as the evolve quickly through this region. Because the time spent in this region of the colour-magnitudediagramis, Because the time spent in this region of the colour-magnitudediagramis "of Seibertetal.(2005a) and a clear bimodality in galaxy colours is present, see Fig.2textitb.","of \cite{SEI05} and a clear bimodality in galaxy colours is present, see \ref{Fig:Hess}." . While mining the preliminary dataset a few exotic objects of high interest were identified., While mining the preliminary dataset a few exotic objects of high interest were identified. " One such object is a star located at (a,5)= (0327""115.7, 82°15'47"".9)."," One such object is a star located at $(\alpha,~\delta)=$ $(03^{h}27^{m}11^{s}.7$, $82^{\circ}15'47''.9)$." " This star was noted for its blue colours: R = 17.44, I = 17.44, NUV = 187.09, FUV = 187.71, corresponding to an A-type star."," This star was noted for its blue colours: R = $^m$ .44, I = $^m$ .44, NUV = $^m$ .09, FUV = $^m$ .71, corresponding to an A-type star." " The star is located in a relatively high-extinction region: Eg_y = 0.29 (Schlegeletal. 1998)), thus it may be of an even earlier spectral type."," The star is located in a relatively high-extinction region: $_{B-V}$ = $^m$ .29 \citealt{SCH98}) ), thus it may be of an even earlier spectral type." Comparing the star coordinates from the NCCS with those of DSS showed that the star is a high-proper motion object., Comparing the star coordinates from the NCCS with those of DSS showed that the star is a high-proper motion object. Fig.3 shows images of the star from different epochs., \ref{Fig:PPM} shows images of the star from different epochs. " We compared the NCCS coordinates of the star with those measured on historical οος surveys and estimated its proper motion to be (Aa, Ad) = (+14+8, -5646) mas/yr, consistent with the estimates from NOMAD (Zachariasetal. 2004)): (Aa, Δδ) = (1-94-Ε22, -60+1) mas/yr."," We compared the NCCS coordinates of the star with those measured on historical photographic surveys and estimated its proper motion to be $\Delta\alpha$ , $\Delta\delta$ ) = $\pm$ 8, $\pm$ 6) mas/yr, consistent with the estimates from NOMAD \citealt{ZAC04}) ): $\Delta\alpha$, $\Delta\delta$ ) = $\pm$ 22, $\pm$ 1) mas/yr." The star is too faint to be included in the PPM and UCAC catalogs., The star is too faint to be included in the PPM and UCAC catalogs. " From its colour, distance, extinction and general astrophysical considerations we conclude tentatively that this star is probably a white dwarf located S;200 pc from the Sun."," From its colour, distance, extinction and general astrophysical considerations we conclude tentatively that this star is probably a white dwarf located $\lesssim200$ pc from the Sun." For a final determination of its nature spectroscopic data is required., For a final determination of its nature spectroscopic data is required. Another example of exotic objects to be mined from the NCCS is QSOs and AGNs., Another example of exotic objects to be mined from the NCCS is QSOs and AGNs. " We downloaded the entire Véron-Cetty&Véron(2010) catalog of quasars and AGN in the survey area, and one of the objects (out of 60) was found in the selected area."," We downloaded the entire \cite{VER10} catalog of quasars and AGN in the survey area, and one of the objects (out of 60) was found in the selected area." " The object is located at (a,5)= (05367 075.2, 82?23'14"".5), which is a region of low galactic extinction: Eg_y = 0.06 (Schlegeletal. 1998)), and it is relatively bright: R = 15”.12, I = 14”.71, NUV = 18.64, FUV = 19.42."," The object is located at $(\alpha,~\delta)=$ $(05^{h}36^{m}07^{s}.2$ , $82^{\circ}23'14''.5)$, which is a region of low galactic extinction: $_{B-V}$ = $^m$ .06 \citealt{SCH98}) ), and it is relatively bright: R = $^m$ .12, I = $^m$ .71, NUV = $^m$ .64, FUV = $^m$ .42." The object was confirmed spectroscopically as an AGN at a redshift z = 0.05 (Xuetal. 2001))., The object was confirmed spectroscopically as an AGN at a redshift z = 0.05 \citealt{XU01}) ). The object was identified as an extended source by NCCS pipeline., The object was identified as an extended source by NCCS pipeline. 'To demonstrate our capability to distinguish between AGNs and hot stellar objects we simulated colour-colour diagrams., To demonstrate our capability to distinguish between AGNs and hot stellar objects we simulated colour-colour diagrams. AGN colours were simulated using the modified composite quasar spectrum from VandenBerketal.(2001).., AGN colours were simulated using the modified composite quasar spectrum from \cite{VAN01}. . " Stellar colours were simulated using theAtlas,, which is an extension of Gunn&Stryker(1983) optical stellar spectra atlas, the and the (Bohlin2003)) atlas, which is used for the calibration of the HST instruments."," Stellar colours were simulated using the, which is an extension of \cite{GUN83} optical stellar spectra atlas, the and the \citealt{BOH03}) ) atlas, which is used for the calibration of the HST instruments." These three atlases provide a sample of ~ 250 stellar spectra encompassing all spectral types and luminosity classes from super-giants to brown dwarfs and covering also a wide range of metallicity., These three atlases provide a sample of $\sim$ 250 stellar spectra encompassing all spectral types and luminosity classes from super-giants to brown dwarfs and covering also a wide range of metallicity. " The AGN spectrum was redshifted from restframe to z<3 and corected for the absorption by Lyman systems (Ly-a forest, Lyman limit and damped a systems) using the transmission function calculated from Mgller&Jakobsen1990.."," The AGN spectrum was redshifted from restframe to $\leq$ 3 and corected for the absorption by Lyman systems $\alpha$ forest, Lyman limit and damped $\alpha$ systems) using the transmission function calculated from \citealt{MOL90}." " AGN and stellar spectra were convolved with the response functions of the FUV, NUV, g, R and I filters to derive object flux."," AGN and stellar spectra were convolved with the response functions of the FUV, NUV, g', R and I filters to derive object flux." The magnitudes were calculated relative to Vega., The magnitudes were calculated relative to Vega. " We conclude, that optical colours alone do not provide a good AGN-stellar separation."," We conclude, that optical colours alone do not provide a good AGN-stellar separation." " The use of NUV-based and FUV-based colours provides an ideal separation for all the redshifts 0500py and p>pij. respectively. in units of its corresponding value at the beginning ol the simulation at 2=10. that is metal-enriched (to various levels with Z«aZj;e.4, with a=(1.0.3.0.1.0.02)."," Figures \ref{fig:v10}- \ref{fig:v300}) ) show the evolution of the amount of mass at $\rho > 500\rho_b$ and $\rho > \rho_{vir}$ respectively, in units of its corresponding value at the beginning of the simulation at $z=10$, that is metal-enriched to various levels with $Z<\alpha Z_{IGM}$ with $\alpha=(1, 0.3, 0.1, 0.03)$." " Figures (3-6)) show cases wilh V;=(10.30.100.300) km/s. From Figure (3)) with V;= IOkm/s we see that for Mj,=10M. only 5% of the gas is contaminated to Z>0.03Z464; lor p>pu. and lor a 101M. halo there is practically no gas with Z>0.02Z,654, in that density range alter about. 11 dynamic time (by 2~6)."," Figures \ref{fig:v10}- \ref{fig:v300}) ) show cases with $V_s = (10,30,100,300)$ km/s. From Figure \ref{fig:v10}) ) with $V_s=10$ km/s we see that for $M_H = 10^6 M_{\odot}$ only $~5\%$ of the gas is contaminated to $Z \ge 0.03 Z_{IGM}$ for $\rho \ge \rho_{vir}$, and for a $10^7M_{\odot}$ halo there is practically no gas with $Z\ge 0.03 Z_{IGM}$ in that density range after about 11 dynamic time (by $z\sim 6$ )." " For p>500py. there is no gas with Z larger than 0.03Z;c5; even for the Mj,=LOOM. halo."," For $\rho > 500\rho_b$, there is no gas with $Z$ larger than $0.03 Z_{IGM}$ even for the $M_H = 10^6M_{\odot}$ halo." It is interesting to note that for this velocity the amount of gas al the two ranges of density considered actually increases instead of decreasing., It is interesting to note that for this velocity the amount of gas at the two ranges of density considered actually increases instead of decreasing. This is due to the compression produced on the halo by the eas from the shock., This is due to the compression produced on the halo by the gas from the shock. We also observe (he acoustic oscillations in (he amount of gas due to (his compression. (, We also observe the acoustic oscillations in the amount of gas due to this compression. ( The fact that acoustic oscillations for the ο halo start earlier is just due to the smaller simulation box size.),The fact that acoustic oscillations for the $10^6 M_{\odot}$ halo start earlier is just due to the smaller simulation box size.) " Figure (4)) shows the case V,—30 km/s. Here we see that for p>500p; again there is not gas that gets more metal-rich than Z=0.03Z,63; by z~6.", Figure \ref{fig:v30}) ) shows the case $V_s = 30$ km/s. Here we see that for $\rho > 500\rho_b$ again there is not gas that gets more metal-rich than $Z = 0.03 Z_{IGM}$ by $z\sim 6$. For p>p. only e5% of the gas ends up with Z20.03Z63; lor a 10M... halo.," For $\rho \ge \rho_{vir}$, only $\sim 5\%$ of the gas ends up with $Z \ge 0.03 Z_{IGM}$ for a $10^7 M_{\odot}$ halo." " However. for Mj,=10M... ©5% of the gas mass reaches Z>να”. "," However, for $M_H = 10^6 M_{\odot}$, $\sim 5\%$ of the gas mass reaches $Z \ge 0.1 Z_{IGM}$." For V;=100 and 300 kin/s (Figures 5.. 6)) the stripping of the outer parts of the halo becomes more important and we start to see that the amount of metal-Iree gas for the density ranges considered starts to decrease significantly for two reasons.," For $V_s = 100$ and 300 km/s (Figures \ref{fig:v100}, \ref{fig:v300}) ) the stripping of the outer parts of the halo becomes more important and we start to see that the amount of metal-free gas for the density ranges considered starts to decrease significantly for two reasons." First. the halo is losing a significant amount of its mass and. therefore. its elobal structure is being modified.," First, the halo is losing a significant amount of its mass and, therefore, its global structure is being modified." " So we observe a decrease in the total amount of mass for p>500p, and p>ο.", So we observe a decrease in the total amount of mass for $\rho > 500\rho_b$ and $\rho > \rho_{vir}$. Second. (his stripping put into contact the IGM eas with the innermost part of the halo. moving ihe mixing laver inward and increasing the effieienev of the mixing to higher density regions in the halo.," Second, this stripping put into contact the IGM gas with the innermost part of the halo, moving the mixing layer inward and increasing the efficiency of the mixing to higher density regions in the halo." " For V;—100 km/s. at p>500”, there is not significant mixing but just a small overall reduction of the mass."," For $V_s = 100$ km/s, at $\rho \ge 500 \rho_b$ there is not significant mixing but just a small overall reduction of the mass." " On the other hand. for p>pj, the total decrease of nass starts lo be significant reaching even ~50% [or Mg;=LOPAL.. and the amount of eas purer than 0.027 is only e30% and ~50% of the original counterparts al z=10 or Mj=10M. and Mj=1LOTAL.. respectively."," On the other hand, for $\rho \ge \rho_{vir}$ the total decrease of mass starts to be significant reaching even $\sim 50 \%$ for $M_H=10^6 M_{\odot}$, and the amount of gas purer than $0.03 Z_{IGM}$ is only $\sim30\%$ and $\sim50\%$ of the original counterparts at $z = 10$ for $M_H=10^6 M_{\odot}$ and $M_H=10^7 M_{\odot}$, respectively." " For V;=300 km/s. at p>500p, we observe significant reduction of the overall mas. especially for Mj;=109. where the mass is reduced to ~30% percent of its original value."," For $V_s = 300$ km/s, at $\rho \ge 500 \rho_b$ we observe significant reduction of the overall mas, especially for $M_H = 10^6 M_{\odot}$ where the mass is reduced to $\sim30\%$ percent of its original value." We can see that the mixing itself does not plav a verv signilicant role at these densities. wilh practically no dillerence between the total nass and the mass of gas with Z « 0.03Z;64; lor Mj=10*M...," We can see that the mixing itself does not play a very significant role at these densities, with practically no difference between the total mass and the mass of gas with Z $<$ $\textrm{Z}_{IGM}$ for $M_H = 10^7 M_{\odot}$." The same thing happens, The same thing happens "We find that the following combination of the paralcters fits the observed proper-anotion data reasonably well: Ey=3.6«10H ere, η--1.5«10.fen7. paLS and --50νὰ The model fit is plotted iu Figure l as the solid line.","We find that the following combination of the parameters fits the observed proper-motion data reasonably well: $E_0=3.6\times10^{44} {\rm erg}$ , $n=1.5\times10^{-4}{\rm cm^{-3}}$ , $\theta_j=1.5^\circ$ and $\theta=50^\circ$ The model fit is plotted in Figure 1 as the solid line." The late time behavior approaches he well-known Sedov solution Rox> (see the dashed ine in Fig., The late time behavior approaches the well-known Sedov solution $R\propto t^{2/5}$ (see the dashed line in Fig. 1)., 1). This is expected since the second term ou he left of Eq.(1) becomes dominant at the late time. so ΠΟ=constant.," This is expected since the second term on the left of Eq.(1) becomes dominant at the late time, so $\beta^2 R^3={\rm constant}$." In addition. i—oe when ο.<1.," In addition, $\frac{dR}{dt}\simeq \beta c$ when $\beta {\rm cos}\theta\ll1$." The earlier phase cau be regarded as the transition regine roni the mildly relativistic motion to the non-rcelativistic notion., The earlier phase can be regarded as the transition regime from the mildly relativistic motion to the non-relativistic motion. " By comparison. we also plot the Roxf"" aud RoxG7 cases in Figure 2. which show clear deviations roni the data."," By comparison, we also plot the $R\propto t^{0.5}$ and $R\propto t^{0.3}$ cases in Figure 2, which show clear deviations from the data." The mferred value of the ISM. density. is surprisingly ow., The inferred value of the ISM density is surprisingly low. Such low deusities with »z10on? have beeu inferred around another to microquasars GRS 1915|105 and GRO J1655-10 bv Πω (2002) from the fact that jets move with constaut velocities up to distance >0.01 , Such low densities with $n\la 10^{-3}{\rm cm^{-3}}$ have been inferred around another two microquasars GRS 1915+105 and GRO J1655-40 by Heinz (2002) from the fact that jets move with constant velocities up to distance $\ga0.04$ pc. As argued bv Heinz (2002). this nuplies that either he sources are located im regions occupied by the hot ISAL phase or previous activities of the jets have created evacuatedbubbles around the sources.," As argued by Heinz (2002), this implies that either the sources are located in regions occupied by the hot ISM phase or previous activities of the jets have created evacuated bubbles around the sources." First. we try to fit the N-rav emission of the eastern jet using the forward shock model. the mechanisin believed to be respousible for CRB afterglows.," First, we try to fit the X-ray emission of the eastern jet using the forward shock model, the mechanism believed to be responsible for GRB afterglows." In the standard picture of GRBs. au afterglow is ecnerally believed to be produced by the svuchrotrou radiation or inverse Compton emission of the shock-accelerated clectrous in an ultva-relativistic shock wave expanding into the ambient medium.," In the standard picture of GRBs, an afterglow is generally believed to be produced by the synchrotron radiation or inverse Compton emission of the shock-accelerated electrons in an ultra-relativistic shock wave expanding into the ambient medium." As more and ore ambient matter is swept up. the shock eradually decelerates while the cmiussiou from such a shock fades down.," As more and more ambient matter is swept up, the shock gradually decelerates while the emission from such a shock fades down." The microquasar jet is similar to the GRB remuaut at the time that its Loreutz factor has decreased to 1 3 usually mouths to vears after the burst.," The microquasar jet is similar to the GRB remnant at the time that its Lorentz factor has decreased to $\Gamma\sim 1-3$ , usually months to years after the burst." So. we expect that simular ΟΙΙΟ processes should also occur in the case of the microquasar decelerating jet.," So, we expect that similar emission processes should also occur in the case of the microquasar decelerating jet." " If the distribution of the shock-accelerated electrous takes a power-law foriiu with the nuuber density given by ntsM5.=Weds, foy xy,«563.56 in the map.," Our revised source list now includes 2 confirmed sources (with coordinates given in Table \ref{tab:confirmedsources}) ) as well as 1 other candidate which is $>3.5\,\sigma$ in the map." Although not confirmed. by photometry. Figs.," Although not confirmed by photometry, Figs." 2 and 4 suggest that SNR 3.5 sources have a reasonable chance of being real., \ref{fig:fake} and \ref{fig:boost} suggest that SNR $>3.5$ sources have a reasonable chance of being real. We are able to calculate a best estimate of the flux for each of these objects using the combination of all available information. including the map measurements. photometry measurements and the source count. prior.," We are able to calculate a best estimate of the flux for each of these objects using the combination of all available information, including the map measurements, photometry measurements and the source count prior." To do this we multiply the measured. (assumed: Gaussian). photometry Hus probability. distribution. {σηση). by the calculated posterior. probability for the map flux. (equation. (1))). which we take as the prior distribution [or Si. and we normalise it to have unit integral.," To do this we multiply the measured (assumed Gaussian) photometry flux probability distribution, $P(S_{\mathrm{p}},\sigma_{\mathrm{p}})$, by the calculated posterior probability for the map flux (equation \ref{eqn:pd}) )), which we take as the prior distribution for $S_{\mathrm{p}}$, and we normalise it to have unit integral." For the candidate source. CGSS850.4. we only know the a posteriori. distribution for the map measurement. since we do not have a photometry measurement for this object.," For the candidate source, GSS850.4, we only know the a posteriori distribution for the map measurement, since we do not have a photometry measurement for this object." In Table 2 we give the peak of these new distributions. along with the error bars describing the 68 per cent confidence regions.," In Table \ref{tab:confirmedsources} we give the peak of these new distributions, along with the error bars describing the 68 per cent confidence regions." We now use our new candidate source List. (see Table 2)) to search for close counterparts at other wavelengths in other data sets which overlap with our coverage., We now use our new candidate source list (see Table \ref{tab:confirmedsources}) ) to search for close counterparts at other wavelengths in other data sets which overlap with our coverage. We also perform stacking analyses to see if there is any overlap between the catalogues and maps., We also perform stacking analyses to see if there is any overlap between the catalogues and maps. The 450jn map of this region is of poor quality: the data are shallow (since the sensitivity at 450μι is worse) and inhomogeneous (being more prone to changes in the weather).," The $450\,\mathrm{\mu m}$ map of this region is of poor quality; the data are shallow (since the sensitivity at $450\,\mathrm{\mu m}$ is worse) and inhomogeneous (being more prone to changes in the weather)." We do not detect any of our S5O j/ini sources in the 450yam map. but we present 95 per cent. confidence upper limits to the 450jim flux for cach 850yam detection in ‘Table 2..," We do not detect any of our $850\,\mu$ m sources in the $450\,\mathrm{\mu m}$ map, but we present 95 per cent confidence upper limits to the $450\,\mathrm{\mu m}$ flux for each $850\,\mathrm{\mu m}$ detection in Table \ref{tab:confirmedsources}. ." The 450sim average (or ‘stackerl7) flux density at the 3 850 jrim-detected positions is 10(Ü)mJv.," The $450\,\mathrm{\mu m}$ average (or `stacked') flux density at the 3 $850\,\mathrm{\mu m}$ -detected positions is $10\,(\pm23)\,\mathrm{mJy}$." " Using an NOksec observation encompassing the northeast— part of the GSS. Mivajietal.(2004). have uncovered. about 150 sources down to flux limits of =1.107"" and z2107""Wun7 in the soft 2keV) and hard 10keV) X-ray. bands. respectively."," Using an $80\,\mathrm{ksec}$ observation encompassing the northeast part of the GSS, \citet{Miyaji} have uncovered about 150 sources down to flux limits of $\simeq 1\times 10^{-20}$ and $\simeq 2\times 10^{-20}\,\mathrm{W}\,\mathrm{m^{-2}}$ in the soft $2\,\mathrm{keV}$ ) and hard $10\,\mathrm{keV}$ ) X-ray bands, respectively." Of these detections. 7 lie within our submillimetre map and the X-ray positional errors are typically about 2/3 aresec.," Of these detections, 7 lie within our submillimetre map and the X-ray positional errors are typically about 2–3 arcsec." No X-rav counterparts exist within the anticipated error circle. of 3. and indeed even there are no counterparts within a full beam of any SCUBA source.," No X-ray counterparts exist within the anticipated error circle of 4"", and indeed even there are no counterparts within a full beam of any SCUBA source." However. the stacked. S50μαι flux. from the 7 X-ray positions bing within the submillimetre map region is 2.5(1.1)mJ.," However, the stacked $850\,\mathrm{\mu m}$ flux from the 7 X-ray positions lying within the submillimetre map region is $2.5\,(\pm1.1)\,\mathrm{mJy}$." This corresponds to a OSmy 95 per cent confidence limit ο 1e mean Hux of these sources.," This corresponds to a $0.8\,\mathrm{mJy}$ 95 per cent confidence limit to the mean flux of these sources." ‘These X-ray sources are therefore brighter than Lynian-oeak galaxies at SSOjin (e.g. Chapmanetal.2000))!," These X-ray sources are therefore brighter than Lyman-break galaxies at $850\,\mathrm{\mu m}$ (e.g. \citealt{Chapman2000}) )!" Lf ACGNs do not comprise a large fraction of our sources. this result indicates that the X-ray emission. originates. [roni oocesses. related to star-formation.," If AGNs do not comprise a large fraction of our sources, this result indicates that the X-ray emission originates from processes related to star-formation." This result. illustrates hat this map can. in fact. be used to make statistical remarks about ~1η) sources even though individual detections are hopeless. and shows a path to populating he confusion sea in the submillimetre (see also Borysetal.2004)).," This result illustrates that this map can, in fact, be used to make statistical remarks about $\sim1\,\mathrm{mJy}$ sources even though individual detections are hopeless, and shows a path to populating the confusion sea in the submillimetre (see also \citealt{Borys2004}) )." We have mapped approximately TOaremin? of the Groth Strip at S50yam with SCUBA on the JCMT to a le depth of around 3.5mJy.," We have mapped approximately $70\,\mathrm{arcmin^{2}}$ of the Groth Strip at $850\,\mathrm{\mu m}$ with SCUBA on the JCMT to a $1\,\sigma$ depth of around $3.5\,\mathrm{mJy}$." Using a robust source detection algorithm. we have founcl 1l candidate sources with SNRc3a.," Using a robust source detection algorithm, we have found 11 candidate sources with $\mathrm{SNR}\geq3\,\sigma$." Monte Carlo simulations suggest that most of these will either be spurious or considerably Dux boosted., Monte Carlo simulations suggest that most of these will either be spurious or considerably flux boosted. Follow-up photometry observations have confirmed 2 of them and rejected 3., Follow-up photometry observations have confirmed 2 of them and rejected 3. Based on these follow-up photometry data. we have determined. not surprisingly. that candidate sources in high-noise regions of the map have implausibly high. apparent Huxes at SNR >Φα. and are likely to be spurious false-positive detections.," Based on these follow-up photometry data, we have determined, not surprisingly, that candidate sources in high-noise regions of the map have implausibly high apparent fluxes at SNR $\geq3\,\sigma$, and are likely to be spurious false-positive detections." We reiterate that bright sources detected in a map should wve SNR&3.56 before they have a reasonable chance of being real. and SNRdo before they should be xdieved: with any confidence.," We reiterate that bright sources detected in a map should have $\mathrm{SNR}>3.5\,\sigma$ before they have a reasonable chance of being real, and $\mathrm{SNR}>4\,\sigma$ before they should be believed with any confidence." Our final source list for the GSS contains 2 confirmed SCUBA sources and | further candidate source with SNIU23.50.," Our final source list for the GSS contains 2 confirmed SCUBA sources and 1 further candidate source with $\mathrm{SNR}>3.5\,\sigma$." Using a combination of he unboosted map Lux posterior probability distributions and the photometry measurements (when available). we present best estimates of the flux for these objects.," Using a combination of the unboosted map flux posterior probability distributions and the photometry measurements (when available), we present best estimates of the flux for these objects." We have measured ai mile statistical cletection of low flux (1 1). sources at. X-ray wavelengths hrough a stacking analysis. and it may be that similar comparisons with data at other wavebancds might also be ruitful.," We have measured a mild statistical detection of low flux ${\sim}\,1\,\mathrm{mJy}$ ) sources at X-ray wavelengths through a stacking analysis, and it may be that similar comparisons with data at other wavebands might also be fruitful." We have therefore mace our maps available athttp://cmbr., We have therefore made our maps available at. physics.ubc.ca/groth. Our simple Bayesian method for correcting the cllects of flux boosting should be useful for future surveys such as SLLADES and those carried out with SCUBA-2. as well as for other instruments which provide data in the low SNR near-confusion regime.," Our simple Bayesian method for correcting the effects of flux boosting should be useful for future surveys such as SHADES and those carried out with SCUBA-2, as well as for other instruments which provide data in the low SNR near-confusion regime." " It may also be useful to adapt this method in order to find sources. bv searching for pixels in a map for which the posterior probability for S,>0 isabove some threshold."," It may also be useful to adapt this method in order to find sources, by searching for pixels in a map for which the posterior probability for $S_{p}>0$ isabove some threshold." were initially seen as possible SNR candidates to the 393 euest star due to their small anenlar sizes of 15% aud 17. respectively (Clark&Stepheuson1977:Stephenson&Croen 2002).,"were initially seen as possible SNR candidates to the 393 guest star due to their small angular sizes of $15'$ and $17'$ , respectively \citep{CS77,SG02}." . IToxcever. these remnauts lie = 10 kpe away (Revuoso&\anemn2000:Aharonianetal.2008:Nakamuractal.2009) and such large distances near he Galactic ceuter likely imply considerable interstellar extinction decreasing the chance of an associated visually night euest star.," However, these remnants lie $\simeq$ 10 kpc away \citep{Rey00,Aharonian08,Nak09} and such large distances near the Galactic center likely imply considerable interstellar extinction decreasing the chance of an associated visually bright guest star." The same is true for the apparently very voung SNR O350.1-3.0 whose distance is only —23.1 spe but lies behind au estimated ~ 20 mae of visual extinction (Caensleretal.2008)., The same is true for the apparently very young SNR G350.1-3.0 whose distance is only $\sim$ 3.4 kpc but lies behind an estimated $\simeq$ 20 mag of visual extinction \citep{Gae08}. . Iu 1996 Pfeffexiuaun&Ascheubach(1996). announced heROSAT discovery of the Galactic remnaut RN J1713.7-3916 (G317.3-0.5) iun Scorpius., In 1996 \citet{Pfeffermann96} announced the discovery of the Galactic remnant RX J1713.7-3946 (G347.3-0.5) in Scorpius. The remuaut’s ocation near the SN 393 reported position along with Pfeffermann aud Aschenbach’s estimated remuaut distance of 1.1 kpc aud 2100 vr age led Wanget to suggest it as the likely remmaut of SN 393., The remnant's location near the SN 393 reported position along with Pfeffermann and Aschenbach's estimated remnant distance of $1.1$ kpc and 2100 yr age led \citet{Wang97} to suggest it as the likely remnant of SN 393. Although Stephenson&Creen(2002) and Nickiforov(2010) have areucd for the remmaut’s distance of 6E1 kpe based on possible associations with nearby molecular clouds (Slaneetal.1999) which would rule out its association with SN 393. more recent distance estimates of RN. J17123.7-3916 &nuulv place it between (91.7 kpe. and most recent xpers on RN J17123.7-3916 cite the Waneetal.(1997) xoposed SN 393 connection.," Although \citet{SG02} and \citet{Nick10} have argued for the remnant's distance of $6 \pm1$ kpc based on possible associations with nearby molecular clouds \citep{Slane99} which would rule out its association with SN 393, more recent distance estimates of RX J1713.7-3946 firmly place it between $0.9 - 1.7$ kpc, and most recent papers on RX J1713.7-3946 cite the \citet{Wang97} proposed SN 393 connection." We note here. however. that a distance less than 2 kpc or RN J17123.7-3916 raises problems with the expected superniova maxim apparent brightuess and durations which appear in conflict with the Chinese records.," We note here, however, that a distance less than 2 kpc for RX J1713.7-3946 raises problems with the expected supernova maximum apparent brightness and durations which appear in conflict with the Chinese records." Below we discuss how ucither the Chinese record of the guest star nor a long known but rarely cited European account of a bright star reported about that same vear are consistent with RN J1713.7-3916 as the remuaut of the probable Chinese supernova of 393 AD., Below we discuss how neither the Chinese record of the guest star nor a long known but rarely cited European account of a bright star reported about that same year are consistent with RX J1713.7-3946 as the remnant of the probable Chinese supernova of 393 AD. The remnant RN J1713.7-39016 exhibits several properties suggesting a relatively voung— age. probally loss than a few thousand vears aud thus potentially consistent with a SN event around 393 AD.," The remnant RX J1713.7-3946 exhibits several properties suggesting a relatively young age, probably less than a few thousand years and thus potentially consistent with a SN event around 393 AD." Its N-rav cCluission is that of a featurcless nonthermal continua consistent with a shock velocity of several LOOO Xi s (INovamaetal.1997:Slanect1999:UchivamaeWw 01).," Its X-ray emission is that of a featureless nonthermal continuum consistent with a shock velocity of several 1000 km $^{-1}$ \citep{Koyama97,Slane99,Uch03,Uch07,Fukui03,CC04}." While the shocks velocity is probably high. i is likely less than L500 kia based on a Πατ of the angular displacement of the remmaut’s outer X-ray Cluission over a 6 vear period (Uchivamaetal.2007).," While the shock's velocity is probably high, it is likely less than 4500 km $^{-1}$ based on a limit of the angular displacement of the remnant's outer X-ray emission over a 6 year period \citep{Uch07}." . Ellisonetal.(2010) found velocities ~ 3000 kn s were required in order to model the shock kinematics iu i1 evacuated cavity at an assumed age of 1000 years., \citet{Ellison10} found velocities $\sim$ 3000 km $^{-1}$ were required in order to model the shock kinematics in an evacuated cavity at an assumed age of 1600 years. RX J17T13.7-3016 is also oue of only a few Calactic SNRs which exhibit ganuna-rays with energies up to 100 TeV. Iu this respect it resembles several other voung Galactic SNRs inchiding ROW 86. (SN. 185) and the SN 1006 remnant., RX J1713.7-3946 is also one of only a few Galactic SNRs which exhibit gamma-rays with energies up to 100 TeV. In this respect it resembles several other young Galactic SNRs including RCW 86 (SN 185) and the SN 1006 remnant. Observations show a close correlation between the remmaut’s N-rayv and eauumnua-rav enissions sueeestiue a causal connection between the processes ecucrating both types of emissious (Aliaroniauetal. 2007)., Observations show a close correlation between the remnant's X-ray and gamma-ray emissions suggesting a causal connection between the processes generating both types of emissions \citep{Aharonian07}. . Since high shock velocities are required to generate a significant uouthermal X-ray and σαλαrav flux (seee.g.Zirakashvili&Aharvonian2007).. the presence of aii X-ray svuchrotron cussion aud comcidenut eanmmia-ray endssiou iu RX J17123.7-3916 favor a distance of ~ 1 kpc. which would rule out the age of 20.000.10.000 vr which is based on the much larger distance estimate of G kpe (Slaneetal.1999).," Since high shock velocities are required to generate a significant nonthermal X-ray and gamma-ray flux \citep[see e.g.][]{zirakashvili07}, the presence of an X-ray synchrotron emission and coincident gamma-ray emission in RX J1713.7-3946 favor a distance of $\sim$ 1 kpc, which would rule out the age of 20,000–40,000 yr which is based on the much larger distance estimate of 6 kpc \citep{Slane99}." . The presence of a compact X-ray source ΝΑ JI713.1-3919 at a projected location near the remmuaut’s center with a similar N-rayv derived Nyy column density to the remnants central regious (Cassam-Chenatctal.2001) nuplies it is associated with the remmnaut thereby indicating the remnant is from a core-collapse SN (CCSN)., The presence of a compact X-ray source 1WGA J1713.4-3949 at a projected location near the remnant's center with a similar X-ray derived $N_{H}$ column density to the remnant's central regions \citep{CC04} implies it is associated with the remnant thereby indicating the remnant is from a core-collapse SN (CCSN). The remuant’s 65«55 aneular size and recent distance estimates ~11.5 kpe (Fukuictal.2003:Morieuchietal.2005) when combined with a liegh-velocity shock sugeests a relatively low ambicut ISM deusity (~0.01 cur3) like that expected ina stellar wind driven cavity eenerated by a liel-ass progenitor which exploded as a Type T/Th.c SN (Cassain-Chenalet.al.2001).," The remnant's $65' \times 55'$ angular size and recent distance estimates $\sim 1 - 1.3$ kpc \citep{Fukui03,Moriguchi05} when combined with a high-velocity shock suggests a relatively low ambient ISM density $\sim0.01$ $^{-3}$ ) like that expected in a stellar wind driven cavity generated by a high-mass progenitor which exploded as a Type II/Ib,c SN \citep{CC04}." . Of the curreutly ποσα SNRs located near the Clinese reported position of SN 393. RN J1713.7-3916 would secni a good candidate remumant for the presumed supernova of 393.," Of the currently known SNRs located near the Chinese reported position of SN 393, RX J1713.7-3946 would seem a good candidate remnant for the presumed supernova of 393." It is a relatively voune SNR aud lies within the tail of Scorpius consistent. with the Clincse report about the location of the 393 enest star., It is a relatively young SNR and lies within the tail of Scorpius consistent with the Chinese report about the location of the 393 guest star. Towever. there are difficulties with this SNSNR. connection.," However, there are difficulties with this SN–SNR connection." Below we discuss these difficulties along with a European report of a bright daytime star around 393 AD but which is unlikely to be a sighting of theChinese 393 SN., Below we discuss these difficulties along with a European report of a bright daytime star around 393 AD but which is unlikely to be a sighting of theChinese 393 SN. As shown in Table 1. recent distance estimates for RN J1713.7-3916 range between 0.9—1.7 kpe (Fukietal.Cassiunu-Clenaletal.2001:Moriguchi 2005)) with a concentration of recent values around 1.1.3 kpe.," As shown in Table 1, recent distance estimates for RX J1713.7-3946 range between $0.9 - 1.7$ kpc \citealt{Fukui03,Koo03,Koo04,Aharonian04,CC04,Moriguchi05}) ) with a concentration of recent values around $1 - 1.3$ kpc." This would place au RX J1713.7-3916 supernova closer thau any historie Galactic SN recorded during the past two iülleunia., This would place an RX J1713.7-3946 supernova closer than any historic Galactic SN recorded during the past two millennia. A distance of just Lo1.3 kpe also means that its SN should have been visually bright if a} the optical extinction to it is fairly low. and b) it was not au unusually fait event.," A distance of just $1 - 1.3$ kpc also means that its SN should have been visually bright if: a) the optical extinction to it is fairly low, and b) it was not an unusually faint event." N-rav derived Aq; colin deusities for the remuuauts central N-ray ciuitting regions range from |...8«&107! cii.7 depeuding ou the blackbody: or power law model adopted (Cassan-Chenaietal.2001)., X-ray derived $N_{\rm H}$ column densities for the remnant's central X-ray emitting regions range from $ 4 - 8 \times 10^{21}$ $^{-2}$ depending on the blackbody or power law model adopted \citep{CC04}. . Adopting Ay=Nyfils«QUU ? for a typical eas-to-dust ratio (Bohlinctal.1978:Predehl&Schinitt1995:ΊναMartin 1996).. vields Ay values around 2.2 Lt mae.," Adopting $A_{\rm V} = N_{H}/1.8 \times 10^{21}$ $^{-2}$ for a typical gas-to-dust ratio \citep{Bohlin78,PS95,KM96}, yields $A_{\rm V}$ values around 2.2 – 4.4 mag." Tn the following discussions. we will adopt an Nyy= ? consistent for the Επs contia compact Ντα source ΝΑ J1713.1-3919 modeled by a two-component blackbody (Cassam-Chenaietal. 2001).. which translates to Ay&2.8 or roughly 3 magnitudes of extinction.," In the following discussions, we will adopt an $N_{H} = 5 \times 10^{21}$ $^{-2}$ consistent for the remnant's central compact X-ray source 1WGA J1713.4-3949 modeled by a two-component blackbody \citep{CC04}, , which translates to $A_{\rm V} \simeq 2.8$ or roughly 3 magnitudes of extinction." As shown in Tables 1 and 2. if the RN. J1713.7-3916 SN had an AA of 1? to. 18 inline with the tvpica absolute visual magnitudes for core-collapse SNe II or SNe I.e (Richardsonetal.2002.2006:Droutct 2011). then the RN. J1712.7-3916. supernova shoul," As shown in Tables 1 and 2, if the RX J1713.7-3946 SN had an $M_{\rm V}$ of $-17$ to $-18$ inline with the typical absolute visual magnitudes for core-collapse SNe II or SNe Ib,c \citep{Richardson02,Richardson06,Drout11}, , then the RX J1713.7-3946 supernova should" expected to synchronize to its orbital period on million year timescales.,expected to synchronize to its orbital period on million year timescales. The secondary likely formed by a sub-catastrophic collision on the primary. and subsequently tidally evolved outward (??)..," The secondary likely formed by a sub-catastrophic collision on the primary, and subsequently tidally evolved outward \citep{merl02,durd04}." Because the orbit is quasi-circular it is likely that the secondary is mechanically weaker than the primary (??).. as might be expected if the body formed by the re-accumulation of impact ejecta.," Because the orbit is quasi-circular it is likely that the secondary is mechanically weaker than the primary \citep{marg03s,tayl10icarus}, as might be expected if the body formed by the re-accumulation of impact ejecta." Our mass measurement with uncertainties provides an important new constraint on the composition and internal structure of B-type asteroids., Our mass measurement with uncertainties provides an important new constraint on the composition and internal structure of B-type asteroids. Combined with an IRAS size measurement. the mass yields a bulk density of 1570 + 500 ke .," Combined with an IRAS size measurement, the mass yields a bulk density of 1570 $\pm$ 500 kg $^{-3}$." This density admits an ice-to-rock mass ratio m the range0-80%.. depending on the porosity of the asteroid.," This density admits an ice-to-rock mass ratio in the range, depending on the porosity of the asteroid." Our density determination is significantly lower than previous estimates for the B-type asteroid (2) Pallas. which may be related to different porosities.," Our density determination is significantly lower than previous estimates for the B-type asteroid (2) Pallas, which may be related to different porosities." We thank referee MMerline for insightful comments and F. Selman. C. Lidman. and N. Ageorges at the VLT for assistance with the observations.," We thank referee Merline for insightful comments and F. Selman, C. Lidman, and N. Ageorges at the VLT for assistance with the observations." We are also grateful for the allocation of telescope time for follow-up observations. without which this binary could not have been fully characterized.," We are also grateful for the allocation of telescope time for follow-up observations, without which this binary could not have been fully characterized." PMR was supported by Center of Excellence in. Astrophysics and Associated Technologies (PFB 06). FONDAP 15010003. and Fondecyt grant 11080271.," PMR was supported by Center of Excellence in Astrophysics and Associated Technologies (PFB 06), FONDAP 15010003, and Fondecyt grant 11080271." JLM was supported by NASA Planetary Astronomy grant NNXO07AK68G/NNX09AQ68G., JLM was supported by NASA Planetary Astronomy grant NNX07AK68G/NNX09AQ68G. Subnuüllunetre (subnuu) surveys have uucovered a population of intriusicallv. bhuninous. but highly obscured. ealaxies at high redshift.,"Submillimetre (submm) surveys have uncovered a population of intrinsically luminous, but highly obscured, galaxies at high redshift." " Iowever. even with iustriusic Duminosities of ~107 LL, (e.g.7).. the brightest SAious are still challenging targets for obsery""tional studies."," However, even with instrinsic luminosities of $\sim10^{13}$ $_{\odot}$ \citep[e.g.][]{ivison98}, the brightest SMGs are still challenging targets for observational studies." m the subnuu aud far-IR. where the bulk of their luminosity escapes. the brightest SAGs have obxved fiux deusilos ofonlv l0nunJy at 850444. pealing at ~ 501uuJv at the waveleneths probed byIHoerschel.," In the submm and far-IR, where the bulk of their luminosity escapes, the brightest SMGs have observed flux densities ofonly $\sim10$ mJy at $\mu$ m, peaking at $\sim50$ mJy at the wavelengths probed by." To alleviate this photon starvation. subiuui πιανους often expot eravitational lensing via iassive. forceround ealaxy clusters. thereby cuhancing the apparent briehtuess of SAICs at all waveleneths(c.g.2?)..," To alleviate this photon starvation, submm surveys often exploit gravitational lensing via massive, foreground galaxy clusters, thereby enhancing the apparent brightness of SMGs at all wavelengths \citep[e.g.][]{smail97, chapman02, cowie02}." " Recently. 7?/— exploited the cluster lensing techuiquc using the Large Apes Bolometer Camera (LABOCA3) on the Ίδια Atacama Pathfinder Experineut (APEN) elescope to map the cluster, 01 (.= 4325). and thereby discovered JJ2135.. an SAIC with Ssyryan= LOGuunSy."," Recently, \citet{swinbank10a} exploited the cluster lensing technique using the Large Apex Bolometer Camera \citep[LABOCA --][]{siringo09} on the 12-m Atacama Pathfinder Experiment (APEX) telescope to map the cluster, $-$ 01 $z=0.325$ ), and thereby discovered J2135, an SMG with $S_{\rm 870\mu m} =106$ mJy." Its brishtuess is due to very Heh amplification (bv 32.5c 15) by the foregrouud cluster (siwilatly bright sources may have receutly beeu unearthed by the South Polk Telescope ?))., Its brightness is due to very high amplification (by $32.5\pm4.5$ ) by the foreground cluster (similarly bright sources may have recently been unearthed by the South Pole Telescope – \citealt{vieira10}) ). The ens model for JJ2135 Is well constrained and its redshift (2=2.32590+η 0001. derived frou the detection of CO 210 in a blind search) and iutriusic," The lens model for J2135 is well constrained and its redshift $z=2.3259\pm 0.0001$ , derived from the detection of CO $J$ =1–0 in a blind search) and intrinsic" emitting material.,emitting material. Phe temperature structure in the inner disk can be allectecdl by the release of energy. for example clue to changes in the accretion rate or the inner hole size.," The temperature structure in the inner disk can be affected by the release of energy, for example due to changes in the accretion rate or the inner hole size." Such processes can thus induce near-infrared variability., Such processes can thus induce near-infrared variability. Disk emission becomes stronger at longer wavelengths. i.c. we expect more pronounced. variations in the Ix-band compared with the J-band.," Disk emission becomes stronger at longer wavelengths, i.e. we expect more pronounced variations in the K-band compared with the J-band." Thus. variable disk emission is expected to make the star bluer as it becomes fainter. in contrast to all aforementioned origins of variabilitv.," Thus, variable disk emission is expected to make the star bluer as it becomes fainter, in contrast to all aforementioned origins of variability." [t is difficult to set firm limits on the amplitudes expected For this tvpe of variation., It is difficult to set firm limits on the amplitudes expected for this type of variation. Based on inner disk models provided. by N. Calvet. conclude that J-band variability up to mmag and Jἐν 7.colour changes of a few tenths of a magnitude are conceivable.," Based on inner disk models provided by N. Calvet, \citet{2001AJ....121.3160C} conclude that J-band variability up to mag and $J-K$ colour changes of a few tenths of a magnitude are conceivable." Changes in disk emission may occur on a variety of timescales. ranging from davs to vears.," Changes in disk emission may occur on a variety of timescales, ranging from days to years." The derived lighteurve characteristics for the various suspected sources of variability allow us to constrain the nature of the variations seen in our observing campaign., The derived lightcurve characteristics for the various suspected sources of variability allow us to constrain the nature of the variations seen in our observing campaign. For the three highly variable sources. 22. 3£]19. and 53. U0 Ls clear that cool spots can be excluded as causes of variability. simply because the amplitudes are too Large.," For the three highly variable sources, 2, 19, and 33, it is clear that cool spots can be excluded as causes of variability, simply because the amplitudes are too large." In. all three cases. the amplitude in J-bane is significantly larger than in Ix-band. ie. they are redder when they are fainter. which excludes disk emission as the dominant source of variability.," In all three cases, the amplitude in J-band is significantly larger than in K-band, i.e. they are redder when they are fainter, which excludes disk emission as the dominant source of variability." To decide between the (wo remaining options. hot spots and extinction. we compare the colour variability in /dv with the predictions derived in Sect.," To decide between the two remaining options, hot spots and extinction, we compare the colour variability in $J-K$ with the predictions derived in Sect." 5.2. and 5.3.., \ref{hs} and \ref{ext}. In Fig., In Fig. G6 we provide J vs. JΑ plots for all three objects., \ref{f4} we provide J vs. $J-K$ plots for all three objects. With solid lines we show linear least-square fits to the data., With solid lines we show linear least-square fits to the data. Large symbols indicate the average values for each individual night., Large symbols indicate the average values for each individual night. Dashed/dash-dotted and dotted Lines show for models for hot spots and extinction. respectively. plotted with arbitrary olfsets for clarity.," Dashed/dash-dotted and dotted lines show for models for hot spots and extinction, respectively, plotted with arbitrary offsets for clarity." s. explained in Sect. 2..," As explained in Sect. \ref{obs}," J- and Weband observations were obtained alternately: therefore the epochs for J-bancl and. Ix-band diller typically by 15-20nmmin., J- and K-band observations were obtained alternately; therefore the epochs for J-band and K-band differ typically by min. As a consequence. the JÁN value corresponding to a given. J-band epoch is only approximately correct.," As a consequence, the $J-K$ value corresponding to a given J-band epoch is only approximately correct." Ες clleet will cause additional scatter in the Jovs. 40dy plots. particularly. for. objects with rapid variability.," This effect will cause additional scatter in the J vs. $J-K$ plots, particularly for objects with rapid variability." In the following. we cliscuss all three highly variable objects separately.," In the following, we discuss all three highly variable objects separately." Whe datapoints follow a straight line in the diagram. with a slope of AyyfAy=0.55+0.03.," The datapoints follow a straight line in the diagram, with a slope of $\Delta_{J-K} / \Delta_J = 0.55 \pm 0.03$." LE we fit the nightly. averages. we obtain à verv similar value. indicating that variations on timescales of hours ancl clays are caused by the same process.," If we fit the nightly averages, we obtain a very similar value, indicating that variations on timescales of hours and days are caused by the same process." In Fig., In Fig. 6 we compare with the expected slope for spot temperatures of 5000 and Why (dashed. dash-dottec line) and variable extinction (dotted line).," \ref{f4} we compare with the expected slope for spot temperatures of 5000 and K (dashed, dash-dotted line) and variable extinction (dotted line)." This slope is inconsistent on a 3e level with the predictions for hot spots. no matter what spot. paramet«ns are chosen.," This slope is inconsistent on a $\sigma$ level with the predictions for hot spots, no matter what spot parameters are chosen." “Phe difference between J- and Ix-band amplitule is simply too large to be explained by hot spots., The difference between J- and K-band amplitude is simply too large to be explained by hot spots. On the other hand. the distribution of datapoints agrees well with the expectations for variable extinction.," On the other hand, the distribution of datapoints agrees well with the expectations for variable extinction." The total J-band amplitude in our observations Corresponds to a change in the extinction of «δν~2 mamas., The total J-band amplitude in our observations corresponds to a change in the extinction of $\Delta A_V \sim 2$ mag. As discussed in Sect. 4.," As discussed in Sect. \ref{per}," jo lighteurve contains periodic components with timescales of dd. which favours the disk as the origin of the extinction changes.," the lightcurve contains periodic components with timescales of d, which favours the disk as the origin of the extinction changes." Assuming Weplerian rotation. this translates to a distance between the star anc the source. of variable extinction between AAU. which is in the range of the typical dust. sublimation radius for VLM objects (?)..," Assuming Keplerian rotation, this translates to a distance between the star and the source of variable extinction between AU, which is in the range of the typical dust sublimation radius for VLM objects \citep{2006ApJ...645.1498S}." Thus. if our interpretation is correct. we are observing a feature at the inner edge of the disk.," Thus, if our interpretation is correct, we are observing a feature at the inner edge of the disk." The variability characteristic for this object presents the most dificult case in the interpretation., The variability characteristic for this object presents the most difficult case in the interpretation. Strong scatter is seen particularly in the left/bluc part of the, Strong scatter is seen particularly in the left/blue part of the We begin by investigating various limits of the global mode equations analycally.,We begin by investigating various limits of the global mode equations analytically. I[ 92Oy.B=D. and the density is constant. the mode equation reduces to allowing a family of solutions describing shear Alfvénn waves in a rigidly rotating homogeneous plasma Uberoi 1932)..," If $\Omega=\Omega_0,\, \BB=B_{z0}$, and the density is constant, the mode equation reduces to $F_0 = \wt - \wab^2/\rho_0=const.$ ): _r _r _r, allowing a family of solutions describing shear Alfvénn waves in a rigidly rotating homogeneous plasma \citep[][]{HasegawaUberoi}." Ilere pois to be interpreted as an effective radial wvavenumber obeving: am, Here $\mu$ is to be interpreted as an effective radial wavenumber obeying: ). ↴∏∐↲∖↽≀↧↴↥⋯↲⊳∖⇁∪↓⋟∕∣⊋≀↧↴↕⋅≼↲≼⇂≼↲∥↲↕⋅∐↓↕⋯↲≺⇂∣↽≻∡∖↽∐↓≀↧↴∩∢∐↕∐≸≟⊔∐↲⊳∖⊽∪↥, The values of $\mu^2$ are determined by matching the solutions of Eq. ∏∐∪∐⋝∖⊽∪↓⋟⊏≺↥⋅∐≨↥∪⊔∐↲↕∐↓↕↽≻∪⊳∖⊽≼↲≼⇂ ∣↽≻⋯∐∐⇂≀↧↴↕, \ref{rigid-1} to the imposed boundaries. ⋅↕≼↲⋟∖⇁⋅↴⊺∐↕⋟∖⊽↕⋅≼↲⋟∖⊽∏∐⋟∖⊽↕∐≀↧↴⋖⋡∣↽≻≼≻∏∐≼⇂≀↕↴↕⋅⋡∖⇁⊣⇂≼↲↕↽≻≼↲∐≺⇂≀↧↴∐↥↕⋝≺∐⋟∖⊽≺∢↕⋅≼↲∩↲⋟∖⊽↕↽≻≼↲≺∢⊔⋅∏∐↓∪↓⋟⋟∖⊽↥≀↧↴∣↽≻↥≼↲≼↲↕≸↽↔↴≼↲∐∐↓⋯⇂≼↲⋟∖⊽ when T>0 (Dubrulle&Knobloch1993).., This results in a (boundary-dependant) discrete spectrum of stable eigenmodes when $\mu^2>0$ \citep[][]{1993A&A...274..667D}. If the dispersion relation of equation (17)) gives a negative value for 77. the solution is a linear combination of the modified Bessel functions Lye) and Ay(yr).," If the dispersion relation of equation \ref{rigid-2}) ) gives a negative value for $\mu^2$ , the solution is a linear combination of the modified Bessel functions $I_1(|\mu| r)$ and $K_1(|\mu| r)$." When the rotation frequency is constant throughout the entire domain. there can be no elobal mocle satishing both boundaries. as both solutions to eq. (16))," When the rotation frequency is constant throughout the entire domain, there can be no global mode satisfying both boundaries, as both solutions to eq. \ref{rigid-1}) )" are monotonic., are monotonic. If only a portion of the domain is subject to rigid rotation (the effective potential is positive in that region but negative elsewhere). the modified Bessel functions provide suitable limiting forms.," If only a portion of the domain is subject to rigid rotation (the effective potential is positive in that region but negative elsewhere), the modified Bessel functions provide suitable limiting forms." In particular. when either the density or the rotation are small for large r. we obtain [j|2f. (vacuum solution).," In particular, when either the density or the rotation are small for large r, we obtain $|\mu| \approx k_z$ (vacuum solution)." We will use this result in Section 4. (0 provide interior ancl exterior boundarymatching conditions for modes localized by the form of the equilibrium, We will use this result in Section \ref{Numerical Results} to provide interior and exterior boundarymatching conditions for modes localized by the form of the equilibrium The kinematical criteria originally defined by Eeeon (1958a. b. 1989. 1995) for determining the possible members of the best documented moving groups are summarized by Montes et al. (,"The kinematical criteria originally defined by Eggen (1958a, b, 1989, 1995) for determining the possible members of the best documented moving groups are summarized by Montes et al. (" 20012.b).,"2001a,b)." Basically. there are two criteria: (i) Phe proper motion criterion. which uses the ratio (v/v) as a measure of how the star turns away from the converging point. where the anc the 7 are the orthogonal components of the proper motion (1) of a test star.," Basically, there are two criteria: (i) The proper motion criterion, which uses the ratio $\tau$ $\nu$ ) as a measure of how the star turns away from the converging point, where the $\nu$ and the $\tau$ are the orthogonal components of the proper motion $\mu$ ) of a test star." The component £ is directed towards the converging point and the z is perpendicular to it on the plane of the sky., The component $\nu$ is directed towards the converging point and the $\tau$ is perpendicular to it on the plane of the sky. A test star becomes a possible member if (7/5)«(0.L/s/0A). where the À is the angle corresponding to the are between the test star and the converging point. (," A test star becomes a possible member if $(\tau/\nu)<(0.1/sin \lambda)$, where the $\lambda$ is the angle corresponding to the arc between the test star and the converging point. (" "i) The radial velocity criterion. which compares the observed. radial velocity (5. the center of mass velocity) of he test star to the predicted. mean radial velocity 1,= VreosA. where Vr ds the magnitude of the space velocity vector representing the MG. as a whole.","ii) The radial velocity criterion, which compares the observed radial velocity $\gamma$, the center of mass velocity) of the test star to the predicted mean radial velocity $V_{p}= V_{T}cos\lambda$ , where $V_{T}$ is the magnitude of the space velocity vector representing the MG as a whole." " The test star is a »ossible member i£ the dilference between + and. V, is less han the dispersions of the radial velocities among the stars in the AIG.", The test star is a possible member if the difference between $\gamma$ and $V_{p}$ is less than the dispersions of the radial velocities among the stars in the MG. Fultilling one of the criteria makes the test star a xossible member., Fulfilling one of the criteria makes the test star a possible member. Fulfilling both eriteria. however. does not euarantee the membership.," Fulfilling both criteria, however, does not guarantee the membership." This is because there is always a possibility that the same velocity space is occupied by the ALG members and the non members., This is because there is always a possibility that the same velocity space is occupied by the MG members and the non members. Further independent criteria implying a common origin and same age as the member stars may be investigated in order to confirm the rue membership., Further independent criteria implying a common origin and same age as the member stars may be investigated in order to confirm the true membership. The parameters of the five best documented. ALG and he possible membership criteria of each of them have been summarized in Table 3., The parameters of the five best documented MG and the possible membership criteria of each of them have been summarized in Table 3. The criteria have been applied one » one to all stars in our CAB sample and 95 svstems out of 237 were found to be satisfying at least one ofthe criteria or one of the MG in Table 3., The criteria have been applied one by one to all stars in our CAB sample and 95 systems out of 237 were found to be satisfying at least one of the criteria for one of the MG in Table 3. Phose potential candidates are marked on Table 2 indicating the number of criteria fulfilled (1l means only one criterion. 2 means both criteria were satisfied) and the name of the MG involved.," Those potential candidates are marked on Table 2 indicating the number of criteria fulfilled (1 means only one criterion, 2 means both criteria were satisfied) and the name of the MG involved." Some already known menibers are also marked on a separate column for a consistency. check After all of the possible AIC: members were determined. the sample was divided into two groups.," Some already known members are also marked on a separate column for a consistency check After all of the possible MG members were determined, the sample was divided into two groups." " “Phe one which contains the possible MG members is called MG"" and. the other. which contains the rest of the sample is named field stars’."," The one which contains the possible MG members is called `MG' and, the other, which contains the rest of the sample is named `field stars'." The (£.V) diagram of these groups are compared in Fig.," The $(U, V)$ diagram of these groups are compared in Fig." 3., 3. The * shaped concentration which was noticed on the (C.V) diagram of the whole sample (Fig.," The $\gamma$ shaped concentration which was noticed on the $(U, V)$ diagram of the whole sample (Fig." 2a) shows itself more clearly in Fig., 2a) shows itself more clearly in Fig. 3a after the removal of stars which fail to be a possible member of anv of the five MC in Tabk DU, 3a after the removal of stars which fail to be a possible member of any of the five MG in Table 3. M2 The smooth distribution (Fig., The smooth distribution (Fig. 3b) with a Larger dispersion of the field. stars is also clear on the comparison with the whole sample (Fig., 3b) with a larger dispersion of the field stars is also clear on the comparison with the whole sample (Fig. 2a) and the possible MG members (Fig., 2a) and the possible MG members (Fig. 3a)., 3a). Comparison of these two groups on the (1.V) diagram are displaved in Fig.," Comparison of these two groups on the $(W, V)$ diagram are displayed in Fig." 4., 4. The kinematical differences between the two groups of CAD can be shown numerically if their mean motions and clispersions are compared., The kinematical differences between the two groups of CAB can be shown numerically if their mean motions and dispersions are compared. The “AIG has a mean motion of (VII)=(169.13.5.7.6) km/s with the dispersions of (20.6. 9.8. 12.8) km/s while the Ποια stars’ appear with à mean motion of (VW)=(119.240.8.4) kms and the dispersions of (45.4. 32.9. 22.9) km/s. According to Wiclen (1977). σι. = 20.81. oy = 9.76. 0 = 12.74 km/s velocity dispersions indicate a kinematical age of 950 Myr. which is slightly. bigger than the known ages of the MG given in Table 3.," The `MG' has a mean motion of $(U, V, W)= (-16.9, -13.5, -7.6)$ km/s with the dispersions of (20.6, 9.8, 12.8) km/s while the `field stars' appear with a mean motion of $(U, V, W)=(-11.2, -24.0, -8.4)$ km/s and the dispersions of (45.4, 32.9, 22.9) km/s. According to Wielen (1977), $\sigma_{U}$ = 20.81, $\sigma_{V}$ = 9.76, $\sigma_{W}$ = 12.74 km/s velocity dispersions indicate a kinematical age of 950 Myr, which is slightly bigger than the known ages of the MG given in Table 3." This is because the dispersion. of stars was computed with respect to the LSR., This is because the dispersion of stars was computed with respect to the LSR. However. true age would be less if the true dispersion point of cach group is considered.," However, true age would be less if the true dispersion point of each group is considered." Considering the fact that some of the possible moving group members are not really members. this age can be treated. an upper limit.," Considering the fact that some of the possible moving group members are not really members, this age can be treated an upper limit." " On the other hand. the kinematical criteria to form the ""M group chooses only a limited number of voung binaries. there can be binaries left in the ""Ποια stars’ vounger than 950 Myr."," On the other hand, the kinematical criteria to form the `MG' group chooses only a limited number of young binaries, there can be binaries left in the `field stars' younger than 950 Myr." Thus. this age (950 Myr) cannot be considered as à lower limit for the Ποια stars’ which are found to have 3.86 Gyr age from the," Thus, this age (950 Myr) cannot be considered as a lower limit for the `field stars' which are found to have 3.86 Gyr age from the" "For E,~QBR/c, we have e?/?|E,|*/?~10 eV. This is typically much smaller than either ¢ or £g.","For $E_s\sim \Omega B R/c$, we have $e^{3/2}|E_s|^{1/2}\sim 10$ eV. This is typically much smaller than either $\phi$ or ${\cal E}_B$." " No vacuum gap will form if the electrons or ions are able to fill the magnetosphere region above the polar cap with the required Goldreich-Julian density; i.e., the vacuum gap will cease to exist when pe=pay or pi=pas."," No vacuum gap will form if the electrons or ions are able to fill the magnetosphere region above the polar cap with the required Goldreich-Julian density; i.e., the vacuum gap will cease to exist when $\rho_e=\rho_{GJ}$ or $\rho_i=\rho_{GJ}$." From Eqs. (48)), From Eqs. \ref{rhoeeq2}) ) " and (47)) we can see that no polar gap will form if < C.kT 3Ts for a negative polar magnetosphere ($2-B,> 0), and Ey—(Zne)3/? < CikT 916 for a positive polar magnetosphere (€?-B,< 0). ["," and \ref{rhoieq2}) ) we can see that no polar gap will form if < C_e kT 3 T_6 for a negative polar magnetosphere $\mathbf{\Omega}\cdot\mathbf{B}_p > 0$ ), and _B-(Z_n < C_i kT 3 T_6 for a positive polar magnetosphere $\mathbf{\Omega}\cdot\mathbf{B}_p < 0$ ). [" For the exact expressions for C. and C; see Eqs. (35)),For the exact expressions for $C_e$ and $C_i$ see Eqs. \ref{Ceeq}) ) and (45)).], and \ref{Cieq}) ).] " For neutron stars in general, the electron work function ¢ is much less than ΟΚΤ~37% keV (see Fig. 4)),"," For neutron stars in general, the electron work function $\phi$ is much less than $C_ekT \sim 3 T_6$ keV (see Fig. \ref{Wfig}) )," so electrons can easily escape from the condensed surface., so electrons can easily escape from the condensed surface. No gap forms for a negative polar magnetosphere under neutron star surface conditions. (, No gap forms for a negative polar magnetosphere under neutron star surface conditions. ( This is contrary to the conclusions of Usov&Melrose1996 and Giletal. 2003..),This is contrary to the conclusions of \citealt{usov96} and \citealt{gil03}. .) " The ion binding energy £p [given by Eq. (38))],"," The ion binding energy ${\cal E}_B$ [given by Eq. \ref{EBeq}) )]," " on the other hand, can be larger than C;kT'~3T& keV under certain neutron star surface conditions (see Figs. 1,, 2,,"," on the other hand, can be larger than $C_ikT \sim 3 T_6$ keV under certain neutron star surface conditions (see Figs. \ref{HeEdfig}, \ref{CEdfig}," and 3))., and \ref{FeEdfig}) ). Ions can tightly bind to the condensed surface and a polar gap can form under these conditions., Ions can tightly bind to the condensed surface and a polar gap can form under these conditions. " Figure 7 shows the critical temperature (determined by £p= C;kT) below which a vacuum gap can form for the Fe, C, and He surfaces."," Figure \ref{gapfig} shows the critical temperature (determined by ${\cal E}_B = C_i kT$ ) below which a vacuum gap can form for the Fe, C, and He surfaces." a efficiency of the star formation per free-fall time (??)..,"a efficiency of the star formation per free-fall time \citep{kennicutt98,dubois08}." This threshold density is chosen so that it is inferior or equal to the maximal Jeans density reached on the finest level., This threshold density is chosen so that it is inferior or equal to the maximal Jeans density reached on the finest level. " In the simulations with supernova feedback, after ~10 Myrs, massive stars undergo Type II supernova explosions, releasing half of their 1051 ergs into their surroundings as kinetic energy and the other half as thermal energy (?).."," In the simulations with supernova feedback, after $\sim 10$ Myrs, massive stars undergo Type II supernova explosions, releasing half of their $10^{51}$ ergs into their surroundings as kinetic energy and the other half as thermal energy \citep{dubois08}." " During this phase, processed heavy elements are dispersed, enriching the interstellar and intergalactic medium."," During this phase, processed heavy elements are dispersed, enriching the interstellar and intergalactic medium." " In what follows, we elaborate on the details of each simulation."," In what follows, we elaborate on the details of each simulation." The sseries make use of the resimulation (also called ‘zoom’ technique to follow the evolution of a Milky Way-type galaxyin) a ACDM cosmology., The series make use of the resimulation (also called `zoom') technique to follow the evolution of a Milky Way-type galaxyin a $\Lambda$ CDM cosmology. ? reported on high redshift results (z > 9) from the ultra-high resolution resimulations in the sseries., \citet{powell11} reported on high redshift results (z $\geq$ 9) from the ultra-high resolution resimulations in the series. These reached a maximum physical spatial resolution of ~ 0.5 pc at all times., These reached a maximum physical spatial resolution of $\sim$ 0.5 pc at all times. " To track the evolution of the galaxy down to lower redshifts, the ssuite also includes three resimulations with lowerspatial resolution (but identical DM particle mass resolution) and the following physics: (i) adiabatic with a uniform UV background turned on instantaneously at z=8.5 (NutAD) (ii) cooling, star formation, and UV background (NutCO) and (iii) same as (ii) but with supernova feedback and metal enrichment (NutFB)."," To track the evolution of the galaxy down to lower redshifts, the suite also includes three resimulations with lower resolution (but identical DM particle mass resolution) and the following physics: (i) adiabatic with a uniform UV background turned on instantaneously at $=8.5$ (NutAD) (ii) cooling, star formation, and UV background (NutCO) and (iii) same as (ii) but with supernova feedback and metal enrichment (NutFB)." " NutAD and NutCO have maximum 48 pc (physical) resolution at all times and reach z—0, whereas NutFB has maximum 12 pc (physical) resolution and only reaches z=3."," NutAD and NutCO have maximum 48 pc (physical) resolution at all times and reach $z=0$, whereas NutFB has maximum 12 pc (physical) resolution and only reaches $z=3$." Fig., Fig. 1 shows snapshot of the DM (upper panel) and gas (lower panel) of a regiona centred on a halo hosting a Milky Way-type galaxy at z—3 in NutFB., \ref{fig:snapshot} shows a snapshot of the DM (upper panel) and gas (lower panel) of a region centred on a halo hosting a Milky Way-type galaxy at $z=3$ in NutFB. We recall the important details of the rresimulations here., We recall the important details of the resimulations here. " The simulation volume is a 9h Mpc comoving periodic box evolving according to a WMAPS5! cosmology (?) (σε=0.8, Ωπι= 0.258, Qa=0.742, h=Ho/(100kms~*Mpc~*)= 0.72)."," The simulation volume is a $h^{-1}$ Mpc comoving periodic box evolving according to a WMAP5 cosmology \citep{dunkley09} $\sigma_8=0.8$, $\Omega_m=0.258$ , $\Omega_{\Lambda}=0.742$, $h\equiv H_0/(100 {\rm km s^{-1} Mpc^{-1}}) = 0.72$ )." " Initial conditions are generated using (?),, a parallel version of the package (?).."," Initial conditions are generated using \citep{prunet08}, a parallel version of the package \citep{bertschinger01}." Within this volume we identify the region where a Milky like galaxy (halo virial mass of ~ 5 x10!Mc at z= 0) will form., Within this volume we identify the region where a Milky Way-like galaxy (halo virial mass of $\simeq$ 5 $\times$ $^{11}$ $_{\odot}$ at $z=0$ ) will form. This region encompasses a volume of side length ~ 2.7 h! Mpc., This region encompasses a volume of side length $\sim$ 2.7 $^{-1}$ Mpc. " While the root grid for the entire simulation volume is 128%, within the (~2.7 h! Mpc)? region, we place an additional three nested grids, giving an equivalent resolution of 10243 dark matter particles, each with mass Mpm ~5x10*Ms."," While the root grid for the entire simulation volume is $^3$, within the $\sim$ 2.7 $^{-1}$ $^3$ region, we place an additional three nested grids, giving an equivalent resolution of $^{3}$ dark matter particles, each with mass $_{\rm DM}$ $\simeq 5\times 10^4 \msun$." " To fix the maximum physical resolution to a constant value (12 pc for NutFB and 48 pc for NutCO and NutAD) as the universe expands and the simulation evolves, we further refine on the finest fixed grid within the 2.7 h! Mpc? region according to a quasi-Lagrangian strategy, i.e. when the number of dark matter particles in cell reaches 8 or equivalently when the baryon plus dark matter densitya in a cell increases by a factor of 8."," To fix the maximum physical resolution to a constant value (12 pc for NutFB and 48 pc for NutCO and NutAD) as the universe expands and the simulation evolves, we further refine on the finest fixed grid within the 2.7 $^{-1}$ $^3$ region according to a quasi-Lagrangian strategy, i.e. when the number of dark matter particles in a cell reaches 8 or equivalently when the baryon plus dark matter density in a cell increases by a factor of 8." Table 1 lists the maximum level triggered for each simulation., Table \ref{SimSummary} lists the maximum level triggered for each simulation. " Because of the higher spatial resolution in NutFB it uses a higher density threshold for star formation (ng,=400 cm?) than the NutCO run (ngin=10cm ?)."," Because of the higher spatial resolution in NutFB it uses a higher density threshold for star formation $n_{\rm H,th} = 400 ~{\rm cm^{-3}}$ ) than the NutCO run $n_{\rm H,th} = 10 ~{\rm cm^{-3}}$ )." The star particle mass (~2—3x 10*Mo) is determined by the combination of minimum grid size and density threshold for star formation (?).., The star particle mass $\simeq 2-3 \times10^4\msun$ ) is determined by the combination of minimum grid size and density threshold for star formation \citep{dubois08}. " In NutFB, we assume that every supernova bubble with an initial radius of 32 pc sweeps up the same amount of gas as that initially locked in the star particles."," In NutFB, we assume that every supernova bubble with an initial radius of 32 pc sweeps up the same amount of gas as that initially locked in the star particles." This is usually expressed as a mass loading factor of unity (7= 1)., This is usually expressed as a mass loading factor of unity $\eta=1$ ). " The other three simulations are large volume cosmological simulations, and as such are performed with lower spatial (1-2 kpc) and mass resolution."," The other three simulations are large volume cosmological simulations, and as such are performed with lower spatial (1–2 kpc) and mass resolution." " More specifically, the mass of each dark matter particle is mpm~10""Mo for the ssimulation, 8x107M for the intermediate size run (Cosmo25) and 6x105Mg for the Cosmo50 run."," More specifically, the mass of each dark matter particle is $m_{\rm DM}\simeq 10^7\msun$ for the simulation, $8\times 10^7\msun$ for the intermediate size run (Cosmo25) and $6\times 10^8\msun$ for the Cosmo50 run." " As in the NutFB run, supernova feedback and UV background heating are included in the simulations, but the radius of the initial supernova bubble is set to twice the minimum size of the grid (see Table 1))."," As in the NutFB run, supernova feedback and UV background heating are included in the simulations, but the radius of the initial supernova bubble is set to twice the minimum size of the grid (see Table \ref{SimSummary}) )." " Note also that the adopted cosmology for the ssimulation (WMAPI) is different from the others, but as we will show this has very little impact on our results, if at all."," Note also that the adopted cosmology for the simulation (WMAP1) is different from the others, but as we will show this has very little impact on our results, if at all." We refer interested readers to ? and ? for a detailed description of the ssimulation set-up., We refer interested readers to \citet{ocvirk08} and \citet{devriendt10} for a detailed description of the simulation set-up. " In all the simulations, we identify (sub) haloes using the algorithm (?),, which is based on the detection of peaks and saddle points in the dark matter density field, supplemented by the most-massive subhalo algorithm developed by ?.."," In all the simulations, we identify (sub) haloes using the algorithm \citep{aubert04}, which is based on the detection of peaks and saddle points in the dark matter density field, supplemented by the most-massive subhalo algorithm developed by \citet{tweed09}." The virial radius of halos is defined as the maximal radius within which the virial theorem is satisfied to better than20%., The virial radius of halos is defined as the maximal radius within which the virial theorem is satisfied to better than. . We further define gas belonging to a satellite galaxy as gas residing within the half-mass radius of its host DM satellite halo., We further define gas belonging to a satellite galaxy as gas residing within the half-mass radius of its host DM satellite halo. " The centre of a halo, which we use to compute angular momentum, is defined as the centre of mass of dark matter and baryons."," The centre of a halo, which we use to compute angular momentum, is defined as the centre of mass of dark matter and baryons." " The mean motion of the halos is determined by computing the centre of mass velocity of dark matter particles, gas, and stars within their virial radii."," The mean motion of the halos is determined by computing the centre of mass velocity of dark matter particles, gas, and stars within their virial radii." " To understand how galaxies acquire their angular momentum, we study the angular momentum evolution of the different components (gas, dark matter, stars) inside their host halos."," To understand how galaxies acquire their angular momentum, we study the angular momentum evolution of the different components (gas, dark matter, stars) inside their host halos." " We compute the specific angular momentum vectors as: where r'; is the radial distance from the centre of mass of the halo (includes dark matter and baryons), V; is the peculiar velocity and m, is the mass of the i-th dark matter (star) particle or gas cell."," We compute the specific angular momentum vectors as: where $\vec{\mathbf{r}}_i$ is the radial distance from the centre of mass of the halo (includes dark matter and baryons), $\vec{\mathbf{v}}_i$ is the peculiar velocity and $m_i$ is the mass of the i-th dark matter (star) particle or gas cell." In what follows we use different subscripts to denote the specific angular momentum of different components in different regions of the halo., In what follows we use different subscripts to denote the specific angular momentum of different components in different regions of the halo. These are summarised in Table 2., These are summarised in Table 2. We begin our investigation of the evolution of angular momentum of the various components of a virialized halo with the simplest (in terms of physics) high resolution NutAD run., We begin our investigation of the evolution of angular momentum of the various components of a virialized halo with the simplest (in terms of physics) high resolution NutAD run. " Since gas cannot cool radiatively in this simulation, newly accreted material is shock heated by the pressure supported intra-halo medium."," Since gas cannot cool radiatively in this simulation, newly accreted material is shock heated by the pressure supported intra-halo medium." " As a result, its radially oriented initial velocity is isotropized, and drives the gas density field towards spherical symmetry."," As a result, its radially oriented initial velocity is isotropized, and drives the gas density field towards spherical symmetry." Accreted dark matter particles are also more or less isotropically redistributed within the host halo by the collisionless violent relaxation process., Accreted dark matter particles are also more or less isotropically redistributed within the host halo by the collisionless violent relaxation process. " Given that (i) gas and dark matter within the halo experience the same scale torques (e.g.??),, and (ii) gas and dark matter are driven by the gravitational collapse to a very similar equilibrium distribution (i.e. to a good approximation that of an isothermal sphere since the total amount of angular momentum provided by tidal torques is very limited), we expect them to have similar 7."," Given that (i) gas and dark matter within the halo experience the same larger-scale torques \citep[e.g.][]{peebles69,book11}, and (ii) gas and dark matter are driven by the gravitational collapse to a very similar equilibrium distribution (i.e. to a good approximation that of an isothermal sphere since the total amount of angular momentum provided by tidal torques is very limited), we expect them to have similar ." ". Indeed, Fig."," Indeed, Fig." " 2shows that cclosely tracks rregardless of whetheror not mergers, easily identified by large"," \ref{fig:jtot_ad} shows that closely tracks regardless of whetheror not mergers, easily identified by large" Magnetic field generation in astrophysical scenarios. such as AGN and GRBs. is not fully understood (Colgateοἱal.2001).," Magnetic field generation in astrophysical scenarios, such as AGN and GRBs, is not fully understood \citep{colgate01}." . While such phenomena are of fundamental interest. they are also closely related (o open questions such non-thermal radiation emission and cosnuc rav acceleration (Bhattacharjeeοἱal.2000).," While such phenomena are of fundamental interest, they are also closely related to open questions such non-thermal radiation emission and cosmic ray acceleration \citep{bhattacharjee00}." . Recently. collisionless plasma effects have been proposed as candidate mechanisms for maenetic field generation (Gruzinov&Waximan1999:Medvedev&Loeb. 1999).. mediating the formation of relativistic shocks via the Weibel instability (Weibel1959:Silvaοἱal.2003).," Recently, collisionless plasma effects have been proposed as candidate mechanisms for magnetic field generation \citep{gruzinovwaxman99, medvedev99}, mediating the formation of relativistic shocks via the Weibel instability \citep{weibel59,silva03}." . The KIL] (D'Angelo1965:Gruzinov2008:Zhangetal.2009) should also be considered since it is capable of generating magnetic fields in the presence of strong velocity shears. which naturally originate in energetic matter outbursis in AGN and GRBs. and which are also present whenever conditions for the formation of relativistic shocks exist.," The KHI \citep{dangelo65,gruzinov08,macfadyen09} should also be considered since it is capable of generating large-scale magnetic fields in the presence of strong velocity shears, which naturally originate in energetic matter outbursts in AGN and GRBs, and which are also present whenever conditions for the formation of relativistic shocks exist." These large-scale fields may also be further amplified by Che magnetic-«dvinanmo effect (Gruzinov.2008:Zhangetal...2009).," These large-scale fields may also be further amplified by the magnetic-dynamo effect \citep{gruzinov08,macfadyen09}." . Recent kinetic simulations have focused on magnetic field generation via electromagnetic plasma instabilities in unmagnetized flows without velocity shears., Recent kinetic simulations have focused on magnetic field generation via electromagnetic plasma instabilities in unmagnetized flows without velocity shears. 3D PIC simulations of Weibel turbulence (Silvaοἱal.2003:FonsecaetFrederiksen2004:Nishikawa.etal.2005). have demonstrated subequipartition magnetic field generation.," 3D PIC simulations of Weibel turbulence \citep{silva03,fonseca03,frederiksen04,nishikawa05} have demonstrated subequipartition magnetic field generation." The Weibel instability. has been shown to be critical in mediating relativistic shocks (Spitkovskyal. 2009).. where a Fermi-like particle acceleration process has also been identified.," The Weibel instability has been shown to be critical in mediating relativistic shocks \citep{spitkovsky08,martins09}, where a Fermi-like particle acceleration process has also been identified." These works have neglected the role of velocity shear in the flow. which are an alternative mechanism to generate sub-equipartition magnetic fields in relativistic outflows 2008).," These works have neglected the role of velocity shear in the flow, which are an alternative mechanism to generate sub-equipartition magnetic fields in relativistic outflows \citep{gruzinov08}." . Furthermore. a shear [low upstream of a shock can lead (ο density inhomogeneities via (he WIT which may constitute important scattering sites for particle acceleration.," Furthermore, a shear flow upstream of a shock can lead to density inhomogeneities via the KHI which may constitute important scattering sites for particle acceleration." In Zhangetal. (2009).. 3D magnetohvdrodynamie (MIID) simulations of KID turbulence are," In \cite{macfadyen09}, , 3D magnetohydrodynamic (MHD) simulations of KH turbulence are" Phe model for cclouds. where these are low-density highly ionized. ealaxy-sized eas aggregates. provides the most basic scenario that is consistent. with our observations.,"The model for clouds, where these are low-density highly ionized galaxy-sized gas aggregates, provides the most basic scenario that is consistent with our observations." Although this is the model preferred by the cata we cannot. unfortunately. rule out other non-local explanations for the inverse elfect.," Although this is the model preferred by the data we cannot, unfortunately, rule out other non-local explanations for the inverse effect." Alore definite conclusions. especially the ones. concerning the isotropy of the emission. could be achieved. by means of observing a Larger sample of QSO pairs.," More definite conclusions, especially the ones concerning the isotropy of the emission, could be achieved by means of observing a larger sample of QSO pairs." AFS thanks Adam Dobrzyveki for uselul comments on an original version of this paper., AFS thanks Adam Dobrzycki for useful comments on an original version of this paper. AES and RC acknowledge support by a research. grant by the Spanish MIC., AFS and RC acknowledge support by a research grant by the Spanish MEC. Partial financial support for this work was provided by the DGICYT under project. PB92-0741 and by the Comission of the European Union under the ‘Lluman Capital and Mobility? contract CILIUN-C'T92-, Partial financial support for this work was provided by the DGICYT under project PB92-0741 and by the Comission of the European Union under the `Human Capital and Mobility' contract CHRX-CT92-0033. The Isaac Newton Telescope (INT) and the William Ποσο Telescope (NIIT): are operated on the island of La Palma by the Roval Cireenwich Observatory in the Spanish Observatorio del Itoque de Los Aluchachos of the Instituto cle sca de Canarias., The Isaac Newton Telescope (INT) and the William Herschel Telescope (WHT) are operated on the island of La Palma by the Royal Greenwich Observatory in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de sica de Canarias. The spectrum of 1305|298 was taken during a service night at WIIT., The spectrum of 1305+298 was taken during a service night at WHT. L,. 996)... Utzetal.(2009) utilized an altered version of the Bovelet&Wichr(2001). alegorithim. aud applied it to Tinode SOT observations.," \cite{Utz09} utilized an altered version of the \cite{Bov01} algorithm, and applied it to Hinode SOT observations." The size of \IBPs was defined by placing an upper aud lower intensity threshold ou the seginented structures. resulting in mean diuneters of 166-215 Xin.," The size of MBPs was defined by placing an upper and lower intensity threshold on the segmented structures, resulting in mean diameters of 166-218 km." Iu this paper we use observations and umuuerical siuulatious to investigate the area distribution of MBPs., In this paper we use observations and numerical simulations to investigate the area distribution of MBPs. An automatic detection and tracking aleoritlin. described iu Crockettetal.(2009) (hereafter. Paper 1). is developed further and applied 9to high resolution C-band images.," An automatic detection and tracking algorithm, described in \cite{Croc09} (hereafter, Paper 1), is developed further and applied to high resolution G-band images." Section 2 discusses the observations. with emphasis on an automated algorithin used for ΠΟΤΟ detection aud size determination.," Section 2 discusses the observations, with emphasis on an automated algorithm used for MBP detection and size determination." A description of the nuunerical simulations are given in Section 3., A description of the numerical simulations are given in Section 3. Our main findings are presented in Section [|. with concluding remarks in Section 5.," Our main findings are presented in Section 4, with concluding remarks in Section 5." The data was obtained bv the uewlv-comauissioned Rapid Oscillations iu the Solar Atmosphere (ROSA) iustriuent. installed at the 76 cii Duun Solar Telescope (DST). in New Moxico. USA (Jessetal.2010).," The data was obtained by the newly-commissioned Rapid Oscillations in the Solar Atmosphere (ROSA) instrument, installed at the 76 cm Dunn Solar Telescope (DST), in New Mexico, USA \citep[]{Jess10}." ". The observations were taken on 28 Max 2009 through a filter. centered at1305À. (C-band). during a period of excellent κοσμο,"," The observations were taken on 28 May 2009 through a filter, centered at (G-band), during a period of excellent seeing." Post-facto speckle recoustruction algorithius AVoeeretal.2008).. in addition to rigorous nuage de-stretehiug using a lOον10 exid. (equating to a wl.7” separation between spatial samples. (Jessetal. 2008))). was implemented to remove effects caused by atinospheric secius.," Post-facto speckle reconstruction algorithms \cite[]{Wog08}, in addition to rigorous image de-stretching using a $40 \times 40$ grid, (equating to a $\approx$ $''$ separation between spatial samples, \citep{Jes08}) ), was implemented to remove effects caused by atmospheric seeing." " We observed a 707&70"" quiet solar region at disk center. achieving diffractiou-limuted imaging with 0.069"""," We observed a $70'' \times 70''$ quiet solar region at disk center, achieving diffraction-limited imaging with $''$ $^{-1}$." Figure 5 lisplavs a typical Ct-band mage from the dataset. with iuultiple MBPs visible iu the central region.," Figure \ref{f1} displays a typical G-band image from the dataset, with multiple MBPs visible in the central region." Analysis of the data was performed with an updated version of a detection algorithia described in Paper 1. which uses intensity thresholding to map the iutererauular lanes.," Analysis of the data was performed with an updated version of a detection algorithm described in Paper 1, which uses intensity thresholding to map the intergranular lanes." À compass search allows MBPs to boe diseutaneled from bright pixels within erauules. while object erowine accounts for anv pixels that might have been removed when mapping the lanes.," A compass search allows MBPs to be disentangled from bright pixels within granules, while object growing accounts for any pixels that might have been removed when mapping the lanes." One of the disadvantages of the aleorithin described iu Paper lois the requirement for the image to be divided into segments. with cach subsequent ποσο! beime processed individually.," One of the disadvantages of the algorithm described in Paper 1 is the requirement for the image to be divided into segments, with each subsequent segment being processed individually." " Tere we use au updated algorithm which operates ou the eutire 70”«TO"" inaese sequence. thus improving computational time and accuracy."," Here we use an updated algorithm which operates on the entire $70'' \times 70''$ image sequence, thus improving computational time and accuracy." This development is particularly imuportant. as it permits accurate cstimates of MDP areas.," This development is particularly important, as it permits accurate estimates of MBP areas." Mapping the location of the iuter-granular lanes. with au overestimation of the iuteusitv threshold. is used to separate out bright objects.," Mapping the location of the inter-granular lanes, with an overestimation of the intensity threshold, is used to separate out bright objects." The threshold set is the cal dmaee intensity plus one sigma., The threshold set is the mean image intensity plus one sigma. All structures uuder this level are considered a lane aud are not investigated by our algorithui., All structures under this level are considered a lane and are not investigated by our algorithm. The vast majority of MBPs retain higher iutensitics. however some very dull MBPs may be lost at this stage.," The vast majority of MBPs retain higher intensities, however some very dull MBPs may be lost at this stage." Objects are then investigated individually., Objects are then investigated individually. We impose a 3-à4e1a intensity variation limit ou each object. in order to fully separate MBPs from the eranules.," We impose a 3-sigma intensity variation limit on each object, in order to fully separate MBPs from the granules." Auv bright object possessing an inteusity range ereater than 3 signa is broken up iuto smaller objects. until the resulting structures comply with this condition.," Any bright object possessing an intensity range greater than 3 sigma is broken up into smaller objects, until the resulting structures comply with this condition." The detection of AIBPs is carried out by an exteuded version of the compass search (see Paper 1 8L3). and incorporates eradicut thresholding through| iuteusity profiling.," The detection of MBPs is carried out by an extended version of the compass search (see Paper 1 4.3), and incorporates gradient thresholding through intensity profiling." A one-ciaensional variation in intensity. across a selected region of the image. is first determined (see left panel of Fig. 6)).," A one-dimensional variation in intensity, across a selected region of the image, is first determined (see left panel of Fig. \ref{f2}) )." Intensity profiles for cach object are established for cight directions. svaunietrically positioned. about the objects ceutre-of-gravity.," Intensity profiles for each object are established for eight directions, symmetrically positioned about the objects centre-of-gravity." The stipulation that a lane must be in close proxiv to the MBP remains., The stipulation that a lane must be in close proximity to the MBP remains. The algorithin now actively searches for iuter-granular anes. bv using the turniug ]ος of the intensity xofiles. which are located at he centre of the lanes (left paucl of Fie. 6)).," The algorithm now actively searches for inter-granular lanes, by using the turning points of the intensity profiles, which are located at the centre of the lanes (left panel of Fig. \ref{f2}) )." Hence. tlie lanes are located from in-tu intensity profiling.," Hence, the lanes are located from in-situ intensity profiling." Each measurement is specific. iof only to individual objects. mt in every considered direction as well," Each measurement is specific, not only to individual objects, but in every considered direction as well." To establish cach turuimg point the one-dimensional line. from which intensity profiles are xocured. is extended until two stationary points exist iu he profile. i.c. where the rate of change im intensity (y) as a function of distauce (x) is zero. dv/dx = 0.," To establish each turning point the one-dimensional line, from which intensity profiles are procured, is extended until two stationary points exist in the profile, i.e. where the rate of change in intensity (y) as a function of distance (x) is zero, dy/dx = 0." A lait ou the distance between the turning poiuts eliminates arge objects. such as eranules.," A limit on the distance between the turning points eliminates large objects, such as granules." Cradicut thresholding is applied to all iuteusitv profiles o discutanele AIBPs from eranules., Gradient thresholding is applied to all intensity profiles to disentangle MBPs from granules. MIBPs retain a very steep intensity chanee in all directions. compared ο a inore gradual variation associated with erauules.," MBPs retain a very steep intensity change in all directions, compared to a more gradual variation associated with granules." The maxuuun eradieut is determined from amy part of a profile falling between the two turning points (see Fie. 6))., The maximum gradient is determined from any part of a profile falling between the two turning points (see Fig. \ref{f2}) ). The threshold eracdient is derived for each individual nuage through a selection of 5080 random objects. aud is calculated prior to the execution of the aleorithin.," The threshold gradient is derived for each individual image through a selection of 500 random objects, and is calculated prior to the execution of the algorithm." A threshold is determined by adding a Ligna value to the median eracdieut recorded for cach inage., A threshold is determined by adding a 1-sigma value to the median gradient recorded for each image. A significant improvement of the present aleoritlin concerns the erowing of MDPs., A significant improvement of the present algorithm concerns the growing of MBPs. À newly developed process provides au independent threshold range for cach object for accurate area represcutation., A newly developed process provides an independent threshold range for each object for accurate area representation. The algorithm rotates a one-dimensional line through 360 deerees. im 5 degree steps. about au objects centre of gravity.," The algorithm rotates a one-dimensional line through 360 degrees, in 5 degree steps, about an object's centre of gravity." luteusitv values at the turning points of the profiles. ic. the lanes. are acquired at cach angle.," Intensity values at the turning points of the profiles, i.e. the lanes, are acquired at each angle." To aid the accurate deteriunation of turning poiuts. the data is re-biuned by a factor of ten aud smoothed.," To aid the accurate determination of turning points, the data is re-binned by a factor of ten and smoothed." Thus a jurow iutereranular lane and the associated turning ont can be clearly ideuti&ed., Thus a narrow intergranular lane and the associated turning point can be clearly identified. The maxiumun turning »omt intensity is taken to provide a lower cutoff to our erowing algorithiu. wlile the upper bouncary is sot as he maxiuun iuteusitv level occurring within the seed reeion.," The maximum turning point intensity is taken to provide a lower cutoff to our growing algorithm, while the upper boundary is set as the maximum intensity level occurring within the seed region." The erowiug procedure mceludes auv conjoiniug κοιν that are above the lower threshold cutoff., The growing procedure includes any conjoining pixels that are above the lower threshold cutoff. The MBP area is deteriuned by totaling the nuuber of pixels within cach structure., The MBP area is determined by totaling the number of pixels within each structure. " Our sampling of 0.069"" pixel! xovides au rea of 2500 kuw?pixel !.", Our sampling of $''$ $^{-1}$ provides an area of 2500 $^2$ $^{-1}$. This procedure. demonstrated in Figure 7.. reproduces of MDPs to within a error of visually ideutifiod areas;," This procedure, demonstrated in Figure \ref{f3}, reproduces of MBPs to within a error of visually identified areas." Setting he lower intensity threshold as the brightest surrounding ane enforces an upper liit on the area of the MDPs. 1.6 MBPs are erown to their maxima dimensions.," Setting the lower intensity threshold as the brightest surrounding lane enforces an upper limit on the area of the MBPs, i.e MBPs are grown to their maximum dimensions." We use the MURAM code (Vógleretal.2005) to cary out simulations of radiative niagueto-convection m the upper solar convection zone and plotosphere., We use the MURaM code \citep{shelyag1} to carry out simulations of radiative magneto-convection in the upper solar convection zone and photosphere. This code uses a fourth-order. central difference scheme for conrputiug the spatial derivatives. aud a fourth-order.," This code uses a fourth-order, central difference scheme for computing the spatial derivatives, and a fourth-order," since 2002 (Danko2003).. aud our TTimer that uses National Centers for Euviroimental Predictio1 (NCEDP)'s Global Forecast (referasGEShereafter:seeSela1950:Whitakeretal.2008.foranoverviewofthe1jiodel) since 2005.,"since 2002 \citep{dan03}, and our 7Timer that uses National Centers for Environmental Prediction (NCEP)'s Global Forecast \citep[refer as GFS hereafter; see][for an overview of the model]{sel80,whi08} since 2005." " These ""direct-from-1inodel? forecasts only have decert spatial aud. vertical resolitiou. (for a comparison. tlie spatial resolution ol the GES inodel is aboiw LOkin. while the regiona moclel operating at MIXWC cau reach Lian). but it doesut require heavy. computation works eiher: the retrieval of the model fields cau be done with an Luteruet-couiected. Persoual Computer (PC) within a couple of miuues. Inaking it the most favorable aud probably the only choice wieu speedy Computer is not available auc the demand on forecast precision/accuracy is not critical."," These “direct-from-model” forecasts only have decent spatial and vertical resolution (for a comparison, the spatial resolution of the GFS model is about 40km, while the regional model operating at MKWC can reach 1km), but it doesn't require heavy computation works either: the retrieval of the model fields can be done with an Internet-connected Personal Computer (PC) within a couple of minutes, making it the most favorable and probably the only choice when speedy computer is not available and the demand on forecast precision/accuracy is not critical." Interestingly. although these services have been put into good use by private. ptblic aud even some professional observatories. there is no quauitative aud systematic uuderstaiicing ou how accurate the model fields are up to now.," Interestingly, although these services have been put into good use by private, public and even some professional observatories, there is no quantitative and systematic understanding on how accurate the model fields are up to now." For example. the ouly reported estimation of the accuracy oL cloud field forecast for a global mocel was done by Erasmus&Saraziu(2001) in 1992-1993. which suggested that ouly of clouds. uights could be identified with the European Centre or Mediuurrage Weather Forecasting modelIWE)®.," For example, the only reported estimation of the accuracy of cloud field forecast for a global model was done by \citet{era01} in 1992-1993, which suggested that only of cloudy nights could be identified with the European Centre for Medium-rage Weather Forecasting model." . This is age old considering there ad )een a number of signifiant upgrades of the glob:il models in the following decade., This is age old considering there had been a number of significant upgrades of the global models in the following decade. The fore‘ast or atinospheric seeing. ou the other haul is mo' complex. since it is related to vertical 7ine structure” of the atmospheric column ancl is not clirectly provided as part of output ina ly eloal uodel.," The forecast for atmospheric seeing, on the other hand, is more complex, since it is related to vertical “fine structure” of the atmospheric column and is not directly provided as part of output in any global model." " In general. there are two tracks lor atinospleric seeing forecast: ""nowcast track using 1ear 'eal-tine meteorological «)bservation profile combining with a statistical model al. 1995): or the “moctel” track eitlier using the derivatious of the Tatarski's formula (TatarskiLOSS) or the utuneric model proposed by Coulmanetal.(LOSG)."," In general, there are two tracks for atmospheric seeing forecast: “nowcast” track using near real-time meteorological observation profile combining with a statistical model \citep[such as][]{mur95}; or the “model” track either using the derivations of the Tatarski's formula \citep{tat61,cou88} or the numeric model proposed by \citet{cou86}." ". The firs traccis relatively intuitive aud is accurate enough in mauy occasions. but it las a very short lorecUs Tawe (usually less thau 21h) aud ieavily depeuds on the availability aud quality of the obse""vatloal data: for the second track. one would need to divide the atmospheric column into a goo« un of layers to gaiu a numeric siiulation close enough to the actual situation. which will agai1 'ecqui assistauce from a speedy computer."," The first track is relatively intuitive and is accurate enough in many occasions, but it has a very short forecast range (usually less than 24h) and heavily depends on the availability and quality of the observational data; for the second track, one would need to divide the atmospheric column into a good number of layers to gain a numeric simulation close enough to the actual situation, which will again require assistance from a speedy computer." In order to solve these shortcomines. takes advantages [rom both tracks and iutroduced the ANP model," In order to solve these shortcomings, \citet{tri06} takes advantages from both tracks and introduced the AXP model." With that moclel. [9] eo ueecs to divide the atmospheric column by a number close to that available in most globa iocdlels. and the consistency from the simulation of the ANP model to the actual situation is saislvi according to the authors.," With that model, one only needs to divide the atmospheric column by a number close to that available in most global models, and the consistency from the simulation of the AXP model to the actual situation is satisfying according to the authors." Tu all. these “direct-from-model” forecasts cau be a practical solulou for the observers without the ability to operate a high precision regional model by their own. and job to do is to assess how accurate these forec:ists are.," In all, these “direct-from-model” forecasts can be a practical solution for the observers without the ability to operate a high precision regional model by their own, and the job to do is to assess how accurate these forecasts are." We organize this paper as follow., We organize this paper as follow. In Section 2. we briefly outline the techuical details of," In Section 2, we briefly outline the technical details of the" io the onset of turbulence.,to the onset of turbulence. The disk pressure affects the problem in two a priori different wavs: first. (he turbulent transport picture presented in this paper requires the underlving Gurbulence to be subsonic (see also [haveefal. 2001)): second. turbulent velocity fIuctuations require a force to produce them. and only the pressure force is available to this purpose in the hydrodsnanmical case. independentlv of the details of the underlving mechanism which sustains (his turbulence.," The disk pressure affects the problem in two a priori different ways: first, the turbulent transport picture presented in this paper requires the underlying turbulence to be subsonic (see also \citealt{HUR01}) ); second, turbulent velocity fluctuations require a force to produce them, and only the pressure force is available to this purpose in the hydrodynamical case, independently of the details of the underlying mechanism which sustains this turbulence." The first. constraint is easily quantified: turbulent motions are subsonic if ο$1 (e; is (he sound speed): in accretion disks. e;O77. and from Eq. (15)).," The first constraint is easily quantified: turbulent motions are subsonic if $v_M/c_s \lesssim 1$ $c_s$ is the sound speed); in accretion disks, $c_s\sim \Omega H$ , and from Eq. \ref{freqcar}) )," this implies that [7=/3; (GE is the disk scale heieht)., this implies that $H \gtrsim l_M$ $H$ is the disk scale height). " To quantify the second constraint. note that a given fluctuating blob of size fy, undergoes a velocity change du~la;(redt2/dr)F4, over a üme-scale evvarflay~Q. because the coupling to the shear is (he source of turbulent motions at the largest scales: the largest pressure variation al any scale is 0P?/p~c. and requiring that the resulting pressure force al scale /4; is able to account lor the turbulent. velocity fhictuations ab (his scale again HZ.aj."," To quantify the second constraint, note that a given fluctuating blob of size $l_M$ undergoes a velocity change $\delta u\sim l_M (r d\Omega/dr)\sim l_M \Omega$ over a time-scale $\sim v_M/l_M\sim \Omega$, because the coupling to the shear is the source of turbulent motions at the largest scales; the largest pressure variation at any scale is $\delta P/\rho\sim c_s^2$, and requiring that the resulting pressure force at scale $l_M$ is able to account for the turbulent velocity fluctuations at this scale again $H \gtrsim l_M$." The turbulent scales (~ /3;) ave connected to the mean flow scales through the mechanism which sustains turbulence., The turbulent scales $\sim l_M$ ) are connected to the mean flow scales through the mechanism which sustains turbulence. In an accretion disk. only (wo such mean flow scales are available locally: A and r.," In an accretion disk, only two such mean flow scales are available locally: $H$ and $r$." The role of r has already been discussed: the role of the vertical scale height depends on the anisotropy of the mechanism which sustains turbulence., The role of $r$ has already been discussed; the role of the vertical scale height depends on the anisotropy of the mechanism which sustains turbulence. In (the absence of constraint on the nature of this mechanism for rotating shear flows. I will examine in (urn (wo limitingasstuplions:," In the absence of constraint on the nature of this mechanism for rotating shear flows, I will examine in turn two limitingassumptions:" "ooperties: however. it is also nearby. extremely bright. and. while it has no interpulse. it has detectable emission over more than 180"" of longitude.","properties; however, it is also nearby, extremely bright, and, while it has no interpulse, it has detectable emission over more than $180^\circ$ of longitude." The identification of these features in the three brightest pulsars with broad. pulse profiles suggests that such features may be common among pulsars with broad. profiles., The identification of these features in the three brightest pulsars with broad pulse profiles suggests that such features may be common among pulsars with broad profiles. As they are apparently seen over a substantial portion of the racio band and evolve little with frequeney. it would seen that they cannot be attributed to absorption in any usua sense.," As they are apparently seen over a substantial portion of the radio band and evolve little with frequency, it would seem that they cannot be attributed to absorption in any usual sense." Thus it would seem that they are either clue to some very puzzling aspect of the emission process or represent an equally puzzling obscuration of the emission along our sigh line., Thus it would seem that they are either due to some very puzzling aspect of the emission process or represent an equally puzzling obscuration of the emission along our sight line. While we cannot more than speculate about the causes of these features. à very novel mechanism is being suggestec by Wright (2003) in à companion paper.," While we cannot more than speculate about the causes of these features, a very novel mechanism is being suggested by Wright (2003) in a companion paper." Clearly. lew pulsars show emission so far from the main pulse or interpulse. so observing this feature in more pulsars will be very clilficul until the advent of more sensitive pulsar instruments such as the SILA.," Clearly, few pulsars show emission so far from the main pulse or interpulse, so observing this feature in more pulsars will be very difficult until the advent of more sensitive pulsar instruments such as the SKA." Llowever. future more sensitive multi-frequencevy observations of the pulsars discussed above. in addition to polarimetric observations. may vield more clues as to the origin of these unusual features.," However, future more sensitive multi-frequency observations of the pulsars discussed above, in addition to polarimetric observations, may yield more clues as to the origin of these unusual features." We thank Leszek Nowakowski and CGeoll Wright [or discussions ancl critical Comments on the manuscript., We thank Leszek Nowakowski and Geoff Wright for discussions and critical comments on the manuscript. One of us (JALR) wishes to acknowledge support. from US National Science. Foundation Crant AST 99-87654., One of us (JMR) wishes to acknowledge support from US National Science Foundation Grant AST 99-87654. . The Arecibo Observatory is. operated. by Cornell University under contract to the US NSE., The Arecibo Observatory is operated by Cornell University under contract to the US NSF. during clisruption owing to the host halo's tidal Ποιά and we have not vet accounted for this delormation.,during disruption owing to the host halo's tidal field and we have not yet accounted for this deformation. A comprehensive treatment of this deformation might be necessary to understand satellite disruption in detail., A comprehensive treatment of this deformation might be necessary to understand satellite disruption in detail. Lasthy. we also need a better understanding of the non-linear processes that occur during satellite evolution.," Lastly, we also need a better understanding of the non-linear processes that occur during satellite evolution." In this study. we characterised the Linear processes: understancing the detailed consequences of the non-linear processes is à daunting future task.," In this study, we characterised the linear processes; understanding the detailed consequences of the non-linear processes is a daunting future task." We should then finally be able to fully constrain the satellite disruption mechanism. which is an essential ingredient of galaxy formation and evolution.," We should then finally be able to fully constrain the satellite disruption mechanism, which is an essential ingredient of galaxy formation and evolution." This work was i part by NASA awards ATP NAGS-13308 ancl aveNAGS5-12038., This work was supported in part by NASA awards ATP NAGS-13308 and NAG5-12038. The effective potential of a spherical satellite as function of a satellite's radius (7) is determined by its sell-gravity. the external potential. and. the centrifugal force.," The effective potential of a spherical satellite as function of a satellite's radius $\bmath{r}$ ) is determined by its self-gravity, the external potential, and the centrifugal force." We set r=RRo where Ris the location relative to the host halo's centre anc Ro is the location of the satellite’s centre relative to the host halo's centre.," We set $\bmath{r} = \bmath{R} - \bmath{R_{0}}$ where $\bmath{R}$ is the location relative to the host halo's centre and $\bmath{R_{0}}$ is the location of the satellite's centre relative to the host halo's centre." The acceleration in the satellite's frame. P. is difference between the acceleration. R. and the ellective acceleration of the satellite. Ro. inthe host frame.," The acceleration in the satellite's frame, $\ddot{\bmath{r}}$ , is difference between the acceleration, $\ddot{\bmath{R}}$, and the effective acceleration of the satellite, $\ddot{\bmath{R_{0}}}$ , inthe host frame." The quantities R and Ho are where (1) is the total potential on the particle and Ω is angular velocity of the satellite., The quantities $\ddot{\bmath{R}}$ and $\ddot{\bmath{R_{0}}}$ are where $\Phi_{tot}(\bmath{R})$ is the total potential on the particle and $\bmath{\Omega}$ is angular velocity of the satellite. " Phe quantity bu(R)=o,LuGRO|uuuCR). where (8) is the host halo potential ancl @..,,CR) is the potential of the satellite."," The quantity $\Phi_{tot}(\bmath{R}) = \Phi_{host}(\bmath{R}) + \Phi_{sat}(\bmath{R})$, where $\Phi_{host}(\bmath{R})$ is the host halo potential and $\Phi_{sat} (\bmath{R})$ is the potential of the satellite." " Using P=—R Ro. the equation of motion in the satellite frame becomes Because we assume a circular orbit. (Πο) is a constant: V«b,(R)-Vu(re) and. VO).Ro)su Vo,Ro)."," Using $\ddot{\bmath{r}} = \ddot{\bmath{R}} - \ddot{\bmath{R_{0}}}$ , the equation of motion in the satellite frame becomes Because we assume a circular orbit, $\Phi_{sat}(\bmath{R_{0}})$ is a constant; $\nabla \Phi_{sat}(\bmath{R}) \rightarrow \nabla \Phi_{sat}(\bmath{r})$ and $\nabla \Phi_{tot} (\bmath{R_{0}}) \rightarrow \nabla \Phi_{host}(\bmath{R_{0}})$ ." The second and third terms in equation CX3)) can be further simplified using a Taylor expansion. The last term in equation 2 (X3)) is the centrifugal term.," The second and third terms in equation \ref{eq:r_Pot}) ) can be further simplified using a Taylor expansion, The last term in equation \ref{eq:r_Pot}) ) is the centrifugal term." Assuming that the orbital plane is equatorial with QO=¢ and r— (rg). we have lor generating initial conditions in re[sec:method. and our idealised models inrefsecimiassloss.. we will approximate equation (A5)) with a spherical average where à is between0 and 1.," Assuming that the orbital plane is equatorial with ${\hat\Omega}={\hat z}$ and $\bmath{r} = (x,y,x)$ , we have For generating initial conditions in \\ref{sec:method} and our idealised models in, we will approximate equation \ref{eq:centri0}) ) with a spherical average where $\alpha$ is between$0$ and $1$." Using this expansion. equation ((X3)) becomes Finally. a satellitesellective potential as function of r using equation (AT)) can be written as:," Using this expansion, equation \ref{eq:r_Pot}) )becomes Finally, a satellite'seffective potential as function of $\bmath{r}$ using equation \ref{eq:r_Pot2}) ) can be written as:" 1997).,. . Depeucdiug on he epocl axd degree of reionization. we expect an overall (somewhat scale-dependent) camping of primary leuperature anisotropies iu tlie CMB. ile generation of new temperature auisotroples o1 the appr¢ypriate scales through the elects of coud-order processes aud the degree of inhomoeeneltv in ile reionizaion process Ixnoxetal. 1998).. aud finally. the creation of a lew polarization signal. as the )'OCeSS Thomso1 scatterlug introduces some degree of »olarizatlol even for incident racdiatior ial is »olarize.," Depending on the epoch and degree of reionization, we expect an overall (somewhat scale-dependent) damping of primary temperature anisotropies in the CMB, the generation of new temperature anisotropies on the appropriate scales through the effects of second-order processes and the degree of inhomogeneity in the reionization process \citep{grhu,ksd98}, and finally, the creation of a new polarization signal, as the process of Thomson scattering introduces some degree of polarization even for incident radiation that is unpolarized." " Scattering [rom the ionuized IGM. or the rep""OC‘essing of starlight into [ar-irare avelenetli4. by dust. fo1ued [rom early superuovae (SNe). will also catse the CMB to dergo sole spect‘al clistoiion (Loeb&Haiman1997): this can be measure experimentaM7 ‘ough the Compt«)l y-paranieer."," Scattering from the ionized IGM, or the reprocessing of starlight into far-infrared wavelengths by dust formed from early supernovae (SNe), will also cause the CMB to undergo some spectral distortion \citep{lh97}; this can be measured experimentally through the Compton $y$ -parameter." These aud other observational siguatures tlat have the poteial to COLstlraln tje ορού. aid lence possibly tle sowce. of reiouigation have been exaiminec in the literature (see Haimanu&Ixuox(1999) [or a sumuiary).," These and other observational signatures that have the potential to constrain the epoch, and hence possibly the source, of reionization have been examined in the literature (see \citet{hk99} for a summary)." A inoxel of reionizatiou is therefore. in priiciple. eimiueitly testable.," A model of reionization is therefore, in principle, eminently testable." Current detecions of the first Doppler peak in the CMB's temperatwe anlsotropies limit the total optica clewth to elecron scatter]ug. Pe. such as αν arise [rom reknization. o be τιXo] (Scottetαἱ.L995).," Current detections of the first Doppler peak in the CMB's temperature anisotropies limit the total optical depth to electron scattering, $\tau_{e}$, such as may arise from reionization, to be $\tau_e \la 1$ \citep{sswhite}." Futwe experiments such as the or the GSLRTF) may detect the high-z sies of rei)izing sources (see. e.g.. )))). ora least exclude currently viable c:ukcdidates. while ipcoming CMB experiments sucl as MAP or thePLANCK surveyor can uieasle 7; o very high accuracies by couüning iufo‘ation Crom teiiperature anisotroples aud polarizatLol in the ChB.," Future experiments such as the or the $SIRTF$ ) may detect the $z$ sites of reionizing sources (see, e.g., \citet{hlngst}) ), or at least exclude currently viable candidates, while upcoming CMB experiments such as $MAP$ or the surveyor can measure $\tau_{e}$ to very high accuracies by combining information from temperature anisotropies and polarization in the CMB." The optimistic [orospects for testing reionization aud tle increasing multiwaveleneth «jew of the high-z universe lave gelleraed a large body of work ou reiouizaion models in the last [ew years. whose tecliniqles fall broadly into uumerical (Cinecdit2000:Chit|&Ostriker&Ostriker1997:CeL&1993) ΟΥ senLanalytie methods (Hainan&Loeb1997.19085a:Tegmarketal.1991:Valageas&Silk 1999).," The optimistic prospects for testing reionization and the increasing multiwavelength view of the $z$ universe have generated a large body of work on reionization models in the last few years, whose techniques fall broadly into numerical \citep{gn99,co99,go97,cenost93} or semi-analytic methods \citep{hl97, hl98,tsb94,valsilk}." . The foruer have the acvattage of beiug able t«) track the details of radiative transfer. incorporating the cluupinuess of tie ICM. ancl the essentially development of iouizing sources. and. perhaJs uost impo‘tantly. describing the of relonization lua quantitative fashion.," The former have the advantage of being able to track the details of radiative transfer, incorporating the clumpiness of the IGM and the essentially non-uniform development of ionizing sources, and, perhaps most importantly, describing the of reionization in a quantitative fashion." The advailage of semi-alalytic ayproaches is their inherent [lexibiity and ability to probe the parameter space of a reioniz:ion mocel at will. which is of value elven. je Maly 1iput c«»uological aud astropliysica paralneter 1volved.," The advantage of semi-analytic approaches is their inherent flexibility and ability to probe the parameter space of a reionization model at will, which is of value given the many input cosmological and astrophysical parameters involved." Fe “astroplissical sources. the process of relouizatjon ls sely related o the evolution of struct wein the iniverse. and could resut in feedbacx effects fcYE ibsequeut object formatiou (see. e.g..ο) Ciardietal. (2000))).," For astrophysical sources, the process of reionization is strongly related to the evolution of structure in the universe, and could result in feedback effects for subsequent object formation (see, e.g., \citet{ciardi}) )." Of the current theories of structure lation. variants of the st:uiarc cold da ‘kimatter (8CDMAIL) model are cous to ideredbe 'elatively s‘cessful at deseribiug the observed universe.," Of the current theories of structure formation, variants of the standard cold dark matter (sCDM) model are considered to be relatively successful at describing the observed universe." This picture postulates a critical deusity universe. wit cold dark natter domihating the mater content: structures. made up of baryous aud CDM. orieinated iu p‘imordial adiabatic fluctuatious aud evolvedsubsequently tποσα gravitational iustaülity.," This picture postulates a critical density universe, with cold dark matter dominating the matter content; structures, made up of baryons and CDM, originated in primordial adiabatic fluctuations and evolvedsubsequently through gravitational instability." Current moclificatious lo this paracligua include. e.g.. the addition of a cosmological constant.," Current modifications to this paradigm include, e.g., the addition of a cosmological constant." viscous time-scale.,viscous time-scale. The Iluctuations propagate inward. with viscous velocity. through the dise and. finally modulate the X-ray emission at the centre., The fluctuations propagate inward with viscous velocity through the disc and finally modulate the X-ray emission at the centre. As the local time-scales clecrease with μαας. the more centrally concentrated emission contains the shortest time-scale Wuctuations. seen especially in the N-ravs.," As the local time-scales decrease with radius, the more centrally concentrated emission contains the shortest time-scale fluctuations, seen especially in the X-rays." Phe resulting light curves for this model have a 1/f power spectrum. bending to steeper slopes above a characteristic frequency. which is. directly related to the shortest variability time-scales included. ic. the viscous time-scale at the inner edee of the accretion flow.," The resulting light curves for this model have a $1/f$ power spectrum, bending to steeper slopes above a characteristic frequency, which is directly related to the shortest variability time-scales included, i.e., the viscous time-scale at the inner edge of the accretion flow." In a standard cise (Shakura&Svunvaey1973)... this characteristic time-scale is proportional to the mass of the black hole and is a function of the disc thickness (////?) and viscosity (à) parameters.," In a standard disc \citep{shakura}, this characteristic time-scale is proportional to the mass of the black hole and is a function of the disc thickness $H/R$ ) and viscosity $\alpha$ ) parameters." We incorporated reprocessing into the implementation of this model described in Arévalo&Uttley(2006)... by adding an X-ray source above the disc and on the axis of symmetry.," We incorporated reprocessing into the implementation of this model described in \citet{arevalouttley06}, by adding an X-ray source above the disc and on the axis of symmetry." We assumed that the optical [lux is emitted thermally by the dise. with local emissivity proportional to the radial gravitational energy. release., We assumed that the optical flux is emitted thermally by the disc with local emissivity proportional to the radial gravitational energy release. This emissivity profile is first modulated by the propagating accretion rate fluctuations and then also by the variable Dux received from the N-rayv source., This emissivity profile is first modulated by the propagating accretion rate fluctuations and then also by the variable flux received from the X-ray source. We incorporate the travel time of the accretion rate fluctuations to the central X-ray emitting region and the light travel time of the X-rays to the different annuli in the accretion disc., We incorporate the travel time of the accretion rate fluctuations to the central X-ray emitting region and the light travel time of the X-rays to the different annuli in the accretion disc. For simplicity. only a face-on viewing angle was considered.," For simplicity, only a face-on viewing angle was considered." We used the observed X-ray. [lux and a distance of 271 Alpe as above. to obtain the N-rav. luminosity.," We used the observed X-ray flux and a distance of 271 Mpc as above, to obtain the X-ray luminosity." The black role mass of thas not been measured but. using the lower limit on the power spectrum. break time-scale of Summons ct ((in yep.)," The black hole mass of has not been measured but, using the lower limit on the power spectrum break time-scale of Summons et (in prep.)" and the relation between this quantity and. black vole mass. derived in Mellardyetal.(2006)... we derived a minimum mass of several times 107AZ...," and the relation between this quantity and black hole mass derived in \citet{mchardynat}, we derived a minimum mass of several times $10^8M_\odot$." We fixed the mass of he black hole to δLO°AL. and varied dise thickness and/or o parameter to obtain the correct. X-ray power spectrum rom the simulated. X-ray. light curve. obtaining a value of (11/I)0—0.08 at the innermost racius.," We fixed the mass of the black hole to $8\times 10^8 M_\odot$ and varied disc thickness and/or $\alpha$ parameter to obtain the correct X-ray power spectrum from the simulated X-ray light curve, obtaining a value of $(H/R)^2\alpha=0.08$ at the innermost radius." As. in the mocel. he tine-scales erow with black hole mass and decrease with a. these parameters are largely. degenerate so we only jicked one set that fits the data but note that other pairs would work equally well.," As, in the model, the time-scales grow with black hole mass and decrease with $\alpha$, these parameters are largely degenerate so we only picked one set that fits the data but note that other pairs would work equally well." We then fixed these parameters and varied the height of the X-ray source and intrinsic mean disc accretion rate. to produce dillerent realisations of the optical light curves.," We then fixed these parameters and varied the height of the X-ray source and intrinsic mean disc accretion rate, to produce different realisations of the optical light curves." One possible geometry for the accretion. disc/corona system is a ecometrically thin aceretion disc that. thickens towards the centre ο produce a geometricallv-thick. optically-thin corona.," One possible geometry for the accretion disc/corona system is a geometrically thin accretion disc that thickens towards the centre to produce a geometrically-thick, optically-thin corona." As the thickening of the Low produces shorter time-scale fluctuations at the same radius. the accretion rate that linally moclulates the N-ravs can have luctuations on time-scales much shorter than the optical emission from the truncated thin disc.," As the thickening of the flow produces shorter time-scale fluctuations at the same radius, the accretion rate that finally modulates the X-rays can have fluctuations on time-scales much shorter than the optical emission from the truncated thin disc." " We kept the thickness ο radius ratio 12/2 constant down to a truncation radius of ry=1LOR,. with a value of (4(τα= 0.04. this produces viscous fluctuations up to time-scales of 300 days at. the runcation radius."," We kept the thickness to radius ratio $H/R$ constant down to a truncation radius of $r_t=10R_g$, with a value of $(H/R)^2\alpha=0.04$ , this produces viscous fluctuations up to time-scales of 300 days at the truncation radius." " Inside ry. we allowed 71 to grow with decreasing radius as (11τα=0.0467/r)3 to reach the desired. value of (H/Ra=008 at r=6A, producing luctuations on time-scales down to 5 cays."," Inside $r_t$, we allowed $H/R$ to grow with decreasing radius as $(H/R)^2\alpha=0.04(r_t/r)^{1.4}$ to reach the desired value of $(H/R)^2\alpha=0.08$ at $r=6R_g$ producing fluctuations on time-scales down to 5 days." We allowed he X-rav source to be higher than the top of the thick disc. but assumed. that it was modulated. by the thick low fluctuations.," We allowed the X-ray source to be higher than the top of the thick disc, but assumed that it was modulated by the thick flow fluctuations." " Phe X-ray source height. however. had to be kept small at 46 2, to. produce sullicientIy. little reprocessing to reproduce the small relative size of the rapid optical Luetuations."," The X-ray source height, however, had to be kept small at 4–6 $R_g$ to produce sufficiently little reprocessing to reproduce the small relative size of the rapid optical fluctuations." Figure 10. shows 500 day long simulated light. curves., Figure \ref{sim_lcs} shows 500 day long simulated light curves. The top panel represents the [uctuations in the innermost region. corresponding to the X-ray light curve. the bottom panel shows a D band light curve modulated. onlv by accretion rate Iuctuations and the middle panel shows this same B light curve when the effect of reprocessing of N-ravs is Incorporated.," The top panel represents the fluctuations in the innermost region, corresponding to the X-ray light curve, the bottom panel shows a B band light curve modulated only by accretion rate fluctuations and the middle panel shows this same B light curve when the effect of reprocessing of X-rays is incorporated." As expected. the resulting X-ray and optical ight curves are well correlated.," As expected, the resulting X-ray and optical light curves are well correlated." Figure 11 demonstrates he effects of reprocessing on the DCE. the dots show the DCE between the simulated X-ray and B band σαι curves if reprocessing is switched olf (ie. between the light curves shown in the top and bottom panels in Fig. 10)).," Figure \ref{dcf_X_B} demonstrates the effects of reprocessing on the DCF, the dots show the DCF between the simulated X-ray and B band light curves if reprocessing is switched off (i.e. between the light curves shown in the top and bottom panels in Fig. \ref{sim_lcs}) )," the DB xuxd. leacs the N-rays by approximately 50 days. which in his case is the travel time of the accretion Lluctuations [rom he main D emitting region to the centre.," the B band leads the X-rays by approximately 50 days, which in this case is the travel time of the accretion fluctuations from the main B emitting region to the centre." IH reprocessing is switched on. so that the rapid. X-ray Hares are imprinted as small optical fluctuations in the same light curve used above (shown in the middle panel of Fig. 10)).," If reprocessing is switched on, so that the rapid X-ray flares are imprinted as small optical fluctuations in the same light curve used above (shown in the middle panel of Fig. \ref{sim_lcs}) )," the DCE peak shifts o à lag of zero days. represented by the crosses in Fig. 1..," the DCF peak shifts to a lag of zero days, represented by the crosses in Fig. \ref{dcf_X_B}." The exact shape of the DCE between B and. X-ray light curves changes with cifferent realisations of the simulation even when exactly the same setup and parameters are used., The exact shape of the DCF between B and X-ray light curves changes with different realisations of the simulation even when exactly the same setup and parameters are used. In Fig., In Fig. 12 we show a few examples of such DCTs. caleulated for cillerent light curve segments. cach 500 days long.," \ref{dcf_X_B_multi} we show a few examples of such DCFs, calculated for different light curve segments, each 500 days long." Given the changes in DCL peak height and direction of asymmetry. we cannot draw any conclusions [roni these structures in either the simulated or observed: DCEs.," Given the changes in DCF peak height and direction of asymmetry, we cannot draw any conclusions from these structures in either the simulated or observed DCFs." The amplitude of short term Ductuations is strongly reduced in the optical compared to the N-ravs ancl higher energy opticalbands cdisplav lareer variability than lower energy ones., The amplitude of short term fluctuations is strongly reduced in the optical compared to the X-rays and higher energy opticalbands display larger variability than lower energy ones. The flux-Iux relation of the simulated. B and, The flux-flux relation of the simulated B and "differential sensitivity curve (that is, its energy dependence) is determined.","differential sensitivity curve (that is, its energy dependence) is determined." " We found that by using the effective area of the MAGIC telescope at its trigger level as Ay (MAGICCol-laboration2011) 5,, we can reproduce well the shape of the official sensitivity curve of CTA at < 200-300 GeV, where the LSTs dominate the sensitivity."," We found that by using the effective area of the MAGIC telescope at its trigger level as $A_\gamma$ \citep{MAGIC2011} , we can reproduce well the shape of the official sensitivity curve of CTA at $\lesssim$ 200–300 GeV, where the LSTs dominate the sensitivity." " Therefore as a functional form of A, at zenith angle θροι=20°, we adopt the MAGIC effective area at the trigger level in our simulation."," Therefore as a functional form of $A_\gamma$ at zenith angle $\theta_{\rm{zen}}=20^\circ$, we adopt the MAGIC effective area at the trigger level in our simulation." " We normalize A, introducing a factor of fa, where fa=1 means that A, corresponds to the effective area at the trigger level of MAGIC."," We normalize $A_\gamma$ introducing a factor of $f_A$, where $f_A=1$ means that $A_\gamma$ corresponds to the effective area at the trigger level of MAGIC." " For any value of fa, we can fit the sensitivity curve of our model to the public one with the normalization of dRyg/dE."," For any value of $f_A$, we can fit the sensitivity curve of our model to the public one with the normalization of $dR_{\rm bg}/dE$." " In Figure 3,, the official differential sensitivity of CTA is shown as the black dotted curve for the exposure time of 0.5 h, where contributions from all types of telescopes (i.e., LSTs, MSTs, and SSTs) are included, though LSTs dominate the sensitivity for E< 200-300 GeV. Because the sensitivity for this exposure time is limited by the statistical significance (see the detection condition (2) described in the last part of Section 3.2)) at <300 GeV, we can determine the normalization of dRpg/dE as a function of fa."," In Figure \ref{fig:toy_model,0.5h}, the official differential sensitivity of CTA is shown as the black dotted curve for the exposure time of 0.5 h, where contributions from all types of telescopes (i.e., LSTs, MSTs, and SSTs) are included, though LSTs dominate the sensitivity for $E\lesssim$ 200–300 GeV. Because the sensitivity for this exposure time is limited by the statistical significance (see the detection condition (2) described in the last part of Section \ref{subsec:detect_conditionCTA}) ) at $<300$ GeV, we can determine the normalization of $dR_{\rm bg}/dE$ as a function of $f_A$ ." " In the case of fa=1, we need Rpg~0.34 Hz for fitting, where Rpg is calculated by the integration of dRpg/dE from 20 GeV to 20 TeV. The sensitivity curve of our model at Ozen=20° is shown as the red solid curve in Figure 3.."," In the case of $f_A=1$, we need $R_{\rm bg}\simeq 0.34$ Hz for fitting, where $R_{\rm bg}$ is calculated by the integration of $dR_{\rm bg}/dE$ from 20 GeV to 20 TeV. The sensitivity curve of our model at $\theta_{\rm zen}=20^\circ$ is shown as the red solid curve in Figure \ref{fig:toy_model,0.5h}." One can see that the two curves are similar., One can see that the two curves are similar. This figure shows the photon energy up to 300 GeV since we calculate the photon counts below this energy in our simulation., This figure shows the photon energy up to 300 GeV since we calculate the photon counts below this energy in our simulation. " Indeed, the GRB spectrum above ~ 100 GeV is expected to be severely attenuated by the EBL, so that our artificial cutoff at this energy does not affect the rate estimate."," Indeed, the GRB spectrum above $\sim$ 100 GeV is expected to be severely attenuated by the EBL, so that our artificial cutoff at this energy does not affect the rate estimate." " Above 200—300 GeV, the MSTs and the SSTs have better sensitivity compared to the LSTs, so that the sensitivity of our model deviates from the total array sensitivity."," Above 200--300 GeV, the MSTs and the SSTs have better sensitivity compared to the LSTs, so that the sensitivity of our model deviates from the total array sensitivity." " In order to keep the two sensitivity curves consistent with each other for arbitrary value of fa, we need Rpg=0.34fà Hz to normalize dRyg/dE considering the detection condition (2)."," In order to keep the two sensitivity curves consistent with each other for arbitrary value of $f_A$, we need $R_{\rm bg} = 0.34f_A^2$ Hz to normalize $dR_{\rm bg}/dE$ considering the detection condition (2)." " Although the value of fa influences the condition (1) and (3), it varies the expected detection rate only a little (see Section 4.4))."," Although the value of $f_A$ influences the condition (1) and (3), it varies the expected detection rate only a little (see Section \ref{subsec:dependence2}) )." " In our fiducial case, we assume fa=1."," In our fiducial case, we assume $f_A=1$." " As @zen increases, the shower maximum height gets higher and Cherenkov light is more absorbed, so that the area of light pool becomes large, while its density becomes low."," As $\theta_{\rm zen}$ increases, the shower maximum height gets higher and Cherenkov light is more absorbed, so that the area of light pool becomes large, while its density becomes low." " In order to take into account the dependence of the effective area on the zenith angle, we use the following form: where E'=E(cos@zen)$, €=1.7 and ¢= (Aharonianetal.1999)."," In order to take into account the dependence of the effective area on the zenith angle, we use the following form: where $E'\equiv E(\cos \theta_{\rm{zen}})^\zeta$, $\xi\,=\,1.7$ and $\zeta\,=\,2.4$ \citep{Aharonian1999}." ". Also for the angular resolution ὁ, we multiply by a factor of (E’(@:en)/E’(20°))~1/?."," Also for the angular resolution $\phi$, we multiply by a factor of $(E'(\theta_{\rm zen})/E'(20^\circ))^{-1/2}$." " 'The differential count rate of gamma rays becomes maximum at ~60(cosOzen)~$ GeV in our model for a source with its photon index of —2, neglecting the EBL attenuation."," The differential count rate of gamma rays becomes maximum at $\simeq 60~(\cos \theta_{\rm{zen}})^{-\zeta}$ GeV in our model for a source with its photon index of $-2$, neglecting the EBL attenuation." " We set Ej, which is the low-energy end of the integration for the photon counts, at an energy lower than this as As we describe in Section 4.4,, the exponent of cosine, —3.3, has only a small influence on the detection rate."," We set $E_{\rm low}$, which is the low-energy end of the integration for the photon counts, at an energy lower than this as As we describe in Section \ref{subsec:dependence2}, the exponent of cosine, $-3.3$, has only a small influence on the detection rate." " In this section, we show the results of our Monte Carlo simulation on the GRB detection rate with the LSTs, which are obtained under the assumptions described in Section 2. and Section 3.."," In this section, we show the results of our Monte Carlo simulation on the GRB detection rate with the LSTs, which are obtained under the assumptions described in Section \ref{sec:GRB_properties} and Section \ref{sec:GRB_obs_cond_rate}. ." Following is a summary of the simulation process., Following is a summary of the simulation process. " First, in order to generate intrinsic GRB samples, we randomly give Πρ, z, a and ϐ according to the distributions described in Section 2.1.."," First, in order to generate intrinsic GRB samples, we randomly give $L_{\rm p}$, $z$, $\alpha$ and $\beta$ according to the distributions described in Section \ref{sebsec:prompt}." " Using several correlations with respect to the prompt emission properties, we determine Γρ, Eiso, Lave, and Too from Ly; for the first two parameters, the deviation from the best fit line of the correlation is given by a Gaussian random variable."," Using several correlations with respect to the prompt emission properties, we determine $E_{\rm p}$, $E_{\rm iso}$, $L_{\rm ave}$, and $T_{90}$ from $L_{\rm p}$; for the first two parameters, the deviation from the best fit line of the correlation is given by a Gaussian random variable." " Then, we can calculate the prompt and afterglow gamma-ray flux arriving at the Earth for each generated burst taking into account the EBL attenuation."," Then, we can calculate the prompt and afterglow gamma-ray flux arriving at the Earth for each generated burst taking into account the EBL attenuation." " Second, we set the trigger and the localization conditions to determine the detected and localized events."," Second, we set the trigger and the localization conditions to determine the detected and localized events." " The former is given in terms of the peak photon flux, while the latter is given by the probability of sufficient localization as a function of the fluence (deduced in Section 3.1))."," The former is given in terms of the peak photon flux, while the latter is given by the probability of sufficient localization as a function of the fluence (deduced in Section \ref{subsec:GBMlocalization}) )." Then it is judged whether each sample is localized sufficiently well and whether it is in the FOV of the LSTs after slewing to the best position., Then it is judged whether each sample is localized sufficiently well and whether it is in the FOV of the LSTs after slewing to the best position. " Finally, at the stage of follow-up observation by LSTs, Tuclay is given by a log-normal distribution, and θ,οι is isotropically distributed independently of Taciay, where we assume a 10 duty cycle and O0zen<60° as the observational criteria."," Finally, at the stage of follow-up observation by LSTs, $T_{\rm delay}$ is given by a log-normal distribution, and $\theta_{\rm zen}$ is isotropically distributed independently of $T_{\rm delay}$, where we assume a $10$ duty cycle and $\theta_{\rm zen}<60^\circ$ as the observational criteria." We evaluate the detection conditions described in Section 9.2 on each sample taking into account the zenith angle dependence ofthe array performance (as shown in Section 3.3))., We evaluate the detection conditions described in Section \ref{subsec:detect_conditionCTA} on each sample taking into account the zenith angle dependence ofthe array performance (as shown in Section \ref{subsec:LSTs}) ). " In this simulation, we consider only one array site and the GBM alerts (with its triggerrate of 250 yr!) alone."," In this simulation, we consider only one array site and the GBM alerts (with its triggerrate of $250$ $^{-1}$ ) alone." " We limit our simulation to the GBM bursts with sec and z< 5, the fraction ofwhich is ~80 of all"," We limit our simulation to the GBM bursts with $T_{90}>2$ sec and $z<5$ , the fraction ofwhich is $\sim 80$ of all" GD165D came to represent (he first new class of main sequence stars in 100 vears. a class believed to retain both stellar and substellar objects over the age of the Galaxy (Burrowsοἱal.1999:Ixirkpatricket2000:Burgasserοἱ 2003).,"GD165B came to represent the first new class of main sequence stars in 100 years, a class believed to retain both stellar and substellar objects over the age of the Galaxy \citep{bur97,kir99,kir00,burg03}." . Since that lime. over two hundred and fifty objects of Chis spectral type have been discovered.," Since that time, over two hundred and fifty objects of this spectral type have been discovered." Rather ubiquitous in the field and in voung clusters. L dwarls have remained relatively infrequent companions to stars with Af=0.2.V. (Zuckerman&Becklin1937.1992:Schroederetal.Carthy&Zuckerman 2004).," Rather ubiquitous in the field and in young clusters, L dwarfs have remained relatively infrequent companions to stars with $M\ga0.2M_{\odot}$ \citep{zuc87,zuc92,sch00,opp01,hin02,far03, mcc04}." . Understanding (he overall statistics and individual properties of the lowest mass companion systems is important for both star and planet formation., Understanding the overall statistics and individual properties of the lowest mass companion systems is important for both star and planet formation. " This paper describes the properties of a very cool companion to the white dwarI GD1400 (WD0145-221. 0147™21.8.—21*56'51.4"" Eq."," This paper describes the properties of a very cool companion to the white dwarf GD1400 (WD0145-221, ${\rm 01^h\ 47^m\ 21.8^s, -21\arcdeg\ 56'\ 51.4''}$ Eq." J2000)., J2000). " Spectroscopic and photometric evidence is presented that indicates the presence of a low mass. L tvpe chwarl within 0.3"" of the primary."," Spectroscopic and photometric evidence is presented that indicates the presence of a low mass, L type dwarf within $0.3''$ of the primary." Optical V. band data were taken 3 January 2004 with the CCD Camera on the Nickel 1 meter telescope at Lick Observatory., Optical $V$ band data were taken 3 January 2004 with the CCD Camera on the Nickel 1 meter telescope at Lick Observatory. GDIJ00 and a nearby Tycho 2 catalog star were both observed [or a total of 3 minutes. each in 3 separate 1 minute exposures. vielding SNR—240 on GD1400 and SNR—7000 on the V=11.24 mag calibrator Dessell 2000)..," GD1400 and a nearby Tycho 2 catalog star (TYC4688-111-1) were both observed for a total of 3 minutes, each in 3 separate 1 minute exposures, yielding ${\rm SNR}\sim240$ on GD1400 and ${\rm SNR}\sim7000$ on the $V=11.24$ mag calibrator \citep{hog00,bes00}." " Conditions were clear but with poor seeing (6~ 4.5"") that appeared lo remain relatively stable between target and calibrator observations.", Conditions were clear but with poor seeing $\theta\sim4.5''$ ) that appeared to remain relatively stable between target and calibrator observations. The individual frames were bias subtracted. flat [ielded. registered and then averaged to create a single reduced image upon which to perform photometric measurements.," The individual frames were bias subtracted, flat fielded, registered and then averaged to create a single reduced image upon which to perform photometric measurements." " Photometry was executed with 10"" and 20” diameter apertures on both GDIJ00. and calibrator. including telluric exünction corrections. producing consistent results to within 0.01 mag."," Photometry was executed with $10''$ and $20''$ diameter apertures on both GD1400 and calibrator, including telluric extinction corrections, producing consistent results to within $0.01$ mag." The error in the measured flux of each object was <0.01 mag., The error in the measured flux of each object was $<0.01$ mag. The published uncertainty in (he magnitude of TYCA633-111-1 is 0.12 mag (logetal.2000)., The published uncertainty in the magnitude of TYC4688-111-1 is 0.12 mag \citep{hog00}. . The result for GD1400 is V=14.8540.12 mag., The result for GD1400 is $V=14.85\pm0.12$ mag. GD1400 was observed on 16 January 2004. using the Near Infrared Spectrograph (NIRSPEC. McLean et 11998) at Keck Observatory.," GD1400 was observed on 16 January 2004, using the Near Infrared Spectrograph (NIRSPEC, McLean et 1998) at Keck Observatory." NIRSPEC was used in low resolution mode with, NIRSPEC was used in low resolution mode with AIST is a nearby. giant. elliptical galaxy (distance = 16 Alpe “Voury (1991)]])possessing a one-siceck jet with projected distance z 2 Ixpc and bright in radio. optical and. X-rav energies.,"M87 is a nearby giant elliptical galaxy (distance = $16$ Mpc \cite{tonry}] ])possessing a one-sided jet with projected distance $\approx$ 2 Kpc and bright in radio, optical and X-ray energies." The jet structure is very well. studied. in radio (Owenetal.(1989):etal. (199629). I. (Perlmanctal.(2001):Sparks (1996))) ancl optical (Aleisenheimerctal.(1996):Sparksetal. (1996))) bands.," The jet structure is very well studied in radio \cite{owen,bire,sparks}) ), IR \cite{perl01,sparks}) ) and optical \cite{meis,sparks}) ) bands." Prior toChandra. AIST jet was not very well studied at X-ray energies due to the limited angular resolution of earlier. X-ray telescopes. and ROSAT.," Prior to, M87 jet was not very well studied at X-ray energies due to the limited angular resolution of earlier X-ray telescopes, and ROSAT." However. due to its better spatial resolution is able to resolve many fainter knots of AIST jet which are observed: only in radio ancl optical bands earlier.," However, due to its better spatial resolution is able to resolve many fainter knots of M87 jet which are observed only in radio and optical bands earlier." Moreover. the position of these knots in) X-ray energies are nearly coincident with their racio/optical counterparts(Perlmanetal.(2001):Perlman&Wilson (2005))).," Moreover, the position of these knots in X-ray energies are nearly coincident with their radio/optical \cite{perl01,perl05}) )." Also AIST is the only racliogalaxy (other. than ConA(Sreckumarοἱal. (L999)))) which is detected in GeV- enereies(Aharonianetal. (2003)))., Also M87 is the only radiogalaxy (other than \cite{sree}) )) which is detected in GeV-TeV \cite{ahar03}) ). Initially it was not well understood whether the TeV. eanima-rav emission region is close to nucleus(Georganopoulosetal. (2005))) or from the knot HIST-L(Stawarzetal. (2006)))., Initially it was not well understood whether the TeV gamma-ray emission region is close to \cite{georg}) ) or from the knot \cite{staw06}) ). However the detection of AIST by LESS confirmed the high energy emission from the region close to the nucleus(Abaronianοἱal. (2006)))., However the detection of M87 by HESS confirmed the high energy emission from the region close to the \cite{ahar06}) ). Reeent VERITAS detection of VILE emission from AIST (Benbow (2008))) again suggests the emission may not be fromLIST-1'., Recent VERITAS detection of VHE emission from M87 \cite{wystan}) ) again suggests the emission may not be from. . Considering the fact MIST jet is misaligned to the observer. explaining this TeV eanima-ray emission required a mocified model other than the one used o explain blazar emission.," Considering the fact M87 jet is misaligned to the observer, explaining this TeV gamma-ray emission required a modified model other than the one used to explain blazar emission." Neronoy&Aharonian(2007) explained TeV. ezmnmia-ray emission due to radiative cooling of electrons accelerated by strong rotation induced. electric ields in the vacuum gaps in black hole magnetospheres., \cite{nero} explained TeV gamma-ray emission due to radiative cooling of electrons accelerated by strong rotation induced electric fields in the vacuum gaps in black hole magnetospheres. Lenainetal.(2008) proposed a multi-blob. model. with several plasma blobs moving in the large opening angle of the jet formation zone., \cite{lenain} proposed a multi-blob model with several plasma blobs moving in the large opening angle of the jet formation zone. TeV eamma-ray emission is explained as Doppler boosted svnchrotron self Compton radiation by the obs moving close to the line of sight., TeV gamma-ray emission is explained as Doppler boosted synchrotron self Compton radiation by the blobs moving close to the line of sight. The radio-to-optical emission [rom the knots of MST jet are quite well accepted as svnchrotron. emission. due o cooling of relativistic non-thermal electrons by. the magnetic field therein(Perlmanctal. (200139)., The radio-to-optical emission from the knots of M87 jet are quite well accepted as synchrotron emission due to cooling of relativistic non-thermal electrons by the magnetic field \cite{perl01}) ). Phe Ilux and he spectral indices at X-ray energies indicates a possible continuation of svnchrotron emission of the radio-to-optical, The flux and the spectral indices at X-ray energies indicates a possible continuation of synchrotron emission of the radio-to-optical above scenario. since the expected proper motion max be detectable al Chandras resolution.,"above scenario, since the expected proper motion may be detectable at 's resolution." Unfortunately. the are typically fallen more or less at a gap between two ACIS-I chips. especially in three early observations.," Unfortunately, the arc typically fallen more or less at a gap between two ACIS-I chips, especially in three early observations." In addition. (he are is heavily contaminated by strong thermal emission in the low energy band.," In addition, the arc is heavily contaminated by strong thermal emission in the low energy band." In 4-6 keV. where nonthermal emission dominates. ihe counting statistics of the are are typically not sufficient in early observations.," In 4-6 keV, where nonthermal emission dominates, the counting statistics of the arc are typically not sufficient in early observations." As a result. we cannot vel get a reliable multi-epoch measurements of the arc positions (o allow for a reliable determination of the proper motion.," As a result, we cannot yet get a reliable multi-epoch measurements of the arc positions to allow for a reliable determination of the proper motion." Future observations with more careful positioning of the are in the detector and with a total exposure time comparable to the AC]IS-I observations in 2009 will make such measurements feasible., Future observations with more careful positioning of the arc in the detector and with a total exposure time comparable to the ACIS-I observations in 2009 will make such measurements feasible. We have shown (hat a sell-consistent single-degenerate binary model provides a natural and unified interpretation of the observed unique X-ray arc/shadow in the Tychos SNR., We have shown that a self-consistent single-degenerate binary model provides a natural and unified interpretation of the observed unique X-ray arc/shadow in the Tycho's SNR. Two sets of parameters of (he progenitor binary svstem have also been presented using the optical observation results of the candidate companion star (νόμο G) obtained by Iuiz-Lapuente and IxXerzendorfοἱal.(2009). respectively.," Two sets of parameters of the progenitor binary system have also been presented using the optical observation results of the candidate companion star (Tycho G) obtained by \cite{Ruiz2004} and \cite{kerz2009} respectively." The main points in favor of our interpretation are: (1) Although the nonthermal X-ray are is half way from the remnant center. (he hieh brightness show that il is viewed almost edge on and so unlikely a projected ealure in the outer laver of the remnant.," The main points in favor of our interpretation are: (1) Although the nonthermal X-ray arc is half way from the remnant center, the high brightness show that it is viewed almost edge on and so unlikely a projected feature in the outer layer of the remnant." Together with its sharp inward convex shape. the are most probably represents the interaction between (he ejecta and a bulk of materials in the interior of the remnant. (," Together with its sharp inward convex shape, the arc most probably represents the interaction between the ejecta and a bulk of materials in the interior of the remnant. (" 2) This bulk of materials can not be due to a pre-existing nolecular cloud or materials ejected by the progenitor binary svstem.,2) This bulk of materials can not be due to a pre-existing molecular cloud or materials ejected by the progenitor binary system. The impact generating the N-vay avc is most likely between SN ejecta and the stripped envelop of the companion star. (, The impact generating the X-ray arc is most likely between SN ejecta and the stripped envelop of the companion star. ( 3) The N-ray emission of the remnant shows an apparent shadow casted by (he arc in the opposite direction of the explosion site. and there are local enhancements in the same direction immediately within the X-ray arc. consistent with the blocking of the SN ejecta by the envelope. (,"3) The X-ray emission of the remnant shows an apparent shadow casted by the arc in the opposite direction of the explosion site, and there are local enhancements in the same direction immediately within the X-ray arc, consistent with the blocking of the SN ejecta by the envelope. (" 4) We obtained a stripped mass of < 0.0083 A... which is consistent with that observed for two extragalactic Ia SNe (Leonard 2007) and close to the recent simulations by Pakimor et al. (,"4) We obtained a stripped mass of $\leq$ 0.0083 $M_{\sun}$, which is consistent with that observed for two extragalactic Ia SNe (Leonard 2007) and close to the recent simulations by Pakmor et al. (" 2003). (,2008). ( 5) The angle between (he motion of the companion candidate and the direction of the arc as well as the derived kick velocity of the companion star are well consistent wilh the theoretical predictions ancl the numerical simulation results.,5) The angle between the motion of the companion candidate and the direction of the arc as well as the derived kick velocity of the companion star are well consistent with the theoretical predictions and the numerical simulation results. llowever. we note that there are still several points that can not be well interpreted bv the current scenario. ancl further work is needed to reveal the physical processes related to the nonthermal X-ray. arc. (," However, we note that there are still several points that can not be well interpreted by the current scenario, and further work is needed to reveal the physical processes related to the nonthermal X-ray arc. (" 1) The properties of Tvcho G and whether it is the stellar remnant of Tychos SN are under debate,1) The properties of Tycho G and whether it is the stellar remnant of Tycho's SN are under debate component of a pair. (,component of a pair. ( 2) At least one of the components has measured redshift. (,2) At least one of the components has measured redshift. ( 3) When both components have measured redshifts. (he velocity difference is not larger (han 500 kin +. (,"3) When both components have measured redshifts, the velocity difference is not larger than 500 km $^{-1}$. (" 4) The projected separation is in the range of 5=0.16. correspouding to Ay1.26. is in a good agrecineut with the activity level expected for a star with rotation period of ddays (Novesetal.198 L)).," Moreover, the mean level of the Ca index, $=0.46$, corresponding to $R'_{HK}=-4.26$, is in a good agreement with the activity level expected for a star with rotation period of days \cite{Noyes}) )." The combination of our rotation period aud lüueasuremnents allows us to estimate that the inclination of the stars rotation axis to our line of sight is approximately /=309., The combination of our rotation period and measurements allows us to estimate that the inclination of the star's rotation axis to our line of sight is approximately $i=30^0$. Notice that in our case the increase of the macroturbulence with the star rotation is negligible., Notice that in our case the increase of the macroturbulence with the star rotation is negligible. It does not change our estimate of the / angle., It does not change our estimate of the $i$ angle. The smooth (i.c.. without plateaus) variations in our radial velocities. jotonietry. and chromospheric emission sugeest that the argest spotted region is always visible to the observer and does not completely disappear when- on the far side of the star.," The smooth (i.e., without plateaus) variations in our radial velocities, photometry, and chromospheric emission suggest that the largest spotted region is always visible to the observer and does not completely disappear when on the far side of the star." Therefore. it is Likely that he spot region is ocated within 30 deerees of the stellar pole and is visible. at least in part. throughout the rotation cvcle.," Therefore, it is likely that the spot region is located within 30 degrees of the stellar pole and is visible, at least in part, throughout the rotation cycle." In this case. projection effects would be responsible for most of he rotational modulation of the stars brightucss.," In this case, projection effects would be responsible for most of the rotational modulation of the star's brightness." Thus. we have shown that surface magnetic activity on he star ΠΟ 166135 can iuinüc the kind of radial-velocity variations observed in stars with true planetary reflex. notions.," Thus, we have shown that surface magnetic activity on the star HD 166435 can mimic the kind of radial-velocity variations observed in stars with true planetary reflex motions." However. further analysis of the spectrcopic ine profiles. plotometiry. auc chromospheric enüssion clearly demonstrates that stellar activity is the origin of he radial-velocity variations.," However, further analysis of the spectrcopic line profiles, photometry, and chromospheric emission clearly demonstrates that stellar activity is the origin of the radial-velocity variations." Our observations of this eculiar object actually strenethen the interpretation of other low-mass conipauions to solu-tvpe stars where a ow-anmplitude. radial-velocity variation has been detected mt where photometric. chromospheric. aud line-profile variations are absent (e.9.. Ποιονotal. 2000)).," Our observations of this peculiar object actually strengthen the interpretation of other low-mass companions to solar-type stars where a low-amplitude, radial-velocity variation has been detected but where photometric, chromospheric, and line-profile variations are absent (e.g., \cite{henryetal00}) )." "edge. gives. ορALD)=vb,.25b&---10""* photos and an SStronunercu radius of We note that the ratio of the extrapolated fluxes at he respective ionization limits is fairly small.","edge, gives $S_0^{\rm (H)} \approx \nu L_{\nu}/3 \approx 5 \times 10^{57}$ photons $^{-1}$ and an Strömmgren radius of We note that the ratio of the extrapolated fluxes at the respective ionization limits is fairly small." Iu theQSO rest-frame. F912A)/P(228A)z5. indicating a ‘aly hard (flat) power-law spectrum Fyx0.+7.," In theQSO rest-frame, $F(912~{\rm \AA})/F(228~{\rm \AA}) \approx 5$, indicating a fairly hard (flat) power-law spectrum $F_{\nu} \propto \nu^{-1.2}$." These estimated. Stromimeren radi are a substantial fraction of the proper distance of 19.5 Alpe between the two xoposed QSO redshifts. .=2.901 and 2=2.885.," These estimated Strömmgren radii are a substantial fraction of the proper distance of 19.5 Mpc between the two proposed QSO redshifts, $z = 2.904$ and $z = 2.885$." Even though the local ionization zone may not exteud as ar as these equilibrimu Strouumeren radii the expected xoxiudtv effect is nininiallv visible. except for a narrow eature with ~6054 flux transmission at 2=2.9055. just low the eedee (Figure tj).," Even though the local ionization zone may not extend as far as these equilibrium Strömmgren radii, the expected proximity effect is minimally visible, except for a narrow feature with $\sim 60$ flux transmission at $z = 2.9055$, just below the edge (Figure 4)." We conclude that ionizing radiatiou roni this QSO is strouglv absorbed in the proximity of the uucleus. possibly bycirciununnuclear eas or by the strong absorber at ;z2.9.," We conclude that ionizing radiation from this QSO is strongly absorbed in the proximity of the nucleus, possibly bycircumnuclear gas or by the strong absorber at $z \approx 2.9$." The photoionization cross sections for aand aabove threshold are approximately σµι=—(6.30«105)αιE/36eV) aud egg=—(158«1015en?XE/5LELeV) 7., The photoionization cross sections for and above threshold are approximately $\sigma_{\rm HI} = (6.30 \times 10^{-18}~{\rm cm}^2)(E/13.6~{\rm eV})^{-3}$ and $\sigma_{\rm HeII} = (1.58 \times 10^{-18}~{\rm cm}^2)(E/54.4~{\rm eV})^{-3}$ . Thus. to absorb a substantial αλλοι of the ioniziung continua requires column densities for contiuuun optical depth 7 at photon cucrey £.," Thus, to absorb a substantial amount of the ionizing continua requires column densities for continuum optical depth $\tau$ at photon energy $E$." For this very bright QSO. the absence of a pproxiuütv cfect indicates a significant attenuation of the 1 rvd coutimuun. with optical depth 7>3 at mean photon energies 1.5 times the 51.1 eV threshold. or μαι>6s1025em7.," For this very bright QSO, the absence of a proximity effect indicates a significant attenuation of the 4 ryd continuum, with optical depth $\tau > 3$ at mean photon energies 1.5 times the 54.4 eV threshold, or $_{\rm HeII} > 6 \times 10^{18}~{\rm cm}^{-2}$." What are the observational consequences of such large column clensitics of ionized eas?, What are the observational consequences of such large column densities of ionized gas? It has been suggested (Reimers 11997) that rresonance lines at 303.115 aand 305.596 uuuieht be detectable. but we fud no obvious caucidates.," It has been suggested (Reimers 1997) that resonance lines at 303.415 and 305.596 might be detectable, but we find no obvious candidates." It would be useful to search for sigus of splittings of these lines. which are separated by 2.182 ΑΙ]z8.5 aat 2%2.9.," It would be useful to search for signs of splittings of these lines, which are separated by 2.182 $(1+z) \approx 8.5$ at $z \approx 2.9$." Some of the associated absorbers have aanomalously strouger thanLL. sugeesting that the eas is close to the QSO with Lelimm mostly fully ionized LEO).," Some of the associated absorbers have anomalously stronger than, suggesting that the gas is close to the QSO with helium mostly fully ionized )." More clues may come frou the stroug aabsorbers at 2=2.9002.001 (lisl71186.2 A)) which would be closest to the. QSO if toso=2.901., More clues may come from the strong absorbers at $z = 2.900-2.904$ (1184.7–1186.2 ) which would be closest to the QSO if $z_{\rm QSO} = 2.904$. This system has high optical depth iu both ad (ος Figure 1)., This system has high optical depth in both and (see Figure 4). Very strong imetalline absorption is seen in with weaker absorption inIV... HE. aud (Reiners 11997: Fechner 22001.," Very strong metal-line absorption is seen in with weaker absorption in, , and (Reimers 1997; Fechner 2004)." Dv fitting Ποια Lxauzneseries absorbers. Fechner ((2001) found log Nyy=16.02£0.03. while the ine absorbers eave log Neq=13.66£0.03. log Nx=13.12cx0.01. and log Novy21162.," By fitting higher Lyman-series absorbers, Fechner (2004) found log $_{\rm HI} = 16.02 \pm 0.03$, while the metal-line absorbers gave log $_{\rm CIV} = 13.66 \pm 0.03$, log $_{\rm NV} = 13.42 \pm 0.04$ , and log $_{\rm OVI} \ga 14.62$." They proposed wat this absorber is exposed to the strongest and uudest radiation from the 050. and therefore may shield the other associated absorbers.," They proposed that this absorber is exposed to the strongest and hardest radiation from the QSO, and therefore may shield the other associated absorbers." However. their photoionization models eave log Nga216.3. which is pa10 times too small to provide the necessary absorption = 16.29 0.05 in the 2=2.9011 absorber.," However, their photoionization models gave log $_{\rm HeII} \approx 16.3$, which is 100 times too small to provide the necessary absorption = 16.29 0.05 in the $z = 2.9041$ absorber." This cohuun is still iusufficieut to shield the QSO's ionizing continua., This column is still insufficient to shield the QSO's ionizing continuum. " We conclude that no satisfactory explanation exists for the absence of a proximity effect around this verv luninous QSO. other than the possibility that it has only recently turued ou (within the last αντ),"," We conclude that no satisfactory explanation exists for the absence of a proximity effect around this very luminous QSO, other than the possibility that it has only recently turned on (within the last Myr)." The high throughput aud low backerouud of the Cosmic Orieius Spectrograph allow us to probe the ircionization epoch toward WE 1312 at redshifts + = 2.12.9., The high throughput and low background of the Cosmic Origins Spectrograph allow us to probe the reionization epoch toward HE $-$ 4342 at redshifts $z$ = 2.4–2.9. " Because of photoionization and recombination rates, His a far more abundant species than L. with typical ratios 1Ξnp/yy varyiug from 10.200 in the filaments of the fforest."," Because of photoionization and recombination rates, is a far more abundant species than , with typical ratios $\eta = n_{\rm HeII}/n_{\rm HI}$ varying from 10–200 in the filaments of the forest." With COS. we find that reionization of tto jis patchy at >=2.72.9. with 510ttroughs of high optical depth (zyqi7 5) punctuated by narrow windows of flix transmission.," With COS, we find that reionization of to is patchy at $z = 2.7-2.9$, with 5–10troughs of high optical depth $\tau_{\rm HeII} > 5$ ) punctuated by narrow windows of flux transmission." " Previous studies of this QSO sieht line (Ixxiss 22001: Shull 22001: Zheng 22001) found a gradual decrease in ooptical depth at 2< 2.7. suggesting a rreionization epoch +,=2.8c 0.2."," Previous studies of this QSO sight line (Kriss 2001; Shull 2004; Zheng 2004) found a gradual decrease in optical depth at $z < 2.7$ , suggesting a reionization epoch $z_r = 2.8 \pm 0.2$ ." With our new COS data. we fud a more complicatedpicture. in which His slowly reionized at 2x2.7.," With our new COS data, we find a more complicatedpicture, in which is slowly reionized at $z \leq 2.7$." We now stumunarize the new observational results acl astroplivsical issues:, We now summarize the new observational results and astrophysical issues: order equation for d.,order equation for $\delta$. After dropping higher order terns. we eet Thus the torsional Alfvéun waves erow exponuenutiallv in time aud their erowth rate depends on the relative amplitude of slow magnetoacoustic waves Le. profpo. Which is typical of weakly nou-Inear X)YOCOSRCR," After dropping higher order terms, we get Thus the torsional Alfvénn waves grow exponentially in time and their growth rate depends on the relative amplitude of slow magnetoacoustic waves i.e. ${{{\hat \rho_{12}}}/{\rho_0}}$, which is typical of weakly non-linear processes." ", Iu order to check the analytical solution. we formed the munerical simulation of spatially averaged equations (21)-(25) with k.=2k4. so hat only the time depeudeuce is retained."," In order to check the analytical solution, we performed the numerical simulation of spatially averaged equations (24)-(25) with $k_z=2k_A$, so that only the time dependence is retained." Then he nuuerical calculation is straightforward aud we find that torsional waves have an exponentiallv erowing solution when their period is twice the iod of the slow maguetoacoustic waves Lo. Ww=2w4 (Fig.2)., Then the numerical calculation is straightforward and we find that torsional waves have an exponentially growing solution when their period is twice the period of the slow magnetoacoustic waves i.e. $\omega=2\omega_A$ (Fig.2). "B. The up-plots refer to the deusity aud velocity compoucuts of the slow waves (py aud ug) and the down-plots refer to the compoucuts of the torsional waves (5,, aud «,,).", The up-plots refer to the density and velocity components of the slow waves $\rho_1$ and $u_R$ ) and the down-plots refer to the components of the torsional waves $b_\phi$ and $u_\phi$ ). Hore 3 is assumed to be ~ 107 and the strong amplification of torsional waves beeius after ~ 10-15 wave periods., Here $\beta$ is assumed to be $\sim$ $^2$ and the strong amplification of torsional waves begins after $\sim$ 10-15 wave periods. Note that the growth rate of torsioual Alfvén waves depends on the value of plasima 9., Note that the growth rate of torsional Alfvénn waves depends on the value of plasma $\beta$. The cherey transfer occurs ouly when the density perturbations in slow imagnuetoacoustic waves are nonzero., The energy transfer occurs only when the density perturbations in slow magnetoacoustic waves are nonzero. When .j eoes to infinity. then the density perturbations vanish aud so there is no energy exchange between the waves.," When $\beta$ goes to infinity, then the density perturbations vanish and so there is no energy exchange between the waves." Thus the resonant process ds of müportance for large. but finite ./. which requires strong magnetic fields in the stellar ΠΟΙΟΥΣ.," Thus the resonant process is of importance for large, but finite $\beta$, which requires strong magnetic fields in the stellar interiors." We have seen that slow maguetoacoustic aud torsional Alfvéóun waves are resonantlv coupled when they propagate with the same Alfvén speed along an unperturbed magnetic field in a >o> Limedimn.," We have seen that slow magnetoacoustic and torsional Alfvénn waves are resonantly coupled when they propagate with the same Alfvénn speed along an unperturbed magnetic field in a $\beta \gg1$ medium." The slow magnuectoacoustic wave xuranmetricallv triggers the torsional wave with the ialf frequency and wave uunuber., The slow magnetoacoustic wave parametrically triggers the torsional wave with the half frequency and wave number. " The erowth rate of the torsional mode depends on the amplitude of the slow maeuctoacoustic wave: the larger is he amplitude of the slow maguectoacoustic wave. he faster is the cnereyv transfer to torsional waves Which is a conuuon scenario for non-inear processes,"," The growth rate of the torsional mode depends on the amplitude of the slow magnetoacoustic wave: the larger is the amplitude of the slow magnetoacoustic wave, the faster is the energy transfer to torsional waves, which is a common scenario for non-linear processes." The erowth rate depends on he value of plasma 3) as well: higher > leads to weaker coupling., The growth rate depends on the value of plasma $\beta$ as well; higher $\beta$ leads to weaker coupling. The reason is that the deusitv perturbations in slow imagnuetoacoustic waves are weaker for higher j aud thus the slow waves do not alter the Alfvénn speed., The reason is that the density perturbations in slow magnetoacoustic waves are weaker for higher $\beta$ and thus the slow waves do not alter the Alfvénn speed. However the situation probably will be changed for nonaciabatic slow waves as the deusity perturbations can be larger due to the compensation by the temperature variation., However the situation probably will be changed for nonadiabatic slow waves as the density perturbations can be larger due to the compensation by the temperature variation. Then the density perturbations will affect significantly the Alfvéun speed. thus the torsional waves.," Then the density perturbations will affect significantly the Alfvénn speed, thus the torsional waves." This process seen to lave interesting consequences aud will be studied iu future., This process seems to have interesting consequences and will be studied in future. The coupliug between these waves may have interesting applications in astrophysics., The coupling between these waves may have interesting applications in astrophysics. The existence of torsional oscillations iu stellar interiors is a long tine dilemma., The existence of torsional oscillations in stellar interiors is a long time dilemma. Uvdromaguetic torsional oscillations of a seed magnetic field have becn suggested to take place in stellar interiors. which may lead to the evelic change in sign of the solar toroidal maeuetic field (Waléu1919:Cowling1953:Piddington1971:Gough 1955).," Hydromagnetic torsional oscillations of a seed magnetic field have been suggested to take place in stellar interiors, which may lead to the cyclic change in sign of the solar toroidal magnetic field \citep{wal,cow,pid,go}." ", ILlowever the oscillations probably are damped because of the trausport of the magnetic flux to the surface and/or the phase mixing (Charbouncau&MacCregor 1993).", However the oscillations probably are damped because of the transport of the magnetic flux to the surface and/or the phase mixing \citep{cha}. . Therefore the abseuce of a plausible energy source which can support torsional oscillations has been au arguineut agaiust their existence (Rosner&Weiss1992)., Therefore the absence of a plausible energy source which can support torsional oscillations has been an argument against their existence \citep{ros}. . However. several different sources have previously been suggested to support torsional oscillations (LavzerCough 2002).. but they are not convincing.," However, several different sources have previously been suggested to support torsional oscillations \citep{la,ma,lan,ga}, but they are not convincing." Receutly stellar radial pulsation iu the fundamental uode. which can be considered as a standing ‘ast iuagnetoacoustic wave iu the presence of nagnetic field. las been sugsested as a source ‘or torsional Alfvén waves (Zaqarashvilietal. 2002).," Recently stellar radial pulsation in the fundamental mode, which can be considered as a standing fast magnetoacoustic wave in the presence of magnetic field, has been suggested as a source for torsional Alfvénn waves \citep{zaq3}." . However. amplified torsional waves can iof eive rise to torsional oscillations due to their short waveleugth as compared to the stellar raciu4. (hecause the Alfvénn speed is much smaller thaw he sound speed}.," However, amplified torsional waves can not give rise to torsional oscillations due to their short wavelength as compared to the stellar radius (because the Alfvénn speed is much smaller than the sound speed)." Therefore. rather than giv rise to large-scale torsional oscillations. they will xopagate upwards to the stellar atimosphere. iuxa can be observed iu the stellar wind (ZaqarashviLBandBelvedere 2005).," Therefore, rather than give rise to large-scale torsional oscillations, they will propagate upwards to the stellar atmosphere, and can be observed in the stellar wind \citep{zaq5}." . It is a natural plivsical process that in closed svstenis (the Sun or a simple tuning fork) almost all cnerey is stored in the fundamental mode., It is a natural physical process that in closed systems (the Sun or a simple tuning fork) almost all energy is stored in the fundamental mode. For example. take an ordinary tumime fork: amv," For example, take an ordinary tuning fork: any" Theoretical studies of eccentricity and inclination growth in planetesimal disks [ind (7)/(e)=0.45 0.5. somewhat larger than this value.,"Theoretical studies of eccentricity and inclination growth in planetesimal disks \citep[e.g.,][]{ida} find $\langle i\rangle/\langle e\rangle=0.45$ –0.5, somewhat larger than this value." A possible explanation is that the eccentricities may have been svstematically overestimated., A possible explanation is that the eccentricities may have been systematically overestimated. [ind that the typical bias clue to measurement errors is Aec0.04 in RV catalogs. ancl thT bias in (his sample is likely to be higher since the SNR is low for low-mass planets.," \cite{zak} find that the typical bias due to measurement errors is $\Delta e\sim 0.04$ in RV catalogs, and the bias in this sample is likely to be higher since the SNR is low for low-mass planets." Possibly a similar bias is present in (he Nepler measurements of the eccentricity distribution., Possibly a similar bias is present in the Kepler measurements of the eccentricity distribution. The Kepler survey can measure transit (ning variations of a minute or less in favorable cases (Fordetal.2011)., The Kepler survey can measure transit timing variations of a minute or less in favorable cases \citep{ford11}. . These variations can be used to detect and characterize additional planets., These variations can be used to detect and characterize additional planets. Given the rms inclination of 0.0.09 radians that we have derived. roughly of the sinele-(ranet IxXepler svstems are expected to have additional planets (Figure 5)). and many of these may be detectable by transit timing; variations.," Given the rms inclination of 0–0.09 radians that we have derived, roughly of the single-tranet Kepler systems are expected to have additional planets (Figure \ref{fig:total}) ), and many of these may be detectable by transit timing variations." Fordetal.(2011) estimate that ~10. 2056 of suitable IXepler tranets show evidence of transit (imine variations. and {his number is likely to increase as the survey. duration grows.," \cite{ford11} estimate that $\sim10$ $20\%$ of suitable Kepler tranets show evidence of transit timing variations, and this number is likely to increase as the survey duration grows." Figure 5. also shows that the fraction of two- or tree-tranet svstems wilh additional planets is substantially higher. and stronglv dependent on the rms inclination.," Figure \ref{fig:total} also shows that the fraction of two- or three-tranet systems with additional planets is substantially higher, and strongly dependent on the rms inclination." A preliminary analvsis by Fordetal.(2011) vields much lower probabilities of 0.1.0.2 for 6wo- and three-tranet svstems: such low probabilities would be difficult to reconcile with any of our models. whatever the rms imcelination may be.," A preliminary analysis by \cite{ford11} yields much lower probabilities of 0.1–0.2 for two- and three-tranet systems; such low probabilities would be difficult to reconcile with any of our models, whatever the rms inclination may be." We have described a methodology for analvzing the multiplicity Function.(the fraction of host stars containing a eiven number of planetsin radial-velocitv (RV) and transit survevs., We have described a methodology for analyzing the multiplicity function—the fraction of host stars containing a given number of planets—in radial-velocity (RV) and transit surveys. Our approach is based on the approximation of separability. that the probability distribution of planetary parameters in an z-planet svstem is the product. of identical distributions relseciseparable)).," Our approach is based on the approximation of separability, that the probability distribution of planetary parameters in an $n$ -planet system is the product of identical 1-planet distributions \\ref{sec:separable}) )." Exoplanet surveys show (hat separability is not precisely satisfied but the departures [rom (his approximation are small enough that 1 provides a powerlul tool for the study of imulti-planet svstems., Exoplanet surveys show that separability is not precisely satisfied but the departures from this approximation are small enough that it provides a powerful tool for the study of multi-planet systems. Using (his approximation we have shown how to relate the observable multipliity. function in survevs with different sensitivilies. so long as thev examine populations of potential host stars with similar properties relsecisurvev)).," Using this approximation we have shown how to relate the observable multiplicity function in surveys with different sensitivities, so long as they examine populations of potential host stars with similar properties \\ref{sec:survey}) )." We have also shown how to derive the multiplicity. fanction Irom transit survevs )) assuming a given form for the inclination distribution (the Fisher distribution. relsec:lisher)).," We have also shown how to derive the multiplicity function from transit surveys \\ref{sec:transit}) ) assuming a given form for the inclination distribution (the Fisher distribution, \\ref{sec:fisher}) )." Our principal conclusions are:, Our principal conclusions are: a negative value of uy. and that for equations of state of the twpe occurring in this problem even (his possibility is excluded. so (hat vp must vanish.,"a negative value of $u_0$, and that for equations of state of the type occurring in this problem even this possibility is excluded, so that $u_0$ must vanish." This can be seen from (he following argument., This can be seen from the following argument. ILaving chosen some particular value of po one mav usually represent (he equation of state in thatpressure range by e=Cj» with sone appropriate value of s.," Having chosen some particular value of $p_0$ one may usually represent the equation of state in thatpressure range by $\epsilon = C p^s$ with some appropriate value of $s$." " Using this equation of state and taking the approximate form of Eq (13)) near the origin lor the case uy« 0. and finite py. one obtains: Integration of this equation shows that lor s<1l. py>0 can not be satisfied. aud for s>1 only the value p,=0 is possible."," Using this equation of state and taking the approximate form of Eq \ref{dpdr}) ) near the origin for the case $% u_0 < 0, and finite $p_0$, one obtains: Integration of this equation shows that for $s<1$, $p_0 \geq 0$ can not be satisfied, and for $s \geq 1$ only the value $p_0 = 0$ is possible." This immediately excludes (he possibility (hat degenerate bosons form an equilibrium structure. because p is independent of e. il p is solely due to thermal bosons (Landau&Lifshitz1980).," This immediately excludes the possibility that degenerate bosons form an equilibrium structure, because $p$ is independent of $\epsilon$, if $p$ is solely due to thermal bosons \citep{landau}." . As we mentioned in 811. a boson star is supported bv the quantum pressure of ground-state bosons. which is outside of the scope of the consideration of the equation of state (Ixaup1963)..," As we mentioned in 1, a boson star is supported by the quantum pressure of ground-state bosons, which is outside of the scope of the consideration of the equation of state \citep{kaup}." For (he equations of state used for degenerate fermions. always s<1 holds.," For the equations of state used for degenerate fermions, always $s<1$ holds." It is also be noted that the above equation together with Eq. (10)), It is also be noted that the above equation together with Eq. \ref{enu}) ) show that ο— y as r— 0. (," show that $% e^{\nu(r)} \rightarrow \inft y as $r \rightarrow 0$ . (" c) A special investigation [for any particular equation of state must be made (o see whether solutions exist in which 0xuj;<—-x and p— y as r—0.,"c) A special investigation for any particular equation of state must be made to see whether solutions exist in which $0 \leq u_0 \leq -\infty$ and $% p \rightarrow \inft y as $r \rightarrow 0$." If the matter consists of fermions of rest mass fy and statistical weight g. and their thermal οποιον and all forces between them are neglected. (hen a parametricform lor the equation of state (Landau&Lifshitz1980). is. where," If the matter consists of fermions of rest mass $\mu_0$ and statistical weight $g$ , and their thermal energy and all forces between them are neglected, then a parametricform for the equation of state \citep{landau} is, where" and (see Eq. 23)).,"and (see Eq. \ref{fineq1}) )," which is too laree compared with (Qzz1/2 for an equilibrium solution to exist., which is too large compared with $Q\approx 1/2$ for an equilibrium solution to exist. Hence. a Poisson-Doltzmann integration using the IF model. or anv other such model. is an inappropriate and futile exercise.," Hence, a Poisson-Boltzmann integration using the HF model, or any other such model, is an inappropriate and futile exercise." Nevertheless. IF perlormed this integration without disk DM and found the result to be compatible with vertical density. profiles of Ix eiant racers.," Nevertheless, HF performed this integration without disk DM and found the result to be compatible with vertical density profiles of K giant tracers." We look at the same data and conclude that the IF model can be compatible with a Poisson-Dolizmann steady. state solution only if disk DM exists., We look at the same data and conclude that the HF model can be compatible with a Poisson-Boltzmann steady state solution only if disk DM exists. For exaniple. suppose that DM has (he sime vertical profile and ο. variance as visible matter. but that. visible matter accounts for only of the total surface mass density.," For example, suppose that DM has the same vertical profile and $v_z$ variance as visible matter, but that visible matter accounts for only of the total surface mass density." " Then o(0) and. X increase by the factor 10/3. and (hus £25, is modified to 1.63x3/10=0.49. which is a plausible value lor Q."," Then $\rho(0)$ and $\Sigma$ increase by the factor $10/3$ , and thus $R_{HF}$ is modified to $1.63\times 3/10=0.49$, which is a plausible value for $Q$." However. the revised model no longer satisfies the Poisson-Doltzmann equation and the change increases the vertical accelerations of (he (racer stars by (he factor 10/3 ancl decreases (heir scale height bv7055.. and such a model conflicts drastically with IX giant. vertical profiles.," However, the revised model no longer satisfies the Poisson-Boltzmann equation and the change increases the vertical accelerations of the tracer stars by the factor $10/3$ and decreases their scale height by, and such a model conflicts drastically with K giant vertical profiles." Introducing DM solves one problem but creates another., Introducing DM solves one problem but creates another. The overall problem can only be resolved by abandoning the requirement that the disk 2 profile is in a steady state or that. gravity. is Newlonian., The overall problem can only be resolved by abandoning the requirement that the disk $z$ profile is in a steady state or that gravity is Newtonian. BFG conceived and examined ten disk models. nine of them containing varving formulations with DM.," BFG conceived and examined ten disk models, nine of them containing varying formulations with DM." " Their Table 4 lists their observed model in Row 1 [p,(0)=0.1026peM. and XQ=49.8pe ΛΙ]. and their 7best fit” model (observed plus dark matter) in Row 3 (3(0)=0.2596peSAL. and X4=83.9pe7AL. |.For the Row 1 model. the ratio of p0/1 "," Their Table 4 lists their observed model in Row 1 $\rho_{1}(0)=0.1026\, {\mathrm pc^{-3}}\,M_{\odot}$ and $\Sigma_{1}=49.8\,{\mathrm pc^{-2}}\, M_{\odot}$ ], and their “best fit” model (observed plus dark matter) in Row 3 $\rho_{3}(0)=0.2596\, {\mathrm pc^{-3}}\,M_{\odot}$ and $\Sigma_{3}=83.9\,{\mathrm pc^{-2}}\, M_{\odot}$ ].For the Row 1 model, the ratio of $\rho_{1}(0)/\Sigma_{1}^2$ " he time it takes the shutter to close. although the readout akes place curing this time. resulting in some smearing.,"the time it takes the shutter to close, although the readout takes place during this time, resulting in some smearing." For his reason. the first image or images and the last image are discarded in the photometric analysis.," For this reason, the first image or images and the last image are discarded in the photometric analysis." CCD pixels can be digitized in 22.4 prs. or discarded in 24 pis. To minimize the time spent reading the CCD. two windows are defined. which mark ranges of columns in which the pixels are digitized. with pixels in all other columns discarded.," CCD pixels can be digitized in 22.4 $\mu$ s, or discarded in 2.4 $\mu$ s. To minimize the time spent reading the CCD, two windows are defined, which mark ranges of columns in which the pixels are digitized, with pixels in all other columns discarded." Each window was 40 pixels wide. which allowed the entire CCD to be read out in 1.5 s. Overhead in the computer operating svstem added up to one second to the total time required. for cach frame.," Each window was 40 pixels wide, which allowed the entire CCD to be read out in 1.5 s. Overhead in the computer operating system added up to one second to the total time required for each frame." The exposure times used in these observations were 5 ms. 10 ms. ancl LOO ms per image. eiving cuty eveles of approximatelyLO%..2054... and .. respectively.," The exposure times used in these observations were 5 ms, 10 ms, and 100 ms per image, giving duty cycles of approximately, and , respectively." The long slit. with two windows defined. ensured that cach image. included. a bright comparison star.," The long slit, with two windows defined, ensured that each image included a bright comparison star." The comparison star used is the photometric standard. 35 of llenden&Honeveutt1997. ο—13.49860.001. 1.194+ 0.004) situated ~ NNNW of X-22.," The comparison star used is the photometric standard 35 of \citealt{hh97} $V=13.498\pm 0.001$, $B-V=1.194\pm 0.004$ ) situated $\sim$ NNW of 2." This star has »en extensively monitore. and has shown no intrinsic variability down to 0.001 mag.," This star has been extensively monitored, and has shown no intrinsic variability down to 0.001 mag." Roughly half of the data was taken with a 3 nm ΕΑΝΝΤΕ filter centred on aand the remainder in white light (see Tab., Roughly half of the data was taken with a 3 nm FWHM filter centred on and the remainder in white light (see Tab. 1)., 1). Phe seeing over three nights ranged from O.S to 1.2 aresec ENIM inLa. and from 1.2 to 1.6 aresec ENIM in white light.," The seeing over three nights ranged from 0.8 to 1.2 arcsec FWHM in, and from 1.2 to 1.6 arcsec FWHM in white light." Liehteurves were constructed. for each observation sequence using square photometric apertures ranging in size from toll. 11 pixels (0.43. 0.4 to 4.4 arcsec)., Lightcurves were constructed for each observation sequence using square photometric apertures ranging in size from $\times$ 1 to $\times$ 11 pixels $\times$ 0.4 to $\times$ 4.4 arcsec). While the use of square photometric apertures. rather than circular apertures. is not conventional. there is little dillerence for," While the use of square photometric apertures, rather than circular apertures, is not conventional, there is little difference for" constrain Qe (Rutledge et al.,constrain $Q_{\rm crust}$ (Rutledge et al. 2002)., 2002). In addition. these results emphasize that determining the superburst recurrence time would strongly constrain the local accretion rate and thermal structure of the star. and thereby composition of the accreted material.," In addition, these results emphasize that determining the superburst recurrence time would strongly constrain the local accretion rate and thermal structure of the star, and thereby composition of the accreted material." A direct effect of hydrogen in the acereted material will be to reduce the amount of carbon made during H/He burning., A direct effect of hydrogen in the accreted material will be to reduce the amount of carbon made during H/He burning. For pure helium aceretion. SBO2 argued that carbon production occurs during stable burning at high 77. for which the temperature is low enough to give a high carbon yield (Brown Bildsten 1998).," For pure helium accretion, SB02 argued that carbon production occurs during stable burning at high $\dot m$, for which the temperature is low enough to give a high carbon yield (Brown Bildsten 1998)." However. if hydrogen is present. protons will rapidly capture on. C. initiating the hot CNO cycle.," However, if hydrogen is present, protons will rapidly capture on $^{12}$ C, initiating the hot CNO cycle." In that case. breakout reactions Οία.) and “Oca.p) become possible (Wallace Woosley 1981: Schatz et al.," In that case, breakout reactions $^{15}$ $(\alpha$ $\gamma)$ and $^{14}$ $(\alpha$ $)$ become possible (Wallace Woosley 1981; Schatz et al." 1998). depleting the CNO abundance. and reducing the carbon yield.," 1998), depleting the CNO abundance, and reducing the carbon yield." For Xo=0.1. there are enough protons for one proton capture on each 'C. The outcome is probably different for Xe above and below this value. which is within the range predicted by models (Podsiadlowski et al.," For $X_0=0.1$, there are enough protons for one proton capture on each $^{12}$ C. The outcome is probably different for $X_C$ above and below this value, which is within the range predicted by models (Podsiadlowski et al." 2002)., 2002). For solar abundance of hydrogen. Schatz et al. (," For solar abundance of hydrogen, Schatz et al. (" 1999) found stable burning gave Xo~10% (still enough to ignite a superburst. however. as CBOI. showed).,"1999) found stable burning gave $X_C\sim 10$ (still enough to ignite a superburst, however, as CB01 showed)." Calculations of the carbon production for stable helium burning with a small amount of hydrogen should be carried out., Calculations of the carbon production for stable helium burning with a small amount of hydrogen should be carried out. Finally. it has been noted that the superburst from 4U 1820-30 is different from the superburst seen in other sources (Kuulkers et al.," Finally, it has been noted that the superburst from 4U 1820-30 is different from the superburst seen in other sources (Kuulkers et al." 2002)., 2002). It was the most energetic. and is the only superburst so far to reach Eddington luminosity.," It was the most energetic, and is the only superburst so far to reach Eddington luminosity." This is probably due to the low hydrogen abundance in the accreted material., This is probably due to the low hydrogen abundance in the accreted material. A lower hydrogen abundance allows greater carbon production. and makes lighter ashes (the heavy nuclei are probably iron group with Az56 rather than rp process ashes with A~ 100) reducing the opacity and giving a deeper ignition.," A lower hydrogen abundance allows greater carbon production, and makes lighter ashes (the heavy nuclei are probably iron group with $A\approx 56$ rather than rp process ashes with $A\sim 100$ ) reducing the opacity and giving a deeper ignition." Both these effects give a larger nuclear energy release. which could explain the more energetic and luminous superburst.," Both these effects give a larger nuclear energy release, which could explain the more energetic and luminous superburst." The calculations described here apply only to the low state. when regular Type I bursts are seen. and do not address the disappearance of bursts in the high state.," The calculations described here apply only to the low state, when regular Type I bursts are seen, and do not address the disappearance of bursts in the high state." This is an important question to answer., This is an important question to answer. In spherically-symmetric models. burning becomes stable at high i's because the temperature-sensitivity of the triple alpha reaction decreases with temperature. and the incoming helium then burns at the rate at which it accretes (Fujimoto. Hanawa. Miyayi 1981: Ayasli Joss 1982: Taam. Woosley. Lamb 1996).," In spherically-symmetric models, burning becomes stable at high $\dot m$ 's because the temperature-sensitivity of the triple alpha reaction decreases with temperature, and the incoming helium then burns at the rate at which it accretes (Fujimoto, Hanawa, Miyaji 1981; Ayasli Joss 1982; Taam, Woosley, Lamb 1996)." However. the transition to stable burning for pure helium accretion occurs at Hagan&%2«10°&em7s! (B9S: Bildsten 1998). much higher than 1920-2035 accretion rate.," However, the transition to stable burning for pure helium accretion occurs at $\dot m_{\rm stab}\approx 2\times 10^6\ {\rm g\ cm^{-2}\ s^{-1}}$ (B95; Bildsten 1998), much higher than 1820-30's accretion rate." The extra nuclear energy release if hydrogen is present will decrease Haas. but not enough to explain the observed transition.," The extra nuclear energy release if hydrogen is present will decrease $\dot m_{\rm stab}$, but not enough to explain the observed transition." B95 suggested that the missing piece of physics was that the bursts become radiative rather than convective in the high state., B95 suggested that the missing piece of physics was that the bursts become radiative rather than convective in the high state. The burning then proceeds as a slowly propagating “fire” over the stellar surface rather than dramatic Type I bursts., The burning then proceeds as a slowly propagating “fire” over the stellar surface rather than dramatic Type I bursts. However. the ignition of a local spot on the surface of the star is not understood. requiring stabilization of pressure gradients. perhaps by rapid rotation (Spitkovsky. Levin. Ushomirsky 2002: Zingale et al.," However, the ignition of a local spot on the surface of the star is not understood, requiring stabilization of pressure gradients, perhaps by rapid rotation (Spitkovsky, Levin, Ushomirsky 2002; Zingale et al." 2002)., 2002). 4U 1820-30 fits into the pattern of bursting seen in other sources: a transition from frequent. regular bursting to infrequent. irregular bursting as accretion rate increases (van Paradis. Penninx. Lewin 1988)," 4U 1820-30 fits into the pattern of bursting seen in other sources: a transition from frequent, regular bursting to infrequent, irregular bursting as accretion rate increases (van Paradijs, Penninx, Lewin 1988)." By comparing BeppoSAX/WFC data for 9 frequent bursters (including 4U 1820-30). Comelisse et al. (," By comparing /WFC data for 9 frequent bursters (including 4U 1820-30), Cornelisse et al. (" 2003) concluded that this transition oceurs at a universal luminosity Ly2«10?ergs.,"2003) concluded that this transition occurs at a universal luminosity $L_X\approx 2\times 10^{37}\ {\rm erg\ s^{-1}}$." If this behavior is common to all bursters. two explanations that have been put forward for hydrogen accretors may be relevant for 4U 1820-30.," If this behavior is common to all bursters, two explanations that have been put forward for hydrogen accretors may be relevant for 4U 1820-30." First. Narayan Heyl (2003) recently studied the linear stability of quasi-steady burning shells. finding that some stable burning occurs during accumulation for accretion rates near the transition to. stability.," First, Narayan Heyl (2003) recently studied the linear stability of quasi-steady burning shells, finding that some stable burning occurs during accumulation for accretion rates near the transition to stability." Whether this. result applies to pure helium aceretion should be investigated further., Whether this result applies to pure helium accretion should be investigated further. Second. for hydrogen accretors. Bildsten (2000) suggested that the fraction of the star covered with fresh fuel increases with increasing global M. so that the local aceretion rate 7decreases.," Second, for hydrogen accretors, Bildsten (2000) suggested that the fraction of the star covered with fresh fuel increases with increasing global $\dot M$, so that the local accretion rate $\dot m$." The observed transition is then from mixed H/He ignition. (uu— fj) giving frequent. regular bursts to pure He ignition. giving irregular. less frequent bursts (fiu7fj).," The observed transition is then from mixed H/He ignition $t_{\rm recur}t_H$ )." The different composition in 4U 1820-30 makes it difficult to apply the same explanation. and the regularity of the bursts perhaps implies complete covering.," The different composition in 4U 1820-30 makes it difficult to apply the same explanation, and the regularity of the bursts perhaps implies complete covering." Increasing area. with. M would explain the small change m recurrence time seen by Clark et al. (," Increasing area with $\dot M$ would explain the small change in recurrence time seen by Clark et al. (" 1977).,1977). " Accurate fluence measurements together with spectral fits to the radius as a function of f, are a way to test this picture.", Accurate fluence measurements together with spectral fits to the radius as a function of $t_{\rm recur}$ are a way to test this picture. I thank Erik Kuulkers. Phillip Podsiadlowskti. Hendrik Schatz and the referee for useful comments. and Lars Bildsten for stressing that Type I bursts might test evolutionary models for LMXBs.," I thank Erik Kuulkers, Phillip Podsiadlowski, Hendrik Schatz and the referee for useful comments, and Lars Bildsten for stressing that Type I bursts might test evolutionary models for LMXBs." This work was supported by NASA through Hubble Fellowship grant HF-01138 awarded by the Space Telescope Science. Institute. which is operated by the Association of Universities for Research in Astronomy. Inc.. for NASA. under contract NAS 5-260555.," This work was supported by NASA through Hubble Fellowship grant HF-01138 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555." ὦ and Wows instead are not a priori the same for cillerent emission lines. as they could originate from different: parts of the irradiated: companion star. or in fact regions in the binary.,"$\varphi$ and $_\mathrm{em}$ instead are not a priori the same for different emission lines, as they could originate from different parts of the irradiated companion star, or in fact regions in the binary." 1n order to measure the FWIIAL of the emission lines. we averaged the spectra in the frame of the companion star.," In order to measure the FWHM of the emission lines, we averaged the spectra in the frame of the companion star." We assumed a circular orbit. shifting the lines by Ixassin(2xo|ye). with o=0.," We assumed a circular orbit, shifting the lines by $v= -$ $_\mathrm{em}sin(2\pi\phi+\varphi)$, with $\varphi=0$." We dic not adopt a priori the Ix obtained from the racial velocity curves of the Balmer lines. since that could be alfected. by. e.g... asymmetry. or variations in the line profile from the individual spectra (as for the La. ?)).," We did not adopt a priori the $_\mathrm{em}$ obtained from the radial velocity curves of the Balmer lines, since that could be affected by, e.g., asymmetry or variations in the line profile from the individual spectra (as for the $\alpha$, \citealt{2009MNRAS.399.2055B}) )." Moreover. the Balmer lines could originate in à dillerent area than the weaker ones and thus have a cdilferent Ica.," Moreover, the Balmer lines could originate in a different area than the weaker ones and thus have a different $_\mathrm{em}$ ." Instead. we proceeded as follows: The spectrum in Figure 4 is the average of individual exposures comprised. between. phase 0.85 and 0.7. (where all the emission lines are visible) for Woy300kms," Instead, we proceeded as follows: The spectrum in Figure \ref{aver} is the average of individual exposures comprised between phase 0.35 and 0.7 (where all the emission lines are visible) for $_\mathrm{em}=300~\rmn{km\,s^{-1}}$." ‘Together with Le? and H5. the averaged spectrum highlights the weak Fe (or Ho) emission lines.," Together with $\beta$ and $\gamma$, the averaged spectrum highlights the weak Fe (or He) emission lines." No absorption lines appear in the averaged: spectrum., No absorption lines appear in the averaged spectrum. As for the individual spectra. a cross-corrclation of the average spectrum with the standard template spectra does not give a match.," As for the individual spectra, a cross-correlation of the average spectrum with the standard template spectra does not give a match." Note that we have also constructed an averaged spectrum in the phase interval 0.8 to 0.2 and 0.9 to 0.1. but we did not detect absorption lines from the non-irracliated [ace of the companion star.," Note that we have also constructed an averaged spectrum in the phase interval 0.8 to 0.2 and 0.9 to 0.1, but we did not detect absorption lines from the non-irradiated face of the companion star." ‘Table 1. presents the parameters of the best-fitting Ciaussian to each line in the averaged spectrum., Table \ref{fittab} presents the parameters of the best-fitting Gaussian to each line in the averaged spectrum. Each line was fitted for FWHIAL. normalisation and for the offset AAo of the line centroid A with respect to the rest-frame wavelength Ag.," Each line was fitted for FWHM, normalisation and for the offset $\lambda-\lambda_0$ of the line centroid $\lambda$ with respect to the rest-frame wavelength $\lambda _0$." As we corrected the spectra for the orbital motion only. the lines in the average spectrum are still shifted with respect to their rest-Erame wavelength by the systemic radial velocity 5.," As we corrected the spectra for the orbital motion only, the lines in the average spectrum are still shifted with respect to their rest-frame wavelength by the systemic radial velocity $\gamma$." The wavelength olfset of the Ll? and the H5 lines is consistent on a 2o level with the values of + derived. from the racial velocity curves (see Section 3.2))., The wavelength offset of the $\beta$ and the $\gamma$ lines is consistent on a $\sigma$ level with the values of $\gamma$ derived from the radial velocity curves (see Section \ref{rvcsec}) ). The weighted average of the messures of + from the racial velocity curves ancl from the offsets of the Balmer lines is 4 =43.8+3.6 kms+.," The weighted average of the messures of $\gamma$ from the radial velocity curves and from the offsets of the Balmer lines is $\gamma=$ $\pm$ $~\rmn{km\,s^{-1}}$." The olfsets of the lines are not consistent with this value. although they agree with each other on a 30 level.," The offsets of the lines are not consistent with this value, although they agree with each other on a $\sigma$ level." " In order to understand this dillerence. we have tested the dependence of the measured. line olfsets in the averaged. spectrum, on the choice of I4, and y in the orbital motion correction."," In order to understand this difference, we have tested the dependence of the measured line offsets in the averaged spectrum on the choice of $_\mathrm{em}$ and $\varphi$ in the orbital motion correction." " I the lines originate in different regions of the companion star. in [act. the two sets of lines will be associated with a different Ix, and οι"," If the lines originate in different regions of the companion star, in fact, the two sets of lines will be associated with a different $_\mathrm{em}$ and $\varphi$." We found that the ollset changes slowly with lau. but is sensitive to variations in s.," We found that the offset changes slowly with $_\mathrm{em}$, but is sensitive to variations in $\varphi$." The olfset of the lines in the average spectrum is consistent with the measure of 5 from the Balmer lines if the orbital motion of their source region is shifted in phase by Q.03z42z— 0.05., The offset of the lines in the average spectrum is consistent with the measure of $\gamma$ from the Balmer lines if the orbital motion of their source region is shifted in phase by $-$ $\lesssim \varphi \lesssim-$ 0.05. As we previously pointed out. the ENCLIIM of the lines (both 15. Le and the group) is not allected by changes in Ix of à few tens of kms around ~300 kms," As we previously pointed out, the FWHM of the lines (both $\gamma$, $\beta$ and the group) is not affected by changes in $_\mathrm{em}$ of a few tens of $\rmn{km\,s^{-1}}$ around $\sim$ 300 $\rmn{km\,s^{-1}}$." Unlike 10 Ollset. it is also not sensitive to changes of a few percent in ο.," Unlike the offset, it is also not sensitive to changes of a few percent in $\varphi$." In other words. our measure of the EWIIM is. not allected by a possible small displacement of the source region with respect to the source region of the Balmer lines.," In other words, our measure of the FWHM is not affected by a possible small displacement of the source region with respect to the source region of the Balmer lines." All the lines in the average spectrum have the same ENIM at a 260 level. withthe exception of the reddest," All the lines in the average spectrum have the same FWHM at a $\sigma$ level, withthe exception of the reddest" ion polarization drift. the electron response along the perturbed field lines is described by the drift-kinetic equation [Eq.(1)].,"ion polarization drift, the electron response along the perturbed field lines is described by the drift-kinetic equation [Eq.(1)]." " We assume a small deviation £j. from an equilibrium Maxwellian distribution fo: The electron density perturbation ts defined as 5,=/fidvyj and the parallel currentperturbation as Jj=—eAy Nolte. {je being the electron parallel velocity.f» απά the electron pressure perturbation ts defined as P,=zn,dv- Hence. Ampere's law and Poisson law can be[f written respectively as νAy=(4πο] and pzV2οὐ/=ne/no."," We assume a small deviation $f_{1}$ from an equilibrium Maxwellian distribution $f_{0}$: The electron density perturbation is defined as $n_{e}=\int f_{1}dv_{\parallel}$ and the parallel currentperturbation as $J_{\parallel}=-e\int v_{\parallel}f_{1}dv_{\parallel}=-en_{0}u_{\parallel e}$ , $u_{\parallel e}$ being the electron parallel velocity, and the electron pressure perturbation is defined as $P_{e}=m_{e}\int v_{\parallel}^{2}f_{1}d v_{z}$ Hence, Ampere's law and Poisson law can be written respectively as $\nabla^{2}_{\perp}A_{\parallel}=-(4/\pi c)J_{\parallel}$ and $\rho_{i}^{2}\nabla_{\perp}^{2} e\phi/T_{0i}=n_{e}/n_{0}$." " On one hand. taking the zeroth order moment ofΤο the electron kinetic equation provides the electron continuity equation: On the other hand. the first moment provides the parallel electron momentum equation: It is usual to refer to the last equation as the Ohms’s law and P,=neToe for an isothermal plasma."," On one hand, taking the zeroth order moment of the electron kinetic equation provides the electron continuity equation: On the other hand, the first moment provides the parallel electron momentum equation: It is usual to refer to the last equation as the Ohms's law and $P_{e}=n_{e}T_{0e}$ for an isothermal plasma." Therefore. there are two possible sources of parallel electric field associated with the electron dynamies: inertia and pressure (or density) variations along the field lines.," Therefore, there are two possible sources of parallel electric field associated with the electron dynamics: inertia and pressure (or density) variations along the field lines." " The continuity equation combined with Poisson law, yields a vorticity equation: Neglecting first the effects of electron inertia and electron pressure gradient m Ohm's law yields the MHD Ohm's law Ej -(.Le. Introducing the stream and flux function for the velocity u_=z V_y. and the magnetic field B_/4pm;=zxVw. defined as e=(c/Boó and w=—Ayj/yA4nnii;. gives with vy=Bo/vsu; being the Alfven velocity."," The continuity equation combined with Poisson law, yields a vorticity equation: Neglecting first the effects of electron inertia and electron pressure gradient in Ohm's law yields the MHD Ohm's law $E_{\parallel}=0$ , i.e. Introducing the stream and flux function for the velocity $\mathbf{u}_{\perp}=\mathbf{z}\times \nabla_{\perp}\varphi$ , and the magnetic field $\mathbf{B}_{\perp}/\sqrt{4\pi n_{0}m_{i}}=\mathbf{z}\times \nabla_{\perp}\psi$, defined as $\varphi=(c/B_{0})\phi$ and $\psi=-A_{\parallel}/\sqrt{4\pi n m_{i}}$, gives with $v_{A}=B_{0}/\sqrt{4\pi n_{0} m_{i}}$ being the Alfven velocity." These two equations are the standard linearized reduced-MHD equations describing shear-Alfven waves with frequency: In the case where the parallel electric field 1s produced by density fluctuation in Ohm's law. we have Ej=Gi—ikyToΠο).," These two equations are the standard linearized reduced-MHD equations describing shear-Alfven waves with frequency: In the case where the parallel electric field is produced by density fluctuation in Ohm's law, we have $E_{\parallel}=-ik_{\parallel}T_{0e}(n_{e}/n_{0})$." Using the Poisson equation. Ey=V—iKjp;6. which also reveals the vortical nature of the parallel electric. field.," Using the Poisson equation, $E_{\parallel}=-ik_{\parallel}\rho_{s}^{2}\nabla_{\perp}^{2} \phi$, which also reveals the vortical nature of the parallel electric field." " The parameterp,=c,/«;VToe/To; is the ton gyroradius at the electron temperature.", The parameter $\rho_{s}=c_{s}/\omega_{ci}=\sqrt{T_{0e}/T_{0i}}\rho_{i}$ is the ion gyroradius at the electron temperature. By including this parallel electric field in Ohim’s law. an extension of the previous reduced-MHD system now takes the form which describes the dynamics of kinetic Alfven waves with frequency It is worth noticing that equations (13))-(14)) can also be obtained directly from two-fluid MHD theory by retaining the Hall and electron pressure effects in Ohm's law(?)..," By including this parallel electric field in Ohm's law, an extension of the previous reduced-MHD system now takes the form which describes the dynamics of kinetic Alfven waves with frequency It is worth noticing that equations \ref{r1}) \ref{r3}) ) can also be obtained directly from two-fluid MHD theory by retaining the Hall and electron pressure effects in Ohm's \citep{Bian2009}." Using the above results. it is easily seen that for kinetic Alfven waves. the magnitude of the parallel electric field is related to B_ by The above fluid derivation of the Alfven wave frequency gives the same result as its kinetic counterpart. however the latter. which ts presented below. is more complete in the sense that it also provides the Imaginary part associated with Landau damping.," Using the above results, it is easily seen that for kinetic Alfven waves, the magnitude of the parallel electric field is related to $B_{\perp}$ by The above fluid derivation of the Alfven wave frequency gives the same result as its kinetic counterpart, however the latter, which is presented below, is more complete in the sense that it also provides the imaginary part associated with Landau damping." The electron kinetic equation can be solved for the perturbed distribution function fj. 1.8. Some notations are introduced: x=Πω. α=W/Kyye and with Zo(c') being the standard plasma dispersion function.," The electron kinetic equation can be solved for the perturbed distribution function $f_{1}$ , i.e. Some notations are introduced: $x=v_{\parallel}/v_{te}$, $\alpha=\omega/k_{\parallel}v_{te}$ and with $Z_{0}(\alpha)$ being the standard plasma dispersion function." " We also summarize some properties of the functions Z,: |2 aZo. Z»=wZ,."," We also summarize some properties of the functions $Z_{n}$: $Z_{1}=1+\alpha Z_{0}$ , $Z_{2}=\alpha Z_{1}$." Moreover. in the limita <| Using the above properties. it follows that the density and current perturbations are related to the parallel electric field through: for the density. and Hence. the relation between parallel current and parallel electric field Is It titheis convenient. to define a. collisionless plasma conductivity c às Its Imaginary part results in the dispersion of the Alfven wave and the its real part yields the collisionless dissipation.," Moreover, in the limit $\alpha\ll 1$ Using the above properties, it follows that the density and current perturbations are related to the parallel electric field through: for the density, and Hence, the relation between parallel current and parallel electric field is It is convenient to define a collisionless plasma conductivity $\sigma$ as Its imaginary part results in the dispersion of the Alfven wave and the its real part yields the collisionless dissipation." " In the limit a=c/Ayv,,«I. the real part is This also gives the energy per united time transferred to the electrons through the relation : Le. with ;1p, being the electronDebye length and Uy=|E|being the energy density of the parallel componentof the electric field."," In the limit $\alpha\equiv \omega/k_{\parallel}v_{te} \ll 1 $, the real part is This also gives the energy per united time transferred to the electrons through the relation : i.e. with $\lambda_{De}$ being the electronDebye length and $U_{E_{\parallel}}=\mid E^{2}_{\parallel}\mid/8 \pi$being the energy density of the parallel componentof the electric field." It is in fact a standard result that the asymptotic, It is in fact a standard result that the asymptotic Hattening (κο independent of the NLACTIO halo.,flattening $q_{\rm NB}$ independent of the MACHO halo. Ht can be shown (Appencix B) that to first order in z near the equatorial plane., It can be shown (Appendix B) that to first order in $z$ = v_c^2 near the equatorial plane. This gives ss , This gives _z^2 = - v_c^2. The lowest value for 6? is obtained for a spherical (q=1.0) non-barvonic halo., The lowest value for $\sigma_z^2$ is obtained for a spherical (q=1.0) non-baryonic halo. A larger value of the vertical velocity. clispersion will drive the transverse velocities up. he event durations down. and ultimately vield a higher mass estimate.," A larger value of the vertical velocity dispersion will drive the transverse velocities up, the event durations down, and ultimately yield a higher mass estimate." Since we are interested here in mocels which lower he ALACΠΟ mass estimates we take qxp=1 and find As we will see. the precise form. of the relationship between the rotation and. velocity dispersion. is. not iniportant for our conclusions.," Since we are interested here in models which lower the MACHO mass estimates we take $q_{\rm NB} = 1$ and find As we will see, the precise form of the relationship between the rotation and velocity dispersion is not important for our conclusions." We use equation. 19 as à &eneral guide to which combinations of rotation and velocity dispersions are reasonable., We use equation \ref{vsigrelation} as a general guide to which combinations of rotation and velocity dispersions are reasonable. We plot our results for the various halo models. in fiewes 4 through 6., We plot our results for the various halo models in figures 4 through 6. The solid. contours. correspond. to the predicted ΑςΠΟ mass estimate. corresponding to the average ALACLILO event duration of 61 days. as a function of the (one-dimensional) velocity dispersion and rotation speed.," The solid contours correspond to the predicted MACHO mass estimate, corresponding to the average MACHO event duration of 61 days, as a function of the (one-dimensional) velocity dispersion and rotation speed." For reference. the standard non-rotating halo with isotropic maxwellian velocity dispersion. has a dimensional dispersion o= I56km/s.," For reference, the standard non-rotating halo with isotropic maxwellian velocity dispersion has a one-dimensional dispersion $\sigma =156 {\rm km/s}$ ." The models within E104 of our Όμῃ curve (equation 19)) lie in the shaded. region between the dotted lines., The models within $\pm 10\%$ of our $\sigma-v_{\rm rot}$ curve (equation \ref{vsigrelation}) ) lie in the shaded region between the dotted lines. Alodels below this region are unlikely to have sullicient support., Models below this region are unlikely to have sufficient support. The trade-olf. of dispersion. velocity for. rotation velocity can be seen clearly., The trade-off of dispersion velocity for rotation velocity can be seen clearly. Figures 4. 5 and 6 show the predicted NLACTIO masses [or the spherical 1/77. Hlattened. 1/77 and spherical L/i7 halo models.," Figures 4, 5 and 6 show the predicted MACHO masses for the spherical $1/r^2$, flattened $1/r^2$ and spherical $1/r^{3.5}$ halo models." In. no case does the predicted. mass for the current NLACTIO event duration &o below 0.2542. in the allowed: region indicated. by equation 19," In no case does the predicted mass for the current MACHO event duration go below $0.25\Msol$ in the allowed region indicated by equation \ref{vsigrelation} ." As expected following the discussion in section 3. ↥↓↥∢⊾⊳∖↓≻↓⊔⋅↓⋰⊔∼⋜↧↓↓∣⋮− ⊔↓⋯⇂⋖⊾↓⋯∼∏⋯∐∙∖⇁↓≻↓⋅⋖⋅∠∐≼∼↿⊳∖⊀↓⊔≼↛↓⋅∢⊾⋜↧⊳∖⊀↓⊔⋏∙≟↳∖↓⇀∖≺⊲∐↻↓↥↓⋜↧≻≻∢⋅≻⇂↕↓↕↓⋜↧↿⋖⊾≻ as it becomes more rotation supported.," As expected following the discussion in section 3, the spherical $1/r^2$ model actually predicts increasing MACHO mass estimates as it becomes more rotation supported." Rotation Increases the velocities along the microlensing tube far [rom the Sun Icaciing to shorter event clurations for a given NLACTIO mass. or conversely. à larger ΔΙΑΠΟ mass estimate for a given observed event duration.," Rotation increases the velocities along the microlensing tube far from the Sun leading to shorter event durations for a given MACHO mass, or conversely, a larger MACHO mass estimate for a given observed event duration." Most microlensing in the standard halo model occurs. at distances where the velocities are increased. when a rotational velocity. component. is. added and hence the mass estimates for a givenevent curation increase., Most microlensing in the standard halo model occurs at distances where the velocities are increased when a rotational velocity component is added and hence the mass estimates for a givenevent duration increase. "From Eq. 14,","From Eq. \ref{C_ne}," we may see the odd-parity preference (i.e. €> 0) leads to lack of large-angle correlation power., we may see the odd-parity preference (i.e. $\epsilon>0$ ) leads to lack of large-angle correlation power. We like to emphasize that the lack of large-correlation is associated with the odd-parity preference at low multipoles (ie. power excess at even multipoles and power deficit at odd multipoles)., We like to emphasize that the lack of large-correlation is associated with the odd-parity preference at low multipoles (i.e. power excess at even multipoles and power deficit at odd multipoles). " On the other hand, simple suppression of overall low multipole power does not necessarily leads to the lack of large-angle correlation."," On the other hand, simple suppression of overall low multipole power does not necessarily leads to the lack of large-angle correlation." " For instance, suppressing octupole power, which mitigates the odd-parity preference, rather increases the large-angle correlation power."," For instance, suppressing octupole power, which mitigates the odd-parity preference, rather increases the large-angle correlation power." " In Fig. 7,,"," In Fig. \ref{C_l3}," " we show of the WMAP team’s Internal Linear Combination 91/2(ILC) map, where we have multiplied the suppression factor r to thequadrupole component of the map."," we show $S_{1/2}$ of the WMAP team's Internal Linear Combination (ILC) map, where we have multiplied the suppression factor $r$ to thequadrupole component of the map." " From Fig. 7,,"," From Fig. \ref{C_l3}," " we may see that the large-angle correlation power increases, as the octupole component are more suppressed."," we may see that the large-angle correlation power increases, as the octupole component are more suppressed." " As discussed previously, we have not found a definite non-cosmological cause of the discussed anomaly."," As discussed previously, we have not found a definite non-cosmological cause of the discussed anomaly." " Therefore, in this section, we are going to consider possible cosmological origins."," Therefore, in this section, we are going to consider possible cosmological origins." " Since primordial fluctuations, which were once on sub-Planckian scales, are stretched to the observable scales by inflation, trans- effects may leave imprints on a primordial power spectrum "," Since primordial fluctuations, which were once on sub-Planckian scales, are stretched to the observable scales by inflation, trans-Planckian effects may leave imprints on a primordial power spectrum \citep{Inflation_Planckian_problem,Inflation_Planckian_spectra,Inflation_Planckian_note,Inflation_Planckian_estimate,CMB_Planckian_signature,WMAP_oscillation,Inflation_Planckian,Inflation_initial}." "Though trans-Planckian imprints are highly(????????).. model-dependent (??),, most of the models predict oscillatory features in primordial power spectrum (???7????7???1).."," Though trans-Planckian imprints are highly model-dependent \citep{Planckian_Astrophysics,CMB_Planckian_observation}, most of the models predict oscillatory features in primordial power spectrum \citep{Inflation,Inflation_Planckian_problem,Inflation_Planckian_spectra,Inflation_Planckian_note,Inflation_Planckian_estimate,CMB_Planckian_signature,WMAP_oscillation,Inflation_Planckian,Inflation_initial,Planckian_Astrophysics,CMB_Planckian_observation,WMAP3:parameter}." " Given certain oscillatory features in primordial power spectrum, the trans-Planckian effects may produce the observed odd parity preference of CMB power spectrum."," Given certain oscillatory features in primordial power spectrum, the trans-Planckian effects may produce the observed odd parity preference of CMB power spectrum." " However, reconstruction of primordial power spectrum and investigation on features have not found a strong evidence for features in the primordial powerspectrum ?77?7?1).."," However, reconstruction of primordial power spectrum and investigation on features have not found a strong evidence for features in the primordial powerspectrum \citep{WMAP7:powerspectra,WMAP5:Cosmology,WMAP7:Cosmology,WMAP3:parameter,power_recon,power_svd,power_features}." " Therefore, we are going to consider what condition the observed odd-parity preference impose on primordial fluctuation, if a primordial power spectrum is a featureless power-law spectrum."," Therefore, we are going to consider what condition the observed odd-parity preference impose on primordial fluctuation, if a primordial power spectrum is a featureless power-law spectrum." " Decomposition coefficients are related to primordial perturbation as follows: where ®(k) is primordial perturbation in Fourier space, and gi(k) is a radiation transfer function."," Decomposition coefficients are related to primordial perturbation as follows: where $\Phi(\mathbf k)$ is primordial perturbation in Fourier space, and $g_{l}(k)$ is a radiation transfer function." " Using Eq. 15,,"," Using Eq. \ref{alm}, ," "we may show the decomposition coefficients of CMB anisotropy are given by: where we used the reality condition ®(—k)=*(k) and Yim(—n)=(—1)Yi,(à).","we may show the decomposition coefficients of CMB anisotropy are given by: where we used the reality condition $\Phi(-\mathbf k)= \Phi^*(\mathbf k)$ and $Y_{lm}(\hat{-\mathbf n})=(-1)^l\,Y_{lm}(\hat{\mathbf n})$." Eq. ," Using Eq. \ref{alm2}, ," "is trivial to show,for the odd number multipolesUsing |16,,=2nit— 1,"," it is trivial to show,for the odd number multipoles $l=2n-1$ ," Our iniial condition is a torus of gas in hverostatie equilibrium. entirely contained within the simulated volume: our goal is to present results characteristic of an accretion flow wilh a fixed aspect ratio in a long-term equilibrium.,"Our initial condition is a torus of gas in hydrostatic equilibrium, entirely contained within the simulated volume; our goal is to present results characteristic of an accretion flow with a fixed aspect ratio in a long-term equilibrium." Belore quoting results directly from the simulation data. we must therefore do (wo things: demonstrate that the fixed aspect ratio is achieved. and define more precisely the degree to which the simulation is in a statistical steady-state with respect to inflow.," Before quoting results directly from the simulation data, we must therefore do two things: demonstrate that the fixed aspect ratio is achieved, and define more precisely the degree to which the simulation is in a statistical steady-state with respect to inflow." We set the parameters of our cooling Iunction so that the ratio of the sound speed to the local orbital speed would produce a disk with a constant aspect ratio /7/r=0.13., We set the parameters of our cooling function so that the ratio of the sound speed to the local orbital speed would produce a disk with a constant aspect ratio $H/r = 0.13$. In Figure 1.. we show how well the temperature was held to 7; bv comparing the time-averaged volume-weighted temperature in the bound accretion flow to the local value of 7.," In Figure \ref{fig:tempcontrol}, we show how well the temperature was held to $T_*$ by comparing the time-averaged volume-weighted temperature in the bound accretion flow to the local value of $T_*$." " In the main disk body. (his mean value was about. 0.95)7,. but it rises sharply inside the 1SCO."," In the main disk body, this mean value was about $0.95)T_*$, but it rises sharply inside the ISCO." In other words. our cooling function succeeded in holding the disk temperature very close to (in tact. slightly below) the target temperature. but inside the ISCO. where the inflow Gime becomes comparable to or shorter than the cooling time. the temperature rises well above J).," In other words, our cooling function succeeded in holding the disk temperature very close to (in fact, slightly below) the target temperature, but inside the ISCO, where the inflow time becomes comparable to or shorter than the cooling time, the temperature rises well above $T_*$." llow well our temperature-regulation led to a disk aspect ratio matching the goal value of 0.13 can be seen in Figure 2.., How well our temperature-regulation led to a disk aspect ratio matching the goal value of 0.13 can be seen in Figure \ref{fig:scaleheight}. The actual H/r was slightly above the goal (70.14) through most of the simulation volume. but with a tendency to diminish invard inside 7=20M.," The actual $H/r$ was slightly above the goal $\simeq 0.14$ ) through most of the simulation volume, but with a tendency to diminish inward inside $r=20M$." At r—10M. Hrc 0.12: by the time the flow reaches the ISCO. it is only 0.07.," At $r=10M$, $H/r \simeq 0.12$ ; by the time the flow reaches the ISCO, it is only $\simeq 0.07$." Comparison with the eurve showing how the scale-height changes as a result of including the relativistic correction to the vertical gravity. (as discussed in 2.3)) demonstrates that this thinning ab small radius can be largely attributed to neglect of Chat effect., Comparison with the curve showing how the scale-height changes as a result of including the relativistic correction to the vertical gravity (as discussed in \ref{sec:radiative-cooling}) ) demonstrates that this thinning at small radius can be largely attributed to neglect of that effect. Thus. use of our cooling function achieved its principal goal: to place (he scale-height of the disk unuder explicit control.," Thus, use of our cooling function achieved its principal goal: to place the scale-height of the disk under explicit control." Because our cooling Iunction has a tuget temperature depending only on radius. al any parücular radius the gas in the main body of the disk is nearly isothermal. and the density profile is therefore close to Gaussian (Fig. 3)).," Because our cooling function has a target temperature depending only on radius, at any particular radius the gas in the main body of the disk is nearly isothermal, and the density profile is therefore close to Gaussian (Fig. \ref{fig:Gaussian}) )." At higher altitudes above the midplane. the density falls slower than (he Gaussian. presumably due to magnetic support.," At higher altitudes above the midplane, the density falls slower than the Gaussian, presumably due to magnetic support." For this reason. ihe moment scale-height is slightly greater than the IIWIIM (Fig. 2)).," For this reason, the moment scale-height is slightly greater than the HWHM (Fig. \ref{fig:scaleheight}) )." We chose a value of [//r small enough that a kev approximation of the NT theory could be approximately replicated in the simulation: the prompt radiation of dissipated heat., We chose a value of $H/r$ small enough that a key approximation of the NT theory could be approximately replicated in the simulation: the prompt radiation of dissipated heat. llowever. if the disk is to have a finite thickness. it cannotradiate all its heat.," However, if the disk is to have a finite thickness, it cannotradiate all its heat." The parameters, The parameters exposures in order to cope with tlie cosiuic rays. as well as to avoid approaching the CCD saturation level.,"exposures in order to cope with the cosmic rays, as well as to avoid approaching the CCD saturation level." The LRIS imagine data were reduced iu the standard fashion., The LRIS imaging data were reduced in the standard fashion. All frames were bias-subtractecd. aic pixel-to-pixel seusitivity variations were removed usiug dome flats.," All frames were bias-subtracted, and pixel-to-pixel sensitivity variations were removed using dome flats." Large-scale eracieuts were removed by dividing each frame by a normalized. two-dimiensioual spline fit to the sky values in a sky-Hat., Large-scale gradients were removed by dividing each frame by a normalized two-dimensional spline fit to the sky values in a sky-flat. The sky-flat was created by generating a nedian image [rom a stack of lrames for each ueht ancl passband., The sky-flat was created by generating a median image from a stack of frames for each night and passband. For the £ baud data. a two-cimenusioual fringe map was also created [rom the uedian filtered image by removing large-scale gradients within the meinu nuage.," For the $I$ band data, a two-dimensional fringe map was also created from the median filtered image by removing large-scale gradients within the median image." Priuging was removed from each { baud frame by subtracting a suitably scaled. version of the fringe map., Fringing was removed from each $I$ band frame by subtracting a suitably scaled version of the fringe map. linage registratiou for a giveu cluster field was performed by identifying approximately 10 saturated stars (detectable in all £ passbauds) to be used as astrometric reference points., Image registration for a given cluster field was performed by identifying approximately 10 unsaturated stars (detectable in all 4 passbands) to be used as astrometric reference points. The uean .X and Y ollsets of these stars in every [rame taken of the cluster were computed relative o their locations in a fiducial B band image., The mean $X$ and $Y$ offsets of these stars in every frame taken of the cluster were computed relative to their locations in a fiducial $B$ band image. All image data for the cluster were shifted to match he B band coordinate system using a flux conserving Lagrangian interpolation scheme to achieve ‘epistratiou at the sub-pixel level., All image data for the cluster were shifted to match the $B$ band coordinate system using a flux conserving Lagrangian interpolation scheme to achieve registration at the sub-pixel level. Ouce all frames of a given cluster were registered to a common coordinate system. the indlependent exposures in each passbaucl were co-added to produce the final our BVRE images.," Once all frames of a given cluster were registered to a common coordinate system, the independent exposures in each passband were co-added to produce the final four $BVRI$ images." The Weck imaging las been calibrated to the staucdard Cousius-Bessell-Laudolt (Cape) system hrough exposures of a number of Landolt standard star fields (Laudolt. 1992)., The Keck imaging has been calibrated to the standard Cousins-Bessell-Landolt (Cape) system through exposures of a number of Landolt standard star fields (Landolt 1992). " For a circular aperture with. a radius. of ""A3 . the approxiuate. limitiug.⋅⋅ magnuitudes⋅ are B=∙∣↡↽25.1. VT=i2Ll.2 R=23.5. and 4=21.7 for a 5-o detection."," For a circular aperture with a radius of $3^{''}$ , the approximate limiting magnitudes are $B = 25.1$, $V = 24.1$, $R = 23.5$, and $I = 21.7$ for a $\sigma$ detection." Multi-slit observations of the cluster field were made with LRIS iu spectroscopic mode using a 300¢nun! erating blazed at 5000A., Multi-slit observations of the cluster field were made with LRIS in spectroscopic mode using a $300~{\rm g~mm^{-1}}$ grating blazed at 5000. . The chosen erating provided a dispersion of 2.35 yper pixel aud a spectral coverage of 5100A., The chosen grating provided a dispersion of 2.35 per pixel and a spectral coverage of 5100. . The erating anele was set in order to provide coverage rom approximately 1100 to 9500 iin the first order., The grating angle was set in order to provide coverage from approximately 4400 to 9500 in the first order. A GG195 elass filter was used to eliminate the overlapping second order spectrum: here is. therefore. no second order contamination below 9700A.," A GG495 glass filter was used to eliminate the overlapping second order spectrum; there is, therefore, no second order contamination below 9700." . In order to obtain the full waveleneth range aloug the dispersion axis. the fiekd-of-view of the spectral observations was reduced rou that of the innagiug mode to approximately 2x8 arcimau.," In order to obtain the full wavelength range along the dispersion axis, the field-of-view of the spectral observations was reduced from that of the imaging mode to approximately $2 \times 8$ arcmin." Spectroscopic candidates were ποσο from preliminary Z2? baud imaging of each cluster field., Spectroscopic candidates were chosen from preliminary $R$ band imaging of each cluster field. All objects brighter than approximately R=23.5+0.1 within the spectroscopic Dield-o[-view ol LRIS were included. as cauclicdates for slit-mmask spectra.," All objects brighter than approximately $R = 23.5 \pm 0.1$ within the spectroscopic field-of-view of LRIS were included as candidates for slit-mask spectra." For each cluster field. six different slitinasks were mace with approximately 30 objects per mask (including MODguide stars and duplicate observations).," For each cluster field, six different slitmasks were made with approximately 30 objects per mask (including guide stars and duplicate observations)." The exposure time lor each mask was1 hour., The exposure time for each mask was1 hour. Flat-fielding aud waveleneth calibration, Flat-fielding and wavelength calibration αλλον. it is it clear observationallv that the disc in (νο X-2 is slightly fainter in the optical than the secondary star tthe observed. disc fractions in D. ancl £2 are zz0.3).,"Namely, it is it clear observationally that the disc in Cyg X-2 is slightly fainter in the optical than the secondary star the observed disc fractions in $B$ and $R$ are $\approx 0.3$ )." Llowever. Jan van Paradijs pointed out to us that relative züntness of the disc is somewhat surprising since one would expect a substantial amount of light from the reprocessing of the X-rays absorbed by the disc.," However, Jan van Paradijs pointed out to us that relative faintness of the disc is somewhat surprising since one would expect a substantial amount of light from the reprocessing of the X-rays absorbed by the disc." Phe He LL A4868 line is in emission. so presumably there is at. least some X-ray reprocessing.," The He II $\lambda4868$ line is in emission, so presumably there is at least some X-ray reprocessing." " Based on the relations given in van ""radijs AleClintock (1994).) the absolute V magnitude of the aceretion disc should be Ady=2.02+0.56."," Based on the relations given in van Paradijs McClintock (1994), the absolute $V$ magnitude of the accretion disc should be $M_V=-2.02\pm 0.56$." We compute Ady=0.38d0.35. for the disc. based on our moclel parameters (the secondary star by itself has Ady=0.54+ 0.24. see Section 4.2).," We compute $M_V=0.38\pm 0.35$ for the disc, based on our model parameters (the secondary star by itself has $M_V=-0.54 \pm 0.24$ , see Section 4.2)." Thus the disc in (νο N-2 is about a factor of 9 fainter in V than expected. based on the simple scaling laws given in van Paradijs MeClintock (1994)., Thus the disc in Cyg X-2 is about a factor of 9 fainter in $V$ than expected based on the simple scaling laws given in van Paradijs McClintock (1994). It is possible that much. of the reprocessed Dux from the disc is emitted. at shorter wavelengths than D. which might account for some of the mismatch between the observed and expected cise brightness.," It is possible that much of the reprocessed flux from the disc is emitted at shorter wavelengths than $B$, which might account for some of the mismatch between the observed and expected disc brightness." Presently. the code does not sell-consistently account for optical Dux from the disc due to reprocessing of absorbed A-ravs.," Presently, the code does not self-consistently account for optical flux from the disc due to reprocessing of absorbed X-rays." The brightness of the dise is set based. on the temperature at. the outer edge. the radial. temperature profile. and the cise radius. and is independent on the adopted value of Lo.," The brightness of the disc is set based on the temperature at the outer edge, the radial temperature profile, and the disc radius, and is independent on the adopted value of $L_x$." " The code is ""Hlexible in the sense that the power-law exponent on the temperature. radial profile can be adjusted to approximate the changes in the disc caused by irradiation.", The code is “flexible” in the sense that the power-law exponent on the temperature radial profile can be adjusted to approximate the changes in the disc caused by irradiation. As we showed above. the moclel cise fractions are not too dillerent than what is observed.," As we showed above, the model disc fractions are not too different than what is observed." lt therefore appears that this. lack of a. sell-consistent computation of the dise Dux is not a major problem., It therefore appears that this lack of a self-consistent computation of the disc flux is not a major problem. " The fits to the D and V. light curves are better if we assume that the disc is ⋠⋠⋠in a steady state where qeZ(r)xr0.73""7.", The fits to the $B$ and $V$ light curves are better if we assume that the disc is in a steady state where $T(r)\propto r^{-0.75}$. However. in this case the model disc is bluer than what is observed. since our predicted disc fraction in D (lg& 0.55) is larger than what is observed (Ag= 0.30).," However, in this case the model disc is bluer than what is observed since our predicted disc fraction in $B$ $k_B\approx 0.55$ ) is larger than what is observed $k_B\approx 0.30$ )." " Lowe assume that the dise is strongly irradiated so that Z'(r)xor""177. then the model disc is recleler and the predicted disc fraction in D (kgz 0.32) is closer to what is observed."," If we assume that the disc is strongly irradiated so that $T(r)\propto r^{-0.425}$, then the model disc is redder and the predicted disc fraction in $B$ $k_B\approx 0.32$ ) is closer to what is observed." However. in this case. the X7ο of the fit is much worse (47=48.4 compared to X7=40.9 with 36 degrees of freedom for the steady-state case).," However, in this case, the $\chi^2$ of the fit is much worse $\chi^2=48.4$ compared to $\chi^2=40.9$ with 36 degrees of freedom for the steady-state case)." Fortunately. the best-fitting values of the inclination are not that dillerent in the two cases: 7zz62.5. for the steady-state dise case and {5ο54.6% for the irradiated case. which is in the 2e range of the steady-state clise case.," Fortunately, the best-fitting values of the inclination are not that different in the two cases: $i\approx 62.5^{\circ}$ for the steady-state disc case and $i\approx 54.6^{\circ}$ for the irradiated case, which is in the $2\sigma$ range of the steady-state disc case." " For the sake of the discussion in Section 4 we adopt the Le inclination from the steady-state case (/=62.5""4°. where we assume the errors are Gaussian) because of the lower 47"," For the sake of the discussion in Section 4 we adopt the $1\sigma$ inclination from the steady-state case $i=62.5^{\circ}\pm 4^{\circ}$, where we assume the errors are Gaussian) because of the lower $\chi^2$." Lt is important to recall here that observed optical light curves consist mainly of two components: the light from the distorted secondary star and the light from the accretion disc., It is important to recall here that observed optical light curves consist mainly of two components: the light from the distorted secondary star and the light from the accretion disc. We have argued that there is very little extra light due to X-ray heating of the secondary star., We have argued that there is very little extra light due to X-ray heating of the secondary star. We assume that the light from the secondary star is modulated. in phase while the light from the disc is not (with the possible exception of a grazing eclipse)., We assume that the light from the secondary star is modulated in phase while the light from the disc is not (with the possible exception of a grazing eclipse). Thus to model the observed light curves we should. compute the relative amounts of disc light. and secondary star light at each observed wavelength region for every observed. phase., Thus to model the observed light curves we should compute the relative amounts of disc light and secondary star light at each observed wavelength region for every observed phase. In our current model we compute the disc light at every observed: wavelength region by specifying four parameters: 10 disc radius in terms of the neutron star Roche lobe radius. the opening angle of the disc rim. the temperature profile of the disc. and the temperature of the dise rim.," In our current model we compute the disc light at every observed wavelength region by specifying four parameters: the disc radius in terms of the neutron star Roche lobe radius, the opening angle of the disc rim, the temperature profile of the disc, and the temperature of the disc rim." The Hus at each grid point across the clise is computed from the local temperature assuming a blackbody Esspectrum., The flux at each grid point across the disc is computed from the local temperature assuming a blackbody spectrum. The code does not account for Dux from the disc due to reprocessing of absorbed: N-rays from the central source., The code does not account for flux from the disc due to reprocessing of absorbed X-rays from the central source. Typically. the spectrum. of the disc (in the optical) will have a rather different shape than the spectrum. of the secondary. star.," Typically, the spectrum of the disc (in the optical) will have a rather different shape than the spectrum of the secondary star." llence one should. have observed. light curves in as many wavelength bands as possible in order to better determine the shapes of the disc and stellar spectra., Hence one should have observed light curves in as many wavelength bands as possible in order to better determine the shapes of the disc and stellar spectra. Eclipsing svstenis with well-defined and smooth light curves like CRO 1655-40 (Orosz Dailyn 1997: van der Hooft et 11998) offer additional constraints on the disc radius. thickness. and Lemperatiure.," Eclipsing systems with well-defined and smooth light curves like GRO J1655-40 (Orosz Bailyn 1997; van der Hooft et 1998) offer additional constraints on the disc radius, thickness, and temperature." On the other hand. there is no particular reason to adopt our parameterization of the disc since the important quantity is the relative amount of disc and star light at a particular wavelength.," On the other hand, there is no particular reason to adopt our parameterization of the disc since the important quantity is the relative amount of disc and star light at a particular wavelength." In fact. by using suitably high quality spectra one could. simply measure the disc fraction Ay at several dilferent wavelengths covering the bandpasses of the observed light curves.," In fact, by using suitably high quality spectra one could simply measure the disc fraction $k_{\lambda}$ at several different wavelengths covering the bandpasses of the observed light curves." " In this case the mocel disc spectrum would be constructed from the model star spectrum, since re quantity Ay=faces(ficedfes) is known an each =vaveloneth point (here fais and faa, refer to the model uxes [rom the disc and star. respectively. at a given orbital hase)."," In this case the model disc spectrum would be constructed from the model star spectrum since the quantity $k_{\lambda}= f_{\rm disc}/(f_{\rm disc}+f_{\rm star})$ is known an each wavelength point (here $f_{\rm disc}$ and $f_{\rm star}$ refer to the model fluxes from the disc and star, respectively, at a given orbital phase)." Then. as before. the model disc spectrums is added o the model star spectrum. and the resulting composite spectrum is integrated with the filter response curves to oduce model fluxes in cach bandpass.," Then, as before, the model disc spectrum is added to the model star spectrum and the resulting composite spectrum is integrated with the filter response curves to produce model fluxes in each bandpass." Thus one could liminate the model parameters 7; and £., Thus one could eliminate the model parameters $T_d$ and $\xi$ . " We note that one μαill needs a model disc to account for the elfects of X-ray ga1aciowing by the disc rim ancl possibly the slight loss of Dux ue to the eclipse. so the model parameters 44, and ry are μαill neecect."," We note that one still needs a model disc to account for the effects of X-ray shadowing by the disc rim and possibly the slight loss of flux due to the eclipse, so the model parameters $\beta_{\rm rim}$ and $r_d$ are still needed." Thus. future modelling of the (νο X-2 light. curves can be improved by observing the light curves in more colours aat least in. D. V. Re and. £ ancl possibly also in the infrared) and by obtaining quasi-simultaneous spectroscopic observations of Cvg N-2 and template stars over a wide wavelength. range.," Thus, future modelling of the Cyg X-2 light curves can be improved by observing the light curves in more colours at least in $B$, $V$, $R$, and $I$ and possibly also in the infrared), and by obtaining quasi-simultaneous spectroscopic observations of Cyg X-2 and template stars over a wide wavelength range." In practice. one needs observations over many orbital eveles in order to average out the variations in the observed disc fractionand to define the lower light curve envelopes.," In practice, one needs observations over many orbital cycles in order to average out the variations in the observed disc fractionand to define the lower light curve envelopes." Iu this paper aud a companion publication (Mullallyal.2009) we have presented the first results from the SWARMS survey. an ongoing project aimed at discovering aud characterizing CWDBs in gcucral aud DDWD SN Ia progenitors in particular amoug the WDs in the spectroscopic SDSS data base.,"In this paper and a companion publication \citep{mullally09:DDWDs} we have presented the first results from the SWARMS survey, an ongoing project aimed at discovering and characterizing CWDBs in general and DDWD SN Ia progenitors in particular among the WDs in the spectroscopic SDSS data base." Further results and a complete description of the survey will be the subject of forthcoming publications., Further results and a complete description of the survey will be the subject of forthcoming publications. Our ultimate goal is to estimate a rate for the mereer of DDWD SN Ta progenitors in the Calasy and to use that rate. in combination with the results from SPY and other survevs. to assess the viability of the DDWD progenitor scenario for Type Ia SNe.," Our ultimate goal is to estimate a rate for the merger of DDWD SN Ia progenitors in the Galaxy, and to use that rate, in combination with the results from SPY and other surveys, to assess the viability of the DDWD progenitor scenario for Type Ia SNe." " To demoustrate the capabilities of SWARAIS. we have focused. on5128.. the first object found by the survey,"," To demonstrate the capabilities of SWARMS, we have focused on, the first object found by the survey." This WD was identified as a member of a binary system from the SDSS spectra. aud follow-up observations were performed to measure its orbital and spectral parameters.," This WD was identified as a member of a binary system from the SDSS spectra, and follow-up observations were performed to measure its orbital and spectral parameters." The RV curve has a poten of 1.5550+0.0007 hix. with a semiuupltude ofi). Te322.7+ i. ," The RV curve has a period of $4.5550 \pm 0.0007$ hr, with a semiamplitude of $322.7 \pm 6.3\,\mathrm{km\,s^{-1}}$ ." The primary WD is cold (~9000 LE makes the spectral analysis somewhat challe bu— we have derived a conservative estimate of 0.92Conrpantionuging.|i5M. for its mass.," The primary WD is cold $\sim9000$ K), which makes the spectral analysis somewhat challenging, but we have derived a conservative estimate of $0.92^{+0.28}_{-0.32}\,\mathrm{M_{\odot}}$ for its mass." This nuplies that the uuseeu iust be larger than 1.ilAES aud is probably a NS ora DIT.," This implies that the unseen companion must be larger than $1.62^{+0.20}_{-0.25}\,\mathrm{M_{\odot}}$, and is probably a NS or a BH." At a distance of D=I8!18 pe. this would be the closest remmant of a SN explosion to the Solar Systeun.," At a distance of $D=48^{+10}_{-19}$ pc, this would be the closest remnant of a SN explosion to the Solar System." We have discussed the implications of our discovery. aud suggested future avenues of research on this object.," We have discussed the implications of our discovery, and suggested future avenues of research on this object." This kind of massive. close binary is a perfect example of the objects that can be found by SWARAIS aud other similar surveys like MUCTIFUSS (Tillichetal.2009)..," This kind of massive, close binary is a perfect example of the objects that can be found by SWARMS and other similar surveys like MUCHFUSS \citep{tillich09:MUCHFUSS}." We anticipate more such discoveries. which we will report in the literature.," We anticipate more such discoveries, which we will report in the literature." We also plan to set up an on-line database of SWARMS objects., We also plan to set up an on-line database of SWARMS objects. IICN(I-0) ας be carefully studied to determine the effects of absorption and excitation.,HCN(1-0) must be carefully studied to determine the effects of absorption and excitation. The colorscale in Figure 9 shows a 1.2 nuu continua image taken bv Zvlka(1908) using the IRAM 30 im telescope., The colorscale in Figure \ref{pbcor} shows a 1.2 mm continuum image taken by \citet{zyl98} using the IRAM 30 m telescope. This 1.2 nun image traces thermal dust eumissiou in the region with adclitional free-free cussion iu the nini-spiral., This 1.2 mm image traces thermal dust emission in the region with additional free-free emission in the mini-spiral. Overlaid on the coutinuuuni cussion is a primacy beau corrected (3.3) velocity iutegrated map.," Overlaid on the continuum emission is a primary beam corrected (3,3) velocity integrated map." The primary beam correction was performed by dividing the velocity inteerated (3.3) cunission by the eaim of the interferometer at each point in the map.," The primary beam correction was performed by dividing the velocity integrated (3,3) emission by the gain of the interferometer at each point in the map." Ouly points with a gain 215% are plotted in Figure 9..., Only points with a gain $\ge$ are plotted in Figure \ref{pbcor}. Primary beau correction results in a imap with varving noise characteristics across the field., Primary beam correction results in a map with varying noise characteristics across the field. Although the rus noise of this image near the ficld center is still ~0.33 Jy t hans i. the noise is scaled up by the reciprocal of tle euin and is ~2.2 Jv + kn + at the map edee.," Although the rms noise of this image near the field center is still $\sim$ 0.33 Jy $^{-1}$ km $^{-1}$, the noise is scaled up by the reciprocal of the gain and is $\sim$ 2.2 Jy $^{-1}$ km $^{-1}$ at the map edge." There is a striking correspondence between the thenual dust aud (3.3) cussion.," There is a striking correspondence between the thermal dust and (3,3) emission." The southern streamer as well as SEL aud SE2 are clearly visible in both (3.3) aud 1.2 nuu dust.," The southern streamer as well as SE1 and SE2 are clearly visible in both (3,3) and 1.2 mm dust." The 20 kins + GAIC is the bright dust feature at LPin’tes. 29°02/30 and is well traced by (3.3) to the ede of the mosaic.," The 20 km $^{-1}$ GMC is the bright dust feature at $17\h45\m41\s$, $-29\dg02'30''$ and is well traced by (3,3) to the edge of the mosaic." " The 50 kins+ cloud cau be seen as the bright dust cunission to the northeast frou οο 2970015"" to LFbe51s. 2875900""."," The 50 km $^{-1}$ cloud can be seen as the bright dust emission to the northeast from $17\h45\m51\s$, $-29\dg00'15''$ to $17\h45\m51\s$, $-28\dg59'00''$." This GAIC is also close to the edge of the umage aud cau be seen as the bright Πο.) feature on the northeasteru edee of the mosaic.," This GMC is also close to the edge of the image and can be seen as the bright (3,3) feature on the northeastern edge of the mosaic." " There is also striking agreement along the ""northeru ridge.”", There is also striking agreement along the “northern ridge.” " This feature is clearly present in the dust image from 17?17Li. 2885900” to 17I5""ire. 28""5N/O0"" where it intersects the 50 kan s+ cloud."," This feature is clearly present in the dust image from $17\h45\m44\s$, $-28\dg59'00''$ to $17\h45\m47\s$, $-28\dg58'00''$ where it intersects the 50 km $^{-1}$ cloud." Both tracers show little or no ciission m the northwest quadrantof the image., Both tracers show little or no emission in the northwest quadrantof the image. " There is also a lack of NII3((3.3) and thermal dust cimission iu the cavity of Ser A East covering LTPismο to WTPineLi and =29°01/00"" to Pehs’|5""."," There is also a lack of (3,3) and thermal dust emission in the cavity of Sgr A East covering $17\h45\m48\s.5$ to $17\h45\m44\s$ and $-29\dg01'00''$ to $-28\dg58'45''$." The deeree of correlation between aud dust emission in the CND is dificult to determine due to he frec-free cussion that dominates the dust inge near Ser A West., The degree of correlation between and dust emission in the CND is difficult to determine due to the free-free emission that dominates the dust image near Sgr A West. Comparison of the 1.2 nun dust map to a 350 gan map w Dowellctal.(1999). shows that the cust cuaission 1s approximately constant over this waveleneth range.," Comparison of the 1.2 mm dust map to a 350 $\mu$ m map by \citet{dow99} shows that the dust emission is approximately constant over this wavelength range." The sinularity of the two maps iuplics that the 1.2 τα dust races cohuun density aud is not strongly correlated with cluperature in the region., The similarity of the two maps implies that the 1.2 mm dust traces column density and is not strongly correlated with temperature in the region. " The dust image has a beam size of —11"". and as a sinele dish map it detects lighly extended cussion."," The dust image has a beam size of $\sim$ $''$, and as a single dish map it detects highly extended emission." Consideriug the lack of zero-spacing information m the data (shortest baseline 35 11). the agreement between the two maps is compelling. sugeesting hat is a relatively unbiased tracer of cola density in the Galactic Center region.," Considering the lack of zero-spacing information in the data (shortest baseline 35 m), the agreement between the two maps is compelling, suggesting that is a relatively unbiased tracer of column density in the Galactic Center region." A few features seen du the NII3((3.3) image are rot observed in the thermal dust image.," A few features seen in the (3,3) image are not observed in the thermal dust image." " The ""westerü streamer is not stronglv correlated with the dust. aud here is almost no dust cussion in the upper two-thirds of this streamer."," The “western streamer” is not strongly correlated with the dust, and there is almost no dust emission in the upper two-thirds of this streamer." Line ratios of more than 1 in this region (sce Figure 5)) iucdicate that the western streamer is heated o Tp50 I. The narrow stream of gas connecting the rorthern ridge to the CND is also not strouglv correlated with the dust aud shows simular hiuts of high line ratios iu Figure 5.., Line ratios of more than 1 in this region (see Figure \ref{temp.fig}) ) indicate that the western streamer is heated to $T_R\simgt30$ K. The narrow stream of gas connecting the northern ridge to the CND is also not strongly correlated with the dust and shows similar hints of high line ratios in Figure \ref{temp.fig}. The heating aud absence of dust iu these features indicate that they may be located plivsically closer to Ser Α or nav originate in a different wav thau the streamers that contain dust., The heating and absence of dust in these features indicate that they may be located physically closer to Sgr A* or may originate in a different way than the streamers that contain dust. The velocity integrated (3.3) emission is overlaid oce 6 cl contiuuui emission (Yusef-Zadeh&MorrisL987) 1 Figure 10..," The velocity integrated (3,3) emission is overlaid on 6 cm continuum emission \citep{yus87} in Figure \ref{sgeast.fig}." The arms of the Ser A West πι]πίτα. can be seen im blue in the ceuter of the image., The arms of the Sgr A West mini-spiral can be seen in blue in the center of the image. " The eastern cedex of Ser A East exteuds to ~1715""505 and the wester- οσο is spatially coiuncideut with the western edge of tlic CND and imiuispiral", The eastern edge of Sgr A East extends to $\sim17\h45\m50\s$ and the western edge is spatially coincident with the western edge of the CND and mini-spiral. Ser A East is expanding with a- energv nore than au order of maguitude ereater tha- a typical supernova remnant (Mezeeretal.1989:CGon-geletal.19903.," Sgr A East is expanding with an energy more than an order of magnitude greater than a typical supernova remnant \citep{mez89,gen90}." . The (3.3) emission closely follows the outer edge of Ser A East.," The (3,3) emission closely follows the outer edge of Sgr A East." The shell is impacting the 50 kan | cloud in the east (Genzeletal.1990:Io1999) where material forms. a “ridge” on the western edee of the cloud.," The shell is impacting the 50 km $^{-1}$ cloud in the east \citep{gen90,ho91,ser92, zyl99} where material forms a “ridge” on the western edge of the cloud." " This ridge is seen in NIL;(C.3) frou Lrismsts. 20970015"" to 17I5""[75..— 28°59/00""."," This ridge is seen in (3,3) from $17\h45\m51\s$, $-29\dg00'15''$ to $17\h45\m47\s$, $-28\dg59'00''$." The northern ridge and western streamer also lie alone the outside edee of Ser A East., The northern ridge and western streamer also lie along the outside edge of Sgr A East. Therefore. it appears that Ser A East is expanding into material on all sides of the CND.," Therefore, it appears that Sgr A East is expanding into material on all sides of the CND." We observe multiple couuectious between the CND aud the ridges on the outside edge of Ser A East (see Section 5)., We observe multiple connections between the CND and the ridges on the outside edge of Sgr A East (see Section 5). These commectious are a strong indication that the CND and Ser A East are in close proximity to cach other., These connections are a strong indication that the CND and Sgr A East are in close proximity to each other. The southern edge of Ser A East is approximately coincident with the two southern clouds aud the southeru streamer., The southern edge of Sgr A East is approximately coincident with the two southern clouds and the southern streamer. Since the 720 law 1° giant molecular cloud Qvlich appears to be the source of at least the southern streamer (Iloetal.1991:Coil&Πο1999. 20003)) as thought to be located in front of Ser A East (Coil&Πο1999. 2000).. Ser A East may be expaudiug iuto the back these fluueuts," Since the “20 km $^{-1}$ ” giant molecular cloud (which appears to be the source of at least the southern streamer \citep{ho91,coi99,coi00}) ) is thought to be located in front of Sgr A East \citep{coi99,coi00}, Sgr A East may be expanding into the back of these filaments." " Iu addition. there is evidence that a uwNR ceutered at A,~st’A;—120"" (Coil&Ποιόσσ100,andreferencesthere) may be impacting Ser A ΕΠast along its southeastern edge."," In addition, there is evidence that a SNR centered at $\Delta_{\alpha}\sim 80'', \Delta_{\delta}\sim -120''$ \citep[and references therein]{coi00} may be impacting Sgr A East along its southeastern edge." This could account for σιie 1720. MIIz ΟΠ iuasers detected by Yusef-Zadehlietal.900) on the boundary between this SNR aud Ser A ast., This could account for the 1720 MHz OH masers detected by \citet{yus99} on the boundary between this SNR and Sgr A East. The interaction of these two expanding shells could also produce filameutary structures like SEL. SE2. aud the southern streiuucer.," The interaction of these two expanding shells could also produce filamentary structures like SE1, SE2, and the southern streamer." Figure l0 is also useful for studving the eap in (3.3) enuüssion in the northern part of the CND at the location of the northerm aru. of the minispiral.," Figure \ref{sgeast.fig} is also useful for studying the gap in (3,3) emission in the northern part of the CND at the location of the northern arm of the mini-spiral." As discussed in Section L1. this gap is also secu in WCN (1- emission.," As discussed in Section 4.1, this gap is also seen in HCN (1-0) emission." The lack of (3.3) cussion in acldition to the lack of TICN(1-0) emission aud the observation of 1720 OIL masers in this gap supports the idea that the northern anu of the nini-spiral originates outside the CND and is crossing over or through the CND on its way to the Galactic Center (Wrightetal. 2001)..," The lack of (3,3) emission in addition to the lack of HCN(1-0) emission and the observation of 1720 OH masers in this gap supports the idea that the northern arm of the mini-spiral originates outside the CND and is crossing over or through the CND on its way to the Galactic Center \citep{wri00}. ." Connections between the CND aud features at larecr distances such as the 20 and 50 kin | cloud cau provide an explanation for the origin of the clouds that compose the CND., Connections between the CND and features at larger distances such as the 20 and 50 km $^{-1}$ cloud can provide an explanation for the origin of the clouds that compose the CND. A connection must show more than, A connection must show more than used directly for à statistical analysis in a straightforward wav.,used directly for a statistical analysis in a straightforward way. The analvsis of the velocity integrated CO luminosity is further complicated by the fact that the CO line width varies from one galaxy to another (and even one position to another ina given galaxy) while the seusitivitv achieved also varies depending on the observing condition even if identical integration times are used (typically 2-£ hours)., The analysis of the velocity integrated CO luminosity is further complicated by the fact that the CO line width varies from one galaxy to another (and even one position to another in a given galaxy) while the sensitivity achieved also varies depending on the observing condition even if identical integration times are used (typically 2-4 hours). Therefore. it is difficult to address the seusitivitv anc completeness lint of the Survey iu terms of the observed CO flux.," Therefore, it is difficult to address the sensitivity and completeness limit of the Survey in terms of the observed CO flux." Instead. taking advantage of the well-known tight correlation between the FIR aud CO luninosity (scoYoungetal.1995).. we utilize the TRAS 60 jan flux deusitv of the individual sample galaxies to define a conplete sample for a statistical analvsis and the derivation of the CO LF.," Instead, taking advantage of the well-known tight correlation between the FIR and CO luminosity \citep[see][]{yng95}, we utilize the IRAS 60 $\mu$ m flux density of the individual sample galaxies to define a complete sample for a statistical analysis and the derivation of the CO LF." We further test the robustuess of the technique aud the selection bias by deriving the CO huninosity function using the optical B-baud selection (see 3.3))., We further test the robustness of the technique and the selection bias by deriving the CO luminosity function using the optical $B$ -band selection (see \ref{sec:COBLF}) ). Previously Briges&Bao(1993) successfully derived the III mass function ftx the field. galaxies using the optical selection. aud the racio Iuninositv function has been successfully derived using he FIR sclection function by Yunetal...(2001).," Previously \citet{br93} successfully derived the HI mass function for the field galaxies using the optical selection, and the radio luminosity function has been successfully derived using the FIR selection function by \citet{yun01}." Taking advautage of the well defined aud well studied IRAS Bright Galaxy Samples (BGSs:Soiferctal.1089:Saudersetal. 1995).. we adopt the sample selection criterion of 60 jan flux density limit greater than 5.21 Jy.," Taking advantage of the well defined and well studied IRAS Bright Galaxy Samples \citep[BGSs;][]{soi89,san95}, we adopt the sample selection criterion of 60 $\mu$ m flux density limit greater than 5.24 Jy." A total of 200 ealaxies in the Survey satisfy this criteria., A total of 200 galaxies in the Survey satisfy this criteria. Most of the selected galaxies are spirals of types σας while Ll salaxies are mcrecrs. 7 salaxies are close pairs. and 3 ealaxies have uo type determined.," Most of the selected galaxies are spirals of types Sa-Sc while 14 galaxies are mergers, 7 galaxies are close pairs, and 3 galaxies have no type determined." Du most cases we adopt the 60 gan fluxes from the BCS surveys., In most cases we adopt the 60 $\mu$ m fluxes from the BGS surveys. For galaxies with angular caaieters lavecr thanSN'.. we adopt the values from Riceet.al(1988). after multipliug by 1.185 in order to match the flux scaling (seeDevereux&Young 1990).," For galaxies with angular diameters larger than, we adopt the values from \citet{ric88} after multiplying by 1.18 in order to match the flux scaling \citep [see][]{dey90}." . This rescaling has little impact on our sample conrpleteness huit because most of our sample galaxies have flux deusities ich larger than 5.21 Jv., This rescaling has little impact on our sample completeness limit because most of our sample galaxies have flux densities much larger than 5.24 Jy. Some of the GU. you flux ceusity measurements come froii Youngctal.(1989. 2002).. and 10 ealaxies satistving our selection criterion are added to the sample.," Some of the 60 $\mu$ m flux density measurements come from \citet{yng89,yng02}, and 10 galaxies satisfying our selection criterion are added to the sample." Five of these galaxies are not in the BCS survev area. aud two are preseut im Riceet.al(1988) but not in the BCS surveys.," Five of these galaxies are not in the BGS survey area, and two are present in \citet{ric88} but not in the BGS surveys." There are 12 galaxies im in ot rwlected sample that are brighter than 5.21 Jv at 60 4i n aud were not detected in CÓ (see Table 1))., There are 12 galaxies in in our selected sample that are brighter than 5.24 Jy at 60 $\mu$ m and were not detected in CO (see Table \ref{tab:missing_galaxies}) ). The CO (10) flux ineasurements for five of these galaxies are foiπιο in the literature., The CO (1–0) flux measurements for five of these galaxies are found in the literature. The ronmuünius 7 galaxies are treatec as two ΜΗας cases: (a) as detectious with zero flux: aud (b) as detections at the upper limit flux value (seeVerter1987)., The remaining 7 galaxies are treated as two limiting cases: (a) as detections with zero flux; and (b) as detections at the upper limit flux value \citep[see][]{ver87}. . A lavee umber of nou-detections would severely Bait the determination of the the true CO LF. but the non-detectious account or less than in our smuple and thus have little overall nupact.," A large number of non-detections would severely limit the determination of the the true CO LF, but the non-detections account for less than in our sample and thus have little overall impact." Some of the galaxw distances come from direct ueasuremenuts such as using Ceplicids., Some of the galaxy distances come from direct measurements such as using Cepheids. We adopt a Hubble constaut of {1=75 luu + Mpe| for the remaining ealaxies., We adopt a Hubble constant of $H_0=75$ km $^{-1}$ $^{-1}$ for the remaining galaxies. Since we are using the CO database obtained ron larecly a single instrument of the sample taken youn other surveys}. the internal consistency of the data and the analysis should be quite οσους," Since we are using the CO database obtained from largely a single instrument of the sample taken from other surveys), the internal consistency of the data and the analysis should be quite good." ", Our sample also includes 26 galaxies in the Vireo cluster.", Our sample also includes 26 galaxies in the Virgo cluster. We adopt a uuiform distance of 16 Mpc for the Virgo galaxies., We adopt a uniform distance of 16 Mpc for the Virgo galaxies. We have constructed a CO LF with aud without Virgo galaxies in order to see if the presence of the cluster galaxies influcneed the shape of the CO LF (see 3)., We have constructed a CO LF with and without Virgo galaxies in order to see if the presence of the cluster galaxies influenced the shape of the CO LF (see 3). To examine the uniforiutv and completeness of our sanrple. we have analyzed the differcutial wmuber cout statistics as a function of the μή flux. density (soo Fig. Lj).," To examine the uniformity and completeness of our sample, we have analyzed the differential number count statistics as a function of the $60 \mu m$ flux density (see Fig. \ref{fig:S60counts}) )." " Th the 604050. sources are uniformly distributed iu a Enclidean space aud are uot evolviug. the resulting differeutial umber count should be a powerlaw distribution with ANxS77,"," If the $60 \mu m$ sources are uniformly distributed in a Euclidean space and are not evolving, the resulting differential number count should be a power-law distribution with $N\propto S^{-3/2}$." " The muuber of sunple ealaxies per biu shown in Figure 1l ds consistent with such a power-law, but the slope is somewhat shallower."," The number of sample galaxies per bin shown in Figure \ref{fig:S60counts} is consistent with such a power-law, but the slope is somewhat shallower." When all of the 8ux density bins are iucluded. the best fit power-law index isa =1.0. where JogN=Ny|a«logS.," When all of the flux density bins are included, the best fit power-law index is $\alpha=-1.0$, where $log~N=N_0+\alpha\times log~S$." For the 60:00 flix density between 10 aud 100 Jy where most of the sample galaxies fall. the differential ΠΙΟ counts are more cousistent with the uniform distribution within the statistical uncertainties.," For the $60 \mu m$ flux density between 10 and 100 Jy where most of the sample galaxies fall, the differential number counts are more consistent with the uniform distribution within the statistical uncertainties." There are several factors contributing to the flatter than expected power-law slo]| jiu the observed απο couuts in Figure 1.., There are several factors contributing to the flatter than expected power-law slope in the observed number counts in Figure \ref{fig:S60counts}. First of all. the spatial distribution of galaxies is in generalnet uniform. particularly eiven the relatively üeh fux density cutoff we adopted.," First of all, the spatial distribution of galaxies is in general uniform, particularly given the relatively high flux density cutoff we adopted." The situation is exacerbated by the fact that our Galaxy is located within a galaxy ageregate called the Local Supercluster., The situation is exacerbated by the fact that our Galaxy is located within a galaxy aggregate called the Local Supercluster. The Hattening of the galaxy counts among the high fiux density dus as seen in Fieure d ds au munediate outcome of the οσα] large scale structures., The flattening of the galaxy counts among the high flux density bins as seen in Figure \ref{fig:S60counts} is an immediate outcome of the local large scale structures. Soiferetal.(1989) noted a simular uuuber count enbhauceuneut in their analysis of the first Bright Galaxy Sample (BGS1)., \citet{soi89} noted a similar number count enhancement in their analysis of the first Bright Galaxy Sample (BGS1). " The mean or our sample is about 0.35. indicating that ou average our sample galaxies are about closer than the uniforiu case."," The mean $$ for our sample is about 0.35, indicating that on average our sample galaxies are about closer than the uniform case." " The $ values are particularly low for the log $L_{60\mu m}$ bins of 9.6-10.4 (see Fig. \ref{fig:vvm}) )," " aud simular treud is also seen iu the plot bv Soiferetal.—(1989).", and similar trend is also seen in the $$ plot by \citet{soi89}. ". Comparison to Soiferetal.(1989) value =0.17 is sugeestiug that major cause of this discrepancy is weak bias in our sample towards ealaxies closer than average expected from the complete sample. while the large scale structure plays less important role."," Comparison to \citet{soi89} value $=0.47$ is suggesting that major cause of this discrepancy is weak bias in our sample towards galaxies closer than average expected from the complete sample, while the large scale structure plays less important role." " Although the FCRAO CO Survey selected target ealaxics ""atf random” from the parent sample of TRAS and B-band selected galaxies. a slight bias favoring ealaxies which were well suited to the FCRAO resolution (1’-5/ in size) is also present."," Although the FCRAO CO Survey selected target galaxies “at random” from the parent sample of IRAS and $B$ -band selected galaxies, a slight bias favoring galaxies which were well suited to the FCRAO resolution $'$ $'$ in size) is also present." Such a bias maifests non-trivially in these statistics. however.," Such a bias manifests non-trivially in these statistics, however." Caven the Πταοτι of our saiuple. such as selecting galaxies suitable for observation with FCRAO telescope aud the local large scale structures. the steep power-law index of a~1.2 shown in Fieure 1 sugeests that our asstuption of rvaudom aud uniformi sampling from the pareut samples still sects reasonable.," Given the limitation of our sample, such as selecting galaxies suitable for observation with FCRAO telescope and the local large scale structures, the steep power-law index of $\alpha\sim -1.2$ shown in Figure \ref{fig:S60counts} suggests that our assumption of random and uniform sampling from the parent samples still seems reasonable." Effects of these potential biases ou the derivation of the LEs are evaluated by the derivation of the 60775 LF using the same sample. as discussed bellos.," Effects of these potential biases on the derivation of the LFs are evaluated by the derivation of the $\mu m$ LF using the same sample, as discussed bellow." A luminosity function represents the space density of the sample galaxies per luminosity bin (AL) centered on L. It represeuts the probability density of fiudiug a galaxy with a specific Iuninosity. aud it also coutaius information ou the total huuinosity in the sampled volune.," A luminosity function represents the space density of the sample galaxies per luminosity bin $\Delta L$ ) centered on L. It represents the probability density of finding a galaxy with a specific luminosity, and it also contains information on the total luminosity in the sampled volume." " We use the classical 1/V,, method (Schinidt1968) to derive the LF", We use the classical $1/V_m$ method \citep{sch68} to derive the LF comoving rate (7?72)..,"comoving rate \citep{le:07,guetta:07,kistler:07}." In this paper. we present the results of additional simulations that we have carried. out to test if the GIU LE can be a broken power-law.," In this paper, we present the results of additional simulations that we have carried out to test if the GRB LF can be a broken power-law." " With two supplementary parameters (the break luminosity £i, ancl the second slope). we have now 6 (resp."," With two supplementary parameters (the break luminosity $L_\mathrm{b}$ and the second slope), we have now 6 (resp." 7) free parameters in the Amati-like relation case (resp., 7) free parameters in the Amati-like relation case (resp. the case of a log-normal peak energy clistribution)., the case of a log-normal peak energy distribution). Lt is dillieult to constrain accurately so many parameters with Monte. Carlo simulations., It is difficult to constrain accurately so many parameters with Monte Carlo simulations. Therefore. we have chosen to keep the maximum luminosity constant in all our simulations.," Therefore, we have chosen to keep the maximum luminosity constant in all our simulations." We adopt Lis=1077ergs1 according to our previous study. (2)...," We adopt $L_\mathrm{max}=10^{53.5}\ \mathrm{erg~s^{-1}}$, according to our previous study \citep{daigne:06}. ." We also keep Lii constant. and. equal to a low value corresponding to weak GRBs that cannot be detected: at cosmological distance.," We also keep $L_\mathrm{min}$ constant, and equal to a low value corresponding to weak GRBs that cannot be detected at cosmological distance." We usually adopt Lui=107erg8.* bat we have also tested. other values (see next section), We usually adopt $L_\mathrm{min}=10^{45}\ \mathrm{erg~s^{-1}}$ but we have also tested other values (see next section). Keeping these two luminosities constant in our Monte Carlo simulation. we have the same number of degrees of freedom. than in the model with a simple power-law LE.," Keeping these two luminosities constant in our Monte Carlo simulation, we have the same number of degrees of freedom than in the model with a simple power-law LF." 1n our whole new set of simulations. we always find a clear minimum of X7.," In our whole new set of simulations, we always find a clear minimum of $\chi^{2}$." Phe parameters of the best model. as well as lo error bars are listed in table 1..," The parameters of the best model, as well as $1\ \sigma$ error bars are listed in table \ref{tab:bestmodels}." " As can be seen. we focus on the scenario where the comoving GRB rate follows SER, and the peak energy is given by the Amati-like relation."," As can be seen, we focus on the scenario where the comoving GRB rate follows $_{3}$ and the peak energy is given by the Amati-like relation." For comparison. we also give the parameters of two reference nmocels with a single power-law LE (2)..," For comparison, we also give the parameters of two reference models with a single power-law LF \citep{daigne:06}." Figure 3. illustrates. in the case SER: |Amatilike relation. the position of the best models in the parameter space of the LE.," Figure \ref{fig:parameterspace} illustrates, in the case $_{3}$ +Amati-like relation, the position of the best models in the parameter space of the LF." " As can be seen. the low-luminosity slope is strongly constrained to be small. 9j1. with a mean value 2,~0.6. while the high-Iuminosity slope is larger. 021.4. with a mean value 92~ 1.7."," As can be seen, the low-luminosity slope is strongly constrained to be small, $\delta_{1}\la 1$, with a mean value $\delta_{1}\sim 0.6$, while the high-luminosity slope is larger, $\delta_{2}\ga 1.4$, with a mean value $\delta_{2}\sim 1.7$ ." " The break luminosity (right panel) is not so well constrained: with. best models having. Li,c4.10""st 6107ergs", The break luminosity (right panel) is not so well constrained with best models having $L_\mathrm{b}\simeq 4\times 10^{50}$ $6\times 10^{51}\ \mathrm{erg~s^{-1}}$. " Figure 40 compares the Π of the data points (logNVlogP? chagram and £54, distribution) with the best model obtained. either with a power-law or a broken power-law LE.", Figure \ref{fig:fit} compares the fit of the data points $\log{N}-\log{P}$ diagram and $E_\mathrm{p}$ distribution) with the best model obtained either with a power-law or a broken power-law LF. Both mocels are in good agreement with data. without a preference for one or the other.," Both models are in good agreement with data, without a preference for one or the other." This is also indicated by the value of the reduced minim X? in both cases: 1.4 (power-law) anc 1.3 (broken power-law) for 37 degrees of freedom., This is also indicated by the value of the reduced minimum $\chi^{2}$ in both cases: 1.4 (power-law) and 1.3 (broken power-law) for 37 degrees of freedom. Figure 6 shows for the best moclel the LE as well as he luminosity distribution of bursts detected. by BATSE. LETTE? and SWIET.," Figure \ref{fig:luminosity} shows – for the best model – the LF as well as the luminosity distribution of bursts detected by BATSE, HETE2 and SWIFT." " Lt appears that the high-Iuminosity xanch above Li, is extremely close to the best model single power-law LE (thin line).", It appears that the high-luminosity branch above $L_\mathrm{b}$ is extremely close to the best model single power-law LF (thin line). These results indicate. that present cata are not sullicient to distinguish between a power-law and a broken power-law LE., These results indicate that present data are not sufficient to distinguish between a power-law and a broken power-law LF. Both models can provide equally good fits to the observations., Both models can provide equally good fits to the observations. Lt is however interesting that a broken power-law remains allowed. as there are good theoretical arguments in favor of such a shape (see Seet.2).," It is however interesting that a broken power-law remains allowed, as there are good theoretical arguments in favor of such a shape (see Sect.2)." " Table 1 show that the properties of the broken power-law LE remain very stable as long as Lagi, is kept to a low value (Luitoheresly he position of the break and especially the values of the two slopes are not. changing much. even for different GRB rates (SER, and SFRe have also been tested)"," Table \ref{tab:bestmodels} show that the properties of the broken power-law LF remain very stable as long as $L_\mathrm{min}$ is kept to a low value $L_\mathrm{min}\la 10^{48}\ \mathrm{erg~s^{-1}}$ ): the position of the break and especially the values of the two slopes are not changing much, even for different GRB rates $_{1}$ and $_{2}$ have also been tested)." Lt seems however that the broken power-law LE is more sensitive to the assumptions on the spectral parameters., It seems however that the broken power-law LF is more sensitive to the assumptions on the spectral parameters. " In the case where the spectral. properties. are not correlated. to the luminosity (log-normal peak energy distribution) the low-luminosity slope is not too cillerent from the ""Xmati-like relation"" case (δι20.7 instead of 0.6). but the break luminosity is larger (Lic107577 instead of 107.7ergs.1) and the high-Iuminositv branch is steeper (0521.8δε instead of 1.7). These results can be partially compared. το other studies."," In the case where the spectral properties are not correlated to the luminosity (log-normal peak energy distribution), the low-luminosity slope is not too different from the “Amati-like relation” case $\delta_{1}\simeq 0.7$ instead of $0.6$ ), but the break luminosity is larger $L_\mathrm{b}\simeq 10^{51-52}$ instead of $10^{50-51}\ \mathrm{erg~s^{-1}}$ ) and the high-luminosity branch is steeper $\delta_{2}\simeq 1.8-2.4$ instead of $1.7$ These results can be partially compared to other studies." Dased on an analysis of the BAVSE logeNΊου diagram. ? have tested. several shapes of CRB Les. includinga power-law anc a broken power-law.," Based on an analysis of the BATSE $\log{N}-\log{P}$ diagram, \citet{stern:02b} have tested several shapes of GRB LFs, includinga power-law and a broken power-law." " Their assumptions concerning GRB spectra are dillerent. [from those chosen in the present paper but are very close to our ""log-normal peak cnerey distribution""scenario.", Their assumptions concerning GRB spectra are different from those chosen in the present paper but are very close to our “log-normal peak energy distribution”scenario. For a GIUD rate similar to our 2 7. (?).., For a GRB rate similar to our $_{3}$ \citet{firmani:04} \citep{fenimore:00}. ?? ," \citet{guetta:05,guetta:07} " we have Although this scheme suggests the immediate reason for the differing dependences on Rossby number. the underlying reason must have to do with the differing magnetic fields on these sequences that are manifested in differing X-ray emission.,"we have Although this scheme suggests the immediate reason for the differing dependences on Rossby number, the underlying reason must have to do with the differing magnetic fields on these sequences that are manifested in differing X-ray emission." If (he X-ray emission scales simply with the total closed topology magnetic field. (hen we have a scheme here which roughly. parallels the suggestion in Barnes (2003) that ο—9d represents an evolutionary progression for solar-(vpe stars.," If the X-ray emission scales simply with the total closed topology magnetic field, then we have a scheme here which roughly parallels the suggestion in Barnes (2003) that $C \rightarrow g \rightarrow I$ represents an evolutionary progression for solar-type stars." In that case. the right-hand panels of 11 imply. in order. the creation/strengthening of a magnetic field on the sequence (super-saturalion in X-rav parlance). the attainment of a maximal field in the gap ο and the steady decay of this Ποιά for stars on theJ sequence (rotation-activity paradigm).," In that case, the right-hand panels of 1 imply, in order, the creation/strengthening of a magnetic field on the sequence (super-saturation in X-ray parlance), the attainment of a maximal field in the gap g (saturation), and the steady decay of this field for stars on the sequence (rotation-activity paradigm)." The paradigm suggested For the rotational evolution of stars is strikinglv parallel., The paradigm suggested for the rotational evolution of stars is strikingly parallel. It was suggested that stars on the convective sequence are initially equipped with only a convective or small-scale magnetic field) which cannot couple to the radiative interior., It was suggested that stars on the convective sequence are initially equipped with only a convective or small-scale magnetic field which cannot couple to the radiative interior. Thus. only the external convection zone is braked.," Thus, only the external convection zone is braked." This results in a large shear al (he convective/radiative interface. which creates an interface-tvpe clyvuamo and magnetic field.," This results in a large shear at the convective/radiative interface, which creates an interface-type dynamo and magnetic field." The field itself then couples the convective and radiative zones of the star. and drives (he star through the gap to the interface sequence. where the entire star is braked subsequently.," The field itself then couples the convective and radiative zones of the star, and drives the star through the gap to the interface sequence, where the entire star is braked subsequently." In this picture. the X-ray observations would therefore be interpreted to indicate the creation ancl strengthening of the interface dynamo among theC sequence stars. (he attainment of a maximal field [or the stars. and the decay of the interface field among the/ sequence stars.," In this picture, the X-ray observations would therefore be interpreted to indicate the creation and strengthening of the interface dynamo among the sequence stars, the attainment of a maximal field for the stars, and the decay of the interface field among the sequence stars." The Chromospherie Call Jxlx emission from soler-twpe stars in the field has been known to decline steadily with age (eg., The Chromospheric II K emission from solar-type stars in the field has been known to decline steadily with age (eg. Wilson 1963: Skumanich 1972)., Wilson 1963; Skumanich 1972). In fact. this decline is well-behaved enough that it is currently used to derive stellar ages for field stars (Soderblom. Duncan Johnson 1991: Donahue 1993).," In fact, this decline is well-behaved enough that it is currently used to derive stellar ages for field stars (Soderblom, Duncan Johnson 1991; Donahue 1998)." These stars might reasonably be expected to be similar to those that obey the rotation-Xrav activity paradigm. ancl to be located on the interlace sequence since {μον are mostly older than several hundred megavears.," These stars might reasonably be expected to be similar to those that obey the rotation-Xray activity paradigm, and to be located on the interface sequence since they are mostly older than several hundred megayears." "mode coupling, creating a high frequency Am=1 gap.","mode coupling, creating a high frequency $\Delta m=1$ gap." " The analysis of these Am=1 gaps was not performed here, but left to future work."," The analysis of these $\Delta m = 1$ gaps was not performed here, but left to future work." We note that the crosses with zero frequency correspond to the Eulerian entropy continuum., We note that the crosses with zero frequency correspond to the Eulerian entropy continuum. Fig., Fig. 12 contains the plot for an equilibrium with intermediate gravity g=0.500., \ref{fig:constantT_intermediateg} contains the plot for an equilibrium with intermediate gravity $g=0.500$. The temperature is again assumed to be a flux function., The temperature is again assumed to be a flux function. " Near the q—1 surface (s£ 0.927), the results of PHOENIX and the four- coupling scheme show excellent agreement for the m=1 Alfvénn and slow continuum."," Near the $q=1$ surface $s \approx 0.927$ ), the results of PHOENIX and the four-mode coupling scheme show excellent agreement for the $m=1$ Alfvénn and slow continuum." Owing to the, Owing to the As discussed in Rosenberg et al. (2000..," As discussed in Rosenberg et al. \cite{rosenberg00}," hereafter Paper D). the heterogeneity of the data often used in the literature for large scale studies of the Galactic globular cluster (GGC) properties has induced us to start a large survey of both southern and northern GGCs by means of I-m class telescopes. i.e. the 9lem European Southern Observatory (ESO) / Dutch telescope and the Im Isaac Newton Group (ING) / Jacobus Kapteyn telescope (JKT).," hereafter Paper I), the heterogeneity of the data often used in the literature for large scale studies of the Galactic globular cluster (GGC) properties has induced us to start a large survey of both southern and northern GGCs by means of 1-m class telescopes, i.e. the 91cm European Southern Observatory (ESO) / Dutch telescope and the 1m Isaac Newton Group (ING) / Jacobus Kapteyn telescope (JKT)." We were able to collect the data for 52 of the 69 known GGCs with GyM)<16.15., We were able to collect the data for 52 of the 69 known GGCs with $(m-M)_{\rm V}\leq16.15$. Thirty-nine objects have been observed with the Dutch Telescope and the data have been already presented in Paper I. The images and the photometry of the remaining 13 GGCs. observed with the JKT are presented in this paper.," Thirty-nine objects have been observed with the Dutch Telescope and the data have been already presented in Paper I. The images and the photometry of the remaining 13 GGCs, observed with the JKT are presented in this paper." A graphical representation of the spatial distribution of our cluster sample ts given in Fig., A graphical representation of the spatial distribution of our cluster sample is given in Fig. | As a first exploitation of this new data base. we have conducted a GGC relative age investigation based on the best 34 CMDs of our catalog (Rosenberg et al. 1999..," \ref{f:galdist} As a first exploitation of this new data base, we have conducted a GGC relative age investigation based on the best 34 CMDs of our catalog (Rosenberg et al. \cite{rosenberg99}," hereafter Paper III). showing that most of the GGCs have the same age.," hereafter Paper III), showing that most of the GGCs have the same age." We have also used the data base to obtair a photometric metallicity ranking seale (Saviane et al. 2000..," We have also used the data base to obtain a photometric metallicity ranking scale (Saviane et al. \cite{saviane00}," hereafter Paper IV). based on the red giant branch (RGB) morphology.," hereafter Paper IV), based on the red giant branch (RGB) morphology." There are many other parameters that can be measured from an homogeneous. well calibrated CMD data base: the horizontal branch (HB) level. homogeneous reddening and distance scales. etc.," There are many other parameters that can be measured from an homogeneous, well calibrated CMD data base: the horizontal branch (HB) level, homogeneous reddening and distance scales, etc." We are presently working on these problems., We are presently working on these problems. However. we believe it is now the time to present to the community the complete data base to give to anyone interested the opportunity to take advantage of it.," However, we believe it is now the time to present to the community the complete data base to give to anyone interested the opportunity to take advantage of it." In the next section. we will describe the observations collected at the JKT in 1997.," In the next section, we will describe the observations collected at the JKT in 1997." The data reduction and calibration is presented in Sect. 3..," The data reduction and calibration is presented in Sect. \ref{dat}," where a comparison of the calibration of the northern and southern clusters is also discussed for three objects observed with both telescopes., where a comparison of the calibration of the northern and southern clusters is also discussed for three objects observed with both telescopes. In order to assist the reader. in Sect.," In order to assist the reader, in Sect." 4 we present the main parameters characterizing our clusters., \ref{parameters} we present the main parameters characterizing our clusters. Finally. the observed fields for each cluster. and the obtained CMDs are presented and briefly discussed in Sect. 5..," Finally, the observed fields for each cluster, and the obtained CMDs are presented and briefly discussed in Sect. \ref{cmds}." The data were collected on May 30-June 2 1997., The data were collected on May 30-June 2 1997. For almost 2 nights we had quite good seeing conditions (FWHM between 0.65 and 0.85 arcsec)., For almost 2 nights we had quite good seeing conditions (FWHM between 0.65 and 0.85 arcsec). Unfortunately. too few standards were observed during this run.," Unfortunately, too few standards were observed during this run." In order to ensure an homogeneous calibration. we reobserved all the same cluster fields (plus," In order to ensure an homogeneous calibration, we reobserved all the same cluster fields (plus" for one particulary calculation (sec Fig. 8)).,for one particular calculation (see Fig. \ref{fig:totaleclipse}) ). Our main conclusion a rather unlikely presence of an disk iu is unchanged. aud thus a better treatment of the back-side ilbuniuated disk is not necessary.," Our main conclusion – a rather unlikely presence of an disk in – is unchanged, and thus a better treatment of the back-side illuminated disk is not necessary." We now calculate the colmbined star plus csk Iuuinositv for S2 (Figure 7)). first asuniug that the disk is inclined at ¢=607 ad that rotation angle ο)=300°.," We now calculate the combined star plus disk luminosity for S2 (Figure \ref{fig:lightcurvenohole}) ), first assuming that the disk is inclined at $i=60$ and that rotation angle $\beta=300$." . The triangles show the times when ?? actually observed the star.," The triangles show the times when \cite{Schoedel02,Schoedel03} actually observed the star." The maxima rear infrared dDundnositv reached by the source is the same. roughly half the stars bolometric hnuuinositv. iu all the three frequency bands.," The maximum near infrared luminosity reached by the source is the same, roughly half the star's bolometric luminosity, in all the three frequency bands." The maxima are reached rwearly simultaneously around the time when the star physically crosses the disk., The maxima are reached nearly simultaneously around the time when the star physically crosses the disk. The very sharp drops iu the disk πιοτν near the maxima are siuplv duc to the act that the disk becomes “too” hot when the star is very close to the surface of the disk (e.¢.. see Fig. 6)).," The very sharp drops in the disk luminosity near the maxima are simply due to the fact that the disk becomes “too” hot when the star is very close to the surface of the disk (e.g., see Fig. \ref{fig:nuLnuvsdist}) )." Iu this case he three near imfrared bands are on the Ravleigh-Jeans part of the disk. dlackbody curves and the emission is therefore weak., In this case the three near infrared bands are on the Rayleigh-Jeans part of the disk blackbody curves and the emission is therefore weak. The part of he light curve between the two maxima in ~2001.8 and z2002. Lis the time when the star is eclipsed by the disk so that the disk emission should be actually reduced at these moments as we explained above., The part of the light curve between the two maxima in $\simeq 2001.8$ and $\simeq 2002.4$ is the time when the star is eclipsed by the disk so that the disk emission should be actually reduced at these moments as we explained above. In Fie., In Fig. S we show the extreme case when the optical depth of the disk is so high that all the eiissiou is absorbed by the disk material diving the eclipse., \ref{fig:totaleclipse} we show the extreme case when the optical depth of the disk is so high that all the emission is absorbed by the disk material during the eclipse. " Comparing the Έπος,", Comparing the Figs. 7 aud 8.. we observe that infinite disk. oricuted as in these Figures. is ruled out by the existing data.," \ref{fig:lightcurvenohole} and \ref{fig:totaleclipse}, we observe that infinite disk, oriented as in these Figures, is ruled out by the existing data." " There las been no changes in S2* A, baud flux down to ~1020% level for all LO vears of the observations (private conmmunication from BR. Schoddel).", There has been no changes in S2's $K_s$ band flux down to $\sim 10-20$ level for all 10 years of the observations (private communication from R. Schöddel). We test the seusitivitv of the result ou the cisk inclination angle. /. in Fig.o 9.. ," We test the sensitivity of the result on the disk inclination angle, $i$, in Fig. \ref{fig:Kslightcurves}, ," where we fx the disk rotation angle.) —3507.. but vary 7.," where we fix the disk rotation angle, $\beta$ =, but vary $i$." Three different values of7 (30. GO aud 807)) are chosen.," Three different values of $i$ (30, 60 and ) are chosen." Oulv the Jv Iuuinositv of the star plus disk svsteimi is shown., Only the $K_s$ luminosity of the star plus disk system is shown. The maxima near imfrared Iniinositv reached by the tliree curves is he sune as iu Fieure 7.. but the times of the maxima and the width of the curves are different.," The maximum near infrared luminosity reached by the three curves is the same as in Figure \ref{fig:lightcurvenohole}, but the times of the maxima and the width of the curves are different." T Is apparent that it is hard to escape the tight observational coustraimts uuless the disk oricuted exactlyedge ou to the observer., It is apparent that it is hard to escape the tight observational constraints unless the disk oriented exactlyedge on to the observer. Finally. we perform a search in the parameter spaceiu the manner simular to that done in §??..," Finally, we perform a search in the parameter spacein the manner similar to that done in \ref{sec:size}. ." In particular. we," In particular, we" Alicrolensing is indicated. either. by independent temporal variability of image Iuxes. or by variation in colour between images at à single epoch (separated by the macro-image delav).,"Microlensing is indicated either by independent temporal variability of image fluxes, or by variation in colour between images at a single epoch (separated by the macro-image delay)." Large. and rapid variation of the continuum Hux is found in the variability record for 2237|0305 (Irwin ct al.," Large, and rapid variation of the continuum flux is found in the variability record for Q2237+0305 (Irwin et al." 1989: Corrigan et al., 1989; Corrigan et al. L991: Ostensen οἱ al., 1991; $\O$ stensen et al. 1996: Wozniak ct al., 1996; Wozniak et al. 2000a.b).," 2000a,b)." This variation has been used to argue that the optical emission. region must. be significantly. smaller than the microlens Einstein. lacius (LER). and therefore the typical scale of the caustic structure (c.g. Wambseanss. Paczvnski Schneider. 1990: \Wyithe. Webster. Turner Mortlock 2000: Yonehara 2001).," This variation has been used to argue that the optical emission region must be significantly smaller than the microlens Einstein Radius (ER), and therefore the typical scale of the caustic structure (e.g. Wambsganss, Paczynski Schneider 1990; Wyithe, Webster, Turner Mortlock 2000; Yonehara 2001)." During a caustic crossing. a small source exhibits colour variability if the emission spectrum is scale dependent (c.g. Wambseanss Paczvnski 1991: Fluke Webster 1999).," During a caustic crossing, a small source exhibits colour variability if the emission spectrum is scale dependent (e.g. Wambsganss Paczynski 1991; Fluke Webster 1999)." Evidence of this elect from broad band observations of a microlensing event was presented by Corrigan ct al. (, Evidence of this effect from broad band observations of a microlensing event was presented by Corrigan et al. ( 1991).,1991). Furthermore. if the quasar emits in one wave-band at a scale much smaller than 1e ER. and on a scale larger than the Elin another band. ren colour change may be seen in two random observations ofa single image (particularly if the observations straclelle a caustic crossing event). or between two cdilferent images. as à result of magnification of the smaller source.," Furthermore, if the quasar emits in one wave-band at a scale much smaller than the ER, and on a scale larger than the ER in another band, then colour change may be seen in two random observations of a single image (particularly if the observations straddle a caustic crossing event), or between two different images, as a result of magnification of the smaller source." Ground based observations have confirmed dillerential amplification of the emission region., Ground based observations have confirmed differential amplification of the emission region. Lewis et al. (, Lewis et al. ( 1998) determined the ratios of emission line equivalent widths relative to one image.,1998) determined the ratios of emission line equivalent widths relative to one image. They show (7) the ratios remain fairly constant for one image fron line to line. suggesting that the sizes of the emission regions for the lines are not greatly. cillerent.(77) that the ratios vary from image to image for a single epoch by a factor of 2.5. and (777) that the ratio for a single image varies as a function of time. ie. as a result of a microlensing event.," They show $(i)$ the ratios remain fairly constant for one image from line to line, suggesting that the sizes of the emission regions for the lines are not greatly different, $(ii)$ that the ratios vary from image to image for a single epoch by a factor of $\sim 2.5$, and $(iii)$ that the ratio for a single image varies as a function of time, i.e. as a result of a microlensing event." These results are consistent with earlier results of Fillipenko (1989) who measured a ~25% dillerence in the width of the Mel lines between the A and D images., These results are consistent with earlier results of Fillipenko (1989) who measured a $\sim25\%$ difference in the width of the MgII lines between the A and B images. " ""The CLEA] line. produced by extended broad Line regions las been measured in an attempt to find the Εαν ratios (2?) using emission scales bevond the inlluence of microlensing (Yeo De Robertis 1992: Racine 1992: bitte Adam 1994: Saust 1904: Lewis et al."," The CIII] line, produced by extended broad line regions has been measured in an attempt to find the flux ratios $(R)$ using emission scales beyond the influence of microlensing (Yee De Robertis 1992; Racine 1992; Fitte Adam 1994; Saust 1994; Lewis et al." 1905)., 1998). Meciavilla οἱ al. (, Mediavilla et al. ( 1998) observed the CHI] line in Q2237|0305. using «νοdimensional spectroscopy. and. found an are (image of the extended narrow line region of the source) extending around hrec of the images.ὃν indicatingo a very extended: region.ὃν of emission.,"1998) observed the CIII] line in Q2237+0305 using two-dimensional spectroscopy, and found an arc (image of the extended narrow line region of the source) extending around three of the images, indicating a very extended region of emission." On the other hand. measurement of A using he CLUJ line is subject to differential extinction. and uncertainties in continuum subtraction.," On the other hand, measurement of $R$ using the CIII] line is subject to differential extinction, and uncertainties in continuum subtraction." To avoid the cllects of extinction. ancl possibly microlensing Falco et al. (," To avoid the effects of extinction, and possibly microlensing Falco et al. (" 1996) imaged Q2237|0305 at 3.Gem. finding tux ratios similar to those inferred. from CHI].,"1996) imaged Q2237+0305 at 3.6cm, finding flux ratios similar to those inferred from CIII]." In addition. Q2237|0305 enshas also been imaged in the Ultraviolet. (Blanton. Wanmbseanss 1908). and in N-ravs (Wambseanss. Brunner. Schindler Falco 1999)," In addition, Q2237+0305 has also been imaged in the Ultraviolet (Blanton, Turner Wambsganss 1998), and in X-rays (Wambsganss, Brunner, Schindler Falco 1999)." Alany models have been proposed for the projected lens mass distribution based. on observations of the [ensed images of OQ2237]|0305 (c.g. INE'SS: S8S: lxochanek. 1991. hereafter IX91: Wanmbsganss Paczvenski. 1994. hereafter WPO4: Witt. Mao Seheehter 1995. hereafter: WMS95: SWLOS: Chae. Turnshek Ixhersonskv 1998. hereafter CHEIO9S).," Many models have been proposed for the projected lens mass distribution based on observations of the lensed images of Q2237+0305 (e.g. KF88; S88; Kochanek 1991, hereafter K91; Wambsganss Paczynski 1994, hereafter WP94; Witt, Mao Schechter 1995, hereafter WMS95; SWL98; Chae, Turnshek Khersonsky 1998, hereafter CTK98)." The majority of these. predict a Εαν ratio for images Band A of ReycO.SO1.1. consistent with the ralio measured in the radio of Rey=1.150.3 (Falco e al.," The majority of these predict a flux ratio for images B and A of $R_{BA}\sim 0.80 - 1.1$, consistent with the ratio measured in the radio of $R_{BA}=1.1\pm0.3$ (Falco et al." 1996)., 1996). However. over the monitoring history. the optica light-curve shows variations in Wey between ~0.2 and ~ 0.," However, over the monitoring history, the optical light-curve shows variations in $R_{BA}$ between $\sim 0.2$ and $\sim 1.0$ ." Phe discrepaney is attributed primarily to microlensing. and firmly demonstrates that the optical Lux ratios canno be used as model constraints (c.g. SSS: INESS: IX91: N94)," The discrepancy is attributed primarily to microlensing, and firmly demonstrates that the optical flux ratios cannot be used as model constraints (e.g. S88; KF88; K91; WP94)." Agol. Jones Blaes (2000) (hereafter A.JBOO) have founc a mid-Hlti. DX [lux ratio of fey~1.1.," Agol, Jones Blaes (2000) (hereafter AJB00) have found a mid-IR B:A flux ratio of $R_{BA}\sim1.1$." This ratio is consistent with observations in the radio (Paleo et al., This ratio is consistent with observations in the radio (Falco et al. 1996), 1996). AJBOO interpreted their results as evidence for an extende region of mid-LH emission. with dimensions larger than the microlens Einstein Raclius.," AJB00 interpreted their results as evidence for an extended region of mid-IR emission, with dimensions larger than the microlens Einstein Radius." In this paper we use microlensing models to caleulate distributions of (lus ratios for sources with dillerent sizes aud intensity. profiles. and hence derive quantitative limits on the scale of the mid-LIE emission.," In this paper we use microlensing models to calculate distributions of flux ratios for sources with different sizes and intensity profiles, and hence derive quantitative limits on the scale of the mid-IR emission." ln Secs., In Secs. 2. and 3. we describe he microlensing models. and summarise published: macro-models for Q2237|0305.," \ref{models} and \ref{macros} we describe the microlensing models, and summarise published macro-models for Q2237+0305." Sec., Sec. 4. discusses the methods used o infer the mid-LHR source size from the observed optical aud micd-L fux ratios. and the source size limits implied by the xiblished: macromocdels.," \ref{results} discusses the methods used to infer the mid-IR source size from the observed optical and mid-IR flux ratios, and the source size limits implied by the published macromodels." Initially we restrict our cliscussion o the particular case of the flux ratio between images D and A. However we present results based on all image ratios in Sec. 4.3.., Initially we restrict our discussion to the particular case of the flux ratio between images B and A. However we present results based on all image ratios in Sec. \ref{sec_pairs}. In the conclusion we mention some implications or quasar physics., In the conclusion we mention some implications for quasar physics. Throughout the paper. standard notation for gravitational lensing is used.," Throughout the paper, standard notation for gravitational lensing is used." The Einstein Raclius is defined be the radius inside which the mean surface mass density is equal to the eritical density., The Einstein Radius is defined to be the radius inside which the mean surface mass density is equal to the critical density. Phe Einstein Iadius yy of a LAL. star projected into the source plane is, The Einstein Radius $\eta_{0}$ of a $M_{\odot} $ star projected into the source plane is Possible detections are generally near 30 threshold or where it has been difficult to establish the presence of the line unambiguously.,Possible detections are generally near $\sigma$ threshold or where it has been difficult to establish the presence of the line unambiguously. There are a variety of issues. such as contamination from Galactic absorption line. aàirglow features. or uncertainties in (he level of (he underlviug stellar continuum.," There are a variety of issues, such as contamination from Galactic absorption line, airglow features, or uncertainties in the level of the underlying stellar continuum." For the purposes of scoring the detections in a simple non-paranmetic fashion. we assign 0 to upper limits. 0.5 to possible detections. ancl 1.0 to detections.," For the purposes of scoring the detections in a simple non-parametic fashion, we assign 0 to upper limits, 0.5 to possible detections, and 1.0 to detections." " The conversion of the OVI Iuminosity to a cooling rate (Mov) has been caleulated by EdgarandChevalier(1986) and by Voit.Donalne.andSlavin(1994).. and here we use the conversion L(1032) = 9x10"" Mo; erg/sec. where Moy, is in ML. 1 (as used in BML)."," The conversion of the OVI luminosity to a cooling rate ${\dot{M}}_{OVI}$ ) has been calculated by \citet{edgar86} and by \cite{voit94}, and here we use the conversion L(1032) = $\times$ $^{38}$ ${\dot{M}}_{OVI}$ erg/sec, where ${\dot{M}}_{OVI}$ is in $_{\odot}$ $^{-1}$ (as used in BMI)." This is probably accurate to30%.. where the uncertainty derives from issues such as whether the cooling gas is isobaric or isochoric.," This is probably accurate to, where the uncertainty derives from issues such as whether the cooling gas is isobaric or isochoric." This is most likely an uncertainty in the absolute calibration and is unlikely to cause an additional random scatter of30%., This is most likely an uncertainty in the absolute calibration and is unlikely to cause an additional random scatter of. ". The quantity Moy, is fairly insensitive to the metallicity provided that the metals remain (he primary cooling agent (Edgar and Chevalier 1936).", The quantity ${\dot{M}}_{OVI}$ is fairly insensitive to the metallicity provided that the metals remain the primary cooling agent (Edgar and Chevalier 1986). " In the temperature range where OVI is the most prominent ion (near 10°"" IX). this requirement is satisfied for metallicities greater than 7 of the Solar value (see SutherlandandDopita 1993))."," In the temperature range where OVI is the most prominent ion (near $^{5.3}$ K), this requirement is satisfied for metallicities greater than $^{-2}$ of the Solar value (see \citealt{suth93}) )." We wish to compare the OVI cooling rate to the X-ray cooling rate within the aperture. and (his depends somewhat on whether gas cools primarily in the center or in a distributed manner throughout the galaxy.," We wish to compare the OVI cooling rate to the X-ray cooling rate within the aperture, and this depends somewhat on whether gas cools primarily in the center or in a distributed manner throughout the galaxy." Effectively. the X-ray cooling rate is E. where Lye is the net cooling rate (the X-rav. luminosity. if there is no opposing heat source) ancl E is the specific thermal energy of the gas.," Effectively, the X-ray cooling rate is ${\dot{M}}_{X} = \eta L_{\rm net}/E$ , where $L_{\rm net}$ is the net cooling rate (the X-ray luminosity, if there is no opposing heat source) and E is the specific thermal energy of the gas." The factor 7 represents the model correction due to fluid effects. such as gravitational reheating as gas flows inware or a sink of mass as gas Cools out of the flow. which can be extracted from model calculations. such as SarazinandAshe(1989).," The factor $\eta$ represents the model correction due to fluid effects, such as gravitational reheating as gas flows inward or a sink of mass as gas cools out of the flow, which can be extracted from model calculations, such as \citet{sarz89}." . We discussed the differences between the predictions in the various models previously (BAIT) ancl here we use the value jj = 0.4. corresponding to the = 1 model.," We discussed the differences between the predictions in the various models previously (BMI) and here we use the value $\eta$ = 0.4, corresponding to the = 1 model." " In (this = 1 model. gas loss is distributed through the galaxy in the sense that hot σας is converted locally to cold gas at a rate inversely proportional to (he instantaneous cooling time /, as given by p=qp/t,."," In this = 1 model, gas loss is distributed through the galaxy in the sense that hot gas is converted locally to cold gas at a rate inversely proportional to the instantaneous cooling time $t_c$ as given by ${\dot{\rho}} = q{\rho}/t_c$." " There is a second consideration in calculating M. having to do with the aperture. a seuare 30 on a side. or an effective radius of 17""."," There is a second consideration in calculating ${\dot{M}}_X$, having to do with the aperture, a square $\arcsec$ on a side, or an effective radius of $\arcsec$." " This is smaller than the effective optical radius (R,. twpically 30-60"") or of the extent of the X-ray emission. which is similar to the optical size."," This is smaller than the effective optical radius $_{e}$, typically $\arcsec$ ) or of the extent of the X-ray emission, which is similar to the optical size." If we were to adopt the cooling flow model without mass drop out. all of the cooling would occur within the aperture (although (his makes an X-ray surface brightness profile that is too sharply peaked in the center).If there is mass drop-out. with," If we were to adopt the cooling flow model without mass drop out, all of the cooling would occur within the aperture (although this makes an X-ray surface brightness profile that is too sharply peaked in the center).If there is mass drop-out with" evel (models Z).,level (models Z). Constraining (he initial mass ratio distribution (models M) will require an even higher 1unber of merger detections: onlv for the case of 500 observed mergers the diflerences become significant., Constraining the initial mass ratio distribution (models M) will require an even higher number of merger detections: only for the case of 500 observed mergers the differences become significant. Models C (no hvpercritival accretion onto a compact object). J GniGal mass unction slope). and 5 (systems circular initially) lead to very small differences in (he observed distribution of chirp masses.," Models C (no hypercritival accretion onto a compact object), J (initial mass function slope), and S (systems circular initially) lead to very small differences in the observed distribution of chirp masses." Models B where the kick velocity distribution is varies begin to show significant differences only with a large number of observations., Models B where the kick velocity distribution is varies begin to show significant differences only with a large number of observations. Changing the kick velocity distribution affects stronglv the absolute rates (Lipunov Postnov Prokhorov 1997. Belezvuski Dulik 1999). and the ratio of double neutron star mergers to the double black hole mergers (Delczvnski. lxalogera and Bulik 2002).," Changing the kick velocity distribution affects strongly the absolute rates (Lipunov Postnov Prokhorov 1997, Belczynski Bulik 1999), and the ratio of double neutron star mergers to the double black hole mergers (Belczynski, Kalogera and Bulik 2002)." We have applied the stellar population svuthesis models (o simulate the distribution ol observed chirp masses in the eravitational wave detection of stellar mergers., We have applied the stellar population synthesis models to simulate the distribution of observed chirp masses in the gravitational wave detection of stellar mergers. We find that the population of observed mergers is dominated by the the black hole - black hole binary mergers., We find that the population of observed mergers is dominated by the the black hole - black hole binary mergers. In most models double black hole mergers constitute more than of the observed events., In most models double black hole mergers constitute more than of the observed events. The exception is model G2. in which the formation of black holes is suppressed because of increased stellar winds.," The exception is model G2, in which the formation of black holes is suppressed because of increased stellar winds." The shapes of observed distributions of chirp asses vary considerably [or different models of stellar binary. evolution., The shapes of observed distributions of chirp masses vary considerably for different models of stellar binary evolution. We simulate the observed distributions of chirp masses in the framework of various stellar evolution models aud estimate (he sensitivity wilh which (hese parameters can be estimated from a given sample of observed mergers., We simulate the observed distributions of chirp masses in the framework of various stellar evolution models and estimate the sensitivity with which these parameters can be estimated from a given sample of observed mergers. We find that there is large number of parameters that can be constrained given a sel of measured chirp masses., We find that there is large number of parameters that can be constrained given a set of measured chirp masses. The main and inmediate constraints come from the [act the (he observed population seems (ο be dominated bv the hiehest mass black hole binaries., The main and immediate constraints come from the fact the the observed population seems to be dominated by the highest mass black hole binaries. Thus even a small set of observations vields constraints on the maximal mass of merging black hole binaries., Thus even a small set of observations yields constraints on the maximal mass of merging black hole binaries. A larger set of observations will lead to constraints on the evolution of high mass binaries., A larger set of observations will lead to constraints on the evolution of high mass binaries. In our simulation we use a simple statistical tool: the Kolmogorov Smirnov test., In our simulation we use a simple statistical tool: the Kolmogorov Smirnov test. Given a set of real observations will some measurements of individual masses of coalescing stars. one could use a more sensitive tool like (he maximum likelihood method.," Given a set of real observations with some measurements of individual masses of coalescing stars, one could use a more sensitive tool like the maximum likelihood method." ILowever. even with such simple statistic as used here we can show the general properties of the expected observations. and demonstrate the sensitivity of the observed distributions to dillerent model parameters.," However, even with such simple statistic as used here we can show the general properties of the expected observations, and demonstrate the sensitivity of the observed distributions to different model parameters." Alass-loss phenomena are. one of the best-known manifestations of the star| formation process.,Mass-loss phenomena are one of the best-known manifestations of the star formation process. In our current understanding of the formation of low-mass stars via accretion(e.g. cessatilyMelxee Ostriker 2007). highly. collimated jets are ne present in the first stages of protostellar evolution. coeval with the formation of cireumstellar disks.," In our current understanding of the formation of low-mass stars via accretion (e.g., McKee Ostriker 2007), highly collimated jets are necessarily present in the first stages of protostellar evolution, coeval with the formation of circumstellar disks." Jets could be the agent releasing angular momentum excess. so that the protostar can continue accreting material from its environment.," Jets could be the agent releasing angular momentum excess, so that the protostar can continue accreting material from its environment." Evidence for highly collimated mass-Ioss is widespread in low-mass voung stellar objects (YSOs): e.g.. jets traced by Uerhig-Llaro objects. radio continuum emission. or masers. as well as bipolar molecular outllows.," Evidence for highly collimated mass-loss is widespread in low-mass young stellar objects (YSOs): e.g., jets traced by Herbig-Haro objects, radio continuum emission, or masers, as well as bipolar molecular outflows." Llowever the case for hieh-mass stars (AJxmS AL.) is less clear., However the case for high-mass stars $M\geq 8$ $_{\odot}$ ) is less clear. Energetic mass loss is indeed. present in those sources. although it is. in general. less eollimated than in low-mass objects (Wuetal. 2004).," Energetic mass loss is indeed present in those sources, although it is, in general, less collimated than in low-mass objects \citep{Wu-etal04}." . Highly collimatec jets seems to be restricted to the earliest phases of the evolution (<107 vears: Shepherd 2005) of massive YSOs., Highly collimated jets seems to be restricted to the earliest phases of the evolution $<10^4$ years; Shepherd 2005) of massive YSOs. This is important. from. a more. global perspective. since it is not vet clear whether high-mass stars lorm via accretion. like their. low-mass counterparts (eg... Yorke Sonnhalter 2002: Melxee Tan 2003: Ixrumbholz et al.," This is important from a more global perspective, since it is not yet clear whether high-mass stars form via accretion, like their low-mass counterparts (e.g., Yorke Sonnhalter 2002; McKee Tan 2003; Krumholz et al." 2009). or by coalescence of lower-mass objects(jonnell. Bate Zinnecker 19958)," 2009), or by coalescence of lower-mass objects (Bonnell, Bate Zinnecker 1998)." The presence of circumstellar disks. and collimated outllows are. kev ingredients of the accretion scenario., The presence of circumstellar disks and collimated outflows are key ingredients of the accretion scenario. The detection of disks (Pateletal.2005) and jets (e.g.Marth. Iodrfesuez Reipurth 1993: ltodrigguez et al.," The detection of disks \citep{Patel-etal05} and jets (e.g., Rodrígguez Reipurth 1993; guez et al." 1994: Davis ct al., 1994; Davis et al. 2X104: Patel et al., 2004; Patel et al. 2005) in several, 2005) in several "Galactic chemical evolution (Tinsley 1980. Pagel 1997) as where ση.f) aud X44.f) are the total and gas surface deusity respectively in the rine centered at Calactocentric distance rat evolution time f: f(t) is often called +ie iufall or accretion rate: oc(rf) is the star formation rate (SER) aud off) is the oeUtial mass function (IME): m, aud z, are the remmanut mass and the lifetime of a y.ar of initial mass 1, respectively, and iy is the correspoucding iuitial mass of a star whose main-scquence lifetime 7,, equates to evolution time f (the turnoff mass).","Galactic chemical evolution (Tinsley 1980, Pagel 1997) as where $\Sigma_{tot}(r,t)$ and $\Sigma_{gas}(r,t)$ are the total and gas surface density respectively in the ring centered at Galactocentric distance $r$ at evolution time $t$; $f(r,t)$ is often called the infall or accretion rate; $\psi(r,t)$ is the star formation rate (SFR) and $\phi(m)$ is the initial mass function (IMF); $m_r$ and $\tau_m$ are the remnant mass and the lifetime of a star of initial mass $m$, respectively, and $m_t$ is the corresponding initial mass of a star whose main-sequence lifetime $\tau_{m}$ equates to evolution time $t$ (the turnoff mass)." Were th| nass ranee of IME is taken from OLAS. to LOOAL..., Here the mass range of IMF is taken from $0.1 M_\odot$ to $100 M_\odot$. " The mass of clement i| in the eas evolves via star formation (putting metals frou the ISM into stars). ejection. aud eas inflows. according to equation (3). where yi, is the stellar vield of clement ἐν 1.6.. the mass fraction of a star of initial mass i that is converted to clement / auc ejected. aud Zig is the mass abundance of clement / ii the falling gas. which is assumed to be piromordial in this study: Zo;=Zr;O"," The mass of element $i$ in the gas evolves via star formation (putting metals from the ISM into stars), ejection, and gas inflows, according to equation (3), where $y_{i,m}$ is the stellar yield of element $i$, i.e., the mass fraction of a star of initial mass $m$ that is converted to element $i$ and ejected, and $Z_{i,f}$ is the mass abundance of element $i$ in the infalling gas, which is assumed to be piromordial in this study: $Z_{O,f}= Z_{Fe,f}=0$." It should be emphasized that the secoud ternis in the right haud of equations (2) aud (3) also include the contribution of Type Ia supernovas (Type Ia SN}. which is detailedly preseuted in Matteucci Cregeio (1986).," It should be emphasized that the second terms in the right hand of equations (2) and (3) also include the contribution of Type Ia supernovas (Type Ia SNs), which is detailedly presented in Matteucci Greggio (1986)." The coustaut A iu equation (9) of Matteucci Cregeio (1986) describes the fraction of systelus with total mass in appropriate range. which eventually succeed in giving rise to a Type Ia SN eveut. aud in this study. it is fixed by requiring to present best-fit to the metal-rich tail of the G-dwarf metallicity distribution in the solar ucighbourhood.," The constant $A$ in equation (9) of Matteucci Greggio (1986) describes the fraction of systems with total mass in appropriate range, which eventually succeed in giving rise to a Type Ia SN event, and in this study, it is fixed by requiring to present best-fit to the metal-rich tail of the G-dwarf metallicity distribution in the solar neighbourhood." It is also assuued that every star ejects its euvolope just after leaving the main sequence., It is also assumed that every star ejects its envelope just after leaving the main sequence. " The adopted relation between main-sequence lifetimes 7,, ( ia units of Ci) and stellar initial mass 52 (in units of AL.) is ( Larson 197D: For the sake of simplicity. we assume that. except for Type Ia SNs. any star evolves as a sinele star even if it is the member of a binary svstem."," The adopted relation between main-sequence lifetimes $\tau_m$ ( in units of Gyr) and stellar initial mass $m$ (in units of $M_\odot$ ) is ( Larson 1974): For the sake of simplicity, we assume that, except for Type Ia SNs, any star evolves as a single star even if it is the member of a binary system." All massive stars (0> OAL.) explode as type II supermovas (Type IT SNs). leaving behiud a neutron star of mass mp=O5AL. (Prautzos Silk 1998).," All massive stars $m > 9 M_\odot$ ) explode as type II supernovas (Type II SNs), leaving behind a neutron star of mass $m_R=0.5 M_\odot$ (Prantzos Silk 1998)." The final stage of the intermediate flow mass stars (ALx OAL.) is white dwarts. aud the flnal-initial mass relation is taken from Weidemanu(lost).," The final stage of the intermediate /low mass stars $M \leq 9 M_\odot$ ) is white dwarfs, and the final-initial mass relation is taken from Weidemann(1984)." Type Ia SNs are thought to originate from carbon deflagration in C-O white dwarts in binary svstems., Type Ia SNs are thought to originate from carbon deflagration in C-O white dwarfs in binary systems. The method included the contribution of Type Ia SNs is the same as Matteucci Creeeioao (1986)., The method included the contribution of Type Ia SNs is the same as Matteucci Greggio (1986). Iu the carly phase both adiabatic aud svuchrotrou losses can be inportant.,In the early phase both adiabatic and synchrotron losses can be important. " Setting 7,τσι oue obtains the characteristic age that separates the two energy loss reemue. estimated as where the Lorentz factor is assuued to he 54,= 5/1, "," Setting $\tau_a=\tau_s/\gamma$, one obtains the characteristic age that separates the two energy loss regime, estimated as where the Lorentz factor is assumed to be $\gamma_*=(4\nu/3\nu_{B0})^{1/2}(t/t_0)^{\alpha_B/4}$ ." "For ag>U3. the svuchrotron losses dominateE? initially and at f>f, the adiabatic losses overtake the svuchrotron losses."," For $\alpha_B>4/3$, the synchrotron losses dominate initially and at $t>t_a$ the adiabatic losses overtake the synchrotron losses." " For op<1/3. the acliabtaic losses dominate first aud then the svuchrotre- losses become miportaut at t>f,."," For $\alpha_B<4/3$, the adiabtaic losses dominate first and then the synchrotron losses become important at $t>t_a$." One max compare the ICS losses with the svuchrotro- losses., One may compare the ICS losses with the synchrotron losses. " The energy loss rate due to ICS is {στοτν ο)where U,=3.6«10οτι.11jiHJaa? is the CMB cnerey density4, at a redshift :."," The energy loss rate due to ICS is $\gamma/\tau_{_{ICS}}\sim 4\gamma_*\sigma_TcU_{_{CMB}}/(3m_ec^2)$ ,where $U_{_{CMB}}=3.6\times10^{-14}(1+z)^4\,{\rm J}\,{\rm m}^{-3}$ is the CMB energy density at a redshift $z$." One may express ως ii terms of au effective magnetic field Bearyzm3.2.10ML123°T.," One may express $U_{_{CMB}}$ in terms of an effective magnetic field $B_{CMB}\approx 3.2\times10^{-10}(1+z)^2\,\rm T$." Equating the ICS energv loss rate to the svuchrotrou loss rate vields a characteristic age:[m] The ICS losses become doiminaut over the svuchrotrou losses at f>ty., Equating the ICS energy loss rate to the synchrotron loss rate yields a characteristic age: The ICS losses become dominant over the synchrotron losses at $t>t_b$. The characteristic age at which the adiabatic phase switches to the ICS plase is estimated to be Simular to the derivation of (17)). the derivation of (19)) involves replacing 5 by +," The characteristic age at which the adiabatic phase switches to the ICS phase is estimated to be Similar to the derivation of \ref{eq:ta}) ), the derivation of \ref{eq:tc}) ) involves replacing $\gamma$ by $\gamma_*$." " We asstune that particles are injected at a coustant rate with spectrum Ξ495."" and the initial condition N(s.fy)=0."," We assume that particles are injected at a constant rate with spectrum $q_l=q_0\gamma^{-p}$ and the initial condition $N(\gamma,t_0)=0$." The formal solution for (11)) is written down iu Appendix., The formal solution for \ref{eq:CEq}) ) is written down in Appendix. There are two limits in which the exact analytical forms are well known., There are two limits in which the exact analytical forms are well known. The first ιά! is when the adiabatic losses are dominant., The first limit is when the adiabatic losses are dominant. One may set τι> &. Which Ieads to the exact solution (Eilek&Shore 1989).. Since the secoud feri in the square brackets is eoncrally 11uch siunaller than 1. Eq (20)) is approximately X5& which implics that the spectral slope is not affected by the adiabatic losses aud the whole spectiua raises proportionally with time.," One may set $\tau_1\to\infty$ , which leads to the exact solution \citep{es89}, Since the second term in the square brackets is generally much smaller than 1, Eq \ref{eq:Nad}) ) is approximately $\propto\gamma^{-p}$, which implies that the spectral slope is not affected by the adiabatic losses and the whole spectrum raises proportionally with time." The secoucd limit is when the energy losses are due to ICS of the CMD raciation or due to svuchrotrou losses iu constaut maguctic fields., The second limit is when the energy losses are due to ICS of the CMB radiation or due to synchrotron losses in constant magnetic fields. " One has the well-known form (ISardashey1962:Melrose1980): where 7=7,,.. for the ICS losses aud το=7. for the svuchrotron losses."," One has the well-known form \citep{k62,m80}: where $\tau_0=\tau_{_{ICS}}$ for the ICS losses and $\tau_0=\tau_s$ for the synchrotron losses." Eq (21)) iust be subject to the condition ffyro/(f—fg). the convection ena in (11)) is more important than the time derivative erm.," In the opposite limit in which the cooling time is much shorter than the age, $\gamma>\tau_0/(t-t_0)$, the convection term in \ref{eq:CEq}) ) is more important than the time derivative term." " One can directly integrate (11)) over 5 to obtain AN(s.t)=qur""!l(p1)."," One can directly integrate \ref{eq:CEq}) ) over $\gamma$ to obtain $N(\gamma,t)=q_0\tau_0\gamma^{-p-1}/(p-1)$." Siuce for radio sources. it is usually true that the radiative cooling time is considerably shorter than the source age. the particle spectrin in the ligh energy approximation is the more relevant.," Since for radio sources, it is usually true that the radiative cooling time is considerably shorter than the source age, the particle spectrum in the high energy approximation is the more relevant." Apart from these two special cases. a third case of relevance. especially for low-luninosity sources (cf.," Apart from these two special cases, a third case of relevance, especially for low-luminosity sources (cf." Sec 5). is the svuchrotrou losses iun magnetic fields that slowly decay with time.," Sec 5), is the synchrotron losses in magnetic fields that slowly decay with time." There is no simple analvtica solution. though the particular case where ap<1. p=2 and 3 was cliscussed in Eilek&Shore(1989).," There is no simple analytical solution, though the particular case where $\alpha_B<1$, $p=2$ and 3 was discussed in \citet{es89}." . However. oue cau express the formal solution iu terms of the hypergeometric function.," However, one can express the formal solution in terms of the hypergeometric function." The derivation is outline in Appendix., The derivation is outlined in Appendix. Here we ouly discuss the case ap1. which corresponds toj =3/2 in the pressure-Inuitiug expansion (cf.," Here we only discuss the case $\alpha_B=1$, which corresponds to $\beta=3/2$ in the pressure-limiting expansion (cf." Sec., Sec. 5)., 5). Other examples are cousidered m the Appendix., Other examples are considered in the Appendix. The solution for ap—1 has the form. where ©=sfoírTu)Xol/lu(f/fy) aud M(a.b.c) is the TIununers function which has the asyuiptotie properties AL(pload(pydele fox a1l (AbramowitzSteeun 1965).," The solution for $\alpha_B=1$ has the form, where $\xi=\gamma t_0/\tau_{s0}\leq 1/\ln(t/t_0)$ and $M(a,b,x)$ is the Kummer's function which has the asymptotic properties $M(p-1,p,x)\approx (p-1)x^{-1}e^x$ for $x\gg1$ \citep{as65}." . Thus. in the low energy linüt 1. one las which is simular to the low energy liuüt of (21)).," Thus, in the low energy limit $\xi\ln(t/t_0)\ll1$ , one has which is similar to the low energy limit of \ref{eq:NSC}) )." Iu the high-enerey regine. one has (c£.," In the high-energy regime, one has (cf." Appendix) The spectrmm with an initial powerdndex p steepens [ορ 1., Appendix) The spectrum with an initial power-index $p$ steepens to $\sim p+1$ . Since FR IIs have already been considered iu the literature. here we rederive the main features of their evolutionary tracks for nearby high luuinosity sources (2« lh in particular the πουfeature due to thetransition from the expansion dominated by adiabatic losses to that by ICS of the CAB.," Since FR IIs have already been considered in the literature, here we rederive the main features of their evolutionary tracks for nearby high luminosity sources $z\ll1$ ), in particular the `knee'feature due to thetransition from the expansion dominated by adiabatic losses to that by ICS of the CMB." To model the, To model the To gain a sense of the velocities with which stars are spreading from their birth regions. we looked for a good example region to study in detail.,"To gain a sense of the velocities with which stars are spreading from their birth regions, we looked for a good example region to study in detail." One of the knots of star formation (RA = 183.5881. DEC for= 36.3683. see Figure 12)) was isolated enough to look y a correlation οσοι the magnitude of the brightest MS stars and re distance frou the ceuter of the knot.," One of the knots of star formation (RA = 183.8884, DEC = 36.3683, see Figure \ref{sfreg}) ) was isolated enough to look for a correlation between the magnitude of the brightest MS stars and the distance from the center of the knot." " Taking the xieltest MS star iui amuuli of 6"", 8"", 10"". aud 2"" (sce Figure 12)). there is a0. weak correlation between 1e niaeuitude of the brightest MS star aud distance from 1e central knot."," Taking the brightest MS star in annuli of $''$ , $''$ , $''$ and $''$ (see Figure \ref{sfreg}) ), there is a weak correlation between the magnitude of the brightest MS star and distance from the central knot." Each 75 pe farther out. the brightest MS y. aris cd maguitude fainter.," Each 75 pc farther out, the brightest MS star is $\sim$ 1 magnitude fainter." If we assume the brightest MS star is a proxy for the MS turnoff maguitude. at 1086 bright magnitudes on the upper main sequence 1 uaenitude corresponds roughly to 10 Myr of age.," If we assume the brightest MS star is a proxy for the MS turnoff magnitude, at these bright magnitudes on the upper main sequence 1 magnitude corresponds roughly to 10 Myr of age." If we ther assiunoe that the weak correlation is real aud that it is due to the diffusion of stars produced iu the ceuter of he knot. the slope of the correPARA ls consistut witha diffusion speed of 8 pe Lens kus i)," If we further assume that the weak correlation is real and that it is due to the diffusion of stars produced in the center of the knot, the slope of the correlation is consistent with a diffusion speed of $\sim$ 8 pc $^{-1}$ $\sim$ 8 km $^{-1}$ )." This value is situilar to the velocity dispersion of D stars in the Milky Way disk aud the ciffusion speed fouud for au outer spiral arm in MBS120095)., This value is similar to the velocity dispersion of B stars in the Milky Way disk and the diffusion speed found for an outer spiral arm in M81. The brightest AIS) stars dn our catalog provide diagnostic tests for massive stellar evolution models., The brightest MS stars in our catalog provide diagnostic tests for massive stellar evolution models. UST UV spectroscopy has been measured for the central starburst. vieldiug au age of 1.5 Myr1996).," HST UV spectroscopy has been measured for the central starburst, yielding an age of 4–5 Myr." .. Our photometry reveals point sources with F336W (C-band equivalent) magnitudes of ~17.6 which is AMgasguo—-9.9 at the distance aud extinction of NCC 1211.," Our photometry reveals point sources with F336W $U$ -band equivalent) magnitudes of $\sim$ 17.6, which is $M_{F336W}$ =-9.9 at the distance and extinction of NGC 4214." We show our F336W-Fi8sWw CAID in Fiewre 2. along with the isochrone for au age of 1. Myr and a metallicity of [MII|2-0.E shifted to the distauce and foreground extinction of NCC 1211., We show our F336W-F438W CMD in Figure \ref{cmds} along with the isochrone for an age of 4 Myr and a metallicity of [M/H]=-0.4 shifted to the distance and foreground extinction of NGC 4214. Assimuiug these objects are not unresolved compact clusters. these brieli stars are consistent with the brightest blue portion of this isochroue. which represeuts model stars with masses of 5256 AL...," Assuming these objects are not unresolved compact clusters, these bright stars are consistent with the brightest blue portion of this isochrone, which represents model stars with masses of 52–56 $_{\odot}$." The low foreground extinction (4= 0.07) and eood agreement between the data and mode isochrone suggests that these stars are not strongly affected by extinction iuterual to NGC 121L., The low foreground extinction $A_V = 0.07$ ) and good agreement between the data and model isochrone suggests that these stars are not strongly affected by extinction internal to NGC 4214. NGC 121 is known to contain just a modest amount of iuterna extinction ΕΙΝ extinction 0.582009). aud these particular UW-bright stars are apparently between us and anv of significant dust within NGC [21L. making them casily detected aud measured iu the UV.," NGC 4214 is known to contain just a modest amount of internal extinction FUV extinction $\sim$ 0.58, and these particular UV-bright stars are apparently between us and any of significant dust within NGC 4214, making them easily detected and measured in the UV." Finally. we estimated the approximate total SER for the galaxv over the past —100 Myr. as it las been relatively lugh divine most of this period.," Finally, we estimated the approximate total SFR for the galaxy over the past $\sim$ 100 Myr, as it has been relatively high during most of this period." If we add together the SFRs from our [ regious. we obtain a total rate of “OL AL. fb. ©80% of which is in the ceutzal UVIS field.," If we add together the SFRs from our 4 regions, we obtain a total rate of $\sim$ 0.1 $_{\odot}$ $^{-1}$, $\sim$ of which is in the central UVIS field." This rate is consistent with the SER receutly measured for NGC 1211 from photometry by (2010a., This rate is consistent with the SFR recently measured for NGC 4214 from photometry by . ")).. Tuterestinely. the overall population is similar to that of the very differcut nearby dwarf galaxy NGC. 101. which is a somewhat more massive (71.5 «10? AE,: 2001)) SO salaxv with very Little recent star formation."," Interestingly, the overall population is similar to that of the very different nearby dwarf galaxy NGC 404, which is a somewhat more massive $\sim$ $\times$ $^9$ $_{\odot}$; ) S0 galaxy with very little recent star formation." The ANGST data for that galaxy show that outside the inner regious ~90% of the stellar population js >S Gyr old and ~75% ds 210 Car old2010)., The ANGST data for that galaxy show that outside the inner regions $\sim$ of the stellar population is $>$ 8 Gyr old and $\sim$ is $>$ 10 Gyr old. . While the overall stellar populations of NGC 101 are older than those of NGC1211I. the difference is not overwhelming.," While the overall stellar populations of NGC 404 are older than those of NGC4214, the difference is not overwhelming." Iu fact. by { Car ago. both galaxies had formed or more of their stellar mass.," In fact, by 4 Gyr ago, both galaxies had formed or more of their stellar mass." Apparceutly. the vast difference in iorphologw between these 2 galaxies is mainly due to just a small percentage of the stellar mnass.," Apparently, the vast difference in morphology between these 2 galaxies is mainly due to just a small percentage of the stellar mass." Our results show that ~1% of the stellar mass in NGC 1211 formed in the past 100 Nr., Our results show that $\sim$ of the stellar mass in NGC 4214 formed in the past $\sim$ 100 Myr. The percentage of stellar mass formed iu the past 100 Myr is much sanaller in NGC 1014. ouly 0.1 outside of the galaxy ceuter.," The percentage of stellar mass formed in the past 100 Myr is much smaller in NGC 404, only $<$ outside of the galaxy center." Iowever. there is evidence for a 1 Car old starburst in the center of NGC LOL2010):: about 1 Gyr ago NGC LOL may have more closelv reseciuibled NGC [21Us present-day appearance.," However, there is evidence for a 1 Gyr old starburst in the center of NGC 404; about 1 Gyr ago NGC 404 may have more closely resembled NGC 4214's present-day appearance." While this difference represents a suall percentage of the total stellar populations of the galaxies. it results in their vastly different iiorphological classifications.," While this difference represents a small percentage of the total stellar populations of the galaxies, it results in their vastly different morphological classifications." Both NGC 1211 and NGC LOL appear to have older median ages than some more massive disks. such as ADOS2009a).," Both NGC 4214 and NGC 404 appear to have older median ages than some more massive disks, such as M33." . Perhaps their old stellar ages are somehow due to their relationship with their euvironnieuts., Perhaps their old stellar ages are somehow due to their relationship with their environments. Both salaxies are the most massive in their local cuviroument., Both galaxies are the most massive in their local environment. " Perhaps it is common for the dominant galaxy bv mass within auv group of galaxies Gvchere NGC LOL ds isolated. making its own ""eroup) to be dominated by ancieut stars."," Perhaps it is common for the dominant galaxy by mass within any group of galaxies (where NGC 404 is isolated, making its own “group”) to be dominated by ancient stars." " If this effect is indeed conumuion. it iav indicate that the most massive galaxy in a eroup dominates eas accretiou iu the carly stages of evolution. winning the local ""downsiziug battle to be the dominant star foriiumg object curing the epoch of formation."," If this effect is indeed common, it may indicate that the most massive galaxy in a group dominates gas accretion in the early stages of evolution, winning the local “downsizing” battle to be the dominant star forming object during the epoch of formation." We have analyzed deep UST/WEPC2 photometry of the NCC 1211 disk and IIST/WEC?2 photometry of the ceutral portion of NGC 1211., We have analyzed deep HST/WFPC2 photometry of the NGC 4214 disk and HST/WFC3 photometry of the central portion of NGC 4214. Full CAID inodcling of the photometry shows that the stellar populatious throughout the disk are old. with ~75% of the stellar mass older than —5 Cor.," Full CMD modeling of the photometry shows that the stellar populations throughout the disk are old, with $\sim$ of the stellar mass older than $\sim$ 8 Gyr." This result shows that overall the stellar populations of NGC 1211 are similar to those of the SO ealaxy NCC 101. other than the vouugest of the stellar mass. which formed iu the past 100 Myr in NGC 1211.," This result shows that overall the stellar populations of NGC 4214 are similar to those of the S0 galaxy NGC 404, other than the youngest of the stellar mass, which formed in the past 100 Myr in NGC 4214." The similarity suggests that a few hunelred Abvr ago. NGC 1211 may have looked very simular to NGC 101 today. though NGC 1211 av have been more eas-rieh.," The similarity suggests that a few hundred Myr ago, NGC 4214 may have looked very similar to NGC 404 today, though NGC 4214 may have been more gas-rich." " Alternatively, NGC 1211 may have recently acquired eas from a merging satellite. such as the merger suggested by(1997)."," Alternatively, NGC 4214 may have recently acquired gas from a merging satellite, such as the merger suggested by." . NCC 1211 currently has more than LO nearby satellites2): therefore such an alternative is a strong possibility., NGC 4214 currently has more than 10 nearby satellites; therefore such an alternative is a strong possibility. Finally. we preseuted au argument that because both galaxies are the dominant members oftheir local environments. they were in favorable positious to forma such a lieh percentage of their stars so carly.," Finally, we presented an argument that because both galaxies are the dominant members of their local environments, they were in favorable positions to form such a high percentage of their stars so early." Support forthiswork was provided by NASA through erxants GO-10915. GO-11719. and GO-11986 from the Space Telescope Science. Institute. which isoperated bv the Association of Uiiversities for Research iu Astronomy. Incorporated.wader NASA contract. NAS5-," Support forthiswork was provided by NASA through grants GO-10915, GO-11719, and GO-11986 from the Space Telescope Science Institute, which isoperated by the Association of Universities for Research in Astronomy, Incorporated,under NASA contract NAS5-26555." As we have shown here. with the enlarged data sauples expected in the next few vears with the continuous operation of he Auger Observatory it will become possible to test in a siguificaut way several possible models for the distribution of the UIIECR.,"As we have shown here, with the enlarged data samples expected in the next few years with the continuous operation of the Auger Observatory it will become possible to test in a significant way several possible models for the distribution of the UHECRs." If the actua CR distiution is different from the model assumptions. this can be put irevidence by comparing» the distrinition of the simulations according to the particular ποσο] and the actual data.," If the actual CR distribution is different from the model assumptions, this can be put in evidence by comparing the distribution of the simulations according to the particular model and the actual data." " The distriibutiou of «listances for a model when one uses tl10 same model as reference. peaks at D,&|Vin. whie on the other hand models different frol the reference one texd to eive rise to larecr average (istances."," The distribution of distances for a model, when one uses the same model as reference, peaks at $D_{peak}\simeq 1/\sqrt{n}$, while on the other hand models different from the reference one tend to give rise to larger average distances." Regarding the isotropic siuulatious. the more anisotropic is the reference catalog to which they are compared. the larger will be the distances otained. as is apparent from fies.," Regarding the isotropic simulations, the more anisotropic is the reference catalog to which they are compared, the larger will be the distances obtained, as is apparent from figs." | aud 2., 1 and 2. The|: 2DKS method can certaily be usec as away fo disproof isotropy. aud the most efficient wav to achieve this will be when using as reference scenario the one closest to the actual source distribution.," The 2DKS method can certainly be used as a way to disproof isotropy, and the most efficient way to achieve this will be when using as reference scenario the one closest to the actual source distribution." We are grateful to Jack Tueller for providing us the 22 mouths BAT catalog prior to publication and to I. Wong for seudiug us the NIIICAT catalog., We are grateful to Jack Tueller for providing us the 22 months BAT catalog prior to publication and to I. Wong for sending us the NHICAT catalog. This work is supported by. ANPCSVT (eraut PIC'T 13562-03) and CONICET (erant PIP 5231|., This work is supported by ANPCyT (grant PICT 13562-03) and CONICET (grant PIP 5231). We want to thauk Paul Somuners for discussions., We want to thank Paul Sommers for discussions. The principal novel result here is (hat (he majority of Li-vich Ix. giants have a luminosity and effective temperature combination suggesüng that Li production occurs al the flash in those stars.,The principal novel result here is that the majority of Li-rich K giants have a luminosity and effective temperature combination suggesting that Li production occurs at the He-core flash in those stars. " Although (his speculation about the IIle-core flash has vet to be supported by calculations. the nuclear physics of Li production is surely that. described by the Cameron-Fowler mechanism. ie.. conversion of ""Ile to ‘Li by a-captire with ‘Be as a radioactive intermediary."," Although this speculation about the He-core flash has yet to be supported by calculations, the nuclear physics of Li production is surely that described by the Cameron-Fowler mechanism, i.e., conversion of $^3$ He to $^7$ Li by $\alpha$ -capture with $^7$ Be as a radioactive intermediary." An earlier suggestion that Li production. also by the mechanism. occurs at the Iuminosity bump of the RIB is required to account for cooler Li-vich stars.," An earlier suggestion that Li production, also by the Cameron-Fowler mechanism, occurs at the luminosity bump of the RIB \citep{charbonnel2000} is required to account for cooler Li-rich stars." Our discovery of (hat Li-rich giants are concentrated within a narrow Iuminositv range does not support a view that. Livich giants result. [rom the swallowing bv the giant of a easeous planet (Alexander1967). or some other external origin., Our discovery of that Li-rich giants are concentrated within a narrow luminosity range does not support a view that Li-rich giants result from the swallowing by the giant of a gaseous planet \citep{alexander1967} or some other external origin. It remains to confirm and interpret suggestions (hat Livvich IX eiants may be unusual wilh respect to other Ix. giants in exhibiting rapid rotation and/or an inlrared excess (see. Lor example. Drakeοἱal.2002:: Charbonnel&Dalachandran 2000)).," It remains to confirm and interpret suggestions that Li-rich K giants may be unusual with respect to other K giants in exhibiting rapid rotation and/or an infrared excess (see, for example, \citealt{drake2002}; \citealt{charbonnel2000}) )." There are certainly Li-rich giants with normal C/C ratios (e.g. LD 108471 in Table 2). and/or rapidly rotating surfaces (e.g.. ID 217352 with eosin’e35 kms |. Strassmeieretal. 2000)). and/or infrared excesses (e.g... PDS 365. Drakeetal. 2002)).," There are certainly Li-rich giants with normal $^{12}$ $^{13}$ C ratios (e.g., HD 108471 in Table 2), and/or rapidly rotating surfaces (e.g., HD 217352 with $v\sin i \simeq 35$ km $^{-1}$, \citealt{strassmeier2000}) ), and/or infrared excesses (e.g., PDS 365, \citealt{drake2002}) )." Perhaps. an area for observational scrutiny is a [ull determination of the C. N. and O elemental ancl isotopic abundances in order (to search for discriminant between the candidate bunmp and clamp ΤΗΠΙΟ stars themselves aud between these Li-rich stars and bump and clump stars exhibiting a normal Li abundance.," Perhaps, an area for observational scrutiny is a full determination of the C, N, and O elemental and isotopic abundances in order to search for discriminant between the candidate bump and clump Li-rich stars themselves and between these Li-rich stars and bump and clump stars exhibiting a normal Li abundance." Finally. a radial velocity study should be undertaken to see if the collection of Li-rich stars have the normal degree of binaritv.," Finally, a radial velocity study should be undertaken to see if the collection of Li-rich stars have the normal degree of binarity." We are thankful to the trainees al CREST and. VDO observatory stall for their help during observations. and G. Pandey [or his observant comments.," We are thankful to the trainees at CREST and VBO observatory staff for their help during observations, and G. Pandey for his observant comments." DLL thanks the Rohert A. Welch Foundation of Houston. Texas for support through grant. F-634.," DLL thanks the Robert A. Welch Foundation of Houston, Texas for support through grant F-634." This research has made use of the SIMDAD database and the NASA ADS service., This research has made use of the SIMBAD database and the NASA ADS service. It was found receutlv for a larvee sample of Sevter AGNs and several observations of the Calactic N-rav uuaries that the amplitude of the reflected componen is eonerally correlated with the slope of the primary oower law cussion (Zdziarskictal. 1999)).,It was found recently for a large sample of Seyfert AGNs and several observations of the Galactic X-ray binaries that the amplitude of the reflected component is generally correlated with the slope of the primary power law emission \cite{zdz1}) ). Based on he umucrous RNTE/PCA observations of CyeX-] Cülfanovοal.1999 (hereafter Paper I) showed tha lis correlation is strong for imnultiple observations of lis source and that the spectral parameters are also ightly correlated with the characteristic noise frequency., Based on the numerous RXTE/PCA observations of CygX-1 \cite{pap2} (hereafter Paper I) showed that this correlation is strong for multiple observations of this source and that the spectral parameters are also tightly correlated with the characteristic noise frequency. Iu particular an increase of the OPO centroid frequency Is accolmpanicd with a steepenius of the slope of the Comptonized raciation aud an increase of the amplitude of the reflected. component., In particular an increase of the QPO centroid frequency is accompanied with a steepening of the slope of the Comptonized radiation and an increase of the amplitude of the reflected component. Studyiug fast variability of the reflected emission Revuivtsevetal.1999. showed that its anunplitude is suppressed with respec to that of the primary cussion at the frequencies hieher than ~1.10 Iz., Studying fast variability of the reflected emission \cite{pap1} showed that its amplitude is suppressed with respect to that of the primary emission at the frequencies higher than $\sim 1-10$ Hz. (Δον is oa bright and well studied X-rav παν, GX339-4 is a bright and well studied X-ray binary. It is usually classified as a black hole candidate and i many aspects is very siuular to Cre A-l (see ce. Tanaka&Lewiu1995.. Trudolvubovetal. 1998.. Zdziarskietal. 1998.. Wilmsctal. 1999.. Nowaketal. 1999)).," It is usually classified as a black hole candidate and in many aspects is very similar to Cyg X-1 (see e.g. \cite{tanakalewin}, \cite{tsp_339}, \cite{zdz}, \cite{wilms_339}, \cite{nowak_339}) )." " The investigations of the connections between the spectral aud tinue properties of Cre X-1 (οι, Cülfanovetal. 19993) and GN 339-1 (e.g. Uedactal 1991)) indicate that these sources could be similar frou this point of view also.", The investigations of the connections between the spectral and timing properties of Cyg X-1 (e.g. \cite{pap2}) ) and GX 339-4 (e.g. \cite{ueda94}) ) indicate that these sources could be similar from this point of view also. Tn this paper we expand the analysis of correlations between spectral aud temporal characteristics of the A-rav endssion of GN 2339-1 in the low spectral state using the Rossi N-vav Timing Explorer data and show that this source demoustrates the same behavior that was previously observed from (νο X-1., In this paper we expand the analysis of correlations between spectral and temporal characteristics of the X-ray emission of GX 339-4 in the low spectral state using the Rossi X-ray Timing Explorer data and show that this source demonstrates the same behavior that was previously observed from Cyg X-1. We used the publicly available data of GN 339-1 observations with RNTE/PCA from 19961997 performed during the low spectral state of the source., We used the publicly available data of GX 339-4 observations with RXTE/PCA from 1996–1997 performed during the low spectral state of the source. Our sample iucludes 23 observations from the proposals 10065. 20056. 20181 and 20183 with a total exposure time of ~130 ksec (Table ||).," Our sample includes 23 observations from the proposals 10068, 20056, 20181 and 20183 with a total exposure time of $\sim$ 130 ksec (Table \ref{gx339_pars_table}) )." " Only observations from the proposal P20183 had sufficient enerevOo, aud tfiningC» resolution to perform. Fourier frequency resolved spectral analysis.", Only observations from the proposal P20183 had sufficient energy and timing resolution to perform Fourier frequency resolved spectral analysis. Therefore the frequency resolved analysis was carried out only for ~61 ksec of he data., Therefore the frequency resolved analysis was carried out only for $\sim61$ ksec of the data. " The data screcuingC» was performed followingC» the RATE QGOF reconunendations: offset angle <0.02"". Earth elevation angle >107. clectrou contamination value (the ""electron ratio] for any of PCUs «O.1."," The data screening was performed following the RXTE GOF recommendations: offset angle $<0.02^\circ$, Earth elevation angle $> 10^\circ$, electron contamination value (the “electron ratio”) for any of PCUs $<0.1$." The data from al DCUs were used for the analysis., The data from all PCUs were used for the analysis. " The energy spectra were extracted roni the PCA mode ~Stauclared 2"" (128 channels. 16 sec time resolution) and averaged over cach observation."," The energy spectra were extracted from the PCA mode “Standard 2” (128 channels, 16 sec time resolution) and averaged over each observation." Fourier frequency resolved spectral analvsis used “Cood Xenon data (256 energy. clhiaunels. lus time resolution).," Fourier frequency resolved spectral analysis used “Good Xenon” data (256 energy channels, $\mu$ s time resolution)." The respouse πακος were built using standard RNTE FTOOLS L2 tasks (Jahoda 1999)., The response matrixes were built using standard RXTE FTOOLS 4.2 tasks (Jahoda 1999). " The backeround spectra for the conventional spectral analysis were constructed with the help of the ""VLE owed ος] (Stark 1999).", The background spectra for the conventional spectral analysis were constructed with the help of the “VLE” based model (Stark 1999). The background. contribution o the frequency resolve spectra is negligible iu the rYequenev and cherey ranges of interest., The background contribution to the frequency resolved spectra is negligible in the frequency and energy ranges of interest. A nuiform systematic uncertainty of was added quadratically o the statistical error in each οποιον channel., A uniform systematic uncertainty of was added quadratically to the statistical error in each energy channel. The value of systematic wucertaimty was chosen basing ou the deviations of the PCA Crab spectra from a power lav nodel (see e.g. Wihusetal. 190901)., The value of systematic uncertainty was chosen basing on the deviations of the PCA Crab spectra from a power law model (see e.g. \cite{wilms_339}) ). The euergv spectra were fit in the 3H20 keV energv range with a spectral model identical to that of Paper 1. The model consisted of a power law without high energv cutoff with superposed contiuumu. reflected from. tre neutral medium (peerae model iu NSPEC. see Maedziarz&Zdziarski 19953) aud au intrinsically wWweTOW chussion line at the energy 6.1 keV. No ionization effects were taken iuto account.," The energy spectra were fit in the 3–20 keV energy range with a spectral model identical to that of Paper I. The model consisted of a power law without high energy cutoff with superposed continuum, reflected from the neutral medium $pexrav$ model in XSPEC, see \cite{m_zdz}) ) and an intrinsically narrow emission line at the energy 6.4 keV. No ionization effects were taken into account." " The binary syste iucliuatiou anele was fixed at 0=15"" (e.g. Zdziarskietal. 1998)). t1ο don abundance αἲ the solar value."," The binary system inclination angle was fixed at $\theta=45^o$ (e.g. \cite{zdz}) ), the iron abundance – at the solar value." In such a inodel the amplitude of the reflected component is characterized. by the reflection scaling factor A. which is au approximate measure of the solid angle subtended by the reflector.," In such a model the amplitude of the reflected component is characterized by the reflection scaling factor $R$ , which is an approximate measure of the solid angle subtended by the reflector," accidental.,accidental. In particular. we need to calculate the probability of accidental agreements.," In particular, we need to calculate the probability of accidental agreements." Let us consider. the 12.15. evele n pair. with. a separation of 0.0078. evele I., Let us consider the 12.15 cycle $^{-1}$ pair with a separation of 0.0078 cycle $^{-1}$. Lo we assume a random distribution of frequencies and adopt a Poisson distribution. we obtain 0.02 expected. pairs.," If we assume a random distribution of frequencies and adopt a Poisson distribution, we obtain 0.02 expected pairs." OF course. the frecucncies are not distributed at random.," Of course, the frequencies are not distributed at random." Let us examine a frequency region which shows the largest number of detected: modes. Lc.1 troms 10 to 133 cyclecevele dol regionooo] (Fig.," Let us examine a frequency region which shows the largest number of detected modes, i.e. from 10 to 13 cycle $^{-1}$ region (Fig." 6)., 6). Sy PheThis increasesInerease the predicted number of accidental© agreements to 0.03 pairs., This increases the predicted number of accidental agreements to 0.03 pairs. For two or more pairs detected in à star. an explanation of all agreements being caused by accident must be rejected.," For two or more pairs detected in a star, an explanation of all agreements being caused by accident must be rejected." An accidental agreement may exist: the doublet: at 42.1030 and 42.1094 evele cot., An accidental agreement may exist: the doublet at 42.1030 and 42.1094 cycle $^{-1}$. Phe value of 42.1030 evcele tisa2fharmonic of a relatively high-amplituce (3 nuimag) mode at 210515 evele d+., The value of 42.1030 cycle $^{-1}$ is a 2f harmonic of a relatively high-amplitude (3 mmag) mode at 21.0515 cycle $^{-1}$. Phe 42.1030 evele d+ peak mas herefore. be ‘a consequencei of ‘a not completely1 sinusoidal‘ ight curve. rather than an independent mode.," The 42.1030 cycle $^{-1}$ peak may, therefore, be a consequence of a not completely sinusoidal light curve, rather than an independent mode." Fig., Fig. 5 has shown the large number of⋅ close frequency⋅ vars. in. pMUS x, 5 has shown the large number of close frequency pairs in FG Vir. usPhere exist. additionalMN |Lose fr.quney ours in FC: Vir Vir.bevond. those examined. in detail in this oper (e.g. at 34.1151 and 34.1192 evele ly but their amplitudes are too small for the tests used in this paper.," There exist additional close frequency pairs in FG Vir beyond those examined in detail in this paper (e.g., at 34.1151 and 34.1192 cycle $^{-1}$ ), but their amplitudes are too small for the tests used in this paper." We. conclude that most. of the close [frequency. pairs ound in FC) Vir (and in some other 0 Scuti stars such as BL CAI) ave not accidental ancl an astrophysical origin needs to be found., We conclude that most of the close frequency pairs found in FG Vir (and in some other $\delta$ Scuti stars such as BI CMi) are not accidental and an astrophysical origin needs to be found. This work is presently in progress., This work is presently in progress. lt ds a pleasure to thank Watrien Ixolenberg for. many helplu discussions., It is a pleasure to thank Katrien Kolenberg for many helpful discussions. Εις investigation has been supported by the Austrian Fonds zur. Forrderung der wissenschaftlichen Forschung. und by the Polish. MNiln grant No., This investigation has been supported by the Austrian Fonds zur Förrderung der wissenschaftlichen Forschung und by the Polish MNiI grant No. - 1 P03D 021 25., 1 P03D 021 28. which describe information propagating to the right and left. respectively.,"which describe information propagating to the right and left, respectively." " To solve eq.A3 over a full time step with second order accuracy. we first advance iw, aud i] over a half time step using the first order upwind donor cell formula."," To solve \ref{eq:lr} over a full time step with second order accuracy, we first advance $u_r$ and $u_l$ over a half time step using the first order upwind donor cell formula." These values are {μοι used to construct a second order accurate upwind flux using auy of the known noulinear TVD limiters such as 1uiniuod. Van Leer. or superbee.," These values are then used to construct a second order accurate upwind flux using any of the known nonlinear TVD limiters such as minmod, Van Leer, or superbee." Finally. given the updated values for d; aud wy. we recoustruct =typ+Uy.," Finally, given the updated values for $u_r$ and $u_l$, we reconstruct $u=u_r+u_l$." For stability. the value of the flux freezing speed c must be chosen larger than the speed at which information propagates.," For stability, the value of the flux freezing speed $c$ must be chosen larger than the speed at which information propagates." As cliscussecl in the text. we se €—fel wher advecting the magnetic Ποια. aud e=cltÜt(sp/pobp)>1 ," As discussed in the text, we set $c=|v|$ when advecting the magnetic field, and $c={\rm cfl}( |v|+(\gamma p/\rho + b^2/\rho)^{1/2} )^{-1}$." "How can one relate TVD to the ""artilicial viscosity"" sclieties?"," How can one relate TVD to the “artificial viscosity"" schemes?" These scues acd in a nonliuear viscosity terim in order to prevent iustajlities. as well as caiip away oscilleious which may occur uear discouintuities.," These schemes add in a nonlinear viscosity term in order to prevent instabilities, as well as damp away oscillations which may occur near disconintuities." However. this viscOslty tends to prevert the formats oL discontiuuities ou scales of order one cell. severely cegracii& the resolution of tle simulation.," However, this viscosity tends to prevent the formation of discontinuities on scales of order one cell, severely degrading the resolution of the simulation." " TV""D may be viewed asa strougly uoulinear flux limiter which acds just enough cdiffusion to preven —umerical instabilities.", TVD may be viewed as a strongly nonlinear flux limiter which adds just enough diffusion to prevent numerical instabilities. TVD can often caj»ure shocks in only one or two cells., TVD can often capture shocks in only one or two cells. Away from cliscojtinultles. maxima or minuna. TVD is secouc order in space. but at a iuaxiuia it is only first order.," Away from discontinuities, maxima or minima, TVD is second order in space, but at a maxima it is only first order." , cnussion is characterized by a uceatively-sloped powcr-law spectrmu at high frequencies. corresponding to optically thin emission. aud a positively-sloped spectra at lower frequencies correspouding to optically thick cnussion.,"emission is characterized by a negatively-sloped power-law spectrum at high frequencies, corresponding to optically thin emission, and a positively-sloped spectrum at lower frequencies corresponding to optically thick emission." ECAL emissiou. however. occurs at frequeucies corresponding to low harmonics of the local exclotrou frequency. aud does uot have a characteristic spectral shape (Molrose2009).," ECM emission, however, occurs at frequencies corresponding to low harmonics of the local cyclotron frequency, and does not have a characteristic spectral shape \citep{m09}." . Time-variable ciission frou UDs is up to circularly polarized aud tightly beamed. aud is hence interpreted as ECAL emissiou (¢.¢..ITallinanetal.2008).," Time-variable emission from UDs is up to circularly polarized and tightly beamed, and is hence interpreted as ECM emission \citep[e.g.,][]{had+08}." . Cyrosvuchrotron emission has been hypothesized. bv a variety of authors for racio-loud UDs in quiesceut states (o...BPOS:Ostenetal.2006).," Gyrosynchrotron emission has been hypothesized by a variety of authors for radio-loud UDs in quiescent states \citep[e.g., BP05;][]{ohb+06}." . The observed radio properties of DENISIOIS are more suggestive of evrosvuchrotron cussion than ECM enission for three reasons: While we cannot conclusively rule out an ECAL Cluission iechanisu. we interpret the radio ciission we observe from DENTSLOLS as optically thin evrosvuchnrotron cluission.," The observed radio properties of DENIS1048 are more suggestive of gyrosynchrotron emission than ECM emission for three reasons: While we cannot conclusively rule out an ECM emission mechanism, we interpret the radio emission we observe from DENIS1048 as optically thin gyrosynchrotron emission." Iu this interpretation.= the laree observed Stokes V fractious are consistent with a strong line-of-sight maguetie field) componcut.," In this interpretation, the large observed Stokes V fractions are consistent with a strong line-of-sight magnetic field component." Firthermore. the number of radiating electrous. NCE). per unit enerev. £. can be written as apower law. AN(QE)xE?. where 6=(122.αλ (Dulls 1985). ," Furthermore, the number of radiating electrons, $N(E)$, per unit energy, $E$, can be written as apower law, $N(E)\propto E^{-\delta}$, where $\delta=(1.22-\alpha)/0.9$ \citep{d85}. ." We find à=3.26+0.09. consistent with expected values between 2 and 7 for evrosvuchrotron-cuutting electrous (Dull1985).," We find $\delta=3.26\pm0.09$, consistent with expected values between $-2$ and $-7$ for gyrosynchrotron-emitting electrons \citep{d85}." . Asstuning Lyc2&Bü? + after Sehnütt&Liefke(2001). for DENISI1018. the CaiddelBenz relation imuplies an average radio flux density between 5CCOIIz and GGIIz of less than jiJy.," Assuming $L_{X}<2\times10^{26}$ $^{-1}$ after \citet{sl04} for DENIS1048, the Güddel-Benz relation implies an average radio flux density between GHz and GHz of less than $\mu$ Jy." At the lowest observiug frequency. the measured flux density is an order of magnitude ercater.," At the lowest observing frequency, the measured flux density is an order of magnitude greater." We propose a iuodel for the magnetosphere of DENIS1018 that accounts for the violation of the Ciüddel-Beuz relation., We propose a model for the magnetosphere of DENIS1048 that accounts for the violation of the Güddel-Benz relation. " For samples of fast-rotating M cdyarfs; an observed decrease in Zsy/L,; with rotation period (Bergeretal.2010:αποct2011) is interpreted as evidence for the decoupling of hot coronal plasma bevoud a co-rotation radius. Re."," For samples of fast-rotating M dwarfs, an observed decrease in $L_{X}/L_{bol}$ with rotation period \citep{bbf+10,jjb+11} is interpreted as evidence for the decoupling of hot coronal plasma beyond a co-rotation radius, $R_{C}$." We Lypothesize that this effect docs not reduce Ly/Lay., We hypothesize that this effect does not reduce $L_{R}/L_{bol}$. We further sugecst that: Iuthis model. the evrosvuchrotron emission we observe originates from non-thermal clectrous streamune radially outwards from Re.," We further suggest that: In this model, the gyrosynchrotron emission we observe originates from non-thermal electrons streaming radially outwards from $R_{C}$." A radial maguetic field structure iu this region is justified by the lack of significant variability in the radio liehteurve., A radial magnetic field structure in this region is justified by the lack of significant variability in the radio lightcurve. The radio emission is characterized by three paralcters: Re. the total non-thermal electron density. Nat Ree aud the radial maguetic field streneth. Be. at Reo.," The radio emission is characterized by three parameters: $R_{C}$, the total non-thermal electron density, $N_{e}$, at $R_{C}$, and the radial magnetic field strength, $B_{C}$, at $R_{C}$." " We attempted to uniquely measure these parameters through a fit to the measured spectruu of DENISLO using expressious frou, Dull(1985) for the totalI8. and circularly-polarized iuteusities of evrosvuchrotrou cussion."," We attempted to uniquely measure these parameters through a fit to the measured spectrum of DENIS1048, using expressions from \citet{d85} for the total and circularly-polarized intensities of gyrosynchrotron emission." A large number of parameter combinations were found to ft the data., A large number of parameter combinations were found to fit the data. Two assuniptious. however. allowed the free parameters to be constrained within the ranges given in Table 2.," Two assumptions, however, allowed the free parameters to be constrained within the ranges given in Table 2." First. we assumed that the spectral peal of the gvrosvuchrotron emission (Dull1985) did not lie within the spectral band. as justified by the regularity of the observed power-law spectrum.," First, we assumed that the spectral peak of the gyrosynchrotron emission \citep{d85} did not lie within the spectral band, as justified by the regularity of the observed power-law spectrum." " We also limited Becτος(πο.8,3 GG in the dipole approximation. where CC is the upper lit on the surface maenetic field streueth placed by Reiners& (2010)."," We also limited $B_{C}<2700/(R_{C}-R_{*})^{3}$ G in the dipole approximation, where G is the upper limit on the surface magnetic field strength placed by \citet{rb10}. ." The stellarracius. A... is further assumed (Cafter. to be equivalent to a Jupiter radius.," The stellarradius, $R_{*}$ , is further assumed \citep[after, e.g.,][]{bag95,bhl+01,bp05,oph+09} to be equivalent to a Jupiter radius." We have utilised the uuprecedeuted frequency coverage of the the uperaded ATCA to characterize the radio, We have utilised the unprecedented frequency coverage of the the upgraded ATCA to characterize the radio We use the same model as in the RGS fit for the analvsis of the IIEZTGS data.,We use the same model as in the RGS fit for the analysis of the HETGS data. The +1 order spectra of both MEG and WEG are jointly fit., The $\pm 1$ order spectra of both MEG and HEG are jointly fit. Because HETGS has very little effective area at the wavelengths of € Ix-shell lines. the C abundance is fixed at the value derived from the RGS fit.," Because HETGS has very little effective area at the wavelengths of C K-shell lines, the C abundance is fixed at the value derived from the RGS fit." The reconstructed. DEM and. abunclances are shown in Figures G and 7 as the red histogram and τος sinbols. respectively.," The reconstructed DEM and abundances are shown in Figures \ref{fig:dem} and \ref{fig:ab} as the red histogram and red symbols, respectively." Both orders of MEG spectva are sunuuedc ancl shown in Figure 10. Lor the spectral region between 6 and 18A., Both orders of MEG spectra are summed and shown in Figure \ref{fig:hetgsp} for the spectral region between 6 and 18. The model and data spectra are seen to agree with each other very. well., The model and data spectra are seen to agree with each other very well. As compared wilh the RGS determination. the total emission measure in the (wo peaks is larger and the abundanees smaller on average.," As compared with the RGS determination, the total emission measure in the two peaks is larger and the abundances smaller on average." This is clearly due to the same reason we discussed in our (wo test cases. ie. the weak continuum emission does not constrain the total emission measure and absolute abundance values well. although relative abundances are reasonably well determined.," This is clearly due to the same reason we discussed in our two test cases, i.e., the weak continuum emission does not constrain the total emission measure and absolute abundance values well, although relative abundances are reasonably well determined." The discrepancy in (he total emission measure derived from the (wo datasets are much larger than (hat seen in (he test cases., The discrepancy in the total emission measure derived from the two datasets are much larger than that seen in the test cases. It is possible (hat the uncertainties in the atomic database. instrument. calibration. ancl background many have caused larger differences.," It is possible that the uncertainties in the atomic database, instrument calibration, and background many have caused larger differences." Another major difference in the DEM is that the secondary peak appears (ο be much stronger relative to the main peak (han in the RGS fit. and slightly shifted to higher temperatures.," Another major difference in the DEM is that the secondary peak appears to be much stronger relative to the main peak than in the RGS fit, and slightly shifted to higher temperatures." ILowever. this peak is poorly constrained in the HHIZTGS data because it does not have significant effective area lor the intermeciate-Z L-shell lines. and we believe that the RGS derived properties for this temperature region are more robust.," However, this peak is poorly constrained in the HETGS data because it does not have significant effective area for the intermediate-Z L-shell lines, and we believe that the RGS derived properties for this temperature region are more robust." For temperatures above log(7)=7.4. the IIETGS fit shows no emission measure while RGS [it gives some significant values.," For temperatures above $\log(T)=7.4$, the HETGS fit shows no emission measure while RGS fit gives some significant values." Because HETGOGS has better sensitivity at shorter wavelengths. and we have reason to believe that the RCS effective area below 8 is underestimated. we conclude that the HIZEGS fit is more reliable than the RGS fit in (his temperature region.," Because HETGS has better sensitivity at shorter wavelengths, and we have reason to believe that the RGS effective area below 8 is underestimated, we conclude that the HETGS fit is more reliable than the RGS fit in this temperature region." The previous sections show that the RGS data is better in constraining (he low temperature part of the DEM while (he HETGS data is more suitable to constrain the high temperature part of the DEM., The previous sections show that the RGS data is better in constraining the low temperature part of the DEM while the HETGS data is more suitable to constrain the high temperature part of the DEM. To combine the strengths of both instruments. we have carried out a joint fit of both datasets using the same model.," To combine the strengths of both instruments, we have carried out a joint fit of both datasets using the same model." Even though the two observations are not made simultaneously. the lack of variability of (he Capella corona makes such an effort possible.," Even though the two observations are not made simultaneously, the lack of variability of the Capella corona makes such an effort possible." I1 is also justified by the fact that the joint fit model describes both HIZEGS and RGS spectra very well., It is also justified by the fact that the joint fit model describes both HETGS and RGS spectra very well. More quantitively speaking. the likelvhood statistics of the goodness of fit. 7. for the model derived from the ILETGS data is 29891: that for the model derived [rom the RGS data is 38489: when the model derived from the joint [it is applied to MEG and RGS," More quantitively speaking, the likelyhood statistics of the goodness of fit, $X^2$, for the model derived from the HETGS data is 29891; that for the model derived from the RGS data is 38489; when the model derived from the joint fit is applied to MEG and RGS" hence the QPO frequencies.,hence the QPO frequencies. For X-ray binaries the cise precession timescale is usually of tens of days to vears (cl., For X-ray binaries the disc precession timescale is usually of tens of days to years (cf. Wijers Pringle 1999 and references therein). which is much longer than the duration of each QPO observation.," Wijers Pringle 1999 and references therein), which is much longer than the duration of each QPO observation." Additionally for accretion-powered millisecond pulsars (he magnetic inclination is likely (ο be very small (Lab οἱ al..," Additionally for accretion-powered millisecond pulsars the magnetic inclination is likely to be very small (Lamb et al.," 2008)., 2008). For the above reasons we expect that the change of the QPO Irequencies induced by oblique magnetic fields might be very small compared with the uncertainties in (he measured frequencies., For the above reasons we expect that the change of the QPO frequencies induced by oblique magnetic fields might be very small compared with the uncertainties in the measured frequencies. Our results indicate that the peak separation is always related to the spin [requency., Our results indicate that the peak separation is always related to the spin frequency. What's more. there seems to be a weak positive correlation between the spin frequency and the parameter 5 lor SSCS. which can be described as 0.53(4£0.08). plotted in the left panel of Fig.," What's more, there seems to be a weak positive correlation between the spin frequency and the parameter $\varepsilon$ for SSCS, which can be described as $\varepsilon=2.28(\pm 0.16)(\nu_s/1000\,{\rm Hz})- 0.53(\pm 0.08)$ , plotted in the left panel of Fig." 5., 5. Substitute this relation into we get a trend of Av changing with the spin frequeney. as plotted in the right panel ol Fig.," Substitute this relation into $\Delta\nu = (1/\sqrt {1 + \varepsilon^2})(\nu_1 + \nu_s) - \nu_1 $ we get a trend of $\Delta\nu $ changing with the spin frequency, as plotted in the right panel of Fig." 5., 5. From the dark black curve to the light gray eurve νι changes from 1000 IIz to 100 llz in a step of 100 Hz., From the dark black curve to the light gray curve $\nu_1$ changes from 1000 Hz to 100 Hz in a step of 100 Hz. " We lind that when 7, increases. Av varies [rom ~7/2 to evs. and finally to ~1/2."," We find that when $\nu_s$ increases, $\Delta\nu$ varies from $\sim \nu_s/2$ to $\sim \nu_s$, and finally to $\sim \nu_s/2$." The transitions occur at ve100 Iz and 500 Lz. respectively.," The transitions occur at $\nu_s\sim 100$ Hz and 500 Hz, respectively." The accretion process can take place only when (he magnetospheric radius is less (han the corotation radius (e.g. Ghosh Lamb 1979)., The accretion process can take place only when the magnetospheric radius is less than the corotation radius (e.g. Ghosh Lamb 1979). In other words. the Neplerian frequency al (he magnetosphere radius should be more than the spin frequency of the NS if accretion process can take place.," In other words, the Keplerian frequency at the magnetosphere radius should be more than the spin frequency of the NS if accretion process can take place." Because of this there is a mininnun value of the lower frequency of the twin kIlz QPOs in SSCS. νι7(142—])z.," Because of this there is a minimum value of the lower frequency of the twin kHz QPOs in SSCS, $\nu _1 > {(\sqrt{1 + \varepsilon^2} - 1)}{\nu _s }$." Besides. due to the [act that the peak separation must be positive values we can get the maximal value for the upper frequency. V»cvll1222—1) for SSCS.," Besides, due to the fact that the peak separation must be positive values we can get the maximal value for the upper frequency, $\nu _2 < \nu _s/(\sqrt{1 + \varepsilon ^2} - 1)$ for SSCS." These may serve as possible evidence to testify this model with future measurements of kHz QPOs in LAINBs., These may serve as possible evidence to testify this model with future measurements of kHz QPOs in LMXBs. The authors thank the anouvinous referee for (he helpful suggestion on the manuscript., The authors thank the anonymous referee for the helpful suggestion on the manuscript. This work was supported by the Natural Science Foundation of China under grant numbers 10573010 and 10221001., This work was supported by the Natural Science Foundation of China under grant numbers 10573010 and 10221001. reeion near the base of the jet can cause the measured core position to move inward along the jet direction as a function of increasing radio frequency of the observations.,region near the base of the jet can cause the measured core position to move inward along the jet direction as a function of increasing radio frequency of the observations. Such core shifts have been measured for sole compact sources (c.g.Lobanov1998:IKovalevetal.2008).," Such core shifts have been measured for some compact sources \citep[e.g.][]{LOBANOV:98, KOVALEV:08}." . Based upon the discussion above. there are potential advantages ο observing astrometric sources αἲ radio frequencies higher than the typical S/N baud observations.," Based upon the discussion above, there are potential advantages to observing astrometric sources at radio frequencies higher than the typical S/X band observations." First. the resolution of the observations Is mnereased. thus improving the astrometric accuracy.," First, the resolution of the observations is increased, thus improving the astrometric accuracy." Second. the effects due to intrinsic source structure nav be reduced since the core aud jet compoucuts have different spectral characteristics aud the core is expected to be more dominant at hieh frequencies.," Second, the effects due to intrinsic source structure may be reduced since the core and jet components have different spectral characteristics and the core is expected to be more dominant at high frequencies." We have undertaken a program5 to observe a nuniber of extragalactic sources at IK baud (21 GIIz) aud OQ baud (13 GITIZ) using the 10 stations of the Very Long Bascline Aivav (VLBA)., We have undertaken a program to observe a number of extragalactic sources at K band (24 GHz) and Q band (43 GHz) using the 10 stations of the Very Long Baseline Array (VLBA). At these higher frequencies. ouly the VLBA provides the stability. imagine capabilities and frequency coverage to enable such a program.," At these higher frequencies, only the VLBA provides the stability, imaging capabilities and frequency coverage to enable such a program." The long term goals of the program inchide: 1) developing a lieh-frequency CRE with a variety of applications including miproved deep space navigation. 2) providing the astronomical commmuity with an extended catalog of calibrator sources for VLBI observatious at 21 aud 13 GIIz. aud 3) studving the effects of the intrinsic structive of extragalactic sources to improve the astrometric accuracy of future high-frequency reference frames.," The long term goals of the program include: 1) developing a high-frequency CRF with a variety of applications including improved deep space navigation, 2) providing the astronomical community with an extended catalog of calibrator sources for VLBI observations at 24 and 43 GHz, and 3) studying the effects of the intrinsic structure of extragalactic sources to improve the astrometric accuracy of future high-frequency reference frames." A detailed discussion of the program aud the astrometric results is contained m a conipanion paper (Lanyvietal.2009.hereafterPaperT).., A detailed discussion of the program and the astrometric results is contained in a companion paper \citep[][hereafter Paper I]{LANYI:09}. " In this paper. we concentrate on the dmaging aspects of the program and the effects of observed source structure and variability on astrometric accuracy,"," In this paper, we concentrate on the imaging aspects of the program and the effects of observed source structure and variability on astrometric accuracy." Theoretically. an optimal CRF would be composed of sources with stroue. non-variable. poiut-like eniission.," Theoretically, an optimal CRF would be composed of sources with strong, non-variable, point-like emission." Iu reality. however. virtually all sources possess some structure and intrinsic variability iu the emission over time.," In reality, however, virtually all sources possess some structure and intrinsic variability in the emission over time." In addition. there is the poteutial for sudden flaring events even for normally quiescent sources.," In addition, there is the potential for sudden flaring events even for normally quiescent sources." Thus it is hiehly desirable to characterize anc monitor the nature of the sources used in a CRE through periodic VLBI imaging., Thus it is highly desirable to characterize and monitor the nature of the sources used in a CRF through periodic VLBI imaging. The VLBA has previously been used to make simultaneous dual-frequency S/X-baud (2.3/8.L (1) observations of a total of 389 ICRE sources (Fev 2000).," The VLBA has previously been used to make simultaneous dual-frequency S/X-band (2.3/8.4 GHz) observations of a total of 389 ICRF sources \citep{FCF:96,FC:97,FC:00}." . To date. approximately 90% of the ICRF sources north of 503 declination have been tuaged at least once at both 2.5 and 8.1 GIIz.," To date, approximately $90\%$ of the ICRF sources north of $-20^\circ$ declination have been imaged at least once at both 2.3 and 8.4 GHz." Based on the initial work of Charlot (1990).. the database of VLBA X-baud aud S-band nuages was analyzed by Fev&Charlot(1997.2000) in order to quautitatively improve our unuderstandiig 6: the relationship between exteuded source structure and the astrometric positions determined from VLBI.," Based on the initial work of \cite{CHARLOT:90}, the database of VLBA X-band and S-band images was analyzed by \cite{FC:97,FC:00} in order to quantitatively improve our understanding of the relationship between extended source structure and the astrometric positions determined from VLBI." Tere we discuss our erowine database of ligh-frequency inages of potential extragalactic reference frame sources., Here we discuss our growing database of high-frequency images of potential extragalactic reference frame sources. We apply simular analysis techuiques in an attempt to characterize the impact of extended source structure ou the astrometric accuracy of the catalog of source positions obtained from our VLBA hieli-frequeucy. data (Paper I)., We apply similar analysis techniques in an attempt to characterize the impact of extended source structure on the astrometric accuracy of the catalog of source positions obtained from our VLBA high-frequency data (Paper I). We observed a total of 351 extragalactic radio sources using the 10 antennas of the VLBA (Napieretal.1991) of the National Badio Astronomy Observatory over the course of LO sessions spauniug five voars from 20022007., We observed a total of 351 extragalactic radio sources using the 10 antennas of the VLBA \citep{NAPIER:94} of the National Radio Astronomy Observatory over the course of 10 sessions spanning five years from 2002–2007. Tn all 10 of the sessions. observatious were recorded at IK-baud (21 GIIz).," In all 10 of the sessions, observations were recorded at K-band (24 GHz)." Additionally. iu. four of the 10 sessions. observations were also recorded at Q-band (13 GITZ).," Additionally, in four of the 10 sessions, observations were also recorded at Q-band (43 GHz)." Iu. two of the sessious. dual S/X-baud (2.3/8.1 GIIz) observations were interspersed with the Is-band observations to investigate potential ionospheric correction methods.," In two of the sessions, dual S/X-band (2.3/8.4 GHz) observations were interspersed with the K-band observations to investigate potential ionospheric correction methods." A sunuuarv of the VLBA Is- aud Q-band observations relevant to the imaging program is preseuted in Table 1.., A summary of the VLBA K- and Q-band observations relevant to the imaging program is presented in Table \ref{TAB:OBS}. The frequency information listed in Table 1. reflects the changing observing strategy over the course of the 10 VLBA sessious., The frequency information listed in Table \ref{TAB:OBS} reflects the changing observing strategy over the course of the 10 VLBA sessions. For the first two sessions. four 8 AIIIz bands cach at 214 and 13 Giz were recorded siauultaneouslv for cach scan using 2 bit sampling vielding a total bandwidth of 32 MIIz.," For the first two sessions, four 8 MHz bands each at 24 and 43 GHz were recorded simultaneously for each scan using 2 bit sampling yielding a total bandwidth of 32 MHz." The remaiming sessions used eight 8 MITz bands with 1 bit sampling for a total bandwidth of 61 MITIz., The remaining sessions used eight 8 MHz bands with 1 bit sampling for a total bandwidth of 64 MHz. For these sessions. scans alternated between I& aud Q bands (sessions 3 aud 5). shuultaneous S/N baud aud I& band (sessions 6 aud &). or just I& band aloue (sessions [. 9. aud 10).," For these sessions, scans alternated between K and Q bands (sessions 3 and 5), simultaneous S/X band and K band (sessions 6 and 8), or just K band alone (sessions 4, 9, and 10)." The first K- session observed a large nunber of poteutial sources found in other VLBI survevs in order to expand the total uunuber of available high-frequency astrometric targets., The first K-only session observed a large number of potential sources found in other VLBI surveys in order to expand the total number of available high-frequency astrometric targets. Iu the final two Is-ouly sessions. cauclicate sources near the ecliptic plane were added for potential future use iu deep space navigation.," In the final two K-only sessions, candidate sources near the ecliptic plane were added for potential future use in deep space navigation." A detailed discussion of the evolving observing strategv aud its relevance to the astrometric goals of the program is prescuted in Paper I. All of the observations were made in a bandwidth svuthesis iiode to facilitate group delay measurements for astrometry the multipliitv of chaunels allows for the determination of a precise group delay (Rogers 1970)., A detailed discussion of the evolving observing strategy and its relevance to the astrometric goals of the program is presented in Paper I. All of the observations were made in a bandwidth synthesis mode to facilitate group delay measurements for astrometry – the multiplicity of channels allows for the determination of a precise group delay \citep{ROGERS:70}. . Observations in this mode also allow snapshot Huaeine., Observations in this mode also allow snapshot imaging. Source scans were typically 2 imunutes in duration at IN band and 3 ainutes for Q band., Source scans were typically 2 minutes in duration at K band and 3 minutes for Q band. Most sources were observed im three or more scans — the one exception beiug the Ik-baud survey. session ou 2003 May 22 m which many of the sources were observed onlv ounce or twice., Most sources were observed in three or more scans – the one exception being the K-band survey session on 2003 May 22 in which many of the sources were observed only once or twice. The raw data bits were correlated with the VLBA correlator at the Array Operations Center in Socorro. New Moexico.," The raw data bits were correlated with the VLBA correlator at the Array Operations Center in Socorro, New Mexico." The correlated data were calibrated and corrected for residual delay and delay rate using the NRAQO’s Astronomical huage Processing System (AIPS)., The correlated data were calibrated and corrected for residual delay and delay rate using the NRAO's Astronomical Image Processing System (AIPS). Initial amplitude calibration for cach intermediate frequency (IF) was accomplished using system teniperature lucasurements taken dunues the observations combined with NRÀO supplied enu curves., Initial amplitude calibration for each intermediate frequency (IF) was accomplished using system temperature measurements taken during the observations combined with NRAO supplied gain curves. Frinec-fitting was done in AIPS using solution intervals equal to the scan durations and a point source model in all cases., Fringe-fitting was done in AIPS using solution intervals equal to the scan durations and a point source model in all cases. After correction for residual delay and delay rate. the data were written to FITS disk files.," After correction for residual delay and delay rate, the data were written to FITS disk files." All subsequeut image processing was carried out using the Caltech VLBI inaeiug software. primarily DIFALAP.," All subsequent image processing was carried out using the Caltech VLBI imaging software, primarily DIFMAP." The visibility data for cach frequency baud were, The visibility data for each frequency band were The DAB stars represent a class of white dwarlk with hvbrid spectra. as weak neutral helium lines are superposed onto the classical hydrogen-line spectrum of DA stars al. 1993)..,"The DAB stars represent a class of white dwarfs with hybrid spectra, as weak neutral helium lines are superposed onto the classical hydrogen-line spectrum of DA stars \citep [see, e.g.,][]{atlas}." The prototvpe of this class. GD323 (WD 1302597; V— 14.52). was," The prototype of this class, GD323 (WD $1302+597$ ; $V=14.52$ ), was" "and velocity v, 200 km s! (Feigelson Montmerle 1999).",and velocity $v_{\rm w}$ $\sim$ 200 km $^{-1}$ (Feigelson Montmerle 1999). X-ray studies indicate particle number densities of the accreting plasma of about 10'* em? (Günnther et al., X-ray studies indicate particle number densities of the accreting plasma of about $10^{12}$ $^{-3}$ (Günnther et al. 2007)., 2007). Variable thermal X-ray emission is also detected from T Tauri stars in the keV band., Variable thermal X-ray emission is also detected from T Tauri stars in the keV band. Luminosities are found tobe in the range ~ 10?! — 108 erg s7!., Luminosities are found tobe in the range $\sim$ $^{31}$ $-$ $^{33}$ erg $^{-1}$. This emission comes from a high density plasma at a typical temperature of ~ 107 K: flares with temperatures ~ 10° K have been detected (Tsuboi et al., This emission comes from a high density plasma at a typical temperature of $\sim$ $^{7}$ K; flares with temperatures $\sim$ $^{8}$ K have been detected (Tsuboi et al. 1998)., 1998). These flares have durations of ~ 10° — 107 s. Such events are expected to occur in magnetic flux tubes with spatial extent of ~ 10'? — 10!! em (e.g Hayashi et al., These flares have durations of $\sim$ $^{3}$ $-$ $^{4}$ s. Such events are expected to occur in magnetic flux tubes with spatial extent of $\sim$ $^{10}$ $-$ $^{11}$ cm (e.g Hayashi et al. 1996)., 1996). Models for the X-ray activity based on the interaction of the stellar object and the circumstellar disk have been proposed by several authors (e.g. Hayashi et al., Models for the X-ray activity based on the interaction of the stellar object and the circumstellar disk have been proposed by several authors (e.g. Hayashi et al. 1996. Birk et al.," 1996, Birk et al." 2000)., 2000). These X-rays flares are widely considered as upscaled versions of solar flares., These X-rays flares are widely considered as upscaled versions of solar flares. The rapid heating and cooling of plasma and acceleration of particles must arise from efficient MHD processes. such as solar-type magnetic reconnection events in twisted flux tubes that connect the central object and the circumstellar disk (Birk et al.," The rapid heating and cooling of plasma and acceleration of particles must arise from efficient MHD processes, such as solar-type magnetic reconnection events in twisted flux tubes that connect the central object and the circumstellar disk (Birk et al." 2000)., 2000). Magnetic reconnection ts one of the fundamental processes in astrophysical plasmas because it explains large-scale. dynamic releases of magnetic energy.," Magnetic reconnection is one of the fundamental processes in astrophysical plasmas because it explains large-scale, dynamic releases of magnetic energy." It is essentially a topological reconfiguration of the magnetic field caused by a change in the connectivity of the field lines., It is essentially a topological reconfiguration of the magnetic field caused by a change in the connectivity of the field lines. It is this change which allows the release of stored magnetic energy. which in many situations is the dominant source of free energy in a plasma.," It is this change which allows the release of stored magnetic energy, which in many situations is the dominant source of free energy in a plasma." Several works have been done on particle acceleration through magnetic reconnection ( e.g. Schopper. Lesch. Birk 1998. Zenitani Hoshino 2001. de Gouveia Dal Pino et al.," Several works have been done on particle acceleration through magnetic reconnection ( e.g. Schopper, Lesch, Birk 1998, Zenitani Hoshino 2001, de Gouveia Dal Pino et al." 2010)., 2010). Strong shocks resulting from supersonic plasma ejections are the likely outcome of massive reconnection in T Taurt magnetospheres., Strong shocks resulting from supersonic plasma ejections are the likely outcome of massive reconnection in T Tauri magnetospheres. " Such shocks can in principle accelerate particles up to relativistic energies through Fermi mechanism,", Such shocks can in principle accelerate particles up to relativistic energies through Fermi mechanism. The expected values of magnetic field in T Tauri stars are ~ | kG (e.g. Johns-Krull 2007) and the field structure is complex and multipolar. as in the Sun.," The expected values of magnetic field in T Tauri stars are $\sim$ 1 kG (e.g. Johns-Krull 2007) and the field structure is complex and multipolar, as in the Sun." For simple flare models. quantitative properties of large-scale magnetic field structures can be inferred (e.g. Montmerle et al.," For simple flare models, quantitative properties of large-scale magnetic field structures can be inferred (e.g. Montmerle et al." 1983. Walter Kuhi 1984).," 1983, Walter Kuhi 1984)." Assuming equipartition conditions. BySi = 2n.kT.the magnetic field strength in the magnetosphere is approximately 10° G (Feigelson Montmerle 1999).," Assuming equipartition conditions, $B_{\rm eq}^{2}/8{\pi}$ = $2n_{\rm e}kT$, the magnetic field strength in the magnetosphere is approximately $^{2}$ G (Feigelson Montmerle 1999)." Diffusive shock acceleration does not work for slow-mode shocks. consequently is thought that diffusive shock acceleration is not important for magnetic reconnection that involves slow-mode shocks (e.g. Priest Forbes 2000).," Diffusive shock acceleration does not work for slow-mode shocks, consequently is thought that diffusive shock acceleration is not important for magnetic reconnection that involves slow-mode shocks (e.g. Priest Forbes 2000)." Under some conditions. however. any obstacle which obstructs the outflow will create a fast-mode shock (Tsuneta Naito 1998).," Under some conditions, however, any obstacle which obstructs the outflow will create a fast-mode shock (Tsuneta Naito 1998)." In a T Taurt magnetosphere the obstacles might be clumps from the strong stellar wind: considerable observational evidence supports the idea that the wind structure is clumpy (e.g. Owocki Cohen 2006)., In a T Tauri magnetosphere the obstacles might be clumps from the strong stellar wind; considerable observational evidence supports the idea that the wind structure is clumpy (e.g. Owocki Cohen 2006). Moreover. shock acceleration is now applied to the outflow regions of coronal magnetic reconnection sites. where first-order Fermi mechanism at the standing fast shock is a leading candidate (Aschwanden 2008).," Moreover, shock acceleration is now applied to the outflow regions of coronal magnetic reconnection sites, where first-order Fermi mechanism at the standing fast shock is a leading candidate (Aschwanden 2008)." The shocks are expected to accelerate charged particles up to high energies by a Fermi-like diffusive process (e.g. Drury 1983)., The shocks are expected to accelerate charged particles up to high energies by a Fermi-like diffusive process (e.g. Drury 1983). Additionally. recent extensive 3D numerical simulations performed by Kowal et al. (," Additionally, recent extensive 3D numerical simulations performed by Kowal et al. (" 2011) show that within contracting magnetic islands or current. sheets. charged particles are accelerated by a first-order Fermi process while outside the current sheets and islands the particles experience. mostly drift acceleration due to magnetic field gradients.,"2011) show that within contracting magnetic islands or current sheets, charged particles are accelerated by a first-order Fermi process while outside the current sheets and islands the particles experience mostly drift acceleration due to magnetic field gradients." These results are supported by observations of solar flares that suggest that magnetic reconnection should be first slow in order to ensure the accumulation of magnetic flux and then suddenly become fast to allow a rapid energy release (e.g. Lazarian Vishniae 1999)., These results are supported by observations of solar flares that suggest that magnetic reconnection should be first slow in order to ensure the accumulation of magnetic flux and then suddenly become fast to allow a rapid energy release (e.g. Lazarian Vishniac 1999). Particles scattered by turbulence between converging magnetic mirrors formed by oppositely-directed magnetic fluxes moving towards each other at the fast reconnection speed can undergo diffusive acceleration without the requirement of strong shock formation (Kowal et al., Particles scattered by turbulence between converging magnetic mirrors formed by oppositely-directed magnetic fluxes moving towards each other at the fast reconnection speed can undergo diffusive acceleration without the requirement of strong shock formation (Kowal et al. 2011)., 2011). Independently of the details of the acceleration mechanism. we assume that a population of non-thermal relativistic particles. electrons and protons. is injected into the magnetosphere of the T Tauri star.," Independently of the details of the acceleration mechanism, we assume that a population of non-thermal relativistic particles, electrons and protons, is injected into the magnetosphere of the T Tauri star." These particles will interact with the large scale magnetic fields. with the existing radiation fields. and with the magnetospheric plasma. producing non-thermal electromagnetic radiation.," These particles will interact with the large scale magnetic fields, with the existing radiation fields, and with the magnetospheric plasma, producing non-thermal electromagnetic radiation." The size of the acceleration region is the spatial scale where reconnection takes place. te the flux tube length.," The size of the acceleration region is the spatial scale where reconnection takes place, i.e the flux tube length." " The power available in the magnetized system is where A isthe area of the flux tube. of length /=10! cm and aspect ratio ~ 0.1 / (Feigelson Montmerle 1999), and v4 is the Alfven speed. vy=\/B?/(4rm,n). with n the particle density and #7, the proton mass."," The power available in the magnetized system is where $A$ isthe area of the flux tube, of length $l = 10^{11}$ cm and aspect ratio $\sim$ 0.1 $l$ (Feigelson Montmerle 1999), and $v_{\rm A}$ is the Alfven speed, $v_{\rm A} = \sqrt{{B^{2}}/({4\pi m_{p} n})}$, with $n$ the particle density and $m_{p}$ the proton mass." For B22«107 G. we get L ~ 10 erg s.," For $B = 2\times 10^{2}$ G, we get $L$ $\sim$ $10^{34}$ erg $^{-1}$." We assume that of this power is released in the reconnection processes., We assume that of this power is released in the reconnection processes. In turn. a fraction qi - of this power goes to relativistic particles.," In turn, a fraction $q_{\rm rel}$ $\sim$ of this power goes to relativistic particles." These values are in accordance to inferred values for the Sun. and can be considered even conservative.," These values are in accordance to inferred values for the Sun, and can be considered even conservative." For instance. in large solar flares the accelerated particles contain up to or more of the total energy released. whereas in gradual events ~ of the total power goes to the accelerated particles (see Lin 2008 and references therein).," For instance, in large solar flares the accelerated particles contain up to or more of the total energy released, whereas in gradual events $\sim$ of the total power goes to the accelerated particles (see Lin 2008 and references therein)." " The efficiency of non-thermal acceleration in. the magnetized plasma is mimicking the efficiency for standard first order Fermi acceleration theory behind (Drury 1983. Vila Aharonian 2009); here D is the particle difussion coefficient. is the particle gyroradius and vj, Is the reconnection Dr.speed."," The efficiency of non-thermal acceleration in the magnetized plasma is mimicking the efficiency for standard first order Fermi acceleration theory behind (Drury 1983, Vila Aharonian 2009); here $D$ is the particle difussion coefficient, $r_{\rm g}$ is the particle gyroradius and $v_{\rm rec}$ is the reconnection speed." If D is in the Bohm limit Dpgonm = 70/3., If $D$ is in the Bohm limit $D_{\rm Bohm}$ $=$ $r_{\rm g}c/3$ . The reconnection speed in violent reconnection events satisfy vj. va (Lazarian Vishniac 1999. Kowal et al.," The reconnection speed in violent reconnection events satisfy $v_{\rm rec}$ $\sim $ $v_{\rm A}$ (Lazarian Vishniac 1999, Kowal et al." " 2009). so we assume vy, = O.6va. that gives an efficiency jj—1079."," 2009), so we assume $v_{\rm rec}$ $=$ $0.6v_{\rm A}$ , that gives an efficiency $\eta\sim10^{-6}$." This efficiency. although not very high. will allow maximum energies well into the 5-ray domain. as we will see.," This efficiency, although not very high, will allow maximum energies well into the $\gamma$ -ray domain, as we will see." 1n this work we compare observed and model SEDs of SDSS quasars with SWIRE counterparts aiming at constraining the model parameters and at quantifying the LX. properties of bright quasars.,In this work we compare observed and model SEDs of SDSS quasars with SWIRE counterparts aiming at constraining the model parameters and at quantifying the IR properties of bright quasars. The need for such an approach. though evident. was also stressed by Gallagheretal.(2007)... who studied a sample of 234 SDSS quasars. most of which also belong to our sample. trying to quantify the ellects off the luminosity on the shape of their SEDs in the MIT," The need for such an approach, though evident, was also stressed by \cite{gallagher07}, who studied a sample of 234 SDSS quasars, most of which also belong to our sample, trying to quantify the effects of the luminosity on the shape of their SEDs in the MIR." Their conclusions were solely based. on the observed. SEDs and claimed that comparison with mocdoels would constrain physical. parameters. many of which are dealt with in the present study.," Their conclusions were solely based on the observed SEDs and claimed that comparison with models would constrain physical parameters, many of which are dealt with in the present study." We use a torus mocel with smooth dust. distribution. originally presented in Fritzetal.(2006).. even though there are conllicting suggestions in the literature as to whether ori could be smooth or clumps.," We use a torus model with smooth dust distribution, originally presented in \cite{fritz06}, even though there are conflicting suggestions in the literature as to whether tori could be smooth or clumpy." Smooth mocels have been ested on a variety ofobjects (e.g. Granato&Danese1994: Fritzetal. 2006)) vielding very good results., Smooth models have been tested on a variety ofobjects (e.g. \citealt{granato94}; \citealt{fritz06}) ) yielding very good results. There is. rowever. evidence that elumpy tori might be more realistic. (ος. lüsaliti.Elvis&Nicastro 2002)). nevertheless. the few models in the literature were tested only on average SEDs (Nenkovaetal.2002). or on individual objects (Ilónigetal. 2006).," There is, however, evidence that clumpy tori might be more realistic, (e.g. \citealt{risaliti02}) ), nevertheless, the few models in the literature were tested only on average SEDs \citep{nenkova02} or on individual objects \citep{hoenig06}." . Furthermore. Nenkovactal.(2002) explicitly aceressed the issue of suppression of the 9.7 silicate eature. predicted. in. emission [roni smooth models. which was never (ill then supported observationally in. type-L objects. but the picture has changed since with Spitzer LARS observations of this feature in emission (Siebenmorgen 2005: Sturmetal. 2005: Haoetal. 2005: 2006:: Shietal. 2006)).," Furthermore, \cite{nenkova02} explicitly addressed the issue of suppression of the 9.7 silicate feature, predicted in emission from smooth models, which was never till then supported observationally in type-1 objects, but the picture has changed since with Spitzer IRS observations of this feature in emission \citealt{siebenmorgen05}; \citealt{sturm05}; \citealt{hao05}; \citealt{buchanan06}; \citealt{shi06}) )." The issue of the inlluence of the acerction Iuminosity on the dust coverage is the source of an ongoing discussion in the literature., The issue of the influence of the accretion luminosity on the dust coverage is the source of an ongoing discussion in the literature. According to the receding torus paraciem (Lawrence1991). the opening anele of the torus depends on the power of the central sources. with more powerful quasars sweeping larger amounts of dust leaving thus larger opening angles around them.," According to the receding torus paradigm \citep{lawrence91} the opening angle of the torus depends on the power of the central sources, with more powerful quasars sweeping larger amounts of dust leaving thus larger opening angles around them." In this approach. the Unified Scheme does not rely uniquely on the orientation of the dusty torus but on the dependence of the geometrical thickness and the optical depths on the central source.," In this approach, the Unified Scheme does not rely uniquely on the orientation of the dusty torus but on the dependence of the geometrical thickness and the optical depths on the central source." Evidence for receding tori is often found in studies of radio-Ioud GN (e.g. Crimes. Rawlings Willott 2003. 2005).," Evidence for receding tori is often found in studies of radio-loud AGN (e.g. Grimes, Rawlings Willott 2003, 2005)." Recently. Maiolinoctal.(2007) presented results of a study of high. luminosity quasars carried out with Spitzer URS pointing towards decreasing covering factors with increasing luminosity.," Recently, \cite{maiolino07} presented results of a study of high luminosity quasars carried out with Spitzer IRS pointing towards decreasing covering factors with increasing luminosity." 1n Section 5.2. we already suggested that the inlluence of Γι on the torus geometry is demonstrated by the larger values of Lace gencraly occuring in objects with ?=6.0., In Section \ref{sec:lir} we already suggested that the influence of $\rm L_{acc}$ on the torus geometry is demonstrated by the larger values of $\rm L_{acc}$ generaly occuring in objects with $\gamma=-6.0$. In fact. Lace as derived from the best fit mocels. also shows a slight dependence on Ck with the average value of Lice in. bins of covering factor (red. squares). decreases with increasing covering factor. as seen in Fig. 14..," In fact, $\rm L_{acc}$ as derived from the best fit models, also shows a slight dependence on CF with the average value of $\rm L_{acc}$ in bins of covering factor (red squares) decreases with increasing covering factor, as seen in Fig. \ref{fig:LaccCF}." Phe dispersion on L;« in each bin. however. is so large that the sucly is inconclusive.," The dispersion on $\rm L_{acc}$ in each bin, however, is so large that the study is inconclusive." The study of the sources. with TO detections. representing of the sample. suggested the presence of à strong starburst component in many of he cases.," The study of the sources with 70 detections, representing of the sample, suggested the presence of a strong starburst component in many of the cases." Accorcling to the best fit models ancl due to the| flux limits of the sample. only objects with Arp220-Lik«' components. were observed in 70jun.," According to the best fit models and due to the flux limits of the sample, only objects with Arp220-like components were observed in 70." One could argue tha Arp220 is a heavily extinguished starburst. prototype ultrauminous Ili galaxy in the local Universe ancl therefore unlikely to be found in high redshift bright quasars.," One could argue that Arp220 is a heavily extinguished starburst, prototype ultraluminous IR galaxy in the local Universe and therefore unlikely to be found in high redshift bright quasars." In a simpler approach. a black body of —301x. could have been used to account for the 70 micron detection but we used observed starburst templates instead. in the line of Fritzetal.(2006).," In a simpler approach, a black body of $\sim$ 30K could have been used to account for the 70 micron detection but we used observed starburst templates instead, in the line of \cite{fritz06}." ".. Llowever. we cid exclude from the model grid. models with Rov /15,2300. originally included. in Fritzetal.(2006)."," However, we did exclude from the model grid models with $_{\rm out}/$ $_{\rm in}$ =300, originally included in \cite{fritz06}." .. These moclels imply larger dust clistributions and lower dust temperatures and could have been used to reproduce the 70 detections., These models imply larger dust distributions and lower dust temperatures and could have been used to reproduce the 70 detections. Llowever. they would also correspond to tori with physical sizes of several hundred parsees. sometimes even προ where star formation is likely to occur.," However, they would also correspond to tori with physical sizes of several hundred parsecs, sometimes even kpc, where star formation is likely to occur." Furthermore. at. those distances the dust temperature would drop to temperatures typical of the dust of starburst or the diffuse dust responsible [or cirrus emission.," Furthermore, at those distances the dust temperature would drop to temperatures typical of the dust of starburst or the diffuse dust responsible for cirrus emission." One of the main points of this work is the use of tori models with low equatorial optical depths at9.7jum.. Tor<1.0.," One of the main points of this work is the use of tori models with low equatorial optical depths at, $\tau_{9.7} < 1.0$." Our study concludes that the presence of low optical depth tort around. active nuclei is a possibility. ancl would imply only a minimum of mocifications in the current picture of the Unified Scheme. namely the possibility of seeing tvpe-1 objects while cust intercepts the line of sight.," Our study concludes that the presence of low optical depth tori around active nuclei is a possibility, and would imply only a minimum of modifications in the current picture of the Unified Scheme, namely the possibility of seeing type-1 objects while dust intercepts the line of sight." A strong implication of this assumption would be the presence of the silicate feature at 9.7 in emission even in tvpe-2 AGN., A strong implication of this assumption would be the presence of the silicate feature at 9.7 in emission even in type-2 AGN. Such a feature was indeed observed recently in X-ray selected type-2 AGN. using the Spitzer IRS (Sturmetal. 2006).," Such a feature was indeed observed recently in X-ray selected type-2 AGN, using the Spitzer IRS \citep{sturm06}." ". Phe comparison between results vielded by all τατ models and only high. 70,7 ones suggests a [lattening of the distribution of the covering factor (see Fig. 4.. "," The comparison between results yielded by all $\tau_{9.7}$ models and only high $\tau_{9.7}$ ones suggests a flattening of the distribution of the covering factor (see Fig. \ref{fig:histoCF}, ," increasing thus the apparent estipated ratio between type-2 and tvpe-1 objects. as dust enshrouded AGN could still be seen as," increasing thus the apparent estimated ratio between type-2 and type-1 objects, as dust enshrouded AGN could still be seen as" but. for the iuterestiug range of parameters. this takes place arouud 10 5 t\Ipe.,"but, for the interesting range of parameters, this takes place around 10 $h^{-1}$ Mpc." The power spectrimm for the linear part (r22:10 5. tMpc). PN). is giveu for a CDM scenario with initial Warrinsou-Zeldovich power spectra (Dardecn ot al.," The power spectrum for the linear part $r>\approx 10$ $h^{-1}$ Mpc), $P(K)$, is given for a CDM scenario with initial Harrinson-Zeldovich power spectra (Bardeen et al." 1986): and we adopt AA—L981«10! (o4= 1) aud Qu= 0.21., 1986): and we adopt $A=1.984\times 10^4$ $\sigma _8=1$ ) and $\Omega _{\rm mat}h=0.21$ . Within μπα] scales (690<0.010 rad). the non-linear part is predominant. so slight variations of the parameter μή or the normalization A will not lead to chanecs in ow results.," Within small scales $\theta _0\le 0.040$ rad), the non-linear part is predominant, so slight variations of the parameter $\Omega _{\rm mat}h$ or the normalization $A$ will not lead to changes in our results." For instance. unuucerical experiments have shown us tha a variation of in the amplitude A leads o variations of z2% in δνΑθ=0.010 rad) or zxVT dnoNZN(OS=0.010 rad) aud much less for lower Oy: since the error bars of ὁ/N axe of this order. we consider icelieible these σα] variations due to the change of the xuanmeters in PIN).," For instance, numerical experiments have shown us that a variation of in the amplitude $A$ leads to variations of $\approx 2$ in $\delta N/N (\theta_0=0.040$ rad) or $\approx 0.7\%$ in $\delta N/N (\theta_0=0.010$ rad) and much less for lower $\theta _0$; since the error bars of $\delta N/N $ are of this order, we consider negligible these small variations due to the change of the parameters in $P(K)$." Iu scales larger than (y=0.010 rad. he errors bars are too large compared to the possible variations in νι," In scales larger than $\theta _0=0.040$ rad, the errors bars are too large compared to the possible variations in $P(K)$." In all ranges. even variations up to in P(A) will not affect ONYN oo nmch compared ο the errors.," In all ranges, even variations up to in $P(K)$ will not affect $\delta N/N$ too much compared to the errors." Two questious might rise as to the suitability of eq. (8):, Two questions might rise as to the suitability of eq. \ref{xiz0}) ): 1) is the assuniption of a power-law for non-linear scales appropriate?:, 1) is the assumption of a power-law for non-linear scales appropriate?; 2) could we apply a power-law for all scales instead of a ACDM. inodel for the non-linear reeine?, 2) could we apply a power-law for all scales instead of a $\Lambda $ CDM model for the non-linear regime? Both questions are answered iu other papers but they will also be answered bv the result of the fit of the counts itself. shown in L (see Fie. 3)).," Both questions are answered in other papers but they will also be answered by the result of the fit of the counts itself, shown in \ref{.comparison} (see Fig. \ref{Fig:fluct_area}) )." " As to the first question. the fit of the power hav with ry=6.66 5. 1Mpc. ~=1.79 is remarkably good for low 0, Gvhich is ucarly independent of the linear part of £). a power law in the nou-luear regine gives a very good fit."," As to the first question, the fit of the power law with $r_0=6.66$ $h^{-1}$ Mpc, $\gamma=1.79$ is remarkably good for low $\theta _0$ (which is nearly independent of the linear part of $\xi $ ), a power law in the non-linear regime gives a very good fit." The auswer to the second question is provided by the following consideration: a power-law iu all scales gives more structure at οLO h!Mpe than the power-luv in the non-linear regime | Ας ΤΝΤ model in the linear regime., The answer to the second question is provided by the following consideration: a power-law in all scales gives more structure at $r>40$ $h^{-1}$ Mpc than the power-law in the non-linear regime + $\Lambda $ CDM model in the linear regime. The first option gives urther fluctuations at large (y: the differcuce is not high chough to reject the first option (we have already said hat the fit is not very seusitive to the parameters in the iuear power spectra). but the AC DAL model iu the linear roeeinue (solid line iu Fig. 3))," The first option gives further fluctuations at large $\theta _0$; the difference is not high enough to reject the first option (we have already said that the fit is not very sensitive to the parameters in the linear power spectra), but the $\Lambda $ CDM model in the linear regime (solid line in Fig. \ref{Fig:fluct_area}) )" is considerably better than he power-law at all scales (long dashed line in Fig. 3))., is considerably better than the power-law at all scales (long dashed line in Fig. \ref{Fig:fluct_area}) ). There are also theoretical reasons to use expression (51) for (7)., There are also theoretical reasons to use expression \ref{xiz0}) ) for $\xi (r)$. " ACDAL simulations lead to a correlation ""uncfion for virialized halos with circular velocity =120 σιήν with this form and 5=1.7 (Primack 2001. Fie."," $\Lambda $ CDM simulations lead to a correlation function for virialized halos with circular velocity $>120 $ km/s with this form and $\gamma =1.7$ (Primack 2001, Fig." 1)., 1). This function turus out to be alinost exactly equal to that or APM galaxies., This function turns out to be almost exactly equal to that for APM galaxies. For K-selected galaxies the correlations do uot need to be equal to that for halos: there may exist sole biasing., For K-selected galaxies the correlations do not need to be equal to that for halos; there may exist some biasing. However. the biasing (b(r)=i£nonslr)fale) ) Is expoectec to be a mild function of r.," However, the biasing $b(r)=\left(\frac{\xi _K(r)}{\xi _{halo}(r)}\right)^{1/2}$ ) is expected to be a mild function of $r$." " So. it sees plausible ο ""se expression (8)) with differeut amplitude aud slightly different 5 with respect to the halos (or APM galaxies)."," So, it seems plausible to use expression \ref{xiz0}) ) with different amplitude and slightly different $\gamma $ with respect to the halos (or APM galaxies)." With this iu nnd. we shall see iu next section vat) with the asstmed shape iu eq. (51).," With this in mind, we shall see in next section that with the assumed shape in eq. \ref{xiz0}) )," there ds qualitative aerecment with the observed varices., there is qualitative agreement with the observed variances. We consider this result as a confirmation of the assumption iat the measured variances are due to the large scale structure., We consider this result as a confirmation of the assumption that the measured variances are due to the large scale structure. This. along with the previously given aremuents supporting this assmuption. male us confident as to its correctness.," This, along with the previously given arguments supporting this assumption, make us confident as to its correctness." So. we consider that large scale structure VAποιά explain not only the main part of the variances. but the whole of them.," So, we consider that large scale structure should explain not only the main part of the variances, but the whole of them." Forcing this by choosing the appropriate values for rg. 5 lead us to an alternative method for deteruinimg the correlation function.," Forcing this by choosing the appropriate values for $r_0$, $\gamma $ lead us to an alternative method for determining the correlation function." The evolution of the correlation function depends on Ogg ale O4 through e., The evolution of the correlation function depends on $\Omega _{\rm mat}$ and $\Omega _{\rm \Lambda}$ through $\epsilon $. In our case. since the average redshift (2)=0.083. (for iiy<13.5 usine the aforementioned LDnuuinositv functiou aud IEK-correction). the exact value of € is not so important. andsinall variations on it will not affect significantly the results from themodel.," In our case, since the average redshift $\langle z\rangle=0.083$ (for $m_K<13.5$ using the aforementioned luminosity function and K-correction), the exact value of $\epsilon $ is not so important, andsmall variations on it will not affect significantly the results from themodel." The evolutionary corrections im this small rage of redshifts are also negligible. specially im I&-baud (Carlbere et al.," The evolutionary corrections in this small range of redshifts are also negligible, specially in K-band (Carlberg et al." 1997)., 1997). We take the value e= 0.1. which comes from the approximation of£&D(:)?. for comoving coordinates [which holds provided that the shape of© does uot evolve. Le. 5 1s coustant with respect to z (proved by Carlberg et al.," We take the value $\epsilon=-0.1$ , which comes from the approximation of $\xi \propto D(z)^2$, for comoving coordinates [which holds provided that the shape of $\xi $ does not evolve, i.e. $\gamma $ is constant with respect to $z$ (proved by Carlberg et al." 1997]. where D. the growing factor ofthe linear deusitv fluctuations. is (Heath 1977. Carroll ct al.," 1997)], where $D$, the growing factor of the linear density fluctuations, is (Heath 1977, Carroll et al." 1992) given bx This leads to a value of εzmO.l for Ομως)= 0.3. O4= 0.7.," 1992) given by This leads to a value of $\epsilon\approx -0.1$ for $\Omega _{\rm mat}(t_0)=0.3$ , $\Omega _{\rm \Lambda}=0.7$ ." Although. aswe have said before. this value changes with other cosinological parameters. our outcome," Although, aswe have said before, this value changes with other cosmological parameters, our outcome" and lorware (imesteps has previously restricted. cosmological simulations to second-order mapping integrators (?)..,and forward timesteps has previously restricted cosmological simulations to second-order mapping integrators \citep{SpringelPrivate2005}. It is straightforwaid to derive the integration equations lor 1+2-point GGL integrators wilh n>1l., It is straightforward to derive the integration equations for $n+2$ -point GGL integrators with $n > 1$. Alb such integrators have implicit equations for the intermediate positions. q.i.q. which must be solved via iteration exactly as in the 9m=1 case discussed above.," All such integrators have implicit equations for the intermediate positions, $q', \ldots, q^{(n)}$, which must be solved via iteration exactly as in the $n = 1$ case discussed above." In the presence of individual timesteps (Section 5)). we must predict the intermediate positionswe cannot iterate the implicit equations to convergence.," In the presence of individual timesteps (Section \ref{IndividualTimeSteps}) ), we must predict the intermediate positions—we cannot iterate the implicit equations to convergence." For integrators of order ereater than four. such predicted positions do not solve the implicit equations accurately enough to make Che svinplecticily error scale better than the trajectory error: as we shall see. we can predict the solution to equation accurately enough to produce lifth-order svanplecticity error in (he [οτιh-orcler integrator.," For integrators of order greater than four, such predicted positions do not solve the implicit equations accurately enough to make the symplecticity error scale better than the trajectory error; as we shall see, we can predict the solution to equation accurately enough to produce fifth-order symplecticity error in the fourth-order integrator." For this reason. the fourth-order integrator is uniquely positioned in the hierarchy of GGL inlegrators for adaptation to individual timesteps This section discusses (wo wars lo solve equation with iteration.," For this reason, the fourth-order integrator is uniquely positioned in the hierarchy of GGL integrators for adaptation to individual timesteps This section discusses two ways to solve equation with iteration." They differ in their choice of initial guess for q'., They differ in their choice of initial guess for $q'$. The choice in Section 3.1 produces an algorithm which is compositional. aud is equivalent to algorithm & from ?..," The choice in Section \ref{OmelyanIteration} produces an algorithm which is compositional, and is equivalent to algorithm 8 from \citet{Omelyan2006}." That algorithm is exactly phase-space-volume and momentum conserving. but only order svinplectic. with three force evaluations per step.," That algorithm is exactly phase-space-volume and momentum conserving, but only fourth-order symplectic, with three force evaluations per step." The choice in Section 3.2. produces an algorithm which is fifth-order svinplecüce (and the same in phase-space-volume error). exactly conserves linear momentum. and conserves angular momentum at fifth-order. with two lorce evaluations per step.," The choice in Section \ref{OurIteration} produces an algorithm which is fifth-order symplectic (and the same in phase-space-volume error), exactly conserves linear momentum, and conserves angular momentum at fifth-order, with two force evaluations per step." ? reports excellent energy conservation lor the algorithm in Section 3.1 when simulating (he one-dimensional Ixepler problem (where phase-space-volume conservation implies sviupleclicily). but we find that the algorithm in Section 3.2. has one to two orders of magnitude better enerev conservation for equivalent numbers of force evaluations in the N-body problem [or AN>2 (see Figure 1)).," \citet{Omelyan2006} reports excellent energy conservation for the algorithm in Section \ref{OmelyanIteration} when simulating the one-dimensional Kepler problem (where phase-space-volume conservation implies symplecticity), but we find that the algorithm in Section \ref{OurIteration} has one to two orders of magnitude better energy conservation for equivalent numbers of force evaluations in the $N$ -body problem for $N > 2$ (see Figure \ref{OmelyanVsUs}) )." This is probably due to the superior svinplecticitv of the algorithm in section 3.2. for multidimensional configuration spaces., This is probably due to the superior symplecticity of the algorithm in Section \ref{OurIteration} for multidimensional configuration spaces. We do not discuss the generalization of the algoritm in Section 3.1.J) to individual and adaptive timesteps. but instead focus on the algorithm in Section 3.2. for the remainder of the paper.," We do not discuss the generalization of the algorithm in Section \ref{OmelyanIteration} to individual and adaptive timesteps, but instead focus on the algorithm in Section \ref{OurIteration} for the remainder of the paper." objects are known to be highly variable al nearly all wavelengths and their spectral energy distributions (SEDs) are thought to be dominated by radiation from relativistic particles in the jets that propagate roughly along the line of sight (Urry Paclovani 1995).,objects are known to be highly variable at nearly all wavelengths and their spectral energy distributions (SEDs) are thought to be dominated by radiation from relativistic particles in the jets that propagate roughly along the line of sight (Urry Padovani 1995). Mrk 421 is also one of the lew BL Lae objects that were discovered to emit strongly at TeV energies in the past decade (Punch et al., Mrk 421 is also one of the few BL Lac objects that were discovered to emit strongly at TeV energies in the past decade (Punch et al. 1992)., 1992). In fact. the total energv output of Alrk 421 in eanmma-ravs sees comparable (ο Chat in X-rays (Buckley et al.," In fact, the total energy output of Mrk 421 in gamma-rays seems comparable to that in X-rays (Buckley et al." 1996: Maraschi οἱ al., 1996; Maraschi et al. 1999: lNrawezvnski et al., 1999; Krawczynski et al. 2001)., 2001). The SED of the source is dominated by the N-ray. ancl gamama-raxy Mnission., The SED of the source is dominated by the X-ray and gamma-ray emission. While (he origi of gamma-ray photons is still being debated. it is generally agreed i X-rav photons originate mostly in the svuchrotron radiation from highlv relativistic Meclrons in (he jets.," While the origin of gamma-ray photons is still being debated, it is generally agreed that X-ray photons originate mostly in the synchrotron radiation from highly relativistic electrons in the jets." BL Lac objects are known for their flaring activities., BL Lac objects are known for their flaring activities. X-ray flares with duration of longer ian à day have been seen from Mrk 421 (Tanihata et al., X-ray flares with duration of longer than a day have been seen from Mrk 421 (Tanihata et al. 2001: Fossati et al., 2001; Fossati et al. 2000: Brinkmann et al., 2000; Brinkmann et al. 2003)., 2003). Remarkably. a strong flare was detected [rom the source al TeV energies that lasted only for about an hour (Gaidos et al.," Remarkably, a strong flare was detected from the source at TeV energies that lasted only for about an hour (Gaidos et al." 1996)., 1996). The TeV flare showed significant that that were of even shorter duirations., The TeV flare showed significant sub-structures that that were of even shorter durations. The origin of X-ray or TeV flares is hardly understood., The origin of X-ray or TeV flares is hardly understood. The flares are often thought to be related to internal shocks in the jets of a blazar (Rees 1973: Spada et al., The flares are often thought to be related to internal shocks in the jets of a blazar (Rees 1978; Spada et al. 2001). or to major ejection events of new components of relativistic plasma into (he jet (e.g.. Dótttcher et al.," 2001), or to major ejection events of new components of relativistic plasma into the jet (e.g., Bötttcher et al." 1997: Mastichiadis irk 1997)., 1997; Mastichiadis Kirk 1997). Despite such uncertainty. the measured short [Laring (ümescale alone has already. severely constrained the size of the TeV emission region and the Doppler of the jets (Gaicdos et al.," Despite such uncertainty, the measured short flaring timescale alone has already severely constrained the size of the TeV emission region and the Doppler of the jets (Gaidos et al." 1996). as well as the accretion process in the svstem (Celotii et al.," 1996), as well as the accretion process in the system (Celotti et al." 1998)., 1998). If X-ray and TeV photons are associated with the same population of emitting electrons. as often postulated based on the observed correlated behaviors of the source in the two energy bands (e.g.. Maraschi et al.," If X-ray and TeV photons are associated with the same population of emitting electrons, as often postulated based on the observed correlated behaviors of the source in the two energy bands (e.g., Maraschi et al." 1999). X-rav flares of similarly short duration should also occur.," 1999), X-ray flares of similarly short duration should also occur." In this context. we conducted a svstematic search for such flares. making use of the rich database on Mrk 421 provided by theErplorer (IRNTE).," In this context, we conducted a systematic search for such flares, making use of the rich database on Mrk 421 provided by the (RXTE)." Mik 421 is one of the X-ray sources (that have been Irequently observed with RATE over (he past 8+ vears., Mrk 421 is one of the X-ray sources that have been frequently observed with RXTE over the past 8+ years. It is certainly the most observed blazar., It is certainly the most observed blazar. The RATE observations ollen represent X-ray coverage of Mrk 421 in a multi-wavelength campaign., The RXTE observations often represent X-ray coverage of Mrk 421 in a multi-wavelength campaign. Archival data is now available from campaigns conducted in 1996 (under the Guest-Observing progranis, Archival data is now available from campaigns conducted in 1996 (under the Guest-Observing programs during typical pulsar survey iutegration times is 230.,during typical pulsar survey integration times is $\lapp 30$. Tf he pulsar uudergoes significant periods iu the null state. as nüght be expected (ποιος 1976). it will be harder o detect in aiΕΕT-based search = (Nice 1999).," If the pulsar undergoes significant periods in the null state, as might be expected \nocite{rit76} (Ritchings 1976), it will be harder to detect in anFFT-based search \nocite{nic99} (Nice 1999)." One wav to tackle this problem is to eiiploy. longer integration times. such as we do here.," One way to tackle this problem is to employ longer integration times, such as we do here." " The EFT-base )oriodicitv search we use is. however. not an icdea ueaus to find loug period signals since the scusitivity is degraded by a stroug ""red j0jsO Component in the auplitude spectrum."," The FFT-based periodicity search we use is, however, not an ideal means to find long period signals since the sensitivity is degraded by a strong “red noise” component in the amplitude spectrum." The noise itselfis a result of DC-Ieve Huctuations (e.g. in the receiver) duriug au observation., The noise itself is a result of DC-level fluctuations (e.g. in the receiver) during an observation. Iu the above analysis of the survey data. we mininisec he effects of this red noise coniponeut by subtracting a vascline off the spectrum before normalising it.," In the above analysis of the survey data, we minimised the effects of this red noise component by subtracting a baseline off the spectrum before normalising it." However. vecatise of the rapid increase of the red noise below about O.1-Ilz. we chose to ignore all spectral signals with requeucies below his value.," However, because of the rapid increase of the red noise below about 0.1-Hz, we chose to ignore all spectral signals with frequencies below this value." Whilst this is common oxactiee in pulsar search codes. it obviously reduces our sensitivity to P>10 s pulsus!," Whilst this is common practice in pulsar search codes, it obviously reduces our sensitivity to $P>10$ s pulsars!" " Iu recognition of this selection effect. we are cinrently re-analvsing our data using a so-called ""fast folding” algovitlin — (e.g. Staclin 1969) to search for periodic signals in the period range 320 s. The results of this analysis. and a detailed discussion of the aleorithiu. will be presented clsewhere (NDülller et al."," In recognition of this selection effect, we are currently re-analysing our data using a so-called “fast folding” algorithm \nocite{sta69} (e.g. Staelin 1969) to search for periodic signals in the period range 3--20 s. The results of this analysis, and a detailed discussion of the algorithm, will be presented elsewhere (Mülller et al." in preparation)., in preparation). A total of seven pulsars were detected during the COULSC of the survey. four of which were previously παπονα.," A total of seven pulsars were detected during the course of the survey, four of which were previously unknown." Follow-up observations carrie« out to confirm he existence of cach of the new pulsars were used to check hat the true period had been correctly identified by the search code., Follow-up observations carried out to confirm the existence of each of the new pulsars were used to check that the true period had been correctly identified by the search code. The basic properties aud detection statistics ofall seven pulsars are stunmmarised in Table 1.., The basic properties and detection statistics ofall seven pulsars are summarised in Table \ref{tab:allpsrs}. Flix values x the previously known pulsars are taken frou Lorimer et al. (," Flux values for the previously known pulsars are taken from \nocite{lylg95} Lorimer et al. (" 1995).,1995). Flux values for the newly discovered pulsars are averages of a παο of independeut lueasurenieuts sed on the timine measurements described in Sec., Flux values for the newly discovered pulsars are averages of a number of independent measurements based on the timing measurements described in Sec. 5 and lave fractional uncertainties of about in each case., \ref{sec:fup} and have fractional uncertainties of about in each case. The relative positions of allthese pulsars are shown on our scusitivity curve in Fig. 2.., The relative positions of allthese pulsars are shown on our sensitivity curve in Fig. \ref{fig:smin}. The astute reader will. bv now. have noticed a striking sinularity between the periods of PSRs and and. to a lesser extent. PSRs and0315.," The astute reader will, by now, have noticed a striking similarity between the periods of PSRs and and, to a lesser extent, PSRs and." . This unexpected result initially eave us sole cause for concern as to whether the signals we had detected were indeed pulsars!, This unexpected result initially gave us some cause for concern as to whether the signals we had detected were indeed pulsars! However. having thoroughly investigated each new pulsar. we are now confident that this is uothine more than a bizarre coincidence.," However, having thoroughly investigated each new pulsar, we are now confident that this is nothing more than a bizarre coincidence." Α muuber of independent facts coufirm this., A number of independent facts confirm this. Firstly. all the new pulsars are separated by a significant muuber of telescope poiutings on the sky.," Firstly, all the new pulsars are separated by a significant number of telescope pointings on the sky." Secondly: the periods are detectedonly at the nominal position of cach pulsar. aud therefore cannot be put down to terrestrial interference.," Secondly, the periods are detected at the nominal position of each pulsar, and therefore cannot be put down to terrestrial interference." Furtheruore. al the dispersion measures are significantly ciffereut.," Furthermore, all the dispersion measures are significantly different." Finally. our timing measurcients show that cach pulsar has a distiuct se of spin-down parameters.," Finally, our timing measurements show that each pulsar has a distinct set of spin-down parameters." We note in passing that this survey places ai upper luit to the pulsed radio enidss3on from the 6.97-s anomalous X-ray pulsar 0300 discovered by Toni ot al. (, We note in passing that this survey places an upper limit to the pulsed radio emission from the 6.97-s anomalous X-ray pulsar $-$ 0300 discovered by Torii et al. ( 19098) that lies iu he search region.,1998) that lies in the search region. No radio pulsations were seen at the exid position closest to this pulsar. setting a 1100-MITz. pulsed fux. Lani of ~0.3(6/LF indy. where à is the pulse city evele in percent.," No radio pulsations were seen at the grid position closest to this pulsar, setting a 1400-MHz pulsed flux limit of $\sim 0.3 (\delta/4)^{1/2}$ mJy, where $\delta$ is the pulse duty cycle in percent." This limit assumes (possibly incorrectly) that the effects of interstellar scattering are negligible alone this Lue of sight at this observing frequency., This limit assumes (possibly incorrectly) that the effects of interstellar scattering are negligible along this line of sight at this observing frequency. Deeper radio searches or this object. aud also for the 11.5-« pulsar in Ies τὸ (Vasishit Cotthelh 1997). should be carried out in future at different observing frequencies.," Deeper radio searches for this object, and also for the 11.8-s pulsar in Kes 73 (Vasisht Gotthelf 1997), \nocite{vg97} should be carried out in future at different observing frequencies." Iu order to obtain more detailed spin and astrometric parameters of the newle-discovered pulsars. followine confirmation. each was imeluded mo our monthly A 21-cni tiniue observations of millisecond pulsars using the Effelsbere-Berkeley-Pulsar-Processor.," In order to obtain more detailed spin and astrometric parameters of the newly-discovered pulsars, following confirmation, each was included in our monthly $\lambda$ 21-cm timing observations of millisecond pulsars using the Effelsberg-Berkeley-Pulsar-Processor." Full details of the scrving procedures are described by ται ct . (, Full details of the observing procedures are described by \nocite{kll+99} Kramer et al. ( 1999).,1999). Iu brief. during cach observing session. a pulse time-of-arrival (TOA) measurement is obtained for each pulsar by cross-correlating the observed pulse profile with a high signal-to-noise “template” profile constructed fron the addition of many observations.," In brief, during each observing session, a pulse time-of-arrival (TOA) measurement is obtained for each pulsar by cross-correlating the observed pulse profile with a high signal-to-noise “template” profile constructed from the addition of many observations." The template profiles obtained in this wav are presented iu Fig. L., The template profiles obtained in this way are presented in Fig. \ref{fig:profs}. For each pulsar. the TOAs obtained from all. the sessjons were referred to the equivaleut time at the solar system barveentre and fitted iu a bootstrap fashion to a sinple spin-down model using the software agel.," For each pulsar, the TOAs obtained from all the sessions were referred to the equivalent time at the solar system barycentre and fitted in a bootstrap fashion to a simple spin-down model using the software ." . In Fig. 5.. ," In Fig. \ref{fig:residuals}, ," we preseut the resulting 1iodelobserved TOA residuals from this analysis., we present the resulting model-observed TOA residuals from this analysis. citepGSH93.. have shown that the 3.294 HEF emission is strongest between the rregion ionization front (traced by H recombination lines) and the ddissociation front (traced by fluorescent eemission lines).,"\\citep{GSH93}, have shown that the 3.29 IEF emission is strongest between the region ionization front (traced by H recombination lines) and the dissociation front (traced by fluorescent emission lines)." Here we present a new high-resolution (0799) narrowband 3.294 image of the bright reflection nebula7023.. and compare the spatial distribution of the 3.29 HEF emission to those of other prominent NIR emission components such as the NIR continuum emission near 2 aand the 1-0 SCI) eemission line at 2.12 citep[thispaper:]| |LFEG90..70," Here we present a new high-resolution 9) narrowband 3.29 image of the bright reflection nebula, and compare the spatial distribution of the 3.29 IEF emission to those of other prominent NIR emission components such as the NIR continuum emission near 2 and the 1–0 S(1) emission line at 2.12 \\citep[this paper;][]{LFG96}. ," 23.. at a distance of 430719?pe (vandenAnckeretal.1997).. is one of the best-studied reflection nebulae and is also one of the first objects in which the NIR continuum emission accompanying the 3.29 HEF emission was detected (Sellgrenetal.1983).," at a distance of $430^{+160}_{-90}\ \mbox{pc}$ \citep{hipparcos}, is one of the best-studied reflection nebulae and is also one of the first objects in which the NIR continuum emission accompanying the 3.29 IEF emission was detected \citep{SWD83}." . It is a part of à much larger molecular cloud. illuminated by the pre-main sequence Herbig Be star200775.. with an effective temperature == 17.000 K (Strometal.1972:Baschek1982).," It is a part of a much larger molecular cloud, illuminated by the pre-main sequence Herbig Be star, with an effective temperature = 17,000 K \citep*{SSY72,BBK82}." . The A’ (broadband 2.1 jim)» image of 1:: see also][]SWD92. which contains a mixture of 2 ccontinuum emission. 2 sscattered starlight. and lline emission. is dominated by extended nebulosity northwest of200775.. and by two filamentary structures. northwest and south/southwest of the star.," The $K'$ (broadband 2.1 ) image of \\citep[Fig.~\ref{f1}; see , which contains a mixture of 2 continuum emission, 2 scattered starlight, and line emission, is dominated by extended nebulosity northwest of, and by two filamentary structures, northwest and south/southwest of the star." Various previous imaging studies show that these two groups of filaments are also seen in the extended red emission (Witt&Schild1988:Watkin.Gledhill.Scarrott1991).. fluorescent eemission lines (Lemaireetal.1996;Takami2000).. IEFs at 6.2 παπά 11.3 citepCLA96.. and eemission (Fuenteetal.1996).," Various previous imaging studies show that these two groups of filaments are also seen in the extended red emission \citep*{WS88,WGS91}, fluorescent emission lines \citep*{LFG96,TUS00}, IEFs at 6.2 and 11.3 \\citep{CLA96}, and emission \citep*{FMN96}." . These filaments are believed to be the interface between the molecular cloud. traced by CO enission (Gerinetal.1998).. and photodissociatedH».. traced by the 21 em line. surrounding the star (Fuenteetal. 1996)..," These filaments are believed to be the interface between the molecular cloud, traced by CO emission \citep{GPK98}, and photodissociated, traced by the 21 cm line, surrounding the star \citep{FMN96}. ." The filaments may represent high density (as high as #7~10° em?) clumps embedded in somewhat lower density gas (7~10 cem) at the unterface (Fuenteetal.1996;Lemaire1996:Martini.Sellgren.," The filaments may represent high density (as high as $n\sim 10^6\ \mbox{cm$ $}$ ) clumps embedded in somewhat lower density gas $n\sim 10^4\ \mbox{cm$ $}$ ) at the interface \citep*{FMN96,LFG96,MSH97,MSD99,TUS00}." etal. 20000. Table | summarizes the observations for the data presented in this paper., Table \ref{obs_log} summarizes the observations for the data presented in this paper. We obtained an image of aat 3.29 wwith the 3 m NASA Infrared Telescope Facility (RTF) at Mauna Kea. Hawai. during an IRTF service observing run.," We obtained an image of at 3.29 with the 3 m NASA Infrared Telescope Facility (IRTF) at Mauna Kea, Hawaii, during an IRTF service observing run." The total integration time on source is 12 minutes., The total integration time on source is 12 minutes. The central position of the field is W N of the illuminating star200775.. and was selected so as to include all the northwest filaments and the central star.," The central position of the field is W N of the illuminating star, and was selected so as to include all the northwest filaments and the central star." The data were reduced in the usual way: sky subtraction and flat field correction., The data were reduced in the usual way: sky subtraction and flat field correction. The sky was observed in an ABBA pattern. chopping between the target field and a field N every 20 seconds.," The sky was observed in an ABBA pattern, chopping between the target field and a field N every 20 seconds." Sky images were used for flat fields as well., Sky images were used for flat fields as well. The final image was formed by combining 40 individual frames using a median filter to Increase the signal-to-noise ratio (S/N). and an average c-clipping algorithm was used during the combination to reject bad pixels.," The final image was formed by combining 40 individual frames using a median filter to increase the signal-to-noise ratio (S/N), and an average $\sigma$-clipping algorithm was used during the combination to reject bad pixels." The final image shows a strong ghost image (instrumental, The final image shows a strong ghost image (instrumental "7,, middle panel).","\ref{ecspecfit_fig}, middle panel)." " Taken at face value, the white dwarf mass is lower than the average mass of single white dwarfs, suggestive of a He-core as a result of the common envelope evolution."," Taken at face value, the white dwarf mass is lower than the average mass of single white dwarfs, suggestive of a He-core as a result of the common envelope evolution." " Only a handful of bona-fide He-core white dwarfs in pre-CVs are known, and a more detailed study appears warranted to confirm this hypothesis for 113349—3237."," Only a handful of bona-fide He-core white dwarfs in pre-CVs are known, and a more detailed study appears warranted to confirm this hypothesis for 13349–3237." " The spectral type of the companion, MM1+0.5."," The spectral type of the companion, $\pm0.5$." " Hence, 1133493237 is a new addition to the still very small number of pre-CVs with early-type companion stars that will start mass transfer above the period gap (Schreiber&Gánsicke 2003).."," Hence, 13349–3237 is a new addition to the still very small number of pre-CVs with early-type companion stars that will start mass transfer above the period gap \citep{schreiber+gaensicke03-1}." The distances determined for the two components are in good agreement., The distances determined for the two components are in good agreement. " This is the brightest of the three pre-CVs of our study, and this made it possible to also use the photometric data from the 2005 runs which suffered from bad weather conditions."," This is the brightest of the three pre-CVs of our study, and this made it possible to also use the photometric data from the 2005 runs which suffered from bad weather conditions." " Unfortunately, the time span between both sets (from 2003 and 2005) is too long for a combined period search."," Unfortunately, the time span between both sets (from 2003 and 2005) is too long for a combined period search." " The periodogram of the 2005 data yields asthe most probable period P,=0.3500(08)d, that agrees well with the result Psy=0.3498(35)d from the radial velocities of the Ha emission line from the 2007 time-resolved spectroscopy refecl4pg yig))."," The periodogram of the 2005 data yields asthe most probable period $P_1 = 0.3500(08)~\mathrm{d}$, that agrees well with the result $P_\mathrm{sp} = 0.3498(35)~\mathrm{d}$ from the radial velocities of the $\alpha$ emission line from the 2007 time-resolved spectroscopy \\ref{ec14pg_fig}) )." "T hephase—folded photometricandspectroscopicdataare, gigandl4, ,respectively."," The phase-folded photometric and spectroscopic data are given in \\ref{ec14phlc_fig} and \ref{ec14phrv_fig}, respectively." "T hesecondhighestpeak f orthe photo d, yields a visually equally good light curve, and further observations will be necessary to definitely break this alias degeneracy."," The second highest peak for the photometric data, $P_2 = 0.3457(08)~\mathrm{d}$ , yields a visually equally good light curve, and further observations will be necessary to definitely break this alias degeneracy." " However, since P, agrees slightly better with the spectroscopic period, we adopt Pow=0.3500(08)d8.40(02)h as the orbital period of 114329-1625."," However, since $P_1$ agrees slightly better with the spectroscopic period, we adopt $P_\mathrm{orb} = 0.3500(08)~\mathrm{d} = 8.40(02)~\mathrm{h}$ as the orbital period of 14329–1625." " A sine fit to the radial velocity data yield the parameters listed in Table 4,, and the corresponding ephemeris is with respect to the inferior conjunction of the emission source."," A sine fit to the radial velocity data yield the parameters listed in Table \ref{rvpar_tab}, and the corresponding ephemeris is with respect to the inferior conjunction of the emission source." " As for the other two targets, the average spectra show a flux difference between the two nights refavspig, , bottom)."," As for the other two targets, the average spectra show a flux difference between the two nights \\ref{avsp_fig}, , bottom)." "FoldingthedatawithBe f iltercurvesyieldssimila 14.79,BV= 0.33forApril3,andV ssell=15.13,BV forAprilS."," Folding the data with Bessell filter curves yields similar differences as for the other systems, with values $V = 14.79$ , $B\!-\!V = 0.33$ for April 3, and $V = 15.13$, $B\!-\!V = 0.38$ for April 5." "Kilkennyetal. (1997)reportV=14.89,BV 0.25, andagaintheA pril3dataagree slightlybetterwiththeirmeasurements."," \citet{kilkennyetal97-1} report $V = 14.89$, $B\!-\!V = 0.25$ , and again the April 3 data agree slightly better with their measurements." " For 114329-1625, the spectroscopic decomposition (see refec12477,ect))resultsinTwq=14600+1300 KK and Μι=0.62+0.14 refspecfit,ab& 7,, middle panel), and similar to 112477-1738, EC114329-1625 has a mass close to the average mass of single white dwarfs."," For 14329–1625, the spectroscopic decomposition (see \\ref{ec12477_sect}) ) results in $T_\mathrm{wd}=14600\pm1300$ K and $M_\mathrm{wd}=0.62\pm0.14$ \\ref{specfit_tab} \ref{ecspecfit_fig}, middle panel), and similar to 12477–1738, 14329–1625 has a mass close to the average mass of single white dwarfs." " Another similarity to 112477-1738 is that we find dec> dwa, which may suggest that the companion star has a radius slightly too large for its spectral type."," Another similarity to 12477–1738 is that we find $d_\mathrm{sec}>d_\mathrm{wd}$ , which may suggest that the companion star has a radius slightly too large for its spectral type." " As already mentioned in refec12477;ect, , thismightberelatedtostellaractivityonthecompanionstar —1"," As already mentioned in \\ref{ec12477_sect}, this might be related to stellar activity on the companion star \citep{rebassa-mansergasetal07-1}. ." 738andEC 114329— —1625exhibitverystrong Balmeremissionlines.," In fact, both 12477--1738 and 14329–1625 exhibit very strong Balmer emission lines." Giv," Given their longorbital periods and modestwhite dwarf temperatures, the strength of the Balmer lines is indicative of chromospheric activity, rather than irradiation/heating of the companion star." scalterings per final photon energy interval for an electron of Lorentz lactor> is: where op is the Thomson cross section.,scatterings per final photon energy interval for an electron of Lorentz factor$\gamma$ is: where $\sigma_T$ is the Thomson cross section. Jones(1963) introduced the approximation i which (he seed photons are treated as coming from the direction opposite to the electron velocity., \citet{jones68} introduced the approximation in which the seed photons are treated as coming from the direction opposite to the electron velocity. " Using this. which is valid for for +>>1. and the full INN cross-section for inelastic Compton scattering. he showed that The maximum observed energy is In the case of Thomson scattering (5e,< 1). Rvbicki&Lightman(1979).. assuming isolropic scattering in the electron frame. showed that and that the maximum. observed final. energy is. €,=4e555Da»D""."," Using this, which is valid for for $\gamma \gg 1$, and the full KN cross-section for inelastic Compton scattering, he showed that The maximum observed energy is In the case of Thomson scattering $\gamma\epsilon_0 \ll 1$ ), \citet{rl79}, assuming isotropic scattering in the electron frame, showed that and that the maximum observed final energy is $\epsilon_{max,T}=4\epsilon_0\gamma_2^2{\cal D}^2$." We now make (he approximation (hat the outgoing photons are directed. along the direction of the scattering electrons. which is justified provided the electron angular distribution varies slowly over angular scales S1/5.," We now make the approximation that the outgoing photons are directed along the direction of the scattering electrons, which is justified provided the electron angular distribution varies slowly over angular scales $\lesssim 1/\gamma$." " To obtain the specilic luminosity one integrates the scaltering rate (4)) over the electron energy. distribution (3)). and multiplies the result. bythe observed photon energy em,c3 and by the photon number density ny=Ufeym,c In the Thomson case. for energies yin€ ej,0. Where eninge=ει] the lower limit of the integration in equation (8)) is 5,,5,= (e/4e,)!?. and the upper limit is 5,,,,= 55D."," To obtain the specific luminosity one integrates the scattering rate \ref{eq:sc_rate}) ) over the electron energy distribution \ref{eq:ele}) ), and multiplies the result bythe observed photon energy $\epsilon m_e c^2$ and by the photon number density $n_p=U/\epsilon_0 m_e c^2$ In the Thomson case, for energies $\epsilon_{min,T}\leq\epsilon\leq\epsilon_{max,T}$ , where $\epsilon_{min,T}=4\epsilon_0\gamma_1^2{\cal D}^2$, the lower limit of the integration in equation \ref{eq:sc_int}) ) is $\gamma_{min}=(\epsilon/4\epsilon_0)^{1/2}$ , and the upper limit is $\gamma_{max}=\gamma_2{\cal D}$ ." Performing the elementaryintegral using equation (7)) we obtain:, Performing the elementaryintegral using equation \ref{eq:thomson}) ) we obtain: with those lound observationally by 2..,with those found observationally by \cite{bernstein03}. Since the power-law slope derived in the steadsy- approximation depends heavily on the particular criterion for catastrophic destruction adopted for the bodies. observations of the NBO size spectrum provide a direct constraint on the bodies internal structure.," Since the power-law slope derived in the steady-state approximation depends heavily on the particular criterion for catastrophic destruction adopted for the bodies, observations of the KBO size spectrum provide a direct constraint on the bodies' internal structure." The close agreement between this slope and break radius aud the best-lit values found by ?/— suggests Chat large INDOs are virtually strengthless bodies held together mainly by gravitv., The close agreement between this slope and break radius and the best-fit values found by \cite{bernstein03} suggests that large KBOs are virtually strengthless bodies held together mainly by gravity. Further survevs of small INRBOs between ~10 and ~70 km in size would better constrain both the exact position of the actual break in the size spectrum and the power-law slope below the break., Further surveys of small KBOs between $\sim$ 10 and $\sim$ 70 km in size would better constrain both the exact position of the actual break in the size spectrum and the power-law slope below the break. Data of this kind would thus confirm or refute our analvsis., Data of this kind would thus confirm or refute our analysis. Such survevs would also allow more detailed comparison of the break locations in the classical and scattered IKRBO populations. which should reflect differences in the surface," Such surveys would also allow more detailed comparison of the break locations in the classical and scattered KBO populations, which should reflect differences in the surface" Galaxy redshift surveys ancl computer. simulations of cosmic structure formation have shown that matter traces out a frothy pattern. the Cosmic Web.,"Galaxy redshift surveys and computer simulations of cosmic structure formation have shown that matter traces out a frothy pattern, the Cosmic Web." Bondefαἱ(1996) established how the tical forces induced by the inhomogencous cosmic matter distribution. are the main agent shaping the Cosmic Web., \cite{bondweb1996} established how the tidal forces induced by the inhomogeneous cosmic matter distribution are the main agent shaping the Cosmic Web. The resulting cosmic tidal force Ποια is the source of the large scale. coherent. anisotropic forces which shape the cosmic matter distribution into characteristic Llamentary ancl sheetlike patterns.," The resulting cosmic tidal force field is the source of the large scale, coherent, anisotropic forces which shape the cosmic matter distribution into characteristic filamentary and sheetlike patterns." Voids are a ominant component of the Cosmic Web (scee.g.“Tullyetal.2007:Romano-Diaz&vandeWev-gacrt 2007).. occupying most of the volume of space.," Voids are a dominant component of the Cosmic Web \citep[see e.g.][]{tully2007, weyrom2007}, occupying most of the volume of space." In this paper we present evidence for significant alignments between neigbouring voids and establish the intimate dynamic link between voids and the cosmic tical force Ποια., In this paper we present evidence for significant alignments between neigbouring voids and establish the intimate dynamic link between voids and the cosmic tidal force field. The Watershed: Void. Finder (VE) procedure (Platen.vancleWevgaert&Jones2007). that we use to identify voids is crucial to the sueces of this analysis., The Watershed Void Finder (WVF) procedure \citep{platen2007} that we use to identify voids is crucial to the succes of this analysis. Phe WVE technique is based on the topological characteristics of the spatial density Ποιά and thereby. provides objectively defined measures for the size. shape and orientation of void. patches.," The WVF technique is based on the topological characteristics of the spatial density field and thereby provides objectively defined measures for the size, shape and orientation of void patches." Large voids form around deep density troughs in the primordial density field., Large voids form around deep density troughs in the primordial density field. The main aspects of the evolution of a large void may be understood on the basis of the expansion. of simple spherical ancl isolated: under-densities (c.g. Bertschinger (1985)))., The main aspects of the evolution of a large void may be understood on the basis of the expansion of simple spherical and isolated under-densities (e.g. \cite{edbert1985}) ). Under-dense regions expand with respect to the background. Universe ancl in general will have the tendency to grow more spherical with time (Icke1984)., Under-dense regions expand with respect to the background Universe and in general will have the tendency to grow more spherical with time \citep{icke1984}. . However. Shandarin.οἱaf(2006). and Park&Lee(2007a) have emphasized that. in realistic cosmological circumstances. voids will be nonspherical.," However, \cite{shandarin2006} and \cite{parklee2007a} have emphasized that, in realistic cosmological circumstances, voids will be nonspherical." This is quite apparent in images of. for example. the Millennium simulation (Springeletal.2005).," This is quite apparent in images of, for example, the Millennium simulation \citep{springmillen2005}." .. Moreover. substructures within voids clisplay à manifest alignment along a preferred direction.," Moreover, substructures within voids display a manifest alignment along a preferred direction." This is. in part. à consequence of the relatively strong influence of the surrounding Inhomogeneous matter distribution on the void's structure and evolution.," This is, in part, a consequence of the relatively strong influence of the surrounding inhomogeneous matter distribution on the void's structure and evolution." Voids evolve. hierarchically: as they expand with respect to the background. Universe they merge with their surrounding peers. building voids of ever larger sizes (ReedsCGottloberefaf2003:Colbereetal. 2005).," Voids evolve hierarchically: as they expand with respect to the background Universe they merge with their surrounding peers, building voids of ever larger sizes \citep{regoes1991, weykamp1993, gottloeber2003, colberg2005}." . Small voicls can survive as substructure within the Larger voids or may disappear under the gravitational impact of surrounding overclense structures (Ssahinietal.1994:Sheth&vandeWev-gacrt 2004).," Small voids can survive as substructure within the larger voids or may disappear under the gravitational impact of surrounding overdense structures \citep{sahni1994, shethwey2004}." . The result is a void population whose scale is distributed around a characteristic void size: we shall show this using our WWE sample., The result is a void population whose scale is distributed around a characteristic void size: we shall show this using our WVF sample. A major manifestation of large scale tidal inlluences is that of the alignment of shape and angular momentum of objects (seeBond.efa£.1996:Desjacques2007).," A major manifestation of large scale tidal influences is that of the alignment of shape and angular momentum of objects \citep[see][]{bondweb1996, desjacques2007}." .. The alignment of the orientations of galaxy haloes. galaxy spins and clusters with larger scale structures such as clusters. filaments and. superclusters have been the subject," The alignment of the orientations of galaxy haloes, galaxy spins and clusters with larger scale structures such as clusters, filaments and superclusters have been the subject" evidence is found for the existence of KDCs in dwarf elliptical galaxies.,evidence is found for the existence of KDCs in dwarf elliptical galaxies. Massive elliptical galaxies with KDCs both in corotation and in counterrotation with the host galaxy (e.g. Efstathiouetaf. (1982).. Cappellanietaf. (2002))) and ellipticals with peculiar central kinematics (Franxefal. (1991))) have been known for a long time.," Massive elliptical galaxies with KDCs both in corotation and in counterrotation with the host galaxy (e.g. \cite{ef}, , \cite{ca02}) ) and ellipticals with peculiar central kinematics \cite{fiz}) ) have been known for a long time." " Bender&Surma(1992) found KDCs in ellipticals to be more metalrich than the galaxies"" main bodies.", \cite{bs} found KDCs in ellipticals to be more metalrich than the galaxies' main bodies. A merger of a giant and a dwarf galaxy was a plausible way of producing KDCs with the observed properties (Balcells&Quinn (1990)))., A merger of a giant and a dwarf galaxy was a plausible way of producing KDCs with the observed properties \cite{bq}) ). The KDC's angular momentum vector is set predominantly by the engulfed dwarf's angular momentum and need not be aligned with that of the giant galaxy., The KDC's angular momentum vector is set predominantly by the engulfed dwarf's angular momentum and need not be aligned with that of the giant galaxy. KDCs in SOs can equally well be explained by the merger of two unequal-mass spiral galaxies (Baleells&González (1998))., KDCs in S0s can equally well be explained by the merger of two unequal-mass spiral galaxies \cite{bg}) ). " KDCs thus provide strong evidence that mergers of (gasrich) progenitor galaxies played an important role in the past evolution of bright elliptical and lenticular galaxies. corroborating the hierarchical merging model for cosmological structure formation,"," KDCs thus provide strong evidence that mergers of (gasrich) progenitor galaxies played an important role in the past evolution of bright elliptical and lenticular galaxies, corroborating the hierarchical merging model for cosmological structure formation." In section 2.. we discuss the details of the observations and the data-reduction process.," In section \ref{obs}, we discuss the details of the observations and the data-reduction process." The stellar kinematics. photometry. and measurements of the strength of the near-infrared triplet (quantified by the CaT index) of these objects are presented in section 3.. followed by a study of their internal dynamics in section 4..," The stellar kinematics, photometry, and measurements of the strength of the near-infrared triplet (quantified by the CaT index) of these objects are presented in section \ref{kin}, followed by a study of their internal dynamics in section \ref{dyn}." The significance of these results in the light of the existing theories for dE evolution is discussed in section 5.., The significance of these results in the light of the existing theories for dE evolution is discussed in section \ref{dis}. We summarize our conclusions in section 6.., We summarize our conclusions in section \ref{con}. Within the framework of an ESO Large Program. we collected Bessel VRI-band images and deep major and minor axis spectra with unprecedented spatial and spectral resolution of a sample of 15 dEs and dwarf lenticulars (450). both in group (NGC5044. NGC5898. and NGC3258 groups) and. cluster environments (Fornax cluster).," Within the framework of an ESO Large Program, we collected Bessel VRI-band images and deep major and minor axis spectra with unprecedented spatial and spectral resolution of a sample of 15 dEs and dwarf lenticulars (dS0), both in group (NGC5044, NGC5898, and NGC3258 groups) and cluster environments (Fornax cluster)." The data were taken with the FORS2 imaging spectrograph mounted on the ΝΕΤ., The data were taken with the FORS2 imaging spectrograph mounted on the VLT. The images were bias-subtracted and flattielded using skyflats taken during twilight of the same night as the science frames., The images were bias-subtracted and flatfielded using skyflats taken during twilight of the same night as the science frames. The sky background was removed by fitting a tilted plane to regions of the images free of stars or other objects and subtracting it., The sky background was removed by fitting a tilted plane to regions of the images free of stars or other objects and subtracting it. The photometric zeropoints in each band were measured using photometric standard stars observed during the same night as the science frames., The photometric zeropoints in each band were measured using photometric standard stars observed during the same night as the science frames. The images were corrected for airmass and interstellar extinction. using the Galactic extinction estimates from Schlegeletaf.(1998).," The images were corrected for airmass and interstellar extinction, using the Galactic extinction estimates from \cite{schlegel98}." " The spectra. with typical exposure times of 5—8 h per position angle and a seeing in the range 0.3""—1.0"" FWHM. cover the wavelength region around the strong triplet absorption. lines. (78600 A)."," The spectra, with typical exposure times of $5-8$ h per position angle and a seeing in the range $0.3''-1.0''$ FWHM, cover the wavelength region around the strong triplet absorption lines $\sim 8600$ )." AIL standard data reduction procedures (bias-subtraction. flatfielding. cosmic removal. wavelength-calibration. sky-subtraction. flux-calibration) were carried out withESO-MIDAS!..ΤΕΑΕ”.. and our own software.," All standard data reduction procedures (bias-subtraction, flatfielding, cosmic removal, wavelength-calibration, sky-subtraction, flux-calibration) were carried out with, and our own software." Fitting the dispersion relation by a cubic spline. the lines of the are spectra are rectified to an accuracy of |—2 km/s FWHM.," Fitting the dispersion relation by a cubic spline, the lines of the arc spectra are rectified to an accuracy of $1-2$ km/s FWHM." We extracted the stellar kinematical information by fitting a weighted mix of late G to late K giant stars. broadened with à parameterised line-of-sight velocity distribution (LOSVD) to the galaxy spectra.," We extracted the stellar kinematical information by fitting a weighted mix of late G to late K giant stars, broadened with a parameterised line-of-sight velocity distribution (LOSVD) to the galaxy spectra." We approximated the LOSVD by a fourth-order Gauss-Hermite series. (Gerhard(1993).vanderMarel&Franx (1993))) (the kinematics of the full sample will be presented in a forthcoming paper).," We approximated the LOSVD by a fourth-order Gauss-Hermite series \cite{gh,vf}) ) (the kinematics of the full sample will be presented in a forthcoming paper)." The strong lines. which contain most of the kinematical information. are rather insensitive to the age and metallicity of an old stellar population (see Michielsenοἱa£.(2003) and references therein). so template mismatch does not significantly affect the results.," The strong lines, which contain most of the kinematical information, are rather insensitive to the age and metallicity of an old stellar population (see \cite{mi03} and references therein), so template mismatch does not significantly affect the results." The spectra contain useful kinematical informatior out to 1.5-2 half-light radi (R.)., The spectra contain useful kinematical information out to 1.5-2 half-light radii $R_{\rm e}$ ). This is the first (me a data set of dE kinematicPA is assembled on a par with what so far has been achieved for bright elliptical galaxies., This is the first time a data set of dE kinematics is assembled on a par with what so far has been achieved for bright elliptical galaxies. Thanks to the excellent quality of the spectra. both in terms of instrumental resolution and of seeing. we are able to spatially resolve small-scale structures in the kinematic profiles.," Thanks to the excellent quality of the spectra, both in terms of instrumental resolution and of seeing, we are able to spatially resolve small-scale structures in the kinematic profiles." Before discussing our observations. we first focus on the environments of FS76 and FS373.," Before discussing our observations, we first focus on the environments of FS76 and FS373." " Using ROSAT observations of the X-ray emitting gas in the NGCS044 group. which is dominated by a single central giant elliptical. NGC504. Davidetaf.(1994) derive a total gravitating mass of M.= within a radius of 250! kpe. corresponding to M/Ly=130hs0 in solar unitsand a galaxy velocity dispersion oy,=330 km/s. The mean systemic velocity"," Using ROSAT observations of the X-ray emitting gas in the NGC5044 group, which is dominated by a single central giant elliptical, NGC5044, \cite{da94} derive a total gravitating mass of $M \approx 1.6 \times 10^{13}h^{-1}_{50} M_\odot$ within a radius of $h^{-1}_{50}$ kpc, corresponding to $M/L_B \approx 130h_{50}$ in solar unitsand a galaxy velocity dispersion $\sigma_{\rm gal}= 330$ km/s. The mean systemic velocity" both high- and low-temperature methane and water transitions.,both high- and low-temperature methane and water transitions. " The models are multiplied by the telluric transmittance model (i.e., attenuated by extinction from the Earth's atmosphere) and filtered using the same high-pass filter used to remove the continuum in the data."," The models are multiplied by the telluric transmittance model (i.e., attenuated by extinction from the Earth's atmosphere) and filtered using the same high-pass filter used to remove the continuum in the data." None of the candidate molecular emission features that could account for the S10 result can be detected in our data., None of the candidate molecular emission features that could account for the S10 result can be detected in our data. " Indeed, in every instance they can be ruled out unequivocally; in most cases the emission would be so bright that the features would be visible in the raw data."," Indeed, in every instance they can be ruled out unequivocally; in most cases the emission would be so bright that the features would be visible in the raw data." " We also performed the same data reduction procedure on three additional NIRSPEC orders, spanning wavelength ranges of 3.41—3.46 um, 3.57—3.63 um, and 3.75—3.81 um; no emission was detected to the same sensitivity limits in any of the orders."," We also performed the same data reduction procedure on three additional NIRSPEC orders, spanning wavelength ranges of $3.41-3.46\,\mu$ m, $3.57-3.63\,\mu$ m, and $3.75-3.81\,\mu$ m; no emission was detected to the same sensitivity limits in any of the orders." " The standard deviation of our observed residuals trace in Figure 4)) is 0.0011 at our observed resolution, (lowerand is even lower when averaged over a line width."," The standard deviation of our observed residuals (lower trace in Figure \ref{data}) ) is 0.0011 at our observed resolution, and is even lower when averaged over a line width." " To see how firmly the various cases are rejected, consider the spectrum of methane excited at 1200K. That spectrum requires a emission feature near jum that would be detected at more than 300 significance in our data, but is not seen."," To see how firmly the various cases are rejected, consider the spectrum of methane excited at 1200K. That spectrum requires a emission feature near $\mu$ m that would be detected at more than $30\sigma$ significance in our data, but is not seen." The other molecular cases illustrated in Figure 4 are rejected at even higher levels of significance., The other molecular cases illustrated in Figure \ref{data} are rejected at even higher levels of significance. " Moreover, as stated above, we have not restricted our search to merely the cases that are illustrated in Figure 4.."," Moreover, as stated above, we have not restricted our search to merely the cases that are illustrated in Figure \ref{data}." In no instance can we find a spectrum that accounts for the 910 results but is also allowed by our data., In no instance can we find a spectrum that accounts for the S10 results but is also allowed by our data. We can only, We can only ~1000 (????) B~230 o* (?)..," $\simeq1000$ \citep{wickramasinghe+ferrario00-1, jordan01-1, gaensickeetal02-5, schmidtetal03-1} $B\simeq230$ $\sigma^+$ \citep{schmidtetal96-1}." ?— B~200 ? B—150 (?).. ?..," \citet{gaensickeetal01-1} $B\simeq200$ \citet{schmidtetal01-1} $B\simeq150$ \citep{jiangetal00-1}. \citet{tovmassianetal01-2}," 2—3 ? their optical spectra as eyclotron harmonics. ?— tentatively suggested a field strength of B=31 MMG for JJ1554.," $2-3$ \citet{thorstensen+fenton02-1} $\Porb=151.865\pm0.009$ their optical spectra as cyclotron harmonics, \citet{tovmassianetal01-2} tentatively suggested a field strength of $B=31$ MG for J1554." Medium-resolution FUV spectroscopy of JJ1554 was obtained with HS7//STIS on February 27. 2003. às part of our ongoing snapshot survey of cataclysmic variables (2)..," Medium-resolution FUV spectroscopy of J1554 was obtained with /STIS on February 27, 2003, as part of our ongoing snapshot survey of cataclysmic variables \citep{gaensickeetal03-1}." " We used the GI40L grating in conjunction with the 52""«0.2” aperture. providing a spectral resolution of —1.2 aand a spectral coverage of 1150—1710AA."," We used the G140L grating in conjunction with the $52\arcsec\times0.2\arcsec$ aperture, providing a spectral resolution of $\simeq1.2$ and a spectral coverage of $1150-1710$." . The STIS spectrum of JJ1554 reff-stis)) contains a blue continuum. superimposed with narrow emission lines of1176.1206.1240. 1335. 1393.1402. 1550. and 1640.," The STIS spectrum of J1554 \\ref{f-stis}) ) contains a blue continuum superimposed with narrow emission lines of, and ." A weak broad emission bump centered on ~1300 mmay be related to the multiplet. the doublet is not detected.," A weak broad emission bump centered on $\sim1300$ may be related to the multiplet, the doublet is not detected." A most unusual feature is the broad (~75 AA)) absorption line centered on ~1280AA., A most unusual feature is the broad $\sim75$ ) absorption line centered on $\sim1280$. . It falls clearly blue-ward of the qquasi-molecular HY absorption observed in cool white dwarfs., It falls clearly blue-ward of the quasi-molecular $H_2^+$ absorption observed in cool white dwarfs. Considering the magnetic nature of JJI554. a tantalising possible identification for this feature is the o* component of ZZeeman-split in. a. field B> IOOMMG. analogous to that observed in the FUV spectrum of UUMa (??)..," Considering the magnetic nature of J1554, a tantalising possible identification for this feature is the $\sigma^+$ component of Zeeman-split in a field $B>100$ MG, analogous to that observed in the FUV spectrum of UMa \citep{schmidtetal96-1, gaensickeetal01-1}." We measured a \S50LPmagnitude of —16.8 (roughly equivalent to the R band) from the STIS CCD acquisition image taken prior to the FUV spectroscopy., We measured a $\times$ 50LPmagnitude of $\simeq16.8$ (roughly equivalent to the $R$ band) from the STIS CCD acquisition image taken prior to the FUV spectroscopy. The system was hence in a state of relatively low accretion activity (22)..," The system was hence in a state of relatively low accretion activity \citep{tovmassianetal01-2, thorstensen+fenton02-1}." We have analysed the STIS spectrum of RXJJI554 using magnetic white dwarf model spectra computed with the code of ? and a fitting routine very similar to the one described by ?.., We have analysed the STIS spectrum of J1554 using magnetic white dwarf model spectra computed with the code of \citet{jordan92-1} and a fitting routine very similar to the one described by \citet{euchneretal02-1}. In brief. our fit involves three free parameters: the magnetic field strength. B (where we restrictedour models to centered dipole fields). the angle between the line-of-sight and the magnetic axis V. and the effective temperature of the white dwarf Τω.," In brief, our fit involves three free parameters: the magnetic field strength $B$ (where we restrictedour models to centered dipole fields), the angle between the line-of-sight and the magnetic axis $\Psi$ , and the effective temperature of the white dwarf ." . Flux and cireular polarization spectra are, Flux and circular polarization spectra are 2:500 HL (222) Gz100 (tv (μου. review by Solomon Vanden Bout 2005))., $>$ $^{-1}$ \\citeyear{bla02}) $z$$>$ $<$ \\citeyear{gre05}) $^{10}$ (see review by Solomon Vanden Bout \citeyear{sv05}) ). However. iiost of these detections are of CO rotational lues from 293 transitions. which παν bias these studies toward hielh-excited gas. aud do uot necessarily trace the ecutive molecular eas reservoir as traced by>0).," However, most of these detections are of CO rotational lines from $J$$\geq$ 3 transitions, which may bias these studies toward highly-excited gas, and do not necessarily trace the entire molecular gas reservoir as traced by." . Indeed. recent studies hint at the presence of substantial amounts of low-cxcitation eas dn some SAIGs (e.g... Ibiulme et citevearluiu06:: Carilli et citevearcarlü: Harris et citevearharlO:: Ivison et citevearivilü:: Biechers et citeveamiel0)).," Indeed, recent studies hint at the presence of substantial amounts of low-excitation gas in some SMGs (e.g., Hainline et \\citeyear{hai06}; Carilli et \\citeyear{car10}; Harris et \\citeyear{har10}; Ivison et \\citeyear{ivi10}; Riechers et \\citeyear{rie10}) )." Unfortunately. previous sstudies im SACs (which do not suffer from excitation bias) were either carried out with single-dish telesopes lacking spatial information. or with the old correlator of the (VLA) lacking detailed spectral information.," Unfortunately, previous studies in SMGs (which do not suffer from excitation bias) were either carried out with single-dish telesopes lacking spatial information, or with the old correlator of the (VLA) lacking detailed spectral information." To overcome the linitatious of previous studies. we have initiated a svstematic study of the ccoutent of SMCs and other galaxy populations with the ((EVLA: Perley et citevearperll)).," To overcome the limitations of previous studies, we have initiated a systematic study of the content of SMGs and other galaxy populations with the (EVLA; Perley et \\citeyear{per11}) )." We here report carly results on two τοι} SAIC that appear to trace different stages of eas-rich. major mergers ouly —1.9 (ανν after the Big Bane.," We here report early results on two $z$$\sim$ 3.4 SMGs that appear to trace different stages of gas-rich, major mergers only $\sim$ Gyr after the Big Bang." ((2=3.316)JO£31hosts two SAICs detected iu. 7251CO cluission. separated by ~30kkpe iu projection. likely represeuntius an early phase of a merger (e... Tacconi,"$z$ =3.346)hosts two SMGs detected in $J$$\geq$ 4CO emission, separated by $\sim$ kpc in projection, likely representing an early phase of a merger (e.g., Tacconi" some assumptions.,some assumptions. From Fig., From Fig. 2 in Sect., 2 in Sect. 2.8 we see that prograde precession is faster when ¢=0 and that. if the inner binary is at the Wozai stationary solution. retrograde precession occurs if /245° and it is faster when 7=907.," 2.3 we see that prograde precession is faster when $i=0$ and that, if the inner binary is at the Kozai stationary solution, retrograde precession occurs if $i>45^\circ$ and it is faster when $i=90^\circ$." " As orbits with high relative inclination. 7. will reach values of c, near unity. these are likely to become unstable or undergo tidal evolution. hence we set a maximum value of 7= 607."," As orbits with high relative inclination, $i$, will reach values of $e_1$ near unity, these are likely to become unstable or undergo tidal evolution, hence we set a maximum value of $i=60^\circ$ ." " Therclore. if deI0 we assume that /=0 and CQ,=Οἱ ia0$ we assume that $i=0$ and $e_1=0$; if $\dot{\omega}_2<0$ we assume $i=60^\circ$ and $e_1=0.76$." These assumptions imply maximum. precession (in absolute value). thus they give us minimum estimates [or the parameter e(lur)ai.," These assumptions imply maximum precession (in absolute value), thus they give us minimum estimates for the parameter $x (1-x)\,a_1^2$." In order to estimate the hidden. inner binary component's Diss. nb. we must provide an estimate for the inner binary semi-major axis. αι.," In order to estimate the hidden inner binary component's mass, $m_1$, we must provide an estimate for the inner binary's semi-major axis, $a_1$." 2 measured the size of stability regionss around. binary star components., \citet{Wiegert&Holman1999AJ} measured the size of stability regions around binary star components. " They assume a massless particle orbiting in the binary system's plane and find that this is stable if e,X with where a» and e» are. respectively. outer binarys major axis and eccentricity. and mass parameter f£= my)."," They assume a massless particle orbiting in the binary system's plane and find that this is stable if $a_1\le a_c$ with where $a_2$ and $e_2$ are, respectively, outer binary's semi-major axis and eccentricity, and mass parameter $\mu=m_2/(m_2+m_b)$ ." To test our. model. we performed: numerical. integrations of the equation. of motion of hierarchical triple svstenis composed. of a star. me. and a close by binary. m».," To test our model, we performed numerical integrations of the equation of motion of hierarchical triple systems composed of a star, $m_2$, and a close by binary, $m_b$." " We chose masses mo=Al. and m,=0.5AZ.. ancl semi-major axes d»=3 AU and a,=0.3 AU. which imply periods Πο=4.24 ve [ος the outer binary and 731=84.9 cay for the inner binary. and semi-major axis ratio a=ayfan0.1."," We chose masses $m_2=M_{\odot}$ and $m_b=0.5\,M_{\odot}$, and semi-major axes $a_2=3$ AU and $a_1=0.3$ AU, which imply periods $T_2=4.24$ yr for the outer binary and $T_1=84.9$ day for the inner binary, and semi-major axis ratio $\alpha=a_1/a_2=0.1$." " The initial angles were ο=90°. O,=Oo0. a,=90"". we=20°."," The initial angles were $I_2=90^{\circ}$, $\Omega_1=\Omega_2=0$, $\omega_1=90^{\circ}$, $\omega_2=20^\circ$." We computed the radial velocity of the star mo. ancl simulated observational data points for a timespan. ἐν. and a certain precision limit.," We computed the radial velocity of the star $m_2$, and simulated observational data points for a timespan, $t_{obs}$, and a certain precision limit." We then applied the traditional techniques used in radial velocity data analysis., We then applied the traditional techniques used in radial velocity data analysis. To test in which circumstances we are able to measure the outer binary’s precession rate we set the outer binary on an eccentric orbit (οὗ= 0.2)., To test in which circumstances we are able to measure the outer binary's precession rate we set the outer binary on an eccentric orbit $e_2=0.2$ ). " Case Lis a coplanar triple svstem (7=0 ie. ἐν={ο 90°) where the inner binary has masses mi=0.42Al. and my,=OOSM... and a nearly circular orbit (0;= 0.01)."," Case I is a coplanar triple system $i=0$ i.e. $I_1=I_2=90^{\circ}$ ) where the inner binary has masses $m_0=0.42\,M_{\odot}$ and $m_1=0.08\,M_{\odot}$, and a nearly circular orbit $e_1=0.01$ )." 1n ‘Table 1 we show the results of fitting a fixed Ixeplerian orbit (fit0) or a precessing Ixeplerian orbit (fit 1) to the data time series with 128 points over fun.7S vr. at. precisions of about 5 m/s (A) and 1 m/s (D). respectively.," In Table 1 we show the results of fitting a fixed Keplerian orbit (fit0) or a precessing Keplerian orbit (fit 1) to the data time series with 128 points over $t_{obs} \approx 8$ yr, at precisions of about $5$ m/s (A) and $1$ m/s (B), respectively." From Fie., From Fig. " 3 (top) we see that since fan,=S vr. Aw29aefons."," 3 (top) we see that since $t_{obs}=8$ yr, $\Delta\omega>\dot{\omega}_2\, t_{obs}$." " Vhe maximum racial velocity απ over fon. is 15.0 m/s. At precision 5.425 m/s (A) the observation error is. 204 of the maximum αρα,", The maximum radial velocity drift over $t_{obs}$ is $18.6$ m/s. At precision $5.425$ m/s (A) the observation error is $29\%$ of the maximum drift. Therefore. lit (1) is only slightly better than fit (0).," Therefore, fit (1) is only slightly better than fit (0)." Llowever. at. precision 1.085 m/s (B) the observation error is only 6% of the maximum drift. thus Gt (1) is clearly better than fit (0).," However, at precision $1.085$ m/s (B) the observation error is only $6\%$ of the maximum drift, thus fit (1) is clearly better than fit (0)." " The theoretical value. (quadrupole approximation) for the precession rate is we=0.098"" /vr while the true value (simulations up to LOO ves) is d»=0.089 vr.", The theoretical value (quadrupole approximation) for the precession rate is $\dot{\omega}_2=0.093^\circ$ /yr while the true value (simulations up to 100 yrs) is $\dot{\omega}_2=0.089^\circ$ /yr. " Case HL has an inner binary with masses mo=0.35M. and m,—0.15M... with +=60° (Le. Z;=30° and fo=90 and e;=0.76 (Ixozalstationary solution)."," Case II has an inner binary with masses $m_0=0.35\,M_{\odot}$ and $m_1=0.15\,M_{\odot}$, with $i=60^{\circ}$ (i.e. $I_1=30^{\circ}$ and $I_2=90^\circ$ ) and $e_1=0.76$ (Kozaistationary solution)." " In Table 2 we show the results offitting a fixed. Ixeplerian orbit. (fit. 0) or a precessing Ixeplerian orbit (fit.1) to data timeseries with 99 points over fun.86 vr (C). and to data time series with 154points over /,4;%12 vr (D). both at. precision of about 5 m/s. The maximum racial velocity drifts over 6 vr and 12 vr are. respectively. 31 m/s and 62 m/s. whichcorrespond to observation errors of. respectively. 16% and S of the maximum drift."," In Table 2 we show the results offitting a fixed Keplerian orbit (fit 0) or a precessing Keplerian orbit (fit1) to data timeseries with 99 points over $t_{obs} \approx 6$ yr (C), and to data time series with 154points over $t_{obs} \approx 12$ yr (D), both at precision of about $5$ m/s. The maximum radial velocity drifts over 6 yr and 12 yr are, respectively, $31$ m/s and $62$ m/s, whichcorrespond to observation errors of, respectively, $16\%$ and $8\%$ of the maximum drift." From Fig., From Fig. 3 (bottom) we see that when fon.=6 vr. Awzdolus while when μι=12 vr. Aw&ae tips.," 3 (bottom) we see that when $t_{obs}=6$ yr, $\Delta\omega\approx \dot{\omega}_2\, t_{obs}$ while when $t_{obs}=12$ yr, $\Delta\omega\ll \dot{\omega}_2\, t_{obs}$ ." " Therefore. when /,4;ο vr (€). Lit (1) is slightlv better than fit (0) but when ρω=12 vr (D). fit (1) is clearly better than fit (0)."," Therefore, when $t_{obs}=6$ yr (C), fit (1) is slightly better than fit (0) but when $t_{obs}=12$ yr (D), fit (1) is clearly better than fit (0)." The theoretical value (quadrupole approximation) for the precession rate is Ge=0272 fvr while the true value (simulationsup to 100 vies) is do=—0.238 fr., The theoretical value (quadrupole approximation) for the precession rate is $\dot{\omega}_2=-0.272^\circ$ /yr while the true value (simulationsup to 100 yrs) is $\dot{\omega}_2=-0.238^\circ$ /yr. We simulated. triple systems as. described. above with the observed. star on an eccentric orbit with e»=02 (outer binary) around an inner binary with masses and m;= O.OSAL.. and semi-major axis AU.," We simulated triple systems as described above with the observed star on an eccentric orbit with $e_2=0.2$ (outer binary) around an inner binary with masses $m_0=0.42\,M_{\odot}$ and $m_1=0.08\,M_{\odot}$ , and semi-major axis $a_1=0.3$ AU." The values of the relative inclination were Q. 207. 407. 507. 55°. 607.," The values of the relative inclination were $i=0^\circ$ , $20^\circ$ , $40^\circ$ , $50^\circ$ , $55^\circ$ , $60^\circ$ ." When ;«40° the inner binary hac a nearly circular orbit (6;= 0.01) and when 7z40° it had an eccentric orbit near theIxozai stationary solution., When $i<40^\circ$ the inner binary had a nearly circular orbit $e_1=0.01$ ) and when $i\ge 40^\circ$ it had an eccentric orbit near theKozai stationary . £Uhuru and5 X-ray surveys. suggesting that it is persistently bright at A-ray energies: (Luohy et al.,", and X-ray surveys, suggesting that it is persistently bright at X-ray energies (Tuohy et al." 1990)., 1990). ROSAT also detected the X-ray counterpart of this CV. but with no evidence for orbital modulation (Rosen et al.," also detected the X-ray counterpart of this CV, but with no evidence for orbital modulation (Rosen et al." 1994)., 1994). The strong ο emission and the detection of X-rays from the system suggests that V348 Pup could be an Intermediate Polar (LP) CV., The strong He emission and the detection of X-rays from the system suggests that V348 Pup could be an Intermediate Polar (IP) CV. V348 Pup also exhibits a persistent modulation in its optical light curve with a period 6 per cent longer than the orbital period (Thomas 1993: Rolfe et al., V348 Pup also exhibits a persistent modulation in its optical light curve with a period 6 per cent longer than the orbital period (Thomas 1993; Rolfe et al. 2000)., 2000). This is interpreted as the superhump period. caused by the slow precession of an eccentric accretion The spectroscopic observations of V348 Pup were performed on 1999 October 2426 with the 2.15-m Ritehey-Chrettion telescope. at. the Complejo Astronomunico cl Leoncito (CASLEO) in San Juan. Argentina.," This is interpreted as the superhump period, caused by the slow precession of an eccentric accretion The spectroscopic observations of V348 Pup were performed on 1999 October 24–26 with the 2.15-m Ritchey-Chrèttien telescope at the Complejo Astronómmico el Leoncito (CASLEO) in San Juan, Argentina." A total of 33 spectra were acquired on the REOSC spectrograph. equipped with ⋅⋠ 1 . ⋜↧↻∪∪↓↓⊔∢⊾⊳∖⊔↓⊔↓⋏∙≟↓⋅⋜∐↓⊔⋏∙≟⋜⋯∠⋜↧↓⋖⋅⊊↓∪−≽≟ op ⋅ 1024 pixel? CCD detector.," A total of 33 spectra were acquired on the REOSC spectrograph, equipped with a 600 lines $^{-1}$ grating and a Tek 1024 $\times$ 1024 $^2$ CCD detector." “Phe instrumental setup gave an spectral range of AABSGO.5340 at 3X spectral resolution., The instrumental setup gave an spectral range of $\lambda\lambda$ 3860–5340 at 3 spectral resolution. The exposure time was Ηχος at 600 s and spectra of a CuAr comparison arc lamp were taken regularlyD after 1-2 spectra of the target5 to secure an optimal wavelength All the individual frames were cle-biasect. αμασα and skyv-subtracted in the standard wav.," The exposure time was fixed at 600 s and spectra of a Cu–Ar comparison arc lamp were taken regularly after 1-2 spectra of the target to secure an optimal wavelength All the individual frames were de-biased, flat-fielded and sky-subtracted in the standard way." The spectra were then optimally extracted (Llorne LOSG)., The spectra were then optimally extracted (Horne 1986). “Phe reduction processes were performed. using routines. whilst for wavelength calibration and most of subsequent analyses we used the package.," The reduction processes were performed using routines, whilst for wavelength calibration and most of subsequent analyses we used the package." A second-order polynomial was fitted to the are data. theris being always less than 0.12A.," A second-order polynomial was fitted to the arc data, the being always less than 0.12." Finally. the spectra were normalized to the continuum and re-binned into an uniform velocity scale.," Finally, the spectra were normalized to the continuum and re-binned into an uniform velocity scale." The full data set covers 2.8 orbital periods of the system., The full data set covers $\sim 2.8$ orbital periods of the system. We obtained. 2-band photometric data during a full orbital cvcle., We obtained $R$ -band photometric data during a full orbital cycle. The observations were made on 1990 November 21 with the 1.0-m telescope at the South African Astronomical Observatory (SAO) and the οΓιο 1024 1024 pixel? CCD detector., The observations were made on 1999 November 21 with the 1.0-m telescope at the South African Astronomical Observatory (SAAO) and the STE4 1024 $\times$ 1024 $^2$ CCD detector. Phe exposure time was 30 s which. together with the read-out time ane overheads. resulted in a time resolution of 45 s. We also performed. Y -band photometry during an entire eclipse of the system.," The exposure time was 30 s which, together with the read-out time and overheads, resulted in a time resolution of 45 s. We also performed $V$ -band photometry during an entire eclipse of the system." The photomoetric data were obtained on 2001 April S with the 1.0-m Optical Ground Station (OCS) telescope at the Observatorio cel Ρος in Tenerife. [rom images taken with a Thomson rm24 1024 pixel CCD camera.," The photometric data were obtained on 2001 April 8 with the 1.0-m Optical Ground Station (OGS) telescope at the Observatorio del Teide in Tenerife, from images taken with a Thomson 1024 $\times$ 1024 $^2$ CCD camera." " ""The exposure time was 90 After de-biasing and Dat-lelding the individual images. 1ο instrumental magnitudes were obtained with the PSE-fitting packages withinIRAP."," The exposure time was 90 After de-biasing and flat-fielding the individual images, the instrumental magnitudes were obtained with the PSF-fitting packages within." From the scatter in 16 comparison star light curves. we estimate that the ilferential photometry is accurate to ~I per cent.," From the scatter in the comparison star light curves, we estimate that the differential photometry is accurate to $\sim1$ per cent." V348. Pup. does not show significant night-to-night variability. (as could be observed. by inspecting each night averaged spectrum)., V348 Pup does not show significant night-to-night variability (as could be observed by inspecting each night averaged spectrum). The full averaged spectrum (see Fig., The full averaged spectrum (see Fig. 1) shows the typical CV. emission lines. namely. Balmer (1117 115) and (A5015. A4922. A4471. A4026 and other Loss intense) as well as the high excitation lines. A4686. the Bowen blend and A4267.," 1) shows the typical CV emission lines, namely, Balmer $\beta$ --H8) and $\lambda$ 5015, $\lambda$ 4922, $\lambda$ 4471, $\lambda$ 4026 and other less intense) as well as the high excitation lines $\lambda$ 4686, the Bowen blend and $\lambda$ 4267." The lines are seen in absorption. with A3968 Iving in the core of He.," The lines are seen in absorption, with $\lambda$ 3968 lying in the core of $\epsilon$ ." Another absorption feature is visible close. to 5200 X... which we identify as A5169.," Another absorption feature is visible close to 5200 , which we identify as $\lambda$ 5169." The presence of this line suggests that the A4922 and A5015 lines are contaminated by A4924 and ASOLS. respectively.," The presence of this line suggests that the $\lambda$ 4922 and $\lambda$ 5015 lines are contaminated by $\lambda$ 4924 and $\lambda$ 5018, respectively." Remarkably. the strength of A4686 is larger than 1.1.," Remarkably, the strength of $\lambda$ 4686 is larger than $\beta$." This has also been observed in SW Sex itself during low state (Groot. Itutten van Paraclijs 2001).," This has also been observed in SW Sex itself during low state (Groot, Rutten van Paradijs 2001)." The emission lines show a single-peak profile in the [ull-orbit. averaged: spectrum., The emission lines show a single-peak profile in the full-orbit averaged spectrum. This is a characteristic of SW Sex systems., This is a characteristic of SW Sex systems. To inspect the shape of the line profiles in different parts of the orbit. we constructed averages from the individual spectra taken at. the orbital. phase ranges 0.350.55. 0.750.90 and 0.9.1.1 (orbital phases are calculated. from the ephemeris given in 3.1).," To inspect the shape of the line profiles in different parts of the orbit, we constructed averages from the individual spectra taken at the orbital phase ranges 0.35–0.55, 0.75–0.90 and 0.9–1.1 (orbital phases are calculated from the ephemeris given in 3.1)." These intervals correspond to the expected phase in which the vpical absorption component in SW Sex systems becomes stronger. the phases of the hot spot and the phases of eclipse. respectively.," These intervals correspond to the expected phase in which the typical absorption component in SW Sex systems becomes stronger, the phases of the hot spot and the phases of eclipse, respectively." The averaged spectra are shown in Fig., The averaged spectra are shown in Fig. 2., 2. In ohases 0.350.55 the Balmer and profiles are double-»eaked. whilst the A4686 and the Bowen blend. profiles remain single.," In phases 0.35–0.55 the Balmer and profiles are double-peaked, whilst the $\lambda$ 4686 and the Bowen blend profiles remain single." In addition. the flux of the Balmer and ines decrease with respect to A4686 (see e.g. the drastic acing of A4471).," In addition, the flux of the Balmer and lines decrease with respect to $\lambda$ 4686 (see e.g. the drastic fading of $\lambda$ 4471)." This ellect seems to be stronger as we move to higher line excitation levels (i.e. the Dux decrease is argeer in Le than in 11:2)., This effect seems to be stronger as we move to higher line excitation levels (i.e. the flux decrease is larger in $\epsilon$ than in $\beta$ ). Double peaks and line fading are caused by the presence of an absorption component reaching maximun streneth in this phase range (5=0.35 0.55). and constitute a defining feature of SW Sex systems.," Double peaks and line fading are caused by the presence of an absorption component reaching maximum strength in this phase range $\varphi=0.35$ –0.55), and constitute a defining feature of SW Sex systems." The phase 0.750.90 average shows the tvpical emission spectrum. but now A4686 is slightly weaker in Dux than 113.," The phase 0.75–0.90 average shows the typical emission spectrum, but now $\lambda$ 4686 is slightly weaker in flux than $\beta$." Given that the Hux of the Balmer lines does not change significatively outside the 0.350.55. phase interval. this [acing of A4686 is probably caused by an absorption component. as can be seen in the trailed spectra we show in 3.1.," Given that the flux of the Balmer lines does not change significatively outside the 0.35–0.55 phase interval, this fading of $\lambda$ 4686 is probably caused by an absorption component, as can be seen in the trailed spectra we show in 3.1." During eclipse (phases 0.9-1.1). the averaged spectrum. does not diller too much from the previous one.," During eclipse (phases 0.9-1.1), the averaged spectrum does not differ too much from the previous one." Taking into accountthat V348 Pupexhibits a deep eclipse. this may indicate that the continuum is more deeply. eclipsed than," Taking into accountthat V348 Pupexhibits a deep eclipse, this may indicate that the continuum is more deeply eclipsed than" is indeed an ejecta component present in this region.,is indeed an ejecta component present in this region. " The SEout spectrum is fitted with the Fe abundance tied to unity, as otherwise this abundance would rise to unrealistically high values."," The $_{\rm out}$ spectrum is fitted with the Fe abundance tied to unity, as otherwise this abundance would rise to unrealistically high values." We note that releasing this component during the fitting procedure will result in an even lower electron temperature (0.3 keV)., We note that releasing this component during the fitting procedure will result in an even lower electron temperature (0.3 keV). Table lists the parameters of the best-fitting spectral model., Table lists the parameters of the best-fitting spectral model. The parameters in Table are in general consistent with parameters obtained in previous work (Rhoetal.2002;Vinketal. 2006).," The parameters in Table are in general consistent with parameters obtained in previous work \citep{Rho2002,Vink2006}." " In the NE, the dominant contribution of synchrotron radiation makes it difficult to determine the electron temperature adequately."," In the NE, the dominant contribution of synchrotron radiation makes it difficult to determine the electron temperature adequately." " However, we note that the high contribution of non-thermal X-ray emission to the spectrum makes it difficult to accurately determine the parameters of the thermal component."," However, we note that the high contribution of non-thermal X-ray emission to the spectrum makes it difficult to accurately determine the parameters of the thermal component." " Our plasma parameters for the SW spectrum differ from previously determined (Rhoetal.2002),, this is probably because we fit the spectrum with two components, of which one probably represents the ejecta and one the shocked ambient medium, whereas Rho et al."," Our plasma parameters for the SW spectrum differ from previously determined \citep{Rho2002}, this is probably because we fit the spectrum with two components, of which one probably represents the ejecta and one the shocked ambient medium, whereas Rho et al." used a single component., used a single component. " We choose our region right behind a Balmer dominated filament, which is non radiative and hence has a relatively low density."," We choose our region right behind a Balmer dominated filament, which is non radiative and hence has a relatively low density." " Additionally, the plasma from the ambient medium was probably only recently shocked."," Additionally, the plasma from the ambient medium was probably only recently shocked." " Note that this solution is not necessarily unique, but given the high C-statistic values for the alternative models, we regard this model as an adequate representation of the spectrum."," Note that this solution is not necessarily unique, but given the high C-statistic values for the alternative models, we regard this model as an adequate representation of the spectrum." The low value for the πο for the ambient medium component therefore seems appropriate., The low value for the $n_{e}t$ for the ambient medium component therefore seems appropriate. " Alternatively, if we choose our temperature similar to Rhoetal.(2002),, Το and Τρ are close to equilibration."," Alternatively, if we choose our temperature similar to \cite{Rho2002}, $T_{\rm e}$ and $T_{\rm p}$ are close to equilibration." Problems with fitting the spectrum around 1.2 keV were also encountered by Kosenkoetal.(2008) for the 0509-67.5 supernova remnant., Problems with fitting the spectrum around 1.2 keV were also encountered by \cite{Kosenko2008} for the 0509-67.5 supernova remnant. " These deviations are possibly caused by uncertainties in the atomic data base of SPEX, presumably by the Fe-L line complex."," These deviations are possibly caused by uncertainties in the atomic data base of SPEX, presumably by the Fe-L line complex." The sub-solar abundances in all fits show that we indeed fit X-ray spectra from shocked ambient medium as opposed to metal-enhanced shocked ejecta., The sub-solar abundances in all fits show that we indeed fit X-ray spectra from shocked ambient medium as opposed to metal-enhanced shocked ejecta. This confirms that the measured electron temperatures are related to the proton temperatures at the shock front., This confirms that the measured electron temperatures are related to the proton temperatures at the shock front. " The width of the broad component is primarily a function of the post-shock proton temperature, but modified by the velocity dependent cross sections for charge and impact excitation."," The width of the broad component is primarily a function of the post-shock proton temperature, but modified by the velocity dependent cross sections for charge and impact excitation." This causes the shape of the broad component to deviate from a perfect Gaussian., This causes the shape of the broad component to deviate from a perfect Gaussian. Nevertheless this remains a decent approximation (seevanAdelsbergerencestherein)., Nevertheless this remains a decent approximation \citep[see][and references therein]{Adelsberg}. Fig., Fig. " 5 of vanAdelsbergetal.(2008) shows that up to 2000 km/s, the FWHM of the broad line increases linearly with the shock velocity."," 5 of \cite{Adelsberg} shows that up to 2000 km/s, the FWHM of the broad line increases linearly with the shock velocity." " 'This shows that interpreting the line width in terms of proton temperature through kT,=mpo? is a decent approximation (withc=FWHM//V8In2inkm s-!,, ?,Table Table 2."," This shows that interpreting the line width in terms of proton temperature through $kT_{\rm p} = m_{\rm p}\sigma^2$ is a decent approximation \citep[with $\sigma = {\rm FWHM}/ in , ][Table ." "1)mainBodyRefEnd2504]Rybicki,Heng2010.shows that Τρ for SEout is higher than T; for the SE;, spectrum, implying a higher shock velocity (equation 1)."," Table shows that $T_{\rm p}$ for $_{\rm out}$ is higher than $T_{\rm p}$ for the $_{\rm in}$ spectrum, implying a higher shock velocity (equation )." " Note that SEout lies outward of SE, which is suggestive for a higher shock velocity as well."," Note that $_{\rm out}$ lies outward of $_{\rm in}$, which is suggestive for a higher shock velocity as well." " For the Northern region of RCW 86, we have the parameters of two Ha spectra (Long&Blair1990;Ghavamianetal.2007) at nearly the same location, which appear to have significantly different proton temperatures (0.2 and 0.9 keV respectively)."," For the Northern region of RCW 86, we have the parameters of two $\alpha$ spectra \citep{Long, Ghavamian2007} at nearly the same location, which appear to have significantly different proton temperatures (0.2 and 0.9 keV respectively)." " As we do not know which value best represents this region, we plotted both values for Ty with one corresponding T, in Fig."," As we do not know which value best represents this region, we plotted both values for $T_{\rm p}$ with one corresponding $T_{\rm e}$ in Fig." "6.. We note that the measured widths of the broad Ha-lines tend to vary a lot (from 325 to 543 km/s) in the Northern region (Ghavamian1999), making it unclear to which Τρ the electron temperature relates a combination)."," We note that the measured widths of the broad $\alpha$ -lines tend to vary a lot (from 325 to 543 km/s) in the Northern region \citep{GhavamianPhD}, making it unclear to which $T_{\rm p}$ the electron temperature relates (probably a combination)." " Also, we note that Τρ appears to vary (probablysignificantly along the eastern rim of the remnant (Ghavamian1999).."," Also, we note that $T_{\rm p}$ appears to vary significantly along the eastern rim of the remnant \citep{GhavamianPhD}." " The proton temperature is obtained from optical spectra directly behind the shock fronts, as the neutral hydrogen will ionize quickly after entering the shock front."," The proton temperature is obtained from optical spectra directly behind the shock fronts, as the neutral hydrogen will ionize quickly after entering the shock front." " To obtainanX-ray spectrum with sufficient signal-over-noise, we extracted over a larger region of the remnant than the region from which the proton temperature was determined."," To obtainanX-ray spectrum with sufficient signal-over-noise, we extracted over a larger region of the remnant than the region from which the proton temperature was determined." " Also, the spatial resolution"," Also, the spatial resolution" of the white dwarf. comparable to the upper Limit. found from eclipse timings of NY Ari.,"of the white dwarf, comparable to the upper limit found from eclipse timings of XY Ari." We propose that the modulation of this component results. [rom foreshortening of the blackbocly emitting regions., We propose that the modulation of this component results from foreshortening of the blackbody emitting regions. We view the heated surface most favourably when either. pole points towards us. so we see a double-peaked modulation in soft N-rays.," We view the heated surface most favourably when either pole points towards us, so we see a double-peaked modulation in soft X-rays." Phe equality of the two maxima requires that the magnetic axis be highly inclined from the spin axis., The equality of the two maxima requires that the magnetic axis be highly inclined from the spin axis. The hard. X-ray omission shows a single-poaked. sawtooth mocdulation.," The hard X-ray emission shows a single-peaked, sawtooth modulation." This does not show the strong energy dependence of absorption. as usual in LPs.," This does not show the strong energy dependence of absorption, as usual in IPs." We suggest that this is because. with the high dipole inclination. the outer parts of the accretion curtains never cross the line of sight.," We suggest that this is because, with the high dipole inclination, the outer parts of the accretion curtains never cross the line of sight." However. electron scatering and opacity in the highly ionized. post-shock column causes the intensity. variation with spin phase.," However, electron scattering and opacity in the highly ionized post-shock column causes the intensity variation with spin phase." The sawooth shape of the pulsation requires that the magnetic axis be olfset from. the white-chwarl centre., The sawtooth shape of the pulsation requires that the magnetic axis be offset from the white-dwarf centre. We also suggest that the high dipole inclination is responsible for the double-peaked optical pulse., We also suggest that the high dipole inclination is responsible for the double-peaked optical pulse. “Phe high dipole inclination appears to be the main reason for the differences between V405 Aur’s pulsation ancl tvpical LP behaviour., The high dipole inclination appears to be the main reason for the differences between V405 Aur's pulsation and typical IP behaviour. The observation reported here was performed by Leicester University. who also constructed the MOS. cameras and developed the analysis. software.," The observation reported here was performed by Leicester University, who also constructed the MOS cameras and developed the analysis software." In. particular we thank Steve Sembay anc Richard Saxton for their help in overcoming calibration dilliculties. and for providing us with the latest’ pre-release CCE and. RAL files for use in this analvsis.," In particular we thank Steve Sembay and Richard Saxton for their help in overcoming calibration difficulties, and for providing us with the latest pre-release CCF and RMF files for use in this analysis." We also thank Liza van Zvl and Gavin Ramsay for some illuminating cliscussions., We also thank Liza van Zyl and Gavin Ramsay for some illuminating discussions. ealaxies in order to examine how the FIR-RC-HCN correlations extend to much smaller size scale.,galaxies in order to examine how the FIR-RC-HCN correlations extend to much smaller size scale. Aburphy (2006. 2008) have taken an initial look at the FIR-RC correlation within the disks of 4. and later increased to 29. nearby [ace-on galaxies in theSpilzer SINGS legacy program (Ixennieutt 2003). ancl found (he trend that the ratio of FIR to RC decreases with increasing raclius. which is consistent with what Marsh IIelou (1995) found al intermediate spatial resolution.," Murphy (2006, 2008) have taken an initial look at the FIR-RC correlation within the disks of 4, and later increased to 29, nearby face-on galaxies in the SINGS legacy program (Kennicutt 2003), and found the trend that the ratio of FIR to RC decreases with increasing radius, which is consistent with what Marsh Helou (1995) found at intermediate spatial resolution." They also studied how the star formation activity allects the FIR-RC correlation within galaxies by testing a phenomenological model which smears ihe FIR images to match the radio images., They also studied how the star formation activity affects the FIR-RC correlation within galaxies by testing a phenomenological model which smears the FIR images to match the radio images. Thev found that the mean distance traveled by the CR electrons is most sensitive to the dominant age of the CR electron population. rather (han (he interstellar medium (ISM) parameters. which may inhibit (heir propagation. such as the ISM density. radiation-fiekdl energy. densitv. ancl magnetic field strength.," They found that the mean distance traveled by the CR electrons is most sensitive to the dominant age of the CR electron population, rather than the interstellar medium (ISM) parameters, which may inhibit their propagation, such as the ISM density, radiation-field energy density, and magnetic field strength." Comparison of such detailed spatially resolved correlations in line wilh our findings in the global quantities could help us reach our final goal. i.e.. understanding the FIR-RC correlation.," Comparison of such detailed spatially resolved correlations in line with our findings in the global quantities could help us reach our final goal, i.e., understanding the FIR-RC correlation." Globally. LCN seems better than CO. the validitv of correlations of RC-CO and FIR-RC on small scale has already been proven: we need high-fidelity ICN imaging and/or resolved ICN observations to truly compare all.," Globally, HCN seems better than CO, the validity of correlations of RC-CO and FIR-RC on small scale has already been proven; we need high-fidelity HCN imaging and/or resolved HCN observations to truly compare all." Both FIR. and RC emission involves physical processes of both small and laree spatial scales even though most of the FIR emission is dominated by active star-orming regions ol small scales., Both FIR and RC emission involves physical processes of both small and large spatial scales even though most of the FIR emission is dominated by active star-forming regions of small scales. Moonev Solomon (19883) showed that the FIR-CO correlation for GMCs improves. once (he diffuse FIR emission (hat originated fom the general interstellar raciation fielcl of large spatial scale was subtracted.," Mooney Solomon (1988) showed that the FIR-CO correlation for GMCs improves, once the diffuse FIR emission that originated from the general interstellar radiation field of large spatial scale was subtracted." RC might be dominated by large-scale shocks/bubbles associated wilh SNRs as well as even larger scale of magnetic fields. where CR. electrons pass along the field lines ancl experience efficient cooling. whereas WCN (races a smaller size scale than that of FIR and RC.," RC might be dominated by large-scale shocks/bubbles associated with SNRs as well as even larger scale of magnetic fields, where CR electrons pass along the field lines and experience efficient cooling, whereas HCN traces a smaller size scale than that of FIR and RC." Yet. (μον are associated with three different periods in the time sequence connected wilh the entire star formation processes.," Yet, they are associated with three different periods in the time sequence connected with the entire star formation processes." FIR. emission originates from the dust that enshrouds the new-born stars while IICN. emission outlines regions of dense molecular gas that eventually nurse new-born stars. whereas RC emission is produced from the significantly. diffused. CR electrons and large-scale shocks. which have traveled. a long distance from the previous star-forming sites.," FIR emission originates from the dust that enshrouds the new-born stars while HCN emission outlines regions of dense molecular gas that eventually nurse new-born stars, whereas RC emission is produced from the significantly diffused CR electrons and large-scale shocks, which have traveled a long distance from the previous star-forming sites." The difference between (hese three emissions in (ime sequence is in de [acto agreement with that of the corresponding locations in spatial scales: dense molecular cores Burther collapse to form massive stars that then quickly evolve and go (rough supernovae to become SNRs., The difference between these three emissions in time sequence is in de facto agreement with that of the corresponding locations in spatial scales: dense molecular cores further collapse to form massive stars that then quickly evolve and go through supernovae to become SNRs. In short. CO and FIR. emission are almost entirely associated with the GMCs. but most FIR emission is probably associated with star-forming sites inside (he dense cores of the much smaller scales traced by the HCN emission.," In short, CO and FIR emission are almost entirely associated with the GMCs, but most FIR emission is probably associated with star-forming sites inside the dense cores of the much smaller scales traced by the HCN emission." On (he other hand. BC is probably dominated by," On the other hand, RC is probably dominated by" inward propagating waves (??)..,"inward propagating waves \citep{cranmer05,verdini07}." " Such imbalance weakens the cascade rate. causing the power spectrum to decrease more rapidly with increasing K, near kjPy=| in response to a fixed KAW damping rate."," Such imbalance weakens the cascade rate, causing the power spectrum to decrease more rapidly with increasing $k_\perp$ near $k_\perp \rho_{\rm p} = 1$ in response to a fixed KAW damping rate." Second. the linear damping rate of KAWs at kipp=I is significantly larger in the D«| conditions of coronal holes than in the typical B~0.51 conditions found at | AU (see. e.g.. figure 2 of 2)).," Second, the linear damping rate of KAWs at $k_\perp \rho_{\rm p} = 1$ is significantly larger in the $\beta \ll 1$ conditions of coronal holes than in the typical $\beta \sim 0.5 - 1$ conditions found at 1 AU (see, e.g., figure 2 of \cite{howes08a}) )." As described in the introduction. linear damping of KAWs by ions is extremely weak when B even in the free-streaming limit.," At $r\gtrsim 2 R_{\sun}$, ion flows are supersonic \citep{kohl98}, and thus $t_{\rm cond}> t_{\rm exp}$ even in the free-streaming limit." lon thermal conduction can «pthus be neglected at r>2R. to a first approximation., Ion thermal conduction can thus be neglected at $r\gtrsim 2 R_{\sun}$ to a first approximation. Because collisions and conduction are weak. minor 10ns at r=2R. evolve towards a state in which for the following reasons.," Because collisions and conduction are weak, minor ions at $r\gtrsim 2 R_{\sun}$ evolve towards a state in which for the following reasons." Minor tons draw very little power from the turbulence. and the power spectrum of the turbulence is essentially independent of the minor-ion heating rate Οι.," Minor ions draw very little power from the turbulence, and the power spectrum of the turbulence is essentially independent of the minor-ion heating rate $Q_{\rm i}$." Equations (1)) and (2)) thus imply that Q; is a highly sensitive function of the minor-ion temperature. with strong heating at small 7;; and exponentially weak heating at sufficiently large Ty).," Equations \ref{eq:defeps}) ) and \ref{eq:th1}) ) thus imply that $Q_{\rm i}$ is a highly sensitive function of the minor-ion temperature, with strong heating at small $T_{\perp \rm i}$ and exponentially weak heating at sufficiently large $T_{\perp \rm i}$ ." If f2fap at some radius 7;. then adiabatic cooling would cause 7); to decrease in proportion to By. and dnTii/dlnr would be <2? near rj.," If $t_{\rm h}\gg t_{\rm exp}$ at some radius $r_1$, then adiabatic cooling would cause $T_{\perp \rm i}$ to decrease in proportion to $B_0$, and $d\ln T_{\perp \rm i}/d\ln r$ would be $\leq -2$ near $r_1$ ." " The radial decrease in 7), near r; would lead to a sharp decrease in fj. and at larger x the minor tons would leave the adiabatic regime."," The radial decrease in $T_{\perp \rm i}$ near $r_1$ would lead to a sharp decrease in $t_{\rm h}$ , and at larger $r$ the minor ions would leave the adiabatic regime." Conversely. If fj<>| near rp.," Conversely, if $t_{\rm h}\ll t_{\rm exp}$ at some radius $r_2$ , then $d\ln T_{\perp \rm i}/d\ln r \gg 1$ near $r_2$." " The radial increase in 7,; would cause rj to increase rapidly with increasing r. and at larger r the tons would again approach a state in which fj~fip."," The radial increase in $T_{\perp \rm i}$ would cause $t_{\rm h}$ to increase rapidly with increasing $r$, and at larger $r$ the ions would again approach a state in which $t_{\rm h} \sim t_{\rm exp}$." The observed Tj; profile of OF ions in coronal holes (see figure 3 below) appears to provide an example of the second case just described. in which 10ns swiftly evolve from a state in which fοςfap to a state in. which f— fp.," The observed $T_{\perp \rm i}$ profile of ${\rm O}^{+5}$ ions in coronal holes (see figure \ref{fig:Tcomp} below) appears to provide an example of the second case just described, in which ions swiftly evolve from a state in which $t_{\rm h} \ll t_{\rm exp}$ to a state in which $t_{\rm h} \sim t_{\rm exp}$ ." The O? temperature is <10’ K at rx1.6R.. presumably due to collisions with protons.," The ${\rm O}^{+5}$ temperature is $ <10^7$ K at $r\leq 1.6 R_{\sun}$, presumably due to collisions with protons." As O? ions flow outward past r=L.6R.. their temperature increases rapidly to ~10° K at r=L9R.. where collisional energy exchange with protons is weak.," As ${\rm O}^{+5}$ ions flow outward past $r=1.6 R_{\sun}$, their temperature increases rapidly to $\sim 10^8$ K at $r= 1.9 R_{\sun}$, where collisional energy exchange with protons is weak." " At r=1.9R.. the O? temperature profile abruptly flattens. with 7,; remaining fairly constant out to 2.7R. . indicating that fyορ at rz2R.."," At $r = 1.9 R_{\sun}$, the ${\rm O}^{+5}$ temperature profile abruptly flattens, with $T_{\perp \rm i}$ remaining fairly constant out to $2.7 R_{\sun}$ , indicating that $t_{\rm h} \sim t_{\rm exp}$ at $r\gtrsim 2 R_{\sun}$." These rapid radial variationsin 74; and dT;/dr present a challenge for theoretical models. but can be naturally explained in terms of stochastic heating — stochastic heating of an initially cool minor-ion population quickly increases Τε. but then saturates at large Τι because of the reduction in orbit The strong dependence of 5j on εἰ implies that tj—A5 only! within a narrow interval of ει values.," These rapid radial variationsin $T_{\perp \rm i}$ and $dT_{\perp \rm i}/dr$ present a challenge for theoretical models, but can be naturally explained in terms of stochastic heating — stochastic heating of an initially cool minor-ion population quickly increases $T_{\perp \rm i}$, but then saturates at large $T_{\perp \rm i}$ because of the reduction in orbit The strong dependence of $t_{\rm h}$ on $\epsilon_{\rm i}$ implies that $t_{\rm h} \sim t_{\rm exp}$ only within a narrow interval of $\epsilon_{\rm i}$ values." The midpoint of this interval can be found by equating fj and fy). which yields The right-hand side of this equation ts >‘>| in coronal holes. leading to values of ει that are «|.," The midpoint of this interval can be found by equating $t_{\rm h} $ and $t_{\rm exp}$ , which yields The right-hand side of this equation is $\gg 1$ in coronal holes, leading to values of $\epsilon_{\rm i}$ that are $ \ll 1$ ." " For example. Qjr/U,=10° for O7? ions at r=2R. given the assumptions listed in the caption of figure 2.."," For example, $\Omega_{\rm i} r/U_{\rm i} = 6.13 \times 10^6$ for ${\rm O}^{+5}$ ions at $r=2 R_{\sun}$ given the assumptions listed in the caption of figure \ref{fig:eps_profile}." " Equation (19)) then gives ει=1077, assuming c»=0.15."," Equation \ref{eq:th2}) ) then gives $\epsilon_{\rm i} = 2.96\times 10^{-2}$ , assuming $c_2 = 0.15$." For such small values of ej. the value of ¢; becomes relatively insensitive to changes in the right-hand side of equation (19)).," For such small values of $\epsilon_{\rm i}$, the value of $\epsilon_{\rm i}$ becomes relatively insensitive to changes in the right-hand side of equation \ref{eq:th2}) )." " For example. if Ojr/U, is increased from 6.13«10° by50%.. the resulting decrease in £j is only5%."," For example, if $\Omega_{\rm i} r/U_{\rm i}$ is increased from $6.13 \times 10^6$ by, the resulting decrease in $\epsilon_{\rm i}$ is only." ". For protons. the comparatively flat 7,; profiles seen in UVCS observations (Kohl et al."," For protons, the comparatively flat $T_{\perp \rm i}$ profiles seen in UVCS observations (Kohl et al." 1998) rule out the possibility that fj<>fap. assuming stochastic heating is the dominant heating mechanism.," 1998) rule out the possibility that $t_{\rm h} \ll t_{\rm exp}$ or $t_{\rm h} \gg t_{\rm exp}$, assuming stochastic heating is the dominant heating mechanism." — Thus. fj—445 and protons approximately satisfy equation (19)).," \nocite{kohl98} Thus, $t_{\rm h} \sim t_{\rm exp}$ and protons approximately satisfy equation \ref{eq:th2}) )." " However. protons can attain the required value of £; not only by getting hotter or cooler. but also by absorbing energy from the turbulence and reducing the value of à; at A,—Pp."," However, protons can attain the required value of $\epsilon_{\rm i}$ not only by getting hotter or cooler, but also by absorbing energy from the turbulence and reducing the value of $\delta v_{\lambda_\perp}$ at $\lambda_\perp \sim \rho_{\rm p}$." No attempt is made in this paper to treat the coupled evolution of protons and gyro-scale KAW fluctuations self-consistently., No attempt is made in this paper to treat the coupled evolution of protons and gyro-scale KAW fluctuations self-consistently. " Instead. proton damping (and electron Landau damping) of fluctuations at A,~ is modeled simplistically by setting oj=0.71 for protons mPp equation (15))."," Instead, proton damping (and electron Landau damping) of fluctuations at $\lambda_\perp \sim \rho_{\rm p}$ is modeled simplistically by setting $\alpha_{\rm i} = 0.71$ for protons in equation \ref{eq:alpha2}) )." This particular value is chosen to match the UVCS observations shown in figure 3.. as described further below.," This particular value is chosen to match the UVCS observations shown in figure \ref{fig:Tcomp}, as described further below." Although helium comprises only ~5% of the ions in the fast solar wind (?).. alpha particles are hotter thar protons in the fast wind. and may also drain a significant amount of power from the cascade (?2)..," Although helium comprises only $\sim 5\%$ of the ions in the fast solar wind \citep{bame77}, alpha particles are hotter than protons in the fast wind, and may also drain a significant amount of power from the cascade \citep{marsch82a,kasper07}." The back reactior of helium heating upon the turbulence. however. is neglected in this paper.," The back reaction of helium heating upon the turbulence, however, is neglected in this paper." To determine ειfrom equation (19). By is taken from equation (9)) and L for protons is set equal to U n equation (10)).," To determine $\epsilon_{\rm i}$from equation \ref{eq:th2}) ), $B_0$ is taken from equation \ref{eq:B0}) ) and $U_{\rm i}$ for protons is set equal to $U$ in equation \ref{eq:defU}) )." For other ion species. U is taken to be 1.75 times the proton speed. which is consistent with. UVCS observations of protons and O? ions at r=3R. (Kohl etal.," For other ion species, $U_{\rm i}$ is taken to be 1.75 times the proton speed, which is consistent with UVCS observations of protons and ${\rm O}^{+5}$ ions at $r=3 R_{\sun}$ (Kohl etal." 1998). but is only arough approximation for otherion species and at other radi.," 1998), \nocite{kohl98} but is only arough approximation for otherion species and at other radii." The resulting values of ει for protons. alpha particles. andO? ions are shown in figure 2 for L8R.«rΙΑ...," The resulting values of $\epsilon_{\rm i}$ for protons, alpha particles, and${\rm O}^{+5}$ ions are shown in figure \ref{fig:eps_profile} for $ 1.8 R_{\sun}< r < 15 R_{\sun}$." Since ion thermal conduction and collisional energy exchange between particle species areneglected. thecurves are not extended to smaller + where these processes become important.," Since ion thermal conduction and collisional energy exchange between particle species areneglected, thecurves are not extended to smaller $r$ where these processes become important." Once £i(7) is determined using equation (19)). Tj; can be determined from equation (16)). which can be re-written às As illustrated in figure 2.. equation (19)) leads to similar values of £j for alpha particles and minor ions.," Once $\epsilon_{\rm i}(r)$ is determined using equation \ref{eq:th2}) ), $T_{\perp \rm i}$ can be determined from equation \ref{eq:eps2})), which can be re-written as As illustrated in figure \ref{fig:eps_profile}, , equation \ref{eq:th2}) ) leads to similar values of $\epsilon_{\rm i}$ for alpha particles and minor ions." If ει and αι , If $\epsilon_{\rm i}$ and $\alpha_{\rm i}$ We follow the tradition of showing iron lines around 4530.A.. started by Gulliver et al.,"We follow the tradition of showing iron lines around 4530, started by Gulliver et al." in 1991 (see Fig. 4))., in 1991 (see Fig. \ref{4530}) ). Ilowever. our profiles are not smooth like Gullivers but rather demonstrate some pattern. which is also (he case in the spectrum of Takeda et al.(2007:; see their Fig.5).," However, our profiles are not smooth like Gulliver's but rather demonstrate some pattern, which is also the case in the spectrum of Takeda et al.(2007; see their Fig.5)." In summary. we present a hieh resolution and high signal-to-nolse ratio atlas of Vega.," In summary, we present a high resolution and high signal-to-noise ratio atlas of Vega." Data are downloadable in digital form., Data are downloadable in digital form. We hope Chat the atlas provides useful information for future studies., We hope that the atlas provides useful information for future studies. GAG and III acknowledge support by KICOS through the grant No., GAG and IH acknowledge support by KICOS through the grant No. 07-179., 07-179. constitutes the extended mGC3 method presented in this paper.,constitutes the extended mGC3 method presented in this paper. We applied this new method to a mock Gaia catalogue containing some 3.5x10° stars that form the smooth Galactic background and stars from simulated satellite galaxies on different orbits and with two types of star formation histories., We applied this new method to a mock Gaia catalogue containing some $3.5\times10^8$ stars that form the smooth Galactic background and stars from simulated satellite galaxies on different orbits and with two types of star formation histories. " The results show that the mGC3 method is capable of tracing remnants of satellites with luminosities down to Ly~4—5x10"" Lo for dynamical ages up to 7 Gyr.", The results show that the mGC3 method is capable of tracing remnants of satellites with luminosities down to $L_V\sim4-5\times10^7$ $_\odot$ for dynamical ages up to $\sim 7$ Gyr. Remnants of brighter satellites (105—10? Lo) can be recovered up to dynamical ages of ~10 Gyr., Remnants of brighter satellites $10^8$ $10^9$ $_\odot$ ) can be recovered up to dynamical ages of $\sim 10$ Gyr. The method works well for most satellites out to a heliocentric distance of 40 kpc., The method works well for most satellites out to a heliocentric distance of $40$ kpc. At larger distances only the brightest and/or dynamically youngest satellites can be recovered., At larger distances only the brightest and/or dynamically youngest satellites can be recovered. Like the original GC3 method our extended version is limited to recovering remnants of satellites of which the orbits are broadly confined to a plane., Like the original GC3 method our extended version is limited to recovering remnants of satellites of which the orbits are broadly confined to a plane. This makes this method well suited for probing the outer halo of our Galaxy where the potential is more nearly spherical or axisymmetric and where dynamical timescales are long., This makes this method well suited for probing the outer halo of our Galaxy where the potential is more nearly spherical or axisymmetric and where dynamical timescales are long. " The mGC3 method thus forms an important complement to the phase space structure characterization methods which will be used in the inner halo, where due to the short dynamical timescales phase space substructures are harder to detect."," The mGC3 method thus forms an important complement to the phase space structure characterization methods which will be used in the inner halo, where due to the short dynamical timescales phase space substructures are harder to detect." In these regions it will be mandatory to use very accurate measurements of integrals of motion employing methods such as those as proposed in Helmi&deZeeuw(2000) and Gómez&Helmi(2010)., In these regions it will be mandatory to use very accurate measurements of integrals of motion employing methods such as those as proposed in \cite{hel00} and \cite{FGomez010}. " In both cases only the use of the highest accuracy parallaxes (relativeerrorsbetterthanabout10percent,seealsoGómezetal.2010) allows the recovery of phase space substructure."," In both cases only the use of the highest accuracy parallaxes \citep[relative errors better than about 10 per cent, see also][]{FGomez010B} allows the recovery of phase space substructure." In contrast the mGC3 method works with 30 per cent accurate parallax data making it suitable for probing larger distances., In contrast the mGC3 method works with $30$ per cent accurate parallax data making it suitable for probing larger distances. The Gaia mission is expected to map the immediate Solar neighbourhood to very high accuracy resulting in some 10 million stars with distances known to better than a few per cent., The Gaia mission is expected to map the immediate Solar neighbourhood to very high accuracy resulting in some 10 million stars with distances known to better than a few per cent. " This will enable a much more accurate calibration of other distance indicators, in particular photometric indicators, which can then be used to extend the mGC3 method also to large samples beyond 40 kpc."," This will enable a much more accurate calibration of other distance indicators, in particular photometric indicators, which can then be used to extend the mGC3 method also to large samples beyond 40 kpc." In addition the Gaia mission will result in a first order smooth dynamical model of the Milky Way Galaxy which can be used to construct an accurate map of the background mGC3 pole count map., In addition the Gaia mission will result in a first order smooth dynamical model of the Milky Way Galaxy which can be used to construct an accurate map of the background mGC3 pole count map. Subtracting a more accurate background map will further enhance the efficiency of the mGC3 method., Subtracting a more accurate background map will further enhance the efficiency of the mGC3 method. We note here two lines of investigation that should be pursued to further investigate and enhance the mGC3 method. (, We note here two lines of investigation that should be pursued to further investigate and enhance the mGC3 method. ( i) The efficiency of the mGC3 method should be explored more extensively by more widely sampling the satellite orbital parameter space.,i) The efficiency of the mGC3 method should be explored more extensively by more widely sampling the satellite orbital parameter space. " More precise limits on the orbital morphologies and dynamical ages, for which satellites remnants can still be recovered, can then be obtained."," More precise limits on the orbital morphologies and dynamical ages, for which satellites remnants can still be recovered, can then be obtained." " In addition, the simulation of the satellites could be made more sophisticated by following the suggestions made in the conclusions of B05. ("," In addition, the simulation of the satellites could be made more sophisticated by following the suggestions made in the conclusions of B05. (" ii) In connection with these studies it is interesting to investigate to what extent the requirement of single peaks in the pole count map for identifying remnants can be relaxed.,ii) In connection with these studies it is interesting to investigate to what extent the requirement of single peaks in the pole count map for identifying remnants can be relaxed. This would enable us to account for the precession of the orbital angular momentum vector and thereby recover a larger fraction of the stellar population of a given disrupted satellite., This would enable us to account for the precession of the orbital angular momentum vector and thereby recover a larger fraction of the stellar population of a given disrupted satellite. A hint of this possibility, A hint of this possibility study we used Z = as found spectroscopically for young stars by Pagel0.004)&Tautvaisiené(1999).,study we used Z = 0.004) as found spectroscopically for young stars by \citet{pagel99}. . An upper age limit was set by the limiting magnitude of the available photometry indicating that clusters that have an MSTO fainter than V=20 mag in the OGLE II field could not be age-dated., An upper age limit was set by the limiting magnitude of the available photometry indicating that clusters that have an MSTO fainter than V=20 mag in the OGLE II field could not be age-dated. C06’s study was restricted to clusters younger than 1 Gyr., C06's study was restricted to clusters younger than 1 Gyr. They derived ages within an age range of 4 Myr and 1 Gyr for clusters covering an area of 2.4 deg? of the SMC main body., They derived ages within an age range of 4 Myr and 1 Gyr for clusters covering an area of 2.4 $^2$ of the SMC main body. 136 of their clusters are also included in our study., 136 of their clusters are also included in our study. In the first panel of Fig., In the first panel of Fig. 4 cluster ages determined in our work are compared to ages presented by C06., \ref{fig:ageallvergleich} cluster ages determined in our work are compared to ages presented by C06. " The ages derived in our work tend to be ~0.2-0.3 in log(age) older than the ages by C06, an offset we anticipated above."," The ages derived in our work tend to be $\sim$ 0.2-0.3 in log(age) older than the ages by C06, an offset we anticipated above." The main reason for the difference is probably the different metallicity of the applied isochrone models as we tested for a subset of CMDs., The main reason for the difference is probably the different metallicity of the applied isochrone models as we tested for a subset of CMDs. " For those clusters with the most significant age deviation large age uncertainties are stated both in their and our work (e.g. BS271, BS272, B114)."," For those clusters with the most significant age deviation large age uncertainties are stated both in their and our work (e.g. BS271, BS272, B114)." The dispersion about the zero line (red solid line) for the sample is Ojog(age) = 0.13., The dispersion about the zero line (red solid line) for the sample is $\sigma_{log(age)}$ = 0.13. " RZ05 derived ages of 204 SMC star clusters using integrated colors, of which 112 clusters are included in our sample."," RZ05 derived ages of 204 SMC star clusters using integrated colors, of which 112 clusters are included in our sample." The second panel of Fig., The second panel of Fig. 4 shows the comparison between our ages and ages adopted by RZO5., \ref{fig:ageallvergleich} shows the comparison between our ages and ages adopted by RZ05. 'The largest deviations are found at the ends of the upper and the lower age limits., The largest deviations are found at the ends of the upper and the lower age limits. A few clusters having ages younger than 25 Myr and older than 1 Gyr show an age deviation of up to 1 Gyr., A few clusters having ages younger than 25 Myr and older than 1 Gyr show an age deviation of up to 1 Gyr. " Stochastic effects on the number of bright stars, uncertainties on the metallicity, dubious cluster membership, and on the adopted stellar models may contribute to the large uncertainties in the conclusion of the cluster age."," Stochastic effects on the number of bright stars, uncertainties on the metallicity, dubious cluster membership, and on the adopted stellar models may contribute to the large uncertainties in the conclusion of the cluster age." RZ05 used a metallicity of Z = 0.004., RZ05 used a metallicity of Z = 0.004. Those clusters with the largest age differences are mostly very sparse objects or objects to which very young isochrones were fitted based on only 2-3 bright stars., Those clusters with the largest age differences are mostly very sparse objects or objects to which very young isochrones were fitted based on only 2-3 bright stars. Large uncertainties for the oldest clusters are caused by large field contamination and unresolved main-sequence turnoff points., Large uncertainties for the oldest clusters are caused by large field contamination and unresolved main-sequence turnoff points. The dispersion about the zero line (red solid line) for the sample is jog(age)=0.3., The dispersion about the zero line (red solid line) for the sample is $\sigma_{log(age)}$ =0.3. " PU99 determined agesfor 93 SMC star clusters from the OGLE catalog (Pietrzynskietal. 1998),, of which"," PU99 determined agesfor 93 SMC star clusters from the OGLE catalog \citep{piet98}, , of which" iu Section 2.3..,in Section \ref{sec:varsel}. The OCLE-TI database 2008a.b))} contains the data for 9 vears (20012009) of continuously monitoring ~35 million objects toward the LAIC., The OGLE-III database ) contains the data for 9 years (2001–2009) of continuously monitoring $\sim$ 35 million objects toward the LMC. We used this database to search for variable objects that are likely quasars based ou the DRW imodel of their light curves (e... 20103).," We used this database to search for variable objects that are likely quasars based on the DRW model of their light curves (e.g., )." We prepared aud analyzed the light curves as described in(2010a)., We prepared and analyzed the light curves as described in. . We use the timescale 7. sealed amplitude a?=26?/rz. aud the likelihood ratio LeperfnLyi between the best fitting model aud a white noise model corresponding to simply expanding he photometric errors.," We use the timescale $\tau$ , scaled amplitude $\hat{\sigma}^2=2\sigma^2/\tau$, and the likelihood ratio $\ln L_{\rm best}/\ln L_{\rm noise}$ between the best fitting model and a white noise model corresponding to simply expanding the photometric errors." We also fit a power-law structure Muction (SE) aud estimated its slope 3 between 30 days and 2 vears. and an amplitude A defined by the uaenitude difference between the first aud third quartile of the sorted lieht curve.," We also fit a power-law structure function (SF) and estimated its slope $\gamma$ between 30 days and 2 years, and an amplitude $A$ defined by the magnitude difference between the first and third quartile of the sorted light curve." To remove mnvanted variable sources. we use the ollowing cuts: The average light curve magnitude is f.<19.5 mae: luLy7InLaon|2: The SF slope 0.1κ5-0.9 (e.g... see 2010)): The [ας amplitude 4<0. limae (this removes large amplitude variable stars): report that some of ~9000 SDSS quasars occupy areas outside the 7 0 cut of(2010a).. therefore we decided to loosen the cut on the 7 parameter aud to ignore σ parameter. so is 1«los(r)5.," To remove unwanted variable sources, we use the following cuts: The average light curve magnitude is $I<19.5$ mag; $\ln L_{\rm best}>\ln L_{\rm noise}+2$; The SF slope $0.1<\gamma<0.9$ (e.g., see ); The $I$ -band amplitude $A<0.4$ mag (this removes large amplitude variable stars); report that some of $\sim$ 9000 SDSS quasars occupy areas outside the $\tau$ $\hat{\sigma}$ cut of, therefore we decided to loosen the cut on the $\tau$ parameter and to ignore $\hat{\sigma}$ parameter, so is $1<\log(\tau)<5$." When simply applied to the OGLE light curve database. this process vields ~21.000 candidates.," When simply applied to the OGLE light curve database, this process yields $\sim 24,000$ candidates." The vast majority are due to two known systematic issues., The vast majority are due to two known systematic issues. First. bright variable stars typically generate several fake. fainter variable stars in their wings. aud these “ghost” variables show loug term regular variability.," First, bright variable stars typically generate several fake, fainter variable stars in their wings, and these “ghost” variables show long term irregular variability." Second. there can be πια magnitude shifts between scasous. aud (for oue field iu particular) the shifts were being misinterpreted as quasar-like variability.," Second, there can be small magnitude shifts between seasons, and (for one field in particular) the shifts were being misinterpreted as quasar-like variability." We carried out a quick visual inspection of all candidates. but this was over kill aud would certainly be automated in any subsequent analysis.," We carried out a quick visual inspection of all candidates, but this was over kill and would certainly be automated in any subsequent analysis." We were left with 1063 variabilitv-sclected candidates., We were left with 1063 variability-selected candidates. The total πο of caneidates is 2121. distributed over ~30 dee? in the LAC.," The total number of candidates is 2434, distributed over $\sim$ 30 $^2$ in the LMC." There are 2019 uiid-IB-selected candidates and 385 nonaukl-IBR-selected candidates., There are 2049 mid-IR-selected candidates and 385 non-mid-IR-selected candidates. Of the 2019. nud-IR (2385. nouaukt-IR) objects. 708 (355) are also variable aud 160 (15) have associated X-ray cuuission.," Of the 2049 mid-IR (385 non-mid-IR) objects, 708 (355) are also variable and 160 (45) have associated X-ray emission." " There are 1063 objects selected as variable. of which 708 are mid-IR sources. 99 are N-rav sources. aud &L both mid-IR and N-ray sources,"," There are 1063 objects selected as variable, of which 708 are mid-IR sources, 99 are X-ray sources, and 84 both mid-IR and X-ray sources." Figure d shows how the samples overlap., Figure \ref{fig:VennCand} shows how the samples overlap. Note that the lamited overlap of the mid-IR aud A-ray-sclected AGNs is also seen in the spectroscopically confined samples of ACNs in the NDWFES field (e.e.. 20113).," Note that the limited overlap of the mid-IR and X-ray-selected AGNs is also seen in the spectroscopically confirmed samples of AGNs in the NDWFS field (e.g., )." The AAOieea fiber allocation software allows to prioritize targets from 1 (the lowest priority) to 9., The AAOmega fiber allocation software allows to prioritize targets from 1 (the lowest priority) to 9. We eave priorities of 9. S. and 7 to sources selected by all three methods (81 sources). sources selected by only two methods (715 sources). aud sources selected by only oue method (1635). respectively.," We gave priorities of 9, 8, and 7 to sources selected by all three methods (84 sources), sources selected by only two methods (715 sources), and sources selected by only one method (1635), respectively." We are mostlv interested iu quasars located im the overlapping areas of the SAGE and OGLE-III surveys., We are mostly interested in quasars located in the overlapping areas of the SAGE and OGLE-III surveys. We divided this LMC area into 12 fields (see Figure 2)). each ~3 dee? and corresponding to the field of view of AAOuucea.," We divided this LMC area into 12 fields (see Figure \ref{fig:MQS_LMC_fields}) ), each $\sim$ 3 $^2$ and corresponding to the field of view of AAOmega." The basic information for cach field is eiveu iu Table 1.., The basic information for each field is given in Table \ref{tab:MQSfields}. The fields overlap slightly to avoid having gaps between them. so some of the quasar candidates were observed up to three times if they happened to fall iuto such an overlapping region.," The fields overlap slightly to avoid having gaps between them, so some of the quasar candidates were observed up to three times if they happened to fall into such an overlapping region." The total πα of targeted objects in all 12 fields was2678. of which several(less than 211)were targeted at least twice.," The total number of targeted objects in all 12 fields was2678, of which several(less than 244)were targeted at least twice." On average there were 220 objects in a field. corresponding to 70 sources," On average there were 220 objects in a field, corresponding to $\sim$ 70 sources" The massive clumps formed in ruus A and D are evidently uot vet BUs.,The massive clumps formed in runs A and B are evidently not yet BHs. To examine the subsequeut dynamics of the chump. we have resimulated the evolution of a typical chuup with higher resolution iu order to reach sanaller spatial scales.," To examine the subsequent dynamics of the clump, we have resimulated the evolution of a typical clump with higher resolution in order to reach smaller spatial scales." We report on this siniulation next., We report on this simulation next. As a representative example. we have selected Run A for initializing the refined simmlation.," As a representative example, we have selected Run A for initializing the refined simulation." We focus on the central region. as shown in Figure Ll. and resample the eas within a radius of 5 pe from the deusity maxima.," We focus on the central region, as shown in Figure 4, and resample the gas within a radius of $\sim 5$ pc from the density maximum." The initial moment of the resampled run is chosen to be somewhat earlier than in Figure Ll. corresponding to 2&10.6. slelitly before a sink particle was created iu the coarse-grain simulation.," The initial moment of the resampled run is chosen to be somewhat earlier than in Figure 4, corresponding to $z\simeq 10.6$, slightly before a sink particle was created in the coarse-grain simulation." " In the resampled region. the baryons comprise a nass of ~6«10737... and are now the dominant component; compared to only ~107AZ. in dark matter,"," In the resampled region, the baryons comprise a mass of $\sim 6\times 10^{5} M_{\odot}$, and are now the dominant component, compared to only $\sim 10^{5}M_{\odot}$ in dark matter." After ~104 vx. we reach the cnd-state of our refined sinulation. at which poiut the Jeans mass again becomes comparable to the resolution limit.," After $\sim 10^{4}$ yr, we reach the end-state of our refined simulation, at which point the Jeans mass again becomes comparable to the resolution limit." The central gas cloud is ina state of free-fall. and we do not sce any sigus of further sub-fraeimenutation.," The central gas cloud is in a state of free-fall, and we do not see any signs of further sub-fragmentation." We lave verified that fraeimoeutation is uot artificially suppressed in the resampling process., We have verified that fragmentation is not artificially suppressed in the resampling process. To this extent. we have carried out a fiducial simulation that docs lead to fragmentation at some poit in the evolution. and a comparison calculation where we resample the fluid fragiucutation occurs.," To this extent, we have carried out a fiducial simulation that does lead to fragmentation at some point in the evolution, and a comparison calculation where we resample the fluid fragmentation occurs." We fund that the resulting fragmentation pattern is very simular in the two cases. as is physically expected.," We find that the resulting fragmentation pattern is very similar in the two cases, as is physically expected." The innermost region. of size <Ü.l pe. comprises iu eas with deusitics iu excess of 10? 7.," The innermost region, of size $\la 0.1$ pc, comprises $\sim 10^{4}M_{\odot}$ in gas with densities in excess of $10^{9}$ $^{-3}$." Tf we were to continue the simulation further im time. the amount of eas residing inside the ceutral ~0.1 pc would rapidly increase.," If we were to continue the simulation further in time, the amount of gas residing inside the central $\sim 0.1$ pc would rapidly increase." Indeed. the mass of the sink particle formedin the large-scale simulation of Run A. of order afew LOPAL... is indicative of the total barvouic mass that will end up in the central compact object.," Indeed, the mass of the sink particle formedin the large-scale simulation of Run A, of order a few $10^{6}M_{\odot}$, is indicative of the total baryonic mass that will end up in the central compact object." At this stage. this object is characterized by a ratio E/|Ew]=0.5. where £4 and EÉ4; are the rotational aud gravitational energies of the central compact object. respectively.," At this stage, this object is characterized by a ratio $E_{\rm rot}/|E_{\rm grav}|\simeq 0.5$, where $E_{\rm rot}$ and $E_{\rm grav}$ are the rotational and gravitational energies of the central compact object, respectively." The aneular momentum present in the central chump must have arisen through torques from the clumpy DM distribution during the relaxation process. as run A has zero initial spin.," The angular momentum present in the central clump must have arisen through torques from the clumpy DM distribution during the relaxation process, as run A has zero initial spin." Again. we plui to revisit this issue in our plauned work on augular momentum trauisport m collapsing DM halos.," Again, we plan to revisit this issue in our planned work on angular momentum transport in collapsing DM halos." The crucial question now is: Tn particular. do we expect the cloud to fraginent. aud eventually form a central stellar cluster?," The crucial question now is: In particular, do we expect the cloud to fragment, and eventually form a central stellar cluster?" " Or else, will fragmentation be inhibited. as in the earlier. large-scale evolution described in the previous section?"," Or else, will fragmentation be inhibited, as in the earlier, large-scale evolution described in the previous section?" Iu the latter case. the additional question arises (Loeb Rasio 1991) whether the gas cloud will continue to collapse directly to a black hole or else settle temporarily iuto a pressure-supported configuration of a supermassive star (see 817 iu Shapiro Teukolskv 1983)?," In the latter case, the additional question arises (Loeb Rasio 1994) whether the gas cloud will continue to collapse directly to a black hole or else settle temporarily into a pressure-supported configuration of a supermassive star (see 17 in Shapiro Teukolsky 1983)?" We can eain iuportaut phnvsical insight iuto these questious bv coluparing three important timescales in the problem. namely: the free-fall time. fg. during which dynamical equilibrimn is established: the cooling time. fo). duiug which the eas iav radiate its thermal energv a8 it contracts and heats to higher temperatures: and the viscous time. fu during which angular mnionieutunàa is transported.," We can gain important physical insight into these questions by comparing three important timescales in the problem, namely: the free-fall time, $t_{\rm ff}$, during which dynamical equilibrium is established; the cooling time, $t_{\rm cool}$, during which the gas may radiate its thermal energy as it contracts and heats to higher temperatures; and the viscous time, $t_{\rm vis}$, during which angular momentum is transported." The cooling time remains relatively short aud allows continued collapse uutil the cloud becomes optically thick to the radiation it produces., The cooling time remains relatively short and allows continued collapse until the cloud becomes optically thick to the radiation it produces. Splerically-sviumeectric calculations indicate that when the particle density iu the contracting sas clump rises above ~101cu 7. the ionization fraction nmereases sharply by 7 orders of," Spherically-symmetric calculations indicate that when the particle density in the contracting gas clump rises above $\sim 10^{17}~{\rm cm^{-3}}$ , the ionization fraction increases sharply by 7 orders of" 2009).,. . In the inner asteroid belt between 2.1 2.8AU. (these would include the 3:1 and 5:2 resonances. currently located at approximately 2.5AU and 2.7AU. respectively.," In the inner asteroid belt between $2.1$ $2.8\AU$, these would include the 3:1 and 5:2 resonances, currently located at approximately $2.5\AU$ and $2.7\AU$, respectively." As shown in Fig., As shown in Fig. 2bb. plausible parameters for the oulwarel migration of Saturn would have allowed the ν lo sweep across the entire inner asteroid belt.," \ref{f:g6vsasat}b b, plausible parameters for the outward migration of Saturn would have allowed the $\nu_6$ to sweep across the entire inner asteroid belt." Therefore the 54 resonance would have been the major excitation mechanism across the 2.1 2.8AU region of the main belt (ancl possibly across the entire main asteroid belt. depending on Saturn's preanigration semimajor axis) during giant planet mieration.," Therefore the $\nu_6$ resonance would have been the major excitation mechanism across the $2.1$ $2.8\AU$ region of the main belt (and possibly across the entire main asteroid belt, depending on Saturn's pre-migration semimajor axis) during giant planet migration." We used the results of our analvtical model to set limits on the rate of migration of Saturn assuming a linear migration profile. with the caveat that many important effects are lgnored. such as asteroid-Jupiter mean motion resonances. and Jupiter-Saturn mean motion resonances (with the exception of the 2:1 resonance).," We used the results of our analytical model to set limits on the rate of migration of Saturn assuming a linear migration profile, with the caveat that many important effects are ignored, such as asteroid-Jupiter mean motion resonances, and Jupiter-Saturn mean motion resonances (with the exception of the 2:1 resonance)." We have confined our analysis io only the region of the main belt spanning 2.1 2.8AU., We have confined our analysis to only the region of the main belt spanning $2.1$ $2.8\AU$. Bevond 2.8AU strong jovian mean molion resonance become more numerous., Beyond $2.8\AU$ strong jovian mean motion resonance become more numerous. Due to the high probabilitv that Che icy planetesimals driving planet migration would be ejected Irom the solar svstem by Jupiter. Jupiter likely migrated inward.," Due to the high probability that the icy planetesimals driving planet migration would be ejected from the solar system by Jupiter, Jupiter likely migrated inward." The migration of Jupiter would have caused strong jovian mean noon resonances (o sweep the asteroid bell. causing additional depletion bevond that of the sweeping z4 resonance (Minton&Malhotra2009)...," The migration of Jupiter would have caused strong jovian mean motion resonances to sweep the asteroid belt, causing additional depletion beyond that of the sweeping $\nu_6$ resonance \citep{Minton:2009p280}." A further complication is thal sweeping jovlan mean motion resonances may have also trapped icy. planetesimals that entered the asteroid belt region from their source region bevond Neptune 2009).., A further complication is that sweeping jovian mean motion resonances may have also trapped icy planetesimals that entered the asteroid belt region from their source region beyond Neptune \citep{Levison:2009p1637}. The effects of these complications are reduced when we consider onlv (he inner asteroid belt., The effects of these complications are reduced when we consider only the inner asteroid belt. From Fig., From Fig. 2bb. we find that the νο would have swept the inner asteroid bell region between 2.1 2.8AU when Saturn was between ~8.5 9.2AU.," \ref{f:g6vsasat}b b, we find that the $\nu_6$ would have swept the inner asteroid belt region between $2.1$ $2.8\AU$ when Saturn was between $\sim8.5$ $9.2\AU$." Therefore the limits on fis Chat we sel using the inner asteroid belt as a constraint. are only applicable for this particular portion of Saturn's migration history., Therefore the limits on $\dot{a}_6$ that we set using the inner asteroid belt as a constraint are only applicable for this particular portion of Saturn's migration history. Our theoretically estimated final eccentricity as a function of initial asteroid semimajor axis and eccentricity is shown in Fig., Our theoretically estimated final eccentricity as a function of initial asteroid semimajor axis and eccentricity is shown in Fig. 6 [or three different adopted migration rates of Saturn., \ref{f:sweepratefigs} for three different adopted migration rates of Saturn. The larger the initial asteroid eccentricities. the wider (he bounds in their final eccentricities.," The larger the initial asteroid eccentricities, the wider the bounds in their final eccentricities." If we adopt the reasonable criterion that an asteroid is lost from the main belt when il achieves a planet-crossing orbit (that is. crossing the orbits of either Jupiter or Mars) and (hat initial asteroid eccentricities were therefore confined to S0.4. then from Fig.," If we adopt the reasonable criterion that an asteroid is lost from the main belt when it achieves a planet-crossing orbit (that is, crossing the orbits of either Jupiter or Mars) and that initial asteroid eccentricities were therefore confined to $\lesssim0.4$, then from Fig." 6 Saturn's migralion rate must have been àgj20.15AUAly© when the vg resonance was sweeping through the inner asteroid belt., \ref{f:sweepratefigs} Saturn's migration rate must have been $\dot{a}_6\gtrsim0.15\AU\My^{-1}$ when the $\nu_6$ resonance was sweeping through the inner asteroid belt. Our results indicate that if Saturns migration rate had been slower than 0.15AUMy.! when it was migrating across ~8.5 9.2AU. then the inner asteroid belt would have been completely swept clear of asteroids by (he 14; resonance.," Our results indicate that if Saturn's migration rate had been slower than $0.15\AU\My^{-1}$ when it was migrating across $\sim8.5$ $9.2\AU$, then the inner asteroid belt would have been completely swept clear of asteroids by the $\nu_6$ resonance." In light of our analvsis and the observed dispersion of eccentricities in the asteroid belt (Fig. 5)).," In light of our analysis and the observed dispersion of eccentricities in the asteroid belt (Fig. \ref{f:MBA-big-dist}) )," we can also immediately conclude that the pre-migration asteroid belt between 2.1 , we can also immediately conclude that the pre-migration asteroid belt between $2.1$ using 7;c0.27 GeV [or the $U(3) deconfinement temperature.,"(T) = = )^4, using $T_c \simeq 0.27$ GeV for the $SU(3)$ deconfinement temperature." The lattice clata are found to decrease much slower and are. as mentioned. in accord with a 1/7? dependence.," The lattice data are found to decrease much slower and are, as mentioned, in accord with a $1/T^2$ dependence." We therefore compare in relbag-delta. the results for 77.NCT) given by the lattice and the bag model forms., We therefore compare in \\ref{bag-delta} the results for $T^2 \Delta(T)$ given by the lattice and the bag model forms. The bag model naturally cannot account for the structure immediately around 7; (the rise to the peak of A(P)). but it also fails in the temperature region above 7...," The bag model naturally cannot account for the structure immediately around $T_c$ (the rise to the peak of $\Delta(T)$ ), but it also fails in the temperature region above $T_c$." Combining the bag model with some form of weak-coupling appproach can somewhat improve the latter. but i( can never reproduce the behavior in the critical region.," Combining the bag model with some form of weak-coupling appproach can somewhat improve the latter, but it can never reproduce the behavior in the critical region." This remains (rue also in various other.conceptually interesting attempts to modify the power of the 7-dependence of A(P) [2224].," This remains true also in various other,conceptually interesting attempts to modify the power of the $T$ -dependence of $\Delta(T)$ \cite{Zwanziger,Rob,Megias}." There (lus remains (he task (o find a non-perturbative approach which takes into account the critical features arising in (he temperature region in (he range above 7). as (μον were obtained in lattice studies.," There thus remains the task to find a non-perturbative approach which takes into account the critical features arising in the temperature region in the range above $T_c$, as they were obtained in lattice studies." We stav in pureSU(3) gauge theory. where. as mentioned. the extrapolation to the continuum limit is known [1]..," We stay in pure$SU(3)$ gauge theory, where, as mentioned, the extrapolation to the continuum limit is known \cite{Boyd}." The basis for our considerations here is (he study of an ideal gas of constituents (“quasi-particles”) having dvnamically or thermally generated masses (25. 27]..," The basis for our considerations here is the study of an ideal gas of constituents (“quasi-particles”) having dynamically or thermally generated masses \cite{Golo93,Peshier,Brau}. ." The behaviour of an ideal gas of such massive gluon modes provides automatically the observed N? scaling and also leads to other features in accord with the functional behaviour found in SU(N) gauge (theories., The behaviour of an ideal gas of such massive gluon modes provides automatically the observed $N_c^2$ scaling and also leads to other features in accord with the functional behaviour found in $SU(N)$ gauge theories. Interpretations of lattice QCD results in ternis of a quasi-parlicle picture have been given innmny versions [0.25 28]..," Interpretations of lattice QCD results in terms of a quasi-particle picture have been given in many versions \cite{Golo93,Peshier,Brau,LH,Gia}. ." ln our approach. asin. [25.21].. we shall include all interaction," In our approach, asin \cite{Golo93,Brau}, , we shall include all interaction" Clusters of galaxies are the most recent bound structures to form in a hierarchical cold dark matter model with a cosmological constant (ACDM).,Clusters of galaxies are the most recent bound structures to form in a hierarchical cold dark matter model with a cosmological constant $\Lambda$ CDM). A precise determination of their mass and shape offer important clues to the understanding of the assembly process of structure in the universe., A precise determination of their mass and shape offer important clues to the understanding of the assembly process of structure in the universe. ;N-body simulations are successful in making detailed theoretical predictions on dark matter halo properties (Navarroetal.1997:Bullock2001:Die-mandetal.2004:Duffy2008:Prada 20113... and lensing measurements are supposed to provide precise and model independent mass measurements.," $N$ -body simulations are successful in making detailed theoretical predictions on dark matter halo properties \citep{nav+al97,bul+al01,die+al04,duf+al08,pra+al11}, and lensing measurements are supposed to provide precise and model independent mass measurements." Whereas the universal Navarro-Freank-White (NFW) density profile (Navarroetal.1996.1997) reproduces many characteristics ofmassive lenses. some puzzling disagreement between the . XCDM theoretical framework and measurements still persists.," Whereas the universal Navarro-Freank-White (NFW) density profile \citep{nfw96,nav+al97} reproduces many characteristics ofmassive lenses, some puzzling disagreement between the $\Lambda$ CDM theoretical framework and measurements still persists." One possible conflict is the detection of extremely large Einstein radii in massive lensing clusters (Broadhurst&Barkana2008:SadehRephaeliOguriBlandford2009:Zitrinetal.201 1a.b).," One possible conflict is the detection of extremely large Einstein radii in massive lensing clusters \citep{br+ba08,sa+re08,og+bl09,zit+al11,zit+al11b}." . Haloes should be to fit the data., Haloes should be over-concentrated to fit the data. Concentrations of massive galaxy clusters are a crucial probe of the mean density of the universe at relatively late. epochs., Concentrations of massive galaxy clusters are a crucial probe of the mean density of the universe at relatively late epochs. The concentration parameter measures the halo central density and should be related to its virial mass. with the concentration decreasing gradually with mass (Bullocketal.2001).," The concentration parameter measures the halo central density and should be related to its virial mass, with the concentration decreasing gradually with mass \citep{bul+al01}." . However. cluster observations have yet to firmly confirm this correlation.," However, cluster observations have yet to firmly confirm this correlation." The observed concentration-mass relation for galaxy clusters has a slope consistent with what found in simulations. though the normalization factor is higher (Comerford&Natarajan2007).," The observed concentration-mass relation for galaxy clusters has a slope consistent with what found in simulations, though the normalization factor is higher \citep{co+na07}." Lensing concentrations appear to be systematically larger than X-ray concentrations (Comerford&Natarajan2007)., Lensing concentrations appear to be systematically larger than X-ray concentrations \citep{co+na07}. .. A similar. though less pronounced. effect is also found in simulations (Hennawietal.2007:Meneghetti 2010)... which show that massive lensing clusters are usually elongated along the line of," A similar, though less pronounced, effect is also found in simulations \citep{hen+al07,men+al10}, , which show that massive lensing clusters are usually elongated along the line of" In Table L. we give the details of planetary orbial constraints used in our Monte Carlo simulations for each binary star we observed. complete with tle separations we measured [or the binaries.,"In Table \ref{tab:binaries}, we give the details of planetary orbital constraints used in our Monte Carlo simulations for each binary star we observed, complete with the separations we measured for the binaries." Note that HD 96061 B is a ¢ose biuary star dn its own right. so planets orbiting it were limited in two ways: the apastron coulc uot be too far out. or tie orbit would be rendered unstable by proximity to HD 96061 A — but the periastrou also could no be too far in. or the binary orbit of HD 96061 Ba aud HD 96061 Bb wouk render it unstable.," Note that HD 96064 B is a close binary star in its own right, so planets orbiting it were limited in two ways: the apastron could not be too far out, or the orbit would be rendered unstable by proximity to HD 96064 A – but the periastron also could not be too far in, or the binary orbit of HD 96064 Ba and HD 96064 Bb would render it unstable." Plajets μονοπαν orbiting HD 96061 Ba or HD 96061 Bb were 1οἱ cousidered in our survey. since o be stable the planets would have to be far too close-in for us to detect trein.," Planets individually orbiting HD 96064 Ba or HD 96064 Bb were not considered in our survey, since to be stable the planets would have to be far too close-in for us to detect them." The constraints described in Table £ account for most of the stars in Table 3.) wit1 few or Dno dletectious reported., The constraints described in Table \ref{tab:binaries} account for most of the stars in Table \ref{tab:sdp} with few or no detections reported. A final question our cdeailecl simulation cau address is how important the AZ band observations were to the survey results., A final question our detailed simulation can address is how important the $M$ band observations were to the survey results. In Table 5.. we show that when AZ band observations were made. (ley cid substantially increase tie uumberof simulated planets cetectect.," In Table \ref{tab:mband}, , we show that when $M$ band observations were made, they did substantially increase the numberof simulated planets detected." voung stars to evolve into supernovae (SN) since these ealaxies are just at the onset of a starburst episode.,young stars to evolve into supernovae (SN) since these galaxies are just at the onset of a starburst episode. Ou the other hand. iu the infrared. dust enussion cau be damped in au optically-thin cuviroument. because the ultraviolet (UV) aud optical light may not be fully reprocessed by the dust. as seen in low huninosity dwarf ealaxies.," On the other hand, in the infrared, dust emission can be damped in an optically-thin environment, because the ultraviolet (UV) and optical light may not be fully reprocessed by the dust, as seen in low luminosity dwarf galaxies." Blue compact dwarf galaxies are a group of extra-ealactic objects that are characterized by their blue optical colors. s32all sizes (<1 kkpe) aud low Iuuinuosities (Mp 7-18).," Blue compact dwarf galaxies are a group of extra-galactic objects that are characterized by their blue optical colors, small sizes $\le$ kpc) and low luminosities $_B>$ -18)." These galaxies do not displav auv ACN and have recent bursts of star formation in a relatively unevolved chemical cuviromment., These galaxies do not display any AGN and have recent bursts of star formation in a relatively unevolved chemical environment. As such they ave been proposed as nearby analogs of star formation in voune galaxies iu the carly universe., As such they have been proposed as nearby analogs of star formation in young galaxies in the early universe. Ta a metal poor environment. star forming regions are usually optically hin and enüt less iu the infrared.," In a metal poor environment, star forming regions are usually optically thin and emit less in the infrared." However. Devereux&Eales(1989) sugsested that in a low lunünositv ealaxy. the radio emission also decreases. aud. probably aster than the infrared.," However, \citet{Devereux89} suggested that in a low luminosity galaxy, the radio emission also decreases, and probably faster than the infrared." The deficiency iu both the nou- hermalracio aud FIR eiissiou may counterbalance cach other aud result in à simular FIR/racdio ratio to the one observed in normal spiral galaxies (Ίναetal.1991)., The deficiency in both the non-thermal radio and FIR emission may counterbalance each other and result in a similar FIR/radio ratio to the one observed in normal spiral galaxies \citep{Klein91}. . This was examined by a study of star formation rates (SERs) iu DCDs performed by Iopkiusetal.(2002).. in which the authors found an excellent aegreeimeut sotween the SFRs estimated from CCGITz aud 60422 muunesitics.," This was examined by a study of star formation rates (SFRs) in BCDs performed by \citet{Hopkins02}, in which the authors found an excellent agreement between the SFRs estimated from GHz and $\mu$ m luminosities." As Bell(2003) has pointed out though. he FIR/radio correlation is almost linear. not because he IR and radio cussion reflect the SERs correctly. mt because in low huuinosity ealaxics they are both uuderestimated by simular factors.," As \citet{Bell03} has pointed out though, the FIR/radio correlation is almost linear, not because the IR and radio emission reflect the SFRs correctly, but because in low luminosity galaxies they are both underestimated by similar factors." " This is iu agrecimeut with Helou&Bicav(1993).. who found from their nodelling work iu disk galaxies that the trausparcucy of the disk was about the same to both re-enüssion xocesses,"," This is in agreement with \citet{Helou93}, who found from their modelling work in disk galaxies that the transparency of the disk was about the same to both re-emission processes." Tutetal.(20053). in their analysis of the spectral energy distributions (SEDs) of low imiectallicity DCDs. noticed that these systems do not follow several of the usual correlations between the mid-IR. FIR aud radio cluission and display a scatter of a factor of —10.," \citet{Hunt05a} in their analysis of the spectral energy distributions (SEDs) of low metallicity BCDs, noticed that these systems do not follow several of the usual correlations between the mid-IR, FIR and radio emission and display a scatter of a factor of $\sim$ 10." TheSpitzer Space telescope has enabled us to study the infrared properties of a laree sample of DCDs. probing the lower cud of the hunuinositv aud metallicity range.," The Space telescope has enabled us to study the infrared properties of a large sample of BCDs, probing the lower end of the luminosity and metallicity range." Iu this paper. the fifth in a seres (IIouckal.200Lb:Wuetal.2006. 2007a.b).. we examine their mid-IR and FIR to radio correlation extending the work of IIopkiusetal.(2002).," In this paper, the fifth in a series \citep{Houck04b,Wu06,Wu07a,Wu07b}, we examine their mid-IR and FIR to radio correlation extending the work of \citet{Hopkins02}." .. We ceseribe the sample sclectiou and the observational data in 82., We describe the sample selection and the observational data in 2. A detailed study of mud-IB and FIR/ractio correlation. as well as its dependence with other parameters. such as metallicity and dust temperature are presented in 83.," A detailed study of mid-IR and FIR/radio correlation, as well as its dependence with other parameters, such as metallicity and dust temperature are presented in 3." We also discuss two extreme cases. [Zwls and SBS0335-052 in 83.," We also discuss two extreme cases, IZw18 and SBS0335-052 in 3." We stuumarize our conclusions iu 841., We summarize our conclusions in 4. As part of tho (IToucketal.2001a). Corarautecd Time Observation (CTO) program (PID: 55). we have compiled a sample of BCD caudidates (~61) selected rom the Second Byurakan Survey (SBS). Bootes void ealaxies (Nirshuecretal.1981:Popescu&Topp2000).. and other commoulv studied BCDs.," As part of the \citep{Houck04a} Guaranteed Time Observation (GTO) program (PID: 85), we have compiled a sample of BCD candidates $\sim$ 64) selected from the Second Byurakan Survey (SBS), Bootes void galaxies \citep{Kirshner81,Popescu00}, and other commonly studied BCDs." " These sources are shown to have low metallicities rangiug from , o 0.5ZZ.""..", These sources are known to have low metallicities ranging from $_\odot$ to $_\odot$. " Their 22,22 fluxes have been. published in Wuetal.(2006).", Their $\mu$ m fluxes have been published in \citet{Wu06}. . We also inchide 10 galaxies roni Eugelbrachtetal.(2005) (PID: 59). which/ are nostly BCDs aud starburst galaxies. aud span a larger uetallicity range ZZ.~ ZZ.)..," We also include 10 galaxies from \citet{Engelbracht05} (PID: 59), which are mostly BCDs and starburst galaxies, and span a larger metallicity range $_\odot$$\sim$ $_\odot$." For all galaxies with gan detections. we searched the literature as well as the public archives C(NVSS and FIRST) for 1.1CGIIz radio coutimmun data.," For all galaxies with $\mu$ m detections, we searched the literature as well as the public archives (NVSS and FIRST) for 1.4GHz radio continuum data." We restirct our sample ο sources with both mid-IR and radio detections which results in a sample of 23 galaxies., We restirct our sample to sources with both mid-IR and radio detections which results in a sample of 23 galaxies. Finally. we also include 5 galaxics that have jan detections aud GCIIz upper LHmits published bv IHopkius et al. (," Finally, we also include 5 galaxies that have $\mu$ m detections and GHz upper limits published by Hopkins et al. (" 2002) for conrparison between ours and Hopkins samples.,2002) for comparison between ours and Hopkins' samples. Note that the sample was not selected. based on diufrare properties. but merelv on DCD-tvpe objects aud the availability of both infrared aud radio data.," Note that the sample was not selected based on infrared properties, but merely on BCD-type objects and the availability of both infrared and radio data." As a result. our sanple is not complete. but the large nunuber of sources that only became detectable iu the iufrare withSpitzer allows us to probe the properties of ow luninositv dwarf galaxies. aud provide statistically ueanineful results.," As a result, our sample is not complete, but the large number of sources that only became detectable in the infrared with, allows us to probe the properties of low luminosity dwarf galaxies, and provide statistically meaningful results." The observational information for his suuple aud previously published data are presentcc in Table 1.. which iucludes the positious of the sources. heir mid-IR. FIR aud 1.1CIIzfux densities. as well as oxveen abundances of the ionized eas.," The observational information for this sample and previously published data are presented in Table \ref{tab1}, which includes the positions of the sources, their mid-IR, FIR and 1.4GHzflux densities, as well as oxygen abundances of the ionized gas." All sources in this study have uud-IR fux neasurements cither at 22¢an with the IRS red )ea-up camera and/or at 214440 with MIPS (Rickeetal.2001)., All sources in this study have mid-IR flux measurements either at $\mu$ m with the IRS red peak-up camera and/or at $\mu$ m with MIPS \citep{Rieke04}. .. The photometric fluxes of these two bands differ by less than for galaxies in the local universe., The photometric fluxes of these two bands differ by less than for galaxies in the local universe. This was confirmed by using a suite of —100 spectra of nearby galaxies frou our IRS/CTO database and calculating thei svuthetic 22 and {μαι fluxes after convolving the spectra with the correspouding filter response curves., This was confirmed by using a suite of $\sim$ 100 spectra of nearby galaxies from our IRS/GTO database and calculating their synthetic 22 and $\mu$ m fluxes after convolving the spectra with the corresponding filter response curves. " For consistency. in our analvsis we use the MIPS 21,422. measurements. and the jan values are only used when the 21;240 values are not available."," For consistency, in our analysis we use the MIPS $\mu$ m measurements, and the $\mu$ m values are only used when the $\mu$ m values are not available." For sources above the IRS 22;au aud MIPS lynn saturation limits we use the IRS low resolution spectrum to estimate a svuthetic {μαι flux., For sources above the IRS $\mu$ m and MIPS $\mu$ m saturation limits we use the IRS low resolution spectrum to estimate a synthetic $\mu$ m flux. We also obtained fu-iufrared fluxes for our sample from the archival[RAS 60 and 100440 data (Moshir&otal.1990:Sandersetal. 2003).," We also obtained far-infrared fluxes for our sample from the archival 60 and $\mu$ m data \citep{Moshir90, Sanders03}." . Most of the CGIIz radio coutimmun data are from the NRAO VLA Skv Survev (NVSS) (Condon 1998).. while one is from the Faint huages of the Badio Sky at Tweuty cii (FIRST) (Beckeretal. 1995).. along with some individual obscrvatious (references in Table 11).," Most of the GHz radio continuum data are from the NRAO VLA Sky Survey (NVSS) \citep{Condon98}, while one is from the Faint Images of the Radio Sky at Twenty cm (FIRST) \citep{Becker95}, , along with some individual observations (references in Table \ref{tab1}) )." A total of seven sources were too faint aud were rot included in the NVSS catalogue., A total of seven sources were too faint and were not included in the NVSS catalogue. For those we used he values of Hopkinsetal.(2002) who studied a, For those we used the values of \citet{Hopkins02} who studied a evaporation of embedded clouds.,evaporation of embedded clouds. Paper I coufiiiied. that Inass Injection can stronglv iufluence reninant evolution. and we also establish. here that the of the 1üass injection process is also nmuportaut in this regard.," Paper I confirmed that mass injection can strongly influence remnant evolution, and we also establish here that the of the mass injection process is also important in this regard." This is due to the fact that mass loadiug through conductive evaporation is extinguished at relatively carly times., This is due to the fact that mass loading through conductive evaporation is extinguished at relatively early times. Hence. conductively driven mass loading does not appreciably alter the later stages of reminant evolution. when the remnant is dominated by swept up ambicut eas.," Hence, conductively driven mass loading does not appreciably alter the later stages of remnant evolution, when the remnant is dominated by swept up ambient gas." Therefore remuauts that ablatively mass load are dominated by loaded mass aud thermal energy at late times (Paper D. while those that couductively mass load are douunated by swept-up mass and kinetic enerev.," Therefore remnants that ablatively mass load are dominated by loaded mass and thermal energy at late times (Paper I), while those that conductively mass load are dominated by swept-up mass and kinetic energy." The ereater donunance of loaded mass in the ablative case nieans that such remnants evolve more quickly. aud reach all dynamical stages earlier.," The greater dominance of loaded mass in the ablative case means that such remnants evolve more quickly, and reach all dynamical stages earlier." At a given age they tend to be both more massive aud sialler than equivalent remuants which are couductively mass loaded., At a given age they tend to be both more massive and smaller than equivalent remnants which are conductively mass loaded. We are able. to ΟΠΗ some of the properties of couductively mass loaded remiuants predicted frou seltEsnailar solutions. aud iu particulary find that such ronunants may displav a thick-shell iiorphologw the lydrodvuamiic results presented in Cowie1981 aud the similarity solutions presented im Dyson Iartquist LOST )).," We are able to confirm some of the properties of conductively mass loaded remnants predicted from self-similar solutions, and in particular find that such remnants may display a thick-shell morphology the hydrodynamic results presented in Cowie\cite{CMO1981} and the similarity solutions presented in Dyson Hartquist \cite{DH1987}) )." Iu this work we have been particularly iuterested in the ranece of conductively mass loaded supernova renimauts at the time at which they have radiated away half of their initial cucrey (see Table 2))., In this work we have been particularly interested in the range of conductively mass loaded supernova remnants at the time at which they have radiated away half of their initial energy (see Table \ref{tab:rad_qst}) ). It was noted in Sec., It was noted in Sec. that Ε mav be dependent on vy., \ref{sec:calcs} that $f'$ may be dependent on $n_{0}$ . This behaviour would, This behaviour would "of MI increase toward higher longitudes and lower latitudes, connecting with MIII whose velocities increase toward lower longitudes and higher latitudes (Fig. 1;;","of MI increase toward higher longitudes and lower latitudes, connecting with MIII whose velocities increase toward lower longitudes and higher latitudes (Fig. \ref{fig:map};" also see Fig., also see Fig. 5 in Wakker 2001))., 5 in \citealt{wak01}) ). " Thus, the sight line likely probes the high velocity end of Complex M. The HVC along the Mrk 421 sight line has been suggested inL,Cu,, and aabsorption lines in the FUSE spectrum."," Thus, the sight line likely probes the high velocity end of Complex M. The HVC along the Mrk 421 sight line has been suggested in, and absorption lines in the spectrum." " Savageetal.(2005) measured a surprisingly large value, Nj=4.862x1018cm? (logNui=18.68+ 0.38) in a component fit to the saturated LLyman lines Ly£—-Lyó, nearly 70 times higher than that (Table 1)) obtained in this work."," \citet{sav05} measured a surprisingly large value, $N_{\rm HI}^{(\rm HVC)} = 4.8^{+6.9}_{-2.8}\times10^{18}~{\rm cm^{-2}}$ $\log N_{\rm HI} = 18.68\pm0.38$ ) in a component fit to the saturated Lyman lines $\beta-$ $\delta$, nearly 70 times higher than that (Table \ref{tab:results}) ) obtained in this work." " To examine possible causes of this discrepancy, we superpose the amount of the four velocity components revealed from the Green Bank observation (Savageetal.2005) on the aabsorption spectra (Fig."," To examine possible causes of this discrepancy, we superpose the amount of the four velocity components revealed from the Green Bank observation \citep{sav05} on the absorption spectra (Fig." 3gg-i)., \ref{fig:MRKb}g g-i). " Clearly, only the blue wing of the IVC at —60kms affects the MV determination."," Clearly, only the blue wing of the IVC at $-60~{\rm km~s^{-1}}$ affects the $N_{\rm HI}^{(\rm HVC)}$ determination." " To further examine possible effects of beam smearing, we extracted the LAB emission data within 1° around the Mrk 421 sight line."," To further examine possible effects of beam smearing, we extracted the LAB emission data within $1^\circ$ around the Mrk 421 sight line." " Unlike the other three emission components, whose brightness temperatures can vary by factor of five, O increases smoothly toward large longitudesa and high NÀYlatitudes, with fluctuations ANY/(NGY)z10% the four beams closest to the Mrk 421 sight line."," Unlike the other three emission components, whose brightness temperatures can vary by a factor of five, $N_{\rm HI}^{(\rm IVC)}$ increases smoothly toward large longitudes and high latitudes, with fluctuations $\Delta N_{\rm HI}^{(\rm IVC)} / \langle N_{\rm HI}^{(\rm IVC)} \rangle \lsim 10\%$ among the four beams closest to the Mrk 421 sight line." " Taking amongthis variation into account in our analysis, we find that the change in NONO is negligible to that caused by the systematic uncertainty of the comparedwavelength calibration."," Taking this variation into account in our analysis, we find that the change in $N_{\rm HI}^{(\rm HVC)}$ is negligible compared to that caused by the systematic uncertainty of the wavelength calibration." " We conclude that our result is not affected by beam smearing, although we cannot completely rule out variations of the IVC absorption on angular scales «10 arcmin, which could significantly change our results."," We conclude that our result is not affected by beam smearing, although we cannot completely rule out variations of the IVC absorption on angular scales $<10$ arcmin, which could significantly change our results." We speculate that the apparently large NONO obtained by Savage et al. (, We speculate that the apparently large $N_{\rm HI}^{(\rm HVC)}$ obtained by Savage et al. ( 2005) is caused by the severely underestimated Nayo in their fit.,2005) is caused by the severely underestimated $N_{\rm HI}^{(\rm IVC)}$ in their fit. The measured NONO and NONO give a metallicity in the HVC along the Mrk 421 sight line of [O/H]= or 0.85-3.5 Zo., The measured $N_{\rm OI}^{(\rm HVC)}$ and $N_{\rm HI}^{(\rm HVC)}$ give a metallicity in the HVC along the Mrk 421 sight line of $=0.32^{+0.22}_{-0.39}$ or 0.85–3.5 $Z_\odot$. The large uncertainty is caused by 0.327022systematic in the wavelength calibration introduced in our joint uncertaintyanalysis of the LLyman series 3))., The large uncertainty is caused by systematic uncertainty in the wavelength calibration introduced in our joint analysis of the Lyman series \ref{sec:results}) ). " Because aand hhave nearly the same ionization and are coupled by resonant charge exchange, this potentialmeasurement accurately reflects the gas-phase oxygen abundance and is not subject to ionization⋅∙∙ correction."," Because and have nearly the same ionization potential and are coupled by resonant charge exchange, this measurement accurately reflects the gas-phase oxygen abundance and is not subject to ionization correction." "⋅ In measuring⋅ (HVC)Nyy”, we assumed by?=/v2. and puo-YO and adopted the local-ISM deuterium abundance, (D/H) = 1.6x102, one of the lowest interstellar abundances (Robertetal. 2000))."," In measuring $N_{\rm HI}^{(\rm HVC)}$, we assumed $b_{\rm DI}^{(\rm IVC)} = b_{\rm HI}^{(\rm IVC)}/\sqrt2$ and $b_{\rm HI}^{(\rm HVC)} = b_{\rm SiII}^{(\rm HVC)}$ and adopted the local-ISM deuterium abundance, (D/H) = $1.6\times10^{-5}$, one of the lowest interstellar abundances \citealt{rob00}) )." Adopting higher values of for D/H or bp; will result in a smaller , Adopting higher values of for D/H or $b_{\rm DI}$ will result in a smaller $N_{\rm HI}^{(\rm HVC)}$. "Therefore the inferred oxygen abundance should be Ngo,regarded as a conservative lower limit.", Therefore the inferred oxygen abundance should be regarded as a conservative lower limit. " Ionization corrections need to be applied in calculating the abundances of Si, S, or Fe."," Ionization corrections need to be applied in calculating the abundances of Si, S, or Fe." " For a photoionized plasma with hydrogen number density ny=0.1cm? and ΊοσΝμι€17.5, the (logarithmic) ionization corrections are 1.30, 1.42, and 0.90 fori,r1, and iL, respectively (Mark Giroux, private communication, 2010)."," For a photoionized plasma with hydrogen number density $n_{\rm H}=0.1~{\rm cm^{-3}}$ and $\log N_{\rm HI}\le17.5$, the (logarithmic) ionization corrections are 1.30, 1.42, and 0.90 for, and , respectively (Mark Giroux, private communication, 2010)." " Taking the best-fit values (Table 1)), we obtain —0.6, «0.22, and 0.07 for Si, S, and Fe."," Taking the best-fit values (Table \ref{tab:results}) ), we obtain $=-0.6$ , $<0.22$, and $0.07$ for Si, S, and Fe." " Owing to the unconstrained ny, the systematic uncertainty could be high in the inferred [Si/H], [S/H], and [Fe/H]."," Owing to the unconstrained $n_{\rm H}$ , the systematic uncertainty could be high in the inferred [Si/H], [S/H], and [Fe/H]." " However, this exercise results in consistently high metal abundances, except for a slightly lower value for Si."," However, this exercise results in consistently high metal abundances, except for a slightly lower value for Si." " Within uncertainties, the high metallicity is consistent with values 0.4-1.8 Zo in MI (Wakker2001),, >0.5Zs in MIII (Ryansetal.1997),, and the near-solar metallicity of [V3 (Spitzer&Fitzpatrick1993)."," Within uncertainties, the high metallicity is consistent with values 0.4–1.8 $Z_\odot$ in MI \citep{wak01}, $>0.5~Z_\odot$ in MIII \citep{rya97}, and the near-solar metallicity of IV3 \citep{spi93}." . The consistency also suggests that the HVC toward Mrk 421 is associated with Complex M and the lower velocity IV Arch., The consistency also suggests that the HVC toward Mrk 421 is associated with Complex M and the lower velocity IV Arch. " The measured oxygen abundance provides a new lower limit to the metallicity of Complex M. The high metallicity, together with the upper limit on distance of other parts of M, shed light on its origin."," The measured oxygen abundance provides a new lower limit to the metallicity of Complex M. The high metallicity, together with the upper limit on distance of other parts of Complex M, shed light on its origin." " Unlike the highly ionizedComplex HVCs, in which the high ions aand ΙΝ)) are significant or even dominant, the HVC toward Mrk 421C is dominated by low ionsL,i,11;; Table 1))."," Unlike the highly ionized HVCs, in which the high ions and ) are significant or even dominant, the HVC toward Mrk 421 is dominated by low ions,; Table \ref{tab:results}) )." " This suggests distinct ionization conditions of this HVC compared to the highly ionized, low ccolumn density HVCs (Sembachetal.2003;Collins2004,2005;Foxetal.2006;Lehner&Howk 2010))."," This suggests distinct ionization conditions of this HVC compared to the highly ionized, low column density HVCs \citealt{sem03, col04, col05, fox06, leh10}) )." " Such mildly ionized, low ccolumn density HVCs have recently been surveyed by several groups (e.g., Richteretal.2009;ShullCollinsetal. 2009))."," Such mildly ionized, low column density HVCs have recently been surveyed by several groups (e.g., \citealt{ric09, shu09, col09}) )." Richter et al. (, Richter et al. ( 2009) also provided ionization modeling for the HVCs with different distances.,2009) also provided ionization modeling for the HVCs with different distances. " Substituting NHVO and NOT? (Table 1)) into their model and assuming no depletion of Si into dust grains, we obtain a gas density nj—3.4cm? and absorption path length L=0.007—0.02 pc for Complex M. The near-solar (likely supersolar) abundance, short path length, and large gas density clearly rule out the WHIM model and disfavor the halo model 1)) for the HVC."," Substituting $N_{\rm OI}^{(\rm HVC)}$ and $N_{\rm SiII}^{(\rm HVC)}$ (Table \ref{tab:results}) ) into their model and assuming no depletion of Si into dust grains, we obtain a gas density $n_{\rm H}=3.4~{\rm cm^{-3}}$ and absorption path length $L=0.007-0.02$ pc for Complex M. The near-solar (likely supersolar) abundance, short path length, and large gas density clearly rule out the WHIM model and disfavor the halo model \ref{sec:intro}) ) for the HVC." Complex M likely traces a supernova shell that has not been ejected too far above the Galactic plane and is now falling back to the Galactic disk., Complex M likely traces a supernova shell that has not been ejected too far above the Galactic plane and is now falling back to the Galactic disk. " In summary, we have presented an interstellar high velocity cloud detected in ultraviolet spectroscopic observations of Mrk 421, which represents the highest velocity end of the HVC Complex M. The combination of HST-COS andFUSE observations enables us to obtain a lower limit, >0.85Zo, to the metallicity of the Complex."," In summary, we have presented an interstellar high velocity cloud detected in ultraviolet spectroscopic observations of Mrk 421, which represents the highest velocity end of the HVC Complex M. The combination of -COS and observations enables us to obtain a lower limit, $>0.85~Z_\odot$, to the metallicity of the Complex." The high metallicity and the short distance are consistent with Complex M being the returning gas of a Galactic fountain., The high metallicity and the short distance are consistent with Complex M being the returning gas of a Galactic fountain. The authors have benefited from the discussions with Nicolas Lehner and comments from an anonymous referee., The authors have benefited from the discussions with Nicolas Lehner and comments from an anonymous referee. " This work at the University of Colorado was partly supported by NASA grant NNXO8AC14G for data analysis and scientific discoveries related to the Cosmic Origins Spectrograph on the Hubble Space Telescope, and byNNX07AGT7G for theoretical work (JMS)."," This work at the University of Colorado was partly supported by NASA grant NNX08AC14G for data analysis and scientific discoveries related to the Cosmic Origins Spectrograph on the Hubble Space Telescope, and byNNX07AG77G for theoretical work (JMS)." YY also appreciates financial support byNASA through ADP grant NNXIOAES6G., YY also appreciates financial support byNASA through ADP grant NNX10AE86G. were obianed lor the WD plus belt composite model (models 12 13).,were obtained for the WD plus belt composite model (models 12 13). The reason the fit is better is (hat the belt. with its high temperature. accounts for the flux shortward of 950 A(where the WD does not contribute). and its high rotational velocity matches better the rather featureless spectrum of the second component.," The reason the fit is better is that the belt, with its high temperature, accounts for the flux shortward of 950 (where the WD does not contribute), and its high rotational velocity matches better the rather featureless spectrum of the second component." Model LO (WD plus disk) has a \2HH. however its WD mass is too large M;=1.21 and the inclination is too high at i = 81 degrees. therefore it can be ruled out.," Model 10 (WD plus disk) has a $\chi^2_{\nu} \approx 11$, however its WD mass is too large $M_{wd}=1.21$ and the inclination is too high at i = 81 degrees, therefore it can be ruled out." " However. its relatively low 42 might be due to the fact that the hot inner disk is the main component in the FUV with (Table 2 in (1998))) a rotational velocity Vi,sinizz5.000km ! and a peak temperature Tong»8230. 00019. The main observational result in (Bis work is the confinmation that theFUSE spectrum of VW Lyi in quiescence cannot be modeled as a single WD temperature. and (hat at least (wo components are needed in (he modeling of the data."," However, its relatively low $\chi^2_{\nu}$ might be due to the fact that the hot inner disk is the main component in the FUV with (Table 2 in \citet{wad98}) ) a rotational velocity $V_{rot} \sin{i}\approx 5,000$ km $^{-1}$ and a peak temperature $T_{max}\approx 30,000$ K. The main observational result in this work is the confirmation that the spectrum of VW Hyi in quiescence cannot be modeled as a single WD temperature, and that at least two components are needed in the modeling of the data." The dominant component is that of a 23. 000Ix. WD. while the second component is some kind of true featureless continuum wilh a color temperature that is higher than that of the WD.," The dominant component is that of a $23,000$ K WD, while the second component is some kind of true featureless continuum with a color temperature that is higher than that of the WD." It is possible that the (wo components exist only in the modeling of the FUV data and not in VW Ενα itself. lor example if the WD is not heated homogeneously then we would have one component with a continuous range of temperatures that contribute to the spectrum.," It is possible that the two components exist only in the modeling of the FUV data and not in VW Hyi itself, for example if the WD is not heated homogeneously then we would have one component with a continuous range of temperatures that contribute to the spectrum." VW να has been previously observed. mainly during quiescence. following normal (3 days) outburst aid superoutburst (about 2 weeks).," VW Hyi has been previously observed mainly during quiescence, following normal (3 days) outburst and superoutburst (about 2 weeks)." From an IUE archival study. (1996) assessed that the WD cools down exponentially to a mean temperature Tyg52 19.0004. with an exponential decay (me of &3 clavs after normal oulburst and es10 davs alter superoutburst.," From an IUE archival study, \citet{gan96} assessed that the WD cools down exponentially to a mean temperature $T_{wd} \approx 19,000K$ , with an exponential decay time of $\approx 3$ days after normal outburst and $\approx 10$ days after superoutburst." From this archival data alone it appears that the maximum temperature the WD reaches is about. 23.000]. just after the end of a normal outburst aud about 26.000Ix. just alter the end of a superoutburst.," From this archival data alone it appears that the maximum temperature the WD reaches is about 23,000K, just after the end of a normal outburst and about 26,000K just after the end of a superoutburst." In Table 3 we recapitulate (he recent observations of WW Ilvi with different instruments., In Table 3 we recapitulate the recent observations of VW Hyi with different instruments. Most of the temperature estimates for the accreting WD are in the range described in Gansicke&Beuermann(1996)., Most of the temperature estimates for the accreting WD are in the range described in \citet{gan96}. . In the present work. the best fitGne model to theFUSE data is a combination of a WD plus an accretion bell. which is noticeably better than the WD alone or the disk models.," In the present work, the best fitting model to the data is a combination of a WD plus an accretion belt, which is noticeably better than the WD alone or the disk models." These two components to the spectrum of VW ναin quiescence help to resolve, These two components to the spectrum of VW Hyiin quiescence help to resolve often have nearly constant amplitudes and may have high fractional mocdulations (see. e.g. 1996 Oct 12).,"often have nearly constant amplitudes and may have high fractional modulations (see, e.g., 1996 Oct 12)." 2., 2. The source seems to have ‘active’ ancl passive periods. with abrupt changes of state between the two.," The source seems to have `active' and `passive' periods, with abrupt changes of state between the two." The most prominent example is the sequence of 4 observations on 1996 May 23. 26 which showed strong QPO activity. bu which were surrounded by long passive periods.," The most prominent example is the sequence of 4 observations on 1996 May 23 – 26 which showed strong QPO activity, but which were surrounded by long passive periods." The abrup changes sometimes last for about 1 day (c.g. 1996 Sep - Nov. see Fig.," The abrupt changes sometimes last for about 1 day (e.g. 1996 Sep - Nov, see Fig." 4). and in a few cases the change has been recordec (1996 Sep 16 and 17).," 4), and in a few cases the change has been recorded (1996 Sep 16 and 17)." 3., 3. Phe event of 1996. Alay 24 was observe simultaneously with the VLBA at 8.3 Giz., The event of 1996 May 24 was observed simultaneously with the VLBA at 8.3 GHz. The two sets of data. over the 2 hours of overlap (limited by the longitude difference between the instruments). are plotted. in Fig.," The two sets of data, over the 2 hours of overlap (limited by the longitude difference between the instruments), are plotted in Fig." 3., 3. There is a delay. in the sense that the 195-111 data leac the 8.3-Gllz. of about 40 5 minutes (based on a subjective estimate of the best Lt when sliding one relative to the other).," There is a delay, in the sense that the 15-GHz data lead the 8.3-GHz, of about 4 – 5 minutes (based on a subjective estimate of the best fit when sliding one relative to the other)." Phere are also substantial changes in spectral index. as can be seen from an inspection of Fig.," There are also substantial changes in spectral index, as can be seen from an inspection of Fig." 3., 3. The Ilux density observed by the VLBA at 2.3 CGLIz during the same run was nearly constant. a result consistent with a model in which ower-Irequeney emission comes from a Larger photosphere. esumably determined. by optical-cdepth elfects. anc with hese emission regions being excited with dillering delays.," The flux density observed by the VLBA at 2.3 GHz during the same run was nearly constant, a result consistent with a model in which lower-frequency emission comes from a larger photosphere, presumably determined by optical-depth effects, and with these emission regions being excited with differing delays." For frequencies where the photosphere exceeds. 10 or 20 ight-minutes in size. only slow variations would be seen.," For frequencies where the photosphere exceeds 10 or 20 light-minutes in size, only slow variations would be seen." The increase in the amplitude of variations with increasing requencey is confirmed. hy inspection of the 2 Cillz data from the Creenbank interferometer for the Iare in 1995 Aue (Foster et al., The increase in the amplitude of variations with increasing frequency is confirmed by inspection of the 2.25 and 8.3-GHz data from the Greenbank interferometer for the flare in 1995 Aug (Foster et al. 1996: see their Pie., 1996: see their Fig. 3)., 3). Our 15-Cillz data on 1995 Aug 11 (Fig., Our 15-GHz data on 1995 Aug 11 (Fig. 2). which have only a very short overlap with the Greenbank data. show larger variations.," 2), which have only a very short overlap with the Greenbank data, show larger variations." The 1996 May 24 event is the only one for which cual-frequeney data are available: the IUE is a single-frequenevy instrument. and the unpredietability of the source makes it difficult to repeat the observation — but we regard. this as important.," The 1996 May 24 event is the only one for which dual-frequency data are available; the RT is a single-frequency instrument, and the unpredictability of the source makes it difficult to repeat the observation – but we regard this as important." As a first attempt to consider the X-rayradio correlations. we have used. the ‘quick-look’ data from theTE ASAL experiment. which give integrated. count-rates over the 2 - 10 keV. band.," As a first attempt to consider the X-ray/radio correlations, we have used the `quick-look' data from the ASM experiment, which give integrated count-rates over the 2 - 10 keV band." Fie., Fig. 4 shows the SM and 15-Cllz data plotted over he same time ranges. from. 1996 Feb 23. when the major xwt of the ASM dataset starts.," 4 shows the ASM and 15-GHz data plotted over the same time ranges, from 1996 Feb 23, when the major part of the ASM dataset starts." The relationship is complex. and changes through the »riod of the observations.," The relationship is complex, and changes through the period of the observations." ALID 50185 50220: varving degrees of X-ray activity are displaved., MJD 50135 – 50220: varying degrees of X-ray activity are displayed. No significant radio emission was detected (although the coverage was rather sparse) apart from one event on MJD 50146. when a l0-mJv event lasting only 10 minutes was observed.," No significant radio emission was detected (although the coverage was rather sparse) apart from one event on MJD 50146, when a 10-mJy event lasting only 10 minutes was observed." " ""This occured. during a period. of somewhat enhanced X-ray activity.", This occured during a period of somewhat enhanced X-ray activity. ALJD 50226 | 50229 (1996 Alay ον 26): raclio emission was observed. on cach of these 4 days (all are displayed. in Fig., MJD 50226 – 50229 (1996 May 23 – 26): radio emission was observed on each of these 4 days (all are displayed in Fig. 2)., 2). Fhev had been preceded: by 5 days. of enhanced X-ray actvitv: the X-ray emission during the radio Hare was lower on average than in the preceding cays. but still appears highly. variable.," They had been preceded by 5 days of enhanced X-ray actvity: the X-ray emission during the radio flare was lower on average than in the preceding days, but still appears highly variable." AIJD 50251 — 50260: a minor radio flare. about 20 milv. which was also associated with a fall in an otherwise active A-rayv state.," MJD 50251 – 50260: a minor radio flare, about 20 mJy, which was also associated with a fall in an otherwise active X-ray state." ALID 50275 - 50310: a major radio llare. with no detected QPOs.," MJD 50275 - 50310: a major radio flare, with no detected QPOs." The examples of the smooth variation of emission shown in Fig., The examples of the smooth variation of emission shown in Fig. 2 during this Hare are typical., 2 during this flare are typical. Εις [are was observed at a number of radio observatories: results will be presented elsewhere., This flare was observed at a number of radio observatories; results will be presented elsewhere. Shortlv after the start of the racio Hare. the X-ray emission became very steady.," Shortly after the start of the radio flare, the X-ray emission became very steady." ALJD 50310 50340: the radio Uare faced (but. not monotonically)., MJD 50310 – 50340: the radio flare faded (but not monotonically). QPOs detected. on ALJD 50329 (Fig., QPOs detected on MJD 50329 (Fig. 2). y>," 2), 50335." ALJD 50340 — 50410: strong QPOs observed on most days. but with interspersed periods of barely detectable Dux density.," MJD 50340 – 50410: strong QPOs observed on most days, but with interspersed periods of barely detectable flux density." See Fig., See Fig. 2 for examples., 2 for examples. ALJD 50411 — 50450: the N-rav. [lux fell to low levels at approximately the same time as the radio., MJD 50411 – 50450: the X-ray flux fell to low levels at approximately the same time as the radio. Phere was almost no detectable radio emission. apart from one clay (ΔΩ 50439): a similar event was also reported on MJD 50444 using the Greenbank Interferometer (I. Waltman. private communication): it was missed. by the RP because of maintenance work.," There was almost no detectable radio emission, apart from one day (MJD 50439); a similar event was also reported on MJD 50444 using the Greenbank Interferometer (E. Waltman, private communication); it was missed by the RT because of maintenance work." We have searched. for observations which coincided: with pointedTE observations., We have searched for observations which coincided with pointed observations. Phere are 10 of these: they are detailed in table , There are 10 of these; they are detailed in table 1. Only two ofthese observations have sullicient racio [Dux densities to make useful comparisons., Only two of these observations have sufficient radio flux densities to make useful comparisons. On 1996 Sep 7 (Fig., On 1996 Sep 7 (Fig. 5(a)) the radio emission. varied. smoothly ancl the X-ray emission at this time-resolution was relatively featureless.," 5(a)), the radio emission varied smoothly and the X-ray emission at this time-resolution was relatively featureless." 1996 October 25 shows the only coincident racio and N-ray QPOs so far recorded. (Fig., 1996 October 25 shows the only coincident radio and X-ray QPOs so far recorded (Fig. 5(b))., 5(b)). The high αν count-rates coincide with the times of low radio emission., The high X-ray count-rates coincide with the times of low radio emission. More observations are needed to allow comparison over all phases. but this result. clearly indicates that the same mechanism drives the two oscillations.," More observations are needed to allow comparison over all phases, but this result clearly indicates that the same mechanism drives the two oscillations." On the other hand. the presence," On the other hand, the presence" Ourfpuck compression progrun (see 82.1)) offers several optious for dealing with this issue.,Our compression program (see \ref{s:fpackfunpack}) ) offers several options for dealing with this issue. Ono simple mettod is to just compress the image using a larger q value to conipensate for the possible MAD roise overestimate. although this can uegativelv affect the overal cona]LOSSIOLL ratio of the image.," One simple method is to just compress the image using a larger q value to compensate for the possible MAD noise overestimate, although this can negatively affect the overall compression ratio of the image." Arother option 1 cases where only a xnall fraction of the rows 1l al nuage nüeht be affected ds tο. conress tlie entire Huage as a single tile. raher than uxiuto; the default row-by-row tiling pattern. so that the MAD noise estimate then more accurately reflects the noise in the background regious of the image as a whole.," Another option in cases where only a small fraction of the rows in an image might be affected is to compress the entire image as a single tile, rather than using the default row-by-row tiling pattern, so that the MAD noise estimate then more accurately reflects the noise in the background regions of the image as a whole." Finally.fpeck users do not need to rely ou the MAD noise estimate at all. and instead can directly specifv the desired spacing between the quantization levels.," Finally, users do not need to rely on the MAD noise estimate at all, and instead can directly specify the desired spacing between the quantization levels." This latter option is especially appropriate for projects that eeucrate large amounts of relatively homogeneous images because it ensures that all the images will be conrpressed using the same quantization factor., This latter option is especially appropriate for projects that generate large amounts of relatively homogeneous images because it ensures that all the images will be compressed using the same quantization factor. This method has the added advantage that it will iuprove the compression speed because it is not necessary to compute the NLAD noise value in this CASO., This method has the added advantage that it will improve the compression speed because it is not necessary to compute the MAD noise value in this case. The effects of linear quantization are naturallv ereater in the faimter areas of an nuage than or the brighter pixels where the Poissonian uncertainty of the photon couuts cau be much arecr than the quantized spacing., The effects of linear quantization are naturally greater in the fainter areas of an image than for the brighter pixels where the Poissonian uncertainty of the photon counts can be much larger than the quantized spacing. " Measurement of the local ""xkv backerouud around the nuage of a star or galaxw can be especially vulucrable o the effects of quautization. in part because it is usually necessary to ideutifv aud correct for yixncls that are affected by other objects or by defects in the detector."," Measurement of the local “sky” background around the image of a star or galaxy can be especially vulnerable to the effects of quantization, in part because it is usually necessary to identify and correct for pixels that are affected by other objects or by defects in the detector." " The issue of detecting sanall amplitude signals in a quautized svsteni is a woelbstudied. problem iu cuginecringe and conmmulicatious fields where the phenomenon is known as ""stochastic resonance’.", The issue of detecting small amplitude signals in a quantized system is a well-studied problem in engineering and communications fields where the phenomenon is known as “stochastic resonance”. The somewhat couuter-iutuitive solution for iniproviug the sigual-to-noise of measurements of quantized data is to add a iuoderate amount of noise iuto the system., The somewhat counter-intuitive solution for improving the signal-to-noise of measurements of quantized data is to add a moderate amount of noise into the system. " When applied to nuages. this technique is conunonly called ""ditherug."," When applied to images, this technique is commonly called “dithering”." Widrow&Isollar(2008) devote 2 chapters of their book to the theory aud practice of dithering aud recomuuend using a clever “subtractive dithering” technique. firs proposed by Roberts(1962).," \cite{widrow2008} devote 2 chapters of their book to the theory and practice of dithering and recommend using a clever “subtractive dithering” technique, first proposed by \cite{roberts1962}." . This technique overcomes the drawback of having to add noise to the image: a dither is added to the quautizer pt and the same dither is subtracted again from the quantizer output.," This technique overcomes the drawback of having to add noise to the image: a dither is added to the quantizer input, and the same dither is subtracted again from the quantizer output." The dither thus behaves as a catalyst which makes the process work better but does uot appear in the output image., The dither thus behaves as a catalyst which makes the process work better but does not appear in the output image. We have adopted this technique when quautiziug floatine-point images by adding a random dither. R;. with a value uniformly distributed between 0 aud 1 during the scaling process. where F; is the original floatius-poiut value and J; is he the quantized integer value.," We have adopted this technique when quantizing floating-point images by adding a random dither, $R_i$, with a value uniformly distributed between 0 and 1 during the scaling process, where $F_i$ is the original floating-point value and $I_i$ is the the quantized integer value." The interesting trick that clistinenishes subtractive ditheriug from ordinary dithering methods is that exactly the random dither value is subtracted when converting back to the quantized float value: The net effect of this subtractive ditheriug operation is to shift the entie erid of linearly spaced intensity levels up or down by a ruwou alliemut on a pixel bv pixel vasis., The interesting trick that distinguishes subtractive dithering from ordinary dithering methods is that exactly the random dither value is subtracted when converting back to the quantized float value: The net effect of this subtractive dithering operation is to shift the entire grid of linearly spaced intensity levels up or down by a random amount on a pixel by pixel basis. [t should be voted that the dithered values are uniforiulv clistvibuted between the quautized levels in this implementation., It should be noted that the dithered values are uniformly distributed between the quantized levels in this implementation. Oue possible ture enlaceluecut nav be fo Use a trianeular or Caussian dither (Widvow&INollar2008) which may more closcly replicate he actua distribution of pixel values iu he nuage., One possible future enhancement may be to use a triangular or Gaussian dither \citep{widrow2008} which may more closely replicate the actual distribution of pixel values in the image. In order to use this subtractive ditherue nethod it is necessary o define a specific pseudo randonm nunber generator (PRNC) algorithin for lise by both the compressor aud the uncomprCSSOL so that the same predictable sequence of raiwou nunubers is used in both cases;, In order to use this subtractive dithering method it is necessary to define a specific pseudo random number generator (PRNG) algorithm for use by both the compressor and the uncompressor so that the same predictable sequence of random numbers is used in both cases. We adopteL the PRNCG algorithm described bv Park&Miller(1988) which has been shown to produce statistically independent random uuubers uniformly distributed between 0 aud 1., We adopted the PRNG algorithm described by \cite{park1988} which has been shown to produce statistically independent random numbers uniformly distributed between 0 and 1. Wowever. for pragmatic reasons we do not compute a unique random number for," However, for pragmatic reasons we do not compute a unique random number for" extragalactic survey. to make use of this opportunity.,"extragalactic survey, to make use of this opportunity." PEP aims to resolve the cosmic 1nfrared background and determine the nature of its constituerts. determine the cosmic evolution of dusty star fornation and of the infrared lumirosity function. elucidate the relation of far-infrared emission and environment and determine clustering properties.," PEP aims to resolve the cosmic infrared background and determine the nature of its constituents, determine the cosmic evolution of dusty star formation and of the infrared luminosity function, elucidate the relation of far-infrared emission and environment and determine clustering properties." " Other main goals include study of AGN/host coevolution. and determination of the infrared emission and energetics of known high redshift galaxy populations,"," Other main goals include study of AGN/host coevolution, and determination of the infrared emission and energetics of known high redshift galaxy populations." PEP encompasses deep observations of blank fields and lensing clusters. close to the cconfusion limit. in order to probe down to representative high redshift galaxies. rather than being restricted to individually interesting extremely luminous cases.," PEP encompasses deep observations of blank fields and lensing clusters, close to the confusion limit, in order to probe down to representative high redshift galaxies, rather than being restricted to individually interesting extremely luminous cases." PEP is focussed on PACS 70. 100. and 160 pm observations.," PEP is focussed on PACS 70, 100, and 160 $\mu$ m observations." SPIRE observations of the PEP fields are obtained in coordination with PEP by the HerMES survey (Oliver et al. 201100)., SPIRE observations of the PEP fields are obtained in coordination with PEP by the HerMES survey (Oliver et al. \cite{oliver11}) ). " Larger and shallower fields are observed by HerMES (70 deg*) as well as by the H-ATLAS survey (570 deg"". Eales et al. 20101)."," Larger and shallower fields are observed by HerMES (70 $^2$ ) as well as by the H-ATLAS survey (570 $^2$ , Eales et al. \cite{eales10}) )," while the GOODS-Herschel program (Elbaz et al. 2011)), while the GOODS-Herschel program (Elbaz et al. \cite{elbaz11}) ) provides deeper observation in (part of) the GOODS fields that are also covered by PEP., provides deeper observation in (part of) the GOODS fields that are also covered by PEP. Finally. the Herschel lensing survey (Egami et al. 2010))," Finally, the Herschel lensing survey (Egami et al. \cite{egami10}) )" substantially increases the number of lensing clusters observed with Herschel. adding about 40 clusters to the 10 objects covered by PEP.," substantially increases the number of lensing clusters observed with Herschel, adding about 40 clusters to the 10 objects covered by PEP." Fig., Fig. | compares for 160m wavelength the area and exposure of the PEP surveys (Table 1)) with that of these other major Herschel extragalactic surveys., \ref{fig:surveys} compares for $\mu$ m wavelength the area and exposure of the PEP surveys (Table \ref{tab:fields}) ) with that of these other major Herschel extragalactic surveys. In this paper. we describe the field selection. observing strategy and data analysis methods of PEP.," In this paper, we describe the field selection, observing strategy and data analysis methods of PEP." We give a complete overview of the planned PEP observations and their execution status as of June 2011 (Table 1))., We give a complete overview of the planned PEP observations and their execution status as of June 2011 (Table \ref{tab:fields}) ). We provide a detailed account of the science demonstration phase (SDP) data sets for GOODS-N and Abell 2218. and give an overview of first science results.," We provide a detailed account of the science demonstration phase (SDP) data sets for GOODS-N and Abell 2218, and give an overview of first science results." A key element in selecting a field for a deep Herschel extragalactic survey is the availability of a strong multi-wavelength database from X-rays to radio wavelengths. which is fundamental to many of the science results discussed in Sect. 6..," A key element in selecting a field for a deep Herschel extragalactic survey is the availability of a strong multi-wavelength database from X-rays to radio wavelengths, which is fundamental to many of the science results discussed in Sect. \ref{sect:science}." In particular. deep optical. near-IR. and Spitzer imaging. as well as a comprehensive set of photometric and spectroscopic redshifts are an essential asset for most of the far-infrared studies of galaxy evolution that we envisage.," In particular, deep optical, near-IR, and Spitzer imaging, as well as a comprehensive set of photometric and spectroscopic redshifts are an essential asset for most of the far-infrared studies of galaxy evolution that we envisage." Deep X-ray data are invaluable for using the potential of Herschel for studying the AGN — host galaxy coevolution., Deep X-ray data are invaluable for using the potential of Herschel for studying the AGN – host galaxy coevolution. Another requirement is a low galactic far-infrared background in order to minimize contamination by galactic ‘cirrus’ structure. and. by individual galactic foreground objects., Another requirement is a low galactic far-infrared background in order to minimize contamination by galactic `cirrus' structure and by individual galactic foreground objects. This naturally coincides with the selection criteria of extragalactic surveys at other wavelengths., This naturally coincides with the selection criteria of extragalactic surveys at other wavelengths. In the X-ray regime. for example. these are pushing for a low galactic foreground obscuration.," In the X-ray regime, for example, these are pushing for a low galactic foreground obscuration." Given thatthe power spectra of, Given thatthe power spectra of stellar objects (Takita et al. 2010)).,stellar objects (Takita et al. \cite{takita2010}) ). Refer to the papers for discussions on each topic., Refer to the papers for discussions on each topic. In the next section we show general characteristics of the AKARI IRC All-Sky Survey point source catalog., In the next section we show general characteristics of the AKARI IRC All-Sky Survey point source catalog. Refer to Ishihara et al. (2010)), Refer to Ishihara et al. \cite{ishihara2010}) ) " for the complete description of the All-Sky Survey, its data reduction processes, the point source catalog compilation processes, and the catalog characteristics."," for the complete description of the All-Sky Survey, its data reduction processes, the point source catalog compilation processes, and the catalog characteristics." The first release version (ver., The first release version (ver. " 8-1) of the AKARI IRC mid-infrared All-Sky Survey point source catalog (hereafter, we call the catalog as IRC-PSC) lists more than 851,000 and 195,000 sources at 9 and 18 µπι bands, respectively."," $\beta$ -1) of the AKARI IRC mid-infrared All-Sky Survey point source catalog (hereafter, we call the catalog as IRC-PSC) lists more than 851,000 and 195,000 sources at 9 and 18 $\mu$ m bands, respectively." " There are about 170,000 sources detected both in the two bands."," There are about 170,000 sources detected both in the two bands." This number is in a range expected from the difference in the dection limit between the two bands and the fall of the Rayleigh-Jeans spectrum since most of the sources are stars., This number is in a range expected from the difference in the dection limit between the two bands and the fall of the Rayleigh-Jeans spectrum since most of the sources are stars. " The estimated 5 o detection limits for one scan are about 50 and 90 mJy at 9 and 18 um bands, respectively."," The estimated 5 $\sigma$ detection limits for one scan are about 50 and 90 mJy at 9 and 18 $\mu$ m bands, respectively." The present catalog includes point-like sources that were detected more than twice., The present catalog includes point-like sources that were detected more than twice. " The sensitivity will be improved in the future catalog, for sources in high visibility regions for AKARI’s sun-synchronous orbit (i.e., high ecliptic latitude regions), where AKARI scanned many times."," The sensitivity will be improved in the future catalog, for sources in high visibility regions for AKARI's sun-synchronous orbit (i.e., high ecliptic latitude regions), where AKARI scanned many times." " The saturation limits depend on the sky region and the brightest source listed in the catalog is about 560 and 1,200 Jy at 9 and 18 um bands, respectively."," The saturation limits depend on the sky region and the brightest source listed in the catalog is about 560 and 1,200 Jy at 9 and 18 $\mu$ m bands, respectively." " The pixel field of view of the survey observation mode is about 10 arcsec, and the positional accuracy of detected sources are better than 3 arcsec."," The pixel field of view of the survey observation mode is about 10 arcsec, and the positional accuracy of detected sources are better than 3 arcsec." " Although the band profiles of AKARI IRC's S9W and L18W bands and IRAS's 12 and 25 jm bands are different, a comparison of the photometry of common sources is useful to test the calibration of the IRC-PSC."," Although the band profiles of AKARI IRC's $S9W$ and $L18W$ bands and IRAS's 12 and 25 $\mu$ m bands are different, a comparison of the photometry of common sources is useful to test the calibration of the IRC-PSC." In Figure 1 we show the normalized spectral response function of the AKARI and the bands., In Figure \ref{filter} we show the normalized spectral response function of the AKARI and the bands. The ISO SWS spectra (Sloan et al. 2003a)), The ISO SWS spectra (Sloan et al. \cite{sloan2003a}) ) of some galactic stars with characteristic circumstellar dust features are also shown to get the rough idea on the cause of differences in photometry between the associated filter bands., of some galactic stars with characteristic circumstellar dust features are also shown to get the rough idea on the cause of differences in photometry between the associated filter bands. " The IRAS-PSC lists 245,888 sources, among which 170,754 have flux quality flag better than 1 in at least one of the 12 and 25 um bands (i.e., fji> lor {5> 1)."," The IRAS-PSC lists 245,888 sources, among which 170,754 have flux quality flag better than 1 in at least one of the 12 and 25 $\mu$ m bands (i.e., $f_{q12} > 1$ or $f_{q25} > 1$ )." " We refer these 170,754 sources as good IRAS sources."," We refer these 170,754 sources as good IRAS sources." " We find AKARI counterparts for 145,751 (> 85%) good IRAS sources using the simple positional matching method with a tolerance radius of 30 arcsec."," We find AKARI counterparts for 145,751 $> 85 \%$ ) good IRAS sources using the simple positional matching method with a tolerance radius of 30 arcsec." " In some cases, more than one AKARI point sources are found for an IRAS source."," In some cases, more than one AKARI point sources are found for an IRAS source." " In these cases, we only adopt the closest one and regard the other(s) as unmatched, even if they are actual multiple sources resolved by the AKARI that appear as one source to the IRAS."," In these cases, we only adopt the closest one and regard the other(s) as unmatched, even if they are actual multiple sources resolved by the AKARI that appear as one source to the IRAS." We compare the AKARI and IRAS photometry of the matched sources., We compare the AKARI and IRAS photometry of the matched sources. " The comparison shows that the photometry in the IRC-PSC and the IRAS-PSC are in agreement within 37 and in SOW v.s. IRASI2, and L18W v.s. IRAS25 for sources with the IRAS flux quality flag of 3."," The comparison shows that the photometry in the IRC-PSC and the IRAS-PSC are in agreement within 37 and in S9W v.s. IRAS12, and L18W v.s. IRAS25 for sources with the IRAS flux quality flag of 3." " If we compare a subsample of high galactic latitude (\b|> 30°) and high quality (S/N > 10 in IRC bands) sources, their photometry are in agreement within 18 and in SOW"," If we compare a subsample of high galactic latitude $|b| > 30^\circ$ ) and high quality (S/N $>$ 10 in IRC bands) sources, their photometry are in agreement within 18 and in S9W" (Ida&Lin200La) assuming an optically thin disk in which T—280(4/1AU)|? Is. Hence. the actual truncation condition may be the thermal condition aud it is very unlikely that gas accretion is truncated by the gap opening al Mj~LION (which corresponds to HDI19026b) far [rom the )arent star. as long as a sufficient amount of disk gas reimaius.,"\citep{IL04a} assuming an optically thin disk in which $T = 280(a/1{\rm AU})^{-1/2}$ K. Hence, the actual truncation condition may be the thermal condition and it is very unlikely that gas accretion is truncated by the gap opening at $M_{\rm p} \sim 110 \mearth$ (which corresponds to HD149026b) far from the parent star, as long as a sufficient amount of disk gas remains." Furthermore. since the gap is replenished by viscous diffusion. gas accretion may not completely be truucated by the gap opening ," Furthermore, since the gap is replenished by viscous diffusion, gas accretion may not completely be truncated by the gap opening \citep*{D'Angelo03}." If a sullicient amouit of disk gas retails. oue way to trumcate gas accretioι αἱ relatively stnall planetary mass is tiat the planet migrates to the vicinity of its parent star beore the planet accretes a large amount of gas.," If a sufficient amount of disk gas remains, one way to truncate gas accretion at relatively small planetary mass is that the planet migrates to the vicinity of its parent star before the planet accretes a large amount of gas." " Both Ad,i; aud Ad)in are small in the immer regions (Eqs. [13]]"," Both $M_{\rm p,vis}$ and $M_{\rm p,th}$ are small in the inner regions (Eqs. \ref{eq:vis_condition}] ]" aud Hn., and \ref{eq:therm_condition}] ]). However. this is utlikely. even if type IL migration occurs when Aly~30M..," However, this is unlikely, even if type II migration occurs when $M_{\rm p} \sim 30 \mearth$." The timescale [or tle WH eas accretion σοκo10! vears for a core of >30M. (Fig. 5)).," The timescale for the KH gas accretion $\la 3 \times 10^4$ years for a core of $\ga 30 \mearth$ (Fig. \ref{fig:KH}) )," while the timescale for theigration is much loiger ( 109—10* vears)., while the timescale for the migration is much longer $\sim 10^6$ $10^7$ years). Furthermore. it is not clear if the οἱip Opening can 3.op eas accretion completely.," Furthermore, it is not clear if the gap opening can stop gas accretion completely." If disk gas is gkally depleted when AL. reaches ilou gas accretion onto the core can be limited by viscous diffusion of disk gas. not by the Ixelviu-Heliiholtz contraction of the envelope (e.g..Cuillot&Hueso2006).," If disk gas is globally depleted when $M_{\rm c}$ reaches $M_{\rm c,crit}$, gas accretion onto the core can be limited by viscous diffusion of disk gas, not by the Kelvin-Helmholtz contraction of the envelope \citep[e.g.,][]{GuillotHueso06}." . That could be possible to account for the stuall amount of H/He., That could be possible to account for the small amount of H/He. However. whether si ‘tha stnall amouut of cisk gas cau bring the planet to the vicinitv of the parent star should be examined.," However, whether such a small amount of disk gas can bring the planet to the vicinity of the parent star should be examined." If it does not work. dilfereut migratiou mechanism such as gravitational scaltering during orital crossing of giant. planets is requirec.," If it does not work, different migration mechanism such as gravitational scattering during orbital crossing of giant planets is required." Auother way to explain the small amount of the H/He gas of HDI19026b is loss of the envelope eas., Another way to explain the small amount of the H/He gas of HD149026b is loss of the envelope gas. There are three possibilities for loss of tle envelope gas: photoevaporation driven by iucideut UV lux from the parent star. the Roche lobe overflow. aud impact erosion by a collision. with alotjer gas giant planet.," There are three possibilities for loss of the envelope gas; photoevaporation driven by incident UV flux from the parent star, the Roche lobe overflow, and impact erosion by a collision with another gas giant planet." Photoevaporation process for gas-rich planets is normally faster for sinaller planetary uiasses. becaine less massive planets are more expauded aud their envelope gas is more loosely bound (Baralleetal.2005).," Photoevaporation process for gas-rich planets is normally faster for smaller planetary masses, because less massive planets are more expanded and their envelope gas is more loosely bound \citep{Baraffe06}." . This means the envelope quickly disappears ouce the evaporation occurs. so tlat it should be relatively rare to observe a planet at a stage when a relatively small amount (30-60 NL. ) of envelope gas remains.," This means the envelope quickly disappears once the evaporation occurs, so that it should be relatively rare to observe a planet at a stage when a relatively small amount (30–60 $\mearth$ ) of envelope gas remains." However. this possibility is not excluded at present. because Z-vich planets such as HDI19026b cau be more compact aud their euvelope gas is uot necessarily," However, this possibility is not excluded at present, because $Z$ -rich planets such as HD149026b can be more compact and their envelope gas is not necessarily" parameters of 22174.,parameters of 2174. " For this purpose, To derive the fundamental parameters we use the Padova isochrones (Girardietal. 2002)) computed for the 2MASSfilters?."," For this purpose, To derive the fundamental parameters we use the Padova isochrones \citealt{Girardi2002}) ) computed for the 2MASS." ". For the PMS we use the isochrones of Siess,Dufour&Forestini (2000).", For the PMS we use the isochrones of \citet{Siess2000}. ". We restrict the analysis to solar metallicity isochrones because the clusters are expected to be young and located not far from the Solar circle (see below), a region essentially occupied by [Fe/H]5’0.0 OCs (Friel 1995))."," We restrict the analysis to solar metallicity isochrones because the clusters are expected to be young and located not far from the Solar circle (see below), a region essentially occupied by $[Fe/H]\approx0.0$ OCs \citealt{Friel95}) )." " Reddening transformations are based on the absorption relations Ay/Ay=0.276, Ag/Av= 0.176, => and Ay=2.76xE(JH) (Dutra, 2002)), with Ry= 3.1,considering-- the extinction curve of Cardelli,Clayton&Mathis (1989)."," Reddening transformations are based on the absorption relations $A_J/A_V=0.276$ $A_H/A_V=0.176$ , $A_{K_S}/A_V=0.118$, and $A_J=2.76\times\ejh$ \citealt{DSB2002}) ), with $R_V=3.1$ ,considering the extinction curve of \citet{Cardelli89}. ." temperature or density (Isella&Natta2005) or the maximum erain size al.2007)..,temperature or density \citep{Isella} or the maximum grain size \citep{Tannirkulam}. However. the edge of the CD disk is a physical wall created by tidal interactions with the binary svstem. and (he vertical density profile may be very different from (hat in standard disks.," However, the edge of the CB disk is a physical wall created by tidal interactions with the binary system, and the vertical density profile may be very different from that in standard disks." Since no detailed models exist to guide us. we have adopted (he simplest eeonmel(ryv: a vertical wall.," Since no detailed models exist to guide us, we have adopted the simplest geometry: a vertical wall." The wall is also assumed (o be circular for simplicity. however. non-axisvmmnietric shapes are expected based on hyelrodvuamiucal simulations of Gimther and Artvmowiez&Lu," The wall is also assumed to be circular for simplicity, however, non-axisymmetric shapes are expected based on hydrodynamical simulations of \citet{Gunther1} and \citet{Artymowicz2}." bow(1996).. In Section 4.1 we show that the SED for an eccentric CD disk does not change appreciably with respect to the circular case. thus the (ον Tau/4 modeling is restricted to the latter.," In Section \ref{sec-var-param-wall} we show that the SED for an eccentric CB disk does not change appreciably with respect to the circular case, thus the CoKu Tau/4 modeling is restricted to the latter." Only a fraction of the walls surface can be detected by the observer. depending on the wall radius. height ancl the inclination angle /.," Only a fraction of the wall's surface can be detected by the observer, depending on the wall radius, height and the inclination angle $i$." There are other portions of the wall that are occulted [rom the observer by absorption due to the disk itsell., There are other portions of the wall that are occulted from the observer by absorption due to the disk itself. The “visible” surface. projected in the plane of the sky (see Figure 17)). is divided in small surface elements (pixels).," The “visible” surface, projected in the plane of the sky (see Figure \ref{fig-configuracion-i}) ), is divided in small surface elements (pixels)." Each one is located at a given height relative to the clisk midplane. Y and at a given distance. X. from (he disk center.," Each one is located at a given height relative to the disk midplane, $Y$ and at a given distance, $X$, from the disk center." In order to describe each pixel position. we use cartesian coordinates see D05).," In order to describe each pixel position, we use cartesian coordinates (see D05)." Each point in the wall has a different temperature distribution. from the surface towarel arger radii (deeper inside the disk).," Each point in the wall has a different temperature distribution, from the surface toward larger radii (deeper inside the disk)." In order to estimate this temperature distribution we use a similar treatment given by Calvetetal.(1991). and. Calvetetal.(1992)., In order to estimate this temperature distribution we use a similar treatment given by \citet{Calvet2} and \citet{Calvet1}. .. However. in (he present case each pixel is being irradiated bv (wo stars. neither of which is al the center of the svstem.," However, in the present case each pixel is being irradiated by two stars, neither of which is at the center of the system." We use the fact that the luminosity [rom the wall is much less than ihe luminosity from the stars in order to neglect its contribution to the heating of the wall., We use the fact that the luminosity from the wall is much less than the luminosity from the stars in order to neglect its contribution to the heating of the wall. Thus. at each pixel we consider the superposition of (wo radiation fields. characterized by two different fluxes and mean intensities. aud. in principle. by (wo distinct incidence directions.," Thus, at each pixel we consider the superposition of two radiation fields, characterized by two different fluxes and mean intensities, and, in principle, by two distinct incidence directions." The incident [Iux from each star is Fy;=(L.;Jin yewilh each star at a different distance from the wall. given by 2). pois the cosine of the incidence angle with respect to the normal io the wall surface.," The incident flux from each star is $F_{0,j}= ({L_{*,j}/4 \pi R_j^2})\mu$ with each star at a different distance from the wall, given by $R_j$, $\mu$ is the cosine of the incidence angle with respect to the normal to the wall surface." Again. for the sake of simplicity. we assume (hat each pixel is a plane parallel atmosphere and the radiation from each star arrives in a single beam. with a normal incidence angle (j(= 1).," Again, for the sake of simplicity, we assume that each pixel is a plane parallel atmosphere and the radiation from each star arrives in a single beam, with a normal incidence angle $\mu=1$ )." This assumption is valid only if the minimum distance between the stars and the wall is much larger Chan the stellar radii., This assumption is valid only if the minimum distance between the stars and the wall is much larger than the stellar radii. In the case of Colxu Tau/4. the minimun distance between one star aud (he wall is 1.2 αον9.10. so the later assumption is justified for this particular object.," In the case of CoKu Tau/4, the minimum distance between one star and the wall is 1.2 $a \sim 9 AU$, so the later assumption is justified for this particular object." " Following Calveletal.(1991). and. 005. (he radiation fiekl arriving at each pixel is then separated into three components: ""stellar 1. ""stellar 2 and ""disk. each one wilh a parüceular wavelength range where most of its emission peaks."," Following \citet{Calvet2} and D05, the radiation field arriving at each pixel is then separated into three components: “stellar 1”, “stellar 2” and “disk”, each one with a particular wavelength range where most of its emission peaks." " Defining the optical clepth at the ""disk wavelength range in the radial direction. measured from the wall surface towards"," Defining the optical depth at the “disk” wavelength range in the radial direction, measured from the wall surface towards" star cluster.,star cluster. Although no definite proof that Virgo dwarls are indeed. MDlI-Iess. the above results imply that MDIIS are more common in large galactic systems.," Although no definite proof that Virgo dwarfs are indeed MBH-less, the above results imply that MBHs are more common in large galactic systems." Our models also indicate that a minimum. velocity. dispersion. exists. below which the probability of finding a central object is very low.," Our models also indicate that a minimum velocity dispersion exists, below which the probability of finding a central object is very low." We make quantitative predictions for the local occupation [fraction of AIBIIs., We make quantitative predictions for the local occupation fraction of MBHs. Our model X predicts that below a.=60kms the probability of a galaxy hosting a AIBL is negligible.," Our model A predicts that below $\sigma_c\approx 60\,{\rm kms}^{-1}$ the probability of a galaxy hosting a MBH is negligible." With increasing. ΔΕΗ formation elliciencies. the minimum mass for a galaxy that hosts a ABIL decreases. ancl it drops below our simulation limits for model €. On the other hand. models based. on lower mass Population LIL star reninant seeds. predict that massive black holes might be present even in low mass galaxies.," With increasing MBH formation efficiencies, the minimum mass for a galaxy that hosts a MBH decreases, and it drops below our simulation limits for model C. On the other hand, models based on lower mass Population III star remnant seeds, predict that massive black holes might be present even in low mass galaxies." We note here that in our investigation we have not included. any mechanism that could further lower the occupation fraction of MBlIs (e.g.. eravitational recoil. three-body SIBLE interactions).," We note here that in our investigation we have not included any mechanism that could further lower the occupation fraction of MBHs (e.g., gravitational recoil, three-body MBH interactions)." For any value of Qo the, For any value of $Q_{\rm c}$ the "SDSS$J094818.6+023004, which shows unambiguous radio emission in the FIRST data (Fig.","SDSSJ094818.6+023004, which shows unambiguous radio emission in the FIRST data (Fig." " 1), has Hó equivalent width (EW) 6.183-1.02A, and most of its stellar mass is younger than 1 Gyr."," 1), has $\delta$ equivalent width (EW) ${\rm 6.18 \pm 1.02 ~ \AA}$, and most of its stellar mass is younger than 1 Gyr." " Meanwhile, SDSSJ160417.34-155503, which does not have a FIRST counterpart, is intermediate between a strong post-starburst galaxy and a passively evolving galaxy, with EW(Hó)=5.4641.25À."," Meanwhile, SDSSJ160417.3+155503, which does not have a FIRST counterpart, is intermediate between a strong post-starburst galaxy and a passively evolving galaxy, with ${\rm EW(H\delta) ~=~ 5.46 \pm 1.25 ~ \AA}$." Its dominant stellar population is also older than 1 Gyr., Its dominant stellar population is also older than 1 Gyr. " The derived stellar masses of the galaxies in the sample range from about 1053 to about "" 10!Mo, as presented in Figure 3.."," The derived stellar masses of the galaxies in the sample range from about $10^{8.4} M_{\odot}$ to about $10^{11.7} M_{\odot}$ , as presented in Figure \ref{fig:vespa}." " The typical M;statistical uncertainty of the stellar mass is about for objects in our sample, although"," The typical statistical uncertainty of the stellar mass is about for objects in our sample, although" distribution for the LMC halo contribution might become a relevant issue (?)..,distribution for the LMC halo contribution might become a relevant issue \citep{novati06}. " The expected duration varies across the observed fields for the LMC self lensing, with larger values expected moving from the LMC centre, with variations up to about (?).."," The expected duration varies across the observed fields for the LMC self lensing, with larger values expected moving from the LMC centre, with variations up to about \citep{mancini04}." In Table 3 we have reported the mean values of the duration across the 21 OGLE fields., In Table \ref{tab:rate} we have reported the mean values of the duration across the 21 OGLE fields. " In particular, as for the lines of sight towards the two candidates it results a median (average) value tg=36(49)days and tg=47(61)days, to be compared with the observed values tg=57.2days and tg=24.2days, for OGLE-LMC-I and OGLE-LMC-II, respectively."," In particular, as for the lines of sight towards the two candidates it results a median (average) value $t_\mathrm{E}=36\,(49)~\mathrm{days}$ and $t_\mathrm{E}=47\,(61)~\mathrm{days}$, to be compared with the observed values $t_\mathrm{E}=57.2~\mathrm{days}$ and $t_\mathrm{E}=24.2~\mathrm{days}$, for OGLE-LMC-I and OGLE-LMC-II, respectively." In Fig., In Fig. " 2 we show the normalised differential rate dI'e/dtg, corrected for the efficiency £(tg), for LMC self lensing and for Galactic dark matter halo lenses of 0.1Mo and 1Mo."," \ref{fig:rate} we show the normalised differential rate $\mathrm{d}\Gamma_\mathcal{E}/\mathrm{d}t_\mathrm{E}$, corrected for the efficiency $\mathcal{E}(t_\mathrm{E})$, for LMC self lensing and for Galactic dark matter halo lenses of $0.1~\mathrm{M}_\odot$ and $1~\mathrm{M}_\odot$." Superimposed on the differential rate we show the values of the evaluated duration for the two events observed using the sample of sources., Superimposed on the differential rate we show the values of the evaluated duration for the two events observed using the sample of sources. " Comparing the expected durations with the observed ones we can see, as for self lensing, that the evaluated duration of OGLE-LMC-1 agrees very well with the median value, and, though somewhat short, that of OGLE-LMC-2, is still fully compatible."," Comparing the expected durations with the observed ones we can see, as for self lensing, that the evaluated duration of OGLE-LMC-1 agrees very well with the median value, and, though somewhat short, that of OGLE-LMC-2, is still fully compatible." " As for the MW MACHO populations, the observed durations are compatible with those expected for MACHO masses in the mass range (0.1—1)Mo."," As for the MW MACHO populations, the observed durations are compatible with those expected for MACHO masses in the mass range $(0.1-1)~\mathrm{M}_\odot$." " The expected number of events for the dark populations (both MW and LMC halos) is shown, as a function of the MACHO mass, in the upper panel of Fig. 3.."," The expected number of events for the dark populations (both MW and LMC halos) is shown, as a function of the MACHO mass, in the upper panel of Fig. \ref{fig:likeli}." " In particular, for a full halo of 0.05Μο(0.5Mc) compact objects we expect, for the MW halo, Nexp=28 and Nexp=12 (Nexp=18 and 7.7) for the and the sample of sources, respectively, whereas for the LMC halo we evaluate Nexp=3.5 and nep=1.5 (Mexp=1.5 and 0.68)."," In particular, for a full halo of $0.05~\mathrm{M}_\odot (0.5~\mathrm{M}_\odot)$ compact objects we expect, for the MW halo, $n_\mathrm{exp}=28$ and $n_\mathrm{exp}=12$ $n_\mathrm{exp}=18$ and $7.7$ ) for the and the sample of sources, respectively, whereas for the LMC halo we evaluate $n_\mathrm{exp}=3.5$ and $n_\mathrm{exp}=1.5$ $n_\mathrm{exp}=1.5$ and $0.68$ )." " For both MW and LMC, the microlensing rate is severely suppressed by the sharp decline of the efficiency function £(tg) (?) for small values of tg: this explains the plateau reached by the expected duration values, as well as the sharp decline for nexp, for compact halo object masses below 103Mo."," For both MW and LMC, the microlensing rate is severely suppressed by the sharp decline of the efficiency function $\mathcal{E}(t_\mathrm{E})$ \citep{lukas09} for small values of $t_\mathrm{E}$: this explains the plateau reached by the expected duration values, as well as the sharp decline for $n_\mathrm{exp}$, for compact halo object masses below $10^{-3}~\mathrm{M}_\odot$." " The evaluation of the microlensing rate together with the result of the OGLE-II observational campaign as for the number of observed microlensing events allows us to put some constraints on the mass halo fraction in form of MACHOs, f."," The evaluation of the microlensing rate together with the result of the OGLE-II observational campaign as for the number of observed microlensing events allows us to put some constraints on the mass halo fraction in form of MACHOs, $f$." " In particular we perform a likelihood analysis with where, for the differential rate, we sum up over all the luminous and dark populations we consider."," In particular we perform a likelihood analysis with where, for the differential rate, we sum up over all the luminous and dark populations we consider." " The halo mass fraction, f, enters as a multiplicative factor of the differential rate and of the expected number of events in front of the contribution of the dark populations (MW and LMC halos)."," The halo mass fraction, $f$, enters as a multiplicative factor of the differential rate and of the expected number of events in front of the contribution of the dark populations (MW and LMC halos)." Keeping the MACHO mass value fixed as a parameter we can evaluate upper and lower limits for the halo mass fraction f., Keeping the MACHO mass value fixed as a parameter we can evaluate upper and lower limits for the halo mass fraction $f$. In Fig., In Fig. " 3 (bottom panel) we display the and confidence levels limits for f, for both the sample and the sample (thick and thin lines, respectively)."," \ref{fig:likeli} (bottom panel) we display the and confidence levels limits for $f$, for both the sample and the sample (thick and thin lines, respectively)." " As noted in the previous Section, the number of expected events from the luminous lens components is compatible with the observed one in both cases, therefore we do not show the corresponding (extremely small) lower limit."," As noted in the previous Section, the number of expected events from the luminous lens components is compatible with the observed one in both cases, therefore we do not show the corresponding (extremely small) lower limit." " Corresponding to the maximum in the number of MACHO events (upper panel, Fig. 3))"," Corresponding to the maximum in the number of MACHO events (upper panel, Fig. \ref{fig:likeli}) )," we find the tighter constraints for the halo component in form of MACHOs in the, we find the tighter constraints for the halo component in form of MACHOs in the least-square fits.,least-square fits. The last three columns of the table indicate other identifications of the stars. the observing runs analysed and the presence of a Blazhko effect. respectively.," The last three columns of the table indicate other identifications of the stars, the observing runs analysed and the presence of a Blazhko effect, respectively." All the periods. amplitudes and light curve shapes of the 29 stars are typical for RRab stars pulsating in their radial fundamental mode. therefore. these classifications are omitted from Table I..," All the periods, amplitudes and light curve shapes of the 29 stars are typical for RRab stars pulsating in their radial fundamental mode, therefore, these classifications are omitted from Table \ref{All_stars}." Generally. it is an easy task to distinguish amplitude modulated and non-modulatedKepler LLyrae light curves.," Generally, it is an easy task to distinguish amplitude modulated and non-modulated Lyrae light curves." A gallery of modulated light curves is shown in refzoo.., A gallery of modulated light curves is shown in \\ref{zoo}. It is obvious at first glance that the modulation cycles are predominantly long and the amplitude of the effect is clearly visible., It is obvious at first glance that the modulation cycles are predominantly long and the amplitude of the effect is clearly visible. Non-sinusoidal envelopes of the light curves (see. e.g.. CCvg: 3386443) or moving bumps (e.g... LLyr: 99578833) are also conspicuous.," Non-sinusoidal envelopes of the light curves (see, e.g., Cyg; 3864443) or moving bumps (e.g., Lyr; 9578833) are also conspicuous." The interesting light curve of LLyr 66186029) is shown separately in refdouble.., The interesting light curve of Lyr 6186029) is shown separately in \\ref{double}. The two observed Blazhko cycles are surprisingly different., The two observed Blazhko cycles are surprisingly different. The high amplitude of the Blazhko modulation extremely distorts the shape of the light curve., The high amplitude of the Blazhko modulation extremely distorts the shape of the light curve. This is demonstrated in the small panels of refdouble.., This is demonstrated in the small panels of \\ref{double}. Signs of complex variations are detectable from the Fourier spectrum as well., Signs of complex variations are detectable from the Fourier spectrum as well. The spectrum of the data prewhitened with the main pulsation frequency and its harmonics shows four peaks around each of the harmonics refd. p) , The spectrum of the data prewhitened with the main pulsation frequency and its harmonics shows four peaks around each of the harmonics \\ref{d_sp}) ). Lwooulerpeaksattheharmonicescanbeident: ficdascleme nihis hypothesis nouis fv)., Two outer peaks at the harmonics can be identified as elements of the Blazhko triplets $f_0\pm f_{\mathrm B}$ ). Two other side peaks closer to the harmonie frequencies show the possible variation of the Blazhko effect on a time-scale longer than the observation run., Two other side peaks closer to the harmonic frequencies show the possible variation of the Blazhko effect on a time-scale longer than the observation run. This may be a result of a cyclic variation (existence of more than one Blazhko modulation). a secular trend. or random changes.," This may be a result of a cyclic variation (existence of more than one Blazhko modulation), a secular trend, or random changes." Several papers have reported multiperiodic and/or unstable behaviours in the Blazhko effect (e.g.. LaCluvzé2008:Juresiketal. 2009c)).," Several papers have reported multiperiodic and/or unstable behaviours in the Blazhko effect (e.g., \citealt{Lac04, Col06, Kol06, NK06, Sod06, Szcz07, Wi08, Jur09}) )." After investigating the two Blazhko cycles noted here. we are not in the position to decide on the nature of this variation. but the 3.5—5 year long time base of Kepler's observations will provide an excellent opportunity to study this strange behaviour.," After investigating the two Blazhko cycles noted here, we are not in the position to decide on the nature of this variation, but the 3.5–5 year long time base of 's observations will provide an excellent opportunity to study this strange behaviour." We were systematically searching for low amplitude Blazhko RRLLyrae stars., We were systematically searching for low amplitude Blazhko Lyrae stars. Instrumental trends of the observed fluxes that are not properly removed could cause apparent amplitude changes in the non-linear magnitude scale., Instrumental trends of the observed fluxes that are not properly removed could cause apparent amplitude changes in the non-linear magnitude scale. A decreasing trend of the averaged fluxes results in increasing amplitudes in magnitudes and vice-versa., A decreasing trend of the averaged fluxes results in increasing amplitudes in magnitudes and vice-versa. Therefore. we always checked the amplitude variation using the raw fluxes.," Therefore, we always checked the amplitude variation using the raw fluxes." " We divided the data sets into small sections (typically dd in length). then calculated the amplitude difference 0.1,(/) of the first Fourier component and its averaged value Act) over the whole time span for all sections by a non-linear tit."," We divided the data sets into small sections (typically d in length), then calculated the amplitude difference $\delta A_1(t)$ of the first Fourier component and its averaged value $\Delta A_1$ over the whole time span for all sections by a non-linear fit." These calculated functions reflect well the variation of pulsation amplitude seen in the light curves., These calculated functions reflect well the variation of pulsation amplitude seen in the light curves. With the help of this tool we found in 111125706 the owest amplitude modulation ever detected in an LLyrae star., With the help of this tool we found in 11125706 the lowest amplitude modulation ever detected in an Lyrae star. Full amplitude of the maximum light. variation ACAine.015 mmag. and the amplitude of the highest side peak in the Fourier spectrum is only κο|fu)=0.0022 mmag.," Full amplitude of the maximum light variation $A(K_{\mathrm p})_{\mathrm max}=0.015$ mag, and the amplitude of the highest side peak in the Fourier spectrum is only $A_{K_{\mathrm p}}(f_0+f_{\mathrm B})=0.0022$ mag." The lowest published amplitude of a Blazhko effect previously ‘ound was the case of CCyg (Juresiketal...2009b). where AADwee=0007 mmag. elyCfo|fp)=0.0006 mmag and “Ufo|fg)= 0.006Lmmag.," The lowest published amplitude of a Blazhko effect previously found was the case of Cyg \citep{JH09} where $A(V)_{\mathrm max}=0.07$ mag, $A_V(f_0+f_{\mathrm B})=0.0096$ mag and $A_I(f_0+f_{\mathrm B})=0.0061$ mag." The two measurements are not strictly comparable because Kepler passband is broad in white ight., The two measurements are not strictly comparable because passband is broad in white light. However. the maximum of its spectral response function (see Kochetal...20105) is about between Johnson—Cousins filters V and 7i.," However, the maximum of its spectral response function (see \citealt{Koch10}) ) is about between Johnson–Cousins filters $V$ and $R$." All the Blazhko LLyrae stars found in our sample are isted in Table 2.., All the Blazhko Lyrae stars found in our sample are listed in Table \ref{Blazhko_stars}. The estimated lengths of the Blazhko cycles are indicated in the third column., The estimated lengths of the Blazhko cycles are indicated in the third column. For the shorter periods than the otal time span they were calculated from the averaged frequency differences of the highest side peaks Cfo|fe and foJ). otherwise a minimum period is given.," For the shorter periods than the total time span they were calculated from the averaged frequency differences of the highest side peaks $f_0+f_{\mathrm B}$ and $f_0-f_{\mathrm B}$ ), otherwise a minimum period is given." " The fourth column shows he amplitude modulation parameter 4.1, defined above.", The fourth column shows the amplitude modulation parameter $\Delta A_1$ defined above. We note here. the triplet structure has always appeared for all Blazhko stars. ie. no stars show frequency doublets.," We note here, the triplet structure has always appeared for all Blazhko stars, i.e. no stars show frequency doublets." The amplitude of the high frequency peak is higher than the lower for 9 stars., The amplitude of the high frequency peak is higher than the lower for 9 stars. The remaining 5 show the opposite pattern., The remaining 5 show the opposite pattern. " The asymmetry parameter €) defined by Alcocketal.(2003) as Q=ACfo|fedAChfo]AGOfolLACfed)* varies from —0.25] to 0.676 (see the 6th column in refBlazhko,/ars)). howecer.lhesevaluesareratherpreliminargduetothelongL "," The asymmetry parameter $Q$ defined by \cite{Al03} as $Q=[A(f_0+f_{\mathrm B})-A(f_0-f_{\mathrm B})] [A(f_0+f_{\mathrm B})+A(f_0-f_{\mathrm B})]^{-1}$ varies from $-0.251$ to 0.676 (see the 6th column in \\ref{Blazhko_stars}) ), however, these values are rather preliminary due to the long Blazhko cycles." Inthe past few years. thanks to high precision ground- and space-based observations. the known occurrence rate of the Blazhko effect among RRLLyrae stars has increased from the ormer estimate of to a ratio close to (see Juresiket 201023).," Inthe past few years, thanks to high precision ground- and space-based observations, the known occurrence rate of the Blazhko effect among Lyrae stars has increased from the former estimate of to a ratio close to (see \citealt{Jur09, Cha09, Kol10}) )." It is even xossible that all LLyrae stars may show a Blazhko modulation with an increasing frequency of Blazhko stars at lower modulation amplitude., It is even possible that all Lyrae stars may show a Blazhko modulation with an increasing frequency of Blazhko stars at lower modulation amplitude. The measurements provide an ideal tool to test Wo, The measurements provide an ideal tool to test this hypothesis. o dh values in Table 2. it can be seen hat we found only two stars with modulation amplitude lower than .lmmag., From our $\Delta A_1$ values in Table \ref{Blazhko_stars} it can be seen that we found only two stars with modulation amplitude lower than $0.1$ mag. To test our detection limit of the amplitude modulation. artificial light curves were generated.," To test our detection limit of the amplitude modulation, artificial light curves were generated." Two sets of grids were constructed: one for LLyr 77742534) and another for 77030715., Two sets of grids were constructed: one for Lyr 7742534) and another for 7030715. These stars have the shortest and the longest sulsation periods (0.45649dd. and dd) in. the sample. respectively.," These stars have the shortest and the longest pulsation periods d and d) in the sample, respectively." In both cases the Fourier parameters of the main oulsation. frequency and its significant harmonics were used to build the artificial light curves., In both cases the Fourier parameters of the main pulsation frequency and its significant harmonics were used to build the artificial light curves. These were modulated by a simple sinusoidal function with amplitudes ranging between 0.1] anc 001 mmag. and with modulation periods from 25 to dd with a step size of dd. according to the general modulation formula 22) in Benkoetal.(2009).," These were modulated by a simple sinusoidal function with amplitudes ranging between $0.1$ and $0.001$ mag, and with modulation periods from 25 to d with a step size of d, according to the general modulation formula 2) in \cite{Ben09}." . Measured averaged fluxes of he non-Blazhko stars are in the range of 1.8«107>£F2.5.10° AADU which means a noise between S.10 anc 6.10 *mmag., Measured averaged fluxes of the non-Blazhko stars are in the range of $1.8\times 10^8>F>2.7\times 10^6$ ADU which means a noise between $8\times 10^{-5}$ and $6\times 10^{-4}$ mag. This was taken into account by adding Gaussian noise with σ=10 and 5«.10. to the artificial data., This was taken into account by adding Gaussian noise with $\sigma = 10^{-4}$ and $5\times 10^{-4}$ to the artificial data. The ligh curves were always calculated at the observed points of time., The light curves were always calculated at the observed points of time. " In our tests. we reckoned the amplitude modulation as detectable if the highest Fourier side peak connected to the modulation exceeds the spectral significance (7,) 5. ("," In our tests, we reckoned the amplitude modulation as detectable if the highest Fourier side peak connected to the modulation exceeds the spectral significance $\sigma_{\mathrm s}$ ) 5. (" For the definition of the σ. we refer Reegen(2007):: the correspondence between more popular amplitude signal-to-noise ratio SYN (Bregeretal.1993) and σ. is yielded as σ.=5&SYN 3.83).,For the definition of the $\sigma_{\mathrm s}$ we refer \cite{Re07}; the correspondence between more popular amplitude signal-to-noise ratio $S/N$ \citep{Bre03} and $\sigma_{\mathrm s}$ is yielded as $\sigma_{\mathrm s}=5\approx \ S/N=3.83$ ). " The obtained limiting values are ACfo|.fg)2 0.001—0.002 mmag Cor Ack,7 0.005-0.01 mmag) depending on the brightness. but highly independent ofthe periods (Py and Py."," The obtained limiting values are $A(f_0+f_{\mathrm B}) > 0.001$ $0.002$ mag (or $\Delta A_1 > 0.005$ $0.01$ mag) depending on the brightness, but highly independent ofthe periods $_0$ and $_{\mathrm B}$ )." Higher sampling rate (ie. short cadence) does not decrease our detection limit because the present sampling frequency ! is much higher than a typical Blazhko frequency dd1 . hence each Blazhko cycle is covered sufticiently.," Higher sampling rate (i.e. short cadence) does not decrease our detection limit because the present sampling frequency $^{-1}$ is much higher than a typical Blazhko frequency $^{-1}$ ), hence each Blazhko cycle is covered sufficiently." Notwithstanding our efforts. we did not detect any modulation for I5 RRLLyrae stars in our Kepler sample. however. some," Notwithstanding our efforts, we did not detect any modulation for 15 Lyrae stars in our sample, however, some" where the astrometric components are o. 6 for the coordinates. ων 4/5 for the proper motion and Ὁ for the parallax.,"where the astrometric components are $\alpha$ , $\delta$ for the coordinates, $\mu_\alpha$, $\mu_\delta$ for the proper motion and $\varpi$ for the parallax." In addition to fitting the orbital and astrometric properties of the system. a timing zero point and a correction to the orbital period of the eclipsing pair (that could lead to a linear secular increase or decrease of the (O-C)'s) were also considered.," In addition to fitting the orbital and astrometric properties of the system, a timing zero point and a correction to the orbital period of the eclipsing pair (that could lead to a linear secular increase or decrease of the (O–C)'s) were also considered." " The initial values of the period and the reference epoch were adopted from Varricatt Ashok (1999),", The initial values of the period and the reference epoch were adopted from Varricatt Ashok (1999). The full set of observational equations includes those related to the timing residuals (Eq. (1))), The full set of observational equations includes those related to the timing residuals (Eq. \ref{eq1}) )) and those coming from the astrometric measurements (Eqs. (2)). (3). (4))).," and those coming from the astrometric measurements (Eqs. \ref{astro1}) ), \ref{astro2}) ), \ref{astro3}) ))." " All these equations were combined together and the 14 unknown parameters (5 for the astrometric components — à. ὃν qr,. fts. ® —. 7 for the orbital elements — «i». €i. wis. do. Pis. TIS"" Oi; — one for the reference epoch — Τομ -. and one for the period of the eclipsing system — Pig —) were recovered via a weighted least-squares fit as deseribed in. e.g.. Arenou (2001) or Halbwachs et al. ("," All these equations were combined together and the 14 unknown parameters (5 for the astrometric components – $\alpha$, $\delta$ , $\mu_\alpha$ , $\mu_\delta$ , $\varpi$ –, 7 for the orbital elements – $a_{12}$, $e_{12}$, $\omega_{12}$, $i_{12}$, $P_{12}$, $T^{\rm peri}_{12}$, $\Omega_{12}$ –, one for the reference epoch – ${T_{\circ}}_{\rm EB}$ –, and one for the period of the eclipsing system – $P_{\rm EB}$ –) were recovered via a weighted least-squares fit as described in, e.g., Arenou (2001) or Halbwachs et al. (" 2000).,2000). Note that the weights of the individual observations were computed as the inverse of the observational uncertainties squared and multiplied by the corresponding. correlation. factors., Note that the weights of the individual observations were computed as the inverse of the observational uncertainties squared and multiplied by the corresponding correlation factors. The uncertainties adopted are given in Tables | and 2.. and in the Hipparcos Catalogue CD-ROM 5.," The uncertainties adopted are given in Tables \ref{tabastro} and \ref{tabtim}, and in the Hipparcos Catalogue CD-ROM 5." Due to the short timespan of the Hipparcos observations. a large uncertainty on the reflex semi major-axis would exist if the Hipparcos astrometric data were used alone.," Due to the short timespan of the Hipparcos observations, a large uncertainty on the reflex semi major-axis would exist if the Hipparcos astrometric data were used alone." As a first step towards better constraining the solution we added the epoch proper motion from Guinan [anna (1983) as an external observation (with. the two subsequent equations for both components of the proper motion)., As a first step towards better constraining the solution we added the epoch proper motion from Guinan Ianna (1983) as an external observation (with the two subsequent equations for both components of the proper motion). To do so. the appropriate equation for the first derivatives of the orbital motion was used.," To do so, the appropriate equation for the first derivatives of the orbital motion was used." As expected. the quality of the solution improved and yielded a semi major axis of aj»=140c16 mas and a tertiary mass of M3=0.424E0.05 M...," As expected, the quality of the solution improved and yielded a semi major axis of $a_{12}=140\pm16$ mas and a tertiary mass of $M_3=0.42\pm0.05$ $_{\odot}$." Yet. a closer inspection of the residuals revealed that this solution was not fully compatible with the ground-based epoch positions mentioned in $??.. as a clear trend appeared in declination.," Yet, a closer inspection of the residuals revealed that this solution was not fully compatible with the ground-based epoch positions mentioned in \ref{astro}, as a clear trend appeared in declination." For this reason we decided to include these positions also in the fit. together with the Guinan [anna proper motion and the photometric (O-C) minimum times.," For this reason we decided to include these positions also in the fit, together with the Guinan Ianna proper motion and the photometric (O–C) minimum times." In total. the least-squares fit had 262 equations for 14 parameters to determine.," In total, the least-squares fit had 262 equations for 14 parameters to determine." A robust fit approach (McArthur. Jefferys. McCartney 1994) was used due to the large dispersion of the ground-based astrometric measurements.," A robust fit approach (McArthur, Jefferys, McCartney 1994) was used due to the large dispersion of the ground-based astrometric measurements." The resulting goodness of the fit was 0.63 and graphical representations of the fits to the eclipse timing residuals and Hipparcos intermediate astrometry are shown in Figure |.., The resulting goodness of the fit was 0.63 and graphical representations of the fits to the eclipse timing residuals and Hipparcos intermediate astrometry are shown in Figure \ref{figfit}. The less-accurate ground-based astrometric positions (with standard errors of about 200 mas on average) are not represented in the figure for the sake of clarity., The less-accurate ground-based astrometric positions (with standard errors of about 200 mas on average) are not represented in the figure for the sake of clarity. The resulting best-fitting parameters together with their standard deviations are listed in Table 3.., The resulting best-fitting parameters together with their standard deviations are listed in Table \ref{tabprop}. . The astrometric solution presented supersedes that of the Hipparcos Catalogue because it is based upon a sophisticated model that accounts for the orbital motion and considers ground-based astrometry., The astrometric solution presented supersedes that of the Hipparcos Catalogue because it is based upon a sophisticated model that accounts for the orbital motion and considers ground-based astrometry. Also. Table 3 includes the mass and semi-major axis of R CMa C that follow from the adoption of a total mass for the eclipsing system.," Also, Table \ref{tabprop} includes the mass and semi-major axis of R CMa C that follow from the adoption of a total mass for the eclipsing system." Finally. our fit also yields new accurate ephemeris for the eclipsing pair: where all times are in the TT scale and the zero epoch refers to the geometric center of the R CMa orbit.," Finally, our fit also yields new accurate ephemeris for the eclipsing pair: where all times are in the TT scale and the zero epoch refers to the geometric center of the R CMa orbit." Note that the accuracy of the new period we determine (see Table 3)) is better than 9 milliseconds., Note that the accuracy of the new period we determine (see Table \ref{tabprop}) ) is better than 9 milliseconds. We have considered in our analysis a linear ephemeris as that in Eq. (5))., We have considered in our analysis a linear ephemeris as that in Eq. \ref{ephem}) ). However. Algol systems have been observed to experience secular decreases of the orbital periods possibly due to non-conservative mass transfer and angular momentum loss (see. e.g.. Qian 2000a).," However, Algol systems have been observed to experience secular decreases of the orbital periods possibly due to non-conservative mass transfer and angular momentum loss (see, e.g., Qian 2000a)." To assess the significance of this effect on R CMa. we modified our fitting program by considering a quadratic term.," To assess the significance of this effect on R CMa, we modified our fitting program by considering a quadratic term." The coefficient of this quadratic term was found to be (-2.1£1.1).107!! d. which translates into a period decrease rate of dP/dt=10° d yr7!.," The coefficient of this quadratic term was found to be $(-2.1\pm1.1)\cdot10^{-11}$ d, which translates into a period decrease rate of $dP/dt = (-6.9\pm3.6)\cdot10^{-9}$ d $^{-1}$." This is a very slow rate compared to other Algol systems (see. e.g.. Qian 2001) yet commensurate with the low activity level of R CMa. which ts near the end of its mass- stage.," This is a very slow rate compared to other Algol systems (see, e.g., Qian 2001) yet commensurate with the low activity level of R CMa, which is near the end of its mass-transfer stage." Because of the poor significance (below 26) of the period decrease rate derived from the analysis. we decided to neglect the quadratic term and adopt a linear ephemeris.," Because of the poor significance (below $\sigma$ ) of the period decrease rate derived from the analysis, we decided to neglect the quadratic term and adopt a linear ephemeris." It should be pointed out. however. that the astrometric and orbital parameters resulting from the fit with quadratic ephemeris are well within one sigma of those listed 1n Table 3..," It should be pointed out, however, that the astrometric and orbital parameters resulting from the fit with quadratic ephemeris are well within one sigma of those listed in Table \ref{tabprop}." Interestingly. a closer inspection of Figure | reveals small excursions of the data from the LTT fit.," Interestingly, a closer inspection of Figure \ref{figfit} reveals small excursions of the data from the LTT fit." To investigate these. we computed the fit residuals which are shown in Figure 2..," To investigate these, we computed the fit residuals which are shown in Figure \ref{figres}." The presence of low-amplitude cyclic deviations seems quite obviousin this plot., The presence of low-amplitude cyclic deviations seems quite obviousin this plot. If these (O-C) timing oscillations were caused by the perturbation of a fourth body in a circular orbit (R CMa D). its orbital period. would be about 45 yr. with a LTT semiamplitude of 275 s. à minimum mass of 0.06 .. and an orbital semi-major axis of about 14. AU.," If these (O–C) timing oscillations were caused by the perturbation of a fourth body in a circular orbit (R CMa D), its orbital period would be about 45 yr, with a LTT semiamplitude of 275 s, a minimum mass of 0.06 $_{\odot}$, and an orbital semi-major axis of about 14 AU." The orbit of the third body ts highly eccentric so that it would be interior to that of R CMa C near its periastron (rip=9.5 AU)., The orbit of the third body is highly eccentric so that it would be interior to that of R CMa C near its periastron ${r_3}_{\rm P}=9.5$ AU). The intersections of the two orbits would result in an apparently unstable configuration., The intersections of the two orbits would result in an apparently unstable configuration. Other possible explanations for the low-amplitude oscillations include abrupt period changes of the binary itself caused by variable angular momentum loss and magnetic coupling (see. e.g.. Qian 2000b). a magnetic activity cycle of the secondary star (see. e.g.. Applegate 1992). or simply a spurious effect caused by the inhomogeneity of the data set.," Other possible explanations for the low-amplitude oscillations include abrupt period changes of the binary itself caused by variable angular momentum loss and magnetic coupling (see, e.g., Qian 2000b), a magnetic activity cycle of the secondary star (see, e.g., Applegate 1992), or simply a spurious effect caused by the inhomogeneity of the data set." Unfortunately. the available astrometric data are not sensitive enough to prove or refute the existence of a fourth body and only new accurate photometric eclipse timing determinations or high-accuracy astrometry will provide the necessary evidence.," Unfortunately, the available astrometric data are not sensitive enough to prove or refute the existence of a fourth body and only new accurate photometric eclipse timing determinations or high-accuracy astrometry will provide the necessary evidence." The orbital. astrometric. and physical properties presented in Table 3 are within Io of the (less accurate) earlier estimates of Radhakrishnan et al. (," The orbital, astrometric, and physical properties presented in Table \ref{tabprop} are within $\sigma$ of the (less accurate) earlier estimates of Radhakrishnan et al. (" 1984). who based their analysis on eclipse timings up to 1982.,"1984), who based their analysis on eclipse timings up to 1982." However. our study. in addition to extending the time baseline. has been able to determine the inclination of the third body's orbit by making use of the available high-precision astrometry (Hipparcos).," However, our study, in addition to extending the time baseline, has been able to determine the inclination of the third body's orbit by making use of the available high-precision astrometry (Hipparcos)." Thus. R CMa joins Algol. the prototype of its class. in having the orbital properties of the third body determined from a combined analysis of the astrometry and LTT.," Thus, R CMa joins Algol, the prototype of its class, in having the orbital properties of the third body determined from a combined analysis of the astrometry and LTT." The long period (~93 yr) ofR CMa C is the longest period detected and confirmed so far for an eclipsing binary., The long period $\sim$ 93 yr) of R CMa C is the longest period detected and confirmed so far for an eclipsing binary. This is chiefly because of the large LTT present in R CMa (total amplitude of 86 min) and the existence of eclipse timings available for this star back to 1887., This is chiefly because of the large LTT present in R CMa (total amplitude of 86 min) and the existence of eclipse timings available for this star back to 1887. It is interesting tonote that the inclination of R CMa C is foundto beof +9245°and thus compatible with an edge-on value of 90°., It is interesting tonote that the inclination of R CMa C is foundto beof $\approx$$92\pm5^{\circ}$and thus compatible with an edge-on value of $^{\circ}$ . In this situation. mutual eclipses of the tertiary component and the close binary pair mightoccur.," In this situation, mutual eclipses of the tertiary component and the close binary pair mightoccur." This tantalizing possibility is. however. very unlikely since eclipses," This tantalizing possibility is, however, very unlikely since eclipses" galaxies is Madau&Pozzetti(2000) and at the upper lo bound of Keenanetal.(2010).,galaxies is \citet{madau00} and at the upper $\sigma$ bound of \citet{keenan10}. ". Our results do not strongly limit the possibility that an excess of a few nW m? sr! from high redshift could exist at or above this wavelength, but do disfavor a scenario in which such an excess continues below a wavelength of ~1.2µπι.."," Our results do not strongly limit the possibility that an excess of a few nW $^{-2}$ $^{-1}$ from high redshift could exist at or above this wavelength, but do disfavor a scenario in which such an excess continues below a wavelength of $\sim 1.2$." " Our intent with this work is not just to compute the current limits on high-redshift star-formation available from gamma-ray observations, but also to demonstrate the usefulness of this method for future observations."," Our intent with this work is not just to compute the current limits on high-redshift star-formation available from gamma-ray observations, but also to demonstrate the usefulness of this method for future observations." Figs., Figs. 5 and 6 illustrate the SFRD limits that could be derived from future detections of high redshift sources withFermi LAT or future telescopes., \ref{fig:sfrdcont_zr6} and \ref{fig:sfrdcont_zr9} illustrate the SFRD limits that could be derived from future detections of high redshift sources with LAT or future telescopes. " In these plots, the axes refer to the redshift and highest observed photon energy E, of a hypothetical gamma-ray source."," In these plots, the axes refer to the redshift and highest observed photon energy $E_\gamma$ of a hypothetical gamma-ray source." The source is then assumed to have a normalization at lower energy such that the expected number of photon, The source is then assumed to have a normalization at lower energy such that the expected number of photon 3διν. and were chosen to give roughly equal numbers in each sub-sample.,"28K, and were chosen to give roughly equal numbers in each sub-sample." The actual numbers of galaxies in the sub-saniples were 4452. 4388 and 4107 respectively.," The actual numbers of galaxies in the sub-samples were 4452, 4388 and 4107 respectively." The mean {τουfoo colour ratios for the hot. warm ancl cold sub-samples were 1.31. 1.98 and 2.91 respectively. corresponding to black-body temperatures of about 34Ix. 901 and. 26.51. respectively.," The mean $f_{100}/f_{60}$ colour ratios for the hot, warm and cold sub-samples were 1.31, 1.98 and 2.91 respectively, corresponding to black-body temperatures of about 34K, 30K and 26.5K respectively." Ehe mean for the whole catalogue is 2.05. corresponding to a black-body temperature of around 29.5Ix. The redshift) distributions for the sub-samples are plotted in Figure 1((a) ancl it can be seen that the cooler samples tend to peak at a slightly lower redshift than the hotter samples.," The mean for the whole catalogue is 2.05, corresponding to a black-body temperature of around 29.5K. The redshift distributions for the sub-samples are plotted in Figure \ref{f_nz}( (a) and it can be seen that the cooler samples tend to peak at a slightly lower redshift than the hotter samples." This rellects the correlation between colour and absolute luminositw as plotted. in. Figure δι cooler ealaxies tend to be fainter. and so are only seen nearby.," This reflects the correlation between colour and absolute luminosity as plotted in Figure \ref{f_colf}: cooler galaxies tend to be fainter, and so are only seen nearby." Nevertheless. these differences in redshift distributions are smaller than the clillerence for luminosity selected samples. as discussed in the next section.," Nevertheless, these differences in redshift distributions are smaller than the difference for luminosity selected sub-samples, as discussed in the next section." The angular clistribution of these sub-samples are plotted in Figure 3.., The angular distribution of these sub-samples are plotted in Figure \ref{f_skyplots}. Lt can be seen that these samples show no obvious gradients as a function of position on the sky. and also that the cooler sample appears to be more strongly clustered.," It can be seen that these samples show no obvious gradients as a function of position on the sky, and also that the cooler sample appears to be more strongly clustered." Figure 4. shows the projection of the galaxies on to a plane along the celestial equator., Figure \ref{f_xyplots} shows the projection of the galaxies on to a plane along the celestial equator. Again the cooler sample appears more clustered than the warmer samples., Again the cooler sample appears more clustered than the warmer samples. Though apparently quite significant. these visual impressions should be treated: with caution.," Though apparently quite significant, these visual impressions should be treated with caution." The cooler sample is shallower than the warmer samples. so the angular clustering would be stronger. even if the samples had the same spatial clustering.," The cooler sample is shallower than the warmer samples, so the angular clustering would be stronger, even if the samples had the same spatial clustering." Also the cool sample has a higher space density than the warmer samples. and this may enhance the visual appearance of clustering.," Also the cool sample has a higher space density than the warmer samples, and this may enhance the visual appearance of clustering." " The parent sample was also civiclecl into sub-samples of absolute luminosity at 60/72: faint galaxies. with ΟδLoo)<9.6: and bright galaxies with log),(Lou)z 9.6. where Loo=tad?foo and d is the luminosity distance to he galaxy (we assumed ©=1 and A=0 to determine the geometry. but at the distances considered here. cosmological ellects are negligible.)"," The parent sample was also divided into sub-samples of absolute luminosity at $60 \mu m$: faint galaxies, with $\log_{10}(L_{60}) < 9.6$; and bright galaxies with $\log_{10}(L_{60}) > 9.6 $ , where $L_{60} = 4 \pi d^2 f_{60}$ and $d$ is the luminosity distance to the galaxy (we assumed $\Omega=1$ and $\Lambda=0$ to determine the geometry, but at the distances considered here, cosmological effects are negligible.)" " The units of Ley are L.h7."" Note hat the usual definition of an ultra-Iuminous£15 galaxy corresponds to log)(Lou)=11.4 (Soifer et al 1987). and so he lower limit of our brighter sample is a factor of ~ 60 zinter than ultra-Iuminous galaxy samples."," The units of $L_{60}$ are $L_{\odot}h^{-2}.$ Note that the usual definition of an ultra-luminous galaxy corresponds to $\log_{10}(L_{60}) \simgt 11.4 $ (Soifer et al 1987), and so the lower limit of our brighter sample is a factor of $\sim$ 60 fainter than ultra-luminous galaxy samples." The bright sample has a higher mean redshift. and ience covers a much larger volume. but the galaxies are a more dilute. sampling of the density field. ancl so a arger number is needed to give a similar number of small separation pairs.," The bright sample has a higher mean redshift, and hence covers a much larger volume, but the galaxies are a more dilute sampling of the density field and so a larger number is needed to give a similar number of small separation pairs." Llence the faint and. bright. samples were chosen to have 4719 and S228 galaxies respectively., Hence the faint and bright samples were chosen to have 4719 and 8228 galaxies respectively. The redshift distribution for these sub-saniples is shown in Figure 1((b)., The redshift distribution for these sub-samples is shown in Figure \ref{f_nz}( (b). Since the parentsample is Hux limited. the low luminosity galaxies have a sharply defined upper redshift," Since the parentsample is flux limited, the low luminosity galaxies have a sharply defined upper redshift" "fzJtot(Z), where fracozJiot(Z)7 is the(4) total charging rate due to collisional charging and photoemission (see Draine Sutin 1987; Weingartner Draine ",", where $J_{\rm tot}(Z)$ is the total charging rate due to collisional charging and photoemission (see Draine Sutin 1987; Weingartner Draine 2001)." Here we averaged over all possible charge states Z to 2001).find rz., Here we averaged over all possible charge states $Z$ to find $\tau_{Z}$. " In an ambient magnetic field B, the grain with mean charge (Z)e gyrates about B on a timescale equal to the Larmor period: ym where m=4/31a?pa with pq being the dust mass density is the grain mass."," In an ambient magnetic field $\Bv$, the grain with mean charge $\langle Z\rangle e$ gyrates about $\Bv$ on a timescale equal to the Larmor period: ), where $m=4/3\pi a^{3}\rho_{d}$ with $\rho_{d}$ being the dust mass density is the grain mass." " We adopt pq=2.2 and 3.0 g cm? for graphite and silicate grains, respectively."," We adopt $\rho_{d}=2.2$ and $3.0$ g $\cm^{-3}$ for graphite and silicate grains, respectively." The Larmorfrequency reads Ω=((Z)eB)/mc., The Larmorfrequency reads $\Omega=(\langle{Z}\rangle eB)/mc$. We calculate the relaxation time of charge fluctuations Tg for both graphite and silicate grains invarious phases of the ISM with physical parameters listed in Table 1., We calculate the relaxation time of charge fluctuations $\tau_{Z}$ for both graphite and silicate grains invarious phases of the ISM with physical parameters listed in Table 1. Figure 2 compares rz with the gas drag time Tarag (see Eq. 8)), Figure \ref{timescale} compares $\tau_{Z}$ with the gas drag time $\tau_{\drag}$ (see Eq. \ref{tau_drag}) ) and the Larmor period Τι., and the Larmor period $\tau_{L}$. It can be seen that TzXTjτι, so that the assumption for grains to have a constant charge is no longer valid."," For grains smaller than $\sim2\times 10^{-7}$ cm, $\tau_{Z} \ge \tau_{L}$, so that the assumption for grains to have a constant charge is no longer valid." " As a result, the fluctuations of grain charge should be accounted for in the treatment of resonance acceleration for such very small grains."," As a result, the fluctuations of grain charge should be accounted for in the treatment of resonance acceleration for such very small grains." " This issue will be addressed in our future paper, in which we employ Monte Carlo method to simulate grain charge fluctuations (see e.g., Hoang Lazarian 2011)."," This issue will be addressed in our future paper, in which we employ Monte Carlo method to simulate grain charge fluctuations (see e.g., Hoang Lazarian 2011)." " In the present paper, for the sake of simplicity, we adopt (Z)e for grain charge within the entire range of the grain size distribution."," In the present paper, for the sake of simplicity, we adopt $\langle Z\rangle e$ for grain charge within the entire range of the grain size distribution." Interactions of dust grains with the ambient gas present the primary mechanism of dissipating translational motions of grains., Interactions of dust grains with the ambient gas present the primary mechanism of dissipating translational motions of grains. " The damping rate of translational motion arising from the interaction with neutral gas is essentially the inverse time for collisions with the mass of the gas equal that of a grain (Purcell 1969), )—1, where Mn, Nn, and T; are the mass, volume density, and temperature of neutrals, and ais the grain radius."," The damping rate of translational motion arising from the interaction with neutral gas is essentially the inverse time for collisions with the mass of the gas equal that of a grain (Purcell 1969), ), where $m_n$, $n_n$, and $T_n$ are the mass, volume density, and temperature of neutrals, and $a$is the grain radius." " When the ionization degree is sufficiently high, the interaction of charged grains with the plasma becomes important."," When the ionization degree is sufficiently high, the interaction of charged grains with the plasma becomes important." The ion-grain cross section due to long-range Coulomb forces is larger than the atom-grain cross section., The ion-grain cross section due to long-range Coulomb forces is larger than the atom-grain cross section. " As a result, the rate of translational motion damping gets modified."," As a result, the rate of translational motion damping gets modified." " For subsonic motions the effective damping time due to gas drag is renormalized: with the following renormalizing factor (Draine Salpeter 1979) ((“BFL))9/2]. Here x; is the abundance of ion i (relative to hydrogen) with mass m; and temperature T;, y=So, ai, Ze "," For subsonic motions the effective damping time due to gas drag is renormalized: with the following renormalizing factor (Draine Salpeter 1979) ] Here $x_{i}$ is the abundance of ion $i$ (relative to hydrogen) with mass $m_{i}$ and temperature $T_i$ , $x=\sum_i x_i$ , $Ze$ " power-law [lux from the to the state. the ICD flux seems to increase with increasing kT. Tis result may suggest (iM (he variability is linked with [Inetuations in the accretion rate.,"power-law flux from the to the state, the MCD flux seems to increase with increasing kT. This result may suggest that the variability is linked with fluctuations in the accretion rate." For the MCD conponent. the lower lini( of 37 km to the inner radius of the disk (Table 2:: the limit is «lue (ο the presence of the vcos [actor accounting for the inclination angle of the disk) impies a lower limit to the nass of the compact object of ~4.2...," For the MCD component, the lower limit of 37 km to the inner radius of the disk (Table \ref{fit}; the limit is due to the presence of the $\sqrt{\cos\theta}$ factor accounting for the inclination angle of the disk) implies a lower limit to the mass of the compact object of $\sim4.2M_{\odot}$." The Eddington limit [or this mass is Liu;=6.3xLO erg/sec. that is consistent with the + disk emission of the source.," The Eddington limit for this mass is $_{Edd}=6.3\times 10^{38}$ erg/sec, that is consistent with the power-law + disk emission of the source." This is in agreement with the conclusion of Parmaretal. (2001).. Takanoetal.(1994) and Dubus&Rutledge(2002) Chat M33. X-8 is most likely a normal binary svsten containing a stellar mass black hole Chat happens to be at the center ol the galaxy. rather than an AGN.," This is in agreement with the conclusion of \citet{parmar}, \citet{takano} and \citet{dubus2} that M33 X-8 is most likely a normal binary system containing a stellar mass black hole that happens to be at the center of the galaxy, rather than an AGN." Although not extreme. the spectral variability of M33 X-8 ds reminiscent of what has been observed in black hole binaries.," Although not extreme, the spectral variability of M33 X-8 is reminiscent of what has been observed in black hole binaries." In the Galactic black hole binaries we usually observe a high/soft state”. dominated by a hot disk. sometimes associated wilh a faint power-law (ail. and a ονμάνα state” dominated by a power-law spectrum. with a colder disk component (see.e.g..Esin.MeClintockandNaravan1997).," In the Galactic black hole binaries we usually observe a “high/soft state”, dominated by a hot disk, sometimes associated with a faint power-law tail, and a “low/hard state” dominated by a power-law spectrum, with a colder disk component \citep[see, e.g., ][]{esin}." . The soft state is explained with high accretion rate. with the accreting disk. going down toward the last stable orbit. while (he hard state is associated to a lower accretion rate that causes (he disruption of the inner part of the disk and the presence of a comptonized corona wrapping the central source.," The soft state is explained with high accretion rate, with the accreting disk going down toward the last stable orbit, while the hard state is associated to a lower accretion rate that causes the disruption of the inner part of the disk and the presence of a comptonized corona wrapping the central source." In the case of M33 X-8 both disk ancl power-law component are always present. but the power-law dominated.L-Ioin state corresponds with a lower flux in (he medium energv band (1.5-4.5 keV).," In the case of M33 X-8 both disk and power-law component are always present, but the power-law dominated state corresponds with a lower flux in the medium energy band (1.5-4.5 keV)." With increasing medium band flux the spectrum evolves to be dominated by the disk component., With increasing medium band flux the spectrum evolves to be dominated by the disk component. The source (hat resembles more M33. N-8 is probably LAIC X-3 (Nowaketal.2001).. à black hole candidate with a probable mass of 9.4. and a luminosity of up to +x109 erg/s. M33 X-8 presents many similuiües with LAIC X-3: the thermal spectrum. that can be modelled with a MCD (with kT~0.8 in LMC X-3 and kT~1.2 in M33 X-3) and a steep power-law: the presence of variability on timescales of some ten thousands of seconds: a long timescale periocicity (116 d for M33 X-8 and 99 or 198 d for LMC: X-3. see and Cowleyetal. 1991)) Chat appears to vary or even disappear in a few vears 2001)...," The source that resembles more M33 X-8 is probably LMC X-3 \citep{nowak}, a black hole candidate with a probable mass of $9 M_{\odot}$ and a luminosity of up to $4\times 10^{38}$ erg/s. M33 X-8 presents many similarities with LMC X-3: the thermal spectrum, that can be modelled with a MCD (with $\sim 0.8$ in LMC X-3 and $\sim 1.2$ in M33 X-8) and a steep power-law; the presence of variability on timescales of some ten thousands of seconds; a long timescale periodicity (116 d for M33 X-8 and 99 or 198 d for LMC X-3, see \citealp{dubus} and \citealp{cowley}) ) that appears to vary or even disappear in a few years \citep{nowak,parmar}." Also. LAIC X-3 is characterized by a lack of fast. variability (on timescales <1 s). but this feature cannot be investigated in M33 X-8. due to the lack of data with high enough temporal resolution.," Also, LMC X-3 is characterized by a lack of fast variability (on timescales $\lesssim 1$ s), but this feature cannot be investigated in M33 X-8, due to the lack of data with high enough temporal resolution." Ilowever the power-law component is relatively more prominent 1n. M23. X-5., However the power-law component is relatively more prominent in M33 X-8. " Concluding.concluding. the spectral variability observations of the nucleus of ofM33M33. (X-3)(X-8) strongly agree with the suggestion that this source is an accreting Z5 M, black hole with a variable accretion disk. comparable to Galactic black hole binaries."," Concluding, the spectral variability observations of the nucleus of M33 (X-8) strongly agree with the suggestion that this source is an accreting $\gtrsim5$ $_{\odot}$ black hole with a variable accretion disk, comparable to Galactic black hole binaries." and the lower panel the 2D spectral image extended residuals after PSF-subtraction.,and the lower panel the 2D spectral image extended residuals after PSF-subtraction. There are very few positive or negative residuals at velocities <—400 or >+500 ss“! which shows how well our spectral PSF-modeling works., There are very few positive or negative residuals at velocities $<-400$ or $>+500$ $^{-1}$ which shows how well our spectral PSF-modeling works. The extended emission appears clumpy both spatially and kinematically., The extended emission appears clumpy both spatially and kinematically. This structure will be investigated further below., This structure will be investigated further below. One of the surprising things about the residual extended emission is that its flux is so low., One of the surprising things about the residual extended emission is that its flux is so low. " Recall that in Section 2 we showed that the extended emission identified in Subaru imaging contributes of the total z’ band flux, assuming a maximal PSF-subtraction."," Recall that in Section 2 we showed that the extended emission identified in Subaru imaging contributes of the total $z'$ band flux, assuming a maximal PSF-subtraction." To compare to the extended flux in the spectrum we need to consider differential slit losses for the PSF and extended emission and the wavelength range over which to integrate., To compare to the extended flux in the spectrum we need to consider differential slit losses for the PSF and extended emission and the wavelength range over which to integrate. Differential slit losses for the ESI seeing based on the Subaru imaging show that we expect of the total observed spectroscopic z’ band flux to come from extended emission., Differential slit losses for the ESI seeing based on the Subaru imaging show that we expect of the total observed spectroscopic $z'$ band flux to come from extended emission. Direct measurement of the flux between 9000 and iin the upper panel of Figure ο shows that the extended emission contributes of the total flux over this narrow wavelength range containing the extended eemission., Direct measurement of the flux between 9000 and in the upper panel of Figure \ref{fig:twodspec} shows that the extended emission contributes of the total flux over this narrow wavelength range containing the extended emission. " Over a wider wavelength range of 9000 toAA,, the extended component is only of the total flux."," Over a wider wavelength range of 9000 to, the extended component is only of the total flux." " Based on the Suprime-Cam z’ band response curve, of the flux from the quasar in this filter comes from 9000 toAA."," Based on the Suprime-Cam $z'$ band response curve, of the flux from the quasar in this filter comes from 9000 to." ". Therefore, only of the z' band flux in the ESI slit comes from the extended component, compared to the expected10%.."," Therefore, only of the $z'$ band flux in the ESI slit comes from the extended component, compared to the expected." The majority of the extended emission observed in Subaru imaging is unaccounted for in our spectroscopy., The majority of the extended emission observed in Subaru imaging is unaccounted for in our spectroscopy. Possible reasons for this missing extended flux are that the broad-line region/continuum flux (which we used to determine the PSF) is also spatially resolved or that we have substantially overestimated the PSF scaling for the narrow part of the Iline., Possible reasons for this missing extended flux are that the broad-line region/continuum flux (which we used to determine the PSF) is also spatially resolved or that we have substantially overestimated the PSF scaling for the narrow part of the line. " (09 proposed that of the extended z' band emission was continuum flux from an extreme starburst (M1459=23.9) in the host galaxy, based on their tentative detection of extended emission at z, band."," G09 proposed that of the extended $z'$ band emission was continuum flux from an extreme starburst $M_{1450}=23.9$ ) in the host galaxy, based on their tentative detection of extended emission at $z_r$ band." We have no evidence for extended continuum based on Figure 4.., We have no evidence for extended continuum based on Figure \ref{fig:snrresid}. " Also the PSF-fit appears to do an equally good job at accounting for all the observed ESI flux at velocities corresponding to the broad eemission (velocities —2000 to —500 ss""! and +500 to +200055!) as it does at longer wavelengthskkm where the quasar kkmcontinuum dominates.", Also the PSF-fit appears to do an equally good job at accounting for all the observed ESI flux at velocities corresponding to the broad emission (velocities $-2000$ to $-500$ $^{-1}$ and $+500$ to $+2000$ $^{-1}$ ) as it does at longer wavelengths where the quasar continuum dominates. " Even the extreme starburst advocated by G09 would be a minor component in the broad wwavelength region, so this argues against significant extended continuum."," Even the extreme starburst advocated by G09 would be a minor component in the broad wavelength region, so this argues against significant extended continuum." " It is more likely that we have overestimated the PSF scaling for the lline, since we have no independent constraint on this normalization."," It is more likely that we have overestimated the PSF scaling for the line, since we have no independent constraint on this normalization." In this case up to half of the narrow eemission could be in the extended component., In this case up to half of the narrow emission could be in the extended component. The fact that our seeing is substantially worse than that of the imaging observations is another complicating factor., The fact that our seeing is substantially worse than that of the imaging observations is another complicating factor. " Even though our observations leave some puzzle about the bulk of the extended emission, it is interesting to consider the spatial structure and kinematics of the resolved eemission."," Even though our observations leave some puzzle about the bulk of the extended emission, it is interesting to consider the spatial structure and kinematics of the resolved emission." Figure 6 shows the velocity profile for the whole hhalo and for the two spatially distinct components on the, Figure \ref{fig:velprofile} shows the velocity profile for the whole halo and for the two spatially distinct components on the science target mages.,science target images. Additionally. was ruu to fit the white dwarf only. with no information provided ou the neighboring source.," Additionally, was run to fit the white dwarf only, with no information provided on the neighboring source." It is noteworthy that the task returned similar results for these two approaches. within at all four IRAC wavelengths.," It is noteworthy that the task returned similar results for these two approaches, within at all four IRAC wavelengths." Second. relative aperture photometry was performed on 00106. 3253 aud a moderately bright. nearby star 3237186: this star cau be seen in Figures 3. and L. 3376 distant from the white dwarf.," Second, relative aperture photometry was performed on $-$ 3253 and a moderately bright, nearby star $-$ 3237486; this star can be seen in Figures \ref{fig4} and \ref{fig5}, $33\farcs6$ distant from the white dwarf." Robust centroids were deteriunued for each star usine both gaussian profile analysis aud PSF fitting: the centroids im all four channels were averaged for cach star and found to agree to within 1 standard deviation of O.1L0ppixels., Robust centroids were determined for each star using both gaussian profile analysis and PSF fitting; the centroids in all four channels were averaged for each star and found to agree to within 1 standard deviation of pixels. The centroid for the comparison star was taken to be fixed while photometry for the white dwarf was performed at a total of uie positions: at the nuonünal ceutroid plus at cight positions along a circle of radius ppixels about this center. spaced eveuly at aueles 45 to 3607 in the wy nuage plane.," The centroid for the comparison star was taken to be fixed while photometry for the white dwarf was performed at a total of nine positions; at the nominal centroid plus at eight positions along a circle of radius pixels about this center, spaced evenly at angles 45 to $360\arcdeg$ in the $xy$ image plane." Photometry was executed in halfpixel steps frπα 1 to Lppixcls., Photometry was executed in half-pixel steps from 1 to pixels. The sale relative photometric analysis was also performed for two raudonilv selected point sources (called starl and μίαν») within the 00106 3253 IRAC feld of view., The same relative photometric analysis was also performed for two randomly selected point sources (called 'star1' and 'star2') within the $-$ 3253 IRAC field of view. Lastly. the 2\LASS comparison star was input todaophot as a refercuce PSF. aud the white dwarfflux was re-nieasured as above.," Lastly, the 2MASS comparison star was input to as a reference PSF, and the white dwarf flux was re-measured as above." Figure 5 plots the results of the relative. flux meastremenuts between the white dwart aud 2MÁSS conrparison star., Figure \ref{fig6} plots the results of the relative flux measurements between the white dwarf and 2MASS comparison star. Each datum is tlicaverage and 30: error among the niue positions where the white dwarf flux was nieasured., Each datum is the average and $3\sigma$ error among the nine positions where the white dwarf flux was measured. Also shown in thο plot are the fluxes as determined bydaophot. averaofayed over the 3 sets of PSF stars. aud the expected white dwart plotospheric fluxes as cleternuned bv the mode] shown in Figure 1..," Also shown in the plot are the fluxes as determined by, averaged over the 3 sets of PSF stars, and the expected white dwarf photospheric fluxes as determined by the model shown in Figure \ref{fig1}. ." Two things are apparent from the figure and analysis: 1) 3253 is photometrically extended bevoud r=2ppixels. aud possibly bevouc 1.5ppixels: 2) thedaophot flux measurements are in good agreement witli the fluxes deteriuued bv relative photometry with the 2ATASS comparison star at r=2 ppixels.," Two things are apparent from the figure and analysis: 1) $-$ 3253 is photometrically extended beyond $r=2$ pixels, and possibly beyond pixels; 2) the flux measurements are in good agreement with the fluxes determined by relative photometry with the 2MASS comparison star at $r=2$ pixels." The fluxes determined by these methods are listed in Table 5.. iux a series of representative images are shown in Fieures 3. and [L..," The fluxes determined by these methods are listed in Table \ref{tbl5}, and a series of representative images are shown in Figures \ref{fig4} and \ref{fig5}." Both methods vield IRAC. fluxes in excess of the predicted. plotspheric chussion of the white dwarf based ou the mode plotted in Figure 1: the weighted average of these is pktted in the Figure. aud listed in Table 2.., Both methods yield IRAC fluxes in excess of the predicted photospheric emission of the white dwarf based on the model plotted in Figure \ref{fig1}; the weighted average of these is plotted in the Figure and listed in Table \ref{tbl2}. The excess at cach IRAC waveleneth los in the range 3.So using the errors derived via the individual measurements. «xr within 560 using the weightcc average errors.," The excess at each IRAC wavelength lies in the range $3-5\sigma$ using the errors derived via the individual measurements, or within $5-6\sigma$ using the weighted average errors." The nearby galaxy caunot account for the results of the PSF fitting photometry where extracted sources list conform to a relatively static. model point source.," The nearby galaxy cannot account for the results of the PSF fitting photometry where extracted sources must conform to a relatively static, model point source." The last paucl of Figures 3 and | displavs the PSF ft aud removal of the white dwarf at the expected shotospheric level: a point-like residual (excess) is seen at the location of the white chart., The last panel of Figures \ref{fig4} and \ref{fig5} displays the PSF fit and removal of the white dwarf at the expected photospheric level; a point-like residual (excess) is seen at the location of the white dwarf. To assess the potential fiux contamination bv the ealaxy. a racial profile aud. vector analysis of the white dwarf Hux was performed.," To assess the potential flux contamination by the galaxy, a radial profile and vector analysis of the white dwarf flux was performed." Doh 1D eaussian profile fitting and a raw vector eut (σας1 of 3ppixcl width) were executed across the white dwart in the direction towards and away from the ealaxy. and he fluxes on either side were compared.," Both 1D gaussian profile fitting and a raw vector cut (each of pixel width) were executed across the white dwarf in the direction towards and away from the galaxy, and the fluxes on either side were compared." " Frou these anaVSCS, it is found that at r= 2ppixels from the white «lwarf coutroid. the side nearest the galaxy contaius at nvost amore flux than the side opposite at pam. aud 10 More than at the three longer wavelenetls."," From these analyses, it is found that at $r=2$ pixels from the white dwarf centroid, the side nearest the galaxy contains at most more flux than the side opposite at $\mu$ m, and no more than at the three longer wavelengths." ", Asstlug a worst case scenario where «w-half of the photometric] :yerture is biased iu this manner certain not to be tlC Case then the galaxy contributes a 1naxinmua of of the neasured flux at all wavelengths except pau. where it is limited to"," Assuming a worst case scenario where one-half of the photometric aperture is biased in this manner – certain not to be the case – then the galaxy contributes a maximum of of the measured flux at all wavelengths except $\mu$ m, where it is limited to." The excess flux ploosphere) relative to the measured fux is 27. 32. 39. and at 3.6. 15. 5.7. aud. jn. imid hence the potential influence of the galaxy caunot account this excess.," The excess flux $-$ photosphere) relative to the measured flux is 27, 32, 39, and at 3.6, 4.5, 5.7, and $\mu$ m, and hence the potential influence of the galaxy cannot account this excess." Frou this analysis. if appears that 3253 has an infrared excess.," From this analysis, it appears that $-$ 3253 has an infrared excess." "0746. Figure l τονreals an infrared excess around 0307|this star basedon the plotted KI, DÀ model and the shortwaveleneth photometry.", Figure \ref{fig1} reveals an infrared excess around this star basedon the plotted K DA model and the shortwavelength photometry. " The HA data are auchored to the PALTASS J-band ueasuremenut of 16.39E0.1 παπάς, where the J Ipaa HDIK colors were derived spectroscopically bv ποetal. (2006).."," The $HK$ data are anchored to the 2MASS $J$ -band measurement of $16.39\pm0.14$ mag, where the $J-H$ and $H-K$ colors were derived spectroscopically by \citet{kil06}. ." sunupled. overdensitics of spectroscopic iuenibers cau be seen around the locations of the most significant peaks in the RCS significance map (see Gladders&Yee 20053).,"sampled, overdensities of spectroscopic members can be seen around the locations of the most significant peaks in the RCS significance map (see \citealt{Gladders:2005oi}) )." The visually-ideutified BCC iu each case has a confident redshift near z=0.90 (0.9008. 0.9025 aud 0.9005 respectively).," The visually-identified BCG in each case has a confident redshift near $=$ 0.90 (0.9008, 0.9025 and 0.9005 respectively)." Cluster A exhibits several strong lensing features (Gladdersetal.2003).., Cluster A exhibits several strong lensing features \citep{2003ApJ...593...48G}. We obtained deep spectroscopy of the B-baud dropout arc (fie., We obtained deep spectroscopy of the $B$ -band dropout arc (fig. 2c. Cdaddersetal. 20033) in 2003 Septemiber-October using GMOS-N ou Comiui-North (program: ID: GN-2003-OQ-19).," 2c, \citealt{2003ApJ...593...48G}) ) in 2003 September-October using GMOS-N on Gemini-North (program ID: GN-2003-Q-19)." The tareet was observed in nod-and-shufile wmode for a total integration time of 9.6 hours and the data reduced as for the Coun data described iu Cilbauketal.(20073.., The target was observed in nod-and-shuffle mode for a total integration time of 9.6 hours and the data reduced as for the Gemini data described in \citet{gilbank:07a}. . The spectrum of the are is shown iu Fig., The spectrum of the arc is shown in Fig. 2. aud is that of a πο]τοςκατ Lviuan-break galaxy (LBC)., \ref{fig:arc} and is that of a high-redshift Lyman-break galaxy (LBG). As discussed in Shapleyetal. (2003).. LBCs frequently display strong outflows. and so the measurement of a redshift i$ complicated by different spectral features tracing kinematically distinet conrponeuts of the galaxy.," As discussed in \citet{Shapley:2003yq}, LBGs frequently display strong outflows, and so the measurement of a redshift is complicated by different spectral features tracing kinematically distinct components of the galaxy." In order to determine a systemic redshift. we use only stellar photospheric lines and plot their positions at different trial redshitts over the spectrum," In order to determine a systemic redshift, we use only stellar photospheric lines and plot their positions at different trial redshifts over the spectrum." We find a redshift of z=3.8605., We find a redshift of $=$ 3.8605. Other commu lines frou interstellar absorption aud nebular enission. aare shown in Fig. 3..," Other common lines from interstellar absorption and nebular emission, are shown in Fig. \ref{fig:arc}." Lye is seen offset to higher redshift (~900 1)) with respect to the systemic velocity. as is often observed (Shapleyetal.2003)..," $\alpha$ is seen offset to higher redshift $\sim$ 900 ) with respect to the systemic velocity, as is often observed \citep{Shapley:2003yq}." The Nav observations aud analysis are described iu Ticksetal.(2008). and are derived frou four observations taken over the period 2005 September 28 - October 23. resulting in a total exposure of 71.539 seconds;," The X-ray observations and analysis are described in \citet{hicks07} and are derived from four observations taken over the period 2005 September 28 - October 23, resulting in a total exposure of 74,539 seconds." Briefly. X-ray temperatures were mieasured within rosy) and used to derive total masses by extrapolating to rogg.," Briefly, X-ray temperatures were measured within $r_{\rm 2500}$ and used to derive total masses by extrapolating to $r_{200}$." The X-ray iasses for all three clusters are eiven in Table 1. and each i$ around 510!A., The X-ray masses for all three clusters are given in Table \ref{table:props} and each is around $\times$ $^{14}M_\odot$. Cluster A has sufficient. spectroscopic menibers (bv including the additional VLT data) to measure au approximate velocity dispersion., Cluster A has sufficient spectroscopic members (by including the additional VLT data) to measure an approximate velocity dispersion. 12 redshift class 1- members vield σ=(990+210) or 9 higher confidence (class 1-3) members vield ¢@=(790+200)5., 12 redshift class 1-4 members yield $\sigma=(990\pm240)$ or 9 higher confidence (class 1-3) members yield $\sigma=(790\pm200)$. These velocity dispersious would correspouc to virial mass estimates (Carlbereetal.1997) of 27«101 M and 3.s1025 ALL. which are 6.1in good agreecnneut with the XN-rav derived mass of GLsLott AL. within the broad uncertaiuties of the dynamical estimate.," These velocity dispersions would correspond to virial mass estimates \citep{carlberg97} of $6.1^{+5.6}_{-3.4} \times 10^{14}$ $_\odot$ and $3.1^{+3.0}_{-1.8} \times 10^{14}$ $_\odot$, which are in good agreement with the X-ray derived mass of $6.4^{+0.6}_{-0.6} \times 10^{14}$ $_\odot$, within the broad uncertainties of the dynamical estimate." " Using the richuess ανασα mass relation established at lower-vedshitt (Blindertetal.2007).. the values ofchisters A-C would correspouc to expected masses of Me(9.5.5.1.1.3]< tot! AL, respectively."," Using the richness – dynamical mass relation established at lower-redshift \citep{blindert07a}, the values of clusters A-C would correspond to expected masses of $=(9.5, 5.4, 1.3) \times$ $^{14}$ $_\odot$ respectively." The 16 intrinsic scatter iu the observe relation is ~0.7 dex (Blindertetal.2007) aud thus the inferred masses are consistent with the measured N-ray lasses Within this broad scatter., The $\sigma$ intrinsic scatter in the observed relation is $\sim$ 0.7 dex \citep{blindert07a} and thus the inferred masses are consistent with the measured X-ray masses within this broad scatter. We can use the radial distance ancl redshift of the strouglv-leused z=3.8605 ealaxy to make au estimate of the mass of cluster A within this radius., We can use the radial distance and redshift of the strongly-lensed $=$ 3.8605 galaxy to make an estimate of the mass of cluster A within this radius. A simple circular ft to the position of the arc with respect to the brieltest cluster ealaxy (BCC) shows that it lies at a radius of ~12” (0.1 AIpe)., A simple circular fit to the position of the arc with respect to the brightest cluster galaxy (BCG) shows that it lies at a radius of $\sim$ (0.1 Mpc). Setting this equal to the Einstein radius and assuniune that the deusitv profile of the cluster is that of au isothermal sphere would nmuplv a ceutral velocity dispersion of 860 Daw). ee. Schueideretal.(1992)]].," Setting this equal to the Einstein radius and assuming that the density profile of the cluster is that of an isothermal sphere would imply a central velocity dispersion of 860 ), e.g., \citet{sef:1992kk}] ]." Using M=7.3«1072/41(0/100 in ye Apc) (Iloekstraetal.2003). eivesM an estimate ofthe mass euclosed within this radius as Ls«1012AZ..., Using $M = 7.3 \times 10^{12} h_{100}^{-1} M_\odot (\sigma /100$ km $^{-1})^2 (r/1$ $)$ \citep{Hoekstra:2003ky} gives an estimate of the mass enclosed within this radius as $4.8 \times 10^{13} M_\odot$. " Recalculating the N-ray mass within a exliuder of radius 0.1 Alpe. to be directly comparable to the lensing mass estimate, gives amass of Wy=(lLΕθν1οAZ... in excellent agreement with that iuferred from the simple strong leusime estimate."," Recalculating the X-ray mass within a cylinder of radius 0.1 Mpc, to be directly comparable to the lensing mass estimate, gives a mass of $M_X = (4.4\pm0.4) \times 10^{13} M_\odot$, in excellent agreement with that inferred from the simple strong lensing estimate." The separations of the componucuts of this svstem. both in the plane of the sky ( 3 Mpc) aud along the line of sieht (~10 Mpc. assuming that the velocity difference is due to IIubble flow) are significantly: closer than those seen in other supercluster cancidates at these redshifts (Lubinetal.2000:Swinhauk2007)..," The separations of the components of this system, both in the plane of the sky $<$ 3 Mpc) and along the line of sight $\sim$ 10 Mpc, assuming that the velocity difference is due to Hubble flow) are significantly closer than those seen in other supercluster candidates at these redshifts \citep{Lubin:2000or,Swinbank:2007eg}." This invites he question: will these meree to forni a more massive cluster?, This invites the question: will these merge to form a more massive cluster? To auswer this. we consider a simple estimate (Sarazin2002)..," To answer this, we consider a simple estimate \citep{Sarazin:2002rv}." If we assume that the clusters are not noving apart with the Wubble dow aud that their relative velocity is comparable to their resttrame LOS velocity difference (~1200 3) thenthe time taken to raverse the ~3 Alpe separation would imply that the individual cluster componcuts would merge by z~0.5.," If we assume that the clusters are not moving apart with the Hubble flow and that their relative velocity is comparable to their restframe LOS velocity difference $\sim$ 1200 ), thenthe time taken to traverse the $\sim$ 3 Mpc separation would imply that the individual cluster components would merge by $\sim$ 0.5." The merger redshift is also comparable if we assuuie that he infall velocity is of the order of the velocity dispersion of cluster A. Thus. this system would evolve into a cluster of mass > 104? AD. at 2~0.5. similar to the z=0.5L cluster AIS0151.5-0305 (Donahue1996:Ellingsonctal. 1998)..," The merger redshift is also comparable if we assume that the infall velocity is of the order of the velocity dispersion of cluster A. Thus, this system would evolve into a cluster of mass $\gsim$ $^{15}$ $_\odot$ at $\sim$ 0.5, similar to the $=$ 0.54 cluster MS0451.5-0305 \citep{Donahue:1996uo,Ellingson:1998tt}. ." We explore the expected space deusitv of such systeis by utilizing the cluster catalogs from the light cone output of the Virgo C'ousortimu Ihubble Volume, We explore the expected space density of such systems by utilizing the cluster catalogs from the light cone output of the Virgo Consortium Hubble Volume "with standard uncertainties. represented bv the otted lines in the plot. of £0.89 kan s| aud +2.79 lan s! respectively,","with standard uncertainties, represented by the dotted lines in the plot, of $\pm$ 0.89 km $^{-1}$ and $\pm$ 2.79 km $^{-1}$ respectively." The total sample of less than 300 is still rather small. especially when binned.," The total sample of less than 300 is still rather small, especially when binned." " Indeed there appears a dearth of objects between M6.5-M8,5. with rotation rates above ~15 km |. which may indicate another population change above M6.5."," Indeed there appears a dearth of objects between M6.5-M8.5 with rotation rates above $\sim$ 15 km $^{-1}$, which may indicate another population change above M6.5." The evidence for this gap is weak at present due to the low uuniber of stars in these spectral bius. therefore further observations and are needed aud anv biases studied to. fully validate the existence of this feature.," The evidence for this gap is weak at present due to the low number of stars in these spectral bins, therefore further observations and are needed and any biases studied to fully validate the existence of this feature." At temperaturesbelow around 280018 (approximately AÍG-MT type objects) dst formation and opacity aro important iu stellar/substellar atmospheres (Pu Tu Tu Tu and references therein)., At temperatures below around 2800K (approximately M6-M7 type objects) dust formation and opacity are important in stellar/substellar atmospheres \citealp{tsuji96}; ; \citealp{jones97}; \citealp{tinney98}; \citealp{chabrier00}; \citealp{baraffe02} and references therein). ? rave shown that late-M. stars mark a transition in the properties of the magnetic feld aud its dissipation. along with high tempcrature plasma cine generated iu the outer atinosphere.," \citet{berger08} have shown that late-M stars mark a transition in the properties of the magnetic field and its dissipation, along with high temperature plasma being generated in the outer atmosphere." They eeo on to hvpothesize that the stellar rotation nay play a part iu this process and indeed the difference shown here between the mid aud late ype M stars seenis o add to this conclusion., They go on to hypothesize that the stellar rotation may play a part in this process and indeed the difference shown here between the mid and late type M stars seems to add to this conclusion. " A [KS test reveals a D-statistic of 0.639. or "". that stars in the range Λη and those iu the range MT.0-M9.5 are drawn roni the same pareut distribution."," A K-S test reveals a D-statistic of 0.639, or $^{-6}$, that stars in the range M0.0-M6.5 and those in the range M7.0-M9.5 are drawn from the same parent distribution." However. eiven hat we have already. shown there to be a large difference between carly Ms. (MO-M3.5). this will das this probability test.," However, given that we have already shown there to be a large difference between early Ms (M0-M3.5), this will bias this probability test." When we remove all stars earlier than AIL we find a D statistic of V5Ll. which relates to a probability of only 7 that these are drawn frou tlie sanie went population.," When we remove all stars earlier than M4 we find a D statistic of 0.544, which relates to a probability of only $^{-3}$ that these are drawn from the same parent population." This 75e result max indicate hat at teniperatures when dust opacity becomes nuportant there is a change iu the rotational waking dinechanisnis auc hence the magnetic oxoperties of ultracool chwarfs., This $>$ $\sigma$ result may indicate that at temperatures when dust opacity becomes important there is a change in the rotational braking mechanisms and hence the magnetic properties of ultracool dwarfs. This uuelt eive vise to the flattening trend indicated between A[6.5-MO9. stars. however a iore conirehensive study is needed. particularly to decouple the age of these stars by studyiug the space motion to determine if they are voung or old disk stars.," This might give rise to the flattening trend indicated between M6.5-M9 stars, however a more comprehensive study is needed, particularly to decouple the age of these stars by studying the space motion to determine if they are young or old disk stars." Also the biases of the literature surveys are important., Also the biases of the literature surveys are important. For imstance. studies like those of ?. focus oulv on selecting inactive. aud hence slowly rotating. late type M stars.," For instance, studies like those of \citet{west09} focus only on selecting inactive, and hence slowly rotating, late type M stars." In addition. current models show that the late M star regime can also be populated by voung brown cwarfs.," In addition, current models show that the late M star regime can also be populated by young brown dwarfs." Finally. this relation also suffers frou the lack of low ο sin / detections already iieutioned above. even nore so given the A6.5 detection boundary.," Finally, this relation also suffers from the lack of low $v$ sin $i$ detections already mentioned above, even more so given the M6.5 detection boundary." Therefore we expect this result might also become more pronounced with further low ce sin / dotectious at spectral types below M6.5., Therefore we expect this result might also become more pronounced with further low $v$ sin $i$ detections at spectral types below M6.5. The ioriínalized cistribution of ce sin /s are represented by the histograms in Fie. 1l.," The normalized distribution of $v$ sin $i$ s are represented by the histograms in Fig. \ref{vsini_hist}," where the solid histogram is for all stars in the spectral range between Αλ and the dashed histogram is for all stars iu the range M1-M9.5., where the solid histogram is for all stars in the spectral range between M0-M3.5 and the dashed histogram is for all stars in the range M4-M9.5. These include all values determined iu this work combined with those in the literature., These include all values determined in this work combined with those in the literature. " It is apparent that both distributions peak at low rotation rates (“3 laus Dy with peak values of 55 aud 12 stars respectively,"," It is apparent that both distributions peak at low rotation rates $\sim$ 3 km $^{-1}$ ), with peak values of 55 and 42 stars respectively." We find that he total πο of eosin is < 10 dans | is 198 and these should represent useful stars for future near infrared radial-velocitv planet search projects such as PRVS., We find that the total number of $v$ sin $i$ s $\le$ 10 km $^{-1}$ is 198 and these should represent useful stars for future near infrared radial-velocity planet search projects such as PRVS. ? show that the information content drops bv a factor of ~3.5 between rotation volocities of ~2-10 kimi 1. making > 10 kin a reasonable M star racial-velocitv selection ct," \citet{bouchy01} show that the information content drops by a factor of $\sim$ 3.5 between rotation velocities of $\sim$ 2-10 km $^{-1}$, making $\ge$ 10 km $^{-1}$ a reasonable M star radial-velocity selection cut." This suaple is still laree (121) when we include all mid-to-late AL stars iu the range MO-MO9.5 (stars where obtaining optical precision racialvelocities becomes extremely difficult)., This sample is still large (124) when we include all mid-to-late M stars in the range M3-M9.5 (stars where obtaining optical precision radial-velocities becomes extremely difficult). Note the binary systems lave boen left out of Pies., Note the binary systems have been left out of Figs. 11 and 9 since the combined huuiuositioes will generate inaccurate photometry and therefore inaccurate spectral types., \ref{vsini_hist} and \ref{vsini_plot} since the combined luminosities will generate inaccurate photometry and therefore inaccurate spectral types. Also. binary svstenis ike these male radial-velocitv exoplanet searches uuch harder since any siuall planetary signature is nasked by the large short period binary velocity. ueanine these are not ideal planet search targets Or precision radial-velocity programs moving mto an unexplored parauieter space.," Also, binary systems like these make radial-velocity exoplanet searches much harder since any small planetary signature is masked by the large short period binary velocity, meaning these are not ideal planet search targets for precision radial-velocity programs moving into an unexplored parameter space." Comparing the distributious of both histograms iclps to probe the possible chaugiug rotation xoperties of AL stars at the ull convective )oundaryv., Comparing the distributions of both histograms helps to probe the possible changing rotation properties of M stars at the fully convective boundary. We ive eniploved two power law fits o each distribution separately iu order to test he changing velocity distribution between these wo reenues., We have employed two power law fits to each distribution separately in order to test the changing velocity distribution between these two regimes. The red (dark curve is fit to he sa1upleof carly M. dwarfs between ALO-AL3.5.," The red (dark curve is fit to the sampleof early M dwarfs between M0-M3.5," rregious.,regions. We find that we can consisteutlv. reproduce the observed relation between the total mass of the star clusterALi. and the maxima stellar iuaass in the cluster Mijas. ομωςXMI.," We find that we can consistently reproduce the observed relation between the total mass of the star cluster$\msinks$ and the maximum stellar mass in the cluster $\mmax$, $\mmax \propto \msinks^{2 / 3}$." This relation secus to be the general outcome of protostellar interaction In a conuuon cluster euvironnient rather thin bene a signpost of competitive accretion only. as previously claimed.," This relation seems to be the general outcome of protostellar interaction in a common cluster environment rather than being a signpost of competitive accretion only, as previously claimed." Iu fact. the dynamical processes discussed here exlibit exactly the opposite behavior of compctitive accretion. rather than runaway acerction outo the most massive star together with the suppression of the growth of loweranass objects. we see that angular mionienutuui conservation aud the presence of lower-imass objects Init the mass growth of massive stars.," In fact, the dynamical processes discussed here exhibit exactly the opposite behavior of competitive accretion, rather than run-away accretion onto the most massive star together with the suppression of the growth of lower-mass objects, we see that angular momentum conservation and the presence of lower-mass objects limit the mass growth of massive stars." Our simulations provide evidence for the rejection of proposals that the observed imaxiuun stellar mass of 100 ML. is set by radiative feedback.," Our simulations provide evidence for the rejection of proposals that the observed maximum stellar mass of $\sim 100\,$ $_\odot$ is set by radiative feedback." When disk. Baesnmentation is artificially suppressed (run A} the central protostar accretes material at very high rate ΠΠΟΕ by the tense UV radiatiou it cuits without any indications of an upper lait (seealsoPetersetal. 2010a)., When disk fragmentation is artificially suppressed (run A) the central protostar accretes material at very high rate unimpeded by the intense UV radiation it emits without any indications of an upper limit \cite[see also][]{petersetal10a}. . When we permit disk fragmentation to occur. it is the process of fragnieutation-mduced: starvation that prevents the stellar mass to become larger than 25 M. with our choice of initial conditions.," When we permit disk fragmentation to occur, it is the process of fragmentation-induced starvation that prevents the stellar mass to become larger than $\sim 25\,$ $_\odot$ with our choice of initial conditions." We expect lore luassive. more centrallv-condensed. audor slower rotating cloud cores to lead to more massive protostars.," We expect more massive, more centrally-condensed, and/or slower rotating cloud cores to lead to more massive protostars." " Tudeed. extensive parameter studies (Carichidisetal.2010) show that the initial density profile dominates the accretion behavior. explaining the formation of a 10 M, star frou a LOOAL.. core in IRrumbholzetal. (2009).."," Indeed, extensive parameter studies \citep{girietal10} show that the initial density profile dominates the accretion behavior, explaining the formation of a $40\,$ $_\odot$ star from a $100\,$ $_\odot$ core in \citet{krumholzetal09}. ." The alternative view is to attribute the apparent stellar mass lait to interual stability constraints., The alternative view is to attribute the apparent stellar mass limit to internal stability constraints. Blue Sky Spectrosocpy Inc. Lethbridge. Department of Physics Astronomy. The Open University. Milton Keynes MK7 GAA. UK,"Blue Sky Spectrosocpy Inc, Lethbridge, Department of Physics Astronomy, The Open University, Milton Keynes MK7 6AA, UK of the collect-and-collapse model of triggered star-formation.}" We require a simple parameterisation of the rotation curves of our target galaxies.,We require a simple parameterisation of the rotation curves of our target galaxies. Since this is required only to convert our Ilux limits into mass-to-light ratios. and as we see below. no halo fux was detected. simple spherical models are the most convenient and appropriate.," Since this is required only to convert our flux limits into mass-to-light ratios, and as we see below, no halo flux was detected, simple spherical models are the most convenient and appropriate." For present purposes. a galactic rotation curve can be considered to rise from zero at the centre. reaching a constant. al," For present purposes, a galactic rotation curve can be considered to rise from zero at the centre, reaching a constant, at" curently the best dataset. [or this calibration because it covers bv far the largest area with both eround- ancl space-based resolution to faint limiting magnitude.,currently the best dataset for this calibration because it covers by far the largest area with both ground- and space-based resolution to faint limiting magnitude. In addition. the Subaru multi-color observations provide photometric redshift estimates (Mobasher οἱ al.," In addition, the Subaru multi-color observations provide photometric redshift estimates (Mobasher et al." 2007) for the majority of galaxies in the survey area., 2007) for the majority of galaxies in the survey area. We use the COSMOS catalog size and photometric redshift information to estimate the redshift distribution of the galaxies that would be resolved in our weak lensing map., We use the COSMOS catalog size and photometric redshift information to estimate the redshift distribution of the galaxies that would be resolved in our weak lensing map. We match galaxies in the COSMOS. Subaru and. ACS catalogs with the additional requirement (hat the catalog I magnitudes match to within 0.3 (This restriction eliminates errors in matching (he (wo catalogs: it also eliminates most objects that cannot be adequately separated [rom neighboring objects in the Subaru imaging)., We match galaxies in the COSMOS Subaru and ACS catalogs with the additional requirement that the catalog I magnitudes match to within 0.3 (This restriction eliminates errors in matching the two catalogs; it also eliminates most objects that cannot be adequately separated from neighboring objects in the Subaru imaging). " Because the Subaru images of the COSMOS field were taken in comparable seeing (median seeing 70.55"" )). this procedure should not alter the COSMOS sample compared with the Subaru sample."," Because the Subaru images of the COSMOS field were taken in comparable seeing (median seeing $\sim$ ), this procedure should not alter the COSMOS sample compared with the Subaru sample." The final catalog contains approximately 124.000 objects with magnitudes. sizes. aud photometric reclshilt estimates.," The final catalog contains approximately 124,000 objects with magnitudes, sizes, and photometric redshift estimates." The galaxy catalog of the GTO?2deg? field has sizes and magnitudes (I magnitdes: MIvazaki et al., The galaxy catalog of the $^2$ field has sizes and magnitudes $_C$ magnitdes; MIyazaki et al. 2007). but not photometric redshifts.," 2007), but not photometric redshifts." To assign redshilts to the galaxies. we assign to everv galaxy in the GTO2deg? field the redshift of a randomly selected galaxy in the COSMOS catalog with the same magnitude and (seeing-deconvolved size). where the list ol of galaxies is taken from all the galaxies that match to within iin size ancl within 0.1 magnitudes.," To assign redshifts to the galaxies, we assign to every galaxy in the $^2$ field the redshift of a randomly selected galaxy in the COSMOS catalog with the same magnitude and (seeing-deconvolved size), where the list of of galaxies is taken from all the galaxies that match to within in size and within 0.1 magnitudes." Although this procedure does not necessarily assign (he correct. redshift to anv single galaxy. it assigns the correct distribution of galaxy recishifts given the size and magnitude distribution of the galaxies in the GTO2dee? field. and thus a correct. effective total weight via equation (1).," Although this procedure does not necessarily assign the correct redshift to any single galaxy, it assigns the correct distribution of galaxy redshifts given the size and magnitude distribution of the galaxies in the $^2$ field, and thus a correct effective total weight via equation (1)." " Given (his catalog of redshilts (which by construction has the same number of objects and the same size distribution as the one used in the construction of the lensing map). we calculate the effective weight Wey, that would be measured as a funetion of lens reclshilt."," Given this catalog of redshifts (which by construction has the same number of objects and the same size distribution as the one used in the construction of the lensing map), we calculate the effective weight $W_{eff}$ that would be measured as a function of lens redshift." We normalize the redshilt dependence of our sensitivity by comparing to simulations., We normalize the redshift dependence of our sensitivity by comparing to simulations. " To minimize the caleulations. we normalize to the sensitivity at a fixed cluster redshift of 0.3. and use the calculation of Wey, to calculate the redshift-dependence of the sensitivity curve."," To minimize the calculations, we normalize to the sensitivity at a fixed cluster redshift of 0.3, and use the calculation of $W_{eff}$ to calculate the redshift-dependence of the sensitivity curve." We [follow a modified version of the procedure for generating simulated catalogs in Khiahanian DellAntonio (2008)., We follow a modified version of the procedure for generating simulated catalogs in Khiabanian Dell'Antonio (2008). We generate simulated galaxies with the same magnitude and magnitude-redshift relations as the HIDE. North and South fields (Williams el al., We generate simulated galaxies with the same size-magnitude and magnitude-redshift relations as the HDF North and South fields (Williams et al. 1996: Casertano et al., 1996; Casertano et al. 2000) using the prescription of IXhiabanian DellAntonio (2008)., 2000) using the prescription of Khiabanian Dell'Antonio (2008). We use these simulated galaxies to populate images rresolution) representing seven logarithimicallv-spaced. redshift shells., We use these simulated galaxies to populate images resolution) representing seven logarithmically-spaced redshift shells. We then clistort the images with a lens modeled as a core-softened. eutoll isothermal sphere with a given rest, We then distort the images with a lens modeled as a core-softened cutoff isothermal sphere with a given rest "directed along the pulsar spin axis (Gaensleretal., 2001)..",directed along the pulsar spin axis \citep[][]{GPG01}. . Proquetetal.(2003) studied G0.9+0.1 using observations byXMM-Newton., \citet[][]{PDW03} studied G0.9+0.1 using observations by. " The X-ray spectrum softens with distance from the core, and the spectrum in the energy range 2 — 10 keV has a power law form with a photon index of ~1.9."," The X-ray spectrum softens with distance from the core, and the spectrum in the energy range 2 – 10 keV has a power law form with a photon index of $\sim1.9$." " Very High-energy (VHE) emission from G0.9+0.1 has been detected with HESS (Aharonianetal.,2005a).", Very High-energy (VHE) emission from G0.9+0.1 has been detected with HESS \citep[][]{A05a}. ". The photon flux above 0.2 TeV is 5.7x1071? cm? s-!, and the spectrum can be fitted with a power-law with a photon index 2.4+0.31."," The photon flux above 0.2 TeV is $5.7\times10^{-12}$ $^{-2}$ $^{-1}$, and the spectrum can be fitted with a power-law with a photon index $2.4\pm0.31$." " The source is a weak TeV emitter, and the VHE -rays appear to originate from the core rather than the shell (Aharonianetal.,2005a)."," The source is a weak TeV emitter, and the VHE $\gamma$ -rays appear to originate from the core rather than the shell \citep[][]{A05a}." . The dynamical and radiative properties of the composite SNR G0.9+0.1 are investigated with the parameters in Table 1 for this source., The dynamical and radiative properties of the composite SNR G0.9+0.1 are investigated with the parameters in Table \ref{para} for this source. " Although the pulsar PSR J1747-2809 has a characteristic age of 5.3 kyr, Camiloetal.(2009) argued that G0.9+0.1 has a small age of no more than 2—3 kyr either from PWN evolution models of Blondin,Chevalier&Frier-son(2001) for the observed ratio iyw/Renr=0.25 or from the PWN energetics (Dubneretal.,2008)."," Although the pulsar PSR J1747-2809 has a characteristic age of 5.3 kyr, \citet[][]{Cet09} argued that G0.9+0.1 has a small age of no more than $2-3$ kyr either from PWN evolution models of \citet[][]{BCF01} for the observed ratio $R_{\rm pwn}/R_{\rm snr} = 0.25$ or from the PWN energetics \citep[][]{DGD08}." ". The distance of the pulsar is likely in the range of 8 kpc to 16 kpc due to the uncertainty of the electron density model toward the distant inner Galactic regions (Dubneretal.,2008)..", The distance of the pulsar is likely in the range of 8 kpc to 16 kpc due to the uncertainty of the electron density model toward the distant inner Galactic regions \citep[][]{DGD08}. " We assume the distance is 8.5 kpc in the calculation, then the radii of the PWN and the shell are 2.55 pc and 10.2 pc, respectively."," We assume the distance is 8.5 kpc in the calculation, then the radii of the PWN and the shell are 2.55 pc and 10.2 pc, respectively." " Moreover, with Εν=10°! erg and Λο=8Mo, an age of 1900 yr and a relatively low density nigsn=0.01 cm""? are needed to well reproduce structure of the system, i.e., the radius of the shell and the ratio Rpwn/Rsnr."," Moreover, with $E_{\rm sn}=10^{51}$ erg and $M_{\rm ej}=8M_{\odot}$, an age of 1900 yr and a relatively low density $n_{\rm ism}=0.01$ $^{-3}$ are needed to well reproduce structure of the system, i.e., the radius of the shell and the ratio $R_{\rm pwn}/R_{\rm snr}$." " A pulsar's velocity of 120 km/s similar as the Crab pulsar (Kaplanetal.,2008) is used to illustrate the evolution of the PWN, which has no influence on the final results for GO.9+0.1 since it is a young remnant, and now the pulsar is safely in the nebula."," A pulsar's velocity of 120 km/s similar as the Crab pulsar \citep[][]{Ket08} is used to illustrate the evolution of the PWN, which has no influence on the final results for G0.9+0.1 since it is a young remnant, and now the pulsar is safely in the nebula." " With these parameters, the resulting radii of the PWN and the SNR shell are 2.6 and 10.2 pc, respectively, consistent with the observational results (upper panel Fig.1))."," With these parameters, the resulting radii of the PWN and the SNR shell are 2.6 and 10.2 pc, respectively, consistent with the observational results (upper panel \ref{Figs1}) )." The influence of the ejecta mass Λάει on the radius of the nebula is shown in the upper panel of Fig.1.., The influence of the ejecta mass $M_{\rm ej}$ on the radius of the nebula is shown in the upper panel of \ref{Figs1}. " With a smaller M,;, both the nebula and the SNR shell expand more quickly, and the nebula collides with the reverse shock at later time."," With a smaller $M_{\rm ej}$, both the nebula and the SNR shell expand more quickly, and the nebula collides with the reverse shock at later time." " As a result, the magnetic field in the PWN is weaker for a smaller M,; due to the bigger volume of the nebula (the lower panel in Fig.1))."," As a result, the magnetic field in the PWN is weaker for a smaller $M_{\rm ej}$ due to the bigger volume of the nebula (the lower panel in \ref{Figs1}) )." The dynamical properties of the SNR during the evolution is similar as those for the Crab remnant in Gelfandetal.(2009) although the new spectrum of the particles is used in this paper., The dynamical properties of the SNR during the evolution is similar as those for the Crab remnant in \citet[][]{GSZ09} although the new spectrum of the particles is used in this paper. " Initially, the pressure of the PWN ismuch bigger that of the surrounding supernova ejecta, so the PWN"," Initially, the pressure of the PWN ismuch bigger that of the surrounding supernova ejecta, so the PWN" (Tamura2009).. (Thalmannctal.2010:ITashiniotoe," \citep{TamSEEDS}. \citep{Thalmann10,Hashimoto10}." t2011).. 0.1 LOAU LOOpc. LOAT LOOAT i6 observations of a disk at NIB waveleneth. which uaiulv observe the scattered πο] from the upper laver of ie disk. and the ποια dust contin observations. which reveal the surface density structure of the disk.," $0.1$ $\sim 10{\mathrm{AU}}$ $100\mathrm{pc}$ $10\mathrm{AU}$ $100\mathrm{AU}$ the observations of a disk at NIR wavelength, which mainly observe the scattered light from the upper layer of the disk, and the sub-mm dust continuum observations, which reveal the surface density structure of the disk." Oue of the fundamental aud important properties of ie protoplanetary disk is its mass., One of the fundamental and important properties of the protoplanetary disk is its mass. " The sub-uua dust contimmuu observation is widely used to estimate the nass of the disk. although it suffers the ambiguity of 1¢ dust opacity, which results in at least a factor of two aucertaiutv in the disk mass."," The sub-mm dust continuum observation is widely used to estimate the mass of the disk, although it suffers the ambiguity of the dust opacity, which results in at least a factor of two uncertainty in the disk mass." In this paper. we consider 1e effects of self-eravitv on the hydrostatic balauce of the disk vertical structure. aud discuss how the effects of scleravitv iav appear in the direct imagine observations.," In this paper, we consider the effects of self-gravity on the hydrostatic balance of the disk vertical structure, and discuss how the effects of self-gravity may appear in the direct imaging observations." Tf there is a feature that reflects the sclferavity. it would eive an alternative duplication about the disk mass other than the streneth of the dust coutiuuuan.," If there is a feature that reflects the self-gravity, it would give an alternative implication about the disk mass other than the strength of the dust continuum." Iu order to isolate the effects of sclberavity in the disk structure. we consider a disk with a simple radial surface density variation. nauelw. a power-law profile with au axisviunietrie gap.," In order to isolate the effects of self-gravity in the disk structure, we consider a disk with a simple radial surface density variation, namely, a power-law profile with an axisymmetric gap." The variation of the surface deusity may be produced by the gravitational perturbation bv an embedded planet. turbulence. or other causes. but we do not query the cause of such a structure.," The variation of the surface density may be produced by the gravitational perturbation by an embedded planet, turbulence, or other causes, but we do not query the cause of such a structure." The question we address is that how such surface deusifv variations may be observed by direct maging observatious at NIR or sub-nuu wavelengths aud we look for a feature that is unique to a selferavitatiug disk., The question we address is that how such surface density variations may be observed by direct imaging observations at NIR or sub-mm wavelengths and we look for a feature that is unique to a self-gravitating disk. There are several works on the modeling of a selberavitatiug disk for direct tuagine observations. especially iu relation to the eravitoturbulence aud the resulting planet formation.," There are several works on the modeling of a self-gravitating disk for direct imaging observations, especially in relation to the gravitoturbulence and the resulting planet formation." Naravananetal.(2006) have performed a detailed caleulatious of lue emission based on the livdrodvuaimic simmlatious of eravitational instability by Boss(2001).. aud have shown that unique features inICO!liuemayappearclose to aforming eiut planet.," \citet{Narayanan06} have performed a detailed calculations of line emission based on the hydrodynamic simulations of gravitational instability by \citet{Boss01}, and have shown that unique features in$\mathrm{HCO}^{+}$linemayappearclose to aforming giant planet." Jane-ConudellandBoss(2007)— have, \citet{JCB07} have The results of these tests are shown in Figure for the atomic-to-molecular transition and the KS relation.,The results of these tests are shown in Figure \ref{fig:conv} for the atomic-to-molecular transition and the KS relation. " In order to perform a genuine resolution test, in each run with [A13]different resolution we only show cells that are refined to the lowest allowed level."," In order to perform a genuine resolution test, in each run with different resolution we only show cells that are refined to the lowest allowed level." " For example, in the run with the maximum level 10, we only show cells from level 10, so that level 9 cells, which are also present in that test run, do not contaminate reffig:conv.."," For example, in the run with the maximum level 10, we only show cells from level 10, so that level 9 cells, which are also present in that test run, do not contaminate \\ref{fig:conv}." " Of course, in realistic simulations cells from all levels that contain molecular gas are going to contribute to the fu,—ny relation, so reffig:conv actually the effect of changing resolution."," Of course, in realistic simulations cells from all levels that contain molecular gas are going to contribute to the $f_\H2 - n_\Ht$ relation, so \\ref{fig:conv} actually the effect of changing resolution." At resolutions Ax<260pc our model performs robustly down to the smallest scales we are able to (Ax«30 pc).," At resolutions $\Delta x \la 260\dim{pc}$ our model performs robustly down to the smallest scales we are able to probe $\Delta x \approx 30\dim{pc}$ )." " At coarser resolution of Ax=520 small molecular clouds in low density gas are not captured properly, proberesulting in a sharper fall-off in the KS relation at low pcvalues of Xy14n,."," At coarser resolution of $\Delta x=520\dim{pc}$ small molecular clouds in low density gas are not captured properly, resulting in a sharper fall-off in the KS relation at low values of $\Sntr$." " In addition, the Sobolev-like approximation for the dust column density (Equation (AT0])) overestimates the column density significantly, which results in the atomic-to-molecular transition shifting towards lower density gas (especially for low dust-to-gas ratio and high FUV flux)."," In addition, the Sobolev-like approximation for the dust column density (Equation \ref{eq:sob}) )) overestimates the column density significantly, which results in the atomic-to-molecular transition shifting towards lower density gas (especially for low dust-to-gas ratio and high FUV flux)." " We conclude, therefore, that spatial resolution of at least 250pc is required for our model to work robustly. [AT5]."," We conclude, therefore, that spatial resolution of at least $250\dim{pc}$ is required for our model to work robustly. \ref{fig:avgsfl}." skv frame.,sky frame. The images were processed bv [first running a simple interpolation program to remove bad: pixels., The images were processed by first running a simple interpolation program to remove bad pixels. A median-combined sky image was then created from the five exposures and subtracted from each image., A median-combined sky image was then created from the five exposures and subtracted from each image. Phe frames were then flat-liclded using images of a tungsten lamp on a dome Hat., The frames were then flat-fielded using images of a tungsten lamp on a dome flat. These were taken with the lamp on and also with the lamp olf so that the thermal component could be subtracted from the fLat-field., These were taken with the lamp on and also with the lamp off so that the thermal component could be subtracted from the flat-field. In order to determine the counts for stars in cach image we first mosaiced cach group of five images so that we could obtain more accurate photometry., In order to determine the counts for stars in each image we first mosaiced each group of five images so that we could obtain more accurate photometry. The counts for λα X1 and a local standard were then computed using the aperture photometry routine described in Shahbaz. Navlor Charles (1994) with a 3 pixel radius aperture.," The counts for Aql X–1 and a local standard were then computed using the aperture photometry routine described in Shahbaz, Naylor Charles (1994) with a 3 pixel radius aperture." The magnitudes of Aql XLd oare given relative to a bright star 25 arcsec West and 4 aresec South of Aql N-1 (Shahbaz 1998)., The magnitudes of Aql X–1 are given relative to a bright star 25 arcsec West and 4 arcsec South of Aql X-1 (Shahbaz 1998). Typical errors in A were 0.08 mags., Typical errors in $K$ were 0.08 mags. We obtained J//A-band images of Aql X Lon the 16th and lsth July 1997 using the InSb infrared array IRCAM-3. on the 3.8-m United. Ixingdom LIafrared Telescope atop \launa ]|xea. Hawaii.," We obtained $JHK$ -band images of Aql X–1 on the 16th and 18th July 1997 using the InSb infrared array IRCAM-3, on the 3.8-m United Kingdom Infrared Telescope atop Mauna Kea, Hawaii." Photometric conditions also allowed. the acquisition of VINER standard. stars., Photometric conditions also allowed the acquisition of UKIRT standard stars. A typical observing sequence consisted of eight consequtive images of 10s for ql X1l. where the object's position on the array was moved between exposures. so that the group could. be median stacked to produce a Hat-field frame.," A typical observing sequence consisted of eight consequtive images of 10s for Aql X–1, where the object's position on the array was moved between exposures, so that the group could be median stacked to produce a flat-field frame." “Phe standard reduction procedures were then followed., The standard reduction procedures were then followed. The counts for Aql X1 and a local standard were then computec using the aperture photometry routine described in Shahbaz. Navlor Charles (1004).," The counts for Aql X–1 and a local standard were then computed using the aperture photometry routine described in Shahbaz, Naylor Charles (1994)." Phe magnitude of the local standard: was measured. which then allowed us to determine the apparent Jiffy magnitude for Aql XN1 in quiescence.," The magnitude of the local standard was measured, which then allowed us to determine the apparent $JHK$ magnitude for Aql X–1 in quiescence." We obtained J=16.59-+0.02. £/=16.0540.03 and A 0.04.," We obtained $J$ $\pm$ 0.02, $H$ $\pm$ 0.03 and $K$ $\pm$ 0.04." We could not determine the colour correction between the ΙΙ and Lowell filter svstems., We could not determine the colour correction between the UKIRT and Lowell filter systems. Therefore we do not use the VINER A-band data in the analysis of the Ht light curve of Aql XN.1., Therefore we do not use the UKIRT $K$ -band data in the analysis of the IR light curve of Aql X–1. We obtained photometry on the SOcm telescope LAC'SNO on the nights of 1997 August 12-16. 20-21 and 30 ancl 1997 september 11 ancl 15-16.," We obtained photometry on the 80cm telescope IAC80 on the nights of 1997 August 12-16, 20-21 and 30 and 1997 September 11 and 15-16." Phe frames were acquired. with a ‘Thomson chip which has a 7.5x7.5 aremin? field of view and a scale of 0.43 aresec 1., The frames were acquired with a Thomson chip which has a 7.5x7.5 $^2$ field of view and a scale of 0.43 arcsec $^{-1}$. Johnson D and V. images were obtained using exposure times of 0005 and 6008s respectively: the seeing was 0.8-1.5 aresee., Johnson $B$ and $V$ images were obtained using exposure times of 900s and 600s respectively; the seeing was 0.8-1.5 arcsec. Fvpical errors were 0.10 and 0.05 mags in B and V. respectively., Typical errors were 0.10 and 0.05 mags in $B$ and $V$ respectively. On LOOT Xugust 5-8. CDV. images were taken at the Nordic Optical Telescope (NOT) at the Observatorio del toque de los Muchachos on La Palma: one image was taken in each filter on each of the four nights.," On 1997 August 5-8, $UBV$ images were taken at the Nordic Optical Telescope (NOT) at the Observatorio del Roque de los Muchachos on La Palma; one image was taken in each filter on each of the four nights." We also have one Y observation from July 30 as well as 2? and 4 observations rom August 5 and 6., We also have one $V$ observation from July 30 as well as $R$ and $I$ observations from August 5 and 6. We used a thinned. coated Loral-Lesser 2000x2000 array with tvpical exposure times of 120 sec in U. 60 sec in D and 30 sec in V.," We used a thinned, coated Loral-Lesser 2000x2000 array with typical exposure times of 120 sec in $U$, 60 sec in $B$ and $30$ sec in $V$." Evpical errors were 0.01 and 1.05 mags in D and V. respectively., Typical errors were 0.01 and 0.05 mags in $B$ and $V$ respectively. ‘The observations were made on 1997 August 19 and 23 using the Canopus I-m telescope of the University of Tasmania at a focal ratio of £/11., The observations were made on 1997 August 19 and 23 using the Canopus 1-m telescope of the University of Tasmania at a focal ratio of f/11. A STG CCD photometer with Cousins V and £ filters was used with exposures of 5 and 10 minutes., A ST6 CCD photometer with Cousins $V$ and $I$ filters was used with exposures of 5 and 10 minutes. All of the optical images have undergone. standard CCD reduction. including bias subtraction. Dat-fielding. and removal of bad. pixels.," All of the optical images have undergone standard CCD reduction, including bias subtraction, flat-fielding, and removal of bad pixels." Aperture photometry was performed on Aql X-1 and a local standard. using the eck ADPPIHOT: routine: the apertures used ranged from 3-5r pixels in radius. varving with the cillerent instruments and seeing conditions.," Aperture photometry was performed on Aql X-1 and a local standard using the $\sc ark$ `APPHOT' routine; the apertures used ranged from 3-5 pixels in radius, varying with the different instruments and seeing conditions." Alagnitudes of Aql X-1 are given relative to the same bright star used for the LR photometry., Magnitudes of Aql X-1 are given relative to the same bright star used for the IR photometry. Acl X.1 was observed with the ISIS spectrograph on the +.2-m William Llerschel telescope on the nights of 1997 August 6-7., Aql X–1 was observed with the ISIS spectrograph on the 4.2-m William Herschel telescope on the nights of 1997 August 6-7. Two 1000s spectra were obtained covering AAX110-4910 ancl AA5900-6700 for the blue and red arms respectively., Two 1000s spectra were obtained covering $\lambda\lambda$ 4110-4910 and $\lambda\lambda$ 5900-6700 for the blue and red arms respectively. A slit width of 0.8 aresee was used. which when combined with the 600 line/mm erating resulted in a spectral resolution of Li ACEWLAIHR5O km I at Ha) for the red arm and. 1.1 A(ENIIMAGS kim tat 12) for the blue arm.," A slit width of 0.8 arcsec was used, which when combined with the 600 line/mm grating resulted in a spectral resolution of 1.1 (FWHM=50 km $^{-1}$ at $\alpha$ ) for the red arm and 1.1 (FWHM=68 km $^{-1}$ at $\beta$ ) for the blue arm." The bias level was removed [rom each image using the mean overscan regions and then Lat-fielcled by using a tungsten lamp., The bias level was removed from each image using the mean overscan regions and then flat-fielded by using a tungsten lamp. One-dimensional spectra were extracted using the standard optimal extraction routines in the PAMELA reduction package. which weights the pixels along," One-dimensional spectra were extracted using the standard optimal extraction routines in the PAMELA reduction package, which weights the pixels along" We applied (he Bavesiaii method of Gregory Loredo (1992) to both the time-corrected and uncorrected Oth order event lists.,We applied the Bayesian method of Gregory Loredo (1992) to both the time-corrected and uncorrected 0th order event lists. The method tests for variability by comparing the fits of periodic stepwise models to the data with the fit of a constant model., The method tests for variability by comparing the fits of periodic stepwise models to the data with the fit of a constant model. " The odds favoring variability. (based on 55.28 of Gregory Loredo 1992. with a maximum number of steps Minas — 12 and limiting angular [requencies wy, and wy, equal to ! and 101. respectively) were found to be 1.45xLO? [or the whole data set and 3.75x10.7? for the data filtered on df—2 ms. both to be compared with an odds value of 107 needed for a confident pulsation or variability detection."," The odds favoring variability (based on 5.28 of Gregory Loredo 1992, with a maximum number of steps $m_{\rm max}$ = 12 and limiting angular frequencies $\omega_{\rm lo}$ and $\omega_{\rm hi}$ equal to $^{-4}$ and $^3$, respectively) were found to be $1.45\times 10^{-4}$ for the whole data set and $3.75\times 10^{-3}$ for the data filtered on $\delta t=2$ ms, both to be compared with an odds value of $10^2$ needed for a confident pulsation or variability detection." Our second method emploved an FFT analvsis applied to the combined Ot and Ist order events. [ollowed bv a likelihood ratio test (LRT) to determine limits on the pulse fraction.," Our second method employed an FFT analysis applied to the combined 0th and 1st order events, followed by a likelihood ratio test (LRT) to determine limits on the pulse fraction." The FET power distribution was consistent with shot noise., The FFT power distribution was consistent with shot noise. For the LRT of a given period. P. the data were binned into N phase bins. giving η counts in each.," For the LRT of a given period, $P$, the data were binned into $N$ phase bins, giving $n_i$ counts in each." The source model was y=Afcos(ó;+Op) where o; is the phase of bin / and @ is the phase of the pulse and f/f is the pulse fraction.," The source model was $y = A + f \cos(\phi_i+\phi_0)$ where $\phi_i$ is the phase of bin $i$ and $\phi_0$ is the phase of the pulse and $f/A$ is the pulse fraction." The likelihood equations were (hen solved for 1 and the process applied to >500 [frequencies where the FFT power exceeded. a critical level in the Irequency. range 0.001-50 Iz., The likelihood equations were then solved for $A$ and the process applied to $> 500$ frequencies where the FFT power exceeded a critical level in the frequency range 0.001-50 Hz. By including also the dispersed events we improved the signal-Lto-noise of the result bv a factor of 1.47 compared to using 0th order alone ancl could obtain a pulse fraction limit lower than the value of oobtained by Ransom et ((2002) in their unaccelerated search., By including also the dispersed events we improved the signal-to-noise of the result by a factor of 1.47 compared to using 0th order alone and could obtain a pulse fraction limit lower than the value of obtained by Ransom et (2002) in their unaccelerated search. A pulse fraction upper limit ccontidence) of wwas derived applying our likelihood ratio method using all data. including the dispersed events with 1«A70A.," A pulse fraction upper limit confidence) of was derived applying our likelihood ratio method using all data, including the dispersed events with $1 < \lambda < 70$." Taking only the events limited by οἱ<2 ms. the pulse fraction limit isLOY.," Taking only the events limited by $\delta t < 2$ ms, the pulse fraction limit is." .. Thirdly. we computed the Lomb-Scargle periodograam for both the time-corrected. aud uncorrected photon arrival ime differences in the frequency range 0.01-1 Hz for the events in ObsID's 3380 3381. 3:32 and 3399.," Thirdly, we computed the Lomb-Scargle periodogram for both the time-corrected and uncorrected photon arrival time differences in the frequency range 0.01-1 Hz for the events in ObsID's 3380 3381, 3382 and 3399." Again. no significant peaks were present.," Again, no significant peaks were present." The assumption of a negligible deceleration term in our period search restricts the range of periods and dipole magnetic field strengths for which our search is valid., The assumption of a negligible deceleration term in our period search restricts the range of periods and dipole magnetic field strengths for which our search is valid. The coherence limit [or phase slippage bv 10 oover the duration of the 2001 October observations implies (hat our result is valid for a magnetic field upper limit D.—2.3x10!P? G [or period P s SShapiro Teukolsky 1983).," The coherence limit for phase slippage by 10 over the duration of the 2001 October observations implies that our result is valid for a magnetic field upper limit $B < 2.3\times 10^{13} P^{3/2}$ G for period $P$ s Shapiro Teukolsky 1983)." As noted by Ransom οἱ ((2002). this range would exclude very. voung and energetic neulron stars. such as the Crab ancl Vela pulsars. though most of these vounger objects are also conspicuously strong radio pulsars.," As noted by Ransom et (2002), this range would exclude very young and energetic neutron stars, such as the Crab and Vela pulsars, though most of these younger objects are also conspicuously strong radio pulsars." All anomalous X-rav pulsars would lie within our sensitivitv limit range., All anomalous X-ray pulsars would lie within our sensitivity limit range. wo orders of magnitude greater than quiescent ellipticals of the same mass at 2~OL.,"two orders of magnitude greater than quiescent ellipticals of the same mass at $z \sim 0.1$." Within the central 1 spe (plysical). however. the deusities of carly-types at Do2 are found to only exceed local mecasurements by a actor of2 32010)..," Within the central $1$ kpc (physical), however, the densities of early-types at $z \sim 2$ are found to only exceed local measurements by a factor of $2$ $3$." Altogether. the observations Sugeest that there is significant evolution iu the size of uassive ellipticals over the past 10 Cir. likely proceeding in an inside-out manner. without the addition of much stellar mass.," Altogether, the observations suggest that there is significant evolution in the size of massive ellipticals over the past $10$ Gyr, likely proceeding in an inside-out manner, without the addition of much stellar mass." Several physical processes have been proposed to explain this strong size evolution within the massive. carly-type population at 2<2.," Several physical processes have been proposed to explain this strong size evolution within the massive, early-type population at $z < 2$." " In particular. eas-poor. collisionless (or ""drv) nünor mergers are often invoked as a lucans for puffüug up the stellar componcut of these lnassive svstenisPOLL)."," In particular, gas-poor, collisionless (or “dry”) minor mergers are often invoked as a means for puffing up the stellar component of these massive systems." .. Iowever. a variety of alternative iuechauisus have also been proposed. iucludiug scenarios in which the observed. structural evolution may be driven by secular processes such as adiabatic expansion resulting frou stellar nass loss and/or strong ACUN-fueled feedback2010:2009::2010b.a:: see also and 2010)).," However, a variety of alternative mechanisms have also been proposed, including scenarios in which the observed structural evolution may be driven by secular processes such as adiabatic expansion resulting from stellar mass loss and/or strong AGN-fueled feedback; see also and )." Oue wav to possibly discriminate between these scenarios Gauinor niergers versus secular processes] is bv quantifvine the role of environment in the structural evolution of the massive galaxy population., One way to possibly discriminate between these scenarios (minor mergers versus secular processes) is by quantifying the role of environment in the structural evolution of the massive galaxy population. While secular processes are lareelv independent of euvirounneut and quasars are not prefercutially found im overdeuse regions at 2~12007).. 1nergers are more Common in higher-deusitv euvironnents such as galaxy groups2010).," While secular processes are largely independent of environment and quasars are not preferentially found in overdense regions at $z \sim 1$, mergers are more common in higher-density environments such as galaxy groups." . Thus. if merecrs are the dominant moechanisii by which the sizes of massive eulv-tvpes evolve at 2«2. we should expect to find a variation in the structural properties of galaxies as a function of environment at D].," Thus, if mergers are the dominant mechanism by which the sizes of massive early-types evolve at $z < 2$, we should expect to find a variation in the structural properties of galaxies as a function of environment at $z \sim 1$." " To test this. we use data drawn from the DEEP2 aud DEEP3 Galaxy Redshift Survevs to investigate the correlation between the local overdensity of ealaxies Qvlich we eenerally refer to as ""environment aud the sizes of massive galaxies ou the red sequence) at intermediate redslüft."," To test this, we use data drawn from the DEEP2 and DEEP3 Galaxy Redshift Surveys to investigate the correlation between the local overdensity of galaxies (which we generally refer to as “environment”) and the sizes of massive galaxies on the red sequence at intermediate redshift." In Section 2.. we describe our data set. with results aud discussion preseuted ia Sections 3 and Lo respectively.," In Section \ref{sec_data}, we describe our data set, with results and discussion presented in Sections \ref{sec_results} and \ref{sec_disc}, respectively." " Throughout. we emplov a ACDM cosuiologv with w=1. O,,=0.3. Q4= 0.7. and a Iubble paramcter of yj=100fh lan + 1. iiless otherwise noted."," Throughout, we employ a $\Lambda$ CDM cosmology with $w = -1$, $\Omega_m = 0.3$, $\Omega_{\Lambda} = 0.7$ , and a Hubble parameter of $H_{0} = 100\ h$ km $^{-1}$ $^{-1}$, unless otherwise noted." All maguitudes are on the AB system1983)., All magnitudes are on the AB system. . To characterize both the cuviromucut aud the structure of galaxies accurately requires spectroscopic observations as well as high-resolutiou inae across a sizable area of sv., To characterize both the environment and the structure of galaxies accurately requires spectroscopic observations as well as high-resolution imaging across a sizable area of sky. Caven the Bnaitations of eround-based adaptive-optics observations. the latter is only possible at intermediate redshift via space-based observations (e.g. with AST).," Given the limitations of ground-based adaptive-optics observations, the latter is only possible at intermediate redshift via space-based observations (e.g., with )." Amone the fields covered by deep. imulti-baud imaging withJST. the Extended Groth Strip (ECGS) is by far the most complete with reeard to spectroscopic coverage at intermediate redshift.," Among the fields covered by deep, multi-band imaging with, the Extended Groth Strip (EGS) is by far the most complete with regard to spectroscopic coverage at intermediate redshift." The EGS is one of four fields surveved by the DEEP2 Galaxy Redshitt Survey2012).. vielding high-precision (6.~30 km +) secure redshifts for 11.701 sources at 2<2<1.1 over roughly 0.5 square degrees m the ECGS.," The EGS is one of four fields surveyed by the DEEP2 Galaxy Redshift Survey, yielding high-precision $\sigma_{z} \sim 30$ km $^{-1}$ ) secure redshifts for $11,701$ sources at $0.2 < z < 1.4$ over roughly $0.5$ square degrees in the EGS." Building upon the DEEP2 spectroscopic sample. the completed DEEPS Galaxy Redshift Survey2011: Cooper et abl.," Building upon the DEEP2 spectroscopic sample, the recently-completed DEEP3 Galaxy Redshift Survey; Cooper et al.," in prep) has brought the tarect sampling rate to ~90% at Ray<2L1I over the central 0.25 square deerees of the EGS the portion of the field inaeed by ZZST/ACS2008).," in prep) has brought the target sampling rate to $\sim \! 90\%$ at $R_{\rm AB} < 24.1$ over the central $0.25$ square degrees of the EGS — the portion of the field imaged by /ACS." Among the current generation of deep spectroscopic redshift surveys at zld. the combination of the DEEP? aud DEEPS3 spectroscopic datasets provides the largest sample of accurate spectroscopic redshifts. the lighest-precision velocity information. and the highest sampling deusity2012: Cooper et al.," Among the current generation of deep spectroscopic redshift surveys at $z \sim 1$, the combination of the DEEP2 and DEEP3 spectroscopic datasets provides the largest sample of accurate spectroscopic redshifts, the highest-precision velocity information, and the highest sampling density; Cooper et al.," in Combined with the relatively wide area imaged with Z/ST/ACS 2001)... these attributes make the EGS one of the best- fields in which to study the relationship between environment aud ealaxy structure at +~1.," in Combined with the relatively wide area imaged with /ACS , these attributes make the EGS one of the best-suited fields in which to study the relationship between environment and galaxy structure at $z \sim 1$." Iu this paper. we utilize a parent sample of 11.193 ealaxies drawn from the joint DEEP?/DEEP3 dataset in the EGS with secure redshifts iu the range 1<2«1.2.," In this paper, we utilize a parent sample of $11,493$ galaxies drawn from the joint DEEP2/DEEP3 dataset in the EGS with secure redshifts in the range $0.4 < z < 1.2$." For cach galaxy in the DEEP?/DEEP3 sample. rest-frame Ü B colors aud absolute B-hanud maguitudes. Afp. are calculated from CFUT BRI photometry using the A-correction procedure clescribed in(2006).," For each galaxy in the DEEP2/DEEP3 sample, rest-frame $U-B$ colors and absolute $B$ -band magnitudes, $M_{B}$, are calculated from CFHT $BRI$ photometry using the $K$ -correction procedure described in." .. For a subset of the ealaxy catalog. stellar masses are calculated by fitting spectral cnerey distributions (SEDs) to WIRC/Palomay J- and Ny-baud photometry in conjunction with the DEEP2 BRI data. according to the prescriptions described. by2006).," For a subset of the galaxy catalog, stellar masses are calculated by fitting spectral energy distributions (SEDs) to WIRC/Palomar $J$ - and $K_{s}$ -band photometry in conjunction with the DEEP2 $BRI$ data, according to the prescriptions described by." .. However. the nem-iufrared photometry. collected as part of the Palomar Observatory Wide-field Iufraved survew. does not cover the cutire DEEP2/DEEDP23 survey area. and often faint blue ealaxies at the ligh-: end of the DEEP2 redshitt range are not detected in A.," However, the near-infrared photometry, collected as part of the Palomar Observatory Wide-field Infrared survey, does not cover the entire DEEP2/DEEP3 survey area, and often faint blue galaxies at the $z$ end of the DEEP2 redshift range are not detected in $K_{s}$." Because of these two effects. the stellar masses of have been used to calibrate stellar mass estimates for the full DEEP2 sample that are based ou rest-frame Alp and B/—V values derived from the DEEP? data in conjunction with the expressionsof (2003).. which relate mass-to-light ratio to optical color.," Because of these two effects, the stellar masses of have been used to calibrate stellar mass estimates for the full DEEP2 sample that are based on rest-frame $M_{B}$ and $B-V$ values derived from the DEEP2 data in conjunction with the expressionsof , which relate mass-to-light ratio to optical color." We clupirically correct these stella mass estimates to the measurements byaccounting for a, We empirically correct these stellar mass estimates to the measurements byaccounting for a Briclly. the merecr tree is constructed by identifving a unique for cach substructure.,"Briefly, the merger tree is constructed by identifying a unique for each substructure." For cach subhalo. we find all haloes that contain its particles in the following snapshot. and then count the particles by giving higher weight to those that are more tightly bound to the halo under consideration.," For each subhalo, we find all haloes that contain its particles in the following snapshot, and then count the particles by giving higher weight to those that are more tightly bound to the halo under consideration." The halo that contains the larges (weighted) number of its particles is selected as descendant., The halo that contains the largest (weighted) number of its particles is selected as descendant. ext all the pointers to the progenitors are constructed.," Next, all the pointers to the progenitors are constructed." Dv. defau the most massive progenitor at each node of he tree is selected. as theprogenilor.," By default, the most massive progenitor at each node of the tree is selected as the." noted tha his can lead to ambiguous selections when. for examplo. here are two subhaloes of similar mass.," noted that this can lead to ambiguous selections when, for example, there are two subhaloes of similar mass." In order to avoic occasional lailures in the merger tree construction algorithm. hey modified the definition. of the main progenitor by selecting the branch that accounts for most of the mass of he final svstem. for the longest time.," In order to avoid occasional failures in the merger tree construction algorithm, they modified the definition of the main progenitor by selecting the branch that accounts for most of the mass of the final system, for the longest time." We have applied this modification to our merger trees., We have applied this modification to our merger trees. In this section. we consider only substructures that contain at least. 100 bound particles. and in a few cases. we use particular mass ranges to ease the comparison with the literature.," In this section, we consider only substructures that contain at least 100 bound particles, and in a few cases, we use particular mass ranges to ease the comparison with the literature." In this section we will also study if the accretion and merger history of substructures depend on the environment. that we will approximate using the parent halo mass.," In this section we will also study if the accretion and merger history of substructures depend on the environment, that we will approximate using the parent halo mass." Lt is worth stressing. however. that our haloes provide likely a biasecl sample for this analysis.," It is worth stressing, however, that our haloes provide likely a biased sample for this analysis." In fact. excluding the most massive sample and some haloes that belong to the sample 82. all the other haloes reside in the regions surrounding the most massive haloes. which might not represent the ‘typical’ environment for halo in the same mass range.," In fact, excluding the most massive sample and some haloes that belong to the sample S2, all the other haloes reside in the regions surrounding the most massive haloes, which might not represent the `typical' environment for halo in the same mass range." In this section. we use the merger trees constructed: for our cluster sample to study the mass accretion histories of subhaloes of dillerent mass and residing in different environments.," In this section, we use the merger trees constructed for our cluster sample to study the mass accretion histories of subhaloes of different mass and residing in different environments." Several previous studies have pointed out that once haloes are acercted onto larger svstenis (i.c. they become substructures). their mass is significantly reduced. by tidal stripping.," Several previous studies have pointed out that once haloes are accreted onto larger systems (i.e. they become substructures), their mass is significantly reduced by tidal stripping." The longer the substructure spends in a more massive halo. the larger is the destructive cHeet of tidal stripping.," The longer the substructure spends in a more massive halo, the larger is the destructive effect of tidal stripping." Previous studies have found. that the ellieieney. of tidal stripping is largely independent of the parent halo mass (??)., Previous studies have found that the efficiency of tidal stripping is largely independent of the parent halo mass . . We re-address these issues using all substructures residing within the virial radius of our haloes. and with mass lareer than 10075TAL. at redshift .=0 (in our simulations. these substructures contain at least 100 xuticles).," We re-address these issues using all substructures residing within the virial radius of our haloes, and with mass larger than $10^{10}\,\hm M_{\odot}$ at redshift $z=0$ (in our simulations, these substructures contain at least 100 particles)." " By walking their merger trees. following the main progenitor branei. we construct the mass accretion history (NLALI) for all of these subhaloes. and record the accretion ime (24,4) as tlje last time the halo is a central halo. i.e. xefore it is accreted onto a larger structure and becomes a oper subhalo."," By walking their merger trees, following the main progenitor branch, we construct the mass accretion history (MAH) for all of these subhaloes, and record the accretion time $z_{accr}$ ) as the last time the halo is a central halo, i.e. before it is accreted onto a larger structure and becomes a proper subhalo." Our final saniple includes 39005 haloes. that we split in two bins of dillerent mass by using either their present clay mass or their mass at the accretion time.," Our final sample includes 39005 haloes, that we split in two bins of different mass by using either their present day mass or their mass at the accretion time." " We end up with 33576 haloes with mass larger than 101hb.ΑΙ, at esent (25:344 when using the mass at the accretion time). and 5429 haloes with mass lower than the adopted threshold (13661 if the accretion mass is used)."," We end up with 33576 haloes with mass larger than $10^{11}\,\hm M_{\odot}$ at present (25344 when using the mass at the accretion time), and 5429 haloes with mass lower than the adopted threshold (13661 if the accretion mass is used)." In order to analyse he environmental dependence of the mass aceretion history. we consider separately subhaloes residing in our 85 and 81 samples (these correspond to our lowest and largest. parent halo mass. respectively).," In order to analyse the environmental dependence of the mass accretion history, we consider separately subhaloes residing in our S5 and S1 samples (these correspond to our lowest and largest parent halo mass, respectively)." The top panels in Figure ο show the distribution of the aceretion times for the two mass bins considered., The top panels in Figure \ref{zaccdist2} show the distribution of the accretion times for the two mass bins considered. Left and right panels. correspond. to a splitting in mass done on the basis of the present day mass and of the mass at accretion. respectively.," Left and right panels correspond to a splitting in mass done on the basis of the present day mass and of the mass at accretion, respectively." When considering the present day mass (left. panel). the dillerences between the two distributions are small. with only a slightlv lower fraction of more massive substructures being acereted very late. and a slightly larger fraction of substructures in the same mass range being accreted between 2~0.1 and 2~1.," When considering the present day mass (left panel), the differences between the two distributions are small, with only a slightly lower fraction of more massive substructures being accreted very late, and a slightly larger fraction of substructures in the same mass range being accreted between $z\sim 0.1$ and $z\sim 1$." A larger dillerence between the two clistribution can be seen when considering the mass at the time of accretion (righ panel)., A larger difference between the two distribution can be seen when considering the mass at the time of accretion (right panel). Substruetures that are less massive at the time of accretion. have been accreted on average later than their more massive counterparts., Substructures that are less massive at the time of accretion have been accreted on average later than their more massive counterparts. In particular. about 90 per cen of the substructures in the least massive bin considered have been accreted below redshift 0.5. while only 50 per cent of the most massive substructures have been acereted over the same redshift range.," In particular, about 90 per cent of the substructures in the least massive bin considered have been accreted below redshift 0.5, while only 50 per cent of the most massive substructures have been accreted over the same redshift range." The distribution obtained for the mos massive substrucures is broader. extending up to redshif 2.," The distribution obtained for the most massive substructures is broader, extending up to redshift $\sim 2$." This is large vaeffect. due to the fact that we are only considering substructures that are still present a ;—0.," This is largely a, due to the fact that we are only considering substructures that are still present at $z=0$." Once accreted onto larger svstems. substructures are stroneglv allected by tidal stripping so that. among those tha were acereted at early times. only the most massive ones will still retain enough bound. particles at. present. to enter our samples.," Once accreted onto larger systems, substructures are strongly affected by tidal stripping so that, among those that were accreted at early times, only the most massive ones will still retain enough bound particles at present to enter our samples." “Phe less massive substructures that were accreted at carb times. have been stripped below the resolution of our simulations and therefore do not show up in the solid histogram that is shown in the top right panel of Figure 6..," The less massive substructures that were accreted at early times, have been stripped below the resolution of our simulations and therefore do not show up in the solid histogram that is shown in the top right panel of Figure \ref{zaccdist2}." The bottom panels of Figure 6 show the distribution of he ratios between present day mass and mass at accretion or subhaloes of dilferent. present dav mass (left panel) and or different mass at accretion (right panel)., The bottom panels of Figure \ref{zaccdist2} show the distribution of the ratios between present day mass and mass at accretion for subhaloes of different present day mass (left panel) and for different mass at accretion (right panel). Less massive subhaloes. which were aceretec on average more recently. ose on average smaller fractions of their mass compared to more massive subhaloes for which the distribution is skewed o higher values.," Less massive subhaloes, which were accreted on average more recently, lose on average smaller fractions of their mass compared to more massive subhaloes for which the distribution is skewed to higher values." The cillerence between these distributions »conies more evident when one split the samples according o the mass at the time of accretion. as shown in the right xuiel.," The difference between these distributions becomes more evident when one split the samples according to the mass at the time of accretion, as shown in the right panel." As explained above. however. this is alfected by the act that many of the least massive substructure will be stripped below the resolution of the simulation at z=0.," As explained above, however, this is affected by the fact that many of the least massive substructure will be stripped below the resolution of the simulation at $z=0$." We jwe repeated the analysis done in Fig., We have repeated the analysis done in Fig. 6 for subhaloes in each of the five samples used in our study. and. we found here is no significant dependency on the environment.," \ref{zaccdist2} for subhaloes in each of the five samples used in our study, and we found there is no significant dependency on the environment." Fig., Fig. 7 shows that. as expected. substructures accreted earlier. sullercd significantly more stripping than substructures that were aceretecd at later times.," \ref{zaccdist} shows that, as expected, substructures accreted earlier suffered significantly more stripping than substructures that were accreted at later times." In particular. about 90 per cent of subhalocs aceretec at redshift larger than 1 have been stripped by more than SO per cent of their mass at accretion.," In particular, about 90 per cent of subhaloes accreted at redshift larger than 1 have been stripped by more than 80 per cent of their mass at accretion." For haloes that have been accreted. at redshift lower than 1. the distribution is much broader. it peaks at. 0.6 (ie. about 40 per cent of the mass has been stripped for about 20 per cent of these haloes) but has a long tail to much lower values.," For haloes that have been accreted at redshift lower than 1, the distribution is much broader, it peaks at $\sim 0.6$ (i.e. about 40 per cent of the mass has been stripped for about 20 per cent of these haloes) but has a long tail to much lower values." Similarly, Similarly values (E10 g ) of these regions for LMXBs. Compton cooling dominates over free-free emission and the relation between the energy flux per unit surface area of corona ὄλων. the radiation energy density *(7) and electron temperature 7;. 1s given by (see also TLM98) where 7) i5 the characteristic optical depth of the TL.,"values $\la 10^{-5}$ g $^{-3}$ ) of these regions for LMXBs, Compton cooling dominates over free-free emission and the relation between the energy flux per unit surface area of corona $\qcor$, the radiation energy density $\varepsilon(\tau)$ and electron temperature $T_e$ is given by (see also TLM98) where $\tau_0$ is the characteristic optical depth of the TL." The distribution στ) is obtained as a solution of the diffusion equation where now Qu;=Qeor|Qaisk Is the sum of the corona (TL) and intercepted disk fluxes. respectively.," The distribution $\varepsilon(\tau)$ is obtained as a solution of the diffusion equation where now $\qtot=\qcor + \qd$ is the sum of the corona (TL) and intercepted disk fluxes, respectively." The two boundary conditions for equation (4)) are written as which represent the case of albedo Az1 at the NS source (r= m) and no diffusion emission falling from outside onto outer corona boundary (7= (0)., The two boundary conditions for equation \ref{diffusion_equation}) ) are written as which represent the case of albedo A=1 at the NS source $\tau=\tau_0$ ) and no diffusion emission falling from outside onto outer corona boundary $\tau=0$ ). " The condition. for Az] arises from the well-established observational result of NS temperature ATi,~ | keV. which implies the presence of a ionized NS atmosphere."," The condition for A=1 arises from the well-established observational result of NS temperature $\ktbb \sim$ 1 keV, which implies the presence of a ionized NS atmosphere." This is different from the case considered by HM93. where the cool disk temperature (< 5 eV) gives rise to an energy-dependent albedo with photoelectric absorption for impinging photons with energy < 10 keV. Another important consideration to keep in mind is. that the diffusion equation (4)) is to be considered frequency-integrated.," This is different from the case considered by HM93, where the cool disk temperature $<$ 5 eV) gives rise to an energy-dependent albedo with photoelectric absorption for impinging photons with energy $ \la$ 10 keV. Another important consideration to keep in mind is that the diffusion equation \ref{diffusion_equation}) ) is to be considered frequency-integrated." This means that we are not dealing with the specific (energy-dependent) shape of the reflected spectrum from the NS surface. we are only dealing with the total energy density.," This means that we are not dealing with the specific (energy-dependent) shape of the reflected spectrum from the NS surface, we are only dealing with the total energy density." The solution for (7) 1s then given by It is worth pointing out that dz/dr>0 for 7 0$ for $\tau<\tau_0$, and as $F_{rad} \propto d\varepsilon/d\tau$ for NS sources the radiative force always plays against gravity, unlike the case of BH sources." Note that the spectra of NS sources both in the soft and hard state can be adequately fitted by single-temperature Comptonization models (Pazis et al., Note that the spectra of NS sources both in the soft and hard state can be adequately fitted by single-temperature Comptonization models (Pazis et al. 2006. Falanga et al.," 2006, Falanga et al." 2005. Farinelli et al.," 2005, Farinelli et al." 2008. Cocchi et al.," 2008, Cocchi et al." 2010)., 2010). This observational fact demonstrates that an assumption of isothermal plasma in the TL can be applicable to X-ray data analysis from NS binaries., This observational fact demonstrates that an assumption of isothermal plasma in the TL can be applicable to X-ray data analysis from NS binaries. The question is how one can estimate this average temperature of the TL which ts. in fact. established by photon scattering and cooling processes.," The question is how one can estimate this average temperature of the TL which is, in fact, established by photon scattering and cooling processes." In order to establish this average plasma temperature T;. one should estimate the mean energy densityin the TL as It is worth emphasizing the similarity between equations (3)) and (8)) in our paper and equation (13) in. Bisnovatyi-Koganetal.(1980) who studied the radiation emission due to gas accretion onto a NS., In order to establish this average plasma temperature $T_e$ one should estimate the mean energy densityin the TL as It is worth emphasizing the similarity between equations \ref{energy_balance}) ) and \ref{average_ene}) ) in our paper and equation (13) in \cite{bk80} who studied the radiation emission due to gas accretion onto a NS. " If we now substitute the result of equation (8)) into equation (3)). after a bit of straightforward algebra we obtain Keeping in mind the definition of the Compton parameter VoxAN. (Rybicki Ligthman 1989). where lL~AKT,fine? and Ny.~ Max(72.7y) are the average photon energy gain per scattering and average number of scatterings. respectively. we can rewrite equation (9)) as follows Equation (10)) is one of the main points of our theoretical model and shows that in the diffusion. approximation the Compton parameter. which determines the spectral index. is just a function of the corona and disk cooling fluxes. "," If we now substitute the result of equation \ref{average_ene}) ) into equation \ref{energy_balance}) ), after a bit of straightforward algebra we obtain Keeping in mind the definition of the Compton parameter $Y \approx A N_{sc}$ (Rybicki Ligthman 1989), where $A\sim 4kT_e/m_ec^2$ and $N_{sc}\sim$ $(\tau_0^2, \tau_0)$ are the average photon energy gain per scattering and average number of scatterings, respectively, we can rewrite equation \ref{ktetau}) ) as follows Equation \ref{compton_par}) ) is one of the main points of our theoretical model and shows that in the diffusion approximation the Compton parameter, which determines the spectral index, is just a function of the corona and disk cooling fluxes. }" As we have shown in Section 2.1. the observed spectral index a of most NS LMXBs undergoes small variation around l. namely à.=10.2 when the electron temperature of Compton cloud varies from about 2.5 to 25 keV (see Fig. 1)).," As we have shown in Section 2.1, the observed spectral index $\alpha$ of most NS LMXBs undergoes small variation around 1, namely $\alpha= 1\pm 0.2$ when the electron temperature of Compton cloud varies from about 2.5 to 25 keV (see Fig. \ref{alpha_data}) )." Thus here we propose a model the spectral formation in the TL (corona) which can explain the stability of index « if energy release in the disk is much less than that in the TL., Thus here we propose a model the spectral formation in the TL (corona) which can explain the stability of index $\alpha$ if energy release in the disk is much less than that in the TL. Namely we show that ol|οΟμQo)., Namely we show that $\alpha \approx 1+ \rm {O} (Q_{disk}/Q_{cor})$. As already pointed out in. classical works (Sunyaev Titarchuk 1950. 1985. hereafter ST85. Titarchuk 1994). spectral formation in. plasma clouds of finite dimensions (bounded medium) is related to the distribution law of the number of scatterings that seed photons experience before escaping.," As already pointed out in classical works (Sunyaev Titarchuk 1980, 1985, hereafter ST85, Titarchuk 1994), spectral formation in plasma clouds of finite dimensions (bounded medium) is related to the distribution law of the number of scatterings that seed photons experience before escaping." " If ων denotes the average number of photon scatterings and the dimensionless scattering number is Ξ N,oret. then the distribution law for &>>H4, 18 given by (see ST835) For a diffusion regime when 7Z 1.5. it results /3. where A, is the first eigenvalue of the diffusion space operator."," If $u_{av}$ denotes the average number of photon scatterings and the dimensionless scattering number is $u=N_e \sigma_T c t$ , then the distribution law for $u\gg u_{av}$ is given by (see ST85) For a diffusion regime when $\tau_0 \ga 1.5$ , it results $\beta=\lambda^2_1/3$ , where $\lambda_1$ is the first eigenvalue of the diffusion space operator." As reported in STS5. the eigenvalue problem for photon diffusion in a slab with total optical depth 27) 1s derivedfrom solution of the differential equation for the zero-moment intensity with absorption boundary conditions d.J/dr (3/2).7—0 and d.Jfdr|(3/2)./= 0. for z=0 and 7= 27). respectively.," As reported in ST85, the eigenvalue problem for photon diffusion in a slab with total optical depth $2\tau_0$ is derivedfrom solution of the differential equation for the zero-moment intensity with absorption boundary conditions $dJ/d\tau-(3/2)J=0$ and $dJ/d\tau+(3/2)J=0$ , for $\tau=0$ and $\tau=2\tau_0$ , respectively." , the Nrav one for the DNMW-IIBI objects classified as extended sources (122 entries) im the cross-correlation with FIRST.,the X–ray one for the BMW-HRI objects classified as extended sources (122 entries) in the cross-correlation with FIRST. Iu the plot. Xrav extensions are the ones derived by our fitting procedure aud subtracting in quadrature the relative PSF at a given offaxis anele.," In the plot, X–ray extensions are the ones derived by our fitting procedure and subtracting in quadrature the relative PSF at a given off–axis angle." All the FIRST paraincters with a brief description are reported in Appendix A (Table A.2)., All the FIRST parameters with a brief description are reported in Appendix A (Table A.2). The Tutvared Astronomical Satellite (RAS) couducted a survev of (of the sla. from January to November 1982. in four waveleneth bands ceutered at 12. 25. 60. and LOO jun leading to the TRAS Point Source Catalogue (PSC).," The Infrared Astronomical Satellite (IRAS) conducted a survey of $\%$ of the sky, from January to November 1983, in four wavelength bands centered at 12, 25, 60, and 100 $\mu$ m leading to the IRAS Point Source Catalogue (PSC)." The catalogue coutains some 250.000 sources (Beichiman et al. 1988)).," The catalogue contains some 250,000 sources (Beichman et al. \cite{beichman88}) )." Away from confused regions of the sky. the PSC is complete to about 0.1. 0.5. 0.6. and 1.0 Jy at 12. 25. 60. and 100 san. The angular resolution of sources detected by IRAS varied between about 0.5 aresec at 12 jaa to about 2 arcmin at 100 pau. The positional accuracy depends on source size. brightuess and spectra Ohorev distribution but is usually better than 20 arcsec.," Away from confused regions of the sky, the PSC is complete to about 0.4, 0.5, 0.6, and 1.0 Jy at 12, 25, 60, and 100 $\mu$ m. The angular resolution of sources detected by IRAS varied between about 0.5 arcsec at 12 $\mu$ m to about 2 arcmin at 100 $\mu$ m. The positional accuracy depends on source size, brightness and spectral energy distribution but is usually better than 20 arcsec." Using a cross-correlation radius of 20 aresce (because ofthe IRAS positional accuracy) we found 1.119 identifications with a uusidentification probability of ~2% (20 miüisnatches).," Using a cross-correlation radius of 20 arcsec (because of the IRAS positional accuracy) we found 1,149 identifications with a misidentification probability of $\sim\,2\%$ (20 mismatches)." We note that all the objects that have been ound iu conumion with this catalogue have een detected in all four TRAS bands., We note that all the objects that have been found in common with this catalogue have been detected in all four IRAS bands. Iu. Fig., In Fig. LL we plot he distributions of the angular separation (rr m arcsec} )otween the infrared iud the Xrav position for the matched objects., 14 we plot the distributions of the angular separation $r$ in arcsec) between the infrared and the X–ray position for the matched objects. Fig., Fig. 15 shows for example the 12 jun flux (in indy) versus Xταν flux (full colin deusitv) for the 1.119 cross-correlated sources.," 15 shows for example the 12 $\mu$ m flux (in mJy) versus X–ray flux (full column density) for the 1,149 cross-correlated sources." All the IRASPSC paraicters with a brief description are reported in Appendix A (Table À.3)., All the IRASPSC parameters with a brief description are reported in Appendix A (Table A.3). The Two Microu All Sky Survey covers over 19.600 dee? (x 504) of sky observed from both the hemispheres.," The Two Micron All Sky Survey covers over 19,600 $^{2}$ $\sim 50\%$ ) of sky observed from both the hemispheres." The catalogue contains positional aud photometric information for 162.213.351 point and 585.056 extended sources observed in the three bids ο; (1.25 yan). HE. (1.65 jn) and IS (2.16 pan).," The catalogue contains positional and photometric information for 162,213,354 point and 585,056 extended sources observed in the three bands $J$ $1.25\,\mu$ m), $H$ $1.65\,\mu$ m) and $K_{s}$ $2.16\,\mu$ m)." " The 10niinal survey coiupletcucss limits are 15.5. 15.1 aud 113U mae respectively,"," The nominal survey completeness limits are 15.8, 15.1 and 14.3 mag respectively." We have cross-correlated the DMWN-MRI with the 2MAÀSS Point Source Catalogue 2000 (Secoud. Incremental Release) finding 7.900 euntis with a nusidentification probability of ~28( (that is 2.171 nüsmatcehes).," We have cross-correlated the BMW-HRI with the 2MASS Point Source Catalogue 2000 (Second Incremental Release) finding 7,900 entries with a misidentification probability of $\sim\,28\%$ (that is 2,174 mismatches)." The umber of NXrav sources found to have an infrared counterpart with a measure in all the three bauds is 7.62|.," The number of X–ray sources found to have an infrared counterpart with a measure in all the three bands is 7,624." Iu Fig., In Fig. 16 we report the distributions of the angular separation (r dn arcsec} between the infrared aud Xταν position for the 7.900 matched objects.," 16 we report the distributions of the angular separation $r$ in arcsec) between the infrared and X–ray position for the 7,900 matched objects." Fie., Fig. 17 shows. for," 17 shows, for" T.spr the spectroscopic temperature measured in the range 0.154250; 25°) to use simple ADI reduction method (?) to remove the PSF of the central star.," Seven of our targets were observed with the rotator off and at an hour angle that allowed sufficient field rotation (typically $\geq 25 \dg$ ) to use simple ADI reduction method \citep{Marois.2006} to remove the PSF of the central star." " We used several advanced variations on the ADI technic on each of these targets. namely smart ADI (?).. LOCI (?).. and the new slightly different method that we describe here. ""weighted"" ADI."," We used several advanced variations on the ADI technic on each of these targets, namely smart ADI \citep{Lagrange.2010}, LOCI \citep{LafreniereLOCI.2007}, and the new slightly different method that we describe here, “weighted"" ADI." Weighted-ADI is a variant of “smart” ADI.," Weighted-ADI is a variant of “smart"" ADI." The references used to build the smart-ADI PSF for à given image are chosen with the constraint that the field must have rotated by a given angle with respect to the image. to mitigate the self-subtraction of possible companions.," The references used to build the smart-ADI PSF for a given image are chosen with the constraint that the field must have rotated by a given angle with respect to the image, to mitigate the self-subtraction of possible companions." The 7 references closest in time to the image. with 7 being a free parameter that we usually set to 10. are then median-combined to produce the PSF that will be subtracted to the image.," The $n$ references closest in time to the image, with $n$ being a free parameter that we usually set to 10, are then median-combined to produce the PSF that will be subtracted to the image." Since the PSF evolve with time. a natural step beyond smart ADI is to weight each reference by a value related to the invert of the time-span between image and reference before combining them.," Since the PSF evolve with time, a natural step beyond smart ADI is to weight each reference by a value related to the invert of the time-span between image and reference before combining them." We used a weighted-ADI method working exactly as a smart ADI but for the use of x as a weight for each reference., We used a weighted-ADI method working exactly as a smart ADI but for the use of $\frac{1}{\Delta t}$ as a weight for each reference. As can be seen in table3 the method vields results that are slightly better compared to smart-ADI. and particularly interesting in case of moderate on-sky rotation (x30 7)," As can be seen in table \ref{detlim_ADI} the method yields results that are slightly better compared to smart-ADI, and particularly interesting in case of moderate on-sky rotation $\leq$ $\dg$ )." Ten of our targets were observed in classical imaging mode. with field tracking on.," Ten of our targets were observed in classical imaging mode, with field tracking on." For these we also used independently several subtraction methods. namely low frequency spatial filtering (a sliding median filter with a box size of 4%FWHM). subtraction of radial profile (for a given annulus centred on the primary. we subtract the median value of all pixels within the annulus) and subtraction of the image rotated by z.," For these we also used independently several subtraction methods, namely low frequency spatial filtering (a sliding median filter with a box size of $\times$ FWHM), subtraction of radial profile (for a given annulus centred on the primary, we subtract the median value of all pixels within the annulus) and subtraction of the image rotated by $\pi$." For all targets. whether or not observed in ADI. a stacked image of the full NACO field of view. extended by the offset of the dither pattern was produced to search for background-limited large separation companions.," For all targets, whether or not observed in ADI, a stacked image of the full NACO field of view, extended by the offset of the dither pattern was produced to search for background-limited large separation companions." Since most of our observations were windowed to 512x512 pixels. the resulting field was 19.5x 19.5”. typically AAU by AAU on sky.," Since most of our observations were windowed to 512x512 pixels, the resulting field was $\times$ $\arcsec$, typically AU by AU on sky." In the case of 2M1207. the full 10241024 frame was read. resulting in a fourfold increase in the research area.," In the case of 2M1207, the full $\times$ 1024 frame was read, resulting in a fourfold increase in the research area." to characterize the AGN and SB contribution to the emission of ULIRGs by means of spectral templates (Paper II).,to characterize the AGN and SB contribution to the emission of ULIRGs by means of spectral templates (Paper II). Our model also takes into account the possible reddening ol the AGN component due to a compact absorber along the line of sight: this localized extinction can not affect the SB component. which is much more diffuse ancl interspersed with the obsenring Llence the degrees of [reedom in our fitting procedure are the amplitudes of the AGN and SB templates and the optical depth to the ACN. which is supposed to follow the extinction law of Draine (1939).," Our model also takes into account the possible reddening of the AGN component due to a compact absorber along the line of sight; this localized extinction can not affect the SB component, which is much more diffuse and interspersed with the obscuring Hence the degrees of freedom in our fitting procedure are the amplitudes of the AGN and SB templates and the optical depth to the AGN, which is supposed to follow the extinction law of Draine (1989)." " Apart from the llux normalization Ae"". the basic parameters of our spectral decomposition are only the AGN contribution to (he intrinsic (1.e. absorption-corrected) emission ag and the optical depth το; where wi?"" and us’ are the AGN and SB templates."," Apart from the flux normalization $f_6^\mathit{int}$, the basic parameters of our spectral decomposition are only the AGN contribution to the intrinsic (i.e. absorption-corrected) emission $\alpha_6$ and the optical depth $\tau_6$ : where $u_\nu^\mathit{agn}$ and $u_\nu^\mathit{sb}$ are the AGN and SB templates." This model allows us to reproduce adequately the main features observed in the 58 san ULIRG spectra (see Fig. Als:, This model allows us to reproduce adequately the main features observed in the 5–8 $\mu$ m ULIRG spectra (see Fig. \ref{apf}; all the spectra are available in Che online publication. in order (to illustrate their quality ancl the reliability of ow spectral clecommposition on the whole sample).," all the spectra are available in the online publication, in order to illustrate their quality and the reliability of our spectral decomposition on the whole sample)." The results of the moclel fitting for each source are filed in Table 1.., The results of the model fitting for each source are filed in Table \ref{t1}. We now introduce another useful diagnostic tool. namely the ratio between the 6 juan and the bolometric Iuminosities: since an AGN is much brighter around 6 jan than a SB of equal bolometric Iuminositv. (his ratio is a straightforward indicator of the significance of nuclear activity within composite ULIRGs.," We now introduce another useful diagnostic tool, namely the ratio between the 6 $\mu$ m and the bolometric luminosities: since an AGN is much brighter around 6 $\mu$ m than a SB of equal bolometric luminosity, this ratio is a straightforward indicator of the significance of nuclear activity within composite ULIRGs." " IIere we make use of the absorption-corrected ratio. delined as follows: where R"" and RY| are the intrinsic. bolometric. corrections. for: the separate AGN""D and SB components (we refer to Paper I for the algebraicoO details)."," Here we make use of the absorption-corrected ratio, defined as follows: where $R^\mathit{agn}$ and $R^\mathit{sb}$ are the intrinsic bolometric corrections for the separate AGN and SB components (we refer to Paper I for the algebraic details)." " The A a, relation [rom equation (3)) has been superimposed to our absorption-corrected points. treating 2” and RU as floating variables."," The $R$ $\alpha_6$ relation from equation \ref{eq}) ) has been superimposed to our absorption-corrected points, treating $R^\mathit{agn}$ and $R^\mathit{sb}$ as floating variables." " The best fit vields log2*7""=—0.53+0.05 and log 0.02. in excellent agreement wilh our previous estimates."," The best fit yields $\log R^\mathit{agn}=-0.53 \pm 0.05$ and $\log R^\mathit{sb}=-1.93 \pm 0.02$ , in excellent agreement with our previous estimates." Incidentallv. (his also proves thatthe possible elfects of the A correction are negligible. and (hat (he average properties of the," Incidentally, this also proves thatthe possible effects of the $K$ correction are negligible, and that the average properties of the" higher e and 7.,higher $e$ and $i$ . " Figure 3 shows the geometric optical depth of the total KB dust population after the full collisional grooming algorithm has been applied, as described above, at four different"," Figure \ref{fig:collisions} shows the geometric optical depth of the total KB dust population after the full collisional grooming algorithm has been applied, as described above, at four different" The study of the elfects. of rotation on the hydrostatic structure of a star is a long-standing problem (Ixddington. rm925. Sweet. 1950).,"The study of the effects of rotation on the hydrostatic structure of a star is a long-standing problem (Eddington, 1925, Sweet, 1950)." LHt ids the key towards a better nderstanding of stellar evolution. and consequently. of the whole observable universe.," It is the key towards a better understanding of stellar evolution, and consequently, of the whole observable universe." “Phe cllects of rotation on )0 stellar evolution can be separated into two. classes: ellect on the contraction or expansion with time of various stellar regions ancl rotational mixing (of chemical. species and angular momentum) through waves. instabilities and centrifugale drivinge of meridional motions.," The effects of rotation on the stellar evolution can be separated into two classes: effect on the contraction or expansion with time of various stellar regions and rotational mixing (of chemical species and angular momentum) through waves, instabilities and centrifugal driving of meridional motions." The ellects of rotational mixing in stars was reviewed bv Pinsonneault (1997) and can be directly observed (e.g. Li abundances and Li dip problem. ATS turnolf. low-mass giants deep mixing ...).," The effects of rotational mixing in stars was reviewed by Pinsonneault (1997) and can be directly observed (e.g. Li abundances and Li dip problem, MS turnoff, low-mass giants deep mixing ...)." tecent works by Maecder Alevnet (2000). or Chabover. Demarque Pinsonneault (1995) for example. attempt to consider the ellects of rotational mixing on stellar evolution wough the resolution of one-dimensional stellar mocels ising various ad-hoc parameterizations.," Recent works by Maeder Meynet (2000), or Chaboyer, Demarque Pinsonneault (1995) for example, attempt to consider the effects of rotational mixing on stellar evolution through the resolution of one-dimensional stellar models using various ad-hoc parameterizations." These moclels are successful in explaining some aspects of the observations but ein predictive power is sometimes limited., These models are successful in explaining some aspects of the observations but their predictive power is sometimes limited. In this paper Lo propose to approach the problem wough a new path. which has dilferent limitations and idvantages thereby providing an interesting complement o the existing models.," In this paper I propose to approach the problem through a new path, which has different limitations and advantages thereby providing an interesting complement to the existing models." E. choose to study the nonlinear elfects of rotationally driven meridional [Lows on the angular-momentum cistribution of a stellar radiative zone., I choose to study the nonlinear effects of rotationally driven meridional flows on the angular-momentum distribution of a stellar radiative zone. In the imit of a slowly rotating star. this is equivalent το the well-known Iddington-Sweet problem.," In the limit of a slowly rotating star, this is equivalent to the well-known Eddington-Sweet problem." In the case of rapid rotation. this problem has received less attention: it can now be studied through the formalism introduced in this paper.," In the case of rapid rotation, this problem has received less attention; it can now be studied through the formalism introduced in this paper." This type of approach has been considered in the past (c.g. ‘Tassoul “Tassoul (1983)): however. in. previous works the nonlinearity of the angular-momoentunm. transport. processes was usually neglected mainly by assuming that the star was rotating nearly uniformly.," This type of approach has been considered in the past (e.g. Tassoul Tassoul (1983)); however, in previous works the nonlinearity of the angular-momentum transport processes was usually neglected mainly by assuming that the star was rotating nearly uniformly." As E shall show. this assumption is not self-consistent.," As I shall show, this assumption is not self-consistent." In Section. 2. L|. present the equations. for. the hyvelrodvnamic structure of a quasi-steady. laminar ancl axisvmmetric radiative zone.," In Section 2, I present the equations for the hydrodynamic structure of a quasi-steady, laminar and axisymmetric radiative zone." The numerical results suggest a new scaling of the variables of the problem which can then be solved. in certain limits. analytically.," The numerical results suggest a new scaling of the variables of the problem which can then be solved, in certain limits, analytically." The solutions are presented in Section 3., The solutions are presented in Section 3. They. provide the first sell-consistent model of the effects of rotation on the centrifugal driving of meridional motions (assuming that the Dow is a ¢uasi-steady. laminar flow) and relies on onc parameter only: the mean rotation rate of the star.," They provide the first self-consistent model of the effects of rotation on the centrifugal driving of meridional motions (assuming that the flow is a quasi-steady, laminar flow) and relies on one parameter only: the mean rotation rate of the star." The results are cüscussed in Section 4., The results are discussed in Section 4. ] shall consider solar-tvpe. stars only and. study their quasi-cquilibrium structure under rotation., I shall consider solar-type stars only and study their quasi-equilibrium structure under rotation. The overlying convection zone is alfected by rotation mainly through the Coriolis distortion of the convective eddies., The overlying convection zone is affected by rotation mainly through the Coriolis distortion of the convective eddies. These. elfects are extremely complex: they are simply. represented in this work through the rotation profile imposed by the convective zone to the uncderlving radiative zone., These effects are extremely complex; they are simply represented in this work through the rotation profile imposed by the convective zone to the underlying radiative zone. The radiative zone, The radiative zone CO observations indicate the presence of a substantial reservoir (3.3x10! AL.) of molecular eas within ~2.5 kpe of the active (western) nucleus (p> 2000 ΔΙ. *: Evans et al.,CO observations indicate the presence of a substantial reservoir $3.3 \times 10^{10}$ $_{\odot}$ ) of molecular gas within $\sim$ 2.5 kpc of the active (western) nucleus $\rho >$ 2000 $_{\odot}$ $^{-3}$: Evans et al. 1999). consistent with measurements in other ultraluminous infrared. galaxies (?)..," 1999), consistent with measurements in other ultraluminous infrared galaxies \citep{Bryant99}." The double nucleus. the distorted. large-scale morphology. the presence of a rich inter-stellar medium (ISM) and. YSPs clearly indicate that PINS1345+12 represents the later stages of a merger involving al least one gas-rich galaxy. (??)..," The double nucleus, the distorted large-scale morphology, the presence of a rich inter-stellar medium (ISM) and YSPs clearly indicate that PKS1345+12 represents the later stages of a merger involving at least one gas-rich galaxy \citep{Heckman86,Surace98}." For the imaging part of the project we have used HIST archive data taken with various cameras and fillers sensitive from the UV to the near-IR., For the imaging part of the project we have used HST archive data taken with various cameras and filters sensitive from the UV to the near-IR. The wide spectral coverage of the observations allows us (to make accurate estimates of the ages of the stellar population associated with the bright knots identified in (he images., The wide spectral coverage of the observations allows us to make accurate estimates of the ages of the stellar population associated with the bright knots identified in the images. For the spectroscopy we have used hieh-quality long-slit spectra presented in ?.., For the spectroscopy we have used high-quality long-slit spectra presented in \cite{Holt03}. The spectroscopic data enable us to investigate the ages and mass contributions of the YSP detected at optical wavelengths in (he diffuse halo of the galaxy., The spectroscopic data enable us to investigate the ages and mass contributions of the YSP detected at optical wavelengths in the diffuse halo of the galaxy. We compare the results with model predictions in order to understaud the past and future of PINXS1345—12., We compare the results with model predictions in order to understand the past and future of PKS1345+12. The HST dataset comprises four sets of images taken with the FOC. WEPC2. ACS and NICMOS cameras.," The HST dataset comprises four sets of images taken with the FOC, WFPC2, ACS and NICMOS cameras." A summary of the observations is presented in Table 1., A summary of the observations is presented in Table 1. The observations and data reduction of the FOC images are described in ?.., The observations and data reduction of the FOC images are described in \cite{Hurt99}. These images were taken with the [/96 relax. with a combination of the F320W filter and three different polarizing fillers (POLO. POLGO and POL120).," These pre-costar images were taken with the f/96 relay, with a combination of the F320W filter and three different polarizing filters (POL0, POL60 and POL120)." The central wavelength of this configuration is À.=3100 lor a power-law spectrum f4xA t., The central wavelength of this configuration is ${\lambda_c}=3100$ for a power-law spectrum $f_{\lambda}{\propto}{\lambda}^{-1}$ . magnetic poles (?)..,magnetic poles \citep{L1988}. In this case. a first order description that accounts only for abundance variation with magnetic co-latitude is an appropriate approximation.," In this case, a first order description that accounts only for abundance variation with magnetic co-latitude is an appropriate approximation." As will be discussed below. such large-scale variations does not seem to be a prominent feature of HD 318107. so this particular model is not a good approximatio to the true abundance map.," As will be discussed below, such large-scale variations does not seem to be a prominent feature of HD 318107, so this particular model is not a good approximation to the true abundance map." However. using it does appear to provide some useful information about the nature of the abundance distributions.," However, using it does appear to provide some useful information about the nature of the abundance distributions." ZEEMAN includes a reasonably complete model of LTE line formation and radiative transfer in a magnetic. field., ZEEMAN includes a reasonably complete model of LTE line formation and radiative transfer in a magnetic field. The stellar atmosphere nodel is interpolated from a grid of precomputed solar abudance ATLAS 9 models., The stellar atmosphere model is interpolated from a grid of precomputed solar abundance ATLAS 9 models. The four equations of radiative transfer for polarised light are solved on a grid with 0.01 sspacing., The four equations of radiative transfer for polarised light are solved on a grid with 0.01 spacing. Local line profiles are computed as Voigt profiles based on atomic parameters taken from the VALD database or reasonable approximations., Local line profiles are computed as Voigt profiles based on atomic parameters taken from the VALD database or reasonable approximations. Line blending 1s correctly computed. by adding (polarised) line opacities due to various lines before solving the equations of transfer.," Line blending is correctly computed, by adding (polarised) line opacities due to various lines before solving the equations of transfer." The correctness of many of the oscillator strengths used has been confirmed by synthesis of a large number of non-magnetic stars (for which the abundance of each element is essentially constant over the surface)., The correctness of many of the oscillator strengths used has been confirmed by synthesis of a large number of non-magnetic stars (for which the abundance of each element is essentially constant over the surface). Note that the modelling uses atmosphere models computed for solar abundance throughout; the atmosphere model is not updated as the abundance analysis proceeds., Note that the modelling uses atmosphere models computed for solar abundance throughout; the atmosphere model is not updated as the abundance analysis proceeds. With rather large overabundances of some Fe peak elements found in this analysis. this fact certainly compromises the accuracy of the resulting abundance values (?)..," With rather large overabundances of some Fe peak elements found in this analysis, this fact certainly compromises the accuracy of the resulting abundance values \citep{KhaShu07}." The nodels ο the field geometry (a low order axisymmetric multipole expansion) and of the distribution of elements over the surface (a few simple discrete rings axisymmetric about the magnetic axis) are quite schematic., The models of the field geometry (a low order axisymmetric multipole expansion) and of the distribution of elements over the surface (a few simple discrete rings axisymmetric about the magnetic axis) are quite schematic. Compared to the sort of mapping done by ??.. who map field vector and element distributions over the surface with ~20° spatial resolution in. both surface coordinates. our models. in general. represent only a very rough approximation.," Compared to the sort of mapping done by \citet{Kochetal04,Kochetal10}, who map field vector and element distributions over the surface with $\sim 20^\circ$ spatial resolution in both surface coordinates, our models, in general, represent only a very rough approximation." However. the data set required for detailed mapping is far more extensivethan the few. irregularly distributed. mostly I spectra. obtained with a variety of resolving powers. and covering a large range in SNR. that are available at present for HD 318107.," However, the data set required for detailed mapping is far more extensivethan the few, irregularly distributed, mostly $I$ spectra, obtained with a variety of resolving powers, and covering a large range in SNR, that are available at present for HD 318107." The type of modelling we carry out here is quite appropriate for the limited data available. and provides a first exploration of physical conditions and chemical abundances in the atmosphere of this star. which can be used for statistical studies in which each star is characterised by only a few numbers. and for identifying stars of such great interest that they warrant the extensive investment in observations needed for detailed mapping.," The type of modelling we carry out here is quite appropriate for the limited data available, and provides a first exploration of physical conditions and chemical abundances in the atmosphere of this star, which can be used for statistical studies in which each star is characterised by only a few numbers, and for identifying stars of such great interest that they warrant the extensive investment in observations needed for detailed mapping." Before starting abundance analysis. we need to establish an approximate magnetic field model to use.," Before starting abundance analysis, we need to establish an approximate magnetic field model to use." An important quality of this model should be to reproduce reasonably well the phase variations of Zeeman splitting. so that the computed spectral line profiles are similar in form to the observed lines. and model fits are primarily sensitive to chemical abundance.," An important quality of this model should be to reproduce reasonably well the phase variations of Zeeman splitting, so that the computed spectral line profiles are similar in form to the observed lines, and model fits are primarily sensitive to chemical abundance." To estimate the inclination 7 of the rotation axis and the parameters of a suitable model magnetic field structure. we follow ?? and ?..," To estimate the inclination $i$ of the rotation axis and the parameters of a suitable model magnetic field structure, we follow \citet{Preston1967,Preston1970} and \citet{LM2000}." An estimate of the radius of the clustermember HD 318107 can be made from the values of log(Ter)=4.072+0.02 and log(L/L.)=1.92x0.1 from ?.., An estimate of the radius of the clustermember HD 318107 can be made from the values of $\log(\te) = 4.072 \pm 0.02$ and $\log (L/L_{\odot}) = 1.92 \pm 0.1$ from \citet{paper2}. The stellar radius is then found to be R=(2.22€0.34)R..., The stellar radius is then found to be $R = (2.22 \pm 0.34) R_{\odot}$. Our adopted rotation period of 9.7088+0.0007 days (Sect., Our adopted rotation period of $P = 9.7088 \pm 0.0007$ days (Sect. 4) and vsiné=7z2 ((see below) may then be used in the equation where vsin is in παπά Α is in solar units. to obtain /=37°+157.," 4) and $v \sin i = 7 \pm 2$ (see below) may then be used in the equation where $v \sin i$ is in and $R$ is in solar units, to obtain $i = 37^\circ \pm 15^\circ$." This is not a very strong constraint. but provides a useful check to the value of (=22° derived below.," This is not a very strong constraint, but provides a useful check to the value of $i = 22^\circ$ derived below." From the form of the aand vvariations with rotational phase. we can get a rough idea of the parameters the multipole model of the field will require.," From the form of the and variations with rotational phase, we can get a rough idea of the parameters the multipole model of the field will require." The fact that both magnetic moments (especially (B-))) vary significantly with phase indicates that / must be substantially different from zero. as we found above.," The fact that both magnetic moments (especially ) vary significantly with phase indicates that $i$ must be substantially different from zero, as we found above." The fact that all the data have the same sign indicates that. as the line of sight executes a cone around the rotation axis on the star. 1t always remains within one magnetic hemisphere. so i+8<907.," The fact that all the data have the same sign indicates that, as the line of sight executes a cone around the rotation axis on the star, it always remains within one magnetic hemisphere, so $i + \beta < 90^\circ$." We expect that the sum of the polar fields will be of order 15 kG. From the phase behaviour of(B... it appears that the closest approach of the line of sight to the magnetic axis occurs at about phase 0.9. even though the value of lis near minimum there: apparently the local field strength increases fairly rapidly into the magnetic hemisphere that is observed only briefly around phase 0.4.," We expect that the sum of the polar fields will be of order 15 kG. From the phase behaviour of, it appears that the closest approach of the line of sight to the magnetic axis occurs at about phase 0.9, even though the value of is near minimum there; apparently the local field strength increases fairly rapidly into the magnetic hemisphere that is observed only briefly around phase 0.4." To obtain a detailed model the FORTRAN programme FLDSRCH (?) was used., To obtain a detailed model the FORTRAN programme FLDSRCH \citep{LM2000} was used. The programme takes as input values of aand aat four equidistant phases., The programme takes as input values of and at four equidistant phases. The relative importance of these two kinds of data can be varied by adjustable weights., The relative importance of these two kinds of data can be varied by adjustable weights. Since we are particularly concerned with having a field model that predicts the correct amount of Zeeman splitting in lines at various phases. we have given a relatively large weight to the ddata.," Since we are particularly concerned with having a field model that predicts the correct amount of Zeeman splitting in lines at various phases, we have given a relatively large weight to the data." " FLDSRCH calculates aand aas functions of phase for a field composed of colinear dipole (By). quadrupole (By). and octopole €B,4) components."," FLDSRCH calculates and as functions of phase for a field composed of colinear dipole $B_{\rm d}$ ), quadrupole $B_{\rm q}$ ), and octopole $B_{\rm oct}$ ) components." The programme iteratively searches for the values of i. B. By. By. and By. that best fit the values aand provided as input.," The programme iteratively searches for the values of $i$, $\beta$, $B_{\rm d}$ , $B_{\rm q}$ , and $B_{\rm oct}$ that best fit the values and provided as input." Along with the best fit parameters. the programme provides calculated values of aand aas functions of phase.," Along with the best fit parameters, the programme provides calculated values of and as functions of phase." IR wavelengths.,IR wavelengths. This figure shows a dip iu the flux of rum and subimia emission. during which au," This figure shows a dip in the flux of mm and submm emission, during which an" Independent of my. our results demonstrate a clear trend of the ratio ry={μήν with initial surface density (Table 1).,"Independent of $m_{pro}$, our results demonstrate a clear trend of the ratio $r_{\Sigma} = t_m/t_{\Sigma}$ with initial surface density (Table 1)." " In massive disks with X,= 12 ο em?. mergers among oligarchs begin before oligarchs contain half of the mass (/,,//sS1)."," In massive disks with $\Sigma_0 \gtrsim$ 12 g $^{-2}$, mergers among oligarchs begin before oligarchs contain half of the mass $t_m/t_{\Sigma} \lesssim 1$ )." In low mass disks with My <2 e@ 7. oligarchs start to merge alter they contain half of the mass {μήν21).," In low mass disks with $\Sigma_0$ $\lesssim$ 2 g $^{-2}$, oligarchs start to merge after they contain half of the mass $t_m/t_{\Sigma} \gtrsim 1$ )." " To test whether variations in the lrequency and strength of dynamical interactions among oligarchs cause the trends in /,, and rs. we deline a ‘nearest neiehbor parameter n, Which measures the average number of oligarchs within 10 Ay of another oligarch."," To test whether variations in the frequency and strength of dynamical interactions among oligarchs cause the trends in $t_m$ and $r_{\Sigma}$, we define a `nearest neighbor parameter' $n_n$ which measures the average number of oligarchs within 10 $R_H$ of another oligarch." " From 833.2. configurations with »Hos> | lead to strong cvnamical interactions among the oligarchs: oligarchs interact mildly when n,ο< [."," From 3.2, configurations with $n_n \gtrsim$ 1 lead to strong dynamical interactions among the oligarchs; oligarchs interact mildly when $n_n \lesssim$ 1." " Table 1 lists the average of the maximum value of n, and its dispersion for our caleulations.", Table 1 lists the average of the maximum value of $n_n$ and its dispersion for our calculations. " Disks with rs2 0.5 have nj,E 1: disks with rm S05 have ρω2 Ll."," Disks with $r_{\Sigma} \gtrsim$ 0.5 have $n_{n,max} \lesssim$ 1; disks with $r_{\Sigma} \lesssim$ 0.5 have $n_{n,max} \gtrsim$ 1." This result confirms the visual impressions from Figures 710: dvnamical interactions among oligarchs are stronger in massive clisks and milder in low mass πο, This result confirms the visual impressions from Figures 7–10: dynamical interactions among oligarchs are stronger in massive disks and milder in low mass disks. To conclude this section. Figure 12 shows the evolution of the mass for each oligarch in one calculation.," To conclude this section, Figure 12 shows the evolution of the mass for each oligarch in one calculation." Here. points of one color correspond to the Gack of one oligarch.," Here, points of one color correspond to the track of one oligarch." From 104 vr to &10? vr. large objects form and grow rapidly.," From $\sim 10^4$ yr to $\sim 10^5$ yr, large objects form and grow rapidly." Once stirring reduces gravitational focusing factors. growth slows.," Once stirring reduces gravitational focusing factors, growth slows." During the late stages of runaway growth and the early stages of oligarchie growth. several neighboring oligarchs merge.," During the late stages of runaway growth and the early stages of oligarchic growth, several neighboring oligarchs merge." As their gravitational reach extends. these larger oligarchs erow faster ancl faster.," As their gravitational reach extends, these larger oligarchs grow faster and faster." Smaller oligarchs cannot compete for leftover planetesimals ancl grow slowly., Smaller oligarchs cannot compete for leftover planetesimals and grow slowly. During chaotic growth. the largest oligarchs merge with smaller oligarchs.," During chaotic growth, the largest oligarchs merge with smaller oligarchs." As the small oligarchs are depleted. the merger rate slows.," As the small oligarchs are depleted, the merger rate slows." With highlv eccentric orbits. a few small oligarchs last for LO30 Myr before colliding with a large oligarch.," With highly eccentric orbits, a few small oligarchs last for 10–30 Myr before colliding with a large oligarch." After 100. Myr. all but one small oligarch have collided and merged with the two laree planets that remain at the end of the evolution.," After 100 Myr, all but one small oligarch have collided and merged with the two large planets that remain at the end of the evolution." These caleulations begin with 5 km planetesimals in a torus extending [rom 0.4 AU (o 2 AU., These calculations begin with 5 km planetesimals in a torus extending from 0.4 AU to 2 AU. We divide this region into 40 annuli and seed each annulus with planetesimalsin nearly circular and coplanar orbits (ey=10? and iy=ey /2)., We divide this region into 40 annuli and seed each annulus with planetesimalsin nearly circular and coplanar orbits $e_0 = 10^{-5}$ and $i_0 = e_0/2$ ). To provide a contrast with previous sinmuations. the planetesimals have surface density X=Xo(a/1AU)!. with X = 216 ¢ ? at 1 AU.," To provide a contrast with previous simulations, the planetesimals have surface density $\Sigma = \Sigma_0 (a / {\rm 1 ~ AU})^{-1}$, with $\Sigma_0$ = 2–16 g $^{-2}$ at 1 AU." " Calculations with the more standard Xx7""72 vjeld similar results.", Calculations with the more standard $\Sigma \propto r^{-3/2}$ yield similar results. As in 833.3. we do not consider fragmentation.," As in 3.3, we do not consider fragmentation." This torus is larger than the 0.51.5 AU region examined by Weidenschillingetal.(1997.seealsoIXominaami&Ida 2002).. but similar to," This torus is larger than the 0.5–1.5 AU region examined by \citet[][see also Kominami \& Ida 2002]{wei97}, , but similar to" The DC flux level fpe: was assumed to be small compared to the fIux level over most οἱ (he map: pe] 0:25!,The DC flux level $f_{DC}$ was assumed to be small compared to the flux level over most of the map: | 0.25. (24) We verified that the actual pe: values obtained from the model fitting were well within {his range., We verified that the actual $f_{DC}$ values obtained from the model fitting were well within this range. Thus. we are confident (hat we have not been too restrictive in setting (his constraint.," Thus, we are confident that we have not been too restrictive in setting this constraint." Finally. we assumed for all models (hat the axis of the filament lies with 45 deerees of the plane of the skv: Nolte. however. that (his quantitv is unconstrained by observations. and it is conceivable that GI1.11-0.12 might be even more severely inclined.," Finally, we assumed for all models that the axis of the filament lies with 45 degrees of the plane of the sky: i Note, however, that this quantity is unconstrained by observations, and it is conceivable that G11.11-0.12 might be even more severely inclined." Biological evolution can be thought of as a powerful ancl robust search ancl optimization algorithm., Biological evolution can be thought of as a powerful and robust search and optimization algorithm. Evolution drives individuals within a population toward better adapted: forms characterized by greater fitness ancl improved survivabilitv., Evolution drives individuals within a population toward better adapted forms characterized by greater fitness and improved survivability. " Genetic algoritlims are a class of search and optimization algorithms that are based on biological evolution. in which the parameters of a model are encoded on the ""genome"" of an individual. aud the goodness of the resulting solution translates into the fitness of the individual. and hence determines the likelihood that it will survive."," Genetic algorithms are a class of search and optimization algorithms that are based on biological evolution, in which the parameters of a model are encoded on the “genome” of an individual, and the goodness of the resulting solution translates into the fitness of the individual, and hence determines the likelihood that it will survive." Genetic algorithms are often associated will computational intelligence research in computer science. since (μον learn by experimenüng with (heir computational environment. and are capable of finding innovative solutions (o. complex optimization and design problems with little human intervention.," Genetic algorithms are often associated with computational intelligence research in computer science, since they learn by experimenting with their computational environment, and are capable of finding innovative solutions to complex optimization and design problems with little human intervention." Traditional genetic algoritlims encode parameters on “genes” composed of low-cardinality (olten binary) integer strings and process information via crossover. mutation and selection," Traditional genetic algorithms encode parameters on “genes” composed of low-cardinality (often binary) integer strings and process information via crossover, mutation and selection" Cambridge. MA 02138. USA," Cambridge, MA 02138, USA" αἱ 307 latitude in the tachoclines of these stars. but other latitude locations of the ας and band-widths can be studied for antisolar differential rotations.,"at $30^{\circ}$ latitude in the tachoclines of these stars, but other latitude locations of the bands and band-widths can be studied for antisolar differential rotations." Full 3D models have been explored by Arlt.Sule&Rüdiger(2007) and Zhang.Liao&Selmbert(2003) lor the stability analvsis of the solar-like differential rotation. and antisolar case is vet to be explored.," Full 3D models have been explored by \citet{asr2007} and \citet{zls2003} for the stability analysis of the solar-like differential rotation, and antisolar case is yet to be explored." We (hank Peter Gilman for reviewing (he manuscript and for many helpful discussions., We thank Peter Gilman for reviewing the manuscript and for many helpful discussions. We also (hank INeith MacGregor for giving us the stellar structure data computed from his ZAMS stellar interior model and Travis Metcalfe for helpful discussions at the early stage of the model-caleulations., We also thank Keith MacGregor for giving us the stellar structure data computed from his ZAMS stellar interior model and Travis Metcalfe for helpful discussions at the early stage of the model-calculations. We extend our thanks (o an anonvmonus referee for a thorough review of the previous version of the manuscript and for his/her many helpful comments. which have helped improve this paper significantlv.," We extend our thanks to an anonymous referee for a thorough review of the previous version of the manuscript and for his/her many helpful comments, which have helped improve this paper significantly." This work is partially supported by NASA's Living With a Star program through the grant NNNOSAQ3IG. The National Center for the Aimospherie Research is sponsored by the National Science Foundation., This work is partially supported by NASA's Living With a Star program through the grant NNX08AQ34G. The National Center for the Atmospheric Research is sponsored by the National Science Foundation. "simulation has to run to wWyet=2000 or wpyjt=500 before a proper equilibrium is established, even though the proper conditions are established at w,.t=1000 (see jumpfigure 4)).","simulation has to run to $\wpet\,=2000$ or $\omega_{pi}\,t\,=500$ before a proper equilibrium is established, even though the proper jump conditions are already established at $\wpet\,=1000$ (see figure \ref{fig:dens}) )." Without the alreadymoving frame approach it would have required a box with a least 28000 cells in the streaming direction to properly establish and thermalize the shock., Without the moving frame approach it would have required a box with a least 28000 cells in the streaming direction to properly establish and thermalize the shock. In this Letter we have studied for the first time the long time behavior of a fully developed 3D collisionless ion-electron shock., In this Letter we have studied for the first time the long time behavior of a fully developed 3D collisionless ion-electron shock. " We find that the development of the shock structure is similar to that of an electron-ion shock in a 2D model, but there are both and differences of importance when making qualitativequantitative quantitativepredictions from shock models for observations."," We find that the development of the shock structure is similar to that of an electron-ion shock in a 2D model, but there are both qualitative and quantitative differences of importance when making quantitative predictions from shock models for observations." " Apart from the dimensionality, which gives rise to different shock jump conditions, the extra degree of freedom the shock in a number of ways: 1) The current channels changesupstream of the shock become more stable."," Apart from the dimensionality, which gives rise to different shock jump conditions, the extra degree of freedom changes the shock in a number of ways: 1) The current channels upstream of the shock become more stable." " 2) Very strong parallel electric fields along the field lines are created at the shock interface giving a new and effective avenue for particle acceleration, as compared to 2D models."," 2) Very strong parallel electric fields along the field lines are created at the shock interface giving a new and effective avenue for particle acceleration, as compared to 2D models." 3) The level of magnetic field energy is lower near the shock interface 4) A power-law tail in the PDF downstream of the shock emerges at late times., 3) The level of magnetic field energy is lower near the shock interface 4) A power-law tail in the PDF downstream of the shock emerges at late times. In with theory the power-law index is shallower in the 3D agreementshock (2.2) compared to the 2D model (~2.5)., In agreement with theory the power-law index is shallower in the 3D shock $\sim$ 2.2) compared to the 2D model $\sim$ 2.5). " In ? it was found that the radiation emitted from the Weibel in 2D and 3D is different, and analogously we instabilityexpect that the differences qualitativelypresented here in the physical development of a 3D shock compared to a 2D shock will give rise to significant differences in the emitted radiation."," In \citet{Trier:2010} it was found that the radiation emitted from the Weibel instability in 2D and 3D is qualitatively different, and analogously we expect that the differences presented here in the physical development of a 3D shock compared to a 2D shock will give rise to significant differences in the emitted radiation." This is a topic for future studies., This is a topic for future studies. TH acknowledges support from the Danish Natural Science Research Council., TH acknowledges support from the Danish Natural Science Research Council. Computer time was provided by the Danish Center for Scientific Computing (DCSC)., Computer time was provided by the Danish Center for Scientific Computing (DCSC). " It is a pleasure to thank J. T. Frederiksen, M. Medvedev, andÀ.."," It is a pleasure to thank J. T. Frederiksen, M. Medvedev, and." Nordlund for many valuable discussions and comments., Nordlund for many valuable discussions and comments. (Beichman et al.,(Beichman et al. 2006)., 2006). " The 7"" aud 21"" angular resolutions of at 21 and 70 pau. respectively. are a siguifcant nuprovenient from the 0.757. 1.67 aud 1.5'.L7 anenlar resolutions of at 25 and 60 jn. respectively. aud better exclude confusion from the backeround and/or other nearby sources."," The $\arcsec$ and $\arcsec$ angular resolutions of at 24 and 70 $\mu$ m, respectively, are a significant improvement from the $\arcmin$$\times$ $\arcmin$ and $\arcmin$$\times$ $\arcmin$ angular resolutions of at 25 and 60 $\mu$ m, respectively, and better exclude confusion from the background and/or other nearby sources." Chen ot al. (, Chen et al. ( 2006) measured the shape of the hot dust continua cluitted from these objects from low resolution IRS spectra and inferred the presence of wari dust with = 100 IX - 150 Is. hotter than estimated from xiotometrieτρ observations alone.,"2006) measured the shape of the hot dust continuum emitted from these objects from low resolution IRS spectra and inferred the presence of warm dust with $T_{gr}$ = 100 K - 150 K, hotter than estimated from photometric observations alone." We present. updated IBS spectra. extracted from $15.3 pipeline products using the IRS team’s SMART xograun (Higdon et al.," We present updated IRS spectra, extracted from S15.3 pipeline products using the IRS team's SMART program (Higdon et al." 2001). overlaid ou I&urucz stellar ohotosphere models that aro iininnun 4? fit to TDI. Johnson UBVRI. and 2MASS stellar photometry (where available) in Figure 1.," 2004), overlaid on Kurucz stellar photosphere models that are minimum $\chi^2$ fit to TD1, Johnson UBVRI, and 2MASS stellar photometry (where available) in Figure 1." Our new reduction improves he signalnoise ratio of the spectra modestly and extends reliable continuum imeasurciunents to 238 gan. ονομα which second-order Πο decreases the SNR.," Our new reduction improves the signal:noise ratio of the spectra modestly and extends reliable continuum measurements to 38 $\mu$ m, beyond which second-order light decreases the SNR." Iu Table 1. we list the fluxes of our objects iu two photometric bands that have been used to search for excess from silicates (8.5-13 gan) aud cold grains (30-31 pan).," In Table 1, we list the fluxes of our objects in two photometric bands that have been used to search for excess from silicates (8.5-13 $\mu$ m) and cold grains (30-34 $\mu$ m)." The calibration uncertainty in the fluxes is 754 and the measured statistical uncertaiutics are listed iu Table 1., The calibration uncertainty in the fluxes is $\sim$ and the measured statistical uncertainties are listed in Table 1. We fit the combined IRS. MIPS. aud TRAS SEDs using two temperature black body models with the parameters listed in Table 2.," We fit the combined IRS, MIPS, and IRAS SEDs using two temperature black body models with the parameters listed in Table 2." We estimate the temperature of the warn coumpoucut by minium 7 fitting the IRS excess at waveleneths shorter than 30 jan and the temperature of the cool component by estimating the color temperature from the remaining 35 gan and IRÁS-60 or MIPS-70 4n. excesses., We estimate the temperature of the warm component by minimum $\chi^{2}$ fitting the IRS excess at wavelengths shorter than 30 $\mu$ m and the temperature of the cool component by estimating the color temperature from the remaining 30-35 $\mu$ m and IRAS-60 or MIPS-70 $\mu$ m excesses. For IIR S799 with published subuullimeter photometry (Williams Andrews 2006). cold dust with au cuussivitv. |y κ pÜ where 3} = 1. is needed to fit the far-infrared aud submillimeter SED.," For HR 8799 with published submillimeter photometry (Williams Andrews 2006), cold dust with an emissivity, $\kappa_{\nu}$ $\propto$ $\nu^{\beta}$ where $\beta$ = 1, is needed to fit the far-infrared and submillimeter SED." Direct imaging of TD 139661 and WR στου has provided additional information about their cieunistellar environments., Direct imaging of HD 139664 and HR 8799 has provided additional information about their circumstellar environments. Wiel contrast neck and Coemini AO imagine has detected three plauctary mass objects orbiting IIR. 8799 with projected. separations of 2]. 3s. and 68 AU and inferred masses 7. 10. and 10 Materred frou. the ineasured. I-baud. counipauion Ajay.1uninosities aud the 160 Myr central star isochronal age (Mawrois et al.," High contrast Keck and Gemini AO imaging has detected three planetary mass objects orbiting HR 8799 with projected separations of 24, 38, and 68 AU and inferred masses 7, 10, and 10 $M_{Jup}$, inferred from the measured K-band companion luminosities and the 160 Myr central star isochronal age (Marois et al." 2008)., 2008). High coutrast ACS scattered ight μασιο has resolved dust iu au edec-on ring around ΠΟ 139661 with a possible inner edge at GO AU. a dus »eak at 83 AU. and a sharp outer boundary at 109. AU away from the ceutral star (I&alas et al.," High contrast ACS scattered light imaging has resolved dust in an edge-on ring around HD 139664 with a possible inner edge at 60 AU, a dust peak at 83 AU, and a sharp outer boundary at 109 AU away from the central star (Kalas et al." 2006)., 2006). I&alas ο al., Kalas et al. speculate on the preseuce of (1) planetary eiibryvos ormiues at 83 AU that dvuamically stir smaller parcu )odies. producing a collisional cascade at this radius. (2) a plauctary body either inside or outside of the disk tha raps nüeratiue dust eraius mto niean motion resonances. also producing a dusty ring. or (3) planetary bodies inside GO AU aud/or bevoud 109 AU that confine dus into the narrow rug.," speculate on the presence of (1) planetary embryos forming at 83 AU that dynamically stir smaller parent bodies, producing a collisional cascade at this radius, (2) a planetary body either inside or outside of the disk that traps migrating dust grains into mean motion resonances, also producing a dusty ring, or (3) planetary bodies inside 60 AU and/or beyond 109 AU that confine dust into the narrow ring." IIR 8799 was known to possess a debris disk well before the three companions orbiting the ceutral star were discovered., HR 8799 was known to possess a debris disk well before the three companions orbiting the central star were discovered. We examine the erain properties to elucidate the planetary svstem architecture., We examine the grain properties to elucidate the planetary system architecture. We assume that the dust detected iu this svsteii via nüd- to fu-iufared thermal cussion is eravitatioually bound to the system., We assume that the dust detected in this system via mid- to far-infared thermal emission is gravitationally bound to the system. In this case. we can estimate the nünunmuuu erai size bv balancing the force due to radiationpressure with the force due to gravity.," In this case, we can estimate the minimum grain size by balancing the force due to radiationpressure with the force due to gravity." For small erains with radius. «. the force due to radiation pressure overconies gravitv for solid particles s12aller than where £. is the stellar Iuuinosity.," For small grains with radius, $a$ , the force due to radiation pressure overcomes gravity for solid particles smaller than where $L_{*}$ is the stellar luminosity." For IIR. 5799 with L. — 6.1 L. aud M.= 1.6 AL. (Chen et al., For HR 8799 with $L_{*}$ = 6.1 $L_{\sun}$ and $M_{*}$= 1.6 $M_{\sun}$ (Chen et al. " 2006). we estimate 0,,;, = 1.7 aud L7 pmi assuuing that the erains are either an amorphous carbonsilicate mixture or water ice (densities p = 2.5 aud (0.91 ο 7). respectively."," 2006), we estimate $a_{min}$ = 1.7 and 4.7 $\mu$ m, assuming that the grains are either an amorphous carbon/silicate mixture or water ice (densities $\rho$ = 2.5 and 0.91 g $^{-3}$ ), respectively." The 150 Ix teiiperature of the wai dust imdicates that this population is unlikely to be composed of water icc., The 150 K temperature of the warm dust indicates that this population is unlikely to be composed of water ice. The sublimation lifetime of L7 uu water ice grains is expected to be (Jura ct al., The sublimation lifetime of 4.7 $\mu$ m water ice grains is expected to be (Jura et al. " 1998) where 6, is the mass rate per surface area (= 3.8 < 105 ο Fe Ee Toa = 5530 Ik: Ford Neufeld 2001)."," 1998) where $\dot{\sigma_{o}}$ is the mass rate per surface area (= 3.8 $\times$ $^{8}$ g $^{-2}$ $^{-1}$ $^{1/2}$, $T_{subl}$ = 5530 K; Ford Neufeld 2001)." For IIR. 8799. we estimate that [.7 jun solid-ice grains sublimate in LO mniuutes.," For HR 8799, we estimate that 4.7 $\mu$ m solid-ice grains sublimate in 40 minutes." Analysis of the 10 juu and 20 4n silicate features enütted bv T-Tauri disks indicates that the wari dust in these systems is predominately composed of silicates (Sargeut et al., Analysis of the 10 $\mu$ m and 20 $\mu$ m silicate features emitted by T-Tauri disks indicates that the warm dust in these systems is predominately composed of silicates (Sargent et al. 2006)., 2006). " Tlowever. silicate eraius with = 150 IK. are expected to produce a stroug 20 pau Tj,silicate cussion feature that should be detected using IRS because the dust is optically thin."," However, silicate grains with $T_{gr}$ = 150 K, are expected to produce a strong 20 $\mu$ m silicate emission feature that should be detected using IRS because the dust is optically thin." The lack of a 20 gan silicate cinission feature may indicate that the warn erains niav be significantly larger than the minimi erain size and can be modeled assuming that they are large. with enussivities that are constant asy. a function of wavelength.," The lack of a 20 $\mu$ m silicate emission feature may indicate that the warm grains may be significantly larger than the minimum grain size and can be modeled assuming that they are large, with emissivities that are constant as a function of wavelength." Another possible reason for the lack of silicate cuuission features is that the erains are colmposed of amorphous carbon., Another possible reason for the lack of silicate emission features is that the grains are composed of amorphous carbon. Amorphous carbon has a flat cuuissivity and therefore lacks spectral features., Amorphous carbon has a flat emissivity and therefore lacks spectral features. Discutaneling the contribution of carbon to this erain composition is challenging., Disentangling the contribution of carbon to this grain composition is challenging. However. since the wari. dust conrponeut of T-Tauni disks is principally composed of silicates and icy bodies such as comets possess silicate cluission features (Min et al.," However, since the warm dust component of T-Tauri disks is principally composed of silicates and icy bodies such as comets possess silicate emission features (Min et al." 2005). we believe that the composition iu the IIR 8799 disk is most likely silicate-rich rather than carbou-rich.," 2005), we believe that the composition in the HR 8799 disk is most likely silicate-rich rather than carbon-rich." " The TRAS 60 jan aud SCUBA 850 ju fluxes can only be modeled using erains with an cuussivity that is inversely proportional to wavelength. sugeestingCoco that the cold eraius are small (a << À/2x — 9.5 inu). possibly below the sub-blow out size of 1 jun. Black bodies (with 220 >> A) in radiative equilibriun around a star with ao luminosity. L.. and erain temperature. are expected to possessa distance. D. from the central T,,.star For IIR. 8799 with T,.(varin) = 150 Is. we estinate Πα. grain distances D;, = 8.7 AU. placing the wari dust well within the orbits of the three companions."," The IRAS 60 $\mu$ m and SCUBA 850 $\mu$ m fluxes can only be modeled using grains with an emissivity that is inversely proportional to wavelength, suggesting that the cold grains are small $a$ $<<$ $\lambda$ $2 \pi$ = 9.5 $\mu$ m), possibly below the sub-blow out size of 1 $\mu$ m. Black bodies (with $\pi a$ $>>$ $\lambda$ ) in radiative equilibrium around a star with a luminosity, $L_{*}$, and grain temperature, $T_{gr}$ , are expected to possessa distance, $D$ , from the central star For HR 8799 with $T_{gr}$ (warm) = 150 K, we estimate minimum grain distances $D_{in}$ = 8.7 AU, placing the warm dust well within the orbits of the three companions," Motivated by new ideas about MD and mass loss in LMXD evolution. we have made a svstematic investigation on the bifurcation periods in binary models. taking into account different MD laws and mass loss mechanisms.,"Motivated by new ideas about MB and mass loss in LMXB evolution, we have made a systematic investigation on the bifurcation periods in binary models, taking into account different MB laws and mass loss mechanisms." We find that the strength of MD is the dominant actor in determining the value of bifurcation periods compared with mass loss., We find that the strength of MB is the dominant factor in determining the value of bifurcation periods compared with mass loss. The stronger AID. the larger the bifurcation periods.," The stronger MB, the larger the bifurcation periods." This also results in an upper limit for (he secondary nasses bevond which no converging svstems exist., This also results in an upper limit for the secondary masses beyond which no converging systems exist. In our calculations we assume either fully conservative (models 1 and 2) or non-conservative amodels 32 and 4) mass transfer to constrain the bifurcation period distribution in dilferent nass transfer modes., In our calculations we assume either fully conservative (models 1 and 2) or non-conservative (models 3 and 4) mass transfer to constrain the bifurcation period distribution in different mass transfer modes. From (he expression of (M4.Ma.à) we always have which means that non-conservative mass transfer contributes more to the increase of the orbital period (han conservative mass (Gransfer.," From the expression of $A(M_1,M_2,\alpha)$ we always have which means that non-conservative mass transfer contributes more to the increase of the orbital period than conservative mass transfer." This explains why we generally. have a ower bifurcation period in non-conservative mass transler models (imoclels 3 and 4) than in conservative mass transfer model (model 2) under the same MD law., This explains why we generally have a lower bifurcation period in non-conservative mass transfer models (models 3 and 4) than in conservative mass transfer model (model 2) under the same MB law. The real situation may ie between these (wo extreme cases., The real situation may lie between these two extreme cases. For binary svstems with donors Ms;~0.5—0.8M... i would take more that 13.7 Gvr belore mass transfer begins via Roche lobe overflow.," For binary systems with donors $M_{\rm 2,i}\sim 0.5-0.8 M_\sun$, it would take more that 13.7 Gyr before mass transfer begins via Roche lobe overflow." So the bifurcation period for (hese svsteni seems meaningless. unless (here exist some unknown nechanisms of loss of orbital angular momentum.," So the bifurcation period for these system seems meaningless, unless there exist some unknown mechanisms of loss of orbital angular momentum." In our semi-analytical analvsis in 83.3 we use the condition P?~0 (io derive the values OL πω., In our semi-analytical analysis in 3.3 we use the condition $\dot{P}\sim 0$ to derive the values of $P_{\rm rlof}$. This expression seems different from J)27Pa. which is the original definition of bihucation period.," This expression seems different from $P_{\rm f}\simeq P_{\rm rlof}$, which is the original definition of bifurcation period." We argue here that these (wo expressions are roughly (he same except Lor binaries wilh As;>LAA. under conservative mass transfer (a= 1). the reason of which has been given in 83.3.," We argue here that these two expressions are roughly the same except for binaries with $M_{\rm 2,i}\ge1.4 M_\sun$ under conservative mass transfer $\alpha=1$ ), the reason of which has been given in 3.3." For Ma;0$ $<0$ ), $\dot{P}/P$ will become larger (smaller) during the evolution, leading to monotonic increase (decrease) of the period, as seen in Fig. \ref{tp}." So for these svstems £7Page is approximately equivalent with P~0., So for these systems $P_{\rm f} \sim P_{\rm rlof}$ is approximately equivalent with $\dot{P} \sim 0$. Several rough assumptions in (his semi-analvtical method contribute to the discrepancies between (he semi-analytical results and the numerical results in Fig., Several rough assumptions in this semi-analytical method contribute to the discrepancies between the semi-analytical results and the numerical results in Fig. 4. especially for Ms;<0.7M...," 4, especially for $M_{\rm 2,i}<0.7M_\sun$." First is the use of P~0 as the definition of Pau. which may not work well sometimes.," First is the use of $\dot{P}\sim0$ as the definition of $P_{\rm rlof}$, which may not work well sometimes." second is (he use of Eq. (, Second is the use of Eq. ( 13). which is most suitable for binaries with Mo;=LA. as pointed out in 83.3.,"13), which is most suitable for binaries with $M_{2,i}=1M_\sun$ as pointed out in 3.3." Third is the assumption we made that magnetic braking law is the dominated mechanism lor the angular momentum loss. while the true case is that the MD max not work sometimes (for example when the convective envelop is too small).," Third is the assumption we made that magnetic braking law is the dominated mechanism for the angular momentum loss, while the true case is that the MB may not work sometimes (for example when the convective envelop is too small)." Fourth is that we use a, Fourth is that we use a NGC 4151 was one of the original Sevfert galaxies classified in the 1940s (Sevfert 1943).,NGC 4151 was one of the original Seyfert galaxies classified in the 1940s (Seyfert 1943). lis optical spectra show both broad and narrow components in the Balmer emission lines. eading (o a classification as a (vpe 1.5 Sevlert galaxy (Osterbrock&Ixoski1976).," Its optical spectra show both broad and narrow components in the Balmer emission lines, leading to a classification as a type 1.5 Seyfert galaxy \citep{ost76}." . The distance of NGC 4151. derived assuming a IIubble constant of Jy=75 km ! |. is 20.3. Mpe (Tully1988).," The distance of NGC 4151, derived assuming a Hubble constant of $H_0 = 75$ km $^{-1}$ $^{-1}$ is 20.3 Mpc \citep{tul88}." .. This prosimity and the consequent scale of 0.160 pe nake NGC 4151 one of the brightest and most well-studied Sevlert galaxies., This proximity and the consequent scale of 0.10 pc $^{-1}$ make NGC 4151 one of the brightest and most well-studied Seyfert galaxies. Reverberation napping of the broad. emission lines shows that the radius of the broad-line region (BL) is e2x10.7 pe (Wandel. Peterson. Malkan 1999). corresponding to an angular radius of only 0.02 mas.," Reverberation mapping of the broad emission lines shows that the radius of the broad-line region (BLR) is $\sim 2\times 10^{-3}$ pc (Wandel, Peterson, Malkan 1999), corresponding to an angular radius of only 0.02 mas." Asstuning that the line widths are largely virialized around a central massive black hole. Wandeletal.(1999) determined a central black hole mass of 1.2x10M...," Assuming that the line widths are largely virialized around a central massive black hole, \citet{wan99} determined a central black hole mass of $\simeq 1.2 \times 10^{7}M_\odot$." NGC 4151 contains a linear radio structure. or “jet.” 3755 (350 pe) in length at an average posilion angle of 77°.," NGC 4151 contains a linear radio structure, or “jet,” 5 (350 pc) in length at an average position angle of $77^\circ$." This structure has been imaged with progressively higher fidelity at sub-aresecond resolution by the Verv Large Array (VLA) (Wilson&Ulvestad1982:Johnstonοἱal.1932:Pedlaret1993) and the Multi-Element Raclio-Linked Interferometer Network (MEBRLIN) (Pedlaretal.1993:Mundell1995)... as well as being imaged with the European VLBI Network by Harrisonetal.(1986).," This structure has been imaged with progressively higher fidelity at sub-arcsecond resolution by the Very Large Array (VLA) \citep{wil82,joh82,ped93} and the Multi-Element Radio-Linked Interferometer Network (MERLIN) \citep{ped93,mun95}, as well as being imaged with the European VLBI Network by \citet{har86}." . Five main radio components in the jet (CL through C5) were identified in the MERLIN images. while milliaresecond-resolution imaging using the VLBA resolved some of the MERLIN components and identified at least eieht separate regions of radio emission. AII (Ulvestadοἱal.1993).," Five main radio components in the jet (C1 through C5) were identified in the MERLIN images, while milliarcsecond-resolution imaging using the VLBA resolved some of the MERLIN components and identified at least eight separate regions of radio emission, A–H \citep{ulv98}." . The correspondence among the different radio components is shown in the top panel of Figure 1.. reproduced from Mundelletal.(2003).," The correspondence among the different radio components is shown in the top panel of Figure \ref{fig:cgm}, reproduced from \citet{mun03}." . The highest resolution 1.4 GIIz VLBI images indicate that the average jet direction incorporates a number of sharp changes in position angle. possibly related to jet interactions with the cireumnuclear environment (Mundelletal.2003).," The highest resolution 1.4 GHz VLBI images indicate that the average jet direction incorporates a number of sharp changes in position angle, possibly related to jet interactions with the circumnuclear environment \citep{mun03}." . In this paper. we discuss only the VLBA components D and E. corresponding to CLAW and CAE in the MERLIN scheme: no other components were detected at our high resolution.," In this paper, we discuss only the VLBA components D and E, corresponding to C4W and C4E in the MERLIN scheme; no other components were detected at our high resolution." Mundelletal.(1995) hvpothliesized that the nucleus of the active galaxy is located in VLBA component D. based largely on the lack of aabsorption toward (hat radio component and the expectation that the inner part of any nuclear torus or accretion disk would be ionized bv the active galactic nucleus (AGN).," \citet{mun95} hypothesized that the nucleus of the active galaxy is located in VLBA component D, based largely on the lack of absorption toward that radio component and the expectation that the inner part of any nuclear torus or accretion disk would be ionized by the active galactic nucleus (AGN)." In contrast. Ulvestadοἱal.(1998). suggested that VLBA component E. located 7 pe further east. is the actual AGN. due to the possible presence of a subcomponent with a flat racio spectrum.," In contrast, \citet{ulv98} suggested that VLBA component E, located 7 pc further east, is the actual AGN, due to the possible presence of a subcomponent with a flat radio spectrum." However.high-resolution VLBA imaging of NGC 4151 recently has shown that," However,high-resolution VLBA imaging of NGC 4151 recently has shown that" gap can reach heliocentric distances ranging betweenAU. depending on the choice of the initial mass and lifetime of the nebula.,"gap can reach heliocentric distances ranging between, depending on the choice of the initial mass and lifetime of the nebula." Each of these positions corresponds to an equilibrium reached at the position where the outward drift of aggregates just balances the accretion flow and in no more than a few hundred thousand vears., Each of these positions corresponds to an equilibrium reached at the position where the outward drift of aggregates just balances the accretion flow and in no more than a few hundred thousand years. With time. the location of these particles slightly rebounds toward the Sun until the dissipation of the disk.," With time, the location of these particles slightly rebounds toward the Sun until the dissipation of the disk." The figure also shows that 107 m particles follow the same trajectory as the larger ones but their equilibrium position 15 reached at lower heliocentric distance AU) and at later epochs in disks owning similar input parameters., The figure also shows that $^{-3}$ m particles follow the same trajectory as the larger ones but their equilibrium position is reached at lower heliocentric distance ) and at later epochs in disks owning similar input parameters. Interestingly enough. the position of smaller aggregates (107—107 m) continuously progresses outward during the evolution of the disks.," Interestingly enough, the position of smaller aggregates $^{-5}$ $^{-4}$ m) continuously progresses outward during the evolution of the disks." particles can even be pushed beyond the outer edge (~50 AU) of the nebula if one selects a low-mass disk (1 MMSN) with a long lifetime (6 Myr)., particles can even be pushed beyond the outer edge $\sim$ 50 AU) of the nebula if one selects a low-mass disk (1 MMSN) with a long lifetime (6 Myr). This is because of the strong decrease of the gas density and opacity in this model that enables the radiation pressure to push the particles at higher heliocentric distance., This is because of the strong decrease of the gas density and opacity in this model that enables the radiation pressure to push the particles at higher heliocentric distance. Figure 4 represents the trajectories of the same particles as in Fig., Figure 4 represents the trajectories of the same particles as in Fig. 3. but for disk models with inner gaps fixed to 2 AU.," 3, but for disk models with inner gaps fixed to 2 AU." Because the Rayleigh scattering through Ης is strongly diminished here. all particles reach higher heliocentric distances than in the cases considered in Fig.," Because the Rayleigh scattering through $_2$ is strongly diminished here, all particles reach higher heliocentric distances than in the cases considered in Fig." 3. but for similar migration timescales.," 3, but for similar migration timescales." Thus. 1077-107! m particles reach heliocentric distances as high asAU. depending on the adopted parameters of the disk.," Thus, $^{-2}$ $^{-1}$ m particles reach heliocentric distances as high as, depending on the adopted parameters of the disk." In similar conditions. 1073 m particles are also able to reach the distance range within the nebula.," In similar conditions, $^{-3}$ m particles are also able to reach the distance range within the nebula." Figures 5 and 6 show the trajectories of 107 to 10! m aggregates with densities of 1000 mm? within disk models with inner gaps of | and 2 AU. respectively.," Figures 5 and 6 show the trajectories of $^{-5}$ to $^{-1}$ m aggregates with densities of 1000 $^{-3}$ within disk models with inner gaps of 1 and 2 AU, respectively." Migration timescales remain similar to the previous cases: larger particles migrate very rapidly toward a maximum heliocentric distance while smaller ones continuously drift outward during the evolution of the disk., Migration timescales remain similar to the previous cases: larger particles migrate very rapidly toward a maximum heliocentric distance while smaller ones continuously drift outward during the evolution of the disk. Because (1) the inward drift linearly 0epends on the mass of the aggregate (see Eq., Because (i) the inward drift linearly depends on the mass of the aggregate (see Eq. " +) and (1) the =radial drift velocity vy, is inversely proportional to this quantity see Eq.", 4) and (ii) the radial drift velocity $v_{dr}$ is inversely proportional to this quantity (see Eq. 6). all particles here migrate at lower heliocentric eeistances than in cases of disks based on similar parameters.," 6), all particles here migrate at lower heliocentric distances than in cases of disks based on similar parameters." ndeed. 1077-107! m particles do not exceed in the case of disks with | AU (2 AU) inner=S gaps.," Indeed, $^{-2}$ $^{-1}$ m particles do not exceed in the case of disks with 1 AU (2 AU) inner gaps." The maximum migration distance reached by ntermediary size particles (107* m) becomes in the case of disks with 1 AU (2 AU) inner gaps., The maximum migration distance reached by intermediary size particles $^{-3}$ m) becomes in the case of disks with 1 AU (2 AU) inner gaps. Particle transport through the combination of photophoresis and radiation pressure has been invoked to explain the presence of ring-shaped dust distributions in young circumstellar disks such as the one around HR 4796A (Krauss Wurm 2005)., Particle transport through the combination of photophoresis and radiation pressure has been invoked to explain the presence of ring-shaped dust distributions in young circumstellar disks such as the one around HR 4796A (Krauss Wurm 2005). Here we show that in some cases. the determination of the dust size distribution within rings and their position relative to the parent star is likely to bring some constraints on the lifetime and eventually on the initial mass of the circumplanetary disk from which they originate.," Here we show that in some cases, the determination of the dust size distribution within rings and their position relative to the parent star is likely to bring some constraints on the lifetime and eventually on the initial mass of the circumplanetary disk from which they originate." Indeed. Figure 7 represents the settling distances reached by particles of different sizes and with densities of 500 mm? at the end of the solar nebula evolution.," Indeed, Figure 7 represents the settling distances reached by particles of different sizes and with densities of 500 $^{-3}$ at the end of the solar nebula evolution." The figure shows. for example. that ring-like structures essentially composed of 105 n particles and located in the distance range from the star could have formed in disks with | AU (2 AU) inner gap. which have short or intermediary lifetimes (here 1-3 Myr). irrespective of the initial disk’s mass.," The figure shows, for example, that ring-like structures essentially composed of $^{-5}$ m particles and located in the distance range from the star could have formed in disks with 1 AU (2 AU) inner gap, which have short or intermediary lifetimes (here 1–3 Myr), irrespective of the initial disk's mass." In addition. same size particles located at long distance to the star. 1... -50 AU (upper limit owing to the truncation of our model) or farther. could have formed in disks with long lifetimes (6 Myr)). irrespective of the size of the inner gap.," In addition, same size particles located at long distance to the star, i.e., $\sim$ 50 AU (upper limit owing to the truncation of our model) or farther, could have formed in disks with long lifetimes (6 Myr), irrespective of the size of the inner gap." To a lesser extent. one can also identify in Fig.," To a lesser extent, one can also identify in Fig." 7 à relationship between the position of ring-like structures dominated by the settling of 107 to 107! m particles and the disk’s lifetime and inner gap size., 7 a relationship between the position of ring-like structures dominated by the settling of $^{-3}$ to $^{-1}$ m particles and the disk's lifetime and inner gap size. the existence of an inner gap at early epochs within the nebula remains questionable., the existence of an inner gap at early epochs within the nebula remains questionable. Indeed. gaps are often found in disks (.e.. transition disks) that are millions of years old.," Indeed, gaps are often found in disks (i.e., transition disks) that are millions of years old." In this context. a significant offset might exist between the times of the different models used in this work and the chronology of the solar system formation and evolution that is testified by meteorite measurements or by the age of disks as inferred from luminosity studies of protostars.," In this context, a significant offset might exist between the times of the different models used in this work and the chronology of the solar system formation and evolution that is testified by meteorite measurements or by the age of disks as inferred from luminosity studies of protostars." For these reasons. the less massive disk models used in this work that are associated to inner gaps correspond to cases that are the most consistent with the structure of transition disks.," For these reasons, the less massive disk models used in this work that are associated to inner gaps correspond to cases that are the most consistent with the structure of transition disks." Moreover. our calculations are based on the assumption that the nebula is essentially devoid of dust. Le.. that the dust opacity ts negligible.," Moreover, our calculations are based on the assumption that the nebula is essentially devoid of dust, i.e., that the dust opacity is negligible." Indeed. if we assume that the smallest aggregates (107? m) have created a prominent opacity in the nebula. larger aggregates could only follow the small ones and reach the formation zone of comets toward the end of the disk evolution.," Indeed, if we assume that the smallest aggregates $^{-5}$ m) have created a prominent opacity in the nebula, larger aggregates could only follow the small ones and reach the formation zone of comets toward the end of the disk evolution." Despite these caveats. the use of a set of disk models covering the whole range of plausible thermodynamic conditions that took place in the primordial nebula allows us to show that hot-temperature minerals can drift up to heliocentric distances reaching ~34 AU for the largest particles and 50 AU or beyond for the smallest ones provided that 1) the existence of an inner gap is postulated within the nebula and 11) the opacity of the smallest dust particles remains negligible," Despite these caveats, the use of a set of disk models covering the whole range of plausible thermodynamic conditions that took place in the primordial nebula allows us to show that hot-temperature minerals can drift up to heliocentric distances reaching $\sim$ 34 AU for the largest particles and 50 AU or beyond for the smallest ones provided that i) the existence of an inner gap is postulated within the nebula and ii) the opacity of the smallest dust particles remains negligible" principle to discriminate the fraction of missed SNe due to the dust extinction and failed SNe.,principle to discriminate the fraction of missed SNe due to the dust extinction and failed SNe. Conversely. we assumed that the SFRs based on and ΕΙΝ luminosity are. reliable and obtained. an observational constraint on the mass range of CC SN progenitors by comparing the expected number of CC SNe from SFR measurements with the observed number in our galaxy samples.," Conversely, we assumed that the SFRs based on and FUV luminosity are reliable and obtained an observational constraint on the mass range of CC SN progenitors by comparing the expected number of CC SNe from SFR measurements with the observed number in our galaxy samples." Our analysis suggests that the minimum mass to produce a CC SN is 8+| .or6z] If we consider FUV and based SFR. respectively.," Our analysis suggests that the minimum mass to produce a CC SN is $8 \pm 1$ or $ 6\pm 1$ if we consider FUV and based SFR, respectively." The first result is in. excellent agreement with that obtained by analysing a sample of nearby SNe with detected progenitor stars (?).., The first result is in excellent agreement with that obtained by analysing a sample of nearby SNe with detected progenitor stars \citep{Smartt2009}. Obviously. assuming SFRs inferred through .a£5 larger mass range is required to fit the expected and observed numbers of CC SNe.," Obviously, assuming SFRs inferred through a larger mass range is required to fit the expected and observed numbers of CC SNe." Recent comparisons between the SFR and CC SN rate at redshifts between 2=0—| have suggested a discrepancy between the two. with the numbers of CC SNe detected being too low by a factor of two (??)..," Recent comparisons between the SFR and CC SN rate at redshifts between $z=0-1$ have suggested a discrepancy between the two, with the numbers of CC SNe detected being too low by a factor of two \citep{Botticella2008,Horiuchi2011}." The very local volume of I1Mpe which we study here does not show that discrepancy., The very local volume of 11Mpc which we study here does not show that discrepancy. This 15 likely due to the faint events (both intrinsically faint. and obscured) being missed outside the 11Mpe volume and would suggest that even m the nearby Universe. SN surveys are incomplete.," This is likely due to the faint events (both intrinsically faint, and obscured) being missed outside the 11Mpc volume and would suggest that even in the nearby Universe, SN surveys are incomplete." The uncertainties in our calculations (Poissonian and systematic) are not low enough to rule out that some massive stars collapse to black holes and produce optically dark SNe., The uncertainties in our calculations (Poissonian and systematic) are not low enough to rule out that some massive stars collapse to black holes and produce optically dark SNe. Keeping the photometry information for stars to V=17. for example. should increase the number of habitable-planet detections by almost a factor 3. while keeping stars with V«20 would increase this number by a [actor 9.,"Keeping the photometry information for stars to $V=17$, for example, should increase the number of habitable-planet detections by almost a factor 3, while keeping stars with $V<20$ would increase this number by a factor 9." See Figure 3.., See Figure \ref{fig:two}. Of course. there are many obstacles to keeping information on stars this faint.," Of course, there are many obstacles to keeping information on stars this faint." For example. there would be an enormous number of giant stars contaminating such a deep sample.," For example, there would be an enormous number of giant stars contaminating such a deep sample." Ii fact. however. distinguishing the later-tvpe dwarls fom the much more nunmerous giants of similar colors is straightforward.," In fact, however, distinguishing the later-type dwarfs from the much more numerous giants of similar colors is straightforward." As shown by Gould&Morgan(2003).. they can easily be identified on a reduced proper motion (RPM) diagram constructed using data from USNO-A (Monet1996.1998) and 2MASS (Skrütskieetal.1997).," As shown by \citet{gm}, they can easily be identified on a reduced proper motion (RPM) diagram constructed using data from USNO-A \citep{usnoa1,usnoa2} and 2MASS \citep{2mass}." . With USNO-B (Monetοἱal.2002) it should be possible to extend coverage to fainter magnitudes and {ο achieve higher precision as well., With USNO-B \citep{usnob} it should be possible to extend coverage to fainter magnitudes and to achieve higher precision as well. The total number of such stars My:<12 is only ~3x104. [ar fewer than the ~10? eiants in the field that could be eliminated using the same RPM diagram (Gould&Morgan2002).," The total number of such stars $M_V\leq 12$ is only $\sim 3\times 10^4$, far fewer than the $\sim 10^5$ giants in the field that could be eliminated using the same RPM diagram \citep{gm}." . A more difficult problem is crowding., A more difficult problem is crowding. TheAepler point spread function (PSF) is deliberately defocused to 10. meaning that the crowding limit is about IOarcmin 7.," The point spread function (PSF) is deliberately defocused to $10''$, meaning that the crowding limit is about $10\,\rm arcmin^{-2}$ ." At the adoptedKepler sight line. (/.b)=(69.6.5.7). this limit is reached al Z2isxo18.2 (as determined bv a query of the USNO-Acatalog).," At the adopted sight line, $(l,b)=(69.6,5.7)$, this limit is reached at $R_{\rm USNO}\sim 18.2$ (as determined by a query of the USNO-Acatalog)." IEKepler were redirected to (/.5b)=(70.15). the density of stars down to Resxo=18.2 would be 3.5arcmin.7. approximately 3 times lower.," If were redirected to $(l,b)=(70,15)$, the density of stars down to $R_{\rm USNO}=18.2$ would be $3.5\,\rm arcmin^{-2}$, approximately 3 times lower." Hence. recovery of faint stars would be much easier.," Hence, recovery of faint stars would be much easier." Presumably.Aepler has chosen to look right in the Galactic plane because of the higher overall star density.," Presumably, has chosen to look right in the Galactic plane because of the higher overall star density." Llowever. since (he stars useful for transits mostly lie within 500 pc. a field at 6=15° would lie only 130 pe above the plane. where the density of such (urget stars is only slightly lower than at the plane.," However, since the stars useful for transits mostly lie within 500 pc, a field at $b=15^\circ$ would lie only 130 pc above the plane, where the density of such target stars is only slightly lower than at the plane." Hence. the crowding problem could be substantially ameliorated al small cost.," Hence, the crowding problem could be substantially ameliorated at small cost." The last problem is skv., The last problem is sky. " At high ecliptic latitude. the skv in space is V.~23.3arcsec 7. or Ve1T in a 10"" PSF."," At high ecliptic latitude, the sky in space is $V\sim 23.3\,\rm arcsec^{-2}$ , or $V\sim 17$ in a $10''$ PSF." Hence.Kepler completeness appears to be fundamentally limited to stars My<9.," Hence, completeness appears to be fundamentally limited to stars $M_V<9$." As shown in Figure 3.. deteetions [rom stars at A4>LO would be highly suppressed.," As shown in Figure \ref{fig:two}, detections from stars at $M_V\geq 10$ would be highly suppressed." Only contracting the PSF (svhich. has been deliberately. defocused to improve the photometry) could overcome this difficulty. (, Only contracting the PSF (which has been deliberately defocused to improve the photometry) could overcome this difficulty. ( Note that at. V717. cerowding would not be a serious problem even for (he current Galactic-plane line of sight.),"Note that at $V\sim 17$, crowding would not be a serious problem even for the current Galactic-plane line of sight.)" While the above remarks applyspecifically to Aepler. any transit experiment attempting to detect habitable planets would[ace similar constraints and trade-olfs.," While the above remarks applyspecifically to , any transit experiment attempting to detect habitable planets wouldface similar constraints and trade-offs." on the 24 um image (data from Fadda et al.,on the 24 $\mu$ m image (data from Fadda et al. " in prep.),"," in prep.)," " which has an even higher spatial resolution, and is clearly extended."," which has an even higher spatial resolution, and is clearly extended." " Hence, the coincidence of the position of detections at various wavelengths makes us confident that the IR emission originates in781."," Hence, the coincidence of the position of detections at various wavelengths makes us confident that the IR emission originates in." ". The SDSS DR7 catalog provides us with 5 detections within the PSF region of951,, three of which are very likely to be artifacts in the source extraction, since we detected them in neither the SDSS nor the UKIDSS images during our visual inspection."," The SDSS DR7 catalog provides us with 5 detections within the PSF region of, three of which are very likely to be artifacts in the source extraction, since we detected them in neither the SDSS nor the UKIDSS images during our visual inspection." " The remaining two, morphologically classified as stellar-like objects, are located at distances of 8"" and 10"", and are also detected in the UKIDSS images."," The remaining two, morphologically classified as stellar-like objects, are located at distances of 8” and 10”, and are also detected in the UKIDSS images." The 24 pum image (see Fig. 1)), The 24 $\mu$ m image (see Fig. \ref{VCC781.pdf}) ) " shows some evidence of emission from both and one of the two aforementioned sources, which is spatially resolved at these wavelengths."," shows some evidence of emission from both and one of the two aforementioned sources, which is spatially resolved at these wavelengths." " Based on these data, we cannot definitely conclude that the IR emission detected by SPIRE comes from our dwarf galaxy, but deeper optical and NIR observations may help us to address the issue."," Based on these data, we cannot definitely conclude that the IR emission detected by SPIRE comes from our dwarf galaxy, but deeper optical and NIR observations may help us to address the issue." " We conclude that, while our analysis is unable to definitely exclude a possible contamination from background sources, the weight of evidence is in favour of a true detection of dust in emission from dEs, and in particular from781."," We conclude that, while our analysis is unable to definitely exclude a possible contamination from background sources, the weight of evidence is in favour of a true detection of dust in emission from dEs, and in particular from." . These detected dEs have remarkable morphologies., These detected dEs have remarkable morphologies. " Binggelietal.(1985) classifies as dS03(5),N and as dS0(2),N or dE2 pec,N. These galaxies are also found by Liskeretal.(2006a) to harbor central substructures other than a disk, while Liskeretal.(2006b) identified blue central colors in and951."," \citet{Binggeli1985} classifies as $_{3}$ (5),N and as dS0(2),N or dE2 pec,N. These galaxies are also found by \citet{Lisker2006_1} to harbor central substructures other than a disk, while \citet{Lisker2006_2} identified blue central colors in and." ". Figure 1 presents the g—i color images in which andVCC951,, respectively, exhibit an obvious gradient in their radial g—i color profiles, strengthening the assumption of recent star formation in the central regions (seealsoLiskeretal. 2006b).."," Figure \ref{VCC781.pdf} presents the $g-i$ color images in which and, respectively, exhibit an obvious gradient in their radial $g-i$ color profiles, strengthening the assumption of recent star formation in the central regions \citep[see also][]{Lisker2006_2}. ." " According to the classification criterion (3 « FUV-H « 6) adopted in Bosellietal.(2008a),, and can also be classified as possible transition objects."," According to the classification criterion (3 $<$ FUV-H $<$ 6) adopted in \citet{2008ApJ...674..742B}, and can also be classified as possible transition objects." " Although the FUV-H colours of 6.6 and 6.9 mag for and951,, respectively, do not satisfy this relation,both galaxies are clearly located at the blue end of the dE galaxies in Boselliet(2008a).."," Although the FUV-H colours of 6.6 and 6.9 mag for and, respectively, do not satisfy this relation,both galaxies are clearly located at the blue end of the dE galaxies in \citet{2008ApJ...674..742B}." That SDSS nuclear spectra of both galaxies exhibit deep Hydrogen absorption lines (EW[Hó] » 4 À)) indicates that they are in a post-starburst phase., That SDSS nuclear spectra of both galaxies exhibit deep Hydrogen absorption lines $\delta$ ] $>$ 4 ) indicates that they are in a post-starburst phase. " This, and their 24 wm emission, which is indeed centered on the optical nuclei and concentrated (~6"" for and point-like for VCC951)), argues in favour of a connection between dust emission and a recent episode of star-formation."," This, and their 24 $\mu$ m emission, which is indeed centered on the optical nuclei and concentrated $\sim 6''$ for and point-like for ), argues in favour of a connection between dust emission and a recent episode of star-formation." " To estimate the dust masses, we determined fluxes in bands where we had detections > 2c."," To estimate the dust masses, we determined fluxes in bands where we had detections $>$ $\sigma$." Initial apertures were fixed in the SPIRE 250 µπι images based on the flattening of the growth curve., Initial apertures were fixed in the SPIRE 250 $\mu$ m images based on the flattening of the growth curve. These apertures were subsequently adjusted to the pixel scale in other bands such that all apertures cover the same physical area., These apertures were subsequently adjusted to the pixel scale in other bands such that all apertures cover the same physical area. We first determined a representative dust temperature using the assumption that the dust is in thermal equilibrium with the interstellar radiation field., We first determined a representative dust temperature using the assumption that the dust is in thermal equilibrium with the interstellar radiation field. " We used the Monte Carlo code SKIRT, which was initially developed to investigate the effects of dust extinction on the photometry and kinematics of galaxies (Baesetal.2003),, but evolved into a flexible tool that can model the absorption, scattering, and thermal emission of circumstellar discs and dusty galaxies (e.gVidal&Baes2007;etal.2010).."," We used the Monte Carlo code SKIRT, which was initially developed to investigate the effects of dust extinction on the photometry and kinematics of galaxies \citep{2003MNRAS.343.1081B}, but evolved into a flexible tool that can model the absorption, scattering, and thermal emission of circumstellar discs and dusty galaxies \citep[e.g][]{2007BaltA..16..101V, Baes}." " The stellar body of each galaxy was represented as an exponential profile, with parameters taken from the Goldmine database."," The stellar body of each galaxy was represented as an exponential profile, with parameters taken from the Goldmine database." The dust was assumed to have the same distribution as the stars., The dust was assumed to have the same distribution as the stars. " For the intrinsic SED of the model, we used the elliptical galaxy template SED from the PEGASE library (Fioc& 1997).."," For the intrinsic SED of the model, we used the elliptical galaxy template SED from the PEGASE library \citep{1997A&A...326..950F}." "Adding these ingredients, we find a representative dust equilibrium temperature of 20.7 K and 19.4 Kfor and VCC951,, respectively."," .Adding these ingredients, we find a representative dust equilibrium temperature of 20.7 K and 19.4 Kfor and respectively." Relying on, Relying on We- can now eliminate- &de— between eqs.,We can now eliminate $\vec k\cdot \delta\!\vec v$ between eqs. " LL and 12..i and (hen use dP?-=ezópDc (vith. c, (he sound speed because we are considering isentropic perturbations) ancl the equation above to obtain where we have called the comoving eigenlrequency. in suitably scaled. units."," \ref{mass1} and \ref{momentum1}, and then use $\delta\!P = c_s^2 \delta\!\rho$ (with $c_s$ the sound speed because we are considering isentropic perturbations) and the equation above to obtain where we have called the comoving eigenfrequency, in suitably scaled units." Eq. 24.. ," Eq. \ref{reldisp}, ," together with the definition of D (eq. 20)).," together with the definition of $\bar D$ (eq. \ref{Dbar}) )," is the sought-after dispersion relation for the coupled small perturbations in a homogeneous medium., is the sought-after dispersion relation for the coupled small perturbations in a homogeneous medium. The case where D is independent of p has been derived before (Ptuskin1981) and coincides with the above equation., The case where $D$ is independent of $p$ has been derived before \citep{ptuskin1981} and coincides with the above equation. Surprisingly. the existence of this mode was not noticed bv Toptvein(1999).. even though a careful treatinent. of his equations vields precisely the same dispersion relation as above: this neglect of this mode has important consequences to be discussed later It is best to begin our discussion with the case when D. and (hus D. is a constant. independent of p.," Surprisingly, the existence of this mode was not noticed by \citet{toptygin1999}, even though a careful treatment of his equations yields precisely the same dispersion relation as above; this neglect of this mode has important consequences to be discussed later It is best to begin our discussion with the case when $D$, and thus $\bar D$, is a constant, independent of $p$." The eq., The eq. 24. then reduces to which is a simple polvnomial equation of the third order.," \ref{reldisp} then reduces to which is a simple polynomial equation of the third order." In (his case two mocles reduce lo pressure waves. as is most easily seen in the test-particle regime 77.=0.," In this case two modes reduce to pressure waves, as is most easily seen in the test-particle regime $P_c = 0$." There is however a (hire solution which is only shehtly more mysterious: in the test particle regime (hese mocles represent a local over-density of particles clissipated by diffusion., There is however a third solution which is only slightly more mysterious: in the test particle regime these modes represent a local over-density of particles dissipated by diffusion. When the test. particle reeime does not apply. a parücle contribution to the sound speed is introduced by the term x£2.," When the test particle regime does not apply, a particle contribution to the sound speed is introduced by the term $\propto P_c$." This new mode (which we call the(hard mode) is the equivalent of the d-mode when however the conditions 17 are satisfied: the basic idea is süll the same. the particle overclensily is dissipated. but since the particle pressure does not vanish. thefluid is consequentlyrullled.," This new mode (which we call the mode) is the equivalent of the d-mode when however the conditions \ref{justahelp} are satisfied: the basic idea is still the same, the particle overdensity is dissipated, but since the particle pressure does not vanish, thefluid is consequentlyruffled." Notice also that there are third modes. traveling in opposite directions.," Notice also that there are third modes, traveling in opposite directions." "(οιο,, van den Berel 1960). referring to the carly-type Sa-Se spiral galaxies. Ferguson Saudage (1991) wrote that ""dwourf spiral galaxies do not appear to exist” (see also Sandage Dingeeli 1981 and Saudage. Diugeeli Tauuuauu 1985).","(e.g., van den Bergh 1960), referring to the early-type Sa-Sc spiral galaxies, Ferguson Sandage (1991) wrote that “dwarf spiral galaxies do not appear to exist” (see also Sandage Binggeli 1984 and Sandage, Binggeli Tammann 1985)." They are a rare species: indeed. their very existence was oulv recognized a few vears ago (Schonibert ot 11995).," They are a rare species; indeed, their very existence was only recognized a few years ago (Schombert et 1995)." Even then. Schombert et cconcluded that dwarf spiral galaxies oulv exist iu the field.," Even then, Schombert et concluded that dwarf spiral galaxies only exist in the field." The harsh cuviroument within a ealaxy cluster due to galaxy merecrs. with each other or the intracluster medium. and/or strong gravitational tidal interactious is commonly thought to have led to the destruction of the delicate spiral patterns in dwarf galaxies.," The harsh environment within a galaxy cluster — due to galaxy mergers, with each other or the intracluster medium, and/or strong gravitational tidal interactions — is commonly thought to have led to the destruction of the delicate spiral patterns in dwarf galaxies." " A comparison of the uunber of such objects in low- and high-deusitv euvironnieuts may shed lieht ou the nature of their existence,", A comparison of the number of such objects in low- and high-density environments may shed light on the nature of their existence. By searching for sigus of appareut spiral structure and/or bars in the optical images from the sample of 15 dE galaxy candidates prescuted in Graham Cowman (2003). we explore here which ealaxics may have enmibedded stellar disks.," By searching for signs of apparent spiral structure and/or bars in the optical images from the sample of 18 dE galaxy candidates presented in Graham Guzmánn (2003), we explore here which galaxies may have embedded stellar disks." The ealaxy selection criteria is described in the following section. asx is the nuage reduction process and analysis.," The galaxy selection criteria is described in the following section, as is the image reduction process and analysis." Section 3 provides a brief quantitative analysis of the disks. aud Section 1 discusses possible evolutionary scenarios for dwart disk galaxies iu clusters.," Section 3 provides a brief quantitative analysis of the disks, and Section 4 discusses possible evolutionary scenarios for dwarf disk galaxies in clusters." We take Coma to be at a distance of LOO Mpc aud use Πτα s+ d 0 therefore corresponds to [7 pe.," We take Coma to be at a distance of 100 Mpc and use $H_0$ =70 km $^{-1}$ $^{-1}$, $\arcsec$ therefore corresponds to 47 pc." Galaxies mecting the following coucditious discussed at leneth im Alatcovie Cuzumáun (2003. in prep) were selected. from the Coma cluster field catalog (Godwin. Metcalfe Peach L983: hereafter CAIP).," Galaxies meeting the following conditions --- discussed at length in Matcović Guzmánn (2003, in prep) — were selected from the Coma cluster field catalog (Godwin, Metcalfe Peach 1983; hereafter GMP)." All galaxies have positions within the ceutral 20< of the Coma cluster: 15.5«Mp 1L5: 0.2.«(UC.B)06 and 1.5(B.R)«1.5: availableZZST NFEPC? nuages and recessioual velocities between 000 and 10.000 luu !.," All galaxies have positions within the central $20\arcmin \times 20\arcmin$ of the Coma cluster; $-17.5 < M_B < -14.5$; $0.2 < (U-B) < 0.6$ and $1.3 < (B-R) < 1.5$; available WFPC2 images and recessional velocities between 4,000 and 10,000 km $^{-1}$." The spectral aualvsis and recessioual velocity derivation is also provided in Matceovió Caiman (2003. in prep).," The spectral analysis and recessional velocity derivation is also provided in Matcović Guzmánn (2003, in prep)." The above requirciuents were expected to result iu the selection of Coma cluster dwarf elliptical ealaxies. and we obtained 18 such candidates.," The above requirements were expected to result in the selection of Coma cluster dwarf elliptical galaxies, and we obtained 18 such candidates." With the exception of GAIP 2960. there were no pre-existing morphological type classifications for these galaxies.," With the exception of GMP 2960, there were no pre-existing morphological type classifications for these galaxies." CAIP 2960 (PCC 11707: Paturel et 11989) is classified iun NED as au SO galaxy. aud according to the type-specific Iuninositv functions derived. frou: three clusters (Jerjen Tauuuaun 1997) we conclude that GAIP 2960 is either a Iuimunositv S0 ora bright dSO ealaxy.," GMP 2960 (PGC 44707; Paturel et 1989) is classified in NED as an S0 galaxy, and according to the type-specific luminosity functions derived from three clusters (Jerjen Tammann 1997) we conclude that GMP 2960 is either a low-luminosity S0 or a bright dS0 galaxy." The reduction process of the IST images is described in Graham Cowimann (2003)., The reduction process of the HST images is described in Graham Guzmánn (2003). Briefly. we used the task to combine the T-pipeliuned exposures. which we then further cleaned of cosmic ravs using (L.A.COSMIC. van Dokkun 2001).," Briefly, we used the task to combine the -pipelined exposures, which we then further cleaned of cosmic rays using (L.A.COSMIC, van Dokkum 2001)." Due to the stellar halos of nearby galaxies. we used the wavelet decomposition method of Vikbhliuiu et (1998) to simultaneously subtract this non-uniforui heht and the sky backeround.," Due to the stellar halos of nearby galaxies, we used the wavelet decomposition method of Vikhlinin et (1998) to simultaneously subtract this non-uniform light and the sky background." Foreground stars and over-lappine backeround galaxies were searched for. aud masked out. before we performed au nuage analysis or surface briehltuess fitting.," Foreground stars and over-lapping background galaxies were searched for, and masked out, before we performed any image analysis or surface brightness fitting." " Iu order to search for nou-sviunietrie structures in the dwarf galaxw nuages. we subtracted the axisviunietrie compoucut of the ealaxy light (sec Jerjeu et 220005). leaving a ""residual image”."," In order to search for non-symmetric structures in the dwarf galaxy images, we subtracted the axisymmetric component of the galaxy light (see Jerjen et 2000b), leaving a “residual image”." Following Barazza e ((2002) and De Rijeke et ((2003). we have aclditionally used an tusharp masking techuique to verity he presence of features such as bars or spiral arms. which would indicate the presence of a flattened stellar isk.," Following Barazza et (2002) and De Rijcke et (2003), we have additionally used an unsharp masking technique to verify the presence of features such as bars or spiral arms, which would indicate the presence of a flattened stellar disk." Although the majority of galaxies showed uo VAien of non-axisviunuetrie structure. two galaxies (ΕΛΠ 3292 and CAMP 3629) were found to possess Hocculeut spiral avius (Figures 1-2).," Although the majority of galaxies showed no sign of non-axisymmetric structure, two galaxies (GMP 3292 and GMP 3629) were found to possess flocculent spiral arms (Figures 1-2)." Their basic oxoperties are given in Table ], Their basic properties are given in Table 1. From our previous analvsis of the racial light-xofles (Craham Cuzináun 2003). we had already ideutified CNIP 3292 as a likely bulge/disk system due to a clear break in its surface brielituess oxofile wmarking the bulee/disk trausition.," From our previous analysis of the radial light-profiles (Graham Guzmánn 2003), we had already identified GMP 3292 as a likely bulge/disk system due to a clear break in its surface brightness profile marking the bulge/disk transition." " With regard to CALP 3629. we had remarked upon the οκματ of an outer disk rot dominating until radi greater than ~10"" (L7 pe} but we could not aud cdi not confirin this due to the ow surface brightness levels at these outer radii."," With regard to GMP 3629, we had remarked upon the possibility of an outer disk — not dominating until radii greater than $\sim 10\arcsec$ (4.7 kpc) — but we could not and did not confirm this due to the low surface brightness levels at these outer radii." We can however now coufina that both of these ealaxies possess stellar disks as iucdicated by the oesence of a spiral pattern., We can however now confirm that both of these galaxies possess stellar disks as indicated by the presence of a spiral pattern. Using the velocity catalog of Edwards et ((2002). Guticizrez ct ((2003) derive a mean recessional velocity of 6862," Using the velocity catalog of Edwards et (2002), Gutiérrrez et (2003) derive a mean recessional velocity of 6862" "There is, in this sense, a recognition that follow-up of time-variable sources is crucial for the scientific impact in many domains of interest to the PTF community.","There is, in this sense, a recognition that follow-up of time-variable sources is crucial for the scientific impact in many domains of interest to the PTF community." Autonomous discovery and classification allows for the initial imaging follow-up to be conducted without astronomers in the real-time loop., Autonomous discovery and classification allows for the initial imaging follow-up to be conducted without astronomers in the real-time loop. Our collaboration also routinely conducts (human-intensive) spectroscopic followup on newly discovered Oarical sources with minimal turnaround times from PTF image to spectroscopy to inference., Our collaboration also routinely conducts (human-intensive) spectroscopic followup on newly discovered Oarical sources with minimal turnaround times from PTF image to spectroscopy to inference. " For instance, we obtained with Keck a spectrum on a newly discovered 29 minutes after Oarical discovery."," For instance, we obtained with Keck a spectrum on a newly discovered 29 minutes after Oarical discovery." " The source was a peculiar Type Ia supernova at a redshift z=0.18, and analysis of the spectrum was published less than 18 hours after it was first observed with PTF (Nugentetal.2010)."," The source was a peculiar Type Ia supernova at a redshift $z=0.18,$ and analysis of the spectrum was published less than 18 hours after it was first observed with PTF \citep{atel2600}." ". Gal-Yametal.(2011) gives a full description of rapid discovery, follow-up, and the scientific results with PTF."," \citet{ptf10vdl} gives a full description of rapid discovery, follow-up, and the scientific results with PTF." The 529 spectroscopically-confirmed SNe discovered autonomously by Oarical since April 2010 represent more than half of the SNe discovered by the PTF collaboration over the lifetime of the project., The 529 spectroscopically-confirmed SNe discovered autonomously by Oarical since April 2010 represent more than half of the SNe discovered by the PTF collaboration over the lifetime of the project. " Several key papers have been the result of Oarical discoveries, including discoveries and real-time classification of a) PTF 10iya, a possible tidal disruption event (Cenkoetal.2011),, b) PTF 10vdl, a subluminous type ΠΡ supernova (Gal-Yametal.2011),, c) PTF 10qpf, a TTauri star that appeared to be an FUOri system in outburst (Milleretal.2011),, d) PTF 10nvg, an outbursting Class I protostar (Coveyetal.2011),, and e) PTF 10hmv, a type Ia supernova found more than 10 days before maximum and observed with the Hubble Space telescope around maximum light (Cookeetal.2011).."," Several key papers have been the result of Oarical discoveries, including discoveries and real-time classification of a) PTF 10iya, a possible tidal disruption event \citep{2011arXiv1103.0779C}, b) PTF 10vdl, a subluminous type IIP supernova \citep{ptf10vdl}, c) PTF 10qpf, a TTauri star that appeared to be an FUOri system in outburst \citep{2011ApJ...730...80M}, d) PTF 10nvg, an outbursting Class I protostar \citep{2011AJ....141...40C}, and e) PTF 10hmv, a type Ia supernova found more than 10 days before maximum and observed with the Hubble Space telescope around maximum light \citep{2011ApJ...727L..35C}." The core discovery and classification codebase has been largely frozen since April 2010 allowing us to study the results under the assumption of relative uniformity., The core discovery and classification codebase has been largely frozen since April 2010 allowing us to study the results under the assumption of relative uniformity. However there are several aspects of the framework that we have identified where improvements could be made in future versions (with PTF or otherwise)., However there are several aspects of the framework that we have identified where improvements could be made in future versions (with PTF or otherwise). " First, we now have a good deal more ground-truth events in the PTF database that we know are real astrophysical candidates."," First, we now have a good deal more ground-truth events in the PTF database that we know are real astrophysical candidates." " This larger training set, coupled with new shaped based metrics on the image differences, should much improve the Type I and Type II errors on the discovery front (Negahbanetal.2011).."," This larger training set, coupled with new shaped based metrics on the image differences, should much improve the Type I and Type II errors on the discovery front \citep{sahand}." " Second, there has been much improvement in the astrometric tie of PTF to SDSS (as well as an expanding footprint of public SDSS imaging), which should continue to improve the reliability of distance-to-host features."," Second, there has been much improvement in the astrometric tie of PTF to SDSS (as well as an expanding footprint of public SDSS imaging), which should continue to improve the reliability of distance-to-host features." " Third, the database-based photometry used to calculate the time-series features is known to be suboptimal."," Third, the database-based photometry used to calculate the time-series features is known to be suboptimal." New routines developed within the collaboration can now allow automated forced-aperture and PSF photometry, New routines developed within the collaboration can now allow automated forced-aperture and PSF photometry (7) (~1/3 15)150 7)) 0.3.10 ?)) ?3) ~LO% ?)) Telescope (LAT. ?)).,"\citep{gehrels04} $\sim 1/3$ $15-150$ \citealt{barthelmy05}) $0.3-10$ \citealt{burrows05}) \citealt{roming05}) $\sim 40\%$ \citealt{meegan09}) Telescope (LAT, \citealt{atwood09}) )." This wide space-based spectral window is broadened further bv erouud based optical. NIR. and radio follow-up observations.," This wide space-based spectral window is broadened further by ground based optical, NIR, and radio follow-up observations." Iu the last 2 wears. the addition of the 30 MeV. to 100 GeV window from Ferm-LAT has led to another theoretical crisis. as we attempt to understand the origi and relationship between these newo observational conrponeuts and the ones traditionally observed frou GRBs in the keV-MeV band.," In the last 2 years, the addition of the 30 MeV to 100 GeV window from -LAT has led to another theoretical crisis, as we attempt to understand the origin and relationship between these new observational components and the ones traditionally observed from GRBs in the keV-MeV band." Just asSwift challenged our theoretical mocels by demonstrating that GRBs have coniplex behavior in the first few hours after the trigger C. LAT is regularly observing a uew set of high euerev conrponeuts in a small very cnerectic subset of bursts (?77777)..," Just as challenged our theoretical models by demonstrating that GRBs have complex behavior in the first few hours after the trigger \citep{nousek06}, -LAT is regularly observing a new set of high energy components in a small very energetic subset of bursts \citep{abdo090902b,abdo080825c,abdo080916c,abdo081024b,abdo090510}." The relationship between the =100 MeV emission aud the well studied keV-MeV. comupoucuts remains unclear (7777?7?2?2)..," The relationship between the $>100$ MeV emission and the well studied keV-MeV components remains unclear \citep{corsi09,corsi10,kumar09,razzaque09,zhang09,ghisellini10,peer10,piran10,toma10,wang10}." The complicated LAT prompt emission spectra do not show suuplv the extension of the lower-energv Band function (7). but rather the joint GDM-LAT spectral fits can also show the presence of an additional hard power-law that can be detected both above aud below the Band function (27). in some cases.," The complicated -LAT prompt emission spectra do not show simply the extension of the lower-energy Band function \citep{band93}, but rather the joint GBM-LAT spectral fits can also show the presence of an additional hard power-law that can be detected both above and below the Band function \citep{abdo090902b,abdo090510} in some cases." There were earlier mdicatious of this additional spectral componoeut in the EGRET detected απο 911017 η., There were earlier indications of this additional spectral component in the EGRET detected GRB 941017 \citep{gonzalez03}. However. the raritv of EGRET CRB detections left it unclear whether this was a conuuon high euergv feature. or if special circtuustances in that GRB were responsible.," However, the rarity of EGRET GRB detections left it unclear whether this was a common high energy feature, or if special circumstances in that GRB were responsible." " This component is too shallow to be due to Svuchrotron selt-Conmpton (SSC) as had been predicted extensively (T?T73,.."," This component is too shallow to be due to Synchrotron self-Compton (SSC) as had been predicted extensively \citep{zhang01,guetta03,galli08,racusin08,band09}." The spectral behavior of the LAT bursts appears to rule out the theory that the soft >- are caused by a SSC or another Iuverse Compton (IC) component (?7?).. Fer," The spectral behavior of the LAT bursts appears to rule out the theory that the soft $\gamma$ -rays are caused by a SSC or another Inverse Compton (IC) component \citep{ando08,piran09}." i-LATSs >LOO MeV temporal behavior is differeut from the. lower-energev counterparts observed from thousands of CRBs., -LAT's $>100$ MeV temporal behavior is different from the lower-energy counterparts observed from thousands of GRBs. The LAT eiissiou often begins a few seconds later than the lower-enerev prompt emission. and," The LAT emission often begins a few seconds later than the lower-energy prompt emission, and" , " H50 (?),, Co (??),, CaH, CN, TiO, VO, and, ZrO (electronic and unpublished Ple#)).","$_2$ O \citep{Barber2006}, $_2$ \citep{Querci1971,Querci1974}, CaH, CN, TiO, VO, and, ZrO (electronic and unpublished )." The list of lines with equivalent widths greater than zero within +0.05 nm (Av~30 km/s) from the used sulphur lines is presented in Table B]., The list of lines with equivalent widths greater than zero within $\pm 0.05$ nm $\Delta v \sim 30$ km/s) from the used sulphur lines is presented in Table \ref{tab:blends}. " The equivalent widths of the 1082 nm [Si], the 1045.5 nm and 1045.7 nm triplet lines, and blends with strengths in parity with the relevant sulphur line are shown in Figs."," The equivalent widths of the 1082 nm ], the 1045.5 nm and 1045.7 nm triplet lines, and blends with strengths in parity with the relevant sulphur line are shown in Figs." [I] - [B]., \ref{fig:SI_eqw} - \ref{fig:Sb_eqw}. The 1045.9 nm triplet line does not have any known signicant blends., The 1045.9 nm triplet line does not have any known signiÞcant blends. " The only blend for the 1] line present in halo giants is that due toCri, but this line is separated enough from the sulphur line to be resolvable in our high resolution spectra, see for example the line in Fig. [5]."," The only blend for the ] line present in halo giants is that due to, but this line is separated enough from the sulphur line to be resolvable in our high resolution spectra, see for example the line in Fig. \ref{fig:allspectra}." For the 1045.5 nm and 1045.7 nm triplet lines the 1045.54 nm and 1045.69 nm lines shown in Fig., For the 1045.5 nm and 1045.7 nm triplet lines the 1045.54 nm and 1045.69 nm lines shown in Fig. and Fig., \ref{fig:Sa_eqw} and Fig. B| are close enough to the relevant sulphur line that D]they would be indistinguishable., \ref{fig:Sb_eqw} are close enough to the relevant sulphur line that they would be indistinguishable. " Our sample stars all have stellar parameters available in the literature (Tem, logg, [Fe/H], and &nicro)."," Our sample stars all have stellar parameters available in the literature $T_{\mathrm{eff}}$, $\log g$, $\left[\mathrm{Fe}/\mathrm{H}\right]$, and $\xi_{\mathrm{micro}}$ )." They are chosen to be cool giants in order to maximize the strength of the [S1] line., They are chosen to be cool giants in order to maximize the strength of the ] line. Since we are interested in halo stars with [Fe/H]x-1 the unresolvable blends expected to most seriously affect the 1045 nm sulphur lines are small compared to the relevant sulphur lines and can safely be ignored., Since we are interested in halo stars with $[\mathrm{Fe} / \mathrm{H}] \le -1$ the unresolvable blends expected to most seriously affect the 1045 nm sulphur lines are small compared to the relevant sulphur lines and can safely be ignored. Our lines can thus be considered blend free and the measured equivalent widths are that of the sulphur lines only., Our lines can thus be considered blend free and the measured equivalent widths are that of the sulphur lines only. " Note that, as can be seen in Figs."," Note that, as can be seen in Figs." [I] - B] one should use these sulphur lines with caution for certain stellar parameters; e.g. for a solar-metallicity dwarf with a temperature of 4500 K the strength of the blending line would be roughly equal to that of the 1045.5 nm triplet line., \ref{fig:SI_eqw} - \ref{fig:Sb_eqw} one should use these sulphur lines with caution for certain stellar parameters; e.g. for a solar-metallicity dwarf with a temperature of 4500 K the strength of the blending line would be roughly equal to that of the 1045.5 nm triplet line. " Also, the neighboringΟτι and i] lines might become unresolvable and therefore blend when observing at lower resolution."," Also, the neighboring and ] lines might become unresolvable and therefore blend when observing at lower resolution." The data were originally reduced using the CRIRES pipeline version, The data were originally reduced using the CRIRES pipeline version. " The pipeline makes use of and automatically handles dark 1.5.0}.frames, flat fields from a halogen lamp and observations of a ThAr lamp for wavelength calibration."," The pipeline makes use of and automatically handles dark frames, flat fields from a halogen lamp and observations of a ThAr lamp for wavelength calibration." To subtract the sky background the telescope was nodded between two positions along the slit during the observations., To subtract the sky background the telescope was nodded between two positions along the slit during the observations. The two frames are subtracted from each other producing two stellar spectra in vertically different places on the detector arrays., The two frames are subtracted from each other producing two stellar spectra in vertically different places on the detector arrays. The pixels are subsequently added column wise in the slit direction and extracted for each spectrum exposure by the pipeline and then added to produce the final spectrum of the star., The pixels are subsequently added column wise in the slit direction and extracted for each spectrum exposure by the pipeline and then added to produce the final spectrum of the star. " Unfortunately there is an optical in certain settings of the spectrometer, clearly visible as broad vertical bands in our flat fields (see Fig."," Unfortunately there is an optical in certain settings of the spectrometer, clearly visible as broad vertical bands in our flat fields (see Fig." " A(a)] and (b), but also as smaller dots in our science frames (see Fig. A(c)},"," \ref{fig:ccd1082} and \ref{fig:ccd1045}) ), but also as smaller dots in our science frames (see Fig. \ref{fig:ccdnodding}," where a smaller version of the ghost shown in Fig., where a smaller version of the ghost shown in Fig. A(a)] can be seen)., \ref{fig:ccd1082} can be seen). The optical ghost is present in some higher order settings for the echelle grating and is a result of retro-reflection from the detector to the grating which is redirected onto the detector in a different order., The optical ghost is present in some higher order settings for the echelle grating and is a result of retro-reflection from the detector to the grating which is redirected onto the detector in a different order. The ghosts in the flat fields lie in such a location on the detector that it will affect one of the two nod positions (compare the flat fields in Fig., The ghosts in the flat fields lie in such a location on the detector that it will affect one of the two nod positions (compare the flat fields in Fig. A(a)] and A(b)) with the stellar spectra in Fig. A(c)))., \ref{fig:ccd1082} and \ref{fig:ccd1045} with the stellar spectra in Fig. \ref{fig:ccdnodding}) ). This results in a spectral artifact in the two spectral, This results in a spectral artifact in the two spectral the total radio luminosity function to match that derived for the 2dFGRS by Sadler shorteitesad02— over the radio luminosity range 107E25 to 10°! ¢. where the errors on the two luminosity function determinations are both small.,"the total radio luminosity function to match that derived for the 2dFGRS by Sadler \\shortcite{sad02} over the radio luminosity range $10^{23}$ to $10^{24.5}$ $^{-1}$, where the errors on the two luminosity function determinations are both small." Note that no correction has been made for incompleteness or misidentification in the radio samples but. as discussed above. it is expected that this will be relatively small.," Note that no correction has been made for incompleteness or misidentification in the radio samples but, as discussed above, it is expected that this will be relatively small." The radio luminosity functions are tabulated in Table 3.., The radio luminosity functions are tabulated in Table \ref{lumfunctab}. The uncertainties quoted on the luminosity function determination are the statistical Poissonian errors only: these have become so small for the SDSS sample at some luminosities that systematic errors are likely to dominate., The uncertainties quoted on the luminosity function determination are the statistical Poissonian errors only; these have become so small for the SDSS sample at some luminosities that systematic errors are likely to dominate. One important source of systematic error will be cosmic variance., One important source of systematic error will be cosmic variance. Another is the separation of AGN and star, Another is the separation of AGN and star Galaxies in the local Universe come. broadly speaking. in two [lavors: objects with blue and. red. optical colors tend to inhabit cillerent regions of the color-magnitude diagram. (CMD.Stratevaetab.2001).. with blue galaxies showing a large spread in color and red. galaxies following a relatively: tight.: sequence.,"Galaxies in the local Universe come, broadly speaking, in two flavors: objects with blue and red optical colors tend to inhabit different regions of the color-magnitude diagram \citep[CMD,][]{strateva}, with blue galaxies showing a large spread in color and red galaxies following a relatively tight sequence." ...This so-called. red. sequence has been observed up to z.2 and has grown in. mass bv a factor of 2 since 2=1. although↦ the evolution in the massive enc of the distribution remains controversial (Lleavensetal..2004:Bellab.Cimattial.2006:Faberetal..2007:Robainactab. 2010).," This so-called red sequence has been observed up to $z\simeq2$ and has grown in mass by a factor of $\sim 2$ since $z=1$, although the evolution in the massive end of the distribution remains controversial \citep{heav, bell04, cimatti, faber07, robaina10}." .. As galaxies with red stellar populations tvpicallv show low levels of star (SE). the mechanism needed. to add: stellar mass to the red. sequence must imply the migration of a certain number of objects from the blue cloud to the red sequence (Brinchmann&Ellis.2000:Belletal..2007: bv quenching of their star formation.," As galaxies with red stellar populations typically show low levels of star (SF), the mechanism needed to add stellar mass to the red sequence must imply the migration of a certain number of objects from the blue cloud to the red sequence \citep{brinch, bell07, walcher} by quenching of their star formation." While galaxies on the blue cloud show predominantly disk-like light profiles. the red. sequence is. dominated: by objects with more concentrated light distributions (Blantonetal.npo 2003).," While galaxies on the blue cloud show predominantly disk-like light profiles, the red sequence is dominated by objects with more concentrated light distributions \citep{blanton03}." . Further. evidence. on the relation. between SEae quenching. ancl galaxy structure is. provided. by )Bell (2008).. who found⋅ that. red. and. dead. stellar populations⊀ tend. to inhabit galaxies with concentrated. light. profiles.," Further evidence on the relation between SF quenching and galaxy structure is provided by \citet{bell08}, who found that red and dead stellar populations tend to inhabit galaxies with concentrated light profiles." Detailed studies of the shape of quiescent galaxies show that spheroidal systems are overwhelmingly dominant at masses, Detailed studies of the shape of quiescent galaxies show that spheroidal systems are overwhelmingly dominant at masses The observations are shown as circles.,The observations are shown as circles. The curves depend only weakly on the neutron star mass., The curves depend only weakly on the neutron star mass. One can therefore craw conclusions from the comparison of the theoretical curves with the observations. although the star masses are unknown.," One can therefore draw conclusions from the comparison of the theoretical curves with the observations, although the star masses are unknown." " Since both prt, and my do not depend on f£ in first approximation. the calculation of the theoretical curves for one specific spin frequency. 7=363 Hz (this corresponds to the spin frequency of the neutron star in 4U1728-34). is sulIicient."," Since both $\nu_{\rm LT}/\nu_{\rm s}$ and $\nu_{\rm K}$ do not depend on $\nu_{\rm s}$ in first approximation, the calculation of the theoretical curves for one specific spin frequency, $\nu_{\rm s}=363$ Hz (this corresponds to the spin frequency of the neutron star in 4U1728-34), is sufficient." As can be seen in Fig. 9..," As can be seen in Fig. \ref{fig:rot.qpo}," the observations of 110731- and 11735-44 agree with the theoretical curves of eroup 1. which contains the stilfest. EOSs of our sample.," the observations of 1731-260 and 1735-44 agree with the theoretical curves of group 1, which contains the stiffest EOSs of our sample." ‘This is in agreement with the results of Stella Victri (1998).., This is in agreement with the results of Stella Vietri \shortcite{Stella97a}. Hlowever. the other observations. including the observations of the Z-sources which are not shown. lie above all theoretical curves.," However, the other observations, including the observations of the Z-sources which are not shown, lie above all theoretical curves." Phe observed. frequeney. vores 18 thus higher than the Lense-Thirring. precession [frequency even for the stillest EOSs., The observed frequency $\nu_{\rm QPO3}$ is thus higher than the Lense-Thirring precession frequency even for the stiffest EOSs. Lone assume that the observed frequencies correspond to the first overtone of the Lense-Thirring precession. the Atoll-source observations are in the range of the theoretical curves.," If one assume that the observed frequencies correspond to the first overtone of the Lense-Thirring precession, the Atoll-source observations are in the range of the theoretical curves." In the case of the Z-sources. the detected. [requencies Moros are not only too large in most sources. but acdelitionally the slope of the relation vorosΟΟΙ} of the Z-source observations is much higher than the slope of vor) For the theoretically determined. mocdels.," In the case of the Z-sources, the detected frequencies $\nu_{\rm QPO3}$ are not only too large in most sources, but additionally the slope of the relation $\nu_{\rm QPO3}(\nu_{\rm QPO1})$ of the Z-source observations is much higher than the slope of $\nu_{\rm LT}(\nu_{\rm K})$ for the theoretically determined models." Even the assumption. that the first. overtone of the Lense-Thirring precession [requeney yr is detected cannot explain these discrepancies.," Even the assumption, that the first overtone of the Lense-Thirring precession frequency $\nu_{\rm LT}$ is detected \cite{Stella97a} cannot explain these discrepancies." In this paper. we derived models of rapidly rotating neutron stars and strange stars by solving the general. relativistic structure equations for a broad collection of modern LOSs.," In this paper, we derived models of rapidly rotating neutron stars and strange stars by solving the general relativistic structure equations for a broad collection of modern EOSs." We compared the space time geometry of these models with recently discovered QPOs in the X-ray brightness of LANDs., We compared the space time geometry of these models with recently discovered QPOs in the X-ray brightness of LMXBs. If one follows the general beat-frequencey interpretation of the kilohertz-QPOs. i.e. that the higher frequency QPO originates at a stable circular orbit. one can constrain the mass of the neutron star to a range which depends on the EOS.," If one follows the general beat-frequency interpretation of the kilohertz-QPOs, i.e. that the higher frequency QPO originates at a stable circular orbit, one can constrain the mass of the neutron star to a range which depends on the EOS." This mass range is for all sources and for all EOSs consistent with a canonical mass. M=L4AM...," This mass range is for all sources and for all EOSs consistent with a canonical mass, $M=1.4\,M_\odot$." As it was gaated by Miller ct al., As it was stated by Miller et al. (1998a). and Thampan et al., \shortcite{Miller98b} and Thampan et al. (1999) 10 exact lower and upper limits of the neutron star's mass can only be determined by using fully relativistic models of rapidly rotating neutron stars., \shortcite{Thampan98a} the exact lower and upper limits of the neutron star's mass can only be determined by using fully relativistic models of rapidly rotating neutron stars. The exact Limits diller [rom 10 approximations with j=O by roughly 10(4., The exact limits differ from the approximations with $j=0$ by roughly 10. As it was shown by [xaaret. ct al., As it was shown by Kaaret et al. (1997). ancl Zhang et al. (1998h).," \shortcite{Kaaret97a} and Zhang et al. \shortcite{Zhang98c}," ". the observation of a maximum. frequency vovo, οἱ the high frequency QPO in the sources 11820-). 4U1608-52. and 11636-536 favour the interpretation that this QPO originates at the innermost stable orbit."," the observation of a maximum frequency $\nu_{\rm QPO1}^{\rm max}$ of the high frequency QPO in the sources 1820-30, 4U1608-52, and 1636-536 favour the interpretation that this QPO originates at the innermost stable orbit." Ht this interpretation is correct. the mass of the neutron star can be exactly (within the observational errors) determined for a given EOS.," If this interpretation is correct, the mass of the neutron star can be exactly (within the observational errors) determined for a given EOS." The approximately obtained mass.M.. of the source L11820-30. is larecr than the maximum mass of most of the considered EOSs.," The approximately obtained mass, of the source 1820-30 is larger than the maximum mass of most of the considered EOSs." " This conclusion is even strengthened if the observed: maximum frequency voro, is compared with the exact. neutron. star models."," This conclusion is even strengthened if the observed maximum frequency $\nu_{\rm QPO1}^{\rm max}$ is compared with the exact neutron star models." The only allowed EOSs of our broad collection are then the aand a. which both describe neutron star matter as consisting of nucleons and leptons only.," The only allowed EOSs of our broad collection are then the and , which both describe neutron star matter as consisting of nucleons and leptons only." The derived masses of the three sources lic in the narrow range between AL=1.92M. and 2.25M...," The derived masses of the three sources lie in the narrow range between $M=1.92\,M_\odot$ and $2.25\,M_\odot$." This result is also of some importance for the nature of the object Left in the supernova LOSTA. During the first ten seconds after the supernova. neutrinos were detected (Chevalier.1997)..," This result is also of some importance for the nature of the object left in the supernova 1987A. During the first ten seconds after the supernova, neutrinos were detected \cite{Chevalier97a}." This means that a protoneutron star was formed in the supernova., This means that a protoneutron star was formed in the supernova. The fact that up to now no pulsar emission could be detected was interpreted by Bethe Brown (1995) that the protoneutron star collapsed to a black hole when the star became transparent to neutrinos alter roughly 10 s. The estimated value of the barvonic mass Alp~163.1.76M. (Bethe&Brown.1995:Thielemannetal.1996). gives thus an upper limit to the maximum gravitational mass of a neutron star: MaasSLGAL. .," The fact that up to now no pulsar emission could be detected was interpreted by Bethe Brown \shortcite{Bethe95a} that the protoneutron star collapsed to a black hole when the star became transparent to neutrinos after roughly 10 s. The estimated value of the baryonic mass $M_{\rm B}\sim 1.63-1.76\,M_\odot$ \cite{Bethe95a,Thielemann94a} gives thus an upper limit to the maximum gravitational mass of a neutron star: $M_{\rm max}\lesssim 1.6\,M_\odot$ ." This limit is in clear contradiction to the derived: mass of. e.g. 11820-30.," This limit is in clear contradiction to the derived mass of, e.g. 1820-30." ]t is generally believed that neutron. stars are. born with a mass about 1.41.5M..," It is generally believed that neutron stars are born with a mass about $1.4-1.5\,M_\odot$." Neutron stars in LMXDs would therefore ποσοο 0.4.OSAL. during their lifetime.," Neutron stars in LMXBs would therefore accrete $0.4-0.8\,M_\odot$ during their lifetime." 4 seems reasonable to assume that some of the neutron stars in LMXDs accrete enough. matter to reach the maximally. stable mass (Aus=2.20M. forΝΕ. Myuas244A4. for ad).," It seems reasonable to assume that some of the neutron stars in LMXBs accrete enough matter to reach the maximally stable mass $M_{\rm max}=2.20\,M_\odot$ for, $M_{\rm max}=2.44\,M_\odot$ for )." The neutron star would then collapse to à black hole., The neutron star would then collapse to a black hole. The interpretation of the QPO with frequencies toros about LO Lz as Lense-Fhirring precession frequency. of the accretion disk seems not to be consistent with the theoretical star moclels. unless one assumes that the first overtone of the oecession is observed.," The interpretation of the QPO with frequencies $\nu_{\rm QPO3}$ about 10 Hz as Lense-Thirring precession frequency of the accretion disk seems not to be consistent with the theoretical star models, unless one assumes that the first overtone of the precession is observed." In the case of Z-sources however. the necessary ratio of the frame dragging frequency. and. spin requeney. and thus the moment of inertia. of the models if oo small compared to the observed frequency. vores or ball of it.," In the case of Z-sources however, the necessary ratio of the frame dragging frequency and spin frequency, and thus the moment of inertia, of the models if too small compared to the observed frequency $\nu_{\rm QPO3}$ or half of it." Our general conclusion is that. the observations of κοπο QPOs in LAINBs provide us another powerful tool or probing the interior of neutron stars., Our general conclusion is that the observations of kilohertz QPOs in LMXBs provide us another powerful tool for probing the interior of neutron stars. Compared to the other tools like observations of the maximum mass (van]xerkwijketal. 1995).. the limiting spin period (Friedmanotal...1986:Weber&CGlendenning. 1992).. and cooling simulations (Vsuruta.1966:SchaabetaL.1996: 1998).. the derived constraints. especially in the sonic-point-interpretation. are rather strong.," Compared to the other tools like observations of the maximum mass \cite{Kerkwijk95a}, the limiting spin period \cite{Friedman86a,Weber92a}, and cooling simulations \cite{Tsuruta66,Schaab95a,Page97a}, the derived constraints, especially in the sonic-point-interpretation, are rather strong." The lower limit. 2.15M. is only consistent with two EOSs. aanda. which are relatively stil at high densities.," The lower limit $M_{\rm max}\gtrsim 2.15\,M_\odot$ is only consistent with two EOSs, and, which are relatively stiff at high densities." Their still behaviour at high5 densities seems to beonly possible if the neutronstar matter consists of neutrons. protons. and leptons only.," Their stiff behaviour at high densities seems to beonly possible if the neutronstar matter consists of neutrons, protons, and leptons only." At the most. à small acimixture of hvperons may be allowed.," At the most, a small admixture of hyperons may be allowed." However. one has to acamit that such a composition somehow contracdicts our conception," However, one has to admit that such a composition somehow contradicts our conception" distribution and kinematics stronely suggest that the solar radius is polluted by wanderers coming from the outer and inner disk. indicating a rather strong radial variation of the metallicity (IIavvood 2003).,"distribution and kinematics strongly suggest that the solar radius is polluted by wanderers coming from the outer and inner disk, indicating a rather strong radial variation of the metallicity (Haywood 2008)." Because radial metallicity gradients in galactic disks may be produced by a number of dillerent processes. the measurement of how these gradients have evolved with time should provide an even stronger constraint (e. g.. Fu et al.," Because radial metallicity gradients in galactic disks may be produced by a number of different processes, the measurement of how these gradients have evolved with time should provide an even stronger constraint (e. g., Fu et al." 2009). thus (he importance of studying metallicity distributions of tracers of different Galactic ages.," 2009), thus the importance of studying metallicity distributions of tracers of different Galactic ages." " Planetary nebulae (DNe) represent the Galactic stellar population with progenitors of turnolf mass Mi, between 1 and 8 M... probing Galactic ages between ~3x10* vr and 210 Gvr (Maraston 1993)."," Planetary nebulae (PNe) represent the Galactic stellar population with progenitors of turnoff mass $_{\rm to}$ between $\sim$ 1 and 8 $_{\odot}$, probing Galactic ages between $\sim3\times10^7$ yr and $\geq$ 10 Gyr (Maraston 1998)." Planetary nebulae are distributed in the Galactie disk. bulge. and halo.," Planetary nebulae are distributed in the Galactic disk, bulge, and halo." Their Galactic distribution and radial velocities offer a first subclivision inlo populations. which can be studied separately.," Their Galactic distribution and radial velocities offer a first subdivision into populations, which can be studied separately." Furthermore. markers such as nitrogen abundances and morphological tvpes allow to further discriminate between disk PNe οἱ relatively. voung and oll progenitors.," Furthermore, markers such as nitrogen abundances and morphological types allow to further discriminate between disk PNe of relatively young and old progenitors." It is then sensible to undergo a study of Galactic metallicitv for the different PN populations., It is then sensible to undergo a study of Galactic metallicity for the different PN populations. This has been done in the past., This has been done in the past. Galactic disk PNe have been studied. among others. by INingsburg Barlow (1994) and. more recently. by Perinotto et al. (," Galactic disk PNe have been studied, among others, by Kingsburg Barlow (1994) and, more recently, by Perinotto et al. (" 2004. PO4). while bulge PNe are the subject of a focused study by Exter et al. (,"2004, P04), while bulge PNe are the subject of a focused study by Exter et al. (" 2004).,2004). The Galactic disk PNe have been the subject of many studies on metallicity eradients: a-element abundances of PNe trace the original progenitor composition. (lus the chemical evolution of the Galactic disk.," The Galactic disk PNe have been the subject of many studies on metallicity gradients: $\alpha$ -element abundances of PNe trace the original progenitor composition, thus the chemical evolution of the Galactic disk." Perinotto Morbidelli (2006. PAIOG) reviewed all Galactic metallicity gradients published since (he seventies. and found that PNe in the Galactic disk Gace a one dimensional. negative oxveen gradient Alog(O/1L)/ ARG =-0.07 (Faundez-Abans Maciel 1987) and -0.03 (Pasquali Perinotto 1993) dex !.," Perinotto Morbidelli (2006, PM06) reviewed all Galactic metallicity gradients published since the seventies, and found that PNe in the Galactic disk trace a one dimensional, negative oxygen gradient $\Delta$ $\Delta$ $_{\rm G}$ =-0.07 (Faundez-Abans Maciel 1987) and -0.03 (Pasquali Perinotto 1993) dex $^{-1}$." The excellent data revision by Perinotto and collaborators provides its own gradient οἱ -0.016 dex | (PMOG). which is shallower than previously known.," The excellent data revision by Perinotto and collaborators provides its own gradient of -0.016 dex $^{-1}$ (PM06), which is shallower than previously known." Almost contemporary Stanghellini et al. (, Almost contemporary Stanghellini et al. ( 2006) found. a shallow gradient of -0.01 dex ! for the oxveen abundances of Galactic disk PNe. consistent with PAIOG’s analysis.,"2006) found a shallow gradient of -0.01 dex $^{-1}$ for the oxygen abundances of Galactic disk PNe, consistent with PM06's analysis." 1.2 kpc.,$\sim1.2$ kpc. In this case the 2\TASS data provide a more solid basis for the reality of the eroup than the UCACS data. although they do not. address the possible membership of TD 193322.," In this case the 2MASS data provide a more solid basis for the reality of the group than the UCAC3 data, although they do not address the possible membership of HD 193322." " The cluster docs rot show up as a siguificaut density enliacemoenut from) star counts, and it is conceivable that Colliuder 119 represeuts merely a clump in one of the many OD associations secu along the direction of the Cyeuus aru."," The cluster does not show up as a significant density enhacement from star counts, and it is conceivable that Collinder 419 represents merely a clump in one of the many OB associations seen along the direction of the Cygnus arm." Table 1| stummarizes the results of the preseut study of four open clusters using 2\LASS observations., Table \ref{tab2} summarizes the results of the present study of four open clusters using 2MASS observations. Most of the inferred parameters for the clusters differ from published results tied το optical photometry. although those for Turner 1 were considered as au alternate possibility iu the study by Turneretal.(1986).," Most of the inferred parameters for the clusters differ from published results tied to optical photometry, although those for Turner 1 were considered as an alternate possibility in the study by \citet{te86}." ". Iu cach case the optical phooluetry was limited by the faiutuess of cluster members arising from aree imterstellar reddening. which is where JK, photometry has advantages over optical band photometry."," In each case the optical photometry was limited by the faintness of cluster members arising from large interstellar reddening, which is where $_s$ photometry has advantages over optical band photometry." The poiut to cluphasize. lowever. is that ΗΝ. observatio1s ofcuster stars often provide relatively complete SOles that can be used to infer reasonably acctrate estimates for he all-iuportant interstellar reddening toward the cluster. iu most cases du more straightforward manucr than what is often TisCC for optical baudRI observations.," The point to emphasize, however, is that $_s$ observations of cluster stars often provide relatively complete samples that can be used to infer reasonably accurate estimates for the all-important interstellar reddening toward the cluster, in most cases in more straightforward manner than what is often used for optical band observations." Once the redening 1s shown. ZAMS fitting. or isochrou5 fittiis in some cases. can then be used to derive the distance o the cluster.," Once the reddening is known, ZAMS fitting, or isochrone fitting in some cases, can then be used to derive the distance to the cluster." That is true despite the relatively low intrinsic precision of existi18o 2A\TASS data or most Galactic fields., That is true despite the relatively low intrinsic precision of existing 2MASS data for most Galactic fields. In the present study we carry out a coherent analysis on one dataset.,In the present study we carry out a coherent analysis on one dataset. The selection criteria are taken from the same set of simulations and the masking ts identical for all three samples., The selection criteria are taken from the same set of simulations and the masking is identical for all three samples. However. without spectroscopic redshift distributions we cannot decide whether the evolutionary trend observed with theBPZ.. thesim.. and the redshift distributions or the non-evolution observed for the redshift distribution is. real.," However, without spectroscopic redshift distributions we cannot decide whether the evolutionary trend observed with the, the, and the redshift distributions or the non-evolution observed for the redshift distribution is real." The simulated redshift distributions have the advantage that they are not affected by a number of systematic errors inherent to the observations (except for the reliance on the observed /-band number counts) or spurious effects introduced by priors in the photo-z codes., The simulated redshift distributions have the advantage that they are not affected by a number of systematic errors inherent to the observations (except for the reliance on the observed $i$ -band number counts) or spurious effects introduced by priors in the $z$ codes. Furthermore. the absolute results from the case and the case agree very well. although different template sets were used.," Furthermore, the absolute results from the case and the case agree very well, although different template sets were used." One disadvantage of the simulations is that both rely on assumptions about the mixture of templates and the fractions of high- to low-z objects which are taken from external data (the HDF-N and the CFRS)., One disadvantage of the simulations is that both rely on assumptions about the mixture of templates and the fractions of high- to $z$ objects which are taken from external data (the HDF-N and the CFRS). We tend to trust the results based on the simulated redshift distributions more. but note that a decision about redshift evolution or non-evolution cannot be taken without additional Nassive spectroscopic support.," We tend to trust the results based on the simulated redshift distributions more, but note that a decision about redshift evolution or non-evolution cannot be taken without additional massive spectroscopic support." The same is true for the influence of contamination or incompleteness on the clustering measurements., The same is true for the influence of contamination or incompleteness on the clustering measurements. Without a deep spectroscopic survey we cannot account for such effects because we do not know how these possible low-z contaminants cluster or which galaxies at high-z are missed by the Lyman-break selection., Without a deep spectroscopic survey we cannot account for such effects because we do not know how these possible $z$ contaminants cluster or which galaxies at $z$ are missed by the Lyman-break selection. This 15 a fundamental limitation of a photometric survey., This is a fundamental limitation of a photometric survey. However. our simulations suggest — and the colour selection criteria and magnitude cuts were chosen in such à way — that contamination and incompleteness are kept low.," However, our simulations suggest – and the colour selection criteria and magnitude cuts were chosen in such a way – that contamination and incompleteness are kept low." Thus. we still think 1t i$ reasonable to assume that the clustering measurements are not seriously affected by either of the two effects.," Thus, we still think it is reasonable to assume that the clustering measurements are not seriously affected by either of the two effects." As detected for B-dropouts (??) and U-dropouts (?) before. we see a significant deviation of the angular correlation function on small scales from the power-law behaviour on large scales," As detected for $B$ -dropouts \citep{2005ApJ...635L.117O,2006ApJ...642...63L} and $U$ -dropouts \citep{2007A&A...462..865H} before, we see a significant deviation of the angular correlation function on small scales from the power-law behaviour on large scales" , change in the ionization balance of iron (?).. potentially leading to a different WLR for such relatively cool stars.,"change in the ionization balance of iron \citep{vink99}, potentially leading to a different WLR for such relatively cool stars." This excludes some targets from the studies by ???..," This excludes some targets from the studies by \cite{trundle04, trundle05, crowther06}." Finally. we did not include the entries from the comprehensive study of ? because. with the exception of the mass-loss rates. the stellar parameters were based on calibrations.," Finally, we did not include the entries from the comprehensive study of \cite{markova04} because, with the exception of the mass-loss rates, the stellar parameters were based on calibrations." We note however that the stellar parameters derived by these authors compare well with other studies., We note however that the stellar parameters derived by these authors compare well with other studies. For the Galaxy we consider a sample based on the analyses performed by ?.. ?.. ? and ?..," For the Galaxy we consider a sample based on the analyses performed by \cite{repolust04}, \cite{mokiem05}, \cite{martins05b} and \cite{crowther06}." Note that the second study includes a reanalysis of the Cyg OB2 stars analysed by ?.. and HD 15629 and Z Oph studied by ?. The relevant atmospheric parameters adopting non-clumped mass-loss rates are listed in Tab. Al..," Note that the second study includes a reanalysis of the Cyg OB2 stars analysed by \cite{herrero02}, , and HD 15629 and $\zeta$ Oph studied by \citeauthor{repolust04} The relevant atmospheric parameters adopting non-clumped mass-loss rates are listed in Tab. \ref{tab:wind_par_gal}." Two entries are given for HD 15629 and HD 93250. as they were analysed separately using aandcMFGEN.," Two entries are given for HD 15629 and HD 93250, as they were analysed separately using and." . In the following determination of the Galactic WLR. we adopt the results of the sstudies for reasons of consistency. but note that the differences of both analyses are not signficant.," In the following determination of the Galactic WLR, we adopt the results of the studies for reasons of consistency, but note that the differences of both analyses are not signficant." In Fig., In Fig. | the distribution of the Galactic stars im the modified wind-momentum lluminosity diagram. ts presented. where black/grey symbols refer to aanalyses.," \ref{fig:wlr-gal} the distribution of the Galactic stars in the modified wind-momentum luminosity diagram is presented, where black/grey symbols refer to analyses." Different luminosity classes are distinguished using circles. triangles and squares for. respectively. class V. HI-II and I objects.," Different luminosity classes are distinguished using circles, triangles and squares for, respectively, class V, III-II and I objects." The open symbols show vvalues resulting from scaling the bby a factor of 0.44. corresponding to —0.37 in logDivo. for supergiants exhibiting eemission line profiles.," The open symbols show values resulting from scaling the by a factor of 0.44, corresponding to $-$ 0.37 in $\log \Dmom$, for supergiants exhibiting emission line profiles." A reduction. of this amount was proposed by ? to correct for the fact that these stars have a systematically higher wind momentum compared to O dwarfs and theoretical predictions (seealso??)..," A reduction of this amount was proposed by \cite{repolust04} to correct for the fact that these stars have a systematically higher wind momentum compared to O dwarfs and theoretical predictions \citep[see also][]{pulsIAUS212, markova04}." The physical interpretation for this systematic offset. proposed by these authors is connected to wind clumping., The physical interpretation for this systematic offset proposed by these authors is connected to wind clumping. Because lis a recombination line. its strength scales with the (wind)density o. squared.," Because is a recombination line, its strength scales with the (wind)density $\rho$ squared." In a uniformly clumped wind. the emission will increase by a factor f=/«p>7. where f is referred to as the clumping factor.," In a uniformly clumped wind, the emission will increase by a factor $f = <\rho^2>/<\rho>^{2}$, where $f$ is referred to as the clumping factor." As the lline-forming region of stars with ΠΠ emission is more extended compared to stars in which the profile is seen in absorption. these more extended regions must be more clumped than the innermost wind regions of those stars with absorption type profiles.," As the line-forming region of stars with in emission is more extended compared to stars in which the profile is seen in absorption, these more extended regions must be more clumped than the innermost wind regions of those stars with absorption type profiles." In this interpretation. therefore. the observed offset suggests a (spatial) gradient in the clumping factor or a difference in the clumping properties of thin and thick winds.," In this interpretation, therefore, the observed offset suggests a (spatial) gradient in the clumping factor or a difference in the clumping properties of thin and thick winds." The (differential) clumping factor that corresponds to the applied scaling is f=1/0.447~5., The (differential) clumping factor that corresponds to the applied scaling is $f = 1/0.44^{2} \simeq 5$. We will return to the issue of clumping in Sect. 8.2.., We will return to the issue of clumping in Sect. \ref{sec:clumping}. The left-hand side of Fig., The left-hand side of Fig. | compares the stars that have been analysed by ? in a homogeneous way by using an automated fitting method., \ref{fig:wlr-gal} compares the stars that have been analysed by \cite{mokiem05} in a homogeneous way by using an automated fitting method. We have constructed a WLR by fitting a power law. while accounting for both the symmetric errors In aand the asymmetric errors in.Dinom- to the observed distribution.," We have constructed a WLR by fitting a power law, while accounting for both the symmetric errors in and the asymmetric errors in, to the observed distribution." This empirical WLR is shown as a solid and dotted black line for uncorrected and clumping corrected wind momenta. respectively.," This empirical WLR is shown as a solid and dotted black line for uncorrected and clumping corrected wind momenta, respectively." The clumping corrected relation is found to be flatter because the clumping corrections only affected the two brightest objects., The clumping corrected relation is found to be flatter because the clumping corrections only affected the two brightest objects. In Sect., In Sect. 7. we will compare the empirical and theoretical WLRs in the observed rrange., \ref{sec:mdot_vs_z} we will compare the empirical and theoretical WLRs in the observed range. On the right-hand side of Fig., On the right-hand side of Fig. 1. the observed ddistribution for the complete Galactic sample is shown., \ref{fig:wlr-gal} the observed distribution for the complete Galactic sample is shown. The empirical WLRs determined for this sample are again shown às a black solid and dotted line for the uncorrected and rates., The empirical WLRs determined for this sample are again shown as a black solid and dotted line for the uncorrected and clumping-corrected rates. As can be seen in Tab., As can be seen in Tab. 3.| the fit coefficients for both relations are in very good agreement with those derivedfrom the homogeneously analysed sample., \ref{tab:wlr-par} the fit coefficients for both relations are in very good agreement with those derivedfrom the homogeneously analysed sample. essential to include the coverage fractions as free parameters in the for these sinceCr—1 does not provide fittingacceptable processfits to these systemsdoublets within the observed uncertainties (Fig. 4;;,essential to include the coverage fractions as free parameters in the fitting process for these systems since$C_{\rm f}=1$ does not provide acceptable fits to these doublets within the observed uncertainties (Fig. \ref{fig-q1700-cf}; Misawa et al. 2007)., Misawa et al. \nocite{mis07}. ". Although multi-band photometry and/or spectra of these three are not available over the entire range, some quasarsobservational data are available to place spectralconstraints on the input SED."," Although multi-band photometry and/or spectra of these three quasars are not available over the entire spectral range, some observational data are available to place constraints on the input SED." We consider three possible quasar SEDs., We consider three possible quasar SEDs. " We utilize three parameters to constrain the SED: αο, OX, and ox, which are the UV/optical spectral slope, X-ray band spectral slope and optical-X-ray spectral slope, respectively (assuming that fy< vt“)."," We utilize three parameters to constrain the SED: $\alpha_{\rm o}$, $\alpha_{\rm x}$, and $\alpha_{\rm ox}$, which are the UV/optical spectral slope, X-ray band spectral slope and optical-X-ray spectral slope, respectively (assuming that $f_\nu\propto \nu^{+\alpha}$ )." " The last is defined as 0x=0.3838log[Cy(2keV)/£,(2500 À)], where £,(2keV) and £,(2500A) are the monochromatic luminosities at 2 keV"," The last is defined as $\alpha_{\rm ox}=0.3838\log\left[\ell_\nu(2\ {\rm keV})/\ell_\nu(2500~{\rm\AA})\right]$ , where $\ell_\nu(2\ {\rm keV})$ and $\ell_\nu(2500~\mbox{\AA})$ are the monochromatic luminosities at 2 keV" in June 2000. but one year later showed a very solt (E25.1). lower luminosity eres!) spectrum (Terashima Wilson 2002a).,"in June 2000, but one year later showed a very soft $\Gamma > 5.1$ ), lower luminosity $L(0.5-8 \, \rm keV) = 5.6 \times 10^{38}$ erg $^{-1}$ ) spectrum (Terashima Wilson 2002a)." Such bebaviour is remitiscent of soft A-ray (ranslents., Such behaviour is reminiscent of soft X-ray transients. Variations iu the X-ray emission of sewreral INOs have been observed both αιrine a sinele observation (e.g.. Okada et al.," Variations in the X-ray emission of several IXOs have been observed both during a single observation (e.g., Okada et al." 1008: Zezas et :1., 1998; Zezas et al. 1999). and between observations which span several years (e.g. La Parola et al.," 1999), and between observations which span several years (e.g., La Parola et al." 2001)., 2001). However. thelel most spectacular evideuce foταν »erio«licity in aui INO has been found by Baueretal.(2001 for a bright compact source 1ithe Ci‘cluus galaxy (CG N-1 or CXOU J111312.3—62201: )3: see alsos uith Wilson 2001).," However, the most spectacular evidence for X-ray periodicity in an IXO has been found by \citet{bau01} for a bright compact source in the Circinus galaxy (CG X-1 or CXOU $-$ 652013; see also Smith Wilson 2001)." The period is 27.02370.7 ks. aud Baueretal.(2001) argue against tle nolion that this source is a foregrounl Galactic AM Her type system based primarily on the low surice density of Galactic S-ray sources iu this «]rection (6=3117.56 —378).," The period is $27.0 \pm 0.7$ ks, and \citet{bau01} argue against the notion that this source is a foreground Galactic AM Her type system based primarily on the low surface density of Galactic X-ray sources in this direction $l=311^{\circ}, b=-3.\!^{\circ}8$ )." Another INO in IC 312 is possibly periodic. with a perioc of 31 or LL hours. in agreement with that expected Or a seini-detacied. binary cousisting of a black hole aud a star of tens of solar masses (Sugilioeal.2001).," Another IXO in IC 342 is possibly periodic, with a period of 31 or 41 hours, in agreement with that expected for a semi-detached binary consisting of a black hole and a main-sequence star of tens of solar masses \citep{sug01}." . Constraints oi ite evolution aud nature of [NOs can be obtained by comparing the X-ray luniosity functions (ΔΕΣ] of tje N-ray swUL‘ce populations in various types of galaxies auc in various evolutioiary 5ages., Constraints on the evolution and nature of IXOs can be obtained by comparing the X-ray luminosity functions (XLFs) of the X-ray source populations in various types of galaxies and in various evolutionary stages. " For exaiuple. the 5opes of NLFs lor starburst galaxies (e.g. N82. ""the Antenae”) are liflater than those found in ealv-type galaxies (e.g... NGC 1553. NGC 1967). but are similar to tlat of the highi-iass N-ray |jary population in our own Galaxy. (Ixilgard οἱ al."," For example, the slopes of XLFs for starburst galaxies (e.g, M82, “the Antennae”) are flatter than those found in early-type galaxies (e.g., NGC 1553, NGC 4967), but are similar to that of the high-mass X-ray binary population in our own Galaxy (Kilgard et al." 2002: Crimi. Gilfanov. Sunyaev 2002: Zezas Fabbiano 2002).," 2002; Grimm, Gilfanov, Sunyaev 2002; Zezas Fabbiano 2002)." IXOs teud o be associated with regios of active star formation in spirals. but there are also [NOs in elliptica galaxies 2002).," IXOs tend to be associated with regions of active star formation in spirals, but there are also IXOs in elliptical galaxies \citep{cp02}." . This stroug association with star formation suggestsMOD that the brielitest X-ray ποσος in spl‘al aud starburst galaxies a'e likely to |ye voung. short-Iived sources. e.g.. X-ray binaries with O aud B type companions. or sipernova remnants (Ixileardetal.2002).," This strong association with star formation suggests that the brightest X-ray sources in spiral and starburst galaxies are likely to be young, short-lived sources, e.g., X-ray binaries with O and B type companions, or supernova remnants \citep{kil02}." ". Ii early-type gaaxles fellipticals aud. lenticulars). the NLF teuds to break at the Edcineton luinosity of a 1,LAL. neutron star (e.g.. Sarazin. Irwiι. Bregman 2000: Blautou. Sarazin. Irwin 2001). UL this seenis not to be the case in active star-formiig regions."," In early-type galaxies (ellipticals and lenticulars), the XLF tends to break at the Eddington luminosity of a $1.4 \, M_{\odot}$ neutron star (e.g., Sarazin, Irwin, Bregman 2000; Blanton, Sarazin, Irwin 2001), but this seems not to be the case in active star-forming regions." The galaxy. NCC LOGS is not only the 1ost. luminous (710HL. ) nearby Seyfert 2. nut also one of the most Iumiuois (also cLOM Lj sarbursts in the local universe (e.g.. Telesco Decher 1988).," The galaxy NGC 1068 is not only the most luminous $\simeq 10^{11} \, L_{\odot}$ ) nearby Seyfert 2, but also one of the most luminous (also $\simeq 10^{11} \, L_{\odot}$ ) starbursts in the local universe (e.g., Telesco Decher 1988)." It has long been Suggestec (e.g.. Weemau 1983) that the two phenomena are relaec. but the exact process remains elusive.," It has long been suggested (e.g., Weedman 1983) that the two phenomena are related, but the exact process remains elusive." The starbi SEIS cireumnuclear. in the galaxy disk aud ou a scale ol 2 kpe.," The starburst is circumnuclear, in the galaxy disk and on a scale of $\sim 2$ kpc." " Ht is thus a very differeut. phenoiuenon to many other regious of star formatio 1iu the universe. such as ""erancd-cdesigi7 late-type spi""als (e.g.. MOL) and star formation induced by galaxy mereers (e.g.. the Antennae)."," It is thus a very different phenomenon to many other regions of star formation in the universe, such as “grand-design” late-type spirals (e.g., M51) and star formation induced by galaxy mergers (e.g., the Antennae)." For this reas3. we felt it. worthwhile to investigate the «'onipact X-ray source population in a galaxy with suc La luminous. circumauuclear starburst.," For this reason, we felt it worthwhile to investigate the compact X-ray source population in a galaxy with such a luminous, circumnuclear starburst." " In this paper. we adopt a distance of |LL.E Mpe to NGC 1068. so 1""=70 pe (e.g.. Bland-Hawthorn et al."," In this paper, we adopt a distance of $14.4$ Mpc to NGC 1068, so $1^{\prime\prime} = 70$ pc (e.g., Bland-Hawthorn et al." 1997)., 1997). "For the SDSS passbands, the relationships with g—i colour are slightly more sensitive to reddening than with V—Ic.","For the SDSS passbands, the relationships with $g-i$ colour are slightly more sensitive to reddening than with $V-I_{C}$." Ggp- ccorrelates better with g—z than with g—i as shown in Fig., $-$ correlates better with $g-z$ than with $g-i$ as shown in Fig. 13 and Table 5.., \ref{fig:transformation-SDSS} and Table \ref{table:coeficients_SDSS}. The transformations from SDSS passbands yield residuals larger than with Johnson passbands., The transformations from SDSS passbands yield residuals larger than with Johnson passbands. We have also plotted G—Gpp aand G—Grp wwith respect to g—r and r—i because in the SDSS system the stellar locus is defined mainly from the g—r vs r—i diagram (?)..,We have also plotted $G-$ and $G-$ with respect to $g-r$ and $r-i$ because in the SDSS system the stellar locus is defined mainly from the $g-r$ vs $r-i$ diagram \citep{1996AJ....111.1748F}. " For stars with Ta<4500 K, dispersions exist in gravity and metallicity for each absorption value."," For stars with $T_{\rm{eff}}<4500$ K, dispersions exist in gravity and metallicity for each absorption value." This dispersion is more present in g—r than in r—i., This dispersion is more present in $g-r$ than in $r-i$. " Finally, Fig."," Finally, Fig." " 14 displays two plots involving the Grys narrow band, Johnson-Cousins, and SDSS passbands."," \ref{fig:RVS_diag} displays two plots involving the $G_{RVS}$ narrow band, Johnson-Cousins, and SDSS passbands." The relationships can be found in Tables 3 and 5.., The relationships can be found in Tables \ref{table:coeficients_Johnson} and \ref{table:coeficients_SDSS}. . Transformations using two Johnson or two SDSS colours have also been computed in the form and they are shown in Table 7.., Transformations using two Johnson or two SDSS colours have also been computed in the form and they are shown in Table \ref{table:coeficients_2colors}. The residuals are lower than using only one colour., The residuals are lower than using only one colour. " For the Johnson-Cousins system, the residuals do not decrease much, but for the SDSS system the improvement is substantial and the residuals are of the same order as those derived with V—Jc."," For the Johnson-Cousins system, the residuals do not decrease much, but for the SDSS system the improvement is substantial and the residuals are of the same order as those derived with $V-I_{C}$." " Thus, for Sloan, transformations with two colours are preferred."," Thus, for Sloan, transformations with two colours are preferred." " The residuals can still be decreased if different transformations are considered for different ranges of colours, reddening values, luminosity classes, and metallicities."," The residuals can still be decreased if different transformations are considered for different ranges of colours, reddening values, luminosity classes, and metallicities." " As an example, for unreddened stars (nearby stars or stars above the galactic plane), the fittings are those in Table 6.."," As an example, for unreddened stars (nearby stars or stars above the galactic plane), the fittings are those in Table \ref{table:coeficients-unred}." Luminosity is a fundamental stellar parameter that is essential for testing stellar structure and evolutionary models., Luminosity is a fundamental stellar parameter that is essential for testing stellar structure and evolutionary models. Luminosity is derived by computing the integrated energy flux over the entire wavelength range (bolometric magnitude)., Luminosity is derived by computing the integrated energy flux over the entire wavelength range (bolometric magnitude). The relation between the absolute magnitude in a specific passband and the bolometric one is done through the bolometric correction (BC)., The relation between the absolute magnitude in a specific passband and the bolometric one is done through the bolometric correction $BC$ ). " For a given filter transmission curve, Sχ(1), the bolometric correction is defined by This correction can be derived for each star of known Teg and logg, using the following equationfrom ? where Μῃοιο=4.75 (?) is the bolometric magnitude of the Sun and Lo=3.856x1036 W is its luminosity’.. f? stands for the reference spectrum (e.g. Vega) at the Earth with its apparent magnitude my n"," For a given filter transmission curve, $S_X(\lambda)$, the bolometric correction is defined by This correction can be derived for each star of known $T_{\rm{eff}}$ and $ \log g$, using the following equationfrom \citet{Girardi2002} where $M_{\rm{bol,\odot}}=4.75$ \citep{1999Obs...119..289A} is the bolometric magnitude of the Sun and $L_{\odot}=3.856\times10^{26}$ W is its $f^{0}_{\lambda}$ stands for the reference spectrum (e.g. Vega) at the Earth with its apparent magnitude $m^{0}_{S_X(\lambda)}$ ." " Fy, is the total flux at thesurface of the star (Foo9.ffFada= σταρ.", $F_{\rm{bol}}$ is the total flux at thesurface of the star $F_{\rm{bol}}=\int_{0}^{\infty} F_{\lambda} d\lambda = \sigma T_{\rm{eff}}^{4}$ ). data [rom OSAT observations. we find that the newly discovered. QSO IX. 1324.213759. belongs to the NLSI class.,"data from $ROSAT$ observations, we find that the newly discovered QSO RX J1334.2+3759 belongs to the NLS1 class." Pherefore. it is referred to as NLOSO here.," Therefore, it is referred to as NLQSO here." Is X-ray and optical characteristics are further discussed below., Its X-ray and optical characteristics are further discussed below. σος X-ray emission from RN J1334.9|3751πι) is highly variable (sce Fig., Soft X-ray emission from RX J1334.9+3759 is highly variable (see Fig. e 2 3)., 2 3). During the 1991. observations. RN 1334.9|3759. showed: soft. X-ray variability on times scales of ~2000040000s bv à factor of ~2.," During the 1991 observations, RX J1334.9+3759 showed soft X-ray variability on times scales of $\sim20000-40000{\rm~s}$ by a factor of $\sim2$." ltapid variability events have also been detected. from RN J1384.9)3759., Rapid variability events have also been detected from RX J1334.9+3759. Phe most significant and extreme variable. event. shown in Vie.," The most significant and extreme variable event, shown in Fig." " 3. has AL(1.9541.02).1077ergs 7. which is similar to that of the extrenie variable event observed from PLIL 1098 (Brandt 1999).Straghtlorward application of the ellicieney. (η) limit: 9>481013""aAL (Fabian 1979). results in an extremely hieh ellicieney. (4)0.93+ 0.49)."," 3, has $\frac{\Delta L}{\Delta t} > (1.95\pm1.02)\times10^{42}{\rm~erg~s^{-2}}$ , which is similar to that of the extreme variable event observed from PHL 1098 (Brandt 1999).Straightforward application of the efficiency $\eta$ ) limit: $\eta > 4.8\times10^{-43}\frac{\Delta L}{\Delta t}$ (Fabian 1979), results in an extremely high efficiency $\eta > 0.93\pm0.49$ )." This can be compared. wih η00.8 for an optimally accreting Kerr BL rotating at t1ο maximum plausible rate (Thorne 1974)., This can be compared with $\eta \sim 0.3$ for an optimally accreting Kerr BH rotating at the maximum plausible rate (Thorne 1974). Thus the radiative cllicicney for the extreme variable event. shown in Fig., Thus the radiative efficiency for the extreme variable event shown in Fig. appears to be substantially larger and suggests relativis ellects: responsible for the extreme variable event., 3 appears to be substantially larger and suggests relativistic effects responsible for the extreme variable event. n suggestion tha relativistic elfects may be responsible for t extreme variability event can also be inferred as follows., The suggestion that relativistic effects may be responsible for the extreme variability event can also be inferred as follows. T variability. time scale. in the absence of relativistic ellec provides an upper limit to the size of the A-ray emitting region. 2ο. and also 5;<1.," At a decreased metallicity, [Fe/H] $= -2$, the lines become weak and are formed in the deeper layers, where $S^{l} > B_{\nu}^l$, and also $b_{i} < 1$." The raised non-LTE source function and decreased opacity cause significant weakening of the line. ancl. thus. large positive non-LTE abundance corrections.," The raised non-LTE source function and decreased opacity cause significant weakening of the line, and, thus, large positive non-LTE abundance corrections." Thus. for the range of stellar parameters investigated here. (he magnitude of the abundance corrections for bot Mn I lines of multiplet 16 is determined primarily by metallicity.," Thus, for the range of stellar parameters investigated here, the magnitude of the non-LTE abundance corrections for both Mn I lines of multiplet 16 is determined primarily by metallicity." Anoncre are largest (~ 0.3 dex) for the most metal-poor v Cen giant ([Fe/II| = -2). while for the red giants with larger metallicity ([Fe/Il] — -1) and low Mn abundances. AnonLr v 0.1 dex The final LTE manganese abundances that are shown in Table 1 are combined with iron abundances (from Smith et al.," $\Delta_{\rm non-LTE}$ are largest $\sim$ 0.3 dex) for the most metal-poor $\omega$ Cen giant ([Fe/H] = -2), while for the red giants with larger metallicity ([Fe/H] = -1) and low Mn abundances, $\Delta_{\rm non-LTE}$ $\sim$ 0.1 dex The final LTE manganese abundances that are shown in Table 1 are combined with iron abundances (from Smith et al." 2000 for w@ Cen and Drake et al., 2000 for $\omega$ Cen and Drake et al. 1992 for M4) and compared with abundances from other stellar samples., 1992 for M4) and compared with abundances from other stellar samples. The discussion begins with a comparison of Mau abundances in w Cen with stars from the thin disk. thick disk. and halo. as well as ser dwarf galaxv members.," The discussion begins with a comparison of Mn abundances in $\omega$ Cen with stars from the thin disk, thick disk, and halo, as well as Sgr dwarf galaxy members." This is then followed by a section that compares w Cen with those abundances from a large sample of Milky Way elobular cluster giants and [field stars., This is then followed by a section that compares $\omega$ Cen with those abundances from a large sample of Milky Way globular cluster giants and field stars. The discussion concludes by highlighüng how the manganese abundances provide additional insight into chemical evolution within w Cen., The discussion concludes by highlighting how the manganese abundances provide additional insight into chemical evolution within $\omega$ Cen. The initial comparison of w Cen stus with other stellar populations is shown in Figure 4. where the LTE abundance ratios of Ca/Fe and Mn/Fe. computed as A(Ca or Mn) - A(Fe). are shown versus A(Fe). with Ca/Fe plotted in the top panel and Mn/Fe in the bottom panel.," The initial comparison of $\omega$ Cen stars with other stellar populations is shown in Figure 4, where the LTE abundance ratios of Ca/Fe and Mn/Fe, computed as A(Ca or Mn) - A(Fe), are shown versus A(Fe), with Ca/Fe plotted in the top panel and Mn/Fe in the bottom panel." lt is of interest to discuss calcium results first. as Ca is à well-studied a-element whose vields are not expected to be metallicity dependant.," It is of interest to discuss calcium results first, as Ca is a well-studied $\alpha$ -element whose yields are not expected to be metallicity dependant." " The solar values are indicated by (he solar symbols and abundances plotted this way can easily be transformed to values of [Ca/Fe| and (Mn/Fe] by using the absolute solar values Ca). —6.34. A(Mn), =5.43. and A(Fe). —7.45: Asplund et al."," The solar values are indicated by the solar symbols and abundances plotted this way can easily be transformed to values of [Ca/Fe] and [Mn/Fe] by using the absolute solar values $_{\odot}$ =6.34, $_{\odot}$ =5.43, and $_{\odot}$ =7.45; Asplund et al." 2009)., 2009). The Milkv. Way field-star samples are plotted as blue small symbols and are (aken [rom Beddy et al. (, The Milky Way field-star samples are plotted as blue small symbols and are taken from Reddy et al. ( 2003: 2006: open circles): Fulbright (2002: open squares): Johnson (2002: open squares): Cavrel οἱ al. (,2003; 2006; open circles); Fulbright (2002; open squares); Johnson (2002; open squares); Cayrel et al. ( 2004: open triangles) and Alewilliam οἱ al. (,2004; open triangles) and Mcwilliam et al. ( 1995: open pentagons).,1995; open pentagons). We also added the results for metal-rich w Cen stars by Pancino et, We also added the results for metal-rich $\omega$ Cen stars by Pancino et "distribution is the cosmological microwave background with e,=24-10? eV. added to which is a small contribution in the infrared band (Franceschinielal.","distribution is the cosmological microwave background with $\epsilon_0=2.4\cdot 10^{-4}$ eV, added to which is a small contribution in the infrared band \citep{franceschini}." 1998).. The resulting expected 5-rav intensity is plotted in Figure 2 for ¢=1. together with that produced in the outer parts of the Milks-Way. halo at heieht 2>10 kpe where IC scattering off the CAIB is also dominant and the expected differential density of electrons ancl positrous [rom dark-anatter decay is larger than the galactic-plane solution (Eq. 8))," The resulting expected $\gamma$ -ray intensity is plotted in Figure \ref{fig1} for $\zeta=1$, together with that produced in the outer parts of the Milky-Way halo at height $z\ge 10$ kpc where IC scattering off the CMB is also dominant and the expected differential density of electrons and positrons from dark-matter decay is larger than the galactic-plane solution (Eq. \ref{eq6}) )" bv the ratio of (he energv-loss lifetime in (he outer halo to that in the galactic plane., by the ratio of the energy-loss lifetime in the outer halo to that in the galactic plane. Η the excess electrons ancl positrons could freely stream in the outer halo. we would be overestimating their 5-rav emission which contributes at most 1/32 of the total dark-matter signal.," If the excess electrons and positrons could freely stream in the outer halo, we would be overestimating their $\gamma$ -ray emission which contributes at most 1/3 of the total dark-matter signal." However. a number of well-known plasma instabilities would sharply impede such free streaming.," However, a number of well-known plasma instabilities would sharply impede such free streaming." As a LOO-GeV electron has a propagation length of only 15 kpe even if the diffusion coefficient is a 100 times that in the galactic plane. the effect of particle propagation is neglected in deriving Eq. 24..," As a 100-GeV electron has a propagation length of only $\sim$ 15 kpc even if the diffusion coefficient is a 100 times that in the galactic plane, the effect of particle propagation is neglected in deriving Eq. \ref{eq6neu}." At 200 MeV s-rav energy. the predicted intensity is close to that observed with Fermi (Ackermann2009).," At 200 MeV $\gamma$ -ray energy, the predicted intensity is close to that observed with Fermi \citep{ackermann}." . The uncertainty in the measured intensity is typically and predominantly svslematic in origi., The uncertainty in the measured intensity is typically and predominantly systematic in origin. Because the electron/positron density is linear in C. (he predicted +-ray intensity would exceed tlie observational limits if the total magnetic-field in the solar vicinity were stronger (han 10μα.," Because the electron/positron density is linear in $\zeta$, the predicted $\gamma$ -ray intensity would exceed the observational limits if the total magnetic-field in the solar vicinity were stronger than $10\ {\rm \mu G}$." " Ht svould also exceed the observational limits if the characteristic enereyv of the injected. pairs were higher (han 7250 GeV. For comparison. Figure 2 also shows the expected intensity for μας=300GeV to be twice that observed at 200 MeV 5-rüv enerey,"," It would also exceed the observational limits if the characteristic energy of the injected pairs were higher than $\sim$ 250 GeV. For comparison, Figure \ref{fig1} also shows the expected intensity for $E_{\rm max}=300\ {\rm GeV}$ to be twice that observed at 200 MeV $\gamma$ -ray energy." The same scaling with energv μις results for flat injection (οἱ., The same scaling with energy $E_{\rm max}$ results for flat injection (cf. Eqs., Eqs. 9 and 10))., \ref{eq-inj-alt} and \ref{eq6alt}) ). The s-ray peak will appear at slightly lower energv and with somewhat reduced ας compared wilh monoenereelic injection al (he same νε. because the mean particle energy is La./3.," The $\gamma$ -ray peak will appear at slightly lower energy and with somewhat reduced flux compared with monoenergetic injection at the same $E_{\rm max}$, because the mean particle energy is $E_{\rm max}/2$." This is demonstrated as well in Figure 2. where we show (he expected s-rav bump resulting from flat injection up to 300 GeV. re. with characteristic energy 150 GeV. We have investigated 5-ray constraints on the notion (hat dark-matter decay is responsible," This is demonstrated as well in Figure \ref{fig1} where we show the expected $\gamma$ -ray bump resulting from flat injection up to 300 GeV, i.e. with characteristic energy $\sim$ 150 GeV. We have investigated $\gamma$ -ray constraints on the notion that dark-matter decay is responsible" "(Ar«50 kpc and Av<300 km/s) companions to that of a population of non-IR luminous cluster galaxies that has been matched, both in K-band luminosity and radial distance from the cluster center, to the IR luminous sample (excluding in both samples all identified AGNs).","$\Delta r < 50$ kpc and $\Delta v < 300$ km/s) companions to that of a population of non-IR luminous cluster galaxies that has been matched, both in K-band luminosity and radial distance from the cluster center, to the IR luminous sample (excluding in both samples all identified AGNs)." " We find that, while the total sample of IR luminous galaxies is indistinguishable from the matched sample of IR faint galaxies (f.~ vs respectively), the IR bright (log),Lrig> 10.8) 121560galaxies in 10*296,Abell 1835 are marginally more likely to have a close neighbour (f,~3071150 vs 9*3% in the respective matched sample)."," We find that, while the total sample of IR luminous galaxies is indistinguishable from the matched sample of IR faint galaxies $f_c \sim 12^{+8}_{-5}\%$ vs $10^{+2}_{-2}\%$, respectively), the IR bright $\log_{10} L_{\rm TIR} > 10.8$ ) galaxies in Abell 1835 are marginally more likely to have a close neighbour $f_c \sim 30^{+21}_{-16}\% $ vs $9^{+3}_{-2}\%$ in the respective matched sample)." Star formation can be triggered by several different physical processes prevalent in clusters and their infall regions; disentangling these effects is one of the main aims of the LoCuSS key programme., Star formation can be triggered by several different physical processes prevalent in clusters and their infall regions; disentangling these effects is one of the main aims of the LoCuSS key programme. " The most promising candidates, ICM ram pressure, galaxy mergers, and galaxy harassment can all perturb the ISM to produce a new generation of stars, but the relative importance of these processes is a strong function of clustercentric radius FFig."," The most promising candidates, ICM ram pressure, galaxy mergers, and galaxy harassment can all perturb the ISM to produce a new generation of stars, but the relative importance of these processes is a strong function of clustercentric radius Fig." 1 in ?))., 1 in \citet{Smith2010}) ). The location of the peak of IR luminosity density just inside the virial radius of Abell 1835 suggests that merging may be driving the bulk of the star formation in these galaxies., The location of the peak of IR luminosity density just inside the virial radius of Abell 1835 suggests that merging may be driving the bulk of the star formation in these galaxies. " This interpretation is corroborated by the large fraction of disturbed morphologies in the infrared luminous sample, and also by our preliminary analysis of their local environment: when compared to a matched sample of galaxies with no detectable infrared emission, infrared bright galaxies are more likely to have close neighbours, although the larger sample of 30 LoCuSS clusters should be used to confirm this correlation."," This interpretation is corroborated by the large fraction of disturbed morphologies in the infrared luminous sample, and also by our preliminary analysis of their local environment: when compared to a matched sample of galaxies with no detectable infrared emission, infrared bright galaxies are more likely to have close neighbours, although the larger sample of 30 LoCuSS clusters should be used to confirm this correlation." The Lyr density profile for Abell 1835 is not spherically symmetric: the brightest galaxies are clustered together in an elongated structure towards the south of the cluster that is dynamically segregated from the rest of the cluster., The $L_{\rm TIR}$ density profile for Abell 1835 is not spherically symmetric: the brightest galaxies are clustered together in an elongated structure towards the south of the cluster that is dynamically segregated from the rest of the cluster. " The structure’s K-band morphology and velocity gradient toward the cluster core suggests that these galaxies may be embedded within a filament that is still currently feeding the cluster with new, actively star forming galaxies."," The structure's K-band morphology and velocity gradient toward the cluster core suggests that these galaxies may be embedded within a filament that is still currently feeding the cluster with new, actively star forming galaxies." imaging of this field reveals the presence of two groups in the outskirts of Abell 1835 (see contours in Fig., imaging of this field reveals the presence of two groups in the outskirts of Abell 1835 (see contours in Fig. " 1), one of which appears to be embedded in the filament that is also feeding the bright LIRGs into the cluster."," 1), one of which appears to be embedded in the filament that is also feeding the bright LIRGs into the cluster." The group is dominated by a large elliptical galaxy with no detectable emission., The group is dominated by a large elliptical galaxy with no detectable emission. " The two groups have X-ray luminosities of 4.6+0.6 and 7.5+0.8 x10? ergs s! (0.1-2.4 keV), from which we estimate masses, using the weak lensing calibration of the Ly—M relation of ?,, of Moo)=4.3 and 5.8x10?M5 respectively."," The two groups have X-ray luminosities of $4.6\pm0.6$ and $7.5\pm0.8$ $\times10^{42}$ ergs $^{-1}$ (0.1-2.4 keV), from which we estimate masses, using the weak lensing calibration of the $L_X-M$ relation of \citet{Leauthaud2010}, of $M_{200} = 4.3$ and $5.8 \times10^{13} M_\odot$ respectively." " Together these amount to 2 1/10th of the mass of the central cluster, reinforcing the view that 11835 continues to grow by feeding on smaller systems from the surrounding large scale structure."," Together these amount to $\gtrsim$ 1/10th of the mass of the central cluster, reinforcing the view that 1835 continues to grow by feeding on smaller systems from the surrounding large scale structure." second-generation abundance patterns.,second-generation abundance patterns. Theoretical studies of the ICMF. early star cluster mass loss. and the evolution of the cluster mass function (e.g.. Baumgardt et al. 2008:;," Theoretical studies of the ICMF, early star cluster mass loss, and the evolution of the cluster mass function (e.g., Baumgardt et al. ;" Parmentier et al. 2009:;, Parmentier et al. ; Decressin et al. 2010), Decressin et al. ) ) all suggest that far more star clusters were initially. formed than have survived to the present day. especially at the lower end of the ICMF.," all suggest that far more star clusters were initially formed than have survived to the present day, especially at the lower end of the ICMF." The study of ?.. which used matched-filter techniques to search for faint tidal tails around Galactic globular clusters in the SDSS imaging footprint. found stars with cluster-like photometry outside the tidal radit of a number of clusters without pronounced tidal tails. indicating that stars continue to escape from globular clusters even in the absence of dramatic tidal features.," The study of , which used matched-filter techniques to search for faint tidal tails around Galactic globular clusters in the SDSS imaging footprint, found stars with cluster-like photometry outside the tidal radii of a number of clusters without pronounced tidal tails, indicating that stars continue to escape from globular clusters even in the absence of dramatic tidal features." Ir the limit where cluster dissolution is the sole source of second-generation field stars. we can estimate the number of present-day globular clusters that would need to be disrupted to provide the observed 2.5% of halo stars with second-generatiol chemistry. Ng.," In the limit where cluster dissolution is the sole source of second-generation field stars, we can estimate the number of present-day globular clusters that would need to be disrupted to provide the observed $2.5\%$ of halo stars with second-generation chemistry, ${\rm N_{d}}$." For a typical present-day 1:1 ratio of first- to second-generation stars. and assuming a stellar halo mass of 10°M.. (e.g.. Freeman Bland-Hawthorn 2002)) and a typical present-day globular cluster mass of 5x10*M.. Nu=~2xpPh(Ma)Ma100.," For a typical present-day 1:1 ratio of first- to second-generation stars, and assuming a stellar halo mass of $10^{9}{\rm M_{\odot}}$ (e.g., Freeman Bland-Hawthorn ) and a typical present-day globular cluster mass of $5 \times 10^{5} {\rm M_{\odot}}$, ${\rm N_{d}} \simeq \frac{2 \times {\rm f_{h}^{2G}} \times {\rm M_{halo}}}{\langle {\rm M_{gc}} \rangle} \simeq 100$." Since the current number of of globular clusters is on the order of 150. this means that the initial population of globular clusters was significantly larger. but this is not an outrageous claim: calculate that the ratio between the initial and present-day number of globular clusters in the Galaxy is 3/2. whereas we derive 5/3.," Since the current number of of globular clusters is on the order of $150$, this means that the initial population of globular clusters was significantly larger, but this is not an outrageous claim: calculate that the ratio between the initial and present-day number of globular clusters in the Galaxy is $3/2$, whereas we derive $5/3$." Whatever the details. it seems clear that first-generation stars lost from globular clusters at early times are an important contribution to the construction of the Galactic halo. if two-generation self-enrichment scenarios for globular cluster formation are indeed the correct model.," Whatever the details, it seems clear that first-generation stars lost from globular clusters at early times are an important contribution to the construction of the Galactic halo, if two-generation self-enrichment scenarios for globular cluster formation are indeed the correct model." The models of?..?..?.. and all predict that 90% of the first generation ought to be lost from globular clusters at early times. while estimates that as much as 95% of the first generation ought to be lost.," The models of, and all predict that $90\%$ of the first generation ought to be lost from globular clusters at early times, while estimates that as much as $95\%$ of the first generation ought to be lost." The mass of first-generation stars lost during this phase by the Nac globular clusters in the present-day system can be expressed as Mi=Mocwen.XEGo-1).," The mass of first-generation stars lost during this phase by the ${\rm N_{GC}}$ globular clusters in the present-day system can be expressed as ${\rm M_{1G}^{lost}}={\rm M_{GC~system}}\times \frac{1}{2} \times (\frac{1}{1-{\rm f_{lost}}}-1)$." Considering the early contributions of. first-generatior stars from globular clusters that have survived to the present day as well as the clusters that have completely dissolved. we estimate that fex has à minimum value of MSMin!halbeHAvil-xXnth!)3Mace=2%]x(5)+Ey)217% ofnof halo fieldi stars. with both first- and second-generation abundance patterns. originally formed within globular clusters. plus an additional unknown contribution of first-generation stars from clusters too low-mass to self-enrich that have dispersed by the present day.," Considering the early contributions of first-generation stars from globular clusters that have survived to the present day as well as the clusters that have completely dissolved, we estimate that ${\rm f_{h}^{GC}}$ has a minimum value of $\frac{\rm M_{1G}^{lost}}{\rm M_{halo}} + (\frac{\rm N_{d}}{\rm N_{GC}} \times \frac{\rm M_{1G}^{lost}}{\rm M_{halo}}) + {\rm M_{GC~system}} = 2\% \times (\frac{9}{2} + \frac{12}{3}) = 17\%$ of halo field stars, with both first- and second-generation abundance patterns, originally formed within globular clusters, plus an additional unknown contribution of first-generation stars from clusters too low-mass to self-enrich that have dispersed by the present day." Based on the current two-generation models for globular cluster formation. the early phase of globular cluster formation must have contributed à significant number of first-generation stars to the Galactic halo.," Based on the current two-generation models for globular cluster formation, the early phase of globular cluster formation must have contributed a significant number of first-generation stars to the Galactic halo." From the data presented herein. by MGIO. and by?.. it is also clear that second-generation globular cluster stars are a component of the halo field.," From the data presented herein, by MG10, and by, it is also clear that second-generation globular cluster stars are a component of the halo field." Further investigations of the process of globular cluster formation will help to clarify the role that globular clusters played in the early assembly of the Galactic halo., Further investigations of the process of globular cluster formation will help to clarify the role that globular clusters played in the early assembly of the Galactic halo. There are two specific directions that new observations could take that would be particularly insightful: investigating the relationship between the mmimum mass for cluster self-enrichment and the larger galactic environment. and searching for star clusters still in the process of self-enrichment.," There are two specific directions that new observations could take that would be particularly insightful: investigating the relationship between the minimum mass for cluster self-enrichment and the larger galactic environment, and searching for star clusters still in the process of self-enrichment." These studies will necessarily require observations of star clusters outside the Milky Way. as a way to compare cluster formation in different large-scale environments.," These studies will necessarily require observations of star clusters outside the Milky Way, as a way to compare cluster formation in different large-scale environments." Observing very young star clusters may offer the opportunity to see the process of self-enrichment m progress., Observing very young star clusters may offer the opportunity to see the process of self-enrichment in progress. " suggest that clusters in the process of violent relaxation (at a few x10"" years old) should have a central compact cluster. an extended. non-bound halo and outflowing gas."," suggest that clusters in the process of violent relaxation (at a few $\times 10^{7}$ years old) should have a central compact cluster, an extended, non-bound halo and outflowing gas." It is suggested in that the extended clusters discovered in M31 by are in this state (see also Huxor et al. 2011)., It is suggested in that the extended clusters discovered in M31 by are in this state (see also Huxor et al. ). If this is the case. the stars at large radius 1n the extended clusters should have almost entirely first-generation chemistry. and strong radial gradients in light-element abundances. most readily observable in CN and CH molecular features. should be present.," If this is the case, the stars at large radius in the extended clusters should have almost entirely first-generation chemistry, and strong radial gradients in light-element abundances, most readily observable in CN and CH molecular features, should be present." To explore the question of the minimum cluster mass for self-enrichment. it would be useful to consider star clusters in lower-mass galaxies.," To explore the question of the minimum cluster mass for self-enrichment, it would be useful to consider star clusters in lower-mass galaxies." claim that the weaker tidal field of the Large Magellanic Cloud (LMC) ought to permit the formation of a second stellar generation at lower cluster mass than in the Milky Way., claim that the weaker tidal field of the Large Magellanic Cloud (LMC) ought to permit the formation of a second stellar generation at lower cluster mass than in the Milky Way. Spectroscopic observations of red giant-branch stars in intermediate-age populous clusters m the LMC would be particularly interesting because recent photometric work (e.g.. Mackey et al.2," Spectroscopic observations of red giant-branch stars in intermediate-age populous clusters in the LMC would be particularly interesting because recent photometric work (e.g., Mackey et al.;" 008:: Milone et al.2, Milone et al.; 009:: Goudfrooi] et al. 2011), Goudfrooij et al. ) ) has uncovered broadened or split main-sequence turnoffs in a large fraction of them., has uncovered broadened or split main-sequence turnoffs in a large fraction of them. Since they are much younger than Galactic globular clusters (typically 1-4 Gyr). age differences on the order of a few hundred million years are visible at the turnoff. and this age difference is suggestively similar to the age difference expected between first- and second-generation stars in Galactic globular clusters.," Since they are much younger than Galactic globular clusters (typically $1$ $4$ Gyr), age differences on the order of a few hundred million years are visible at the turnoff, and this age difference is suggestively similar to the age difference expected between first- and second-generation stars in Galactic globular clusters." Obtaining spectra of turnoff stars at the distance of the LMC would be extremely difficult — indeed. high-resolution spectroscopic studies of RGB stars in these clusters are limited to fairly small samples (e.g.. Mucctarelli et al. 2008)).," Obtaining spectra of turnoff stars at the distance of the LMC would be extremely difficult – indeed, high-resolution spectroscopic studies of RGB stars in these clusters are limited to fairly small samples (e.g., Mucciarelli et al. )." However. a lower-resolution study using a multiobject spectrograph could collect CN and CH data analogous to the data presented in this paper. anc would allow a search for star-to-star variations in carbon and nitrogen abundance for a larger data set per cluster.," However, a lower-resolution study using a multiobject spectrograph could collect CN and CH data analogous to the data presented in this paper, and would allow a search for star-to-star variations in carbon and nitrogen abundance for a larger data set per cluster." A modified version of the SSPP has been developed for application to spectra with resolving power as low as R~ 1000) and is already being used with a variety of low-resolutiot data from on-SDSS sources (e.g.. see Li et al.2," A modified version of the SSPP has been developed for application to spectra with resolving power as low as $R \sim 1000$ ), and is already being used with a variety of low-resolution data from non-SDSS sources (e.g., see Li et al.;" 010:: Humphreys et al 2011)., Humphreys et al ). These data would also permit an investigation of theoretical claims (e.g.. Conroy Spergel 2011)) that lower-mass galaxies permit the formation of multiple stellar generations in lower-mass star. clusters. by comparing the CN-CH behavior of intermediate-age LMC clusters across a range of masses.," These data would also permit an investigation of theoretical claims (e.g., Conroy Spergel ) that lower-mass galaxies permit the formation of multiple stellar generations in lower-mass star clusters, by comparing the CN-CH behavior of intermediate-age LMC clusters across a range of masses." showed |ow the star formation rate varies with local galaxy density. varies with position ina galaxy. and studied the mean star formatioi rate.,"showed how the star formation rate varies with local galaxy density, varies with position in a galaxy, and studied the mean star formation rate." The pixel-z method does uot iuclude any sinootLine techuiques., The pixel-z method does not include any smoothing techniques. This current work will be complementary to that work. by providing a sinootLine techuique that will minimize the efect data noise will have on the best-[it stelar population paranjeters.," This current work will be complementary to that work, by providing a smoothing technique that will minimize the effect data noise will have on the best-fit stellar population parameters." Adaptsmoot1 (Zibetti.Charlot.Rix2009) isa multi-waveleugth smoothing algoritlun tha is similar to this work., Adaptsmooth \citep{zib09} is a multi-wavelength smoothing algorithm that is similar to this work. Adaptsimooth uses a circulalv symunetric radial median to 'educe noise., Adaptsmooth uses a circularly symmetric radial median to reduce noise. The 'adius of the circe is defined so that inedian sicothed data bas a signal-to-noise of 20., The radius of the circle is defined so that median smoothed data has a signal-to-noise of 20. All of he luaeine waveleneth data (Le. wgric-bands) are snoothed to the same radius. wlich is deermined ron the maxim.u radius of the multi-wavelenet1 data in question. which is usudly the vw- bau Or z-band ii SDSS data as they have the lowest signal-to-noise.," All of the imaging wavelength data (i.e. $ugriz$ -bands) are smoothed to the same radius, which is determined from the maximum radius of the multi-wavelength data in question, which is usually the $u$ -band or $z$ -band in SDSS data as they have the lowest signal-to-noise." Adaptsmooth is adadive. iu he seise hat the dius varies with position in tlie galaxy. as the sigual-to-noise varies.," Adaptsmooth is adaptive, in the sense that the radius varies with position in the galaxy, as the signal-to-noise varies." However. t10 Facial nediau filter is still azimuthally syiumetric.," However, the radial median filter is still azimuthally symmetric." This meaus that blue star fornation regions cai get nedian fiΠοιος together with redder disk., This means that blue star formation regions can get median filtered together with redder disk. " Tve PCA-smoothing method p""'éselled iu this paper. nedian filte‘s over pixels that are associated in PCA space according to their color."," The PCA-smoothing method presented in this paper, median filters over pixels that are associated in PCA space according to their color." We Us OU SDSS because it is a large auc| uniform clata-set., We focus on SDSS because it is a large and uniform data-set. SDSS las Coverage over of the sky. where the imagine data covers a arge range of optical waveeneths. aud does so in a titeUn Wahler.," SDSS has coverage over of the sky, where the imaging data covers a large range of optical wavelengths, and does so in a uniform manner." The distribution of galaxy sroperties has been well sticaied for SDSS data sets (Blawouetal.2003)., The distribution of galaxy properties has been well studied for SDSS data sets \citep{bla03}. . Many semi-analytic models have been constrained =Sine SDSS data 2007 )..," Many semi-analytic models have been constrained using SDSS data \citep{gne07,li07}." Iu the following paper the tecluique is described in Section 2. a comyarison to other methocs is done in Section 3. case studies are presented in Section {. aud the conclusion is presented iu Section 5.," In the following paper the technique is described in Section 2, a comparison to other methods is done in Section 3, case studies are presented in Section 4, and the conclusion is presented in Section 5." The goal of ilis ruethod is to smooth data without mixine cdillerent coors., The goal of this method is to smooth data without mixing different colors. For examp e.a simple racial siu0hing method may mix a red bulge with a blue star formit[n]0 region. which will result iu poorly fit stellar population models.," For example, a simple radial smoothing method may mix a red bulge with a blue star forming region, which will result in poorly fit stellar population models." The method must be automated so that it caji be applied to large «la aosels. sich as the SDSS. iux| not have input parameters hat vary withit the data-set.," The method must be automated so that it can be applied to large data sets, such as the SDSS, and not have input parameters that vary within the data-set." Siu'e the οίκο Characteristics nay vary amone clillerent data sets (i.e. SDSS vs. 2MLASS). the inethod must also have tunable paraneters.," Since the noise characteristics may vary among different data sets (i.e. SDSS vs. 2MASS), the method must also have tunable parameters." It is shown below that au advauage of this 1Jehod is that it is not ove‘ly sensitive to the iput parameters., It is shown below that an advantage of this method is that it is not overly sensitive to the input parameters. Tle Inehod presented rere uses Principal Component Analysis (hereafter PCA) in oder to quautitatively associate pixels according o their color., The method presented here uses Principal Component Analysis (hereafter PCA) in order to quantitatively associate pixels according to their color. PCA can be used to reduce the dimensionality of data. illuminate hidden correlatious. uantily levels of proportionality. and rotate data iuto Lew axes.," PCA can be used to reduce the dimensionality of data, illuminate hidden correlations, quantify levels of proportionality, and rotate data into new axes." PCA las beet usecl in inany different. areas of data analysis. aud has been described ii detail iu other papers tIng it as an analysis ool for astronomical spectra," PCA has been used in many different areas of data analysis, and has been described in detail in other papers using it as an analysis tool for astronomical spectra" star a Ara.,star $\alpha$ Ara. " The ""S"" shape of the phase variation and the “W” shape of some visibility variations clearly favor the hypothesis that the circumstellar environment velocity field is dominated by rotation.", The “S” shape of the phase variation and the “W” shape of some visibility variations clearly favor the hypothesis that the circumstellar environment velocity field is dominated by rotation. " Using either differential visibility or phase, we can roughly determine the major-axis position angle in the plane of the sky for a purely rotating disk knowing that: Thus, both the phase and visibility variations through the observed lines favor the hypothesis of a major-axis roughly in the North-South orientation."," Using either differential visibility or phase, we can roughly determine the major-axis position angle in the plane of the sky for a purely rotating disk knowing that: Thus, both the phase and visibility variations through the observed lines favor the hypothesis of a major-axis roughly in the North-South orientation." " To model the wavelength dependence of the visibility, the differential phase, and the closure phase in the observed emission lines we use a simple kinematic model developed for fast model fitting of an expanding and/or rotating thin equatorial disk."," To model the wavelength dependence of the visibility, the differential phase, and the closure phase in the observed emission lines we use a simple kinematic model developed for fast model fitting of an expanding and/or rotating thin equatorial disk." This model is described in detail in Delaa et al. (, This model is described in detail in Delaa et al. ( 2011).,2011). " The star is modeled as a uniform disk, the envelope emission in the continuum and the emission line has an elliptical Gaussian distribution with a flattening due to a projection effect of the geometrically thin equatorial disk, i.e., f=l/cos(i), where i the the object inclination angle."," The star is modeled as a uniform disk, the envelope emission in the continuum and the emission line has an elliptical Gaussian distribution with a flattening due to a projection effect of the geometrically thin equatorial disk, i.e., $f = 1/cos(i)$, where i the the object inclination angle." The radial and azimuthal velocities are given by: For each spectral channel in the line an iso-velocity map projected along the line of sight is then calculated and multiplied by the whole emission map in the line., The radial and azimuthal velocities are given by: For each spectral channel in the line an iso-velocity map projected along the line of sight is then calculated and multiplied by the whole emission map in the line. " Finally the whole emission map for each wavelength consists of the weighted sum of the stellar map, the disk continuum map and the emission line map within the spectral channel under consideration."," Finally the whole emission map for each wavelength consists of the weighted sum of the stellar map, the disk continuum map and the emission line map within the spectral channel under consideration." " The map is then rotated by the major-axis PA, and scaled using the stellar radius and distance."," The map is then rotated by the major-axis PA, and scaled using the stellar radius and distance." A 256x256x100 data-cube (i.e. 256x256 for 100 wavelengths) can be computed in less than one second on a standard computer., A 256x256x100 data-cube (i.e. 256x256 for 100 wavelengths) can be computed in less than one second on a standard computer. " Finally, visibilities, differential phases, and closure phases are extracted using two-dimensional fast-Fourier transforms (FFT)."," Finally, visibilities, differential phases, and closure phases are extracted using two-dimensional fast-Fourier transforms (FFT)." We note that the pixel size was set to avoid sampling problems., We note that the pixel size was set to avoid sampling problems. " The model free-parameters can be classified into 4 categories: Consequently, for simultaneous fit of these three emission lines, we need a model with a total of 15 free parameters."," The model free-parameters can be classified into 4 categories: Consequently, for simultaneous fit of these three emission lines, we need a model with a total of 15 free parameters." " To reduce the number of free parameters we have finally decided: Moreover, the lines EW are easily and efficiently constrained by the spectra plotted in Fig [] except for the VEGA/CHARA Ha line for which the intensity is underestimated by a factor 2-3 due to a saturation of the photon counting algorithm that is affecting the line EW but not the corresponding visibilities, as already outlined in Delaaet al. ("," To reduce the number of free parameters we have finally decided: Moreover, the lines EW are easily and efficiently constrained by the spectra plotted in Fig \ref{lines} except for the VEGA/CHARA $\alpha$ line for which the intensity is underestimated by a factor 2-3 due to a saturation of the photon counting algorithm that is affecting the line EW but not the corresponding visibilities, as already outlined in Delaaet al. (" 2010).,2010). " Thus the ""true"" Ha line profile used to compute the EW was taken from the BeSS where we found spectra recorded at the same epoch as our interferometric VEGA/CHARA measurements."," Thus the ""true"" $\alpha$ line profile used to compute the EW was taken from the BeSS where we found spectra recorded at the same epoch as our interferometric VEGA/CHARA measurements." " Finally, running hundreds of models, we tried to constrain the nine remaining free parameters."," Finally, running hundreds of models, we tried to constrain the nine remaining free parameters." Values of the best-fit model parameters are presented in Table]., Values of the best-fit model parameters are presented in Table \ref{model_params}. . The corresponding differential visibilities, The corresponding differential visibilities where Ar;jy; is the modeled time delay from equation (8)). Atijobs Is the observed time delay for a particular system. and TEM is the error in that observed time delay.,"where $\Delta t_{i,j, Mod}$ is the modeled time delay from equation \ref{equ:timedelayab}) ), $\Delta t_{i,j, Obs}$ is the observed time delay for a particular system, and $\sigma_{Obs}^{2}$ is the error in that observed time delay." This process allows us to build up a grid of y values in a 2-D plane of Ho and η., This process allows us to build up a grid of $\chi^{2}$ values in a 2-D plane of $H_{0}$ and $\eta$. As an additional constraint. we add in a gaussian prior to expression (10)) based on the HST Key Project value Hy = 72r 8kms ! Mpe*: One can then relate these y values to confidence levels based upon the number of degrees of freedom.," As an additional constraint, we add in a gaussian prior to expression \ref{equ:chi}) ) based on the HST Key Project value $H_{0}$ = 72 $\pm$ 8 km $^{-1}$ $^{-1}$: One can then relate these $\chi^{2}$ values to confidence levels based upon the number of degrees of freedom." " Note that when dealing with a single time delay there is 1 data point (Nj, = 1) and 2 free parameters (Vy, = 2). and hence the number of degrees of freedom are -1 (since Nj,;-2N4,-N 5)."," Note that when dealing with a single time delay there is 1 data point $N_{dp}$ = 1) and 2 free parameters $N_{fp}$ = 2), and hence the number of degrees of freedom are -1 (since $N_{dof}$ $N_{dp}$ $N_{fp}$ )." This means that the problem is under-constrained in this instance., This means that the problem is under-constrained in this instance. Despite the 1clusion of the HST A prior. there exists a notable degeneracy in the Hp - jj plane and we highlight this in for the time delay PG1115+080 (A-B).," Despite the inclusion of the HST $H_{0}$ prior, there exists a notable degeneracy in the $H_{0}$ - $\eta$ plane and we highlight this in \\ref{plot2} for the time delay PG1115+080 (A-B)." The direction of the degeneracy ts such that the time delay data are consistent with a range of more (less) centrally concentrated mass distributions and higher (lower) values for Πο., The direction of the degeneracy is such that the time delay data are consistent with a range of more (less) centrally concentrated mass distributions and higher (lower) values for $H_{0}$. We include the best fit 7 and corresponding Io error for all the systems included m our sample (see Table 2)., We include the best fit $\eta$ and corresponding $\sigma$ error for all the systems included in our sample (see Table 2). The result of combining the constraints from all 14 time delays. including the HST Ho prior. is shown in refplot3..," The result of combining the constraints from all 14 time delays, including the HST $H_{0}$ prior, is shown in \\ref{plot3}. ." Since we have a total of 14 data points and 2 free parameters. there are 12 degrees of freedom.," Since we have a total of 14 data points and 2 free parameters, there are 12 degrees of freedom." The overall reduced y for the data displayed in refplot3 is Vou=49.1., The overall reduced $\chi^{2}$ for the data displayed in \\ref{plot3} is $\chi^{2}_{\rm red} = 49.1$. Such a high value for a combination of all the data reflects the simplified lens model. and the lack of a common density profile slope (1.9. that galaxies have a range of slopes for their profiles).," Such a high value for a combination of all the data reflects the simplified lens model, and the lack of a common density profile slope (i.e. that galaxies have a range of slopes for their profiles)." The extent of the contours is greatly reduced over that of refplot2.. thus providing bounds on η.," The extent of the contours is greatly reduced over that of \\ref{plot2}, thus providing bounds on $\eta$." The best fit density profile slope is 7 = 2.1140.12 (3c)., The best fit density profile slope is $\eta$ = $\pm0.12$ $\sigma$ ). If instead we exclude redundant time delays from our sample based on the largest fractional error rather than absolute error. we obtain the same result.," If instead we exclude redundant time delays from our sample based on the largest fractional error rather than absolute error, we obtain the same result." This 15 also the case 1f we include every time delay. not excluding any which could be derived from the others.," This is also the case if we include every time delay, not excluding any which could be derived from the others." The selection of our sample described in Section 4 above means that these results are relevant to lens systems in which there ts a single primary lens - in other words to galaxies which are not undergoing mergers. or in very dense environments.," The selection of our sample described in Section 4 above means that these results are relevant to lens systems in which there is a single primary lens - in other words to galaxies which are not undergoing mergers, or in very dense environments." Probing the density profiles of galaxies in complex environments requires detailed modeling to account for external perturbers., Probing the density profiles of galaxies in complex environments requires detailed modeling to account for external perturbers. Note also that our error bars are formal errors from. the calculations. and do not address the systematics of sample selection or simplifications in modeling.," Note also that our error bars are formal errors from the calculations, and do not address the systematics of sample selection or simplifications in modeling." When the data are separated into time delays resulting from quad image systems and doubles. then from the 7 time delays coming from each we obtain 7 = 1.7940.15 (3c) and η = 2.23+40.2 (307) respectively.," When the data are separated into time delays resulting from quad image systems and doubles, then from the 7 time delays coming from each we obtain $\eta$ = $\pm0.15$ $\sigma$ ) and $\eta$ = $\pm0.2$ $\sigma$ ) respectively." When considering just the four systems PGI115-080. SBS1520+530. B1600+434. and HE2149-2745. before application of the prior on the Hubble constant. we find a steeper best fit slope than for the remainder of the sample. in keeping with Kochanek (2002).," When considering just the four systems PG1115+080, SBS1520+530, B1600+434, and HE2149-2745, before application of the prior on the Hubble constant, we find a steeper best fit slope than for the remainder of the sample, in keeping with Kochanek (2002)." Kochanek et al. (, Kochanek et al. ( 2006) note that this may well be due to the environment of the lensing galaxies (e.g. halo stripping of group satellite galaxies).,2006) note that this may well be due to the environment of the lensing galaxies (e.g. halo stripping of group satellite galaxies). Indeed. other authors have noted that lens galaxy environments could potentially have a great impact on halo profiles (Dalal Watson 2004; Keeton Zabludotf 2004).," Indeed, other authors have noted that lens galaxy environments could potentially have a great impact on halo profiles (Dalal Watson 2004; Keeton Zabludoff 2004)." This also suggests that the profile slopes of the other systemswe have excluded, This also suggests that the profile slopes of the other systemswe have excluded these two functions.,these two functions. As an additional coustraiut we generate ouly augles greater than 0;=0.01rad., As an additional constraint we generate only angles greater than $\theta_{\rm j} = 0.01 ~\rm rad$. Another parameter in the simulation is the observational angle Oo... which is distributed nifonaulv between 0 and x (due to jet bimodality).," Another parameter in the simulation is the observational angle $\theta_{\rm obs}$, which is distributed uniformly between 0 and $\pi$ (due to jet bimodality)." Tere. we preseut results for both parts of the simulation.," Here, we present results for both parts of the simulation." All results are given for a time period of five vears. which is the expected operational time of Gata," All results are given for a time period of five years, which is the expected operational time of $\textit{Gaia}$." Al results are averaged OVCT 1000 and 10 siauulatious for on-axis aud OA. respectively.," All results are averaged over 1000 and 100 simulations for on-axis and OA, respectively." Figure 5. shows the number of GRB optical terelossdetected by Geiaiu five vears depending ou the value of Guias limiting magnitude., Figure \ref{fig5} shows the number of GRB optical afterglows detected by $\textit{Gaia}$ in five years depending on the value of $\textit{Gaia}$ 's limiting magnitude. Results or the case of the on-axis simulation are nof very promising., Results for the case of the on-axis simulation are not very promising. In the nominal Gora Ag=20 nae. we can expect to see less than 10 on-axis afterelows in five vears.," In the nominal $\textit{Gaia}$ $M_{\rm lim} = 20$ mag, we can expect to see less than 10 on-axis afterglows in five years." " Possible detection of OAs Is more pronusing: with Aj,=20 mae. we expect o detect several teus of OAs in five vears."," Possible detection of OAs is more promising: with $M_{\rm lim} = 20$ mag, we expect to detect several tens of OAs in five years." The atter is actually an upper limit: possible light extinction iu the line of sight iu the Galaxy aud GRD host galaxies (Schadyetal.2010). has not σοι included in the calculation of the OAs’ light curves., The latter is actually an upper limit: possible light extinction in the line of sight in the Galaxy and GRB host galaxies \citep{schady} has not been included in the calculation of the OAs' light curves. The results of the ou-axis simulation. which is based on observational data. already include the extinction effect.," The results of the on-axis simulation, which is based on observational data, already include the extinction effect." Also (aud this applies to both on-axis and OAs). the simulation was done for the case of the regular Joliusou-C'ousins Ro maguitude (Bessell1990)... while the Gate G magnitude is obtained with a filter of a much wider passhand (Jordietal. 2010)..," Also (and this applies to both on-axis and OAs), the simulation was done for the case of the regular Johnson-Cousins $R$ magnitude \citep{bessel}, while the $\textit{Gaia}$ $G$ magnitude is obtained with a filter of a much wider passband \citep{jordi}. ." This results in an overall slightly fainter limiting magnitude., This results in an overall slightly fainter limiting magnitude. " IIereafter. all results are given for Mj,=20."," Hereafter, all results are given for $M_{\rm lim} = 20$." For the on-axis case. the distribution of initia maenitudes of optical afterglows. which were etected by (at least) one of the Cure telescopes. is given in Fieure 6 (left).," For the on-axis case, the distribution of initial magnitudes of optical afterglows, which were detected by (at least) one of the $\textit{Gaia}$ telescopes, is given in Figure \ref{fig6} (left)." It is a norma istribution with the mean value 13.5 mae., It is a normal distribution with the mean value $\sim 13.5$ mag. " This was expected. since the afterelows with brighter oeutial maenitudes are more likely to be detecte their fj, is longer)."," This was expected, since the afterglows with brighter initial magnitudes are more likely to be detected (their $t_{\rm lim}$ is longer)." It is interesting to see the istribution of maeuitudes at the time of their first ctection (οταν distribution in Figure 6))., It is interesting to see the distribution of magnitudes at the time of their first detection (gray distribution in Figure \ref{fig6}) ). Since +he majority of detected afterelows are already uite faint. we cannot expect many of them to )e detected by the second. telescope.," Since the majority of detected afterglows are already quite faint, we cannot expect many of them to be detected by the second telescope." Tudeed. the istribution of twice-detected afterelows showu in Figure 6 in red tells us that. eiven the stall nuuber of detectious with one telescope. the probability to detect an afterglow with both telescopes is low.," Indeed, the distribution of twice-detected afterglows shown in Figure \ref{fig6} in red tells us that, given the small number of detections with one telescope, the probability to detect an afterglow with both telescopes is low." A similar ot was made for the OA simmlation and is shown in Figure 6 (right)., A similar plot was made for the OA simulation and is shown in Figure \ref{fig6} (right). The distribution of uaenitudes iu the case of pj=0.1cu5m js no eiven here. since it strongly resembles that of 7=1.0cm? (but with the lower umberof detections).," The distribution of magnitudes in the case of $n = 0.1 \rm ~cm^{-3}$ is not given here, since it strongly resembles that of $n = 1.0 \rm ~cm^{-3}$ (but with the lower numberof detections)." The fraction of twice-detected OAs is larger here., The fraction of twice-detected OAs is larger here. The decay in, The decay in The computation ofEy can most easily be done in Fourier space because of (he pressure term.,The computation of${\bf E}_1$ can most easily be done in Fourier space because of the pressure term. Thus. we write the equation for the velocity in Fourier space and then plug it into the electromotive lorce expression to obtain:dpJ[dqE p)hButqbk +0.," Thus, we write the equation for the velocity in Fourier space and then plug it into the electromotive force expression to obtain: ) +." "MA""A- To compute £44. we assume (hat the statistics of small scale magnetic fields is homogeneous and isotropic but not necessarily invariant under plane reflection. with the following correlation [unction: I)e ies where A/(/') is (he magnetic energv spectrin tensor and F(A) is (he magnetic helicity spectrum tensor."," To compute $E_{1\alpha}$, we assume that the statistics of small scale magnetic fields is homogeneous and isotropic but not necessarily invariant under plane reflection, with the following correlation function: ^2) + i , where $M(k)$ is the magnetic energy spectrum tensor and $F(k)$ is the magnetic helicity spectrum tensor." By using ((3)) in (26)) and by keeping terms up to & (stretching and diffusion term). we obtain: Duk) m - p) (8," By using \ref{StatB}) ) in \ref{EFourier}) ) and by keeping terms up to $k$ (stretching and diffusion term), we obtain: ) - - ) +." ") since all integrals with odd numbers of p; vanish. £4, reduces to: PED.[pK04 +ifdp ο. — Ρλ))) ⋅"," Since all integrals with odd numbers of $p_i$ vanish, $E_{1\alpha}$ reduces to: /p^2) + i - - )] ." ⋅ The first part (proportional to). contvibuting to ο. vanishes when integrated over angles. while the second. part gives the correction term to a due to back reaction.," The first part (proportional to $k_\mu$ ), contributing to $\beta$, vanishes when integrated over angles, while the second part gives the correction term to $\alpha$ due to back reaction." Thus. (here is no change in 2. namely.drift! This result sharply contrasts to the Claim made in the literature. based on strong coupling approximation. (hat bipolar αν! enhances the diffusion of à mean magnetic field in 3D (e.g..Subramanian 1993)..," Thus, there is no change in $\beta$, namely, This result sharply contrasts to the claim made in the literature, based on strong coupling approximation, that ambipolar drift enhances the diffusion of a mean magnetic field in 3D \citep[e.g.,][]{Subramanian98}. ." Note thatthe result for fully ionized gas(Gruzinov&Diamond1996) is recovered simply by taking," Note thatthe result for fully ionized gas\citep{Gruzinov96} is recovered simply by taking" of the clwark with a resultant best fit rotational velocity of TGcl2kms5 this rotation curve is overplotted as a solid line in Figure 6 as well as two additional fiducial rotation curves of 0 and Skims.1.,"of the dwarf, with a resultant best fit rotational velocity of $7.7\pm1.2 {\rm km\ s^{-1}}$; this rotation curve is overplotted as a solid line in Figure \ref{fig6} as well as two additional fiducial rotation curves of 0 and ${\rm km\ s^{-1}}$." " ""Ehe dotted line represents a linear mocel. representing solid body rotation. with a best fit of .1""n −≽⋅⋅↱≻∶∶∪⋅≟↳⊔↓⊳∖⋜⋯∼⊔∐⊔⊳↓⊔↓⋅⋖⊾⊔↓∪∖⇁↓"," The dotted line represents a linear model, representing solid body rotation, with a best fit of $2.5\pm0.4{\rm km\ s^{-1} arcmin^{-1}}$." ⊔⋏∙≟↿↓⊔⋅⊳∖↓⋏∙≟⊔⋜∐⊔↓⋅⋖⋅∪⇂↿↓↥⋖⊾. . ⋅ best fit constant rotation velocity. the velocity. dispersion within the inner 5 aremins falls to 148 kms with a do clipping). and to 8S kms when applving a more stringent 26 clipping.," In removing the signature of the best fit constant rotation velocity, the velocity dispersion within the inner 5 arcmins falls to 14 ${\rm km\ s^{-1}}$ with a $\sigma$ clipping), and to 8 ${\rm km\ s^{-1}}$ when applying a more stringent $\sigma$ clipping." Hence. i£ real. the rotation of Cetus represents a significant kinematic component in this svstenm.," Hence, if real, the rotation of Cetus represents a significant kinematic component in this system." As noted. previously. Cetus is one of only two isolated dSph galaxies in the Local Group.," As noted previously, Cetus is one of only two isolated dSph galaxies in the Local Group." Hence. measurement of its heliocentric velocity. provides a vital constraint on its orbit through the Local Group. under reasonable assumptions about its proper motion and the mass distribution of the Local Croup.," Hence, measurement of its heliocentric velocity provides a vital constraint on its orbit through the Local Group, under reasonable assumptions about its proper motion and the mass distribution of the Local Group." In estimating the Local Group velocity. ey. of Cetus. the first step involves transforming its heliocentric velocity into a galactocentric radial velocity. finding 25 ," In estimating the Local Group velocity, $v_{lg}$, of Cetus, the first step involves transforming its heliocentric velocity into a galactocentric radial velocity, finding $v_g = -25$ $^{-1}$." tot is assumed that the Milky Way ancl MAI account for all the mass of the Local Croup. and that their mass ratio is e=1.," It is assumed that the Milky Way and M31 account for all the mass of the Local Group, and that their mass ratio is $a = 1$." Einasto&Lynelen-Bell(1982). present arguments which suggest that the total angular momentunir of the Local Group is close to zero. which requires that these two galaxies are on à nearly racial orbit with respect to one another.," \citet{1982MNRAS.199...67E} present arguments which suggest that the total angular momentum of the Local Group is close to zero, which requires that these two galaxies are on a nearly radial orbit with respect to one another." " Hf Cetus is on a purely radial orbit with respect to the centre of mass of the Local Group then its racial velocity. ery. is constrained. by where Bois the unit vector in the direction of Cetus and v,,, is the Local Group. velocity of the Milkv Way (Cus=Gl5kkmss + fora= 1)."," If Cetus is on a purely radial orbit with respect to the centre of mass of the Local Group then its radial velocity, $v_{lg}$ , is constrained by where $\mathbf{\hat{r}}$ is the unit vector in the direction of Cetus and $\mathbf{v}_{mw}$ is the Local Group velocity of the Milky Way $v_{mw} = -61.5$ $^{-1}$ for $a = 1$ )." " M it is assumed. that Cetus is moving racially away from the center of the Local Group then cj,=14 sslat a barvcentric distance of 602 kkpe."," If it is assumed that Cetus is moving radially away from the center of the Local Group then $v_{lg} = 14$ $^{-1}$, at a barycentric distance of $602$ kpc." Figure 7. shows the Local Group. velocity. of Cetus plotted against its barveentric distance., Figure \ref{fig7} shows the Local Group velocity of Cetus plotted against its barycentric distance. Also shown as red open circles are other candidate isolated Local Group dwarl galaxies. while blue open squares represent. ealaxies belonging to other nearby. groups.," Also shown as red open circles are other candidate isolated Local Group dwarf galaxies, while blue open squares represent galaxies belonging to other nearby groups." Magenta and green solic circles represent cwarf galaxies which are satellites of M31 and the Milkv Way. respectively.," Magenta and green solid circles represent dwarf galaxies which are satellites of M31 and the Milky Way, respectively." For these galaxies. the approximation that their dvnamics are governed by the ne Local Group potential is not valid. and so the velocities derived. will not be with respect to the Local Group centre of mass.," For these galaxies, the approximation that their dynamics are governed by the net Local Group potential is not valid, and so the velocities derived will not be with respect to the Local Group centre of mass." The dot-dashed. line represents the apocentre of orbits in the Local Coup and the clashed curves represen the maximum distance that a galaxy could reach given its current velocity. for a total Local Group mass of 2.3 and 4LOMAL. (inner to outer curves).," The dot-dashed line represents the apocentre of orbits in the Local Group and the dashed curves represent the maximum distance that a galaxy could reach given its current velocity for a total Local Group mass of $2, 3$ and $4 \times 10^{12}M_\odot$ (inner to outer curves)." The solid curves represent the escape velocity of the Local Group for these masses., The solid curves represent the escape velocity of the Local Group for these masses. Thus galaxies which are above the top set of solid ines or below the bottom set of solid lines cannot be bound o theLocal Group., Thus galaxies which are above the top set of solid lines or below the bottom set of solid lines cannot be bound to theLocal Group. Likewise. galaxies to the right of the dashed: curves would. not. have. been able to reach their »xosition if they. are Local Croup members (Irwin.1999)..," Likewise, galaxies to the right of the dashed curves would not have been able to reach their position if they are Local Group members \citep{1999IAUS..192..409I}." Several interesting results are immediately apparent in Figure 7:5 Cetus is close to the apocentre of its orbit. in he Local Group. while the other isolated dSph. Tucana. is similarly at apocentre. along with the Sagittarius clrr anc he transition galaxy Aquarius (DDO210).," Several interesting results are immediately apparent in Figure \ref{fig7}; Cetus is close to the apocentre of its orbit in the Local Group, while the other isolated dSph, Tucana, is similarly at apocentre, along with the Sagittarius dIrr and the transition galaxy Aquarius (DDO210)." The Sagittarius dier. and Aquarius can only have reaching their current »ositions if the mass of the Local Group is 210A1.. and they are on very racial orbits.," The Sagittarius dIrr and Aquarius can only have reaching their current positions if the mass of the Local Group is $\gta 2 \times 10^{12}M_\odot$, and they are on very radial orbits." There is some overlap in this plot between Local Group galaxies and members of nearby groups. which reflects the well known result. that their are no distinct. boundaries between the hundred. or so groups which form the Local Supercluster.," There is some overlap in this plot between Local Group galaxies and members of nearby groups, which reflects the well known result that their are no distinct boundaries between the hundred or so groups which form the Local Supercluster." Particularly. the Seulptor group Joins with the Local Group via a bridge of galaxies including NGC55. UIS82323-326 and 1€5152.," Particularly, the Sculptor group joins with the Local Group via a bridge of galaxies including NGC55, UKS2323-326 and IC5152." Sextans A.B. Xntlia and NCO3109 form a distinct erouping in the sky (the λές2100 eroup).," Sextans A, B, Antlia and NGC3109 form a distinct grouping in the sky (the NGC3109 group)." Figure 7. shows that they are dynamically. distinct. from. other Local Group galaxies and that they can only be bound to the Local Group if its miss is a4107A4., Figure \ref{fig7} shows that they are dynamically distinct from other Local Group galaxies and that they can only be bound to the Local Group if its mass is $\gta 4 \times 10^{12}M_\odot$. This paper has presented. a study of. the Cetus dwarf galaxy. utilizing. a matched. filter. analysis of the INTP/WEC observations of Cetus dwarf galaxy presented bv MeConnachieetal.(2005)...," This paper has presented a study of the Cetus dwarf galaxy, utilizing a matched filter analysis of the INT/WFC observations of Cetus dwarf galaxy presented by \citet{2005MNRAS.356..979M}." Phe results of this analvsis. however. suggests that Cetus does not possess the extra-tidal stars indicative of any significant interaction in the past.," The results of this analysis, however, suggests that Cetus does not possess the extra-tidal stars indicative of any significant interaction in the past." Ilence. it can be concluded that Cetus truly does represent a lonely and isolated member of the Local Group.," Hence, it can be concluded that Cetus truly does represent a lonely and isolated member of the Local Group." In addition. this paper has presented. a spectroscopic survey of the Cetus dwarf. utilizing a kinematic survey to study its dyvnamical properties.," In addition, this paper has presented a spectroscopic survey of the Cetus dwarf, utilizing a kinematic survey to study its dynamical properties." A maximum likelihood analvsis of the kinematicsample reveals that Cetus has à svstemic velocity of ST2 kms and an internal velocity. dispersion of 17d2 kmsL c., A maximum likelihood analysis of the kinematicsample reveals that Cetus has a systemic velocity of $-87\pm2$ ${\rm km\ s^{-1}}$ and an internal velocity dispersion of $17\pm2$ ${\rm km\ s^{-1}}$ . Furthermore. a viral," Furthermore, a viral" Furthermore. a viral.," Furthermore, a viral" We note here tha the TPE of ype 2 feQSOs could the same as that o ftvpe 1 feQSOs if the obserration. which leads t otje classificatio1 of type 1 and 2 QSOs. id (lue ο Isotropicalvo distributed. chu absorbers. rat10r han the uuiforu torus-like structure.,"We note here that the TPE of type 2 fgQSOs could be the same as that of type 1 fgQSOs if the obscuration, which leads to the classification of type 1 and type 2 QSOs, is due to isotropically distributed clumpy absorbers, rather than the uniform torus-like structure." Tn principle. h the LOSPE and TPE can be well understood. by ailed 3D nuuercal simmlatious that can successful vrxoduce the Lyo forest at anv redshift2008b).," In principle, both the LOSPE and TPE can be well understood by detailed 3D numerical simulations that can successfully reproduce the $\alpha$ forest at any redshift." . Those simulations with detailed radiaive trausfer nav ο able to accommodate all the statistical and systematic effects and the density euliiucemenu 11 the vicinity of QSOs. but they are very time consume and dependen on the asstuptions of the QSO host cark," Those simulations with detailed radiative transfer may be able to accommodate all the statistical and systematic effects and the density enhancement in the vicinity of QSOs, but they are very time consuming and dependent on the assumptions of the QSO host dark" star ó Ori (οἱ.,star $\delta $ Ori (cf. Voels et al., Voels et al. 1989). which has a relatively high esin’ (144 kmss.+. Howarth et al.," 1989), which has a relatively high $v \sin i$ (144 $^{-1}$, Howarth et al." 1997)., 1997). There is one absorption feature from the WCG star: the -Cveni absorption component of the ASSSOA line. bluc-shifted by 2630 to3854.5.," There is one absorption feature from the WC6 star; the P-Cygni absorption component of the $\lambda$ line, blue-shifted by 2630 $^{-1}$ to." .. This ine arises from the same metastable level as the AIOSSQ0N lino from whieh Eenens Williams (1994). derived. a erminal wind velocity (v4 ) of 2900 + by profile fitting and. like the ALOSS0A line. is expected to form. in the outer regions of the WCG wind.," This line arises from the same metastable level as the $\lambda $ line from which Eenens Williams (1994) derived a terminal wind velocity $_{\infty}$ ) of 2900 $^{-1}$ by profile fitting and, like the $\lambda $ line, is expected to form in the outer regions of the WC6 wind." These results are consistent with the v4=2700 kmss measured by Willis et al., These results are consistent with the $_{\infty}=2700$ $^{-1}$ measured by Willis et al. from the A15.5-jim fine-structure line. also formed in the outer wind.," from the ] $\lambda $ $\mu $ m fine-structure line, also formed in the outer wind." The other absorption lines (Fable 3)) are formed in the OB-companion star., The other absorption lines (Table \ref{opt}) ) are formed in the OB-companion star. Each of the hydrogen lines is blendec with the nearby member of the Pickering series of out. the relative weakness of the unblencecd oddanumbere Pickering line at aand the closer proximity of the hydrogen-line wavelengths o the observed wavelengths suggests. that the contribution is relatively small., Each of the hydrogen lines is blended with the nearby member of the Pickering series of but the relative weakness of the unblended odd-numbered Pickering line at and the closer proximity of the hydrogen-line wavelengths to the observed wavelengths suggests that the contribution is relatively small. is represented. by he AA 4472 and lines: the latter is blended with and is verelore no very useful for diagnostic purposes., is represented by the $\lambda\lambda$ 4472 and lines; the latter is blended with and is therefore not very useful for diagnostic purposes. Other lines in the Walborn Fitzpatrick (1990) atlas of hot-star spectra are nol seen in our spectrum., Other lines in the Walborn Fitzpatrick (1990) atlas of hot-star spectra are not seen in our spectrum. The relative strength of the A triplet is a little surprising but the continuum here is uncertain as it falls between two emission features from the WCG spectrum., The relative strength of the $\lambda$ triplet is a little surprising but the continuum here is uncertain as it falls between two emission features from the WC6 spectrum. In order to establish the continuum in the regions of each of the absorption lines so that we could measure their equivalent widths. we compared our rectified spectrum with that of another WCG star. WIULIIS5 (LID 79573). artificially diluted: so as to match the spectrum. of WIULI1146.," In order to establish the continuum in the regions of each of the absorption lines so that we could measure their equivalent widths, we compared our rectified spectrum with that of another WC6 star, 15 (HD 79573), artificially diluted so as to match the spectrum of 146." The spectrum of WILLS was observed with the 19m telescope at the South African Astronomical Observatory and will be discussed. elsewhere., The spectrum of 15 was observed with the 1.9m telescope at the South African Astronomical Observatory and will be discussed elsewhere. As a by-product of this matching. we estimated the dilution of the WC€6 spectrum in 146. finding OIN1t z 3. consistent with the ratio. OD:WH =2+1. found by Willis et al. (," As a by-product of this matching, we estimated the dilution of the WC6 spectrum in 146, finding OB:WR $\approx $ 3, consistent with the ratio, OB:WR $=$ $\pm $ 1, found by Willis et al. (" 1997) from stronger emission lines between aand6560...,1997) from stronger emission lines between and. We are chary of putting too much weight on this result as it depends heavily on the rectification process and the presumption that the WCG emission lines in W1t1146 have the same strengths as those in WILLIS., We are chary of putting too much weight on this result as it depends heavily on the rectification process and the presumption that the WC6 emission lines in 146 have the same strengths as those in 15. Instead we concentrate on the absorption lines. to. be discussed below.," Instead, we concentrate on the absorption lines, to be discussed below." ‘To investigate the nature of the OB companion. we begin by using the helium-lIine ratios to estimate its spectral type.," To investigate the nature of the OB companion, we begin by using the helium-line ratios to estimate its spectral type." Our optical spectrum includes contributions from both No and So but the ratios of the absorption lines in the companion will be equal to those measured. from our combined-light spectrum. and independent of the dilution bv the WR star. provided that the dilution does not change significantly over the wavelength range of the spectrum.," Our optical spectrum includes contributions from both $_{\rm O}$ and $_{\rm O}$ but the ratios of the absorption lines in the companion will be equal to those measured from our combined-light spectrum, and independent of the dilution by the WR star, provided that the dilution does not change significantly over the wavelength range of the spectrum." Formal O-star spectra classification is based on the ratio of the A4541A ancl A4472A lines., Formal O-star spectra classification is based on the ratio of the $\lambda$ and $\lambda $ lines. Since the former was not available. we used the A42 line from the same series.," Since the former was not available, we used the $\lambda $ line from the same series." We formed an empirical calibration of A4472.X /A4200A rratios against spectral tvpe using the line strengths measured for a large (~ LOO) sample of O stars by Conti Alschuler (1971) ancl Conti (1973)), We formed an empirical calibration of $\lambda$ $\lambda$ ratios against spectral type using the line strengths measured for a large $\sim $ 100) sample of O stars by Conti Alschuler (1971) and Conti (1973). Using this calibration. the ratio of our measured: equivalent widths: (Lable 3)) indicates a type of OS. with an uncertainty of half a subclass.," Using this calibration, the ratio of our measured equivalent widths (Table \ref{opt}) ) indicates a type of O8, with an uncertainty of half a subclass." The type is close to that inferred by Willis et al., The type is close to that inferred by Willis et al. from their OD:WHB light ratio and an average luminosity for the WCG star: but this agreement is fortuitous., from their OB:WR light ratio and an average luminosity for the WC6 star; but this agreement is fortuitous. The luminosity class criterion adopted by Conti Alschuler for the middle ane Iate-type O stars was the ratio of the ALOSOA aand A43143.X lines., The luminosity class criterion adopted by Conti Alschuler for the middle and late-type O stars was the ratio of the $\lambda $ and $\lambda $ lines. Unfortunately. the silicon line is too weak (Wy~ 0.06)) to measure with confidence and the ALI43A line is not seen at all.," Unfortunately, the silicon line is too weak $_{\lambda } \sim $ ) to measure with confidence and the $\lambda $ line is not seen at all." Another significant. line that is apparently missing is the AL3SSA. ssinelet line., Another significant line that is apparently missing is the $\lambda $ singlet line. " The strength. of this relative to that of the A4412.A line (vsinelet to triplet. ratio”) has long been known to be sensitive to. luminosity owing to the relative overpopulation of the 2*P"" state in extended atmospheres (e.g. Voels et al.", The strength of this relative to that of the $\lambda $ line (“singlet to triplet ratio”) has long been known to be sensitive to luminosity owing to the relative overpopulation of the $^{3}P^{o}$ state in extended atmospheres (e.g. Voels et al. 1989 and references therein), 1989 and references therein). Using the equivalent-width measurements bv Conti Alschuler (1971) and Conti (1973). we examined the," Using the equivalent-width measurements by Conti Alschuler (1971) and Conti (1973), we examined the" debris from a disrupted dwarf galaxy (e.g..Pefiarrubiaetal.2005). or primarily consist of material stirred up from the outer disk of the Milky Way (see.e.g..Ibataetal.2005;Mo-possibility).,"debris from a disrupted dwarf galaxy \citep[e.g.,][]{pena05}, or primarily consist of material stirred up from the outer disk of the Milky Way \citep[see, e.g.,][for discussion of this possibility]{ibata05,momany06,kaz08}." reffig:map shows the low-latitude structure to be almost devoid of BHB stars. implying in a broad sense a lack of metal-poor old populations.," \\ref{fig:map} shows the low-latitude structure to be almost devoid of BHB stars, implying in a broad sense a lack of metal-poor old populations." This is in contrast to many of the other halo substructures (at least parts of Sagittarius. Virgo. and Hercules/Aquila).," This is in contrast to many of the other halo substructures (at least parts of Sagittarius, Virgo, and Hercules/Aquila)." If it is found in the future that the outer thin disk of the Milky Way is deficient in BHB stars. this may provide tentative support to the notion that the low-latitude structure is composed primarily of material stirred up from off the Milky Way's outer disk.," If it is found in the future that the outer thin disk of the Milky Way is deficient in BHB stars, this may provide tentative support to the notion that the low-latitude structure is composed primarily of material stirred up from off the Milky Way's outer disk." At the very least. the lack of BHB stars (one of the few options for precise distance determination) is a significant practical challenge for those attempting to understand the 3-dimensional distribution of the low-latitude structure.," At the very least, the lack of BHB stars (one of the few options for precise distance determination) is a significant practical challenge for those attempting to understand the 3-dimensional distribution of the low-latitude structure." A feature of particular interest in reffig:map is the change in BHB content along the Sagittarius tidal stream., A feature of particular interest in \\ref{fig:map} is the change in BHB content along the Sagittarius tidal stream. It is interesting to note that Niederste-Ostholtetal.(2010) argue for a constant BHB/MSTO ratio along the Sgr stream in the very region that we claim a significant difference in BHB/MSTO ratio (from ~1/55 to ~ 1/80)., It is interesting to note that \citet{niederste} argue for a constant BHB/MSTO ratio along the Sgr stream in the very region that we claim a significant difference in BHB/MSTO ratio (from $\sim 1/55$ to $\sim 1/80$ ). Niederste-Ostholtetal.(2010) subtract off the CMD of the region with the same 5 but /eonro)=180—/s4. then count the number of MSTO stars and BHB stars left in the residual CMD.," \citet{niederste} subtract off the CMD of the region with the same $b$ but $l_{\rm control} = 180-l_{\rm Sgr}$, then count the number of MSTO stars and BHB stars left in the residual CMD." We have confirmed that the BHB/MSTO ratios of the control areas systematically change. from ~1/50 1n the mirror region of the BHB star-rich part of Sgr. to =1/250 in the mirror region of the BHB star-poor part of Sgr (this is apparent in reffig:map:: the top part of the last set of panels is relatively BHB-rich. whereas the lower parts of the last set of panels 1s poor in BHB stars both in Sgr and elsewhere).," We have confirmed that the BHB/MSTO ratios of the control areas systematically change, from $\sim 1/50$ in the mirror region of the BHB star-rich part of Sgr, to $\la 1/250$ in the mirror region of the BHB star-poor part of Sgr (this is apparent in \\ref{fig:map}; the top part of the last set of panels is relatively BHB-rich, whereas the lower parts of the last set of panels is poor in BHB stars both in Sgr and elsewhere)." This change in the properties of the control sample drives the apparent constancy of the BHB/MSTO ratio in their work., This change in the properties of the control sample drives the apparent constancy of the BHB/MSTO ratio in their work. It is not obvious (to us at least) how to properly interpret such a situation., It is not obvious (to us at least) how to properly interpret such a situation. From the perspective of an underlying smooth stellar halo (with abrupt changes in BHB/MSTO in the ‘smooth’ halo) with a superimposed stream. subtracting off the control fields 1s defensible.," From the perspective of an underlying smooth stellar halo (with abrupt changes in BHB/MSTO in the `smooth' halo) with a superimposed stream, subtracting off the control fields is defensible." " from NAPthe perspective of. viewing ↼↼⋋∐↾⊜∥⇈⊖⋋↜∐⋔⇪⋋∣⊃∐∣⊃⊖∣⋪∖∖⇁⊖∣⊺≏↧∖⇁⊖⋋∣⋯∖∖⇁∏↾∣⊺≏↧↾⋅≏⋯⋂↾∣↴⊖∣⋪∣⊃∣⋪⊜∐≣∁⊓≼↘the stellar halo as a combination cX"" i numberber ""ofof structure: In. x'ariousartous. stages stagesof (didisruptiondisr. m.:su""o""actioactic.Vo of Ea control ofield is less structuresdefensible. and wouldof lead to artificial changes in the inferred properties of the structure of interest."," Yet, from the perspective of viewing the stellar halo as a combination of a number of structures in various stages of disruption, subtraction of a control field is less defensible, and would lead to artificial changes in the inferred properties of the structure of interest." Viewed from the latter perspective. such a difference in the BHB/MSTO ratio would demonstrate that population gradients within a progenitor galaxy could in practice lead to population differences in the resulting tidal debris (a gradient in the Sagittarius tidal tail has been detected before using other stellar population diagnostics: e.g.. Martínez-Delgadoetal.2004:Bellazzini2006:Chouetal. 2007).," Viewed from the latter perspective, such a difference in the BHB/MSTO ratio would demonstrate that population gradients within a progenitor galaxy could in practice lead to population differences in the resulting tidal debris (a gradient in the Sagittarius tidal tail has been detected before using other stellar population diagnostics; e.g., \citealp{martinez04,bellazzini06,chou07}) )." It may well be that the apparent abruptness of the change in the BHB/MSTO ratio between the Sagittarius debris in the anticenter direction and the NGP direction is because the debris streams in those directions were stripped from Sagittarius during different passages (see. e.g.. Lawetal.2005. and Law&Majewski2010. for models in which these two parts of the debris stream were stripped at significantly different times).," It may well be that the apparent abruptness of the change in the BHB/MSTO ratio between the Sagittarius debris in the anticenter direction and the NGP direction is because the debris streams in those directions were stripped from Sagittarius during different passages (see, e.g., \citealp{law05} and \citealp{law10} for models in which these two parts of the debris stream were stripped at significantly different times)." Material closer to the edges of a satellite is preferentially stripped first; thus. in this interpretation we would hypothesize that the outermost parts of the Sagittarius dwarf galaxy were devoid of BHB stars. whereas the central parts of the dwarf were richer in BHBstars?.," Material closer to the edges of a satellite is preferentially stripped first; thus, in this interpretation we would hypothesize that the outermost parts of the Sagittarius dwarf galaxy were devoid of BHB stars, whereas the central parts of the dwarf were richer in BHB." . Spectroscopic follow-up of stream members. with the goal of weeding out phase-mixed stars from stars in a dynamically-cold stream. will help to differentiate between the two possible interpretations of the apparent population gradient in Sgr (see Keller.Yong&DaCosta2010 for such an investigation of the Ser trailing arm).," Spectroscopic follow-up of stream members, with the goal of weeding out phase-mixed stars from stars in a dynamically-cold stream, will help to differentiate between the two possible interpretations of the apparent population gradient in Sgr (see \citealp{keller10} for such an investigation of the Sgr trailing arm)." In this paper. we have studied the spatial structure of stellar population variations in the stellar halo of the Milky Way.," In this paper, we have studied the spatial structure of stellar population variations in the stellar halo of the Milky Way." We made use of à new color selection method to isolate a sample of high-probability BHB star candidates. and compare their spatial density to that of color-selected MSTO stars (taken to represent the general stellar content of the halo).," We made use of a new color selection method to isolate a sample of high-probability BHB star candidates, and compare their spatial density to that of color-selected MSTO stars (taken to represent the general stellar content of the halo)." The abundance of BHB stars MMSTO stars) is known to vary strongly among stellar populations with globular cluster-like ranges in age and metal abundance. where broadly speaking high BHB abundance signposts particularly old and metal-poor populations. and redder Horizontal Branch populations are characteristic of younger. more metal-rich populations. though the physical origin of such variations is currently debated.," The abundance of BHB stars MSTO stars) is known to vary strongly among stellar populations with globular cluster-like ranges in age and metal abundance, where broadly speaking high BHB abundance signposts particularly old and metal-poor populations, and redder Horizontal Branch populations are characteristic of younger, more metal-rich populations, though the physical origin of such variations is currently debated." We mapped the relative distributions of BHB and MSTO stars across the Heliocentric distance range 5=r/kpe30 for ~1/4 of the celestial sphere. providing a panoramic view of the content of the stellar halo.," We mapped the relative distributions of BHB and MSTO stars across the Heliocentric distance range $5 \la r/{\rm kpc} \la 30$ for $\sim 1/4$ of the celestial sphere, providing a panoramic view of the content of the stellar halo." We found large variations of the BHB/MSTO star ratio in the stellar halo., We found large variations of the BHB/MSTO star ratio in the stellar halo. Most importantly. variations trace different previously-identified structures. indicating distinet populations and hence origins for them (in common. for example. with M31: MeConnachieetal. 2009)).," Most importantly, variations trace different previously-identified structures, indicating distinct populations and hence origins for them (in common, for example, with M31; \citealp{mcconnachie09}) )." Some halo features. e.g.. the low-latitude structure. appear to be almost completely devoid of BHB stars. whereas other structures appear to be rich in BHB stars.," Some halo features, e.g., the low-latitude structure, appear to be almost completely devoid of BHB stars, whereas other structures appear to be rich in BHB stars." The Sagittarius tidal stream shows an apparent variatio in the BHB/MSTO ratio along its extent. which we interpret in terms of population gradients within the progenitor dwarf galaxy leaving observable signatures in our stellar halo.," The Sagittarius tidal stream shows an apparent variation in the BHB/MSTO ratio along its extent, which we interpret in terms of population gradients within the progenitor dwarf galaxy leaving observable signatures in our stellar halo." I à previous paper (Belletal.2008).. we had shown that the level of density substructure in the Milky Way's stellar halc is consistent with models (e.g..Bullock&Johnston2005) 1 which this component is built up exclusively from disrupted Yet.," In a previous paper \citep{bell08}, we had shown that the level of density substructure in the Milky Way's stellar halo is consistent with models \citep[e.g.,][]{bullock05} in which this component is built up exclusively from disrupted satellites." of such models is qualitatively borne out: significant populatio variations.lati traced by. the BHB/MSTO5 star ratio in the Milkysl Way's stellar halo. and with à spatial structure that correlates with the density substructures.," In this paper we have shown that another prediction of such models is qualitatively borne out: significant population variations, traced by the BHB/MSTO star ratio in the Milky Way's stellar halo, and with a spatial structure that correlates with the density substructures." This lends further observational support to the view that the stellar halo is predominantly assembled from the disrupted debris of dwarf galaxies., This lends further observational support to the view that the stellar halo is predominantly assembled from the disrupted debris of dwarf galaxies. We thank the referee for their helpful suggestions., We thank the referee for their helpful suggestions. We wish to thank Jorge Penarrubia and Frank van den Bosch for useful discussions., We wish to thank Jorge Penarrubia and Frank van den Bosch for useful discussions. wwas supported by the Emmy Noether Programme of the Deutsche Forschungsgemeinschaft. and is a member of the Heidelberg International Max Planck Research School program.," was supported by the Emmy Noether Programme of the Deutsche Forschungsgemeinschaft, and is a member of the Heidelberg International Max Planck Research School program." ts a research fellow of the Alexander von Humboldt Foundation of Germany., is a research fellow of the Alexander von Humboldt Foundation of Germany. Funding for the SDSS has been provided by the Alfred P. Sloan Foundation. the Participating Institutions. the National," Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National" where p is the path length integration variable between the source of X-rays (p= 0) andthe distance p.,where $\rho'$ is the path length integration variable between the source of X-rays $\rho'\equiv 0$ ) andthe distance $\rho$ . The distance A ds related to f. the orbital separation 4. and the angle 4 between the X-ray photon direction and the orbital plane (see Fig. AI) ," The distance $\Lambda$ is related to $\rho'$, the orbital separation $d$ and the angle $\theta$ between the X-ray photon direction and the orbital plane (see Fig. \ref{fig_disk}) )" the relation A=p+d—2yfdsin., the relation $\Lambda^2=\rho'^2+d^2-2\rho'd\sin\theta$. At | keV. the photoelectric absorption cross section is about c(lkeV)2x1077 em? (2) (assuming that the abundance of metals per unit mass in the wind is similar to cosmic abundances).," At 1 keV, the photoelectric absorption cross section is about $\sigma_{\rm{PE}}(1~\rm{keV})\approx 2\times 10^{-22}~$ $^2$ \citep{1983ApJ...270..119M} (assuming that the abundance of metals per unit mass in the wind is similar to cosmic abundances)." The photoelectric optical depth in the wind is Tale)=Νμίρσρί!keV)z Lif pz10! em (for the black hole and the neutron star case)., The photoelectric optical depth in the wind is $\tau_{\rm{w}}(\rho)=N_{\rm{H}}(\rho)\sigma_{\rm{PE}}(1~\rm{keV})\gtrsim 1$ if $\rho\gtrsim 10^{10}~$ cm (for the black hole and the neutron star case). This critical distance is much bigger than the gamma-ray photosphere radius in the black hole case but is comparable for the neutron star solution., This critical distance is much bigger than the gamma-ray photosphere radius in the black hole case but is comparable for the neutron star solution. This is probably an overestimate in aas the wind should be fully ionized around the X-ray source over distances comparable to the orbital separation ~10!! em (?).. hence much larger than the extension of the gamma-ray photosphere.," This is probably an overestimate in as the wind should be fully ionized around the X-ray source over distances comparable to the orbital separation $\sim 10^{11}~$ cm \citep{2008MNRAS.386..593S}, hence much larger than the extension of the gamma-ray photosphere." We conclude that absorption of soft X-rays in the wind should not affect the gamma-ray opacity above the accretion disk., We conclude that absorption of soft X-rays in the wind should not affect the gamma-ray opacity above the accretion disk. Thomson scattering between X-rays and unbound electrons in the wind could result in a redistribution and tsotropization of the directions of the photons., Thomson scattering between X-rays and unbound electrons in the wind could result in a redistribution and isotropization of the directions of the photons. " For a fully tonized wind. the Thomson optical depth in Sglves Tp-2Ny«ry 0.5-1.8. for ὁ=30° and 70° respectively (where the factor 2 accounts for 2 electrons per He atoms. oy is the Thomson cross section. and Ny, is the helium column density integrated up to infinity in Eq. 8))."," For a fully ionized wind, the Thomson optical depth in gives $\tau_T\sim 2 N_{\rm{He}}\sigma_{\rm{T}} \approx$ 0.5-1.8, for $\psi=30\degr$ and $70\degr$ respectively (where the factor 2 accounts for 2 electrons per He atoms, $\sigma_{\rm{T}}$ is the Thomson cross section, and $N_{\rm{He}}$ is the helium column density integrated up to infinity in Eq. \ref{Nhe}) )." Gamma rays would see a different angular distribution (more isotropic) of the incoming X-ray distribution., Gamma rays would see a different angular distribution (more isotropic) of the incoming X-ray distribution. This might increase the gamma-ray optical depth (as collisions between photons would be on average closer to head-on) and reduce the anisotropic pattern of the gamma-ray photosphere in Fig. 4..," This might increase the gamma-ray optical depth (as collisions between photons would be on average closer to head-on) and reduce the anisotropic pattern of the gamma-ray photosphere in Fig. \ref{fig_map}," in particular m the neutron star case., in particular in the neutron star case. To address this question more quantitatively. we performed the same calculation of the gamma-ray optical depth as in the previous section assuming that the angular distribution of the photons from each unit surface of the disk is isotropic (the integrand in Eq.," To address this question more quantitatively, we performed the same calculation of the gamma-ray optical depth as in the previous section assuming that the angular distribution of the photons from each unit surface of the disk is isotropic (the integrand in Eq." Al is averaged over a uniform distribution of pitch angle 4)., \ref{tau_gg} is averaged over a uniform distribution of pitch angle $\theta_0$ ). This extreme situation of full isotropization yields αἱ upper-limit to the effect of X-ray scattering in the stellar wind on the gamma-ray optical depth., This extreme situation of full isotropization yields an upper-limit to the effect of X-ray scattering in the stellar wind on the gamma-ray optical depth. Calculations show that the gamma-ray photosphere is nearly spherical of radius =10! em (Fig. 4..," Calculations show that the gamma-ray photosphere is nearly spherical of radius $\approx 10^{10}~$ cm (Fig. \ref{fig_map}," dashed lines)., dashed lines). The photosphere is about a hundred times more extended in the black hole case., The photosphere is about a hundred times more extended in the black hole case. The inclination of the system has a weak impact on this result., The inclination of the system has a weak impact on this result. The real gamma-ray photosphere would likely be contained between the anisotropic and the isotropic case 10°-10'° em. regardless the nature of the compact object in Cygnus X-3.," The real gamma-ray photosphere would likely be contained between the anisotropic and the isotropic case $10^{8}$ $10^{10}$ cm, regardless the nature of the compact object in Cygnus X-3." The goal of this part is to investigate the role of a corona in emission and absorption of high-energy gamma rays., The goal of this part is to investigate the role of a corona in emission and absorption of high-energy gamma rays. First. we estimate the contribution of non-thermal hard X-rays from the corona to the gamma-ray opacity (33.1)).," First, we estimate the contribution of non-thermal hard X-rays from the corona to the gamma-ray opacity \ref{sect_hard}) )." Second. we model the emission of the corona and look whether GeV gamma rays can be produced and escape the system in (($3.2)).," Second, we model the emission of the corona and look whether GeV gamma rays can be produced and escape the system in \ref{sect_corona_gev}) )." We modeled the corona as a spherical region of radius Αι centered at the location of the compact object where energetic electrons are injected and radiate synchrotron and inverse Compton scattering., We modeled the corona as a spherical region of radius $R_{\rm{c}}$ centered at the location of the compact object where energetic electrons are injected and radiate synchrotron and inverse Compton scattering. For an optically thin and homogeneous spherical source. the emerging photon density has a radial dependence (??)..," For an optically thin and homogeneous spherical source, the emerging photon density has a radial dependence \citep{1979A&A....76..306G,1985ApJ...298..128B}." We approximate the emission inside the corona (p<Δι. where p is the distance to the center) as homogeneous and isotropic.," We approximate the emission inside the corona $\rhoRe). photons are assumed to escape radially. hence the flux decreases as 1/7 and the corona appears as a point-like emitter.," Outside $\rho>R_{\rm{c}}$ ), photons are assumed to escape radially, hence the flux decreases as $1/\rho^2$ and the corona appears as a point-like emitter." X-ray photons are injected with a power-law energy distribution of index —2 ranging from 10 keV to 100 keV. corresponding to a total power injected in the corona of L.=5x1079 erg s7!.," X-ray photons are injected with a power-law energy distribution of index $-2$ ranging from 10 keV to 100 keV, corresponding to a total power injected in the corona of $L_{\rm{c}}=5\times 10^{36}~$ erg $\rm{s}^{-1}$." This simple spectral parametrization 1s a rather good representation for the hard X-ray tail observed in the soft state above 10 keV (and radio flares. see ? Fig.," This simple spectral parametrization is a rather good representation for the hard X-ray tail observed in the soft state above 10 keV (and radio flares, see \citealt{2008MNRAS.388.1001S} Fig." 8)., 8). Appendix ?? gives more details on the model adopted., Appendix \ref{app_b} gives more details on the model adopted. Fig., Fig. 6 shows the contribution to the gamma-ray optical depth at | GeV integrated along the line of sight as a function of the location of thegamma-ray source above the accretion disk (for r= 0)., \ref{abs_corona} shows the contribution to the gamma-ray optical depth at 1 GeV integrated along the line of sight as a function of the location of thegamma-ray source above the accretion disk (for $r=0$ ). " Inside the corona. 7,4 is almost constant and gamma rays are only marginally absorbed even if the corona is compact (Ας= Αι)."," Inside the corona, $\tau_{\gamma\gamma}$ is almost constant and gamma rays are only marginally absorbed even if the corona is compact $R_{\rm{c}} \approx R_{\rm{in}}$ )." Outside.the gamma-ray optical depth drops because of the decrease of the coronal photon density with distance ος1/57.," Outside,the gamma-ray optical depth drops because of the decrease of the coronal photon density with distance $\propto 1/\rho^2$." " Gamma-ray absorption by hard X-rays dominates over absorption by the accretion disk photornr beyond a certain altitude z if the corona is extended. but the optical depth is very small in this case (7,4.« 1) unlesu the luminosity in the corona is very high L.>10? erg s7!."," Gamma-ray absorption by hard X-rays dominates over absorption by the accretion disk photons beyond a certain altitude $z$ if the corona is extended, but the optical depth is very small in this case $\tau_{\gamma\gamma}\ll 1$ ) unless the luminosity in the corona is very high $L_{\rm{c}}\gtrsim 10^{38}~$ erg $^{-1}$." However. such high flux is not observed in hard X-rays even during major radio flares where £L. can be as high as <5x erg s! (between IO and 100 keV).," However, such high flux is not observed in hard X-rays even during major radio flares where $L_{\rm{c}}$ can be as high as $\lesssim 5\times 10^{37}$ erg $^{-1}$ (between 10 and 100 keV)." This simple calculation shows that the non-thermal X-ray component in the soft state is not intense enough to produce an extra absorption feature in gamma rays., This simple calculation shows that the non-thermal X-ray component in the soft state is not intense enough to produce an extra absorption feature in gamma rays. The results obtained in the previous section are unchanged by the presence of the corona., The results obtained in the previous section are unchanged by the presence of the corona. In this section. we aim to model more precisely the emission from the corona in X-3.. andsee whether it could explain the observed gamma-ray emission.," In this section, we aim to model more precisely the emission from the corona in , andsee whether it could explain the observed gamma-ray emission." In ? the X-ray spectra of the ultra-soft state of Cygnus X-3 were fitted with the thermal/nonthermal Comptonization model (?).., In \citet{2009MNRAS.392..251H} the X-ray spectra of the ultra-soft state of Cygnus X-3 were fitted with the thermal/nonthermal Comptonization model \citep{1999ASPC..161..375C}. . In this model the X-ray source is modeled as a spherical Comptonizing cloud in which soft photons are uniformly and isotropically injected with a multicolor accretion, In this model the X-ray source is modeled as a spherical Comptonizing cloud in which soft photons are uniformly and isotropically injected with a multicolor accretion Extended inflow models represent long term. inflow of gas into the region being modelled. (c.g. Samland et al.,Extended inflow models represent long term inflow of gas into the region being modelled (e.g. Samland et al. 1997)., 1997). The lone duration of the inflow is consistent with formation of the bulge both by in-fall of eas from the disc (perhaps ov the action of bars) as well as by the accretion of gas rom the halo or captured satellite galaxies over an extenelec »eriod., The long duration of the inflow is consistent with formation of the bulge both by in-fall of gas from the disc (perhaps by the action of bars) as well as by the accretion of gas from the halo or captured satellite galaxies over an extended period. The models assume constant SE ellieiency. (C) with relatively modest gas inflow over a period of 2 to 17 Gyr and model spectral indices at à variety of points in the jstorv of the population., The models assume constant SF efficiency (C) with relatively modest gas inflow over a period of 2 to 17 Gyr and model spectral indices at a variety of points in the history of the population. With reasonable choices for C (0.1 - 4.0 +) and inflow rate (107- 10° AL. +) the observed. «bez. Ales and LL? in bulges can simultaneously »e reproduced to within errors.," With reasonable choices for C (0.4 - 4.0 $^{-1}$ ) and inflow rate $^{5}$ - $^{6}$ $_{\odot}$ $^{-1}$ ) the observed $<$ $>$, $_{2}$ and ${\beta}$ in bulges can simultaneously be reproduced to within errors." An inflow rate of LO” n corresponds to an increase. in. mess in. the volume nmoclelled equal to the initial mass every Gyr., An inflow rate of $^{6}$ $_{\odot}$ $^{-1}$ corresponds to an increase in mass in the volume modelled equal to the initial mass every Gyr. Phe range «[ SE elliciencics excludes low values (0$ and $<$ $>$ vs ${\beta}$ planes to within the errors. However. it shoule be noted that the models are highly degenerate with respec to inflow rate ancl curation. SE. elliciency. and time of SE onset (galaxy age).," However, it should be noted that the models are highly degenerate with respect to inflow rate and duration, SF efficiency, and time of SF onset (galaxy age)." Consequently. the models are only shown to illustrate their ability to achieve the indices.," Consequently, the models are only shown to illustrate their ability to achieve the indices." Phe range of SE elliciencies ancl inflow durations that can reproduce the «pe. Ales and indices in our 4 bulges are consisten with the fincines of Samland. Llensler Vheis (1997) using a chemo-clynamical moclel of disc galaxy formation.," The range of SF efficiencies and inflow durations that can reproduce the $<$ $>$, $_{2}$ and ${\beta}$ indices in our 4 bulges are consistent with the findings of Samland, Hensler Theis \shortcite{SHT97} using a chemo-dynamical model of disc galaxy formation." Blum et al., Blum et al. (1996). showed that τοῦ giants in the Galactic bulge possess approximately solar metallicities and suggest that multiple epochs of SE have occurred in the centre of the bulge in the last 7 - 100 Myr., \shortcite{BSD96} showed that red giants in the Galactic bulge possess approximately solar metallicities and suggest that multiple epochs of SF have occurred in the centre of the bulge in the last 7 - 100 Myr. ConsequentIy. extended inflow models of spiral bulge formation are. so far. entirely consistent. with both observations of Lick indices. the stars in our own bulge and chemo-dynamical modelling.," Consequently, extended inflow models of spiral bulge formation are, so far, entirely consistent with both observations of Lick indices, the stars in our own bulge and chemo-dynamical modelling." Our study of the bulges of 4 spiral galaxies using the Lick system of spectral indices has shown that central line-strengths are high., Our study of the bulges of 4 spiral galaxies using the Lick system of spectral indices has shown that central line-strengths are high. < bes indices are similar to those found in the centres of elliptical galaxies., $<$ $>$ indices are similar to those found in the centres of elliptical galaxies. However. a cilference in Ales index at à given «Fez: exists between elliptical galaxies and our sample of spiral bulges.," However, a difference in $_{2}$ index at a given $<$ $>$ exists between elliptical galaxies and our sample of spiral bulges." Spiral bulges lie within the region of the Ales vs «Lec plane occupied by the solar abundance ratio SSPs of Worthey (1994).. while cllipticals exhibit enhanced Mg». (he known Mg/Ee] exeess).," Spiral bulges lie within the region of the $_{2}$ vs $<$ $>$ plane occupied by the solar abundance ratio SSPs of Worthey \shortcite{W94}, while ellipticals exhibit enhanced $_{2}$ (the known [Mg/Fe] excess)." This dilference between the (wo object types relleets differences in their star formation histories., This difference between the two object types reflects differences in their star formation histories. Our data are consistent with both correlations of Ales with central velocity dispersion and Ale» eracicnt with central velocity. dispersion observed. in elliptical ealaxies., Our data are consistent with both correlations of $_{2}$ with central velocity dispersion and $_{2}$ gradient with central velocity dispersion observed in elliptical galaxies. Using our GCIS code. we have shown that the central line-strengths. in spiral bulges cannot be achieved with primordial collapse mocels of spheroid formation with or without the assumption of constant. Salpeter IME.," Using our GCE code, we have shown that the central line-strengths in spiral bulges cannot be achieved with primordial collapse models of spheroid formation with or without the assumption of constant, Salpeter IMF." Indeed. the inferred solar Mg/Fe] argues against a biased LXE in spiral bulges.," Indeed, the inferred solar [Mg/Fe] argues against a biased IMF in spiral bulges." Models of bulge formation with gas inllow and star formation extended over 2-17 vr can achieve the observed. central line-strengths in all of our sample., Models of bulge formation with gas inflow and star formation extended over 2-17 Gyr can achieve the observed central line-strengths in all of our sample. These models are consistent. with the chemo-dvnamical modelling of Samland. Hensler Theis (1997). as well as observations of individual stars in the bulge of our own Galaxy (Minnitictal.1992:Blumal.1996).," These models are consistent with the chemo-dynamical modelling of Samland, Hensler Theis \shortcite{SHT97} as well as observations of individual stars in the bulge of our own Galaxy \cite{Mea95,BSD96}." . Lt has been shown that at least one bulge (NGC 5689) must contain a population of relatively. voung stars (x; 5 (ιν) again consistent with extended inflow moclels of bulge formation., It has been shown that at least one bulge (NGC 5689) must contain a population of relatively young stars $\la$ 5 Gyr) again consistent with extended inflow models of bulge formation. Νέας 3623 shows the presence of kinematic substructure., NGC 3623 shows the presence of kinematic substructure. X dip in velocity dispersion. is. observe in the centre of this galaxy coincident with a sharp peak in metallicity sensitive indices., A dip in velocity dispersion is observed in the centre of this galaxy coincident with a sharp peak in metallicity sensitive indices. This structure suggests the presence. of a bar. or perhaps disc. at the centre of this galaxy.," This structure suggests the presence of a bar, or perhaps disc, at the centre of this galaxy." Analysis of a much larger sunple of galaxies. including a repeat observation of NGC 3623. i8 being carried out with observations from the WIPE. to test the findings of this paper.," Analysis of a much larger sample of galaxies, including a repeat observation of NGC 3623, is being carried out with observations from the WHT, to test the findings of this paper." These data will be presented in a future paper and will include other age sensitive indices. such as the newly calibrated H8. anc H5. indices. which are less allectecd by emission than the Ll? index.," These data will be presented in a future paper and will include other age sensitive indices, such as the newly calibrated ${\delta}$ and ${\gamma}$ indices, which are less affected by emission than the ${\beta}$ index." Increased accuracy of age determination. coupled with the larger number of metallicity sensitive indices. will permit tighter constraint of our models of bulge formation and their star formation histories.," Increased accuracy of age determination, coupled with the larger number of metallicity sensitive indices, will permit tighter constraint of our models of bulge formation and their star formation histories." We thank our referee D. Γιο for his constructive comments., We thank our referee D. Friedli for his constructive comments. The authors acknowledge the data analysis facilities provide by the Starlink Project which is run by CCLRC on behalf of PPARC., The authors acknowledge the data analysis facilities provide by the Starlink Project which is run by CCLRC on behalf of PPARC. In addition. the ΗΛ software package was used.," In addition, the IRAF software package was used." LRA is distributed by the National Optical Astronomy Observatories.. which is operated by AULA. Ince... uncer cooperative agreement with the National Science Foundation.," IRAF is distributed by the National Optical Astronomy Observatories, which is operated by AURA, Inc., under cooperative agreement with the National Science Foundation." This work is based on observations obtained at Palomar observatory. which is owned and operated by the California. Institute. of ‘Technology.," This work is based on observations obtained at Palomar observatory, which is owned and operated by the California Institute of Technology." obscures the submaiu-radio emission from the accretion flow. aud has a lower brightuess temperature.,"obscures the submm-radio emission from the accretion flow, and has a lower brightness temperature." aud that of NGC 1172 aud AIST are that the NCC 5128 system has not vet conie to equilibrium aud transported angular ποιοται outwards. or that NGC 5128 is a lower luminosity elliptical which teud to be more rotationally supported.,"and that of NGC 4472 and M87 are that the NGC 5128 system has not yet come to equilibrium and transported angular momentum outwards, or that NGC 5128 is a lower luminosity elliptical which tend to be more rotationally supported." Measurements of the racial velocities of globular clusters also provide information about the mass distribution of the host ealaxy and the orbits of the clusters., Measurements of the radial velocities of globular clusters also provide information about the mass distribution of the host galaxy and the orbits of the clusters. Globular clusters are particularly useful probes of the dynamics of the outer halos of elliptical galaxies because they can be observed out to much larger radii than it is possible to obtain spectroscopy of the inteerated light., Globular clusters are particularly useful probes of the dynamics of the outer halos of elliptical galaxies because they can be observed out to much larger radii than it is possible to obtain spectroscopy of the integrated light. A very large uuuber of velocities are required to independently determine the, A very large number of velocities are required to independently determine the It is therefore not surprising that the constraints that can be set from the present day SNIa Hubble diagram are not very tight.,It is therefore not surprising that the constraints that can be set from the present day SNIa Hubble diagram are not very tight. The bottom figure illustrates the effect of changing wi: changing η from 0 to —0.6 produces changes that are small and easy to understand as the model becomes degenerate with the ACDM model as w; tends to —1., The bottom figure illustrates the effect of changing $w_\START$: changing $w_\START$ from $0 $ to $-0.6$ produces changes that are small and easy to understand as the model becomes degenerate with the $\Lambda$ CDM model as $w_\START$ tends to $-1$. For this reason. in the following. we concentrate our analysis on αι.," For this reason, in the following, we concentrate our analysis on $a_\TRANS$ ." " We have redone the above analysis on e, for à simulated survey with the precision and statistics expected from space experiments.", We have redone the above analysis on $a_\TRANS$ for a simulated survey with the precision and statistics expected from space experiments. " The constraints inferred from this simulated sample again reveal that the transition epoch a, is moderately constrained: transitions at redshift as low as 0.5 (2 c& CL) are still acceptable when a rapid transition (T> 2) is assumed.", The constraints inferred from this simulated sample again reveal that the transition epoch $a_\TRANS$ is moderately constrained: transitions at redshift as low as $0.5$ (2 $\sigma$ CL) are still acceptable when a rapid transition $\Gamma > 2$ ) is assumed. The situation is therefore paradoxical: although space survey precision improves the constraints by pushing the acceptable redshift)transitions). this last result is modest as a significant fraction of the high precision data provided by the experiment extends up to redshift ~2.," The situation is therefore paradoxical: although space survey precision improves the constraints by pushing the acceptable redshift, this last result is modest as a significant fraction of the high precision data provided by the experiment extends up to redshift $\sim 2$." The reason for this apparent paradox ts clarified in Sec. 4.., The reason for this apparent paradox is clarified in Sec. \ref{secliv}. Given that SNIa Hubble diagram hardly suggests the presence of a transition in thedark energy content of the universe.," Given that SNIa Hubble diagram hardly suggests the presence of a transition in thedark energy content of the universe," esin? for E to M stars (large octagon) together with the quartile values (horizontal bars).,$v \sin i$ for F to M stars (large octagon) together with the quartile values (horizontal bars). These numbers have been taken from Quelozetal.(1993) (their Fig., These numbers have been taken from \citet{1998A&A...335..183Q} (their Fig. 6. averaged over all masses).," 6, averaged over all masses)." In. this plot we show for each model (wo evolutionary. (racks. the first starts al MMyr and caleulates forward in (ime (as in the upper panel). the second starts αἱ MMvr and caleulates backwards.," In this plot we show for each model two evolutionary tracks, the first starts at Myr and calculates forward in time (as in the upper panel), the second starts at Myr and calculates backwards." Solid lines show again model A. econservation of angular momentum without anv rotational braking.," Solid lines show again model A, conservation of angular momentum without any rotational braking." The tracks from model A are barely consistent with the observational data., The tracks from model A are barely consistent with the observational data. When started at MMyr. (he predicted median in the Pleiades is 1 and thus too high: when started at MMvr. they give a median of tat MMvr. which is clearly too low.," When started at Myr, the predicted median in the Pleiades is $^{-1}$ and thus too high; when started at Myr, they give a median of $^{-1}$ at Myr, which is clearly too low." Thus. rotational braking is likely involved in the evolution to the ZAMS.," Thus, rotational braking is likely involved in the evolution to the ZAMS." On the main-sequence. rotation is mainlv braked by angular momentum losses due to stellar winds. where the standard rotational braking law has been found to be vrx (Skumanich1972:Barnes2001)..," On the main-sequence, rotation is mainly braked by angular momentum losses due to stellar winds, where the standard rotational braking law has been found to be $v \propto t^{-1/2}$ \citep{1972ApJ...171..565S,2001ApJ...561.1095B}." Model C. shown in dotted lines. assumes. angular momentum losses according to the Skumanich law. again calculated in both directions.," Model C, shown in dotted lines, assumes angular momentum losses according to the Skumanich law, again calculated in both directions." The tracks from model C. however. are clearly not in agreement with the observations.," The tracks from model C, however, are clearly not in agreement with the observations." When calculated. forwaadl. the predicted median for the Pleiades is well below the detection limit.," When calculated forward, the predicted median for the Pleiades is well below the detection limit." Conversely. for MMvr the model gives an unrealistically high median.," Conversely, for Myr the model gives an unrealistically high median." Thus. Skumanich braking appears to be too strong.," Thus, Skumanich braking appears to be too strong." We can reproduce (he esin/ evolution either by using an exponent of —0.1 to —0.3 instead of —0.5 in the braking law. by using an exponential braking law with (sin/xexp(—/) or by switching on the braking at about half wav through (he pre-main-sequence evolution.," We can reproduce the $v\sin i$ evolution either by using an exponent of $-0.1$ to $-0.3$ instead of $-0.5$ in the braking law, by using an exponential braking law with $v\sin i \propto \exp{(-t)}$ or by switching on the braking at about half way through the pre-main-sequence evolution." The latter scenario is not implausible. as most objects in the considered mass range develop a radiative core and thus the prevequisile to operate a solaa-(wpe cvnamo alter about MMyr. see relintro..," The latter scenario is not implausible, as most objects in the considered mass range develop a radiative core and thus the pre-requisite to operate a solar-type dynamo after about Myr, see \\ref{intro}. ." Thus. our comparison with models gives the following results: a) Ou timescales of e»100 MMyr. weak rotational braking. possibly due to a Skumanich-(wpe activitv-rotation connection. is required to [ind a good match to the observations.," Thus, our comparison with models gives the following results: a) On timescales of $\sim 100$ Myr, weak rotational braking, possibly due to a Skumanich-type activity-rotation connection, is required to find a good match to the observations." " b) From MMyr the rotational evolution is fully consistent with angular momentum conservation: effects of possible rotational braking are too weak to alleet the (sin? distribution significantly,", b) From Myr the rotational evolution is fully consistent with angular momentum conservation; effects of possible rotational braking are too weak to affect the $v\sin i$ distribution significantly. Again it should be emphasised (hat these results do only apply to the total sample., Again it should be emphasised that these results do only apply to the total sample. In we do find that rotational velocities depend on spectral tvpe for objects earlier than M2., In \\ref{rotspt} we do find that rotational velocities depend on spectral type for objects earlier than M2. Thus. for objects with ages between 5 and MMwvr. stellar mass is the major factor whieh determines the rotation. rather than age.," Thus, for objects with ages between 5 and Myr, stellar mass is the major factor which determines the rotation, rather than age." In (he previous sections we have already made connections between rotation aud activity. to explain the evolution and mass-dependence of Πα emission and rotational velocities.," In the previous sections we have already made connections between rotation and activity, to explain the evolution and mass-dependence of $\alpha$ emission and rotational velocities." The obvious next stepis to investigate directly possible correlations between rotation and activity.," The obvious next stepis to investigate directly possible correlations between rotation and activity," 'These scalings are identical to those found by in a more involved analysis.,These scalings are identical to those found by \cite{Popov} in a more involved analysis. " So (1993)far, the light curves described have only accounted for shock deposited energy."," So far, the light curves described have only accounted for shock deposited energy." Radioactive ssynthesized in the explosion introduces an additional energy source concentrated near the center of the debris., Radioactive synthesized in the explosion introduces an additional energy source concentrated near the center of the debris. 'The heating from radioactive decay helps maintain the ionization of the debris and so extends the duration of the plateau., The heating from radioactive decay helps maintain the ionization of the debris and so extends the duration of the plateau. " To incorporate this effect into the scalings, we generalize the expression for the internal energy where Eyze0.6x1099Mw; ergs, Eco®109?My; ergs are the total energy released from aand ddecay (with iin units of and ty©8.8,tc;7:113 days are the lifetimes."," To incorporate this effect into the scalings, we generalize the expression for the internal energy where $E_{\rm ni} \approx 0.6 \times 10^{50} \Mni$ ergs, $E_{\rm co} \approx 1.2 \times 10^{50} \Mni$ ergs are the total energy released from and decay (with in units of ) and $t_{\rm ni} \approx 8.8, t_{\rm co} \approx 113$ days are the lifetimes." This Mo))correction for radioactivity can be written Pin(t)=Eo(te/tsn)faa with where Es;= E/10?! ergs., This correction for radioactivity can be written $E_{\rm int}(t) = E_0(t_e/\tsn) f_{\rm rad}$ with where $E_{51} = E/10^{51}$ ergs. " Following the same arguments leading to Eq. 8,,"," Following the same arguments leading to Eq. \ref{Eq:popov}, ," we see that the plateau timescale scales as tenος1/8.," we see that the plateau timescale scales as $\tsn \propto f_{\rm rad}^{1/6}$." " For example, a mmass of 0.1 should extend the plateau by ~24% for E53;=1."," For example, a mass of $0.1~\Msun$ should extend the plateau by $\sim 24\%$ for $E_{51} = 1$." " AlthoughMe one might anticipate a change to aas well, the models show that the decay energy does not typically have enough time to diffuse out and affect the plateau luminosity (see Section 6))."," Although one might anticipate a change to as well, the models show that the decay energy does not typically have enough time to diffuse out and affect the plateau luminosity (see Section \ref{sec:onemod}) )." " Below we compare the analytic scalings to our numerical simulations and show that the simple relations, particularly Eqs. 8,,"," Below we compare the analytic scalings to our numerical simulations and show that the simple relations, particularly Eqs. \ref{Eq:popov}," agree quite well., agree quite well. The models allow us to refine the exponents and calibrate the numerical constants in front., The models allow us to refine the exponents and calibrate the numerical constants in front. " For our numerical models, we consider stellar progenitors with main sequence masses in the range M;—12—25 Mo, the range expected to produce most of the observed events."," For our numerical models, we consider stellar progenitors with main sequence masses in the range $\Min = 12-25~\Msun$ , the range expected to produce most of the observed events." " Properties of the presupernova models are summarized in Table 1 which gives the zero age main sequence and presupernova masses in solar masses (Mi and the presupernova radius in solar radii the iron Mt),core mass in solar masses (Mp), and the (Ro),surface helium mass fraction."," Properties of the presupernova models are summarized in Table 1 which gives the zero age main sequence and presupernova masses in solar masses $\Min$ and $\Mf$ ), the presupernova radius in solar radii $R_0$ ), the iron core mass in solar masses $M_{\rm Fe}$ ), and the surface helium mass fraction." " All models were computed with the Kepler code, which follows stellar evolution including the most up-to-date opacities, prescriptions for mass loss, and nuclear reaction rates (Rauscheretal.2002;Woosleyetal.2002;&Heger 2007)."," All models were computed with the Kepler code, which follows stellar evolution including the most up-to-date opacities, prescriptions for mass loss, and nuclear reaction rates \citep{Rau02,Woo02,Woo07}." ". Stars with larger initial masses experience more mass loss, especially during the red giant phase,and this narrows the range of final masses to M;=10.9—15.8Mo."," Stars with larger initial masses experience more mass loss, especially during the red giant phase,and this narrows the range of final masses to $\Mf = 10.9-15.8$." ". For Mi>20Mo, the presupernova mass declines with increasing M;."," For $\Min > 20~\Msun$, the presupernova mass declines with increasing $\Min$." " More massive stars do, however, maintain significantly larger radii at the time of explosion."," More massive stars do, however, maintain significantly larger radii at the time of explosion." 'The helium mass fraction in the stellar envelope is also a function of ((Table 1) varying from for M;=12 tto for M;=25Mo., The helium mass fraction in the stellar envelope is also a function of (Table 1) varying from for $\Min = 12$ to for $\Min = 25~\Msun$. " This variation is due to mass loss and convective dredge up from the helium core, which are greater in more massive stars."," This variation is due to mass loss and convective dredge up from the helium core, which are greater in more massive stars." " As the envelope helium abundance affects both the electron scattering opacity and the recombination temperature of the ejecta,we will find it has a significant effect on the light curves of SNe ΠΕ."," As the envelope helium abundance affects both the electron scattering opacity and the recombination temperature of the ejecta,we will find it has a significant effect on the light curves of SNe IIP." " While most stars in our survey have solar abundances, a lower metallicity (Z=0.1 solar) 15Mc model was also included."," While most stars in our survey have solar abundances, a lower metallicity $Z = 0.1$ solar) $15~\Msun$ model was also included." The chief effect of the lower metallicity was a smaller presupernova radius and less total mass loss., The chief effect of the lower metallicity was a smaller presupernova radius and less total mass loss. " The explosion of each model was simulated by moving a piston outward from an inner boundary at mass coordinate (Woosley&Weaver1995;Woosleyetal. 2002),, Mpisttypically taken to be the outer edge of the iron core, and following the subsequent hydrodynamics assuming radial symmetry."," The explosion of each model was simulated by moving a piston outward from an inner boundary at mass coordinate $M_{\rm pist}$ \citep{Woo95,Woo02}, typically taken to be the outer edge of the iron core, and following the subsequent hydrodynamics assuming radial symmetry." " Each star was exploded several times to obtain variable kinetic energies at infinity within the set of approximately 0.3,0.6,1.2,2.4, and 4.8x10°! erg."," Each star was exploded several times to obtain variable kinetic energies at infinity within the set of approximately $0.3, 0.6, 1.2, 2.4$, and $4.8 \times 10^{51}$ erg." The results are summarized in Table 2., The results are summarized in Table 2. " Polarization observations of SNe IIP suggest that the hydrogen envelopes are indeed spherically symmetric, although thecores may appear aspherical, perhaps due to an asymmetric explosion mechanism (Leonardetal. "," Polarization observations of SNe IIP suggest that the hydrogen envelopes are indeed spherically symmetric, although thecores may appear aspherical, perhaps due to an asymmetric explosion mechanism \citep{Leonard_asph, Leonard_99em}. ." "Any asymmetry in the shock wave, however, is likely 2001)..smoothed out by propagating through the large hydrogen envelope."," Any asymmetry in the shock wave, however, is likely smoothed out by propagating through the large hydrogen envelope." ihe model were relatively coarser than ours (the simulation volume included 32x elements). and a simplified treatment of the hvelrocwuamics (the anelastic approximation) was used. the larger temperature contrast of the visible surface was present.,"the model were relatively coarser than ours (the simulation volume included $32 \times 32 \times 32$ elements), and a simplified treatment of the hydrodynamics (the anelastic approximation) was used, the larger temperature contrast of the visible surface was present." Nordlund Dravins (1990) also noted the position of the granules in the (hin atmosphere (naked eranules). in contrast with the Sun.," Nordlund Dravins (1990) also noted the position of the granules in the thin atmosphere (“naked” granules), in contrast with the Sun." Some features of the striking difference between the properties of convection in an E-tvpe main sequence stellar alinosphere and (he solar atmosphere had already. been noted by Nelson (1980) using a simpler model of eranulation developed for the Sun (Nelson Musiman 1077)., Some features of the striking difference between the properties of convection in an F-type main sequence stellar atmosphere and the solar atmosphere had already been noted by Nelson (1980) using a simpler model of granulation developed for the Sun (Nelson Musman 1977). Stochastic [actuations in (he turbulent lavers are believed to be responsible for (he excitation of p-modes in the Sun aud stars with similar convection zones., Stochastic fluctuations in the turbulent layers are believed to be responsible for the excitation of $p$ -modes in the Sun and stars with similar convection zones. The 3D numerical simulations of the solar atmosphere have been successful in explaining (he excitation mechanism aud power distribution of solar p-modes (Stein Nordlund 2000)., The 3D numerical simulations of the solar atmosphere have been successful in explaining the excitation mechanism and power distribution of solar $p$ -modes (Stein Nordlund 2000). We have seen that Procyon exhibits a much shallower convection zone than (he Sun. and il is interesting (o query whether the SAL region in Procvon also favors the excitation of p-modes.," We have seen that Procyon exhibits a much shallower convection zone than the Sun, and it is interesting to query whether the SAL region in Procyon also favors the excitation of $p$ -modes." The turbulent velocity fIuctuations in a convection zone must be stochastically distributed for the excitation of p-imodes to take place., The turbulent velocity fluctuations in a convection zone must be stochastically distributed for the excitation of $p$ -modes to take place. We suggest that only when the coherence time for the velocity fluctuations becomes shorter Chan the period of the oscillation modes where the oscillation power is concentrated. can the fInctuations contribute to the stochastic excitation.," We suggest that only when the coherence time for the velocity fluctuations becomes shorter than the period of the oscillation modes where the oscillation power is concentrated, can the fluctuations contribute to the stochastic excitation." To enable stochastic (random motions) excitation of p-modes by turbulence. (he turbulent velocily (or temperature) field shoulel be stochastic over a time interval smaller (han the p-mode oscillation it is intended. to excite.," To enable stochastic (random motions) excitation of $p$ -modes by turbulence, the turbulent velocity (or temperature) field should be stochastic over a time interval smaller than the $p$ -mode oscillation it is intended to excite." Otherwise its not temporally stochastic with respect to the oscillation., Otherwise its not temporally stochastic with respect to the oscillation. For the Sun. the relevant oscillation period is ο~5 minutes. in Procvon. it is believed to peak around ο15 minutes (Alartié et al.," For the Sun, the relevant oscillation period is $\wp\sim 5$ minutes, in Procyon, it is believed to peak around $\wp\sim 15$ minutes (Martić et al." 2004)., 2004). The autocorrelation coefficient of vertical velocity (which is a function of depth aad time) is defined as where, The autocorrelation coefficient of vertical velocity (which is a function of depth and time) is defined as where where we have made use of the relation as,where we have made use of the relation as $x \rightarrow 0$. e and We note that i£; =0 this reduces to where we have made use of the identities ντος)=R/(2z) and LOL/2)=νπ., Rearranging we now find and We note that if $\beta=0$ this reduces to where we have made use of the identities $K_{1/2}(z)=e^{-z}\sqrt{\pi/(2z)}$ and $\Gamma (1/2)=\sqrt{\pi}$. This is the solution found bv C£Scheuer&Feiler(1996)., This is the solution found by \cite{SF}. . The radius where the warp in the disc typically occurs. Reap (Scheuer&Feiler1996).. can be found by balancing the terms on either side of equation (9)).," The radius where the warp in the disc typically occurs, $R_{\rm warp}$ \citep{SF}, can be found by balancing the terms on either side of equation \ref{balance}) )." We find In order to compare cdillerent power laws for viscosity ina reasonable way we want to keep £j. ο and X the same ad {αμ where the torques are greatest.," We find In order to compare different power laws for viscosity ina reasonable way we want to keep $\nu_1$, $\nu_2$ and $\Sigma$ the same at $R_{\rm warp}$ where the torques are greatest." We therefore set and note that £e now Corresponds to the value of f£» at the radius where the dise is warped., We therefore set and note that $\nu_{20}$ now corresponds to the value of $\nu_2$ at the radius where the disc is warped. Equation (20)) with w=HN becomes Note that we choose the negative root of 7 in equation (12)) because we want the real part of the argument— of the Bessel function to be positive., Equation \ref{W2}) ) with $\kappa=-i R_{\rm warp}^{1+\beta}$ becomes Note that we choose the negative root of $-i$ in equation \ref{kappahalf}) ) because we want the real part of the argument of the Bessel function to be positive. " We note that in this solution we have a term of the form where ker, and kei, are Kelvin functions (Watson 1966).", We note that in this solution we have a term of the form where ${\rm ker}_\nu$ and ${\rm kei}_\nu$ are Kelvin functions \citep{W66}. . The second. order term. |Ot/of)2. which we choose to neglect. from equation (6)) has a magnitude that is largest in the clise around. Roop but is negligible for small inclination angles.," The second order term, $\left|\partial \bm{l} /\partial R \right|^2$, which we choose to neglect, from equation \ref{int}) ) has a magnitude that is largest in the disc around $R_{\rm warp}$ but is negligible for small inclination angles." The largest error occurs when the outer disc is inclined. at an angle of w/2 to the black hole., The largest error occurs when the outer disc is inclined at an angle of $\pi/2$ to the black hole. Then the relative magnitude ofthe neglected term is 0.049£ovio For 1Ξ0.," Then the relative magnitude of the neglected term is $0.049 \, \nu_{20}/\nu_{10}$ for $\beta=0$." For 3— it grows to 0.093£u vu.," For $\beta=3$ it grows to $0.093 \, \nu_{20}/\nu_{10}$ ." LW νουqo the analysis is σους for all inclinations of the outer disc., If $\nu_{20}<\nu_{10}$ the analysis is good for all inclinations of the outer disc. When this inclination is reduced to z/6 the relative magnitude of the neglected term has fallen to 0.023voyfii for 3= and 0.012voyfii Lor 3=0.," When this inclination is reduced to $\pi/6$ the relative magnitude of the neglected term has fallen to $0.023 \, \nu_{20}/\nu_{10}$ for $\beta=3$ and $0.012 \, \nu_{20}/\nu_{10}$ for $\beta=0$." " In Figure 1 we plot the solution V.—/,|i£, for various values of jas ἐν=JV) against /,=SOV) with Ws=I.", In Figure \ref{doub} we plot the solution $W = l_x + i l_y$ for various values of $\beta$ as $l_x=\Re (W)$ against $l_y=\Im (W)$ with $W_\infty=1$. Note that since the problem is a linear one. we may take WA=1.," Note that since the problem is a linear one, we may take $W_\infty = 1$." In this plane. the completely flat. but. inclined. disc would be a point at M—1.," In this plane, the completely flat, but inclined, disc would be a point at $W = 1$." As A.O the disc becomes steadily more aligned with the black hole spin and Wo} 0., As $R \rightarrow 0$ the disc becomes steadily more aligned with the black hole spin and $W \rightarrow 0$ . The lower the value of 7 the less the disc is twisted., The lower the value of $\beta$ the less the disc is twisted. " The lines begin at #2= Oat /,—=0 and the dots on the curves are where ReRea,=1. 10.100 ancl 100"," The lines begin at $R=0$ at $l_x=l_y=0$ and the dots on the curves are where $R/R_{\rm warp} =1$, $10$ $100$ and $1000$." kelvin functions are in elfect combinations of the ordinary. oscillatory Bessel functions JGr) and YGe) and the mocified. non-oscillatory Bessel functions. fOr) and AGr).," Kelvin functions are in effect combinations of the ordinary, oscillatory Bessel functions $J(x)$ and $Y(x)$ and the modified, non-oscillatory Bessel functions $I(x)$ and $K(x)$." Decause of the nature of Ixelvin functions ancl because. as R+ Othe argument of the Bessel function tends to infinity. the solution WC?) circles the origin an infinite number of times as £20 while at the same time approaching the origin exponentially.," Because of the nature of Kelvin functions and because, as $R \rightarrow 0$, the argument of the Bessel function tends to infinity, the solution $W(R)$ circles the origin an infinite number of times as $R \rightarrow 0$ while at the same time approaching the origin exponentially." Thus. as we approach the origin. the dise becomes very. twisted. but very flat.," Thus, as we approach the origin, the disc becomes very twisted, but very flat." Fhis explains wha. as remarked. by Scheuer&Feiler (1996)... numerical integration packages tend to fail for this problem.," This explains why, as remarked by \cite{SF}, , numerical integration packages tend to fail for this problem." The inclination of the clise relative to the black bolespin direction £ at radius £2 is The solution for WV is in the [rame of the black hole whereJ//=(0.0.1) and we have the cise angular momentum. vector ‘Thus the inclination of the disc at racius 7? is this frame," The inclination of the disc relative to the black holespin direction $\hat{\bm{z}}$ at radius $R$ is The solution for $W$ is in the frame of the black hole where$\bm{J}/J=(0,0,1)$ and we have the disc angular momentum vector Thus the inclination of the disc at radius $R$ is this frame" "η=10 to perform the energy cutoff calculations along the orbit,shock).","$\eta=10$ to perform the energy cutoff calculations along the orbit,." The orbital dependency of the maximum electron energy for 7=10 is shown in Fig. 3.., The orbital dependency of the maximum electron energy for $\eta=10$ is shown in Fig. \ref{fig:emax}. " During periods of low X-ray flux E, has a behaviour proportional to faq (see Fig. 2))."," During periods of low X-ray flux $E_\mathrm{e,max}$ has a behaviour proportional to $t_\mathrm{ad}$ (see Fig. \ref{fig:tcool}) )." " During the outburst peaks, on the other hand, high energy losses are dominated by synchrotron and the cutoff is constant (following Eq."," During the outburst peaks, on the other hand, high energy losses are dominated by synchrotron and the cutoff is constant (following Eq." 6 for constant magnetic field)., \ref{eq:synemax} for constant magnetic field). " For each position along the orbit, we calculate the emitted synchrotron spectrum from the evolved particle distribution and the magnetic field."," For each position along the orbit, we calculate the emitted synchrotron spectrum from the evolved particle distribution and the magnetic field." Synchrotron emission in the X-ray range will be generally characterized by a photon index of Ix=(a+1)/251.5., Synchrotron emission in the X-ray range will be generally characterized by a photon index of $\Gamma_\mathrm{X}=(\alpha_\mathrm{e}+1)/2\approx1.5$. " The orbital dependence of the electron maximum energy will affect the shape of the spectrum, typically hardening (softening) it for high (low) fluxes, which correspond to lower (higher) adiabatic losses and therefore a higher (lower) maximum electron energy."," The orbital dependence of the electron maximum energy will affect the shape of the spectrum, typically hardening (softening) it for high (low) fluxes, which correspond to lower (higher) adiabatic losses and therefore a higher (lower) maximum electron energy." " However, since the cutoff in the particle distribution is located at energies significantly higher than those responsible for X-ray emission, this effect is small in the X-ray energy band (AIx~ 0.2)."," However, since the cutoff in the particle distribution is located at energies significantly higher than those responsible for X-ray emission, this effect is small in the X-ray energy band $\Delta\Gamma_\mathrm{X}\sim 0.2$ )." " We calculate the IC component of the spectrum using the anisotropic cross section and the stellar radiation field (blackbody radiation at kT=2 eV and L,=1035 ergs)) as the source of seed photons for the interaction.", We calculate the IC component of the spectrum using the anisotropic cross section and the stellar radiation field (blackbody radiation at $kT=2$ eV and $L_\star=10^{38}$ ) as the source of seed photons for the interaction. Following Eqs., Following Eqs. " 20 and 21 of?,, the photon spectrum emitted by a population of isotropically distributed electrons can be described with a precision better than (for e>>ερ and y> 1) by where e and ερ are the energies of the scattered and incident photons, respectively, in units of m,c?, 0 is the scattering angle, στ is the Thomson cross section, na is the number density of the stellar photon field, and where bg=2(1—cos0)epy and z=e/y."," 20 and 21 of, the photon spectrum emitted by a population of isotropically distributed electrons can be described with a precision better than (for $\epsilon\gg\epsilon_0$ and $\gamma\gg1$ ) by where $\epsilon$ and $\epsilon_0$ are the energies of the scattered and incident photons, respectively, in units of $m_ec^2$, $\theta$ is the scattering angle, $\sigma_\mathrm{T}$ is the Thomson cross section, $n_{\epsilon_0}$ is the number density of the stellar photon field, and where $b_\theta=2(1-\cos\theta)\epsilon_0\gamma$ and $z=\epsilon/\gamma$." " For a blackbody— seed photon distribution, the shape of the resulting emitted spectrum only depends on the parameter bg and the relativistic electron energy distribution."," For a blackbody seed photon distribution, the shape of the resulting emitted spectrum only depends on the parameter $b_\theta$ and the relativistic electron energy distribution." The intense radiation field can also absorb very high energy y-ray emission through pair production yy—e*e™(?)., The intense radiation field can also absorb very high energy $\gamma$ -ray emission through pair production $\gamma\gamma\rightarrow\mathrm{e}^+\mathrm{e}^-$. . An exploration of the effects that this absorption can have on the observed spectrum of gamma-ray binaries can be found in and references therein., An exploration of the effects that this absorption can have on the observed spectrum of gamma-ray binaries can be found in and references therein. " The differential opacity for an emitted y-ray of energy e is given by where / is the distance along the line of sight, ερ is the energy of the stellar photon, v is the interaction angle and the absorption Cross section can be represented in the form: where 8=(1—1/s)!2, and s=ee(1—cosw)/2."," The differential opacity for an emitted $\gamma$ -ray of energy $\epsilon$ is given by where $l$ is the distance along the line of sight, $\epsilon_0$ is the energy of the stellar photon, $\psi$ is the interaction angle and the absorption cross section can be represented in the form: where $\beta=(1-1/s)^{1/2}$, and $s=\epsilon\epsilon_0(1-\cos\psi)/2$." " Pair production can only occur for s>1, when the centre of mass energy of the incoming photons is sufficiently high to create an electron positron pair."," Pair production can only occur for $s>1$ , when the centre of mass energy of the incoming photons is sufficiently high to create an electron positron pair." " The cross section maximum takes place for s~3.5, with a value of σγγ~0.207, and then decreases for s>1."," The cross section maximum takes place for $s\simeq3.5$, with a value of $\sigma_{\gamma\gamma}\simeq0.2\sigma_\mathrm{T}$, and then decreases for $s\gg1$." " The optical depth owing to pair production Ty, is calculated at each point along the orbit by integrating the differential opacity (Eq. 10))", The optical depth owing to pair production $\tau_{\gamma\gamma}$ is calculated at each point along the orbit by integrating the differential opacity (Eq. \ref{eq:difgg}) ) along the line of sight and over the blackbody seed photon distribution., along the line of sight and over the blackbody seed photon distribution. " The attenuation factor x=exp(—Ty,) is applied to the intrinsic IC spectrum (dashed line in Fig. 4))", The attenuation factor $\kappa=\exp(-\tau_{\gamma\gamma})$ is applied to the intrinsic IC spectrum (dashed line in Fig. \ref{fig:sed}) ) to obtain the spectrum emitted out of the binary system (solid line in Fig. 4))., to obtain the spectrum emitted out of the binary system (solid line in Fig. \ref{fig:sed}) ). " As seen in Fig. 6,"," As seen in Fig. \ref{fig:lc}," we were able to reproduce the X-ray and VHE light curves obtained during the 2007 multiwavelength campaign., we were able to reproduce the X-ray and VHE light curves obtained during the 2007 multiwavelength campaign. " Although the good agreement with the X-ray light curve is expected because we derived the dominant adiabatic losses from the observed X-ray fluxes, the VHE light curve is a prediction of the model taking into account the binary geometry, the stellar photon field, and the non-thermal particle distribution."," Although the good agreement with the X-ray light curve is expected because we derived the dominant adiabatic losses from the observed X-ray fluxes, the VHE light curve is a prediction of the model taking into account the binary geometry, the stellar photon field, and the non-thermal particle distribution." " Furthermore, the spectral indices in the X-ray and VHE energy bands for the outburst at phases 0.6<$«0.7 are well reproduced, as can be seen in Fig. 4.."," Furthermore, the spectral indices in the X-ray and VHE energy bands for the outburst at phases $0.6<\phi<0.7$ are well reproduced, as can be seen in Fig. \ref{fig:sed}." We found that the best fit to the X-ray and VHE photon indices can be obtained by taking a particle energy distribution with slope @=2.1., We found that the best fit to the X-ray and VHE photon indices can be obtained by taking a particle energy distribution with slope $\alpha_\mathrm{e}=2.1$. " As mentioned above, the photon index in the X-ray band directly depends on the particle index of the parent electron population."," As mentioned above, the photon index in the X-ray band directly depends on the particle index of the parent electron population." " In the X-ray band, the observations show a photon index between 1.58+0.02 and 1.66+0.02 (plus a 1.85+0.02 outlier) for the observations,which is anti-correlated with the X-ray flux."," In the X-ray band, the observations show a photon index between $1.58\pm0.02$ and $1.66\pm0.02$ (plus a $1.85\pm0.02$ outlier) for the observations,which is anti-correlated with the X-ray flux." The time-dependent energy cutoff given by the variability of cooling time scales provides a small time dependent variation of the photon index through a modification of the shape of the spectrum., The time-dependent energy cutoff given by the variability of cooling time scales provides a small time dependent variation of the photon index through a modification of the shape of the spectrum. " Regarding the VHE observations, the measured photon index is 2.7+0.3,0.2,,, for the three observations during the first outburst."," Regarding the VHE observations, the measured photon index is $2.7\pm0.3_\mathrm{stat}\pm0.2_\mathrm{sys}$ for the three observations during the first outburst." " Because absorption is low at the orbital phases of the maximum, the photon index is determined by ας and the IC interaction angle."," Because absorption is low at the orbital phases of the maximum, the photon index is determined by $\alpha_\mathrm{e}$ and the IC interaction angle." " The parent particle population with a,=2.1 results in computed X-ray photon indices in the range 1.55—1.67 andreproduces the observed anti-correlation between Ix and Fx."," The parent particle population with $\alpha_\mathrm{e}=2.1$ results in computed X-ray photon indices in the range $1.55$ $1.67$ andreproduces the observed anti-correlation between $\Gamma_{\rm X}$ and $F_{\rm X}$ ." In the VHE band the adopted ας results in photon indices in the range 2.6—2.8 for, In the VHE band the adopted $\alpha_{\rm e}$ results in photon indices in the range $2.6$ $2.8$ for We assume (hat a fraction of the swept-up electrons will be instantaneously accelerated into a power-law. which can be described by an injection function of the form where //Grg.04)=1 lor ry.," As for NGC 1068, the nucleus is completely hidden at all energies, which implies a column density $\simgt$ $^{25}$ $^{-2}$." The emission above a few keV is dominated by a cold rellection component. ancl the evidence for ionized reflection is scanty.," The emission above a few keV is dominated by a cold reflection component, and the evidence for ionized reflection is scanty." The apparently: broad. iron line can actually be fitted by a blend of Ixo and [Luorescent lines., The apparently broad iron line can actually be fitted by a blend of $\alpha$ and $\beta$ fluorescent lines. " This is the archetypal ""moderately. thick” source. where he nucleus becomes visible above about LO keV. (lwasawa et al."," This is the archetypal “moderately thick"" source, where the nucleus becomes visible above about 10 keV (Iwasawa et al." 1993: Done. Smith Alacdejski 1996).," 1993; Done, Smith Madejski 1996)." Modeling he BeppoSAN cata (Ciuainazzi et al., Modeling the BeppoSAX data (Guainazzi et al. " 2000a) with the ransmission model mentioned before. a column density .or the absorber ofye o.471). 2 tem272, and a power law οποίο index of 1.4250.3 are obtained."," 2000a) with the transmission model mentioned before, a column density for the absorber of $^{+0.3}_{-0.4}$ $\times$ $^{24}$ $^{-2}$, and a power law photon index of $\pm$ 0.3 are obtained." Phe intrinsic 2.10 keV uminosityv is LOY erg s.., The intrinsic 2–10 keV luminosity is $\times$ $^{42}$ erg $^{-1}$. " ""Phis value dilfers significantly rom that quoted in bwasawa et al. (", This value differs significantly from that quoted in Iwasawa et al. ( 1993) because they did not include Compton scattering in the fitting model.,1993) because they did not include Compton scattering in the fitting model. Contrary to the other sources. no clear evidence is found or either the cold or the ijonized. reflector. the spectrum. odow S keV being dominated by extended. rather than nuclear. emission.," Contrary to the other sources, no clear evidence is found for either the cold or the ionized reflector, the spectrum below 8 keV being dominated by extended, rather than nuclear, emission." Vololo 0109-383. (NGC 424) has been observed by 3epposAX on 1999 July 2628 for a net exposure time of 64 ks in the MIECS and PDS. and 24.6 ks in the LECS.," Tololo 0109-383 (NGC 424) has been observed by BeppoSAX on 1999 July 26–28 for a net exposure time of 64 ks in the MECS and PDS, and 24.6 ks in the LECS." Phe fit with the usual model gives a column density of about 1071 7 (with the power law index fixed to 2: the quality of the cata is not good enough to allow for à simultaneous estimate of both the column density and the power law index)., The fit with the usual model gives a column density of about $\times$ $^{24}$ $^{-2}$ (with the power law index fixed to 2: the quality of the data is not good enough to allow for a simultaneous estimate of both the column density and the power law index). The resulting intrinsic 2LO keV luminosity is 1077 erg , The resulting intrinsic 2–10 keV luminosity is $\times$ $^{43}$ erg $^{-1}$. Evidence for both a cold and ionized rellection components are present., Evidence for both a cold and ionized reflection components are present. A complete analysis of the BeppoSAX data. along with those from a previous ASC observation. will be presented in Iwasawa et al. (," A complete analysis of the BeppoSAX data, along with those from a previous ASCA observation, will be presented in Iwasawa et al. (" 2000).,2000). The first question to address is the spatial distribution of the NXray absorbing matter. and in particular its covering factor.," The first question to address is the spatial distribution of the X–ray absorbing matter, and in particular its covering factor." Even if formally the transmitted spectrum depends on the covering factor. as it changes the importance. of Compton scattering into our line of sight of photons initially emitted in other. directions (Matt. Pompilio Lalranca 1999). the quality of the data is not good enough to reach any conclusion from spectral fitting.," Even if formally the transmitted spectrum depends on the covering factor, as it changes the importance of Compton scattering into our line of sight of photons initially emitted in other directions (Matt, Pompilio LaFranca 1999), the quality of the data is not good enough to reach any conclusion from spectral fitting." We have therefore to resort to indirect. arguments., We have therefore to resort to indirect arguments. The first one comes from the common presence of reflection from cold matter. signaled by the 6.4 keV Uuorescent iron line and the Compton rellection component. the latter often. dominating the spectrum. at energies where the nuclear emission is completely blocked.," The first one comes from the common presence of reflection from cold matter, signaled by the 6.4 keV fluorescent iron line and the Compton reflection component, the latter often dominating the spectrum at energies where the nuclear emission is completely blocked." When the intensities of these features are compared with the direct continuum. a rather large covering factor is deduced (sec next section).," When the intensities of these features are compared with the direct continuum, a rather large covering factor is deduced (see next section)." Further. and even stronger. evidence in favour of a large covering [actor comes from a statistical argument.," Further, and even stronger, evidence in favour of a large covering factor comes from a statistical argument." As shown by Maiolino ct al. (, As shown by Maiolino et al. ( 1998) and. Risaliti. Maiolino Salvati (1999). the fraction of Comptonthick sources. is fairly high. being possibly as large as one half of all Sevfert 2 galaxies. (,"1998) and Risaliti, Maiolino Salvati (1999), the fraction of Compton–thick sources is fairly high, being possibly as large as one half of all Seyfert 2 galaxies. (" Because the Iusaliti. Maiolino Salvati 1999 sample is based on OLLI] Duxes. this fraction may even be underestimated. as e.g. NGC 6240 and. NGC 4945 would have been nmüssed. see below).,"Because the Risaliti, Maiolino Salvati 1999 sample is based on [OIII] fluxes, this fraction may even be underestimated, as e.g. NGC 6240 and NGC 4945 would have been missed, see below)." The covering factor of the Comptonthick matter must. therefore. be large.," The covering factor of the Compton–thick matter must, therefore, be large." As mentioned above. the fraction of Compton.thick sources among optically-sclected Seyfert 2 galaxies is large. 50 por cent at least.," As mentioned above, the fraction of Compton–thick sources among optically-selected Seyfert 2 galaxies is large, 50 per cent at least." As Sevlert 2 galaxies outnumber Sevlert 1 ealaxies by a large factor. this means that most ACN are heavily obseured.," As Seyfert 2 galaxies outnumber Seyfert 1 galaxies by a large factor, this means that most AGN are heavily obscured." Moreover. this fraction may be even larger among LR.selected sources.," Moreover, this fraction may be even larger among IR–selected sources." A simple argument may be used [or a crude estimate of the fraction of highly obscured AGN., A simple argument may be used for a crude estimate of the fraction of highly obscured AGN. ‘The three nearest AGN. the Cireinus Galaxy. NGC 4945 and Centaurus A are all heavily obscured (Centaurus A has a column density of 107Du em27 and an intrinsic 2.10 keV," The three nearest AGN, the Circinus Galaxy, NGC 4945 and Centaurus A are all heavily obscured (Centaurus A has a column density of $\sim$ $^{23}$ $^{-2}$ and an intrinsic 2–10 keV" We have compared the vvalues measured in a sample of 62 star-forming galaxies with the predictions by our evolutionary synthesis models. aiming to analyze the validity of semiempirical and theoretical calibrations of ads a star formation rate estimator.," We have compared the values measured in a sample of 62 star-forming galaxies with the predictions by our evolutionary synthesis models, aiming to analyze the validity of semiempirical and theoretical calibrations of as a star formation rate estimator." The main results can be summarized as follows:, The main results can be summarized as follows: In Einstein's (heory of General Relativity. linearization of the field equations shows that small perturbations of the metric obev a wave equation (Misner. Thorne Wheeler 1973).,"In Einstein's theory of General Relativity, linearization of the field equations shows that small perturbations of the metric obey a wave equation (Misner, Thorne Wheeler 1973)." These small disturbances. referved. {ο as gravitational waves. (travel al the speed of light.," These small disturbances, referred to as gravitational waves, travel at the speed of light." llowever. some other gravitv theories predict a dispersive propagation (see Will(2004) [or relerences).," However, some other gravity theories predict a dispersive propagation (see \citet{wy04} for references)." " The most commonly considered form of dispersion supposes that the waves obev a Ixlein.Gordan tvpe equation: Physically. the dispersive term is ascribed to the quantum of gravitation having a rest mass mu. or equivalently a non-inlinite Compton wavelength A,=hímygc."," The most commonly considered form of dispersion supposes that the waves obey a Klein–Gordan type equation: Physically, the dispersive term is ascribed to the quantum of gravitation having a non-zero rest mass $m_{\rm g}$, or equivalently a non-infinite Compton wavelength $\lambda_{\rm g} = h/m_{\rm g}c$." " The group velocity of propagation for a wave of frequency fa; is then valid for Aj,«A4: only in the infinite frequency limit is General Relativity recovered. wilh waves traveling at the speed of light (Will1993)."," The group velocity of propagation for a wave of frequency $f_{\rm gw}$ is then valid for $\lambda_{\rm gw} \ll \lambda_{g}$; only in the infinite frequency limit is General Relativity recovered, with waves traveling at the speed of light \citep{will98}." . Over the past few decades a number of different tests of this dispersive hypothesis have been described. i.e. tests making use of direct. observations of gravitational waves or (heir radiation reaction effects (Cutlerοἱal.2003:2000:Will1993:&Yunes 2004).," Over the past few decades a number of different tests of this dispersive hypothesis have been described, i.e. tests making use of direct observations of gravitational waves or their radiation reaction effects \citep{chl03,fs02,lh00,will98,wy04}." In (his paper we add another method to this list: we consider gravitational radiation rom binary svstems., In this paper we add another method to this list; we consider gravitational radiation from binary systems. Such binaries emit gravitational radiation al (infinitely many) iunmonies of the orbital frequency. (Peters&.Mathews1963)., Such binaries emit gravitational radiation at (infinitely many) harmonics of the orbital frequency \citep{pm63}. . Our idea lies simply in neasuring the phase of arrival of these harmonies., Our idea lies simply in measuring the phase of arrival of these harmonics. Dispersion of the form described by equation (2)) would be signaled by the higher harmonics arriving slishtlv earlier (han the ower harmonics. as compared to (he General Relativistic waveform.," Dispersion of the form described by equation \ref{eq:vg}) ) would be signaled by the higher harmonics arriving slightly earlier than the lower harmonics, as compared to the General Relativistic waveform." We present a rough estimate of the bounds that might be obtained. deferring a more accurate caleulation to a uture study (Barack Jones. in preparation).," We present a rough estimate of the bounds that might be obtained, deferring a more accurate calculation to a future study (Barack Jones, in preparation)." The plan of this paper is as follows., The plan of this paper is as follows. In 82. we derive lormulae (to make a simple estimate ol the bounds that might be obtained using our method., In \ref{sect:dotb} we derive formulae to make a simple estimate of the bounds that might be obtained using our method. " In 82. we estimate bounds obtainable on A, for LISA observations of two sorts of binary svstenis.", In \ref{sect:r} we estimate bounds obtainable on $\lambda_{\rm g}$ for LISA observations of two sorts of binary systems. Finally in 84 we simniarize our lindings and compare will those of other authors., Finally in \ref{sect:c} we summarize our findings and compare with those of other authors. the gas at lower gas surface densities inert to star formation.,the gas at lower gas surface densities inert to star formation. This is consistent with observations of local dwarf low surface brightness galaxies. which exhibit very low molecular gas fractions and anemic star formation rates (??2??)., This is consistent with observations of local dwarf low surface brightness galaxies which exhibit very low molecular gas fractions and anemic star formation rates . . The examples described above illustrate the importance of further investigation of the effects of environmental dependencies of the KS relation discussed in this. paper., The examples described above illustrate the importance of further investigation of the effects of environmental dependencies of the KS relation discussed in this paper. The results and fitting formulae that we present should aid in implementing such dependencies in both cosmological simulations and semr-analytie models and should thus help to explore a wide range of possible effects., The results and fitting formulae that we present should aid in implementing such dependencies in both cosmological simulations and semi-analytic models and should thus help to explore a wide range of possible effects. This work was supported in part by the DOE at Fermilab. by the NSF grants AST-0507596 and AST-0708154. and by the Kavli Institute for Cosmological Physics at the University of Chicago through the NSF grant PHY-0551142 and an endowment from the Kavli Foundation.," This work was supported in part by the DOE at Fermilab, by the NSF grants AST-0507596 and AST-0708154, and by the Kavli Institute for Cosmological Physics at the University of Chicago through the NSF grant PHY-0551142 and an endowment from the Kavli Foundation." The simulations used in this work have been performed on the Joint Fermilab - KICP Supercomputing Cluster. supported by grants from Fermilab. Kavli Institute for Cosmological Physics. and the University of Chicago.," The simulations used in this work have been performed on the Joint Fermilab - KICP Supercomputing Cluster, supported by grants from Fermilab, Kavli Institute for Cosmological Physics, and the University of Chicago." This work made extensive use of the NASA Astrophysics Data System and preprint server., This work made extensive use of the NASA Astrophysics Data System and preprint server. In this Appendix we present the chemical reaction network of hydrogen and helium. as well as our phenomenological model for the formation of molecular hydrogen. in full detailpaper).," In this Appendix we present the chemical reaction network of hydrogen and helium, as well as our phenomenological model for the formation of molecular hydrogen, in full detail." . We follow in detail 8 species of hydrogen and helium: HI. HIL HeL HeIL. HeHI. H>. H. and H5.," We follow in detail 8 species of hydrogen and helium: $\HI$ , $\HII$ , $\GI$, $\GII$, $\GIII$, $\H2$, $\Hm$, and $\Hp$." " It is not. however. necessary to follow electrons separately. since. in all physical regimes of interest. abundances of H7 and H are extremely small. so Note that this equation does not include any negative terms and thus 7, will always be calculated with the error similar to the relative errors of ΤΗ. Της. ANd 75;gi. but not larger."," It is not, however, necessary to follow electrons separately, since, in all physical regimes of interest, abundances of $\Hp$ and $\Hm$ are extremely small, so Note that this equation does not include any negative terms and thus $n_e$ will always be calculated with the error similar to the relative errors of $n_\HII$, $n_\GII$, and $n_{\GIII}$, but not larger." " We follow all other species self-consistently and separately by solving the corresponding ODEs to avoid potentially unbounded increase of relative error in subtracting abundance of one specie from another (sometimes called “loss of precision"").", We follow all other species self-consistently and separately by solving the corresponding ODEs to avoid potentially unbounded increase of relative error in subtracting abundance of one specie from another (sometimes called “loss of precision”). For example. if the abundance of HeHI would be calculated by subtracting the abundance of He1 and HeII from the constant total abundance of He. the relative error of HeHII can be arbitratily large when the fraction of He[Lis small.," For example, if the abundance of $\GIII$ would be calculated by subtracting the abundance of $\GI$ and $\GII$ from the constant total abundance of He, the relative error of $\GIII$ can be arbitratily large when the fraction of $\GIII$ is small." We explicitly assume that all species are advected with the same peculiar gas velocity i5, We explicitly assume that all species are advected with the same peculiar gas velocity $\vec{v}$ . In this case the equations for the evolution of their number densities can be concisely represented as where j=HI. HII. Hel. HeIl. HeLIL. Hs. H. and H5. the divergence is taken in comoving space ¥ and three terms on the right hand side include reactions due to ionization balance. molecular chemistry. and dust chemistry respectively.," In this case the equations for the evolution of their number densities can be concisely represented as where $j=\HI$, $\HII$, $\GI$, $\GII$, $\GIII$, $\H2$, $\Hm$, and $\Hp$, the divergence is taken in comoving space $\vec{x}$ and three terms on the right hand side include reactions due to ionization balance, molecular chemistry, and dust chemistry respectively." This subdivision of the reactions into three sets is primarily for the sake of convenience and because we use different sources for different reaction rates., This subdivision of the reactions into three sets is primarily for the sake of convenience and because we use different sources for different reaction rates. This separation 15. of course. artificial - all the reactions take place together in a fluid element.," This separation is, of course, artificial - all the reactions take place together in a fluid element." The OTVET radiative transfer solver produces the radiation field at each computational cell that is used to calculate the rates for reactions between chemical species and radiation (including photo-ionization)., The OTVET radiative transfer solver produces the radiation field at each computational cell that is used to calculate the rates for reactions between chemical species and radiation (including photo-ionization). " We generically label these rates as I""! with various indicies."," We generically label these rates as $\Gamma^{\rm RT}$ with various indicies." " Since the self-shielding of molecular hydrogen and shielding by dust are not included in the OTVET solver. but are the ingredients of our empirical model. they are encapsulated into two factors. Sy, and Sp. with which we multiply the appropriate rates."," Since the self-shielding of molecular hydrogen and shielding by dust are not included in the OTVET solver, but are the ingredients of our empirical model, they are encapsulated into two factors, $S_\H2$ and $S_{\rm D}$ , with which we multiply the appropriate rates." These factors are described below., These factors are described below. Ionization balance terms include standard processes of photo-ionization. collistonal ionization. and radiative recombination. and therefore only involve j=HI. HII. Hel. Hell. HeUL.," Ionization balance terms include standard processes of photo-ionization, collisional ionization, and radiative recombination, and therefore only involve $j=\HI$, $\HII$, $\GI$ , $\GII$, $\GIII$." " We label all terms that include at least one of H». H. and H5 as ""molecular chemistry”. and describe them all in the following subsection."," We label all terms that include at least one of $\H2$, $\Hm$, and $\Hp$ as “molecular chemistry”, and describe them all in the following subsection." Here C; are collisional ionization rates. are radiative recombination rates. and are dielectronic recombination rates.," Here $C_j$ are collisional ionization rates, $R_j$ are radiative recombination rates, and $D_j$ are dielectronic recombination rates." Por these rates we use highly accurate fitting formulaeA; from?., For these rates we use highly accurate fitting formulae from. . The recombination coefficientsD; are computed self-consistently as a combination of case A and case B recombination. depending on the gas opacity.," The recombination coefficients are computed self-consistently as a combination of case A and case B recombination, depending on the gas opacity." The photo-ionization rates are derived from those returned by the radiative transfer solver and include the shielding by dust as In particular. we use the same factor to account for dust shielding in all three photo-ionization rates.," The photo-ionization rates are derived from those returned by the radiative transfer solver and include the shielding by dust as In particular, we use the same factor to account for dust shielding in all three photo-ionization rates." Obviously. thisis notexact. as the dust cross-section is a function of wavelength.," Obviously, thisis notexact, as the dust cross-section is a function of wavelength." However. since the effect of helium on molecularchemistry inside molecular clouds is thought to be small. helium ionization 1iside molecularclouds is sufficient to be treatedrather approximately.," However, since the effect of helium on molecularchemistry inside molecular clouds is thought to be small, helium ionization inside molecularclouds is sufficient to be treatedrather approximately." respectively. and the speed of light e.,"respectively, and the speed of light $v_c$." Phe magnification is then simply (e.g. Schneider. Ehlers and Falco 1992).," The magnification is then simply (e.g. Schneider, Ehlers and Falco 1992)." Using frxpw in Equation 3.. we perform the maximum. likelihood analysis for an NEW. profile on Abell 2219.," Using $\mu_{\rm NFW}$ in Equation \ref{eqn-l}, we perform the maximum likelihood analysis for an NFW profile on Abell 2219." We reduce the model to one parameter by assuming a reasonable value for the concentration parameter. namely e= 6. and fitting for ry.," We reduce the model to one parameter by assuming a reasonable value for the concentration parameter, namely $c=6$ , and fitting for $r_s$." We find a maximum at 7 corresponding to an angular length of 52 aresee., We find a maximum at $r_s$ corresponding to an angular length of 52 arcsec. At the redshift of the cluster this gives a scale length of 1255.+ kpe (where Lo=1005 km s +). whieh compares well to the à;~2505.7 predicted from numerical simulations of CDAL models (Dartelmann 1996).," At the redshift of the cluster this gives a scale length of $h^{-1}$ kpc (where $H_0=100h$ km $^{-1}$ $^{-1}$ ), which compares well to the $r_s \sim 250 h^{-1}$ predicted from numerical simulations of CDM models (Bartelmann 1996)." Fig., Fig. Ὁ shows the form of an NEW depletion curve resultingfrom the substitution of xps in Equation 1.. for such a cluster with ο=6 and r;=125h+ kpe.," \ref{fig-nfw} shows the form of an NFW depletion curve resultingfrom the substitution of $\mu_{\rm NFW}$ in Equation \ref{eqn-N}, for such a cluster with $c=6$ and $r_s=125 h^{-1}$ kpc." The observed. depletion. curve of Abell 2219 is overplottec for comparison. and we see that the data are also consistent with this model.," The observed depletion curve of Abell 2219 is overplotted for comparison, and we see that the data are also consistent with this model." However. the data do not allow us to clistinguish between the NEW ane SIS models.," However, the data do not allow us to distinguish between the NFW and SIS models." In the further analysis we choose to continue with the SIS for simplicity., In the further analysis we choose to continue with the SIS for simplicity. Yo further test the robustness of the depletion elfect we have simulated a population of galaxies with the same properties as our putative background population., To further test the robustness of the depletion effect we have simulated a population of galaxies with the same properties as our putative background population. In our observed sample the intrinsic power law form of the background. number counts is modified. by the incompleteness function., In our observed sample the intrinsic power law form of the background number counts is modified by the incompleteness function. As shown in Appendix A. it is jowever equivalent to use a renormalized power law for the counts in the simulations.," As shown in Appendix A, it is however equivalent to use a renormalized power law for the counts in the simulations." " Specifically. we keep the same observed. slope. à.=0.185 but. lower the normalization o maintain the same observed unlensed. number density D,=20.3 arcmin2"," Specifically, we keep the same observed slope, $\alpha=0.185$ but lower the normalization to maintain the same observed unlensed number density $\tilde{n}_o=20.3$ $^{-2}$." Scattering. the simulated galaxies randomly across 1e field of view. we then adjusted. their. positions and magnitudes as i£ they were lensed by à singular isothermal sphere with 8e=13.7 aresec.," Scattering the simulated galaxies randomly across the field of view, we then adjusted their positions and magnitudes as if they were lensed by a singular isothermal sphere with $\theta_{\rm E} = 13.7$ arcsec." We created. a catalogue of those galaxies whose lensed magnitudes were brighter than our limiting magnitude ancl whose lensed positions =μαvre not obscured by the Abell 2219 cluster mask and applied the same maximum likelihood technique., We created a catalogue of those galaxies whose lensed magnitudes were brighter than our limiting magnitude and whose lensed positions were not obscured by the Abell 2219 cluster mask and applied the same maximum likelihood technique. Fie., Fig. 10 shows the distribution of the resulting best-Litting models for 200 realizations., \ref{fig-mldist} shows the distribution of the resulting best-fitting models for 200 realizations. We see that the distribution of recovered Einstein radii is centredἱ around the input value of 13.7 arcsec. and deduce the confidence interval to span the rangearcesec.. Yo translate the estimates of into an statement regarding the cluster mass. we use the relation for a SIS: where a7 is the velocity dispersion of the lens. 2a. and D. ave the angular-diameter distances [rom lens to source and. from observer to source. respectively.," We see that the distribution of recovered Einstein radii is centred around the input value of 13.7 arcsec, and deduce the confidence interval to span the range To translate the estimates of into an statement regarding the cluster mass, we use the relation for a SIS: where $\sigma^2_v$ is the velocity dispersion of the lens, $D_{\rm ds}$ and $D_{\rm s}$ are the angular-diameter distances from lens to source and from observer to source, respectively." "Modelling the background. N(2) from the A-band surveys of Cowie (1996). we find the median recdshiftfor the background is =1.0 for Lf< 22. inereasing to —19 αἱ 4< 24.Given spa.=0.22 ancl assuming a cosmology of 5. qe=0.5) we obtain o,=S42112ii, kms ‘for (23= Land","Modelling the background $N(z)$ from the $K$ -band surveys of Cowie (1996), we find the median redshiftfor the background is $\left< z \right>=1.0$ for $H<22$ , increasing to $\left< z \right>=1.3$ at $H<24$ .Given $z_{\rm lens}=0.22$ and assuming a cosmology of , $q_o=0.5$ we obtain $\sigma_v = 842^{+112}_{-141}$ km $^{-1}$ for $\left< z \right>=1$ and" "Modelling the background. N(2) from the A-band surveys of Cowie (1996). we find the median recdshiftfor the background is =1.0 for Lf< 22. inereasing to —19 αἱ 4< 24.Given spa.=0.22 ancl assuming a cosmology of 5. qe=0.5) we obtain o,=S42112ii, kms ‘for (23= Lando","Modelling the background $N(z)$ from the $K$ -band surveys of Cowie (1996), we find the median redshiftfor the background is $\left< z \right>=1.0$ for $H<22$ , increasing to $\left< z \right>=1.3$ at $H<24$ .Given $z_{\rm lens}=0.22$ and assuming a cosmology of , $q_o=0.5$ we obtain $\sigma_v = 842^{+112}_{-141}$ km $^{-1}$ for $\left< z \right>=1$ and" "Modelling the background. N(2) from the A-band surveys of Cowie (1996). we find the median recdshiftfor the background is =1.0 for Lf< 22. inereasing to —19 αἱ 4< 24.Given spa.=0.22 ancl assuming a cosmology of 5. qe=0.5) we obtain o,=S42112ii, kms ‘for (23= Lando,","Modelling the background $N(z)$ from the $K$ -band surveys of Cowie (1996), we find the median redshiftfor the background is $\left< z \right>=1.0$ for $H<22$ , increasing to $\left< z \right>=1.3$ at $H<24$ .Given $z_{\rm lens}=0.22$ and assuming a cosmology of , $q_o=0.5$ we obtain $\sigma_v = 842^{+112}_{-141}$ km $^{-1}$ for $\left< z \right>=1$ and" laree enough to induce an iron peak convection zone for any of the three models. though iron peak opacity might extend the SCZ slightly inward for the 1.50W5E-14. model.,"large enough to induce an iron peak convection zone for any of the three models, though iron peak opacity might extend the SCZ slightly inward for the 1.50W5E-14 model." If the mass loss rate is €107Mayr!. an iron convection zone may appear after the PMS (see 55 of Paper D.," If the mass loss rate is $\leq 10^{-14}\Mloss{}$, an iron convection zone may appear after the PMS (see 5 of Paper I)." Significant abundance variations appear in the interior of our PMS models., Significant abundance variations appear in the interior of our PMS models. " For example. in the model (bottom row of reffig:flux). a. l.1ddex Ca overabundance develops at logAM/M,zx-9. as early as 4MMyr."," For example, in the model (bottom row of \\ref{fig:flux}) ), a $1.1$ dex Ca overabundance develops at $\DM \simeq -9.4$ as early as Myr." It might seem puzzling however that such an overabundance transforms into a strong underabundance which reaches below —1 ddex at 30MMyr., It might seem puzzling however that such an overabundance transforms into a strong underabundance which reaches below $-$ dex at Myr. Why should the behavior at 4MMvr be so different from the rest of the star's evolution and why does a strong overabundance develop in a region where e44(€Ca) is below gravity?, Why should the behavior at Myr be so different from the rest of the star's evolution and why does a strong overabundance develop in a region where (Ca) is below gravity? The reason stems from the fact that the wind progressively advects matter from deeper within the star., The reason stems from the fact that the wind progressively advects matter from deeper within the star. That depth is simply given by: So. at MMyr. the wind brings to the surface matter which originates from 4x10° yyr-5x107Mayr!22x1077107 M...," That depth is simply given by: So, at Myr, the wind brings to the surface matter which originates from $4\times 10^{6}$ $\cdot\, 5 \times 10^{-14}\Mloss = 2 \times 10^{-7}\Msol \sim 10^{-7}M_*$ ." Correspondingly. one sees in the top row of reffig:flux that the flux is nearly constant from the surface down to that depth (except over CZs). while it is clearly not constant below that depth.," Correspondingly, one sees in the top row of \\ref{fig:flux} that the flux is nearly constant from the surface down to that depth (except over CZs), while it is clearly not constant below that depth." Naturally. the depth above which the flux is conserved due to advection from the wind increases with age (compare the curves at 4. 30 and 300MMyr).," Naturally, the depth above which the flux is conserved due to advection from the wind increases with age (compare the curves at 4, 30 and Myr)." In order to conserve the flux. X(Ca) at MMyr increases above AM/M.~1077 to compensate for the decrease inV.," In order to conserve the flux, $X$ (Ca) at Myr increases above $\Dm \sim 10^{-7}$ to compensate for the decrease in." .. This process can be described by: where 7(7) is the local flux at radius 7. p is the local density. C and C are the advective part of the atomic diffusion velocity and wind velocity respectively. and ο istion’.," This process can be described by: where $\mathcal{F}(r)$ is the local flux at radius $r$, $\rho$ is the local density, $U$ and $U_{{\rm w}}$ are the advective part of the atomic diffusion velocity and wind velocity respectively, and $c$ is." Although gravity is stronger than over a fraction of the stellar envelope for all elements shown in reffig:flux.. the downward diffusion velocity 1s never larger than the wind velocity (see reffig:vwind for an example with a model).," Although gravity is stronger than over a fraction of the stellar envelope for all elements shown in \\ref{fig:flux}, the downward diffusion velocity is never larger than the wind velocity (see \\ref{fig:vwind} for an example with a model)." Therefore. as long as the absolute value of the wind velocity is larger than the downward diffusion velocity. any given element is dragged toward the surface. and its local abundance adjusts in order to conserve flux.," Therefore, as long as the absolute value of the wind velocity is larger than the downward diffusion velocity, any given element is dragged toward the surface, and its local abundance adjusts in order to conserve flux." Notice that the fraction of the envelope AM which can be described by 2]] increases with time since the wind progressively advects more mass toward the surface., Notice that the fraction of the envelope $\Delta M$ which can be described by ] increases with time since the wind progressively advects more mass toward the surface. With this 1n mind. one can understand that at 24 MMyr. the increase of X(Ca) above AM/M.~1077 is generated by the large flux arriving from regions where ej4((C3) is larger than gravity and which is conserved even as g;44((Ca) decreases toward the surface.," With this in mind, one can understand that at $t = 4$ Myr, the increase of $X$ (Ca) above $\Dm \sim 10^{-7}$ is generated by the large flux arriving from regions where (Ca) is larger than gravity and which is conserved even as (Ca) decreases toward the surface." " As time passes. Ca arrives at the surface from deeper within the star. where g,,u((Ca) 1s much smaller than its value at AM/M,~1077. so that the flux is smaller. the flux conservation applies over a larger mass and the surface abundance consequently decreases."," As time passes, Ca arrives at the surface from deeper within the star, where (Ca) is much smaller than its value at $\Dm \sim 10^{-7}$, so that the flux is smaller, the flux conservation applies over a larger mass and the surface abundance consequently decreases." This shows the importance of a solution over the whole star. as done here. since applying an inner boundary condition at AM/M.~1077 would lead to an erroneous solution after MMyr.," This shows the importance of a solution over the whole star, as done here, since applying an inner boundary condition at $\Dm \sim 10^{-7}$ would lead to an erroneous solution after Myr." On the PMS. the internal concentration variations are much smaller for Li. O and Fe than for Ca.," On the PMS, the internal concentration variations are much smaller for $^7$ Li, O and Fe than for Ca." " However. after the star arrives on the MS. as illustrated by the curve at MMyr. larger variations appear. including a nearly -0.8 ddex overabundance of Fe which spans from the surface down to logAM/M,~--δ."," However, after the star arrives on the MS, as illustrated by the curve at Myr, larger variations appear, including a nearly $\sim$ dex overabundance of Fe which spans from the surface down to $\DM \sim -8$." " As shown in reffig:vwind.. for a mass loss rate of 107ΜΟΙ, the downward diffusion velocity is greater than the wind velocity for some elements. whereby the flux conservation regime as described by 2]] cannot be extended to all elements."," As shown in \\ref{fig:vwind}, for a mass loss rate of $10^{-14}\Mloss$ , the downward diffusion velocity is greater than the wind velocity for some elements, whereby the flux conservation regime as described by ] cannot be extended to all elements." The regime shift approximately occurs at 2x107Mayr! (see Fig.55 of Paper I and corresponding discussion)., The regime shift approximately occurs at $2 \times 10^{-14}\Mloss$ (see 5 of Paper I and corresponding discussion). This mass loss rate also marks the limit below which tron accumulation near T~200000 KK can lead to tron peak convection (see 55 of Paper D.," This mass loss rate also marks the limit below which iron accumulation near $T\sim 200\,000$ K can lead to iron peak convection (see 5 of Paper I)." An element's surface abundance depends on age. stellar mass and mass loss rate.," An element's surface abundance depends on age, stellar mass and mass loss rate." " In reffig:HR.. the surface abundances of He. ‘Li. Ca and Fe are shown for models of 1.5. 1.9. 2.5 and with a mass loss rate of 5x1077ΜΥΤΗ,"," In \\ref{fig:HR}, the surface abundances of He, $^7$ Li, Ca and Fe are shown for models of 1.5, 1.9, 2.5 and with a mass loss rate of $5 \times 10^{-14}\Mloss$." " As stellar mass increases, anomalies appear at the surface earlier."," As stellar mass increases, anomalies appear at the surface earlier." For instance. at around 3MMyr the 2.50W5E-I4 model has a ddex overabundance of Ca while all other models still have their initial abundances reftis: HRe).," For instance, at around Myr the 2.80W5E-14 model has a dex overabundance of Ca while all other models still have their initial abundances \\ref{fig:HR}{ )." The same can be said for Fe overabundances or He underabundances. which appear later in smaller stellar mass models.," The same can be said for Fe overabundances or He underabundances, which appear later in smaller stellar mass models." Nonetheless. it is evident that for a given element. the overall shape of the surface abundance evolution curve Is very similar for the three heavier models.," Nonetheless, it is evident that for a given element, the overall shape of the surface abundance evolution curve is very similar for the three heavier models." This is due to two things: the appearance of a separate HI CZ. as well as flux conservation as described in the previous section.," This is due to two things: the appearance of a separate II CZ, as well as flux conservation as described in the previous section." For all four elements shown in reffig: HR... the initial. short-lived abundance maxima are caused by evolutionary effects.," For all four elements shown in \\ref{fig:HR}, the initial, short-lived abundance maxima are caused by evolutionary effects." The appearance of a radiative zone which separates the II CZ from the SCZ allows for chemical separation to occur near the surface., The appearance of a radiative zone which separates the II CZ from the SCZ allows for chemical separation to occur near the surface. The direction of the anomaly is determined by e44-g within that region (between logAM/M.~-—10.5 and —9). and thus He. ‘Li and Ca become underabundant. whereas Fe develops an overabundance (compare middle panelof with reffig;HR)).," The direction of the anomaly is determined by $g$ within that region (between $\DM\sim -10.5$ and $ -9$ ), and thus He, $^7$ Li and Ca become underabundant, whereas Fe develops an overabundance (compare middle panelof \\ref{fig:flux} with \\ref{fig:HR}) )." Following this. brief episode. thesurface abundance is determined by flux conservation. and so results from chemical separation occuring deeper within the," Following this brief episode, thesurface abundance is determined by flux conservation, and so results from chemical separation occuring deeper within the" Sxmnnmetiry of the physical process in our Universe and particular mechanisms of its violation is golden mind of the modern physics.,Symmetry of the physical process in our Universe and particular mechanisms of its violation is golden mind of the modern physics. " Since pioneering Lee and Yang investigations of the parity svmmetiry in the weak interaction. (he principle of svimnetry is deeply incorporated into the modern parlicle physics. including the lliggs mechanism of svuumeliyv breaking. in chemistry. in physics of condensed matter and. in general. in the theorv of the phase transition,"," Since pioneering Lee and Yang investigations of the parity symmetry in the weak interaction, the principle of symmetry is deeply incorporated into the modern particle physics, including the Higgs mechanism of symmetry breaking, in chemistry, in physics of condensed matter and, in general, in the theory of the phase transition." Passing from (he microscopic physies to the properties of the space and (ime αἱ large. we have to acimit that the Cosmic Microwave Dackeround (CAIB) radiation anisotropy provides invaluable test [or (he investigation of parity al (he megascopic scales above the scale of inhomogeneity ~ 100Mpc.," Passing from the microscopic physics to the properties of the space and time at large, we have to admit that the Cosmic Microwave Background (CMB) radiation anisotropy provides invaluable test for the investigation of parity at the megascopic scales above the scale of inhomogeneity $\sim100$ Mpc." The problem of the parity asymmetry of the CMD has been investigated in (Land&Magueijo2007;IximNaselsky2010a.b:Gruppusoetal.2011:llansenetal.2011:MarisBen-David 2011).. showing significant dominance of the power spectrum stored in the odd multipoles over the even ones.," The problem of the parity asymmetry of the CMB has been investigated in \citep{evil,jk1,jk2,grup,hansen,maris,david}, showing significant dominance of the power spectrum stored in the odd multipoles over the even ones." Recently. in," Recently, in" frame.,frame. " The calculation of C, in the two dillerent regimes leads to(", The calculation of $U_{rad}$ in the two different regimes leads to. 26) electrons in region A are in the slow cooling regime. Coen new steady state confieuration is Hldev.," If electrons in region A are in the slow cooling regime, the new steady state configuration is." (34)PES slow cooling (δν \tilde{\gamma}_{cB}$ ). Ae T.ds very unlikely. (36) if the electrons in region A have two sources of energv i£ (8 and SSC’). because ἐν \tilde{\gamma}_{c}$ is very unlikely, even if the electrons in region A have two sources of energy loss (S and SSC), because $t_bος and 3< 1. and a varicty ofMIID effects. including the magueto-acoustic mode Conversion. may be observabe at this waveleneth.," This means that in the MBP centre, the continuum is originating from strongly magnetised plasma with $v_A > c_s$ and $\beta < 1$ , and a variety ofMHD effects, including the magneto-acoustic mode conversion, may be observable at this wavelength." Tusciting (60)) iuto (57)) then vields or which can be integrated to where oxxfom0 and f=0 corresponds to arrival at the critical configuration.,Inserting \ref{rdot3}) ) into \ref{mdot4}) ) then yields or which can be integrated to where $-\infty \leq t \leq 0$ and $t=0$ corresponds to arrival at the critical configuration. Defining the last equation can be rewritten Note that £44; is iudepenudoeut of the mass of the star. and determines the evolutionary timescale of SMSs.," Defining the last equation can be rewritten Note that $t_{\rm crit}$ is independent of the mass of the star, and determines the evolutionary timescale of SMSs." Iu ces units. it takes the value (compare Shapiro Teukolskv 1983. where a similar timescale has been derived for SALSs that are stabilized by eas pressure rather than rotation).," In cgs units, it takes the value (compare Shapiro Teukolsky 1983, where a similar timescale has been derived for SMSs that are stabilized by gas pressure rather than rotation)." Suuilar expressions for Π aud J can be found bv inserting (66)) into (603) and (61)): Using the idoutitv Ay=2h;3. we find that the dimensionlessB quantitieseye J/M7Di and R/ÀA evolve accordingB to We plot M. J/M? aud R/M as a function of time in Figme 5..," Similar expressions for $R$ and $J$ can be found by inserting \ref{mdot5}) ) into \ref{rdot3}) ) and \ref{jdot3}) ): Using the identity $k_R = 2 k_J - 3$, we find that the dimensionless quantities $J/M^2$ and $R/M$ evolve according to We plot $M$, $J/M^2$ and $R/M$ as a function of time in Figure \ref{fig5}." Note that J/A/7 and R/AL evolve ou the timescale fair. Which is why we adopt this value for our estimates in Section 2..," Note that $J/M^2$ and $R/M$ evolve on the timescale $t_{\rm crit}$, which is why we adopt this value for our estimates in Section \ref{Sec2}." The mass AM aud similarly A. however. effectively evolve on a much longer timescale. which is a consequence of the siall numerical value of the exponent L/(lAy)00119.," The mass $M$ and similarly $K$, however, effectively evolve on a much longer timescale, which is a consequence of the small numerical value of the exponent $1/(1-k_R) = - 0.0179$." Ouce the supermassive star becomes unstable. it will start to collapse on a clyvnaimical timescale.," Once the supermassive star becomes unstable, it will start to collapse on a dynamical timescale." The outcome of this collapse depends ou many factors. and can be determined. only with a nuuerical threce-cimenusional lydrodvuamics simulation iu ecueral relativity.," The outcome of this collapse depends on many factors, and can be determined only with a numerical, three-dimensional hydrodynamics simulation in general relativity." Such a calculation is onlv now underway (Diimugarte. Shapiro Shibata 1999).," Such a calculation is only now underway (Baumgarte, Shapiro Shibata 1999)." The only dynamical. fully relativistic simulatious of the collapse of SMSs have been performed or nonrotatiue configurations iu spherical svauietry (sec. or example. Shapiro Teukolskv. 1979). for which black hole formation is well established.," The only dynamical, fully relativistic simulations of the collapse of SMSs have been performed for nonrotating configurations in spherical symmetry (see, for example, Shapiro Teukolsky, 1979), for which black hole formation is well established." These calculations. however. do not shed much ight on the problem at haud. since rotation nav plav a crucial role in the cvnamical evolution.," These calculations, however, do not shed much light on the problem at hand, since rotation may play a crucial role in the dynamical evolution." The issue of he final fate of a collapsing. rapidly rotating SMS can herefore only be resolved bw uonspherical. relativistic ποΊσα simulations.," The issue of the final fate of a collapsing, rapidly rotating SMS can therefore only be resolved by nonspherical, relativistic numerical simulations." " Iu the meantime. however, we can attempt to assess crudely whether this collapse can actually lead to the orlation of a supermassive black hole."," In the meantime, however, we can attempt to assess crudely whether this collapse can actually lead to the formation of a supermassive black hole." To do so. we asstune that each mass shell conserves its angular uonmnentuni during the collapse (cf.," To do so, we assume that each mass shell conserves its angular momentum during the collapse (cf." the discussion at the ead of Section 2)). aud consider two criteria.," the discussion at the end of Section \ref{Sec2}) ), and consider two criteria." First. a particle can ouly be captured by a black hole if it is not be repelled by the augular ποιοι barrier.," First, a particle can only be captured by a black hole if it is not be repelled by the angular momentum barrier." For simplicity. we take the newly formed black hole to be a Sclawarzschild black hole. in which case a particle is iu a capture orbit if where J is the particles specific angular moment. aud m the mass of the black hole.," For simplicity, we take the newly formed black hole to be a Schwarzschild black hole, in which case a particle is in a capture orbit if where $l$ is the particle's specific angular momentum, and $m$ the mass of the black hole." Here we ignore the effects of pressure. assunune that in relativistic collapse the matter approaches the nascent black hole supersouically by the time it cuters the stroug feld domain.," Here we ignore the effects of pressure, assuming that in relativistic collapse the matter approaches the nascent black hole supersonically by the time it enters the strong field domain." Second. for any portion of the star to form a Nery black hole. the angular momentum J of that portion caunot be larger than the square of its niass 11) We crudely evaluate these two criteria neglecting post-Newtoman corrections aud nousplierical distortions due torotation.," Second, for any portion of the star to form a Kerr black hole, the angular momentum $J$ of that portion cannot be larger than the square of its mass $m$ We crudely evaluate these two criteria neglecting post-Newtonian corrections and nonspherical distortions due to." The specific angular momentum of a particle at radius rin the equatorial plane. at the ouset of iustabilitv. is where the critical orbital velocity O4: can UYbe written Tere. (ReMeir~450 as the uniquely determined value at the ouset ofinstability (sce Table 2).," The specific angular momentum of a particle at radius $r$ in the equatorial plane, at the onset of instability, is where the critical orbital velocity $\Omega_{\rm crit}$ can be written Here, $(R/M)_{\rm crit} \sim 450$ is the uniquely determined value at the onset ofinstability (see Table 2)." Iuserting the last two equations iuto (72)). we find where we have assuued that the mass of the black hole. mis the mass euclosed by a sphere of radius r.," Inserting the last two equations into \ref{crit1}) ), we find where we have assumed that the mass of the black hole, $m$ , is the mass enclosed by a sphere of radius $r$ ." supporting the evidence thatchannel.,supporting the evidence that. In the early stage of mass transfer in W. UMa (Sfage-1). the Gransfered mass could come from the unprocessed material aud the resulting str would have normal C-O abundances.," In the early stage of mass transfer in W UMa ), the transfered mass could come from the unprocessed material and the resulting star would have normal C-O abundances." As the transfer continues reaching into the region of CNO processing. first C and then both C and O would appear depleted. (5/age-2).," As the transfer continues reaching into the region of CNO processing, first C and then both C and O would appear depleted )." Thus it is possible to find depleted C. normal O DSS/W UMuma stars. like 800267.," Thus it is possible to find depleted C, normal O BSS/W UMa stars, like 800267." After the merger the star would appear as CO depleted non-variable BSS CStage-2)., After the merger the star would appear as CO depleted non-variable BSS ). In our sample we have found 2 or 3 stars inSlage-2. aud 4 inSlage-3.," In our sample we have found 2 or 3 stars in, and 4 in." . Classical BAIT would also result in BSS with CO depletion. perhaps with a low mass Ie white dwar! companion.," Classical BMT would also result in BSS with CO depletion, perhaps with a low mass He white dwarf companion." Since (he donor star is evolving olf the MS. the translered mass nieht be more heavily processed.," Since the donor star is evolving off the MS, the transfered mass might be more heavily processed." The resulüing BSS would be very similar to aSlage-2 W Όλα Bss., The resulting BSS would be very similar to a W UMa BSS. The number of BSS with CO depletion and the Wo UMa systems show that the BAIT channel is active even in a high-density cluster like 47 Tuc., The number of BSS with CO depletion and the W UMa systems show that the BMT channel is active even in a high-density cluster like 47 Tuc. At least of the BSS are being produced by the BAIT channel., At least of the BSS are being produced by the BMT channel. This finding is in good agreement with the results of cdenamical simulations which have shown that a significant contribution of BSS (25%) generated by the natural evolution of primordial binaries is needed in order to reproduce (he bimodal radial distribution of the BSS in (his cluster2004)., This finding is in good agreement with the results of dynamical simulations which have shown that a significant contribution of BSS $25\%$ ) generated by the natural evolution of primordial binaries is needed in order to reproduce the bimodal radial distribution of the BSS in this cluster. ]lowever. the vast majority )) of BSS in our spectroscopic sample is located in the external region of the cluster.," However, the vast majority ) of BSS in our spectroscopic sample is located in the external region of the cluster." Hence. accordingly with Mapelli et al. (," Hence, accordingly with Mapelli et al. (" 2004. 2006). thev should imainiv be DMT-DSS (since C-BSS are expected to be stronely segregated in the cluster centre).,"2004, 2006), they should mainly be BMT-BSS (since C-BSS are expected to be strongly segregated in the cluster centre)." Thus. most of them should show CO-depletion. at odd with what observed.," Thus, most of them should show CO-depletion, at odd with what observed." llowever. from their relative location in (he CMD. CO-depleted BSS appear to be less evolved (han non-depleted ones. possibly indicating (hat (heir following evolution converts abundances back to normal.," However, from their relative location in the CMD, CO-depleted BSS appear to be less evolved than non-depleted ones, possibly indicating that their following evolution converts C-O abundances back to normal." Certainly. once C and O have been processed into N producing CO-depletion. further nuclear processing would not restore normal C-O abundances during the BSS phase.," Certainly, once C and O have been processed into N producing CO-depletion, further nuclear processing would not restore normal C-O abundances during the BSS phase." Instead. mixing processes could play a role in this game.," Instead, mixing processes could play a role in this game." Indeed. the distribution of rotational velocities provides a clue.," Indeed, the distribution of rotational velocities provides a clue." Most BSS in our sample are slow rotators. with velocities compatible with those measured in unperturbed TO stars," Most BSS in our sample are slow rotators, with velocities compatible with those measured in unperturbed TO stars" GOODS-south field. with the assumption that there is 10 significant. evolution of the ii]] LF from :—1 to 2=L.8h.,"GOODS-south field, with the assumption that there is no significant evolution of the ] LF from $z$ =1 to $z$ =1.85." " In our ccandidate selection. cluission line sources with {το zinter than 25.9 magnitude, aud with EW).>160A can contaminate our sample."," In our candidate selection, emission line sources with $I_{AB}$ fainter than 25.9 magnitude, and with $\rm EW_{obs}>460 \AA$ can contaminate our sample." We determined which sources frou Strangluetal.(2009) would have passed hese criteria if redshüfted to τ=1.55. and scaled the result by the ratio of volumes between the two sirvers.," We determined which sources from \citet{str09} would have passed these criteria if redshifted to $z = 1.85$, and scaled the result by the ratio of volumes between the two surveys." We find that less than oue (0.1) |OIT| cinitter is expected ο contaminate our ccandidate sample., We find that less than one (0.1) [OII] emitter is expected to contaminate our candidate sample. To be conservative. even if we relax he above magnitude cut by 0.5 mae to account for any color correction. and lower the EW).>200A. we find hat less than 0.3 uj} emitters should be expected to contanunate our sample.," To be conservative, even if we relax the above magnitude cut by 0.5 mag to account for any color correction, and lower the $\rm EW_{obs}>200 \AA$, we find that less than 0.3 ] emitters should be expected to contaminate our sample." We apply a similar methodology toestimate the contamination from foreground 11]] cmitters (INakazu at (25zLL iu our NEWFIRM data using the 11]| cluission liue sources at (2) =0.5 iu Stranghuetal. (2009).," We apply a similar methodology toestimate the contamination from foreground ] emitters \citep{kak07, hu09, str09, str10} at $\langle z \rangle \approx 1.1$ in our NEWFIRM data using the ] emission line sources at $\langle z \rangle=$ 0.5 in \citet{str09}." . We found that less than two (1.7) ΟΠ enmütters can be misidentified as. οσους dà our survey., We found that less than two (1.7) ] emitters can be misidentified as emitters in our survey. Iu addition to the above estimate. we used a recent sample of enmüssion- line ealaxies obtained frou: IST ΝΕΟ carly release scieuce data (Straughnctal.2010).," In addition to the above estimate, we used a recent sample of emission line galaxies obtained from HST WFC3 early release science data \citep{str10}." . This sample of uj enütters is closer in redshift. with median :=1.1. to our foreground interloper redshift of +=1.12. this minimizing the [Oud]error in our UL] estimate due to possible evolution in the LF of [ΟΠΗ cmitters.," This sample of ] emitters is closer in redshift, with median $z=1.1$, to our foreground ] interloper redshift of $z=1.12$, thus minimizing the error in our ] estimate due to possible evolution in the LF of ] emitters." Using this recent sample. we found that about one ΠΠ cluitter is expected to contaminate our ccandidate sample.," Using this recent sample, we found that about one ] emitter is expected to contaminate our candidate sample." As inentioned earlier. Πα cmitters at :—0.62 can contanunate our candidate sample.," As mentioned earlier, ${\alpha}$ emitters at $z$ =0.62 can contaminate our candidate sample." Several authors (Tressectal.2002:Straughnet2000) have studied Ta enutters at sinular redshift.," Several authors \citep{tre02, str09} have studied ${\alpha}$ emitters at similar redshift." Tresseetal.(2002). (see their Figure 6) have plotted the huninosity vs the continui D-baud magnitude of cmitters., \citet{tre02} (see their Figure 6) have plotted the luminosity vs the continuum B-band magnitude of emitters. " To pass our selection criteria. an emitter would require a luminosity ercater than d«LoMeres1. aud fux density fe,<75«10orecu2stzt which correspouds to Map=15.97 imag."," To pass our selection criteria, an emitter would require a luminosity greater than $1\times10^{40} \rm erg \; s^{-1}$, and flux density $f_{B_{w}}< 7.5\times10^{-20} \rm erg\; cm^{-2} s^{-1} Hz^{-1}$ which corresponds to $\rm M_{AB}=-15.97$ mag." " Auv source brighter than Map--15.97 mag would be detected in the B, image. aud heuce rejected from candidate list."," Any source brighter than $\rm M_{AB}$ =-15.97 mag would be detected in the $B_{w}$ image, and hence rejected from candidate list." Frou figure 6 (Tresseetal. 2002).. we expect to find no sources that cam pass this selection criteria.," From figure 6 \citep{tre02}, we expect to find no sources that can pass this selection criteria." In addition. we used Πα cutters at (2) =0.27 (Straughuetal.2009).. aud found that less than one (0.1) Πα cutters are expected to contaminate our ccandidate sample.:," In addition, we used ${\alpha}$ emitters at $\langle z \rangle$ =0.27 \citep{str09}, and found that less than one (0.4) ${\alpha}$ emitters are expected to contaminate our candidate sample.:" We rule out the possibility of contanunation of our ccandidates by transicut objects such as superuovac. because these objects would appear in both UND aud J baud stacks.," We rule out the possibility of contamination of our candidates by transient objects such as supernovae, because these objects would appear in both UNB and J band stacks." Both UND anc J data were obtained on cach clear might of the: Following Ilibouetal.(2009) we determined the expected wmuber of L/T dwarfs in our survey., Both UNB and J data were obtained on each clear night of the: Following \citet{hib09} we determined the expected number of L/T dwarfs in our survey. From the spectral type vs. absolute magnitude relations given bv fgure 9 in Tinneyetal.(2003).. we infer that we could detect L dwarfs at a distance of LOO to 1300 pe aud T dwarfs at a distance of 150 to 600 pc. from the coolest to the warmest spectral types.," From the spectral type vs. absolute magnitude relations given by figure 9 in \cite{Tinney}, we infer that we could detect L dwarfs at a distance of 400 to 1300 pc and T dwarfs at a distance of 150 to 600 pc, from the coolest to the warmest spectral types." Our field is located at a high galactic latitude. so that we would be able todetect L/T dxarfs well bevoud the Galactic disk scale height.," Our field is located at a high galactic latitude, so that we would be able todetect L/T dwarfs well beyond the Galactic disk scale height." However. ouly a Galactic disk scale height of 350 pe is applicable to the population of L/T dwarts (Ryanctal.2005).," However, only a Galactic disk scale height of 350 pc is applicable to the population of L/T dwarfs \citep{Ryan}." . We derive then a sampled vole of ~ 750 pe?., We derive then a sampled volume of $\sim$ 750 $^3$. Considering a volume deusity of L/T dwarfs of a few 10 peP. we expect uo more than oue L/T dwarf in our field.," Considering a volume density of L/T dwarfs of a few $^{-3}$ $^{-3}$, we expect no more than one L/T dwarf in our field." While we expect about one L/T dwarf in our survey. we further investigate if any of the observed L/T dwarf pass our selection criteria.," While we expect about one L/T dwarf in our survey, we further investigate if any of the observed L/T dwarf pass our selection criteria." To do this we selected about 160 observed spectra of L/T dwarf (Colimowskiotal.2001:I&knappetChiuct 2006).. aud calculated the flux transiuitted through the UND. aud J-baud filter.," To do this we selected about 160 observed spectra of L/T dwarf \citep{gol04, kna04, chi06}, and calculated the flux transmitted through the UNB and J-band filter." We found that none of the L/T cwart has sufficicut narrowband excess to pass our selection criteria., We found that none of the L/T dwarf has sufficient narrowband excess to pass our selection criteria. Therefore it is unlikelv that our ccandidate sample is contaminated by L/TSpikes: Noise iu the detector cam cause random fux increase in the UND filter., Therefore it is unlikely that our candidate sample is contaminated by L/T: Noise in the detector can cause random flux increase in the UNB filter. To avoid contanunation from such noise spikes. we constructed helt curves of cach candidate using individual might stacks ic. we selected. candidates ouly if their fiux was constant over all nights.," To avoid contamination from such noise spikes, we constructed light curves of each candidate using individual night stacks i.e. we selected candidates only if their flux was constant over all nights." This method of candidate selection based on the constant flux in the individual elt stacks also climinates the possible contamination roni Finally. we performed a false detection test to estimate he πο of false detection that cau pass our. ssclection criteria.," This method of candidate selection based on the constant flux in the individual night stacks also eliminates the possible contamination from Finally, we performed a false detection test to estimate the number of false detection that can pass our selection criteria." To do this we multiplied the UND stack bv -l and repeated the exact same procedure as he real ccancdidate selection (see section 3)., To do this we multiplied the UNB stack by -1 and repeated the exact same procedure as the real candidate selection (see section 3). We did not ect any ase detection passing our selection criteria., We did not get any false detection passing our selection criteria. Based on the above estimates less than two ΟΠΗ cluitters are expected to be uusidentified as. eolutters in our survey., Based on the above estimates less than two ] emitters are expected to be misidentified as emitters in our survey. To estimate the nuuber of sources that should be detected in our survey for a given LLF. we performed detailed Monte-Carlo simulations.," To estimate the number of sources that should be detected in our survey for a given LF, we performed detailed Monte-Carlo simulations." This is needed. since the width of the filter is comparable to or slightly sinaller than the expected lue width in these galaxies. so many of the sources will not be detected at their real line fluxes.," This is needed, since the width of the filter is comparable to or slightly smaller than the expected line width in these galaxies, so many of the sources will not be detected at their real line fluxes." In these simulations. we used the :=6.6 LLF derived by Kashikawaetal. (2006)..," In these simulations, we used the $z=6.6$ LF derived by \citet{kas06}. ." First. we generated oue million random galaxics distributed according to the observed LF at :26.6 (I&ashikiwaetal. 2006).," First, we generated one million random galaxies distributed according to the observed LF at $z$ =6.6 \citep{kas06}. ." . Each of these ealaxies was assigued a, Each of these galaxies was assigned a Tylenda (2003)).,Tylenda \cite{soktyl}) ). The first one assumes that V4332 Ser is a young object., The first one assumes that V4332 Sgr is a young object. This hypothesis is however inconsistent with the position of the object in Galaxy and. particularly. with its radial velocity significantly different from the Galactic rotation curve.," This hypothesis is however inconsistent with the position of the object in Galaxy and, particularly, with its radial velocity significantly different from the Galactic rotation curve." Future observations of V4332 Ser in the infrared. particularly in longer wavelengths might be crucial for understanding the nature of the object.," Future observations of V4332 Sgr in the infrared, particularly in longer wavelengths might be crucial for understanding the nature of the object." A lower limit to the mass of this object accreted in the merger scenario of Soker Tylenda (2003)) can be obtained from the total energy emitted in the eruption., A lower limit to the mass of this object accreted in the merger scenario of Soker Tylenda \cite{soktyl}) ) can be obtained from the total energy emitted in the eruption. The luminosity of V4332 Ser integrated since the discovery of the 1994 eruption till 2003 is 4.5x10? eergs., The luminosity of V4332 Sgr integrated since the discovery of the 1994 eruption till 2003 is $\sim 4.5 \times 10^{43}$ ergs. " Equating this to GM,Mace/Re one obtains (assuming My,=1.0Mo and Ry= 1.0Rq) Mace10°Me.", Equating this to $G M_\star M_\mathrm{acc}/R_\star$ one obtains (assuming $M_\star = 1.0 M_{\sun}$ and $R_\star = 1.0 R_{\sun}$ ) $M_\mathrm{acc} \simeq 10^{-5} M_{\sun}$. Note that this estimate does not take into account the energy radiated away before the discovery (it is very likely that the eruption of V4332 Ser started well before 28 February 1994). nor the energy stored in the matter now circulating the central star. nor the kinetic energy in mass loss.," Note that this estimate does not take into account the energy radiated away before the discovery (it is very likely that the eruption of V4332 Sgr started well before 28 February 1994), nor the energy stored in the matter now circulating the central star, nor the kinetic energy in mass loss." " Given the above estimate as well as that of M, in Sect. 5.."," Given the above estimate as well as that of $M_\mathrm{e}$ in Sect. \ref{contrac}," we can conclude that the mass of the accreted object was 2107Mo., we can conclude that the mass of the accreted object was $\ga 10^{-4} M_{\sun}$. The unusual emission line spectrum observed in April 2003 and described in Sect., The unusual emission line spectrum observed in April 2003 and described in Sect. 3 deserves futher studies às it can provide important insight into the current state of V4332 Ser., \ref{spectr} deserves futher studies as it can provide important insight into the current state of V4332 Sgr. From our preliminary analysis in Sect., From our preliminary analysis in Sect. 3 we can conclude that it must originate in an optically thin. neutral. molecular. cold medium.," \ref{spectr} we can conclude that it must originate in an optically thin, neutral, molecular, cold medium." Low optical thickness means low column density which. with large equivalent widths of many lines in the spectrum. requires large volume — considerably larger than that of the central star.," Low optical thickness means low column density which, with large equivalent widths of many lines in the spectrum, requires large volume – considerably larger than that of the central star." This obviously rules out the stellar atmosphere and regions in its near vicinity., This obviously rules out the stellar atmosphere and regions in its near vicinity. The low rotational temperature inferred in Sect., The low rotational temperature inferred in Sect. 3 (from different emission bands) implies that the medium. in the bulk. is significantly cooler than KK. This is the sort of temperature we have found for the disc-like structure in Sect. 6..," \ref{spectr} (from different emission bands) implies that the medium, in the bulk, is significantly cooler than K. This is the sort of temperature we have found for the disc-like structure in Sect. \ref{ire}." However. this structure Is expected to be mostly optically thick.," However, this structure is expected to be mostly optically thick." It seems that possible sites for the emision line spectrum to originate might be in regions between the stellar surface and the dise where the contracting stellar envelope might have left some matter circulating now near the equatorial plane., It seems that possible sites for the emision line spectrum to originate might be in regions between the stellar surface and the disc where the contracting stellar envelope might have left some matter circulating now near the equatorial plane. BAO+ have found that the observed width of the KI emission lines if interpreted with Doppler broadening give a velocity of 260 km/s. The measured FWHM of the Cal line in our spectrum (see Table 2)) when corrected for the instrumental FWHM (5.6 A)) gives a similar value. i.e. 280 km/s. This value would correspond to a Keplerian velocity at ~10 Rg for à | Me star.," \cite{banash} have found that the observed width of the KI emission lines if interpreted with Doppler broadening give a velocity of 260 km/s. The measured FWHM of the CaI line in our spectrum (see Table \ref{spectr_t}) ) when corrected for the instrumental FWHM (5.6 ) gives a similar value, i.e. 280 km/s. This value would correspond to a Keplerian velocity at $\sim$ 10 $R_{\sun}$ for a 1 $M_{\sun}$ star." The required excitation could result from the stellar radiation or viscous processes. or both.," The required excitation could result from the stellar radiation or viscous processes, or both." The galactic position of V4332 Ser. /=13°63 b= —-9740. might suggest that the object is related to the Galactic bulge.," The galactic position of V4332 Sgr, $l = 13\fdg63$ $b = -9\fdg40$ , might suggest that the object is related to the Galactic bulge." Thus V4332 Ser would be at a distance of ~ 8.5 kpe. which. on the one hand. seems to be too large for the observed redenning. as discussed in Sect. 4.2..," Thus V4332 Sgr would be at a distance of $\sim$ 8.5 kpc, which, on the one hand, seems to be too large for the observed redenning, as discussed in Sect. \ref{dist}." On the other hand. however. it would be easier in this case to understand the observed radial velocity of V4332 Ser which is. as discussed in Sect. 6..," On the other hand, however, it would be easier in this case to understand the observed radial velocity of V4332 Sgr, which is, as discussed in Sect. \ref{ire}," inconsistent with the rotation of the Galactic disc., inconsistent with the rotation of the Galactic disc. At a distance of 8.5 kpe all the radit and luminosities derived in this paper would increase by a factor of 4.7 and 22. respectively.," At a distance of 8.5 kpc all the radii and luminosities derived in this paper would increase by a factor of 4.7 and 22, respectively." In particular. the. progenitor would be à G type subgiant of à mass of ~ 2 Mo. as can be inferred from stellar evolutionary tracks (e.g. Iben 1965)). evolving from the main sequence to the red giant branch.," In particular, the progenitor would be a G type subgiant of a mass of $\sim$ 2 $M_{\sun}$, as can be inferred from stellar evolutionary tracks (e.g. Iben \cite{iben}) ), evolving from the main sequence to the red giant branch." The star would have a ~ 0.2 Me helium core and an envelope with a mean density of 0.02 ο em., The star would have a $\sim$ 0.2 $M_{\sun}$ helium core and an envelope with a mean density of 0.02 g $^{-3}$. Thus one could refer to the scenario of Retter Marom (2003)) while interpreting the eruption of V4332 Ser., Thus one could refer to the scenario of Retter Marom \cite{retmar}) ) while interpreting the eruption of V4332 Sgr. Indeed Mace=107Mo is then required to explain the energy emitted in the eruption so a massive planet or a brown dwarf would be involved in the merger event., Indeed $M_\mathrm{acc} \simeq 10^{-4} M_{\sun}$ is then required to explain the energy emitted in the eruption so a massive planet or a brown dwarf would be involved in the merger event. However. the accreted object. being significantly denser than the subgiant envelope. would be expected to penetrate deeply 1 the envelope. as discussed e.g. in Livio Soker (1984)).," However, the accreted object, being significantly denser than the subgiant envelope, would be expected to penetrate deeply in the envelope, as discussed e.g. in Livio Soker \cite{livsok}) )." Thus most of the subgiant envelope would be disturbed and the whole event. the contraction phase in particular. would procede o a much longer time scale than observed.," Thus most of the subgiant envelope would be disturbed and the whole event, the contraction phase in particular, would procede on a much longer time scale than observed." Indeed. modelling analogous to that in Sect.," Indeed, modelling analogous to that in Sect." 5. but done to match the observed increase of the radius by a factor of 4.7. assuming a central star mass of 2 Me. requires M;=I07M.," \ref{contrac} but done to match the observed increase of the radius by a factor of 4.7, assuming a central star mass of 2 $M_{\sun}$, requires $M_\mathrm{e} \simeq 3 \times 10^{-4}M_{\sun}$ ." In the discussed case we would rather expect M.=1Mo to be involved., In the discussed case we would rather expect $M_\mathrm{e} \simeq 1 M_{\sun}$ to be involved. Note that Livio Soker (1984)) show that à merger event in the case of a giant and a nassive planet may last several thousands years., Note that Livio Soker \cite{livsok}) ) show that a merger event in the case of a giant and a massive planet may last several thousands years. There is no doubt that futher detailed observations of V4332 Ser are necessary., There is no doubt that futher detailed observations of V4332 Sgr are necessary. Photometric and spectroscopic measurements in the near and far infrared. would be of particular value às the object is emitting. most of its energy in this wavelength range., Photometric and spectroscopic measurements in the near and far infrared would be of particular value as the object is emitting most of its energy in this wavelength range. High quality spectroscopy in the optical would also be very important for understanding the origin of the unusual emission-line spectrum as well as for analysing the underlying stellar component., High quality spectroscopy in the optical would also be very important for understanding the origin of the unusual emission-line spectrum as well as for analysing the underlying stellar component. In particular. high resolution spectroscopy in the atomic lines would allow precise determination of the radial velocity of the object. as well as investigation of the kinematic structure of the emitting region.," In particular, high resolution spectroscopy in the atomic lines would allow precise determination of the radial velocity of the object, as well as investigation of the kinematic structure of the emitting region." The object is probably evolving on a time scale of years so long term observational monitoring should be undertaken., The object is probably evolving on a time scale of years so long term observational monitoring should be undertaken. We hope that the analysis of the existing observational data in this paper. followed by our interpretation and conclusions(which in several points may be regarded as speculative) will stimulate deeper astrophysical interest in V4332 Ser V838 Mon and. possibly. other objects of similar nature.," We hope that the analysis of the existing observational data in this paper, followed by our interpretation and conclusions(which in several points may be regarded as speculative) will stimulate deeper astrophysical interest in V4332 Sgr, V838 Mon and, possibly, other objects of similar nature." temperature. surface gravity ancl Πο ratio.,"temperature, surface gravity and He/H ratio." The first. set of models assumed zero metals. while the second. included an adopted. distribution of metals based on the analysis of FUSE spectra of five sdB stars by 2.. see also νι," The first set of models assumed zero metals, while the second included an adopted distribution of metals based on the analysis of FUSE spectra of five sdB stars by \citet{BlanchetteChayer2008}, see also \citet{Van-GrootelCharpinet2010}." From the set of models wihon metals. we derive logg=5.45 £0.04. Yap=34400+ 9201 and log(lle/1l)=—L37+0.05," From the set of models without metals, we derive $\log g=5.45\pm0.04$ $T_{\rm{eff}}=34\,400\pm220\,$ K and $\log(\rm{He}/\rm{H})=-1.37\pm0.05$." Assuming the Blanchette composition. we find logg=5.434 04. Diary=341304250 NW and log(Hle/11)=1.3640.04 ," Assuming the Blanchette composition, we find $\log g=5.43\pm0.04$ , $T_{\rm{eff}}=34\,730\pm250\,$ K and $\log(\rm{He}/\rm{H})=-1.36\pm0.04$ ." These results are in good agreement with logg=5.87+0.10 dig= 34500-1000Ix. οσο)1200.10 determined by ? and logg=54340.10. ων=3420model.0 Ix. determined by 2? using different spectra and -.," These results are in good agreement with $\log g=5.37\pm0.10$, $T_{\rm{eff}}=34\,500\pm1000\,$ K, $\log(\rm{He}/\rm{H})=-1.35\pm0.10$ determined by \citet{Morales-RuedaMaxted2003} and $\log g=5.43\pm0.10$, $T_{\rm{eff}}=34\,200\pm500\,$ K determined by \citet{GeierHeber2010} using different spectra and model grids." The fit definitely improves when going from the zero-metal solution (Fig. 6)), The fit definitely improves when going from the zero-metal solution (Fig. \ref{FIG_Fnometals}) ) to the Blanchette composition (lig. 7)).," to the Blanchette composition (Fig. \ref{FIG_Fmetals}) )," although there still remains a slight. “Balmer” problem. especially noticeable in the core of 1.," although there still remains a slight “Balmer” problem, especially noticeable in the core of $\beta$." Phere are definitely metals in the spectrum of43340: the strongest features are 1) an unresolved | complex around 4649A (compare the two figures for that [eature). and 2) another weaker complex | TID) in the blue wing of Llé that the Blanchette model. reprocuces quite well.," There are definitely metals in the spectrum of: the strongest features are 1) an unresolved + complex around $4649\,\rm\AA$ (compare the two figures for that feature), and 2) another weaker complex + ) in the blue wing of $\delta$ that the Blanchette model reproduces quite well." All of the major discrepancies between the spectra and the models are due to strong interstellar absorption: the Ix line of in the blue wing of Hc. the HH line in the core of H«c. and the doublet strongly. alfecting the red wing of 5876.," All of the major discrepancies between the spectra and the models are due to strong interstellar absorption: the K line of in the blue wing of $\epsilon$, the H line in the core of $\epsilon$, and the doublet strongly affecting the red wing of 5876." Lt is reassuring that the derived atmospheric parameters are not too strongly dependent on the presence of metals. as might be expected for such a hot star. particularly one in which downwards diffusion of metals is Important.," It is reassuring that the derived atmospheric parameters are not too strongly dependent on the presence of metals, as might be expected for such a hot star, particularly one in which downwards diffusion of metals is important." The beaming factor we derived for uüusing ALCAIC runs is (D?=1.3350.02. which is in perfect agreement with the theoretically expected value caleulated in Section ??..," The beaming factor we derived for using MCMC runs is $\left = 1.33\pm0.02$, which is in perfect agreement with the theoretically expected value calculated in Section \ref{sec_lc_BF}." Phe uncertainty on the beaming factor is a direct. reflection of the uncertainty on the spectroscopic radial velocity. amplitude. of the sclB. 1 contrary to our assumption. thefvepler tluxes would be severely contaminated bv light from other (constant) stars. the observed beaming factor would be lower.," The uncertainty on the beaming factor is a direct reflection of the uncertainty on the spectroscopic radial velocity amplitude of the sdB. If, contrary to our assumption, the fluxes would be severely contaminated by light from other (constant) stars, the observed beaming factor would be lower." The distribution of beaming factors from our MCMC computations is shown in Fig. S., The distribution of beaming factors from our MCMC computations is shown in Fig. \ref{FIG_BF}. 1 the racial velocity would be measured. [rom the Doppler beaming aniplituce. using the theoretical beaming factor. the result would be 168+4knis+ compared to 1640+L9knis derived. from spectroscopy.," If the radial velocity would be measured from the Doppler beaming amplitude, using the theoretical beaming factor, the result would be $168\pm 4\,\kms$ compared to $164.0\pm1.9\,\kms$ derived from spectroscopy." The uncertainty on the photometric radial velocity is dominated bv the uncertainty on the theoretical beaming factor. primarily due to its dependence on the poorly known metallicity of the sdB. and to a [esser extent clue to the uncertainties on the sdB's ellective temperature and surface gravity.," The uncertainty on the photometric radial velocity is dominated by the uncertainty on the theoretical beaming factor, primarily due to its dependence on the poorly known metallicity of the sdB, and to a lesser extent due to the uncertainties on the sdB's effective temperature and surface gravity." Under the assumption of corotation. we find a projected rotational velocity of the sdB of esin(/)=26.6+40.8kms," Under the assumption of corotation, we find a projected rotational velocity of the sdB of $v \sin(i) = 26.6 \pm 0.8\, \kms$." From spectroscopy ancl using LDPE models with ten times Solar metallicity. ? found esin(z)=26.0£1.0kms+. whieh is in agreement with our photometric result.," From spectroscopy and using LTE models with ten times Solar metallicity, \citet{GeierHeber2010} found $v \sin(i) = 26.0 \pm 1.0\, \kms$, which is in agreement with our photometric result." We conclude that the assumption of corotation is likely to be correct., We conclude that the assumption of corotation is likely to be correct. The speetroscopically determined: surface gravity of the sdl3 (logg=5.43x0.04 and 5.45+0.04 using atmosphere models with and. without metals respectively) agrees perfectly with the surface gravity of 5.452+0.006 we derived from the masseradius distribution of our light curve mocels., The spectroscopically determined surface gravity of the sdB $\log g=5.43\pm0.04$ and $5.45\pm0.04$ using atmosphere models with and without metals respectively) agrees perfectly with the surface gravity of $5.452\pm0.006$ we derived from the mass-radius distribution of our light curve models. As concluded: earlier by the sdD. is probably in a post-ELLB phase.," As concluded earlier by \citet{Morales-RuedaMaxted2003}, the sdB is probably in a post-EHB phase." This is illustrated in Fig. 9.. ," This is illustrated in Fig. \ref{FIG_evolution}, ," which shows the zeroage extended horizontal branch (ZAXELHD) and the terminal age extended horizontal branch CEXIZIIDB) for an sdD with a typical core mass of 0.47 M... together with evolutionary tracks for different hydrogen envelope masses (40 75.10 7.2.10 7.3. 10 and lOM.) from 7.," which shows the zeroage extended horizontal branch (ZAEHB) and the terminal age extended horizontal branch (TAEHB) for an sdB with a typical core mass of $0.47\,$ $_\odot$, together with evolutionary tracks for different hydrogen envelope masses $10^{-4}$, $10^{-3}$, $2\times10^{-3}$ , $3\times10^{-3}$ and $4\times10^{-3}\,$ $_\odot$ ) from \citet{KawalerHostler2005}." Beeause of its low surface gravity. the sdB component of IxXPD1946 falls in a region of the Z;jlogg plane relatively ar from the center of the instability strip.," Because of its low surface gravity, the sdB component of KPD1946 falls in a region of the $T_{\rm{eff}}-\log g$ plane relatively far from the center of the instability strip." However. at east one pulsator exists in this region of the Zia—logg plane. V338 Ser. that should be in a post-ELLD. phase (see7.Vig. 3).," However, at least one pulsator exists in this region of the $T_{\rm{eff}}-\log g$ plane, V338 Ser, that should be in a post-EHB phase \citep[see][Fig.~3]{Ostensen2009}." " Aloreover. ""transient. pulsators with varving »ulsation amplitudes that can go down to uncletectable in à particular epoch might exist (seethecaseofIXICes91276in?). ."," Moreover, `transient pulsators' with varying pulsation amplitudes that can go down to undetectable values in a particular epoch might exist \citep[see the case of KIC 2991276 in][]{OstensenSilvotti2010}." For these reasons. ancl because we found at east one candidate p mode pulsation frequency. it is worth continuing a photometric monitoring hy Ixepler.," For these reasons, and because we found at least one candidate $p-$ mode pulsation frequency, it is worth continuing a photometric monitoring by Kepler." The white dwarf mass implies that it is a CO white dwarf., The white dwarf mass implies that it is a CO white dwarf. Phe progenitor of the sdl3 must have been the less massive star in the original binary and by the time it reached the ZAELHD. the white dwarf was already. cooling.," The progenitor of the sdB must have been the less massive star in the original binary and by the time it reached the ZAEHB, the white dwarf was already cooling." “Phe accretion of material by the white dwarf does not change the WD's internal energy. content significantly (see e.g. related work on cataclysmic variables by ?2))., The accretion of material by the white dwarf does not change the WD's internal energy content significantly (see e.g. related work on cataclysmic variables by \citealt{TownsleyBildsten2002}) ). The cooling time of the white dwarf therefore. sets an upper limit to the ime since the sdD was on the ZALIID., The cooling time of the white dwarf therefore sets an upper limit to the time since the sdB was on the ZAEHB. For our best estimates of the temperature and mass of the white dwarf.he cooling tracks a? indicate that it has been cooling or about 55 to na170 MMsr. (depending on the unknown envelope ," For our best estimates of the temperature and mass of the white dwarf,the cooling tracks of\citet{HolbergBergeron2006} indicate that it has been cooling for about $155$ to $170$ Myr (depending on the unknown envelope composition)." ThesdBs evolution from the Zero AgeExtended Horizontal Branch to its current. took 125 to Dedhicdependingontheexactcur- OWh means that the sdB must je formed. very after the white cart.," ThesdB's evolution from the Zero AgeExtended Horizontal Branch to its current post-EHB-phase took 125 to Myr \citep[][depending on the exact current evolutionary stage]{KawalerHostler2005}, , which means that the sdB must have formed very shortly after the white dwarf." of star formation experienced by à dwarf galaxy. iron can be expelled more easily than oxygen.,"of star formation experienced by a dwarf galaxy, iron can be expelled more easily than oxygen." The hypothesis of different ejection efficiencies α for O and Fe is therefore a reasonable assumption that can be tested by our models., The hypothesis of different ejection efficiencies $\alpha$ for O and Fe is therefore a reasonable assumption that can be tested by our models. " We assume two different values for these ejection efficiencies oo and αι, and. by means of eq. (12))."," We assume two different values for these ejection efficiencies $\alpha_O$ and $\alpha_{Fe}$ and, by means of eq. \ref{eq:diffwsol}) )," we calculate how [O/Fe] varies with [Fe/H]., we calculate how [O/Fe] varies with [Fe/H]. The results would not change significantly if we assume eqs. (16)), The results would not change significantly if we assume eqs. \ref{eq:complsol}) ) or eq. (20)), or eq. \ref{eq:fountsol}) ) instead of eq. (12)., instead of eq. \ref{eq:diffwsol}) ). In Fig., In Fig. Ὁ we show for instance the comparisons of models for which (ag. ape) = (5. 2) (solid line). (2. 5) (dotted line) and (2. 2) (dashed line).," \ref{ofe} we show for instance the comparisons of models for which $\alpha_O$, $\alpha_{Fe}$ ) = (5, 2) (solid line), (2, 5) (dotted line) and (2, 2) (dashed line)." We show the results for our reference set of parameters (0=3 and A= D) in the left panel., We show the results for our reference set of parameters $\lambda = 3$ and $\Lambda = 1$ ) in the left panel. To study the dependence of these curves on the inflow and outflow parameters. we also plot the results for 1= and A=3 (right panel).," To study the dependence of these curves on the inflow and outflow parameters, we also plot the results for $\lambda = 1$ and $\Lambda = 3$ (right panel)." In order to calculate the yields. we have assumed a Salpeter IMF between 0.1] and 40 M. and the nucleosynthetic prescriptions of Woosley Weaver (1995)) for solar metallicity (case B).," In order to calculate the yields, we have assumed a Salpeter IMF between 0.1 and 40 $_\odot$ and the nucleosynthetic prescriptions of Woosley Weaver \cite{ww95}) ) for solar metallicity (case B)." For the solar abundances we adopt the Anders Grevesse (1989)) values., For the solar abundances we adopt the Anders Grevesse \cite{ag89}) ) values. We use this set of solar abundances in order to be consistent with the choice of Woosley Weaver's (1995)) vields., We use this set of solar abundances in order to be consistent with the choice of Woosley Weaver's \cite{ww95}) ) yields. " As expected. as the galaxy ages (and. therefore. [Fe/H]increases). [O/Fe] bends down if the oxygen ejection efficiency is larger (solid line). whereas it starts increasing qf ay,>ae (dotted line)."," As expected, as the galaxy ages (and, therefore, [Fe/H]increases), [O/Fe] bends down if the oxygen ejection efficiency is larger (solid line), whereas it starts increasing if $\alpha_{Fe} > \alpha_O$ (dotted line)." The model with Ξ] anc A=3 shows the same behavior but with reduced variations of the abundance ratios., The model with $\lambda = 1$ and $\Lambda = 3$ shows the same behavior but with reduced variations of the abundance ratios. This is due to the fact that the difference between the metallicities attained for «e=2 and wv=5 in the case CL. A) 3. 1) is larger than in the case Ct. A) = (1. 3) (see Figs.," This is due to the fact that the difference between the metallicities attained for $\alpha = 2$ and $\alpha = 5$ in the case $\lambda$, $\Lambda$ ) = (3, 1) is larger than in the case $\lambda$, $\Lambda$ ) = (1, 3) (see Figs." 3 and 4))., \ref{diff31} and \ref{diff13}) ). Of course. the model in which the ejection efficiencies are the same (dashed line) does not show any variation of [O/Fe] with [Fe/H] (see eq. 29)).," Of course, the model in which the ejection efficiencies are the same (dashed line) does not show any variation of [O/Fe] with [Fe/H] (see eq. \ref{eq:abratio}) )." The [O/Fe] attained by this model (~ 0.2) is lower than the [O/Fe| of halo stars and of the most metal-poor stars of Local Group dwarf galaxies. whose chemical enrichment should have been dominated by SNell ejecta.," The [O/Fe] attained by this model $\sim$ 0.2) is lower than the [O/Fe] of halo stars and of the most metal-poor stars of Local Group dwarf galaxies, whose chemical enrichment should have been dominated by SNeII ejecta." Indeed. it is known since quite some time that Woosley Weaver's yields overpredict iron (Timmes et al. 1995:;," Indeed, it is known since quite some time that Woosley Weaver's yields overpredict iron (Timmes et al. \cite{tww95};" Chiappini et al. 1997))., Chiappini et al. \cite{cmg97}) ). As we have said. the model with 2=3 and A=| can be representative of dwarf spheroidal galaxies.," As we have said, the model with $\lambda = 3$ and $\Lambda = 1$ can be representative of dwarf spheroidal galaxies." Indeed. in this model the metallicity remains significantly lower than the solar value and. if O is ejected more easily than Fe. a knee at [Fe/H ~ -].5 appears. in agreement with observations (see e.g. Venn et al. 2004)).," Indeed, in this model the metallicity remains significantly lower than the solar value and, if O is ejected more easily than Fe, a knee at [Fe/H] $\sim$ -1.5 appears, in agreement with observations (see e.g. Venn et al. \cite{venn04}) )." We point out once more that we are neglecting SNela therefore. in the framework of simple models. O anc Fe are both produced by massive stars. on similar timescales.," We point out once more that we are neglecting SNeIa therefore, in the framework of simple models, O and Fe are both produced by massive stars, on similar timescales." As à consequence. they should share a similar fate and have comparable ejection efficiencies.," As a consequence, they should share a similar fate and have comparable ejection efficiencies." Recchi et al. (2004)).," Recchi et al. \cite{rec04}) )," " by means of detailed chemodynamical simulations. found similar values of cj and ay, when complex star formation histories are assumed."," by means of detailed chemodynamical simulations, found similar values of $\alpha_O$ and $\alpha_{Fe}$ when complex star formation histories are assumed." Therefore. simple models predict that variations in the [O/Fe] vs. [Fe/H] plot cannot be attributed to differential winds and SNela must necessarily be considered 1n order to properly interpret this diagram.," Therefore, simple models predict that variations in the [O/Fe] vs. [Fe/H] plot cannot be attributed to differential winds and SNeIa must necessarily be considered in order to properly interpret this diagram." Would this conclusion still hold tf we relax IRA. and take properly into account stellar lifetimes?, Would this conclusion still hold if we relax IRA and take properly into account stellar lifetimes? In order to test that. we have performed a series of numerical simulations of the chemical evolution of a dwarf spheroidal galaxy whose structural parameters resemble those of Local Group such as Carina. Draco. Ursa Minor. Sculptor.," In order to test that, we have performed a series of numerical simulations of the chemical evolution of a dwarf spheroidal galaxy whose structural parameters resemble those of Local Group such as Carina, Draco, Ursa Minor, Sculptor." " In. particular we have run a simulation very similar to the ""standard"" model of Lanfranchi Matteucci (2003)).", In particular we have run a simulation very similar to the “standard” model of Lanfranchi Matteucci \cite{lm03}) ). The standard model ts adjusted to reproduce the average [a/Fe] and neutron capture abundance ratios of six local dwarf spheroidals., The standard model is adjusted to reproduce the average $\alpha$ /Fe] and neutron capture abundance ratios of six local dwarf spheroidals. It is assumed that the galaxy forms through the fast and continuous infall of pristine gas until a mass of ~10° M. is reached., It is assumed that the galaxy forms through the fast and continuous infall of pristine gas until a mass of $\sim 10^8$ $_{\odot}$ is reached. The star formation consists of one long episode (8 Gyr) with low efficiency ἐν= 0.05 Gyr!) and is affected by very intense galactic winds (with a rate 2 times higher than the SFR)., The star formation consists of one long episode (8 Gyr) with low efficiency $\nu =$ 0.05 $^{-1}$ ) and is affected by very intense galactic winds (with a rate 2 times higher than the SFR). As the galactic winc develops. it removes a large gas fraction thus decreasing the SFR.," As the galactic wind develops, it removes a large gas fraction thus decreasing the SFR." This effect. coupled with the low star formation rate and the injection of Fe into the ISM by SNe la. gives rise to the knee observed in [a/Fe] and [r-process/Fe|.," This effect, coupled with the low star formation rate and the injection of Fe into the ISM by SNe Ia, gives rise to the knee observed in $\alpha$ /Fe] and [r-process/Fe]." The models we show now contain non-selective winds., The models we show now contain non-selective winds. We plotted the [O/Fe] vs. [Fe/H] resulting from the standard model in Fig., We plotted the [O/Fe] vs. [Fe/H] resulting from the standard model in Fig. 10. (solid line)., \ref{ofe2} (solid line). We have then run the same model without SNela (dot-short-dashed line) and without SNela and without galactic winds (long-dashed line)., We have then run the same model without SNeIa (dot-short-dashed line) and without SNeIa and without galactic winds (long-dashed line). We have also considered a model without Sela in which the ejection efficiency of a-elements 1s enhanced (selective winds) (short-dashed line)., We have also considered a model without SNeIa in which the ejection efficiency of $\alpha$ -elements is enhanced (selective winds) (short-dashed line). Similarly to what we have seen in Fig. 9.. ," Similarly to what we have seen in Fig. \ref{ofe}, ," if we neglect SNela. there is a negligible variation of the |O/Fe] ratio as a function of [Fe/H] (dot-short-dashed and long-dashed lines) and a knee can be attained only in the presence of a- winds. namely winds in which O ts ejected out of," if we neglect SNeIa, there is a negligible variation of the [O/Fe] ratio as a function of [Fe/H] (dot-short-dashed and long-dashed lines) and a knee can be attained only in the presence of $\alpha$ -enhanced winds, namely winds in which O is ejected out of" The production of hot. highl-ionized gas m galactic environments is closely related to the iuput of energy and matter from stars and supernovae into the interstellar medium (ISM).,"The production of hot, highly-ionized gas in galactic environments is closely related to the input of energy and matter from stars and supernovae into the interstellar medium (ISM)." " Such ""feedback"" cau shape the ISM on kiloparsec scales in regions with high concentrations of early-type stars.", Such “feedback” can shape the ISM on kiloparsec scales in regions with high concentrations of early-type stars. " Iu disk galaxies. with differing pressure eradicuts m the vertical aud radial directions. such energv mput is responsible for the production of vertically-extcuded “halos” or ""coronae? about these systenis [1.5].."," In disk galaxies, with differing pressure gradients in the vertical and radial directions, such energy input is responsible for the production of vertically-extended “halos” or “coronae” about these systems \cite{deavillez00,normanikeuchi89}." Towk et al., Howk et al. |1]. have recently completed a study of interstellar in the Large Magellanic Cloud (LAC)., \cite{howk02} have recently completed a study of interstellar in the Large Magellanic Cloud (LMC). Because the ionization cherey required for its creation (ονoy=Li beV) precludes its production via photoionization by starlight. iis a tracer of hot (~3410? Ky. collisionally-ionized gas in galactic environinents.," Because the ionization energy required for its creation $_{\rm O\, V - O\, VI} = 114$ eV) precludes its production via photoionization by starlight, is a tracer of hot $\sim3\times10^5$ K), collisionally-ionized gas in galactic environments." Therefore. the Howk et al.," Therefore, the Howk et al." study of iu the LMC provides fiudameutal information ou the conteut. distribution. and kinematics of material created by the interactions of stars aud superunovae with the ISM in the closest aud best-studied disk galaxy bevoud the Milky Wav.," study of in the LMC provides fundamental information on the content, distribution, and kinematics of material created by the interactions of stars and supernovae with the ISM in the closest and best-studied disk galaxy beyond the Milky Way." IT stnunarize the principle results of this study below., I summarize the principle results of this study below. Table 1 stammarizes the statistical properties of the, Table 1 summarizes the statistical properties of the the OCDAL simulation the number of outputs was 345 and for the ACDAL simulation. 499.,"the OCDM simulation the number of outputs was 345 and for the $\Lambda$ CDM simulation, 499." “Phe box size chosen. was 100h Mpe for all three simulations which gave a particle nass of 2.6.Lott for LCDAML and 7.9.107 for the other two simulations., The box size chosen was $h^{-1}$ Mpc for all three simulations which gave a particle mass of $2.6\times10^{11}$ for $\Gamma$ CDM and $7.9\times10^{10}$ for the other two simulations. Groups of particles were found. for each output using a standard. [riendis-of-friends algorithm with linking length set to b—0.2 times the mean interparticle separation., Groups of particles were found for each output using a standard friends-of-friends algorithm with linking length set to $b=0.2$ times the mean interparticle separation. The multiplicity function averaged over all output. times is presented. from. each of the simulations in Fig. 1.., The multiplicity function averaged over all output times is presented from each of the simulations in Fig. \ref{fig:nbody_mult}. Llere we have only considered: groups containing over 45. particles in order to limit the number of false detections due to numerical effects., Here we have only considered groups containing over 45 particles in order to limit the number of false detections due to numerical effects. In. compiling the data in this wav. we have assumed that converting from mass to In£ does indeed convert the form. of the mass function into one which is independent. of epoch.," In compiling the data in this way, we have assumed that converting from mass to $\ln\nu$ does indeed convert the form of the mass function into one which is independent of epoch." This Figure has been produced. in such a wav as to be directly. comparable with figure 2 of Sheth ‘Tormen (1999).., This Figure has been produced in such a way as to be directly comparable with figure 2 of Sheth Tormen \shortcite{sheth}. For comparison we also plot their best it mocel and the predictions of standard PS theory., For comparison we also plot their best fit model and the predictions of standard PS theory. We have also. plotted the model of Sheth Tormen (1999) (Equation 20)) after allowing the parameters to vary o simultaneously fit the data from all three simulations.," We have also plotted the model of Sheth Tormen \shortcite{sheth} (Equation \ref{eq:sheth}) ) after allowing the parameters to vary to simultaneously fit the data from all three simulations." We ind slighthy dillerent best fit. parameters to those of Sheth Tormen., We find slightly different best fit parameters to those of Sheth Tormen. Our best fit parameters are e=0.774.p 274. compared to standard. PS theory @=1.p0 and Sheth Tormen e=0.707.p0.3.," Our best fit parameters are $a=0.774, p=0.274$ , compared to standard PS theory $a=1, p=0$ and Sheth Tormen $a=0.707, p=0.3$." Note that the dillerence oetween our best fit. values and those of Sheth Tormen could be explained by the different group finding algorithms usec., Note that the difference between our best fit values and those of Sheth Tormen could be explained by the different group finding algorithms used. Although we have argued that the monotonic increase in mass means that all epochs are ‘creation’ times for a given halo. we cannot simply compare the creation rate formulae with the distribution of halo numbers at. dillerent epochs: each halo should only be counted: once.," Although we have argued that the monotonic increase in mass means that all epochs are `creation' times for a given halo, we cannot simply compare the creation rate formulae with the distribution of halo numbers at different epochs: each halo should only be counted once." To determine the distribution. of creation times of halos of mass AJ. we therefore sequentially analysed the FOL output from z=50 to present day.," To determine the distribution of creation times of halos of mass $M$ , we therefore sequentially analysed the FOF output from $z=50$ to present day." All halos of mass >M were examined at each epoch to determine whether they were “new., All halos of mass $>M$ were examined at each epoch to determine whether they were `new'. The definition of πο adopted: was that at least half of the particles in a halo were not included in any halo of mass >AJ at a previous output time., The definition of `new' adopted was that at least half of the particles in a halo were not included in any halo of mass $>M$ at a previous output time. The number of these halos in the required. mass range was taken to be the minimum number which could have been created between that output. time and the previous one., The number of these halos in the required mass range was taken to be the minimum number which could have been created between that output time and the previous one. In order not to miss creation events where a halo was created and subsumec into a larger halo all within the time interval between two outputs. we analysed the progenitors of all new halos with mass greater than the required range.," In order not to miss creation events where a halo was created and subsumed into a larger halo all within the time interval between two outputs, we analysed the progenitors of all new halos with mass greater than the required range." Those with a progenitor distribution at the previous step which could sum to a halo of the required miss were recorded asa possible halo of the required mass., Those with a progenitor distribution at the previous step which could sum to a halo of the required mass were recorded asa possible halo of the required mass. vanCent(1932.1933)..," \cite{1932BAN.....6..163V,1933BAN.....7...21V}." Udalskietal.(1991.1995a.h.1996.1997) Two-hundred aud fifteen of these objects were classified as RR Lav.," \cite{1946PASP...58..249B} \cite{1994AcA....44..317U, 1995AcA....45....1U, 1995AcA....45..433U, 1996AcA....46...51U, 1997AcA....47....1U} Two-hundred and fifteen of these objects were classified as RR Lyr." Analvsis of the OGLE-II data brought a mach larger list of 2713 RR Lav (Mizerski2003))., Analysis of the OGLE-II data brought a much larger list of 2713 RR Lyr \citealt{2003AcA....53..307M}) ). Later. using the same source of data. Collingeetal.(2006) prepared a catalog of 1888 fundamental mode RR Lyr stars (type RRab}.," Later, using the same source of data, \cite{2006ApJ...651..197C} prepared a catalog of 1888 fundamental mode RR Lyr stars (type RRab)." The ALTACTIO inicrolensing project also observed a merous saniple of RR Lyr stars toward the Calactic ceuter. Minuitietal.(1998)..," The MACHO microlensing project also observed a numerous sample of RR Lyr stars toward the Galactic center. \cite{1998IAUS..184..123M}," using a sample of 115 RRab aud 550 RRe stars. showed that the spatial distribution of RR Lyr between 0.3 aud 23 kpe followpA a power law with an inclination of —.[3.0..," using a sample of 1150 RRab and 550 RRc stars, showed that the spatial distribution of RR Lyr between 0.3 and 3 kpc follows a power law with an inclination of $-3.0$ ." Alcocketal.(1998) examined the mean colors and magnitudes of ~1s00 RR Lav aud found that the bulk of the population is not barred., \cite{1998ApJ...492..190A} examined the mean colors and magnitudes of $\sim$ 1800 RR Lyr and found that the bulk of the population is not barred. Ouly RR Lyr located toward the iuner fields closer to the Galactic ceuter (F< p.52 1} sec to follow the barred distribution observed for red chip eqauts (ROCs) (Staneketal.199 1)).," Only RR Lyr located toward the inner fields closer to the Galactic center $l<4\degr$, $b>-4\degr$ ) seem to follow the barred distribution observed for red clump giants (RCGs) \citealt{1994ApJ...429L..73}) )." Recently. Iunuderetal.(2008) analyzed photometric data on 3525 MACTIO RRab stars to assess the reddening toward the Galactic bulee.," Recently, \cite{2008AJ....135..631K} analyzed photometric data on 3525 MACHO RRab stars to assess the reddening toward the Galactic bulge." They derived the selective. extinction cocficicut Πτα=AEQR)L34z02. which correspouds to the average value observed in the solar neighborhood RepoHAVfE(BV)251x03 (Cardellietal.1989:Fitzpatrick 1999)).," They derived the selective extinction coefficient $R_{V,VR}=A_V/E(V-R)=4.3\pm0.2$, which corresponds to the average value observed in the solar neighborhood $R_{V,BV}=A_V/E(B-V)=3.1\pm0.3$ \citealt{1989ApJ...345..245C,1999PASP..111...63F}) )." The first metallicity iueasuremeuts of bulee. RR. Lxx stars were made by Butleretal.(1976) using the AS incthod (Preston 1959))., The first metallicity measurements of bulge RR Lyr stars were made by \cite{1976ApJ...210..120B} using the $\Delta S$ method \citealt{1959ApJ...130..507P}) ). Using 9 stars in the 100 variable sample of Baacdeetal.(1963) list. they obtained (Fe/Il] =0.65+0.15 dex aud concluded. that the stars are muldly metal-poor.," Using 9 stars in the 100 variable sample of \cite{1963Sci...140..658I} list, they obtained $\langle\feh\rangle$ $=-0.65\pm0.15$ dex and concluded that the stars are mildly metal-poor." CGrattonetal.(1986). used a suuple of 17 bulge RR Ίων variables aud fouud awide ranee of iron abundanees. between —L8 and |0.1 dex.," \cite{1986A&A...169..111G} used a sample of 17 bulge RR Lyr variables and found awide range of iron abundances, between $-1.8$ and $+0.1$ dex." Later. from spectra of 59 RRab aud RRe variables. Walker& Terudrup(1991)— determined an average uictallicity of ([Fe/II; =1.0 dex ou the," Later, from spectra of 59 RRab and RRc variables, \cite{1991ApJ...378..119W} determined an average metallicity of $\langle\feh\rangle$ $=-1.0$ dex on the" iteration in order (ο re-evaluate (he mean planes is performed. we just assign membership probabilities to the stars according to the planes estimated in Paper I. Also. spatial outliers are eliminated according to the procedure explained in that paper: the remaining sample has T7G stus.,"iteration in order to re-evaluate the mean planes is performed, we just assign membership probabilities to the stars according to the planes estimated in Paper I. Also, spatial outliers are eliminated according to the procedure explained in that paper; the remaining sample has 776 stars." We obtain a separation between the GB and the LGD based exclusively in the spatial position of these stars., We obtain a separation between the GB and the LGD based exclusively in the spatial position of these stars. Yel we can see in Figure 3 how a difference in their velocity fields is obtained as a result., Yet we can see in Figure 3 how a difference in their velocity fields is obtained as a result. " The most striking difference is Chat in the UV projection (top panels of Figure 3) the (hree moving eroups that we had found in the full sample (top panel of Figure 2) now distinctly belong either to the GB or the LGD,", The most striking difference is that in the $UV$ projection (top panels of Figure 3) the three moving groups that we had found in the full sample (top panel of Figure 2) now distinctly belong either to the GB or the LGD. The two maxima associated with the Pleiacles and IC: 2391 appear only in the GB velocity field (Figure 3. top left panel). while the Cassiopeia-Taurus peak remains only visible in (he LGD field (Figure 3. top right panel).," The two maxima associated with the Pleiades and IC 2391 appear only in the GB velocity field (Figure 3, top left panel), while the Cassiopeia-Taurus peak remains only visible in the LGD field (Figure 3, top right panel)." This is not surprising. if we consider (hat the Pleiades moving eroup is spatially related (o the Sco-Cen association. which is one of the main components of the GB 1999).," This is not surprising, if we consider that the Pleiades moving group is spatially related to the Sco-Cen association, which is one of the main components of the GB \citep{Mor99}." . Also. we know that 16 2391 is a voung cluster. its age being about 30 Myr. 1997).," Also, we know that IC 2391 is a young cluster, its age being about 30 Myr \citep{Sta97}." . In a recent study of the tangential velocities. Piskunovetal.(2006) conclude (hat its kinematic probability of belonging to the GB is a 73%.," In a recent study of the tangential velocities, \citet{Pis06} conclude that its kinematic probability of belonging to the GB is a $73\%$." Note that we have arrived to a similar conclusion by a process based solely on (he spatial position of the stars. ancl (hus independent of the result in the cited paper.," Note that we have arrived to a similar conclusion by a process based solely on the spatial position of the stars, and thus independent of the result in the cited paper." We must also note that a Iate-tvpe population of voung stars has been associated to both the Pleiades and IC 2391 by Montesοἱal.(2001)., We must also note that a late-type population of young stars has been associated to both the Pleiades and IC 2391 by \citet{Mon01}. . In that paper. these moving eroups are described as centered. around (U.V.)=(—11.6.21.211.4) and km |. respectively. with a dispersion of about 8 kms 1| around the central positions.," In that paper, these moving groups are described as centered around $(U, V, W) = (-11.6, -21, -11.4)$ and $(U, V, W) = (-20.6, -15.7, -9.1)$ km $^{-1}$, respectively, with a dispersion of about 8 km $^{-1}$ around the central positions." Not surprisingly. a late-tvpe component of stars of about 30-80 Myr of age had already been associated to the GB disk structure by Guilloutetal.(1993). studying the X-ray sources in the ROSAT All-Sky Survey.," Not surprisingly, a late-type component of stars of about 30-80 Myr of age had already been associated to the GB disk structure by \citet{Gui98} studying the X-ray sources in the ROSAT All-Sky Survey." Finally. we also observe that in the OV projection (Figure 3. middle right panel) it Clearly rises a new maxinnun (hat has a correspondence with a small protuberance around (i=IL kms !'inthe UV projection (Figure 3. top right panel).," Finally, we also observe that in the $UW$ projection (Figure 3, middle right panel) it clearly rises a new maximum that has a correspondence with a small protuberance around $U = 11$ km $^{-1}$ in the $UV$ projection (Figure 3, top right panel)." It was also present. although weak. in (he velocity density field of the full sample (Figure 2. top and middle panels).," It was also present, although weak, in the velocity density field of the full sample (Figure 2, top and middle panels)." We havent [ound an exact correspondence to this possible moving group among the structures in (he solar neighborhood. but the positive value of the U component makes us think (hat il mav be related to the Sirius supercluster (eg.," We haven't found an exact correspondence to this possible moving group among the structures in the solar neighborhood, but the positive value of the $U$ component makes us think that it may be related to the Sirius supercluster (eg." Eeoen 1996. Dehnen 1998. Asiain et al.," Eggen 1996, Dehnen 1998, Asiain et al." 1999)., 1999). "contribution from minor merging of low mass companions with uw«1/10 is yet to be estimated, but we expect that this contribution would have only limited effects.","contribution from minor merging of low mass companions with $\mu < 1/10$ is yet to be estimated, but we expect that this contribution would have only limited effects." " To expand on our observational results, the study of the minor merger fraction in other fields will be needed to minimize cosmic variance effect, on larger samples to better constrain the evolution of fmm with redshift."," To expand on our observational results, the study of the minor merger fraction in other fields will be needed to minimize cosmic variance effect, on larger samples to better constrain the evolution of $f_{\rm mm}$ with redshift." " In addition, the study of the dependence of minor mergers on properties like mass, morphology or environment will provide other important clues about the role of mergers in the evolution of galaxies since z~1."," In addition, the study of the dependence of minor mergers on properties like mass, morphology or environment will provide other important clues about the role of mergers in the evolution of galaxies since $z \sim 1$." " It is also worth noting that direct measurements of the minor merger fraction have yet to be secured at low redshift, while these will be needed to better constrain the minor mergerfraction evolution with z."," It is also worth noting that direct measurements of the minor merger fraction have yet to be secured at low redshift, while these will be needed to better constrain the minor mergerfraction evolution with $z$ ." IR emission.,IR emission. " This is directly connected to the corresponding surface temperatures of the planets, which are the lowest in the case of the F-type star and almost 20K higher for the M-type star planet (cf."," This is directly connected to the corresponding surface temperatures of the planets, which are the lowest in the case of the F-type star and almost $20 \ \mathrm{K}$ higher for the M-type star planet (cf." Fig., Fig. 2 and Paper I)., \ref{surface} and Paper I). " However not only the overall IR flux is different, also the absorption features of O3, CO», and H2O change due to the central star."," However not only the overall IR flux is different, also the absorption features of $\mathrm{O_3}$ , $\mathrm{CO_2}$, and $\mathrm{H_2O}$ change due to the central star." The depths of the absorption bands of e.g. the planet around the F-type star are rather small compared to the M star case., The depths of the absorption bands of e.g. the planet around the F-type star are rather small compared to the M star case. " In particular, the CO»? absorption band at 4.3um cannot be seen for the F-type star case in the low-resolution spectrum (cf."," In particular, the $\mathrm{CO_2}$ absorption band at $4.3 \ \mathrm{\mu m}$ cannot be seen for the F-type star case in the low-resolution spectrum (cf." Fig. 5))., Fig. \ref{spectra_single_layer}) ). The different clear sky spectra are a direct consequence of the different atmospheric temperature profiles., The different clear sky spectra are a direct consequence of the different atmospheric temperature profiles. The planet around the F-type star has a very large temperature inversion in the upper atmosphere (seealso??)..," The planet around the F-type star has a very large temperature inversion in the upper atmosphere \citep[see also][]{Segura03,Grenfell07}." " This temperature inversion leads to enhanced emission in the O5 and CO; bands, thereby effectively reducing the depths of their absorption features."," This temperature inversion leads to enhanced emission in the $\mathrm{O_3}$ and $\mathrm{CO_2}$ bands, thereby effectively reducing the depths of their absorption features." The planets around the M-type and K-type stars on the other hand show no large atmospheric temperature inversion which leaves the depths of the absorption features almost unaltered from emission (see ?? for a description of these temperature profile characteristics.," The planets around the M-type and K-type stars on the other hand show no large atmospheric temperature inversion which leaves the depths of the absorption features almost unaltered from emission (see \citet{Segura03,Segura05} for a description of these temperature profile characteristics." " Note however, that these cloud free spectra are not directly comparable to those of ?? because of differences in the atmospheric modelling (e.g. different treatments of the atmosphericchemistry and the incident stellar spectra) as outlined above."," Note however, that these cloud free spectra are not directly comparable to those of \citet{Segura03,Segura05} because of differences in the atmospheric modelling (e.g. different treatments of the atmosphericchemistry and the incident stellar spectra) as outlined above." only uncertain single source redshift estimates are present.,only uncertain single source redshift estimates are present. " In practical application, this would degrade the performance of S--U filters even more since they weight the central regions more heavily."," In practical application, this would degrade the performance of $S+U$ filters even more since they weight the central regions more heavily." " By the linear least squares method outlined in Section 2.2 we have found filters for the tangential shear signal of simulated halos that minimize the variance between mass estimates and true Maoom of the clusters in the presence of shape noise, uncorrelated projected LSS and the intrinsic variability of halo shear profiles."," By the linear least squares method outlined in Section \ref{sec:mvf} we have found filters for the tangential shear signal of simulated halos that minimize the variance between mass estimates and true $M_{200m}$ of the clusters in the presence of shape noise, uncorrelated projected LSS and the intrinsic variability of halo shear profiles." We have shown in Section 3.2 that taking into account the last source of noise can improve upon the mass estimates of filters that assume a constant NFW profile., We have shown in Section \ref{sec:imu} that taking into account the last source of noise can improve upon the mass estimates of filters that assume a constant NFW profile. " This improvement is comparable to the improvement that has been previously noted as resulting from the inclusion of uncorrelated LSS in the filter optimization, compared to optimizing solely for shape noise at M21.5:10Ma and a background galaxy density of 40arcmin 2 or more."," This improvement is comparable to the improvement that has been previously noted as resulting from the inclusion of uncorrelated LSS in the filter optimization, compared to optimizing solely for shape noise at $M\geq1.5\cdot10^{14}\Msol$ and a background galaxy density of $40$ $^{-2}$ or more." The most obvious difference from filters that do not take intrinsic profile variability into account is a suppression of weight on the central region of the halo (cf., The most obvious difference from filters that do not take intrinsic profile variability into account is a suppression of weight on the central region of the halo (cf. " Section 3.3)), where intrinsic variability of profiles has its most important contribution to the overall noise (cf."," Section \ref{sec:laf}) ), where intrinsic variability of profiles has its most important contribution to the overall noise (cf." Section 3.1))., Section \ref{sec:ipv}) ). " Apart from these observations, this has a number of important conclusions for weak lensing measurements of cluster masses:"," Apart from these observations, this has a number of important conclusions for weak lensing measurements of cluster masses:" of meliuation. aud provide simple paranmetrizatious of the relative extinction in a galaxy as a function of disk iuclination.,"of inclination, and provide simple parametrizations of the relative extinction in a galaxy as a function of disk inclination." These new mucthods allow us to correct ealaxv properties for iuclination effects and revisit the problemi of automated ealaxy classification., These new methods allow us to correct galaxy properties for inclination effects and revisit the problem of automated galaxy classification. Iu this paper. we preseut a new method for classifving ealaxies that uses iclination-corrected values for galactic concentration. color. aud absolute maguitude. along with the apparent axis ratio.," In this paper, we present a new method for classifying galaxies that uses inclination-corrected values for galactic concentration, color, and absolute magnitude, along with the apparent axis ratio." We use the statistical power of SDSS. which allows us to examine the multivariate distribution of galaxy properties with ample signal-to-noise. aud the MGC. which provides deep liel-resolution nuages for direct visual classification.," We use the statistical power of SDSS, which allows us to examine the multivariate distribution of galaxy properties with ample signal-to-noise, and the MGC, which provides deep high-resolution images for direct visual classification." We describe the selection of the ealaxy samples in section ??.., We describe the selection of the galaxy samples in section \ref{sample-section}. The expressions for the iuclinatiou-corrected quantities are defined im section ?? aand a face-on colorAuagnitude diagram of SDSS ealaxies is presented., The expressions for the inclination-corrected quantities are defined in section \ref{face-on-values-section} and a face-on color-magnitude diagram of SDSS galaxies is presented. Iu section ?? we present our method of classifving galaxies aud demonstrate its effectiveness. aud finally we present our couclisious im section ??..," In section \ref{classification-section} we present our method of classifying galaxies and demonstrate its effectiveness, and finally we present our conclusions in section \ref{conclusions-section}." Our primary galaxy sample comes from SDSS. a Ὁ-baud optical aud near-infrared inagiug aud spectroscopic survey covering oue quarter of the sky (?)..," Our primary galaxy sample comes from SDSS, a 5-band optical and near-infrared imaging and spectroscopic survey covering one quarter of the sky \citep{sdss-technical-summary}." The final data release. DRG (2).. contains inagius aud spectroscopy of over half a mullion galaxies with well defined selection criteria.," The final data release, DR6 \citep{sdss-dr6}, contains imaging and spectroscopy of over half a million galaxies with well defined selection criteria." " Our sample consists of the 186305 ealaxics that meet the Main Galaxy Sample tarecting criteria (?).. have spectra thatare classified as galaxies with confident redshifts (2¢onp29 0.85). have dereddened Petrosian (àbaud maeuitudes r«17.7. lie iun the redshift rauge OL0.85$ ), have dereddened Petrosian $r$ -band magnitudes $r<17.7$, lie in the redshift range $0.01 < z < 0.2$, and have absolute magnitudes $\absmag < -17.5$ ." Petrosian magnitudes are usec throughout. aud +- quantities are used for all photometric parameters.," Petrosian magnitudes are used throughout, and$r$ -band quantities are used for all photometric parameters." Colors and absolute maguitudes are k-corrected to +=0 with IKCORRECT littl (?).., Colors and absolute magnitudes are k-corrected to $z=0$ with KCORRECT 4 \citep{kcorrect}. We adopt Oy=0.3. Q4—07. and Ly=τοΊαν!Mpe|.," We adopt $\Omega_0=0.3$, $\Omega_{\Lambda}=0.7$, and $H_0=70~\mathrm{km~s^{-1}~Mpc^{-1}}$." While SDSS provides us with the statistics necessary to measure the multivariate distribution of ealactic paralucters. the Πασάς is relatively shallow aud often taken in poor seciug couditions.," While SDSS provides us with the statistics necessary to measure the multivariate distribution of galactic parameters, the imaging is relatively shallow and often taken in poor seeing conditions." Therefore. i order to obtain confident visual classifications of a subset of ealaxies. we have used the deeper aud higher resolution imaging data from the MGC (?)..," Therefore, in order to obtain confident visual classifications of a subset of galaxies, we have used the deeper and higher resolution imaging data from the MGC \citep{mgc-imaging}." This 37.5dee? B-band survey ds cutively contained within the SDSS footprint. allowing cross-identification of all ealaxies.," This $37.5~\mathrm{deg}^2$ $B$ -band survey is entirely contained within the SDSS footprint, allowing cross-identification of all galaxies." " We have rvaudomly selected LOO SDSS ealaxics from the above suuple""C that are also contained in the cleaned bright MGC galaxy or direct visual classification Iu Paper L we presented a method to correct the Petrosian concentration ffor iuchnation effects."," We have randomly selected $400$ SDSS galaxies from the above sample that are also contained in the cleaned bright MGC galaxy for direct visual classification In Paper I, we presented a method to correct the Petrosian concentration for inclination effects." We briefly review the method here., We briefly review the method here. As disk galaxies are seen closer to edge-on. the isophotal axis ratio b/« decreases while the global concentration of the light profile increases.," As disk galaxies are seen closer to edge-on, the isophotal axis ratio $b/a$ decreases while the global concentration of the light profile increases." As a result. the loci of intrinsically similar galaxies iu the b/a plane curve to ligher aat smaller bfa.," As a result, the loci of intrinsically similar galaxies in the $b/a$ plane curve to higher at smaller $b/a$." By constructing models of a pure exponential disk viewed at a variety of inclinations. we have ceteruuned the expected concentration of the disk ο as a fuuction of the observed isophotal axis ratio b/a.," By constructing models of a pure exponential disk viewed at a variety of inclinations, we have determined the expected concentration of the disk $C_{\mathrm{Petro}}^{\mathrm{disk}}$ as a function of the observed isophotal axis ratio $b/a$." " We use this relationship to define the normalized conceutration. Chom; for a galaxy with observed isophotal axis ratio (5/0); aud observed Petrosian concentration Cpo,; to be: The loci of ealaxies in the inclination-corrected bfa plane no lonecr depeud on axis ratio. validating the use of aas ano duclination-indepoeudeut ieasure of galaxy conceutratiou."," We use this relationship to define the normalized concentration, $\cnorm_{,i}$, for a galaxy with observed isophotal axis ratio $(b/a)_i$ and observed Petrosian concentration $\cpetro_{,i}$ to be: The loci of galaxies in the inclination-corrected $b/a$ plane no longer depend on axis ratio, validating the use of as an inclination-independent measure of galaxy concentration." Note that although elliptieal galaxies do not suffer from the same inclination effect as disks. they all have large apparent axis ratios.," Note that although elliptical galaxies do not suffer from the same inclination effect as disks, they all have large apparent axis ratios." At these laree axis ratios. CURES is almost independent of b/a. aud therefore the maenitude of the iuclination correction is mininal.," At these large axis ratios, $C_{\mathrm{Petro}}^{\mathrm{disk}}$ is almost independent of $b/a$, and therefore the magnitude of the inclination correction is minimal." Therefore. applying the correction to all galaxies docs not introduce any bias in the coucentrations of elliptical ealaxies.," Therefore, applying the correction to all galaxies does not introduce any bias in the concentrations of elliptical galaxies." 7? find that the extinction in au inclined disk galaxy relative to a face-ou disk galaxy iu a eiven band is well described by: for observed absolute maeuitude AM. facc-on absolute maenitude MP. inclination / (defined to be 0° for facc-on disks aud 90° for edee-on disks). and relative extinction cocfiicicnt 5».," \citetalias{shao-etal07} find that the extinction in an inclined disk galaxy relative to a face-on disk galaxy in a given band is well described by: for observed absolute magnitude $M$, face-on absolute magnitude $M^{\mathrm{F}}$, inclination $i$ (defined to be $0\degr$ for face-on disks and $90\degr$ for edge-on disks), and relative extinction coefficient $\gamma_2$." Values of 5» for cach SDSS baud are giveu iu 7.., Values of $\gamma_2$ for each SDSS band are given in \citetalias{shao-etal07}. " Tn ?.. the inclination / was doeteruüned from the apparent axis ratio of the exponential couponcut of the surface brightuess decomposition (""expab iu the SDSS database) bv Monte Carlo simnulatious."," In \citetalias{shao-etal07}, the inclination $i$ was determined from the apparent axis ratio of the exponential component of the surface brightness decomposition (“expab” in the SDSS database) by Monte Carlo simulations." We simply use the median mapping between expab aud cos; eiven m their fleure 3., We simply use the median mapping between expab and $\cos i$ given in their figure 3. " We then calculate the face-on absolute ;- maguitucde. ΑΠΕ, and face-on ccolor. δι, using equation (2)): Correcting for the disk inchuation presumes the presence of a disk. while many ealaxics are almost eutirelv spheroidal systems."," We then calculate the face-on absolute $r$ -band magnitude, , and face-on color, , using equation \ref{magcorrect-eq}) ): Correcting for the disk inclination presumes the presence of a disk, while many galaxies are almost entirely spheroidal systems." Unlike the concentration 77)). the photometry is sensitive to the inclination correction even at relatively large axis ratios. aud should be onütted for clliptical galaxies.," Unlike the concentration \ref{face-on-concentration-section}) ), the photometry is sensitive to the inclination correction even at relatively large axis ratios, and should be omitted for elliptical galaxies." We therefore ouly, We therefore only Iu the next section. we will find that the central luminosities of the [spectral classes (see Table 1) range over a factor of arouncl LO—20.,"In the next section, we will find that the central luminosities of the 4 spectral classes (see Table 1) range over a factor of around $10-50$." This iuakes it possible to coustruct the luminosity function ol GRBs., This makes it possible to construct the luminosity function of GRBs. The derivation for each of the spectral classes is similar to that employed. previously in Schmidt(1900) for the entire luminosity function., The derivation for each of the spectral classes is similar to that employed previously in \citet{sch99b} for the entire luminosity function. We use the cosmological parameters km | |. Q4;=0.3. and Qy=0.7.," We use the cosmological parameters $H_0 = 65~$ km $^{-1}$ $^{-1}$, $\Omega_M = 0.3$, and $\Omega_{\Lambda} = 0.7$ ." We assiune that the GRB luminosity function (£L.z.sp) of the spectral class sp cau be writter where sp refers to the four spectral classes (see Table 1). L is the peak luminosity in the giver euergy band. PyCL.sp) is the 2=0 luminosity fuuction of class sp. and ;gp(z) the comoving GRB density distribution normalized at z=0.," We assume that the GRB luminosity function $\Phi(L,z,sp)$ of the spectral class $sp$ can be written as where $sp$ refers to the four spectral classes (see Table 1), $L$ is the peak luminosity in the given energy band, $\Phi_0(L,sp)$ is the $z=0$ luminosity function of class $sp$, and $R_{\rm GRB}(z)$ the comoving GRB density distribution normalized at $z=0$." " We assume that each has a gaussian distributioi ol logL with a dispersion oj,;7 around a central peak lumiuosity £,.", We assume that each has a gaussian distribution of $\log L$ with a dispersion $\sigma_{\log L}$ around a central peak luminosity $L_c$. The CRB luninosity Duuctiol is the sun of the spectral luminosity fuuctious ., The GRB luminosity function is the sum of the spectral luminosity functions . ". We assume that the photon spectrum is proportional to Επ,", We assume that the photon spectrum is proportional to $E^{\alpha_{23}}$. The peak flux PCL.z) observe for a GRB of luminosity £ at redshift z is where A(z) is the bolometric luminosity distauce for the cosmological model.," The peak flux $P(L,z)$ observed for a GRB of luminosity $L$ at redshift $z$ is where $A(z)$ is the bolometric luminosity distance for the cosmological model." The peak flux distribution lor GRBs of spectral class sp is. where zCL.P.sp) is derived from equation (2). V(z) is the comoving volume aud the term (1+2)1 represeuts the time dilation (Totani1999).," The peak flux distribution for GRBs of spectral class $sp$ is, where $z(L,P,sp)$ is derived from equation (2), $V(z)$ is the comoving volume and the term $(1+z)^{-1}$ represents the time dilation \citep{tot99}." . With the known distribution of flux limits Priyy in the BD2 sample. we can derive the Euclidean value of from the individual values =(P/Piu)??.," With the known distribution of flux limits $P_{lim}$ in the BD2 sample, we can derive the Euclidean value of from the individual values $ = (P/P_{lim})^{-3/2}$." " The central peak buninositv. L, of each spectral class is iterated util agrees with the observed value.", The central peak luminosity $L_c$ of each spectral class is iterated until agrees with the observed value. " The limiting peak flux. £;,, depends ou the CRB spectrum.", The limiting peak flux $P_{lim}$ depends on the GRB spectrum. Based on the BATSE detector ‘espouse matrix. log £j increases by 0.11 from the softest to the hardest class.," Based on the BATSE detector response matrix, log $P_{lim}$ increases by $\sim 0.11$ from the softest to the hardest class." This does uot allect the derivation described above since 2 is equally affected., This does not affect the derivation described above since $P$ is equally affected. The lumiuosity {ως derived or spectral class sp scales as Pri., The luminosity $L_c$ derived for spectral class $sp$ scales as $P_{lim}$. The comoving GRB cleusity distribution isofteu referred to as the ‘star formation ‘ate’ based ou the expectation that GRBsare caused by massive stars., The comoving GRB density distribution isoften referred to as the 'star formation rate' based on the expectation that GRBsare caused by massive stars. have parametrized) various moclels for the evolution of the cosmic star formation rate (SFR) with, \citet{por00} have parametrized various models for the evolution of the cosmic star formation rate (SFR) with of the simulation being only one year. it would be impossible to see a superposed SLO since its timescale 15 expected to be of about a few years. according to the KTZ99 calculations.,"of the simulation being only one year, it would be impossible to see a superposed SLO since its timescale is expected to be of about a few years, according to the KTZ99 calculations." Furthermore. since RGOG have a reduced wave flux compared to KTZ99. this timescale would be even longer. and thus clearly beyond the possibilities of the RGOG simulation.," Furthermore, since RG06 have a reduced wave flux compared to KTZ99, this timescale would be even longer, and thus clearly beyond the possibilities of the RG06 simulation." We must also look at the secular effect of IGWs in the deep intertor (see TCOS for details)., We must also look at the secular effect of IGWs in the deep interior (see TC05 for details). In the presence of differential rotation. the dissipation of prograde and retrograde waves in the SLO is not symmetric. and this leads to a finite amount of angular momentum being deposited in the interior beyond the SLO.," In the presence of differential rotation, the dissipation of prograde and retrograde waves in the SLO is not symmetric, and this leads to a finite amount of angular momentum being deposited in the interior beyond the SLO." reffig:specnetl shows the net amplitude of waves at a depth of 0.05Ν.. defined by for a local gradient of 0.0014(Hz/0.05R..," \\ref{fig:specnetI} shows the net amplitude of waves at a depth of $0.05\,R_*$, defined by for a local gradient of $0.001\,\mu{\rm Hz}/0.05\,R_*$." " Multiplied by the angular momentum luminosity of waves. this is the filtered angular momentum luminosity £j"" given in Table 1. for our selected evolutionary points."," Multiplied by the angular momentum luminosity of waves, this is the filtered angular momentum luminosity ${{\cal L}_J}^{\rm fil}$ given in Table \ref{tab:popI} for our selected evolutionary points." Let us mention that. in fact. the existence of an SLO is not even required to obtain this differential damping between prograde and retrograde waves. so as long as differential rotation exists at the base of the convection zone. waves will have a net impact on the rotation rate of the interior.," Let us mention that, in fact, the existence of an SLO is not even required to obtain this differential damping between prograde and retrograde waves, so as long as differential rotation exists at the base of the convection zone, waves will have a net impact on the rotation rate of the interior." " The timescale required to delete the imposed differential rotation ts of the order of 100 £;"". The SLO's dynamies is studied by solving Eq. (9) ", The timescale required to delete the imposed differential rotation is of the order of = I /. The SLO's dynamics is studied by solving Eq. \ref{ev_omega}) ) with small timesteps and using the whole wave spectrum. while for the secular evolution of the star. one has to instead use the filtered angular momentum luminosity (see TCOS for details).," with small timesteps and using the whole wave spectrum, while for the secular evolution of the star, one has to instead use the filtered angular momentum luminosity (see TC05 for details)." All the relevant quantities are given in Table | for our selected evolutionary points., All the relevant quantities are given in Table \ref{tab:popI} for our selected evolutionary points. Let us also mention here that differential damping is required both for the SLO and for the filtered angular momentum luminosity., Let us also mention here that differential damping is required both for the SLO and for the filtered angular momentum luminosity. Since this relies on the Doppler shift of the frequency (see Eqs., Since this relies on the Doppler shift of the frequency (see Eqs. 7 and 8)). angular momentum redistribution will be dominated by the low-frequency waves. which experience a larger Doppler shift. but that is not so low that they will be immediately damped.," \ref{optdepth} and \ref{sigma}) ), angular momentum redistribution will be dominated by the low-frequency waves, which experience a larger Doppler shift, but that is not so low that they will be immediately damped." Numerical tests indicate that this occurs around (σ=| μΗ7)., Numerical tests indicate that this occurs around $\sigma \simeq 1~\mu {\rm Hz}$ ). We start with a fully convective contracting star., We start with a fully convective contracting star. As it descends along the Hayashi track. a radiative core appears (Fig. 1)).," As it descends along the Hayashi track, a radiative core appears (Fig. \ref{fig:HRI}) )." In mass coordinates. the top of this radiative region migrates towards the surface until the star reaches the main sequence.," In mass coordinates, the top of this radiative region migrates towards the surface until the star reaches the main sequence." This is accompanied by a growth of the characteristic convective length scale at the bottom of the convection zone, This is accompanied by a growth of the characteristic convective length scale at the bottom of the convection zone whether different apertures would lead to significant differences in the index—o relations.,whether different apertures would lead to significant differences in the $\sigma$ relations. No major difference is found between the gradients of any index at each aperture: the slopes and points agree within the errors (Table 1))., No major difference is found between the gradients of any index at each aperture: the slopes and zero-points agree within the errors (Table \ref{Tab:Fits}) ). It is interesting to see that none of our bulges give à measurement of the oor indices that Hes above the predictions of the models (VÀZO3)., It is interesting to see that none of our bulges give a measurement of the or indices that lies above the predictions of the models \citepalias{vazdekis03}. . This result agrees with the model predictions that the aand undices tend to saturate for metallicities above |---0.4 (VAZO3).. which are also supported by the data of CENO2 and SAGO2..," This result agrees with the model predictions that the and indices tend to saturate for metallicities above $\sim$ -0.4 \citepalias{vazdekis03}, which are also supported by the data of \citetalias{centhesis} and \citetalias{saglia02}." Given that our sample contains bulges from SO to Sbe. we can study whether the index—o relations depend on morphological type (see Fig. 1)).," Given that our sample contains bulges from S0 to Sbc, we can study whether the $\sigma$ relations depend on morphological type (see Fig. \ref{Fig:indexsigma}) )." Due to our limited number of galaxies. we split the sample in just two groups: one of them containing galaxies of types SO. SO/a (T0) and a second group with the Sa to Sbe galaxies (T0).," Due to our limited number of galaxies, we split the sample in just two groups: one of them containing galaxies of types S0, S0/a $\le$ 0) and a second group with the Sa to Sbc galaxies $>$ 0)." No differences are found for any of the relations., No differences are found for any of the relations. We have compared our index—a relations with those found by CENO2 measured for an aperture of 2x4 aresec?.," We have compared our $\sigma$ relations with those found by \citetalias{centhesis} measured for an aperture of 2x4 $^2$." An accurate comparison with SAGO2 ts not possible since their aperture is four times smaller than the smallest we can get given the size of some of our bulges., An accurate comparison with \citetalias{saglia02} is not possible since their aperture is four times smaller than the smallest we can get given the size of some of our bulges. We perform the comparison with at a similar aperture size and at the same spectral resolution (400 +))., We perform the comparison with \citetalias{centhesis} at a similar aperture size and at the same spectral resolution (400 ). In figure 2. we show the comparison of the undex., In figure \ref{Fig:comparison} we show the comparison of the index. The results are in good agreement at the I-c level. with the slopes agreeing within the errors Us]2-0.69—0.18. CENO2]=-0.56£0.15).," The results are in good agreement at the $\sigma$ level, with the slopes agreeing within the errors $\pm$ 0.18, $\pm$ 0.15)." The exclusion of one of our low- dispersion galaxies (NGC 7457). provides an even better agreement in the slope values (b[Us]=-0.52-+40.19).," The exclusion of one of our low-velocity dispersion galaxies (NGC 7457), provides an even better agreement in the slope values $\pm$ 0.19)." However the rms of our data around the best fit is much smaller ((Us)]|20.14) than the one measured by CENO2 ((CENO2)=0.28).," However the rms of our data around the best fit is much smaller (Us)]=0.14) than the one measured by \citetalias{centhesis} (CEN02)=0.28)." On the other hand. our sample shows values for the index slightly higher than those of CENO2 for ellipticals (70.03 aat 400 rresolution).," On the other hand, our sample shows values for the index slightly higher than those of \citetalias{centhesis} for ellipticals $\sim$ 0.03 at 400 resolution)." Previous studies of the same sample by some of us. studying deviations of bulges from the FP of ellipticals and SOs (Faleón-Barrosoetal.2002) or color-color diagrams (Peletieretal.1999a).. conclude that bulge populations are old. but could be younger than ellipticals by up to 2.5 Gyr.," Previous studies of the same sample by some of us, studying deviations of bulges from the FP of ellipticals and S0s \citep{fpb02} or color-color diagrams \citep{pb99}, conclude that bulge populations are old, but could be younger than ellipticals by up to 2.5 Gyr." The higher vvalues. and correspondingly younger ages for bulges could also be due to young stars in the centre of our galaxies.," The higher values, and correspondingly younger ages for bulges could also be due to young stars in the centre of our galaxies." However. model predictions indicate that young populations (<1 Gyr). which increase the value of the index. also lower the value ofCaT.. which is opposite to what we find here.," However, model predictions indicate that young populations $<$ 1 Gyr), which increase the value of the index, also lower the value of, which is opposite to what we find here." Given the small significance of the offset it is more likely that flux calibration differences contribute to the observed shift., Given the small significance of the offset it is more likely that flux calibration differences contribute to the observed shift. For the most extreme case in the sample (NGC 5965.PaT=00.91 Á)) the high could be due to star formation induced by the presence of a strong bar in this galaxy (Kuijken&Merrifield1995)., For the most extreme case in the sample (NGC 0.91 ) the high could be due to star formation induced by the presence of a strong bar in this galaxy \citep{kuijken95}. . On the other hand. we find no correlation of the undex with o. a result supported by CENO2 for Es. and contrary to the strong trend found by SAGO2..," On the other hand, we find no correlation of the index with $\sigma$, a result supported by \citetalias{centhesis} for Es, and contrary to the strong trend found by \citetalias{saglia02}." An explanation for that difference could be in the velocity dispersion correction they have applied to each galaxy in their sample., An explanation for that difference could be in the velocity dispersion correction they have applied to each galaxy in their sample. A large correction for more massive galaxies could explain the positive correlation of the index and the flatness of the index as a function of velocity dispersion., A large correction for more massive galaxies could explain the positive correlation of the index and the flatness of the index as a function of velocity dispersion. The origin and abundance evolution of the atomic element Ca has been a matter of debate., The origin and abundance evolution of the atomic element Ca has been a matter of debate. Due to its nature as an a element. an evolution history similar to that of Mg is predicted (Woosley&Weaver1995).," Due to its nature as an $\alpha$ element, an evolution history similar to that of Mg is predicted \citep{ww95}." However several observations reveal a more complex picture where Ca and Mg originate and evolve differently., However several observations reveal a more complex picture where Ca and Mg originate and evolve differently. The problem has resuscitated again recently in the light of CENO2.. SAGO2..," The problem has resuscitated again recently in the light of \citetalias{centhesis},, \citetalias{saglia02}." For early-type galaxies. the Ca abundance does not follow Mg and there is evidence that it is not enhanced to Fe. from. e.g. measurements of the Ca4227 line (Vazdekisetal.1997.2001) or the ," For early-type galaxies, the Ca abundance does not follow Mg and there is evidence that it is not enhanced to Fe, from, e.g. measurements of the Ca4227 line \citep{vazdekis97,vazdekis01} or the \\citepalias{centhesis,vazdekis03}." On the other hand. the Meg - log(o) relation has been interpreted as a mass-metallicity relation for early-type galaxies (Terlevichetal.1981).," On the other hand, the Mg - $\sigma$ ) relation has been interpreted as a mass-metallicity relation for early-type galaxies \citep{terlevich81}." . In the light of the new results obtained by Cenarroetal.(2003) and model predictions (VAZO3).. such statement does not necessarily hold for the -- log(a) relation (see Worthey1998 and Henry1999 for extensive reviews).," In the light of the new results obtained by \citet{cenletter} and model predictions \citepalias{vazdekis03}, such statement does not necessarily hold for the - $\sigma$ ) relation (see \citealt{worthey98} and \citealt{henry99} for extensive reviews)." The large discrepancy between the observed aand values for a Salpeter-IMF model for galaxies with large velocity dispersions can be interpreted. as underabundance of Ca wart., The large discrepancy between the observed and values for a Salpeter-IMF model for galaxies with large velocity dispersions can be interpreted as underabundance of Ca w.r.t. the other metals in more massive galaxies., the other metals in more massive galaxies. Other possibilities are: 1) An IMF biased towards low-mass stars. 2) Composite Stellar Populations including a low metallicity component or a young and old population of the same metallicity. and 3) Ca depletion.," Other possibilities are: 1) An IMF biased towards low-mass stars, 2) Composite Stellar Populations including a low metallicity component or a young and old population of the same metallicity, and 3) Ca depletion." We discuss the advantages/disadvantages of each one of these possible explanations in turn., We discuss the advantages/disadvantages of each one of these possible explanations in turn. The problem of the Ca underabundance has been previously addressed by several authors (O'Connell.1976;McWilliamVazdekisetal. 2001.. VAZO3)).," The problem of the Ca underabundance has been previously addressed by several authors \citealt{oconnell76,mcwill94,vazdekis97,peletier99,vazdekis01}, \citetalias{vazdekis03}) )." It is hard to find an evolutionary scenario that can produce non-solar Ca/Mg values., It is hard to find an evolutionary scenario that can produce non-solar Ca/Mg values. " Assuming that both Ca and Mg are produced by two ""flavours"" of SNe in which moremassive stars (20-40 ..)) produce Mg before (~2.6 Myr) Ca. generated in less massive stars (12-30 ..)). one could explain a small discrepancy in abundances between Me and Ca (Molla&Garefa-Vargas 2000).."," Assuming that both Ca and Mg are produced by two ""flavours"" of SNe in which moremassive stars (20-40 ) produce Mg before $\approx$ 2.6 Myr) Ca, generated in less massive stars (12-30 ), one could explain a small discrepancy in abundances between Mg and Ca \citep{molla00}. ." However. large abundance ratio differences are hard to obtain in this way. and," However, large abundance ratio differences are hard to obtain in this way, and" "EppMfuloas is apparent by inspecting the limits iu the Heavisidefunction (Jet./rjx€,De.. so that Cpl-XmJf. j.","$\e_{pk} \propto t_z^{-1}$, as is apparent by inspecting the limits in the Heavisidefunction $\beta c t_z/r_0 \propto \ep_u/\Gamma\e_z$, so that $\e_{pk} \propto \ep_{pk}/t_z$ )." The validity of ((B3}) can be checkedby deriving the fiueuce y=fydeIxdtf.(t)fe. using normalization (B2)). from which ((A2)) is recovered.," The validity of \ref{fet30}) ) can be checkedby deriving the fluence $\varphi = \int_0^\infty d\e \; \int_{-\infty}^\infty dt \; f_\e(t)/\e$, using normalization \ref{K}) ), from which \ref{varphi}) ) is recovered." We now derive an approximate analytic expression for a radiation pulse inthe curvature Iuuit., We now derive an approximate analytic expression for a radiation pulse inthe curvature limit. Substituting expressions (6)) and (7)) for the comoving spectral cucrey density iuto ((5)). the πορτα can be approximately solved by ΠΕ ΗΕὑπ ," Substituting expressions \ref{uep}) ) and \ref{uep1}) ) for the comoving spectral energy density into \ref{fet2}) ), the $r$ -integral can be approximately solved by letting $\int dr r^2[\dots]/\Delta r^\prime\rightarrow r_0^2 |dr/dr^\prime| [\dots ]\cong \delta r_0^2 [\dots ]$." In the limit [>>1. one obtains where 2D?etfry. yp =TeAtfrypefy.aud we set fly =L(otherwise the terms IT? are replaced witli 2p?ipi) in (€2)) and (C5 3)) above).," In the limit $\Gamma \gg 1$, one obtains where $u \equiv 2\Gamma^2 c t_z/r_0$ , $\eta \equiv\Gamma c \Delta \tp/r_0 = \eta_t/\eta_r$, and we set $\mu_j = -1$ (otherwise the terms $4\Gamma^2$ are replaced with $ 2\Gamma^2(1-\beta\mu_j)$ in \ref{Qa}) ) and \ref{Qb}) ) above)." The Εν peak euerev observed at the start of the pulse is denoted by eji=Teph.UG!τ).," The $\nu F_\nu$ peak energy observed at the start of the pulse is denoted by $\e_{pk,0} =2\Gamma \ep_{pk,0}/(1+z)$." By examining the limits iun ((C2)). one finds that with related expressions for Qr.," By examining the limits in \ref{Qa}) ), one finds that with related expressions for $Q_b$." Iu the limit à«1. correspoudiug to the curvature limit where variability arises principally from curvature effects. the fourth relation in ((C1)) applies. giviug This expression applies equally to the late-time asviuptote t>(1|τ)Δ2T.," In the limit $\eta \ll 1$, corresponding to the curvature limit where variability arises principally from curvature effects, the fourth relation in \ref{Qaapprox}) ) applies, giving This expression applies equally to the late-time asymptote $t \gg (1+z)\Delta\tp/2\Gamma$." " At the peak of the pF, spectrum. «=0. and recovering the dependence derived in ((0B3))."," At the peak of the $\nu F_\nu$ spectrum, $a = 0$, and recovering the dependence derived in \ref{fet30}) )." " Note that because ry xy. feX gap. (Ctr, 5j) "," Note that because $r_0\propto \eta_r$ , $f_\e\propto \eta_r\eta_t$ . \ref{curvaapprox}) )" relates fe(t) aud wf in the curvature Init., relates $f_\e(t)$ and $u_0^\prime$ in the curvature limit. " If the GRB spectral fix is described by a power-law spectuu with wf, iudex e. then curvature effectswould produce the behavior"," If the GRB spectral flux is described by a power-law spectrum with $\nu F_\nu$ index $ a$ , then curvature effectswould produce the behavior" "thheir high states of accretion,",heir high states of accretion. although with considerably larger error bars (note that both sets of error bars were derived from the inverse Hessian matrix).,although with considerably larger error bars (note that both sets of error bars were derived from the inverse Hessian matrix). " Using pulsation computations of a grid of stellar models and the first asteroseismic results on mode lifetimes of solar-like stars, ? suggested a simple scaling relation between the mean mode linewidth of the most prominent p modes and Terr: Figure [IO] also displays the resulting predictions of mean linewidths of the most prominent modes (we have considered (Do*1.2uHz and T,g=5777K, and taken the recalibrated KIC temperatures)."," Using pulsation computations of a grid of stellar models and the first asteroseismic results on mode lifetimes of solar-like stars, \citet{Chaplin09} suggested a simple scaling relation between the mean mode linewidth of the most prominent p modes and $T_{\rm{eff}}$ : Figure \ref{widths} also displays the resulting predictions of mean linewidths of the most prominent modes (we have considered $\langle\Gamma\rangle_{\sun}\!\approx\!1.2\:{\rm{\mu Hz}}$ and $T_{\rm{eff}\,\sun}\!=\!5777\:{\rm{K}}$, and taken the recalibrated KIC temperatures)." The agreement with the observed values is fairly good in the case of KIC 10273246., The agreement with the observed values is fairly good in the case of KIC 10273246. " On the other hand, the predicted value obtained for KIC 10920273 using Eq."," On the other hand, the predicted value obtained for KIC 10920273 using Eq." overestimates the observed linewidths., \ref{width_temp} overestimates the observed linewidths. " Assuming validity of this equation, this might be the result of the combination of two factors, namely, an overestimation of Τεῃand an overestimation"," Assuming validity of this equation, this might be the result of the combination of two factors, namely, an overestimation of $T_{\rm{eff}}$and an overestimation" obtained for our default. value of ox. suggesting that there is a strong degeneracy between ax and the halo mocel parameters used in this analvsis.,"obtained for our default value of $\sigma_8$, suggesting that there is a strong degeneracy between $\sigma_8$ and the halo model parameters used in this analysis." The changing ex alfected the best-fitting value of Aly much more strongly than the value of 3., The changing $\sigma_8$ affected the best-fitting value of $M_0$ much more strongly than the value of $\beta$. " We also tried lowering the value οἱ the scalar spectral index of the primordial power spectrum from ης=l to n,=0.95. as supported. by recent observations of the Cosmic Microwave. Background. radiation. (Spergel «1 22007)."," We also tried lowering the value of the scalar spectral index of the primordial power spectrum from $n_{\rm s} = 1$ to $n_{\rm s} = 0.95$, as supported by recent observations of the Cosmic Microwave Background radiation (Spergel et 2007)." Assuming ox=OLS. the best-fitting elective masses are (13.59.13.66.13.72.13.78). which do not. cüffer significantly from our default. values presented in Table 2..," Assuming $\sigma_8 = 0.8$, the best-fitting effective masses are $(13.59, 13.66, 13.72, 13.78)$ which do not differ significantly from our default values presented in Table \ref{tabhalofit}." several previous studies have fitted halo model paramoeters o populations of red. galaxies. for example: Magliocchetti Porciani (2003. 2dEGBS): Zehavi et ((2004. 2005b. SDSS): Collister Lahay (2005. 2411 groups catalogue): hleps et ((2006. COMDO-17 survey): and White et ((2007. NDWES).," Several previous studies have fitted halo model parameters to populations of red galaxies, for example: Magliocchetti Porciani (2003, 2dFGRS); Zehavi et (2004, 2005b, SDSS); Collister Lahav (2005, 2dFGRS groups catalogue); Phleps et (2006, COMBO-17 survey); and White et (2007, NDWFS)." We make comparisons to these analyses low. where possible.," We make comparisons to these analyses below, where possible." llalo model fits to the 2dECGIUS galaxy correlation tunction for late-twpe and. carky-tvpe galaxies were verformecd by Magliocchetti Porciani (2003)., Halo model fits to the 2dFGRS galaxy correlation function for late-type and early-type galaxies were performed by Magliocchetti Porciani (2003). In addition. Collister Lahay (2005) directlv investigated the distribution of galaxies within 2dECGIUS eroups.," In addition, Collister Lahav (2005) directly investigated the distribution of galaxies within 2dFGRS groups." These two studies produced. a reasonably Consistent measurement of the slope 3z1 of the HOD at high masses for earlv-tvpe galaxies., These two studies produced a reasonably consistent measurement of the slope $\beta \approx 1$ of the HOD at high masses for early-type galaxies. " Our best-fitting slope. 1Ξ1.5:2.0. is much. higher due to two factors: (1) the stgnificanthy: higher luminosity of our galaxy samples: (2) we make the distinction between central and satellite galaxies. separating out a central galaxy contribution NV,zz1 at hieh masses."," Our best-fitting slope, $\beta = 1.5 \rightarrow 2.0$, is much higher due to two factors: (1) the significantly higher luminosity of our galaxy samples; (2) we make the distinction between central and satellite galaxies, separating out a central galaxy contribution $N_c \approx 1$ at high masses." This latter has the effect of significantly steepening the slope of the power-Iaw. HOD fitted. to the remaining satellite ealaxies (which in fact contribute only ο104 of our sample. as noted in Section 5)).," This latter has the effect of significantly steepening the slope of the power-law HOD fitted to the remaining satellite galaxies (which in fact contribute only $5-10\%$ of our sample, as noted in Section \ref{secparfit}) )." In other words. we effectively lit à model N=ΑιNo)&1|CAZ/Mo) at high masses. rather than N=GU/Mo).," In other words, we effectively fit a model $N = N_c(1 + N_s) \approx 1 + (M/M_0)^\beta$ at high masses, rather than $N = (M/M_0)^\beta$." " Zehavi et ((2004) analyzed a luminous subset. of galaxies from the SDSS “main” spectroscopic database with Al,<2] and mean redshift z 0.1.", Zehavi et (2004) analyzed a luminous subset of galaxies from the SDSS “main” spectroscopic database with $M_r < -21$ and mean redshift $z \approx 0.1$ . They found that a HOD of the form produced a eood fit to the clustering data. where Mow0107775TAL Ado=1077PALL and 3=0.89.," They found that a HOD of the form produced a good fit to the clustering data, where $M_{\rm cut} = 10^{12.79} \, h^{-1} \, M_\odot$, $M_0 = 10^{13.68} \, h^{-1} \, M_\odot$ and $\beta = 0.89$." The cllective mass corresponding to these parameters. is Alay=41057755ΑΙ. (or their choice of σε= 0.9).," The effective mass corresponding to these parameters is $M_{\rm eff} = 10^{13.83} \, h^{-1} M_\odot$ (for their choice of $\sigma_8 = 0.9$ )." " The number density of the Zehavi ct ((2004) sample is n,=9.9.10147 7. whieh is a factor of 2.3 higher than our study."," The number density of the Zehavi et (2004) sample is $n_g = 9.9 \times 10^{-4} \, h^3$ $^{-3}$, which is a factor of $2-3$ higher than our study." Although the effective masses are similar. we note that the recshift dillerence between the Zehavi et ((2004) sample and ours may be important: the number density of a sample of dark matter haloes of fixed mass increases with decreasing redshift owing to the growth of structure.," Although the effective masses are similar, we note that the redshift difference between the Zehavi et (2004) sample and ours may be important; the number density of a sample of dark matter haloes of fixed mass increases with decreasing redshift owing to the growth of structure." The difference in the best-fitting value of the power-law slope between Zehavi et aand our analysis is again connected to the different forms of HOD fittecl (owing to our central ealaxy contribution. as discussed above).," The difference in the best-fitting value of the power-law slope between Zehavi et and our analysis is again connected to the different forms of HOD fitted (owing to our central galaxy contribution, as discussed above)." Zehavi ct ((2005b) presented: an extended: analysis of the SDSS data in which central ancl satellite galaxy contributions are considered separately., Zehavi et (2005b) presented an extended analysis of the SDSS data in which central and satellite galaxy contributions are considered separately. Vheir default mocel includes a sharp cut-olf for the central galaxy HOD at a fixed mass. rather than our 7oftened transition from 0 to lealaxies.," Their default model includes a sharp cut-off for the central galaxy HOD at a fixed mass, rather than our “softened” transition from 0 to 1 galaxies." They find that the slope of the power-law satellite 1IOD increases systematically with luminosity in a manner entirely consistent with our high-Iuminosity moeasurenients of 3=15+2.0., They find that the slope of the power-law satellite HOD increases systematically with luminosity in a manner entirely consistent with our high-luminosity measurements of $\beta = 1.5 \rightarrow 2.0$. " In addition. Zehavi et ((2005b) note hat the step function for «AN,Ado produces a poor Lit o the data in their highest-Iuminosity bin. consistent with our requirement for a softened transition parameterized by Jou."," In addition, Zehavi et (2005b) note that the step function for $$ produces a poor fit to the data in their highest-luminosity bin, consistent with our requirement for a softened transition parameterized by $\sigma_{\rm cut}$." Γον also find. in agreement with our analvsis. that he great majority of luminous galaxies are central galaxies of their host dark matter haloes. rather than satellites in more massive systems.," They also find, in agreement with our analysis, that the great majority of luminous galaxies are central galaxies of their host dark matter haloes, rather than satellites in more massive systems." A low (=10%) satellite fraction for he most luminous elliptical galaxies is also found in galaxy-ealaxw lensing studies (Seljak ct 22005: Mancdelbaum οἱ 22006a) and other clustering studies (linker et 22007: van den Bosch et 22007," A low $\la 10\%$ ) satellite fraction for the most luminous elliptical galaxies is also found in galaxy-galaxy lensing studies (Seljak et 2005; Mandelbaum et 2006a) and other clustering studies (Tinker et 2007; van den Bosch et 2007)." Phleps ct sstudied: various populationsof galaxies in the COMDO-17. survey at a mean redshift =0.6 which is similar to our dataset., Phleps et studied various populationsof galaxies in the COMBO-17 survey at a mean redshift $\overline{z} = 0.6$ which is similar to our dataset. For red-sequence galaxies. Phleps et qquote an elfective halo mass for their best-fitting model of Age=1077ΑΗ... whereas we find Alay=10?ΑΙ. (Fable 2)).," For red-sequence galaxies, Phleps et quote an effective halo mass for their best-fitting model of $M_{\rm eff} = 10^{13.2} \, h^{-1} M_\odot$, whereas we find $M_{\rm eff} = 10^{13.7} \, h^{-1} M_\odot$ (Table \ref{tabhalofit}) )." This apparentlylarge discrepancy is caused by the significant dillerence in the luminosity threshold of the (wo samples: the number density of our LRG catalogue is more than an order of magnitude smaller (there is also a dillerence in the assumed. value of Ox)., This apparentlylarge discrepancy is caused by the significant difference in the luminosity threshold of the two samples: the number density of our LRG catalogue is more than an order of magnitude smaller (there is also a difference in the assumed value of $\sigma_8$ ). White ct ((2007). fitted à. Llalo Occupation Distribution model to the clustering of Luminous Reel Galaxies in the NOAO Deep Wide-Field Survey (NDAVES) Bootes field of 9 deg?. analvzed in redshift: slices between 2=O0 and ο= 1.0.," White et (2007) fitted a Halo Occupation Distribution model to the clustering of Luminous Red Galaxies in the NOAO Deep Wide-Field Survey (NDWFS) Bootes field of 9 $^2$, analyzed in redshift slices between $z = 0.4$ and $z = 1.0$ ." The luminosity thresholds are fixed such that the galaxy number density in each redshift slice is 105? ?. exceeding our sample by a [actor z3 alc=0.5.White ct ddemonstrated that the clustering of the +=0.5 sample cannot be accounted. for by simple passive evolution of the z=0.9 sample. but rather there must be merging or disruption of the most luminous satellite ealaxies in massive haloes.," The luminosity thresholds are fixed such that the galaxy number density in each redshift slice is $10^{-3} \, h^3$ $^{-3}$, exceeding our sample by a factor $\approx 3$ at $z = 0.5$.White et demonstrated that the clustering of the $z = 0.5$ sample cannot be accounted for by simple passive evolution of the $z = 0.9$ sample, but rather there must be merging or disruption of the most luminous satellite galaxies in massive haloes." The best-fitting satellite fraction in the NDWES sample is found to be 1884 c a Little higher than the results of our study. but consistent with a trend in which satellite fraction decreases with increasing Luminosity.," The best-fitting satellite fraction in the NDWFS sample is found to be $18\%$ , a little higher than the results of our study, but consistent with a trend in which satellite fraction decreases with increasing luminosity." In conclusion. our halo model parameter measurements appear broadly consistent with previous work. allowing for differing luminositv thresholds.," In conclusion, our halo model parameter measurements appear broadly consistent with previous work, allowing for differing luminosity thresholds." X. fully consistent comparison of our analysis at 22:0.55 with results at 2=0 is bevond the scope of this work. owing to the cdillering forms of halo occupation distribution assumed. by dilferent authors. but a topic worthy of farther investigation.," A fully consistent comparison of our analysis at $z \approx 0.55$ with results at $z \approx 0$ is beyond the scope of this work, owing to the differing forms of halo occupation distribution assumed by different authors, but a topic worthy of further investigation." Aleasurement of the 3-point clustering functions will aclel further insight into the LI: clustering properties., Measurement of the 3-point clustering functions will add further insight into the LRG clustering properties. ltecent. work byKulkarni et ((2007). analyzing the SDSS spectroscopic LRG sample at zzz0.37 5. favoured a shallower slope for the satellite LOD. 3zz1.4. with ahigher satellite fraction of 114.," Recent work byKulkarni et (2007), analyzing the SDSS spectroscopic LRG sample at $z \approx 0.35$ , favoured a shallower slope for the satellite HOD, $\beta \approx 1.4$, with ahigher satellite fraction of $17\%$ ." Further study is required. to. understand these dillerences., Further study is required to understand these differences. Salpeter's initial mass function and age 13Gyr. namely an elliptical galaxy and three different spiral galaxies (Sa. Sb and Se).,"Salpeter's initial mass function and age 13Gyr, namely an elliptical galaxy and three different spiral galaxies (Sa, Sb and Sc)." We also included the model fit to multi-wavelength observations of M82 as a semi-empirical template to represent the typical SED of local starburst galaxies (Silvaetal. 1998)., We also included the model fit to multi-wavelength observations of M82 as a semi-empirical template to represent the typical SED of local starburst galaxies \citep{silva98}. . For spiral galaxies. the SEDs correspond to a weighted average over the different lines of sight. from face-on to edge-on. in order to statistically account for the mean spatial orientations. of cluster galaxies.," For spiral galaxies, the SEDs correspond to a weighted average over the different lines of sight, from face-on to edge-on, in order to statistically account for the mean spatial orientations of cluster galaxies." The five templates are displayed in Fig. 1.., The five templates are displayed in Fig. \ref{fig:seds}. The SED models deseribed above were used to derive the expected IR luminosities from observed fluxes and corresponding lummosities in the 7 band., The SED models described above were used to derive the expected IR luminosities from observed fluxes and corresponding luminosities in the $r$ band. For a given template. the luminosity in the 7 band is given by where L(A) is the luminosity per unit wavelength and 7;(À.) is the SDSS + filter transmission.," For a given template, the luminosity in the $r$ band is given by where $L(\lambda)$ is the luminosity per unit wavelength and $T_r(\lambda)$ is the SDSS $r$ filter transmission." For the purpose of this work. we define the IR luminosity following LeFloc'hetal.(2005): Therefore. for each template SED. the scaling ratio can be defined as follows Table |) summarizes the Κιν values for the different templates used in this paper.," For the purpose of this work, we define the IR luminosity following \cite{lefloch05}: Therefore, for each template SED, the scaling ratio can be defined as follows Table \ref{tab:gal_pop} summarizes the $R_{{\rm IR},r}$ values for the different templates used in this paper." " For a given L,. the corresponding ccan be different by almost three orders of magnitude depending on the spectral type of the galaxy."," For a given $L_r$, the corresponding can be different by almost three orders of magnitude depending on the spectral type of the galaxy." The modelisation of the luminosity of early-type and late-type galaxy populations is explained in the details in the next sections., The modelisation of the luminosity of early-type and late-type galaxy populations is explained in the details in the next sections. Early-type galaxies are characterized by àn old stellar population and a star-formation history which ts essentially compatible with passive evolution: for this reason they are not expected to dominate the emission in the bbands., Early-type galaxies are characterized by an old stellar population and a star-formation history which is essentially compatible with passive evolution: for this reason they are not expected to dominate the emission in the bands. In fact. for a fixedLig.. the amount of energy emitted at wavelengths A=40 iis one order of magnitude lower with respect to normal spirals (see Fig.1)).," In fact, for a fixed, the amount of energy emitted at wavelengths $\lambda \ga 40$ is one order of magnitude lower with respect to normal spirals (see \ref{fig:seds}) )." However. it is known that in dense environments elliptical galaxies largely dominate the galactic population. being about 4 times more frequent than spirals (see.e.g.Dressler1980:etal. 1997)..," However, it is known that in dense environments elliptical galaxies largely dominate the galactic population, being about 4 times more frequent than spirals \citep[see, e.g.,][]{dressler80,dressler97}." Moreover red galaxies are usually more massive and more luminous in the + band than blue ones., Moreover red galaxies are usually more massive and more luminous in the $r$ band than blue ones. For these reasons their total contribution on the clusters IR signal may be non-negligible., For these reasons their total contribution on the clusters IR signal may be non-negligible. " As mentioned in Section 2.1.. Koesteretal.(2007) identified the number oof E/SO galaxies (M,«16) inside R»oo of each of the 7 476 clusters of our sample."," As mentioned in Section \ref{ssec:maxbcg}, \cite{koester07} identified the number of E/S0 galaxies $M_r<-16$ ) inside $R_{200}$ of each of the 7 476 clusters of our sample." For each cluster. the authors provide the luminosity. k-corrected at 7=0.25. in the / band.," For each cluster, the authors provide the luminosity, $k$ -corrected at $z$ =0.25, in the $r$ band." of the BCG and of the other E/SO members as a whole., of the BCG and of the other E/S0 members as a whole. " We corrected these luminosities into rest-frame luminosities by using the LRG template of (Blanton&Roweis2007):: we refer to LBC? and L?*"" for the luminosity of the BCG and of the cluster as a whole. respectively. after this correction."," We corrected these luminosities into rest-frame luminosities by using the LRG template of \citep{blanton07}: we refer to $L_{r}^{\rm BCG}$ and $L_{r}^{{\rm memb}}$ for the luminosity of the BCG and of the cluster as a whole, respectively, after this correction." Given the uniform properties of early-type galaxies. and the high number of such objects in our sample. their typical SED should be well represented by the E/SO template described above.," Given the uniform properties of early-type galaxies, and the high number of such objects in our sample, their typical SED should be well represented by the E/S0 template described above." In fact. although the IR signal of every single galaxy is lost in the stacking process. the E/SO template still represents the average behavior of the early-type population of galaxies.," In fact, although the IR signal of every single galaxy is lost in the stacking process, the E/S0 template still represents the average behavior of the early-type population of galaxies." For every cluster we assign a ;7-band luminosity to all of its early-type members contained in the SDSS-maxBCG catalogue., For every cluster we assign a $r$ -band luminosity to all of its early-type members contained in the SDSS-maxBCG catalogue. " For the BCG we use the value of LBC, while for the other galaxies we use the average luminosity of the BCG E/SO galaxies. determined as From eq. 3.."," For the BCG we use the value of $L_{r}^{\rm BCG}$, while for the other galaxies we use the average luminosity of the non-BCG E/S0 galaxies, determined as From eq. \ref{eq:f_ir}," " we translated these r-band luminosities into IR luminosities: Lip=Rig,«L,. subsequently used to normalise the SED and further on to derive the fluxes in the 60 aand 100 bbands (see Sect. 5))."," we translated these $r$ -band luminosities into IR luminosities: $L_{\rm IR} = R_{{\rm IR},r} \times L_r$, subsequently used to normalise the SED and further on to derive the fluxes in the 60 and 100 bands (see Sect. \ref{sec:flux}) )." Although the majority of optically bright galaxies in clusters environment are elliptical. and despite spiral galaxies in dense environments tend to be quickly stripped of their gas and have their star-formation quenched. they are still expected to provide a dominant contribution to the IR emission. due to their higher SFRs.," Although the majority of optically bright galaxies in clusters environment are elliptical, and despite spiral galaxies in dense environments tend to be quickly stripped of their gas and have their star-formation quenched, they are still expected to provide a dominant contribution to the IR emission, due to their higher SFRs." Therefore. the contribution of late-type galaxies to the IR emission is crucial for our purposes and," Therefore, the contribution of late-type galaxies to the IR emission is crucial for our purposes and" tween 10171079ergs.1keV. 1).,"between $10^{43} - 10^{46} \rm ~erg~s^{-1}~keV^{-1}$ )." Phe NLSIs contribute of this emissivity. DLSIs42%.. and the BL Lac objects he remainder.," The NLS1s contribute of this emissivity, BLS1s, and the BL Lac objects the remainder." This high contribution of NLS1s is in contrast o the situation at hard. X-ray energies. where NLS1s make a negligible contribution to the volume emissivity (c.g. fjeccinotti et al.," This high contribution of NLS1s is in contrast to the situation at hard X-ray energies, where NLS1s make a negligible contribution to the volume emissivity (e.g., Picccinotti et al." 1982)., 1982). Hlowever. it is interesting to note hat a similar value for the volume emissivitv at 200 eV. is obtained by extrapolating downward with a spectral slope ax=O07 from the 210 keV. AGN volume emissivity derived from the ssample (Piecinotti ct al.," However, it is interesting to note that a similar value for the volume emissivity at 200 eV is obtained by extrapolating downward with a spectral slope $\alpha_{X} =-0.7$ from the 2–10 keV AGN volume emissivity derived from the sample (Piccinotti et al." 1982)., 1982). This paper focuses on a sample of extragalactic sources selected. on the basis of their detection in the EUV by the ROSAT WC., This paper focuses on a sample of extragalactic sources selected on the basis of their detection in the EUV by the ROSAT WFC. Using an approach optimized to find such sources we construct an initial catalogue of 34 sources. which after the exelusion of sources identified with Galactic objects. reduces to a sample of 19 EUV-bright AGN.," Using an approach optimized to find such sources we construct an initial catalogue of 34 sources, which after the exclusion of sources identified with Galactic objects, reduces to a sample of 19 EUV-bright AGN." This is the first reasonably sized. complete ancl unbiased. sample of EUV-selected AGN to be available.," This is the first reasonably sized, complete and unbiased sample of EUV-selected AGN to be available." NLSIs are wel represented in the sample making up just under hall of the total. with BLSIs and BL Lac objects comprising the remainder.," NLS1s are well represented in the sample making up just under half of the total, with BLS1s and BL Lac objects comprising the remainder." This is in stark contrast with hard X-ray selectec samples. in which NLSIs have negligible. representation.," This is in stark contrast with hard X-ray selected samples, in which NLS1s have negligible representation." " Lt is expected that these data will allow the first. reliable statistical studies of this important emerging subclass of Cextreme"" ACN."," It is expected that these data will allow the first reliable statistical studies of this important emerging subclass of “extreme"" AGN." In the first such preliminary study. presented. in this paper. a correlation was seen between the ssoft ancl hard. band. hardness. ratios. 42/21 and. 14/02. indicating that sources with strong EUV excesses also have steeper soft X-ray spectra.," In the first such preliminary study, presented in this paper, a correlation was seen between the soft and hard band hardness ratios, $HR1$ and $HR2$, indicating that sources with strong EUV excesses also have steeper soft X-ray spectra." " ""These cata were also used o directly derive the first. luminosity function. for AGN measured at EUV energies. (specifically at 200 eV).", These data were also used to directly derive the first luminosity function for AGN measured at EUV energies (specifically at 200 eV). The uminosity. function implies à roughly equal contribution to he EUV volume emissivity from cach decade of luminosity ⋅or Logo between 107⊥⇁⋆≻ to LO1PoresΚονnον but with. a sharp cut olf at higher luminosities.," The luminosity function implies a roughly equal contribution to the EUV volume emissivity from each decade of luminosity for $L_{200}$ between $10^{43}$ to $10^{46}\rm~erg~s^{-1}~keV^{-1}$, but with a sharp cut off at higher luminosities." This luminosity function srovicles an independent. estimate of the mean intergalactic ionizing photon field. whieh until now has been estimated wo extrapolation from the optical luminosity. function. of AGN.," This luminosity function provides an independent estimate of the mean intergalactic ionizing photon field, which until now has been estimated by extrapolation from the optical luminosity function of AGN." Finally. we note that NLSIs contribute roughly half of the volume enmissivity at 200 eV. again in contrast to the situation pertaining at harder X-ray energies.," Finally, we note that NLS1s contribute roughly half of the volume emissivity at 200 eV, again in contrast to the situation pertaining at harder X-ray energies." The authors would like to thank John Pye. Steve Sembas. Keith Sohl and the Leicester WEC team for help compiling the deep WEC data and correlating it with the ος and. other ata.," The authors would like to thank John Pye, Steve Sembay, Keith Sohl and the Leicester WFC team for help compiling the deep WFC data and correlating it with the RBSC and other data." This research mace use of data obtained from the Ligh Enerey Astrophysics Science Archive Research Center (IIEASARC). provided hy NASA's Goddard Space Flight Center. from the NASA/LPAC Extragalactic Database (NIZD). provided. by NASA/JPL under contract with Caltech. from the Leicester Database and Archive Service (LEDAS) at the Department of Physics and Astronomy. Leicester University. Ulx.. ancl from the set of Identifications. Measurements and. Bibliography for Astronomical Data (SIAIBAD). maintained by the Centre de Donnees astronomiques de Strasbourg.," This research made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center, from the NASA/IPAC Extragalactic Database (NED), provided by NASA/JPL under contract with Caltech, from the Leicester Database and Archive Service (LEDAS) at the Department of Physics and Astronomy, Leicester University, UK, and from the Set of Identifications, Measurements and Bibliography for Astronomical Data (SIMBAD), maintained by the Centre de Donnees astronomiques de Strasbourg." We thank the stall at the Anelo-Australian Observatory for. obtaining the spectrum of RN J043747 during service time. and Thomas Boller for a quick ancl helpful referees report.," We thank the staff at the Anglo-Australian Observatory for obtaining the spectrum of RX J0437–47 during service time, and Thomas Boller for a quick and helpful referee's report." SV acknowledges support from PPARC., SV acknowledges support from PPARC. In the following. we present the main findings of our work concerning with tidal tails structive and evolution.,"In the following, we present the main findings of our work concerning with tidal tails structure and evolution." When we refer to the center-ol-censity of the cluster. we mean a mass densitv-weighted center as defined by Casertano&πα(1985).," When we refer to the center-of-density of the cluster, we mean a mass density-weighted center as defined by \citet{ch85}." . In all the simulations performed. the cluster starts moving around the galaxy center in a clockwise direction (seen from the positive x axis).," In all the simulations performed, the cluster starts moving around the galaxy center in a clockwise direction (seen from the positive x axis)." The different loop orbits have been followed Lor about 30 fara. In Fig.l.. 2.. 3.. 4..5..6.. 7 and &.. the formation ancl subsequent development of tails around the globular cluster is Alter about 8 /uuu. dal tails are clearly formed.," The different loop orbits have been followed for about 30 $t_{\rm{cross}}$ In \ref{orb1}, , \ref{orb2}, , \ref{orb3}, , \ref{orb4}, \ref{orb5}, \ref{orb6}, \ref{orb7} and \ref{orb8}, the formation and subsequent development of tails around the globular cluster is After about 8 $t_{\rm{cross}}$, tidal tails are clearly formed." " They continuosly acerete by stars leaving the cluster. so (hat after 30 /,,,. in (he case of quasi-circular orbit (e—0.03). they are elongated [for more than 3 ry each ancl contain about. 75% of the initial cluster mass."," They continuosly accrete by stars leaving the cluster, so that after 30 $t_{\rm{cross}}$, in the case of quasi-circular orbit $e=0.03$ ), they are elongated for more than 3 $r_b$ each and contain about $75\%$ of the initial cluster mass." As it is clearly visible from these figures. (he degree of elongation of the tails along the cluster orbital path strongly depends on the ellipticity € (Eq.7)) of the cluster orbit.," As it is clearly visible from these figures, the degree of elongation of the tails along the cluster orbital path strongly depends on the ellipticity $e$ \ref{ell}) ) of the cluster orbit." Indeed. while in the case of the quasi-cireular orbit tails are a clear tracer of the cluster path. in the most eccentric orbit (e= 0.57). tails are strictly elongated along the orbital path only when the cluster is near the perigalacticon. while at the apogalacticon thev tend to deviate [rom the cluster path.," Indeed, while in the case of the quasi-circular orbit tails are a clear tracer of the cluster path, in the most eccentric orbit $e=0.57$ ), tails are strictly elongated along the orbital path only when the cluster is near the perigalacticon, while at the apogalacticon they tend to deviate from the cluster path." Nevertheless. in Miocchietal.(2004) à remarkable tailsorbit alignment is found for clusters moving on quasiradial orbits in the same bulge potential.," Nevertheless, in \citet{mioc} a remarkable tails—orbit alignment is found for clusters moving on quasi–radial orbits in the same bulge potential." ILowever. it is important to stress that. in order to perform accurate predictions of the cluster orbit from observational detections of tidal (ails. it is necessary (0 look at (he spatial distribution of stars. well outside the cluster (tvpicallv 2—3 times the cluster limiting radius).," However, it is important to stress that, in order to perform accurate predictions of the cluster orbit from observational detections of tidal tails, it is necessary to look at the spatial distribution of stars well outside the cluster (typically $2-3$ times the cluster limiting radius)." Indeed. in the vicinitv of the globular cluster. stars in the tails are not aligned with the cluster orbit. neither in (he case of small ellipticity (see Fie.C)). but they. distribute along thepeculiar 5—shape profilenot aligned along the," Indeed, in the vicinity of the globular cluster, stars in the tails are not aligned with the cluster orbit, neither in the case of small ellipticity (see \ref{zoom}) ), but they distribute along thepeculiar $S-$shape profilenot aligned along the" locally parallel to the princiwal arms (Fig.,locally parallel to the principal arms (Fig. EMi)., 3). The strougest peaA. of the polarized brightuess. with the polarization degre| reaching locally Is located west of the ealaxvs ceire. at the positio1i of the unusually straight dust lane segment (see also Fie.," The strongest peak of the polarized brightness, with the polarization degree reaching locally, is located west of the galaxy's centre, at the position of the unusually straight dust lane segment (see also Fig." 5)., 5). No bright star-formune regions are present there., No bright star-forming regions are present there. The secoud. weaker peak does not coiicide with a promirent dist lane but ix locaed in the interarm region between fre northern seenieut of the easern arn aud the bar where ouly suall. barelv visible dust filameuts are prese1ο," The second, weaker peak does not coincide with a prominent dust lane but is located in the interarm region between the northern segment of the eastern arm and the bar where only small, barely visible dust filaments are present." " No xolaunizatiou was deected in the vicinity of à partiCularly heavy dust lane segment in the southern part of 10 Casorn aiu at RAjosy of about 11177127 and 959 of 13*15'30"", accolnuxuided by a chain of star-forming regioIs,"," No polarization was detected in the vicinity of a particularly heavy dust lane segment in the southern part of the eastern arm at $_{1950}$ of about $11^{h}17^{m}42^{s}$ and $_{1950}$ of $13\degr 15\arcmin 30\arcsec$, accompanied by a chain of star-forming regions." Wihi a polarization deeree less tha the bar aids aro οςnoerallv weakly pe)arized., With a polarization degree less than the bar ends are generally weakly polarized. " Ilowever. clear xilarization patches in the vicinity of osu of 1117""11:5 Decyosy of 1:41307 ancl BRAÀq1)0 of li17""33 Decyysy of 13717"":DA surrounding the bar ends aid being iiareimallv significant in Fig."," However, clear polarization patches in the vicinity of $_{1950}$ of $11^{h}17^{m}41\fs5$ $_{1950}$ of $13\degr 14\arcmin 30\arcsec$ and $_{1950}$ of $11^{h} 17^{m} 35\fs3$ $_{1950}$ of $13\degr 17\arcmin 32\arcsec$, surrounding the bar ends and being marginally significant in Fig." 3.Mi exceed the 30 noise level after convolving the data to a beannvidth of 1/3 (Fie.," 3, exceed the $3\sigma$ noise level after convolving the data to a beamwidth of 3 (Fig." D)., 4). The degree of polarization iu these regious is aboutο, The degree of polarization in these regions is about. "ν, The orieutatious of the polarization D-vectors ivected to face-on position are shown iu Fie.", The orientations of the polarization B-vectors rected to face-on position are shown in Fig. 5., 5. West of the ceitre hey run parallel to a straight scement of the dust ane. following its beud iu the southern disk.," West of the centre they run parallel to a straight segment of the dust lane, following its bend in the southern disk." Iu the polarized peak iu the NE disk the B-vectors iu the interarm regk)1 follow the direction of the dus lane which itself is oilv weakly polarized., In the polarized peak in the NE disk the B-vectors in the interarm region follow the direction of the dust lane which itself is only weakly polarized. Tut1C above mentioned weak polarization] )atches near he bar ends. vest Visible in Fie.," In the above mentioned weak polarization patches near the bar ends, best visible in Fig." L the B-vecors tend to nr 511toothy around the terminal points of the bar.," 4, the B-vectors tend to turn smoothly around the terminal points of the bar." No (xcderec optica or IIo structures are preseut here., No ordered optical or $\alpha$ structures are present there. Close o the rorthe1’1 uw eud the vector oricutatioIS SOOlily join tlicSSC da t15 western arm (see also Fig., Close to the northern bar end the vector orientations smoothly join these in the western arm (see also Fig. 5), 5). Near the souther nbarexd the B-vectors deviate stronelv to the cast with a large ]itc ranele., Near the southern bar end the B-vectors deviate strongly to the east with a large pitch angle. Across the προ]χοd region iu he southern ut of the easteru arm their orieutations juup bv abou 907., Across the unpolarized region in the southern part of the eastern arm their orientations jump by about $90\degr$. The question of possible geonmetrical depolwization a this position is discussed 1i detail iu Sect., The question of possible geometrical depolarization at this position is discussed in detail in Sect. 1., 4. The inteerationC» of the polarized iteusity 1nap shown in Fie., The integration of the polarized intensity map shown in Fig. 3 in the same rings as described in Sec 3.1vields an inteerated polarized flux deusitv of 6.0+41.8 indy., 3 in the same rings as described in Sect 3.1yields an integrated polarized flux density of $6.0\pm 1.8$ mJy. This nuplies a mean polarization degree of 5.8+ LS..., This implies a mean polarization degree of $5.8\pm 1.8$ . Chile.,Chile. " VYSOS-6 is equipped with a 4096x pixel CCD yielding a field-of-view of 2.7°, and seven broad- and narrow-band We obtained light curves with a median sampling of 2 days in the B-band (Johnson, 4330+500 AA)), the redshifted Ha (NB 6721+30 aat z= 0.0258) and Hf lines (NB 5007+30 aat z= 0.0327)."," VYSOS-6 is equipped with a $4096 \times 4096$ pixel CCD yielding a field-of-view of $2.7^{\circ}$, and seven broad- and narrow-band We obtained light curves with a median sampling of 2 days in the $B$ -band (Johnson, $4330 \pm 500$ ), the redshifted $\alpha$ (NB $6721 \pm 30$ at $z = 0.0258$ ) and $\beta$ lines (NB $5007 \pm 30$ at $z = 0.0327$ )." " For 1120 we also obtained a light curve in the V-band (Johnson, 5500+500 AA))."," For 120 we also obtained a light curve in the $V$ -band (Johnson, $5500 \pm 500$ )." " In addition, we observed PG0003+199 in both B and V on July 25 2010 and June 26” 2011."," In addition, we observed PG0003+199 in both $B$ and $V$ on July $^{th}$ 2010 and June $^{th}$ 2011." Figure 1 shows the effective transmission of the filters used here., Figure \ref{fig_transmission} shows the effective transmission of the filters used here. " To perform absolute photometric calibration, each night we observed standard stars in the fields SA092, SA095, SAI11 from Landoldt (2009)."," To perform absolute photometric calibration, each night we observed standard stars in the fields SA092, SA095, SA111 from Landoldt (2009)." " For both targets, a single contemporaneous spectrum was obtained with CAFOS at the mm telescope on Calar Alto, Spain, with a slit width of 154."," For both targets, a single contemporaneous spectrum was obtained with CAFOS at the m telescope on Calar Alto, Spain, with a slit width of $\farcs$ 54." " We reduced all data in a standard manner, using IRAF and custom written tools."," We reduced all data in a standard manner, using IRAF and custom written tools." " Because the flux calibration using the standard star fields introduces additional errors in the light curves, we created relative light curves (in normalised flux units) using 20-30 non-variable stars located on the same images within 30' around the AGN and of similar brightness as the AGN."," Because the flux calibration using the standard star fields introduces additional errors in the light curves, we created relative light curves (in normalised flux units) using 20-30 non-variable stars located on the same images within $\arcmin$ around the AGN and of similar brightness as the AGN." For the analysis of time lags we used the mean and standard deviation of these relative light curves., For the analysis of time lags we used the mean and standard deviation of these relative light curves. " For the photometric analysis (to obtain the AGN luminosities), we kept the shape of the mean light curves fixed and calibrated them by a least-squares fit to the photometry derived from the standard star fields."," For the photometric analysis (to obtain the AGN luminosities), we kept the shape of the mean light curves fixed and calibrated them by a least-squares fit to the photometry derived from the standard star fields." Source parameters and photometry results are summarized in Table 1.., Source parameters and photometry results are summarized in Table \ref{table1}. PG0003+199 is essentially a point-like low-luminosity quasar (Narrow Line Seyfert-1) without a bright extended host., PG0003+199 is essentially a point-like low-luminosity quasar (Narrow Line Seyfert-1) without a bright extended host. The Ha line is strong and well covered by the narrow-band filter., The $\alpha$ line is strong and well covered by the narrow-band filter. This makes PG0003--199 a clear-cut test case., This makes PG0003+199 a clear-cut test case. Fig., Fig. 2 shows the spectrum of PG0003+199., \ref{fig_spectrum_pg0003} shows the spectrum of PG0003+199. " The contribution of higher order Balmer lines (and that of the host galaxy) to the B-band is negligible, thus the B-band is dominated by the AGN continuum."," The contribution of higher order Balmer lines (and that of the host galaxy) to the $B$ -band is negligible, thus the $B$ -band is dominated by the AGN continuum." " Taking into account the spectral resolution, the observed Ha line dispersion σ= 1300kkm/s reduces to an intrinsic value σ= 870kkm/s. The narrow-band filter effectively covers the line between velocities —2800 kkm/s and +1800kkm/s, so that at least of the line flux is contained in the band pass, as we determined after line profile deconvolution."," Taking into account the spectral resolution, the observed $\alpha$ line dispersion $\sigma = 1300$ km/s reduces to an intrinsic value $\sigma = 870$ km/s. The narrow-band filter effectively covers the line between velocities $-2800$ km/s and $+1800$ km/s, so that at least of the line flux is contained in the band pass, as we determined after line profile deconvolution." The contribution of both the [N aand narrow-line Ha flux is predicted to be smaller than of the [O III] emission (Bennert et al., The contribution of both the [N and narrow-line $\alpha$ flux is predicted to be smaller than of the [O III] emission (Bennert et al. " 2006), hence negligible (« 1096)."," 2006), hence negligible $<10\%$ )." " The continuum underneath the emission line is small, contributing to only of the total flux in the band pass."," The continuum underneath the emission line is small, contributing to only of the total flux in the band pass." " Therefore, the narrow-band light curves will be dominated by the Ha echo of the BLR gas clouds."," Therefore, the narrow-band light curves will be dominated by the $\alpha$ echo of the BLR gas clouds." " Comparison with simulated line profiles of echo models (Welsh Horne 1991, Horne et al."," Comparison with simulated line profiles of echo models (Welsh Horne 1991, Horne et al." " 2004) ascertains that the line flux outside the band pass has only a marginal effect (« 2%)) on the BLR size determination: The narrow-band echo may miss only a small fraction (« 20%)) of the innermost part of the BLR, namely that part which exhibits the fastest line-of-sight velocity, while the innermost gas clouds moving closer along"," 2004) ascertains that the line flux outside the band pass has only a marginal effect $< 2$ ) on the BLR size determination: The narrow-band echo may miss only a small fraction $< 20$ ) of the innermost part of the BLR, namely that part which exhibits the fastest line-of-sight velocity, while the innermost gas clouds moving closer along" we derive total metal abuudances usiug cotun deusities of singly ionized species sununued up over the detected components (see Table 21).,we derive total metal abundances using column densities of singly ionized species summed up over the detected components (see Table \ref{tabmet}) ). The resul of fitting to individual componcuts is presented in Table 3.., The result of fitting to individual components is presented in Table \ref{tabmet2}. Weal additional. undetected components caunot represent more than 15 per cent of the otal column density (1.6. 0.06 dex).," Weak additional, undetected components cannot represent more than 15 per cent of the total column density (i.e. 0.06 dex)." The best-fitting curves shown in Fig., The best-fitting curves shown in Fig. 3 have been determined iu two steps., \ref{figmetals} have been determined in two steps. Iu order to derive accurate b values. we first fitted trausiion lines frou covering a wide range of oscilator strengths with 22 components. six of which are r-doetected.," In order to derive accurate $b$ values, we first fitted transition lines from covering a wide range of oscillator strengths with 22 components, six of which are -detected." . Using fixed b values as previcnmslv lueasurcd. we the1 fitted altogether the lines fromSill.ir.SIL. 1... Mul. Fell. and IL.," Using fixed $b$ values as previously measured, we then fitted altogether the lines from, and ." For a given component. the same Doppler parameter iux redshift were used for all species.," For a given component, the same Doppler parameter and redshift were used for all species." Due to the smoothness of the metal ine profiles (see Fig. 3)).," Due to the smoothness of the metal line profiles (see Fig. \ref{figmetals}) )," we did not impose the Doppler paraincters from the fitting o lines., we did not impose the Doppler parameters from the fitting to lines. " It is wel known that noise leads to overestimae the widh of weak. lines,", It is well known that noise leads to overestimate the width of weak lines. Sia] shifts Plans 1) between the positious of the compoucuts in the metal aud ine profiles can be roted as wel (see Tables 3. iux 5j .," Small shifts $<3$ km $^{-1}$ ) between the positions of the components in the metal and line profiles can be noted as well (see Tables \ref{tabmet2} and \ref{tabphy}) )." They are παο han half of the FWIAL of the observations lOWOCVOT., They are smaller than half of the FWHM of the observations however. This nuplies hat the uucertaiutv on the absolute metallicities is of the order o30% but this is πιο smaller on the abundance ratios., This implies that the uncertainty on the absolute metallicities is of the order of but this is much smaller on the abundance ratios. The metalicity of the gas derived. from the absolute abundance of zinc is close to Solar. |Zu/U=0.13.," The metallicity of the gas derived from the absolute abundance of zinc is close to Solar, $]=-0.13$." This is the first finie such a high inetallicitv is observed in a DLA svsteii at high redshift., This is the first time such a high metallicity is observed in a DLA system at high redshift. The abundance of S relative to Zu is not oversolar but is on the contrary slightly nndersolar. in aerccinent with the observations of Galactic," The abundance of S relative to Zn is not oversolar but is on the contrary slightly undersolar, in agreement with the observations of Galactic" spectrum in ,spectrum in $k_\|$. The Fourier coefficients inside that range are Gaussian kj.random numbers with amplitude chosen so that the resulting rms velocity fluctuations are of order unity., The Fourier coefficients inside that range are Gaussian random numbers with amplitude chosen so that the resulting rms velocity fluctuations are of order unity. " The individual random values are refreshed independently at time intervals 7=0.1L,/(2xU;4.).", The individual random values are refreshed independently at time intervals $\tau= 0.1~L_\perp/(2\pi U_{rms})$. " The parameters n; and L, control the degree to which condition (2)) or (3)) is satisfied at the forcing scale.", The parameters $n_z$ and $L_z$ control the degree to which condition \ref{weak-turb}) ) or \ref{crit}) ) is satisfied at the forcing scale. Note that we donot drive the kj—0 modes but allow them to be generated by nonlinear interactions., Note that we do drive the $k_\|=0$ modes but allow them to be generated by nonlinear interactions. " The Reynolds number is defined as Re=U;ms(L1/27)/v, where L, (=2m) is the field-perpendicular box size, v is fluid viscosity, and δις (~ is the rms value of velocity fluctuations."," The Reynolds number is defined as $Re=U_{rms}(L_{\perp}/2\pi)/\nu$, where $L_{\perp}$ $(=2\pi)$ is the field-perpendicular box size, $\nu$ is fluid viscosity, and $U_{rms}$ $(\sim 1)$ is the rms value of velocity fluctuations." " In our 1)case magnetic resistivity and fluid viscosity are the same, v=η."," In our case magnetic resistivity and fluid viscosity are the same, $\nu=\eta$." " The system is evolved until a stationary state is reached, as determined by the time evolution of the total energy of the fluctuations."," The system is evolved until a stationary state is reached, as determined by the time evolution of the total energy of the fluctuations." A typical run produces from 30 to60 snapshots., A typical run produces from 30 to60 snapshots. " The field-perpendicular energy spectrum is obtained by averaging the angle-integrated Fourier spectrum, E(k.)=0.5(|v(ki)|)k,+ 0.5(/b(k1)|?)k1, over field-perpendicular planes in all snapshots."," The field-perpendicular energy spectrum is obtained by averaging the angle-integrated Fourier spectrum, $E(k_\perp)=0.5\langle|{\bf v}({\bf k_\perp})|^2\rangle k_\perp+0.5\langle|{\bf b}({\bf k_\perp})|^2\rangle k_\perp$ , over field-perpendicular planes in all snapshots." " We performed series of simulations for By=5, LD,= and n,=1,a2,4,8,16."," We performed a series of simulations for $B_0=5$, $L_z=5L_\perp$ and $n_z=1,\,2,\,4,\,8,\,16$." " We used the resolution 256? mesh points in these simulations Re— except for the case n;= 16, where the resolution(and was 800),512x512x256 (and Re,— 2000)."," We used the resolution $256^3$ mesh points in these simulations (and $Re=800$ ), except for the case $n_z=16$ , where the resolution was $512\times 512\times 256$ (and $Re_\perp =2000$ )." " We also performed a simulation with Bo=5, DL;=6L,, and n;=1 and the resolution 512x256 (and Re,= 2000)."," We also performed a simulation with $B_0=5$, $L_z=6L_\perp$, and $n_z=1$ and the resolution $512\times 512\times 256$ (and $Re_\perp =2000$ )." Fig., Fig. 1 shows the field-perpendicular energy spectra for each run., \ref{spectrum} shows the field-perpendicular energy spectra for each run. All the runs have different values of parameter κ.=(2x/L;)n; that measures deviation from the critical balance (3)) condition., All the runs have different values of parameter $\kappa\equiv (2\pi/L_z)n_z$ that measures deviation from the critical balance \ref{crit}) ) condition. " We found that as the spectral width of the forcing along increases, higher and higher frequency modes of the kjvelocity and magnetic fields are excited."," We found that as the spectral width of the forcing along $k_\|$ increases, higher and higher frequency modes of the velocity and magnetic fields are excited." " For run &=1/6, all the forced modes have linear frequency w=Κο81, which corresponds to a critically balanced In this case, the spectrum isE(k.)οςki ."," For run $\kappa=1/6$, all the forced modes have linear frequency $\omega = k_\|B_0 \approx 1$, which corresponds to a critically balanced In this case, the spectrum is$E(k_\perp)\propto k_\perp^{-3/2}$ ." " This result is consistent with recent numerical simulation of full MHD by Masonetal.(2007),, since the reduced MHD system approximates the full MHD system when the critical balance condition is satisfied."," This result is consistent with recent numerical simulation of full MHD by \citet{mason2}, since the reduced MHD system approximates the full MHD system when the critical balance condition is satisfied." " As we increase the parameter &, we break the critical balance condition at the forcing scales."," As we increase the parameter $\kappa$, we break the critical balance condition at the forcing scales." " As a result, the spectrum monotonically steepens from —3/2 in the strong turbulence case to —2 in the weak turbulence case, as shown in Fig. 1.."," As a result, the spectrum monotonically steepens from $-3/2$ in the strong turbulence case to $-2$ in the weak turbulence case, as shown in Fig. \ref{spectrum}." Fig., Fig. " 2 shows isocontours of the full energy spectrum E(kj,κ) as a function of k, and kj for the three typical cases &=1/6,4/5,16/5."," \ref{spectrum2d} shows isocontours of the full energy spectrum $E(k_{\|}, k_{\perp})$ as a function of $k_\perp$ and $k_\|$ for the three typical cases $\kappa=1/6,\, 4/5, \, 16/5$." " The bottom frame presents the energy distribution for the case &—1/6, where the random force preserves the critical balance."," The bottom frame presents the energy distribution for the case $\kappa=1/6$, where the random force preserves the critical balance." " As the cascade continues deeper into the inertial range, higher frequency modes w=kjBo are generated by virtue of nonlinear interactions, just enough to maintain the critical balance condition at all scales, and establish a strong turbulence spectrum."," As the cascade continues deeper into the inertial range, higher frequency modes $\omega = k_\|B_0$ are generated by virtue of nonlinear interactions, just enough to maintain the critical balance condition at all scales, and establish a strong turbulence spectrum." " As the frequency of the forced Alfvénn modes increases in the cases &— (2,...,16)/5, the parallel cascade is slightly inhibited as the weaker interaction among the large scale Alfvénn modes dominates the energy transfer to smaller scales, resulting in a steepening of the field-perpendicular energy spectrum."," As the frequency of the forced Alfvénn modes increases in the cases $\kappa =(2, \dots , 16)/5$ , the parallel cascade is slightly inhibited as the weaker interaction among the large scale Alfvénn modes dominates the energy transfer to smaller scales, resulting in a steepening of the field-perpendicular energy spectrum." " This can be seen in the middle and top frames in Fig. 2,,"," This can be seen in the middle and top frames in Fig. \ref{spectrum2d}, ," " where the distribution of energy becomes more and more elongated along k, rather than ky.", where the distribution of energy becomes more and more elongated along $k_\perp$ rather than $k_\|$ . " Our numerical results demonstrate that if the energy spectrum has a limited extent, increasingthe width of the forcingspectrum leads to the energy spectrumkj of"," Our numerical results demonstrate that if the energy spectrum has a limited extent, increasingthe $k_\|$ width of the forcingspectrum leads to the energy spectrum of" follow the same method that is often adopted in the analvsis of observational data.,follow the same method that is often adopted in the analysis of observational data. We first identify the detectable clumps by visual inspection of the X-ray maps., We first identify the detectable clumps by visual inspection of the X–ray maps. The corresponding regions are then masked out both in the X-ray and in the tSZ maps., The corresponding regions are then masked out both in the X–ray and in the tSZ maps. The masked regions are excluded from the computation of the signals to be deprojected., The masked regions are excluded from the computation of the signals to be deprojected. This leads to an increase of the statistical uncertainties in those rings which have a significant overlap with the masked regions., This leads to an increase of the statistical uncertainties in those rings which have a significant overlap with the masked regions. Clearly. due to the finite photon statistics in the X-ray maps. small clumps may fall below the detection threshold. while their presence may still affect the emissivity.," Clearly, due to the finite photon statistics in the X–ray maps, small clumps may fall below the detection threshold, while their presence may still affect the emissivity." The recovered density and temperature profiles of C? and C4 are shown in Figures 9. and 11.., The recovered density and temperature profiles of C2 and C4 are shown in Figures \ref{fi:c29931jof.vir} and \ref{fi:c001jof.vir}. Once all the detectable clumps are masked out the reconstruction of the density profile is generally good. but with a systematic overestimate of ~S per cent. that we attribute to a residual small-scale gas clumping.," Once all the detectable clumps are masked out the reconstruction of the density profile is generally good, but with a systematic overestimate of $\sim$ 5 per cent, that we attribute to a residual small–scale gas clumping." Although this effect is rather small. its presence highlights the need to have a sufficient photon—count statistics to identify gas inhomogeneities and remove their contribution in the deprojection procedure.," Although this effect is rather small, its presence highlights the need to have a sufficient photon–count statistics to identify gas inhomogeneities and remove their contribution in the deprojection procedure." " The slight density overestimate corresponds. as expected. to a small underestimate of the temperature. which is forced by the requirement of reproducing the tSZ signal. yx9,2)."," The slight density overestimate corresponds, as expected, to a small underestimate of the temperature, which is forced by the requirement of reproducing the tSZ signal, $y\propto n_e T_e$." For these two objects we also note that there are rather small differences in the 3D profiles recovered from three orthogonal projection directions. thus indicating that they are almost spherical and without significant substructures along the different projection directions.," For these two objects we also note that there are rather small differences in the 3D profiles recovered from three orthogonal projection directions, thus indicating that they are almost spherical and without significant substructures along the different projection directions." Errorbars are always of the order of a few percent.," Errorbars are always of the order of a few percent," The striking nuage preseuted of the bulee in Figure 11 highliehts au issuc that also can be secu iu skv-subtracted image of the whole galaxy iu Figure 1: there seems to be far fewer faint objects iu the lower SW side of the galaxy disk than in the upper NE side of the ealaxy disk.,The striking image presented of the bulge in Figure 11 highlights an issue that also can be seen in sky-subtracted image of the whole galaxy in Figure 4: there seems to be far fewer faint objects in the lower SW side of the galaxy disk than in the upper NE side of the galaxy disk. As seen in Figure L this asviuuetry m uber of eiaut objects secus to extend to 2-3 arcuuin in the SW direction.," As seen in Figure 4, this asymmetry in number of giant objects seems to extend to 2-3 arcmin in the SW direction." Uufortunately. we cannot appeal to TST observations of this galaxy. as such imaging (Iissler-Patie.etal.1999)) avoided the NE side owing to the bright star there.," Unfortunately, we cannot appeal to HST observations of this galaxy, as such imaging \cite{KP99}) ) avoided the NE side owing to the bright star there." The ouly reasonable interpretation we can eive to the existence of an asvinmetry in the faint objects around NGC 1565 is that there is obscuring matter between NGC 1565 and the backeround galaxies., The only reasonable interpretation we can give to the existence of an asymmetry in the faint objects around NGC 4565 is that there is obscuring matter between NGC 4565 and the background galaxies. If this proves to be true (and we plan to investigate this issue further in another paper). then it could be evidence for a face-on warp in this galaxy.," If this proves to be true (and we plan to investigate this issue further in another paper), then it could be evidence for a face-on warp in this galaxy." Such a warp would have to be part of the disk facing away from us. as the uucleus of this galaxy is obviously wot obscured.," Such a warp would have to be part of the disk facing away from us, as the nucleus of this galaxy is obviously not obscured." We have obtained deep interiueciate-band (G660A) surface photometry of the nearby. brieht.oO edec-onc» ealaxv NGC 1565.," We have obtained deep intermediate-band $\rm 6660\AA$ ) surface photometry of the nearby, bright, edge-on galaxy NGC 4565." The combination of having a nearly d square degree feld of view. the ability to use the dome to obtain highoO S/N flat fields. accurate subtraction of the PSF winesc» of stars. and an accurate method for. two-dimensional. sky subtraction. combine. to vield. a limiting⋅⋅⋅ maeuitude⋅ of asc28.77 mag arcsec)7 (at which. the observational. error reaches 0.75- mae aresec»7: or 0.25. imag at a surface. brightuess. ofDa 27.5 mae D ?).," The combination of having a nearly 1 square degree field of view, the ability to use the dome to obtain high S/N flat fields, accurate subtraction of the PSF wings of stars, and an accurate method for two-dimensional sky subtraction combine to yield a limiting magnitude of 28.77 mag $\rm arcsec^{-2}$ (at which the observational error reaches 0.75 mag $\rm arcsec^{-2}$; or 0.25 mag at a surface brightness of 27.5 mag $^{-2}$ )." " The sky background iu our image is 20.72 mae !. about 0.5 mag 7 ""ENbrighter than the sky found in our NGC 5907 observatious in the same filter (cf."," The sky background in our image is 20.72 mag $^{-1}$, about 0.5 mag $^{-2}$ brighter than the sky found in our NGC 5907 observations in the same filter (cf." Zheng et al., Zheng et al. 1999)., 1999). The total magnitude of NGC 1565 in G660A-hand is 8.9940.02 mae (equivalent to R = 9.10) to a surface brightness of 28 mae ," The total magnitude of NGC 4565 in $\rm \AA$ -band is $\pm$ 0.02 mag (equivalent to R = 9.10) to a surface brightness of 28 mag $^{-2}$." The huninosity distribution of the galaxw is presented iu a seres of cuts both parallel to its minor axis (z-profiles) aud parallel to its major axis CH-profiles)., The luminosity distribution of the galaxy is presented in a series of cuts both parallel to its minor axis $z$ -profiles) and parallel to its major axis $R$ -profiles). Excluding the dust lane. the z-profiles are sviunietric in all four quadrauts out to a radius of 6 arcuuin.," Excluding the dust lane, the $z$ -profiles are symmetric in all four quadrants out to a radius of 6 arcmin." The :-profiles exteud to nearly 30 kpe (at 29 mag aresec 7). farther than giveu by previous studies of this galaxy.," The $z$ -profiles extend to nearly 30 kpc (at 29 mag $\rm arcsec^{-2}$ ), farther than given by previous studies of this galaxy." We coustruct a two-dimensional model of the outer parts of this galaxy. comprised of three components (thin-disk | thick-disk | halo)., We construct a two-dimensional model of the outer parts of this galaxy comprised of three components (thin-disk + thick-disk + halo). Altogether the model iuchudes 12 parineters. including a cut-off radius for the disk.," Altogether the model includes 12 parameters, including a cut-off radius for the disk." The values of these paramcters are determined by the 47 values from a series of 3.700 initial starting values which eventually converge to distinct values.," The values of these parameters are determined by the $\chi^2$ values from a series of 3,700 initial starting values which eventually converge to distinct values." The parameters so-derived for the thin aud thick disks eenerally agree with those derived bv previous studies., The parameters so-derived for the thin and thick disks generally agree with those derived by previous studies. As our halo observations go much deeper than those of previous studies. we obtain a more reliable measurement of the powerlaw behavior," As our halo observations go much deeper than those of previous studies, we obtain a more reliable measurement of the power–law behavior" during the time intervals when the highest energy. gamma ravs were emitted.,during the time intervals when the highest energy gamma rays were emitted. " Lf the electron Lorentz factor was at least ~10"". then emission that could. be observed. by NLAGIC would. not be allected."," If the electron Lorentz factor was at least $\sim 10^3$, then emission that could be observed by MAGIC would not be affected." Llowever. as the most. powerful GRB on record. parameters for CRB OSOOLGC may not be representative of the total sample.," However, as the most powerful GRB on record, parameters for GRB 080916C may not be representative of the total sample." One potential danger is that the tvpical energy. of the cutol could exist at roughly the same GeV energies where we expect EBL attenuation features to be seen., One potential danger is that the typical energy of the cutoff could exist at roughly the same GeV energies where we expect EBL attenuation features to be seen. Not only could a sharp spectral eutoll be mistaken for attenuation by background radiation. but the factor of (1|2)+ from cosmology could mimic the redshift evolution of EBL attenuation.," Not only could a sharp spectral cutoff be mistaken for attenuation by background radiation, but the factor of $(1+z)^{-1}$ from cosmology could mimic the redshift evolution of EBL attenuation." One reason we have restricted ourselves {ο curren experiments in this discussion is that. as we have seen. the details of instrument. capabilities can have a large impact on predictions. and our results are most meaningfu when we can incorporate well-tested and verified instrumen parameters into our model," One reason we have restricted ourselves to current experiments in this discussion is that, as we have seen, the details of instrument capabilities can have a large impact on predictions, and our results are most meaningful when we can incorporate well-tested and verified instrument parameters into our model." But as the GeV emission of GRBs and subsequent extinction. are. certainly no questions that are going to be decisively answered. by the current generation of instruments. our cliscussion would no be complete without mentioning brielly a few importan upcoming experiments.," But as the GeV emission of GRBs and subsequent extinction are certainly not questions that are going to be decisively answered by the current generation of instruments, our discussion would not be complete without mentioning briefly a few important upcoming experiments." The next phase of the LEJZ.S.S. array will feature a 600 m? mirror at the center of its curren 4d-telescope configuration: this central 7E5 telescope. wil be the largest LACE vet. built., The next phase of the H.E.S.S. array will feature a 600 $^2$ mirror at the center of its current 4-telescope configuration; this central `T5' telescope will be the largest IACT yet built. This upgrade is schedule for completion later this vear. and will lower the energy threshold down to ~30 GeV. at zenith angle 18. degrees Becherinietal.2008).," This upgrade is scheduled for completion later this year, and will lower the energy threshold down to $\sim$ 30 GeV at zenith angle 18 degrees \citep{becherini08}." . Over the next decade. severa eround-based experiments can provide more sensitivity to VILE photons from GRBs (Williamsetal.2009).," Over the next decade, several ground-based experiments can provide more sensitivity to VHE photons from GRBs \citep{williams09}." .. Phe Advanced CGanuna-Ray lmaging System. CAGIS) (Buckleyetal.2008) and Cherenkov Telescope Array (CEA) (Martinez2008) are two future concepts for LACT arrays that may be constructed during the next decade., The Advanced Gamma-Ray Imaging System (AGIS) \citep{buckley08} and Cherenkov Telescope Array (CTA) \citep{martinez08} are two future concepts for IACT arrays that may be constructed during the next decade. Both of these arrays. when fully constructed. would have much Larger collection areas than any current experiment. and would likely have energy coverage over most ofthe 10 to 100 Gey decade.," Both of these arrays, when fully constructed, would have much larger collection areas than any current experiment, and would likely have energy coverage over most of the 10 to 100 GeV decade." The low energy threshold. <20 GeV. anc greater sensitivity will enable detection of GRBs and measurement of attenuation by the EBL out to very high redshift. which could. clarify the nature of. high-redshift. star formation.," The low energy threshold, $<20$ GeV, and greater sensitivity will enable detection of GRBs and measurement of attenuation by the EBL out to very high redshift, which could clarify the nature of high-redshift star formation." Unfortunately. these telescopes will not be able to overcome the intrinsic dilliculties of the Cherenkoy technique. namely low cluty evele. loss of sensitivity away from zenith. and the need to be triggered for transient observations by another experiment.," Unfortunately, these telescopes will not be able to overcome the intrinsic difficulties of the Cherenkov technique, namely low duty cycle, loss of sensitivity away from zenith, and the need to be triggered for transient observations by another experiment." Our results suggest that due to the stochastic nature of CRBs. persistence may ultimately be the Κον to detecting these events from the ground.," Our results suggest that due to the stochastic nature of GRBs, persistence may ultimately be the key to detecting these events from the ground." RG. and J.P. acknowledge support from a Fermi. Guest Investigator Grant and NSE-AST-0607712. and J.P. and I.I. acknowledge support from a NASA ATP erant.," R.G. and J.P. acknowledge support from a Fermi Guest Investigator Grant and NSF-AST-0607712, and J.P. and F.P. acknowledge support from a NASA ATP grant." We thank Stefano Covino. Markus Garezarezvk. Markus Gaug. Nepomuk Otte. Stefano Profumo. and. David A. Williams for helpful discussion. and. comments.," We thank Stefano Covino, Markus Garczarczyk, Markus Gaug, Nepomuk Otte, Stefano Profumo, and David A. Williams for helpful discussion and comments." We are particularly grateful to Nepomuk Otte for providing a great deal of assistance in understanding the MLXCIC telescope. and to David A. Williams for making us aware of the antisolar bias present in observations. an important. factor in our calculations related to grouncd-based instruments.," We are particularly grateful to Nepomuk Otte for providing a great deal of assistance in understanding the MAGIC telescope, and to David A. Williams for making us aware of the antisolar bias present in observations, an important factor in our calculations related to ground-based instruments." Recent work revealed that several Galactic globular clusters (hereafter GGC) had a much more complex star-formation history than previously thought.,Recent work revealed that several Galactic globular clusters (hereafter GGC) had a much more complex star-formation history than previously thought. This has implications for their use as simple stellar population (SSP) templates to study more complex and distant stellar systems and galaxies. and therefore requires careful study.," This has implications for their use as simple stellar population (SSP) templates to study more complex and distant stellar systems and galaxies, and therefore requires careful study." Based on deep and accurate photometric studies. GGC were found to contain different stellar populations. in the form of multiple evolutionary sequences in their color-magnitude diagrams (CMD).," Based on deep and accurate photometric studies, GGC were found to contain different stellar populations, in the form of multiple evolutionary sequences in their color-magnitude diagrams (CMD)." The first cluster found to host multiple stellar populations was w Cen2007).., The first cluster found to host multiple stellar populations was $\omega$ Cen. Lately NGC 28082007).. NGC 18512009).. NGC 63882009).. M 222009).. and 47 Tuc joined the rapidly growing group of complex stellar population GGC.," Lately NGC 2808, NGC 1851, NGC 6388, M 22, and 47 Tuc joined the rapidly growing group of complex stellar population GGC." But even before the multiple photometric sequences were detected. anti-correlations between the strength of the CN and CH bands around 3880. 4200. and 4300 were found. starting with the pioneering work of(1971)... im all. properly observed clusters.," But even before the multiple photometric sequences were detected, anti-correlations between the strength of the CN and CH bands around 3880, 4200, and 4300 were found, starting with the pioneering work of, in all properly observed clusters." These anti-correlations are sometimes bimodal in nature (see Sect., These anti-correlations are sometimes bimodal in nature (see Sect. 4.1. for references). with two separate groups of CN-strong and CN-weak stars.," \ref{sec-bimo} for references), with two separate groups of CN-strong and CN-weak stars." The first detections were of course limited to the red giant branch (RGB) starsreviews).. because of the instrumental limitations at that time. but later they were also found among sub giant branch (SGB) stars and even among main sequence (MS) stars2005).," The first detections were of course limited to the red giant branch (RGB) stars, because of the instrumental limitations at that time, but later they were also found among sub giant branch (SGB) stars and even among main sequence (MS) stars." . Anti-correlations were found among other light elements such as Na. O. Al. Mg and F2005).. No sample of Milkv Way field stars observed so far showed any sign of anti-correlations2006).," Anti-correlations were found among other light elements such as Na, O, Al, Mg and F. No sample of Milky Way field stars observed so far showed any sign of anti-correlations." . Also. no chemical anomalies were found in open clusters or in the field stars belonging to dwarf galaxies in the Local Group.," Also, no chemical anomalies were found in open clusters or in the field stars belonging to dwarf galaxies in the Local Group." Only recently. Na-O anti-correlations were detected in extragalactic GC (globular clusters) of the Fornax dwarf galaxy and of the Large Magellanie Clouds2009).," Only recently, Na-O anti-correlations were detected in extragalactic GC (globular clusters) of the Fornax dwarf galaxy and of the Large Magellanic Clouds." . The presence of CH-C anti-correlations was soon interpreted as a signature of CN(O) cycle processing. which tends to deplete C and to enhance N. and of mixing that can bring CN(O) processed material to the stellar surface. during the first dredge-up that happers at the base of the RGB.," The presence of CH-CN anti-correlations was soon interpreted as a signature of CN(O) cycle processing, which tends to deplete C and to enhance N, and of mixing that can bring CN(O) processed material to the stellar surface, during the first dredge-up that happens at the base of the RGB." To reach this conclusion. it 1s assumed that CN traces the N abundace and CH the C abundance1996).," To reach this conclusion, it is assumed that CN traces the N abundace and CH the C abundance." . This is well supported by abundance analysis work based on spectral synthesis. which revealed [C/Fe] and [N/Fe| spreads of up to more than | dex2005).," This is well supported by abundance analysis work based on spectral synthesis, which revealed [C/Fe] and [N/Fe] spreads of up to more than 1 dex." . However. this scenario. often referred to as thescenario. was soon put into trouble by two observational facts: CH and CN anti-correlations in MS stars cannot be produced by the stars themselves. because they have low mass (M=0.8 M.) in GGC and do not burn hydrogen through the CNO cycle: the presence of Na. Al. Mg. and O (anti-)correlations points towards the NeNa and MgAI chains that take place at much higher temperatures2007).. which are not reached in the AS or RGB phases of GGC stars.," However, this scenario, often referred to as the, was soon put into trouble by two observational facts: CH and CN anti-correlations in MS stars cannot be produced by the stars themselves, because they have low mass $\simeq$ 0.8 $_{\odot}$ ) in GGC and do not burn hydrogen through the CNO cycle; the presence of Na, Al, Mg, and O (anti-)correlations points towards the NeNa and MgAl chains that take place at much higher temperatures, which are not reached in the MS or RGB phases of GGC stars." The addition of internal pollution mechanisms such as rotation-induced mixing or the so-called canonical extra-mixing, The addition of internal pollution mechanisms such as rotation-induced mixing or the so-called canonical extra-mixing (sxtinctions of order or larger thin LOO iaguitudes if ]esent;,extinctions of order or larger than 100 magnitudes if present. We believe therefore that oue should stil I)Ó -VOLV C‘autious about ruling out peaked density distriltions (such as the SIS) ou the basis of the available dat, We believe therefore that one should still be very cautious about ruling out peaked density distributions (such as the SIS) on the basis of the available data. Using for the first time a reliable dust teur)oratiure (listiibution. we lave obtained reasonable agrecuent j)etweon our models basxcc pon the CB σαςτν (listiibutiou at time fj5 corresponding to a ceutra clensity 6of τς109 aand the available millimeter aud sub-willimeter data for L151LL.," Using for the first time a reliable dust temperature distribution, we have obtained reasonable agreement between our models based upon the CB density distribution at time $t_{3}$ corresponding to a central density of $4\times 10^6$ and the available millimeter and sub-millimeter data for L1544." This is a strong areinent iu vor of the validitv of the model of CB as far as L151L1s ¢concerned., This is a strong argument in favor of the validity of the model of CB as far as L1544 is concerned. We favor however higher iuclinations «X L1511 o the line of sight than eiven by CB aud cau fit oth the SED :ux the aspect ratio for au inclination of , We favor however higher inclinations of L1544 to the line of sight than given by CB and can fit both the SED and the aspect ratio for an inclination of $^{\circ}$. There is on the other hand a considerable marein of errY iu this (tiniate and we do not eutirelv exclude the vali of 16° oeferved by CD., There is on the other hand a considerable margin of error in this estimate and we do not entirely exclude the value of $16^{\circ}$ preferred by CB. We conclude in auv case that it would be useful to fit other cores with similar models., We conclude in any case that it would be useful to fit other cores with similar models. " There may be some oossibilitv in this wav of relating the observed. structure o ""age though it remains to be seen how effective this is dn practise.", There may be some possibility in this way of relating the observed structure to “age” though it remains to be seen how effective this is in practise. The high ceutral colaun cleusity is the vest iudicator of an age close to the pivotal situation where dynamical collapse can comunence., The high central column density is the best indicator of an age close to the pivotal situation where dynamical collapse can commence. ", Uuortunuatelv. he lower temperature of the high density nucleus caused x the increased extinction makes this high central cohuun (liffieult to discern."," Unfortunately, the lower temperature of the high density nucleus caused by the increased extinction makes this high central column difficult to discern." Tt should be realised also that other models are ikelv to be capable of fitting observational constraints., It should be realised also that other models are likely to be capable of fitting observational constraints. Receut relevaut theoretical studies icelude those of Safier. Aled&ee. aud Stahler (1997). Calli ct al. (," Recent relevant theoretical studies include those of Safier, McKee, and Stahler (1997), Galli et al. (" 2001) aud Tudehetoww and Zsveibel(2000).,"2001), and Indebetouw and Zweibel(2000)." We noe that Ca11 et al. (, We note that Galli et al. ( "2001) obtain an excellent fit to the observed intensity (listribution at 1.3 nuu of L151£L with their model of a slightly inclined ""siugulu isothermal disk” or SID.","2001) obtain an excellent fit to the observed intensity distribution at 1.3 mm of L1544 with their model of a slightly inclined “singular isothermal disk"" or SID." This Is à nonaNnisvuuuetric structure with feld lines running io»proxinatelv in the line of sight., This is a non–axisymmetric structure with field lines running approximately in the line of sight. It would be useul also to compute the temperature structure of such à model iu iialoeous fashion to that uxd iu this paper for he CB models., It would be useful also to compute the temperature structure of such a model in analogous fashion to that used in this paper for the CB models. We have not considered i detail in tlis study the effect 6 external radiation fields other than the παλιοαι7 fields 6Mff MMP aud Black (1991)., We have not considered in detail in this study the effect of external radiation fields other than the “standard” fields of MMP and Black (1994). Towever. it is likely tiat the iuctual fields incident upou deuse cores vary frou core to ore aud still more between molecular cloud an molecular loud.," However, it is likely that the actual fields incident upon dense cores vary from core to core and still more between molecular cloud and molecular cloud." Such difference:μα ausiblv occur due to the presence in the vicinity of nearby OB stars., Such differences plausibly occur due to the presence in the vicinity of nearby OB stars. The Dacumaun et Hal. , The Bacmann et al. ( 2000) study (see their table Land subtract the zodiacal (contribution) sugecsts that there may be as uch as an order of magnitude difference iu the ISO IAV2 (5-8.5 pan)} ivackeround towards differeut cores.,2000) study (see their table 1 and subtract the zodiacal contribution) suggests that there may be as much as an order of magnitude difference in the ISO LW2 (5-8.5 ) background towards different cores. It iu fact also suggests that we underestinate bv a factor of order 3 the field (at 7 juu0)) incident ou LISLL using the Black (1991) werage field., It in fact also suggests that we underestimate by a factor of order 3 the field (at 7 ) incident on L1544 using the Black (1994) average field. We have examined IRAS maps of L5LL and iweraged inteusitfies iu an annulus surrounding the core with inner radius aad outer radius cceutred ou the wm dust emission peak., We have examined IRAS maps of L1544 and averaged intensities in an annulus surrounding the core with inner radius and outer radius centred on the mm dust emission peak. We conclude that the field adjaceut to the core is a factor 2.5-1 ercater than the Black (1991) field at 12 aud 25 ssugeesting that we nuderestimate the MUR coutribution to the icicenut field (section 3)., We conclude that the field adjacent to the core is a factor 2.5-4 greater than the Black (1994) field at 12 and 25 suggesting that we underestimate the MIR contribution to the incident field (section 3). This may cause our temperature estimate to © low (by a factor of roughly 1.2) at extinctious of 20-30 uaenitudes (see Fig. 2))., This may cause our temperature estimate to be low (by a factor of roughly 1.2) at extinctions of 20-30 magnitudes (see Fig. \ref{analytic_temp}) ). We aay also be undercstimating the FIR field., We may also be under–estimating the FIR field. L1511 is quite clearly prescut ou TRAS πας though iof present at shorther wavelengths., L1544 is quite clearly present on IRAS maps though not present at shorther wavelengths. " This sugeests that he incident UVoptical radiation field. (prestmably also responsible for exciting the MIR) is converted into far IR radiation ina ""PDR laver surrouudiug the cold core.", This suggests that the incident UV–optical radiation field (presumably also responsible for exciting the MIR) is converted into far IR radiation in a “PDR” layer surrounding the cold core. This xesinably should be added to the average iucideut field which we have used in our computations., This presumably should be added to the average incident field which we have used in our computations. We thus may also be underestimating the FIR heating., We thus may also be underestimating the FIR heating. We expect temperatures in these cores to vary as xEND where \ ds the scaling factor for the external radiation field (see section 3) and thus we expect differences as large as 1.5 between different objects;, We expect temperatures in these cores to vary as $\chi ^{1/5.6}$ where $\chi $ is the scaling factor for the external radiation field (see section 3) and thus we expect differences as large as 1.5 between different objects. We would expect for example the nucleus of a core like OphD ou this basis to be roughly 1.5 times hotter than L1511 using the mid IR intensities of Daciuaun ct al. (, We would expect for example the nucleus of a core like OphD on this basis to be roughly 1.5 times hotter than L1544 using the mid IR intensities of Bacmann et al. ( 2000).,2000). This will have some effect on parameters such as the accretio- rate but probably not au miportaut one since the reeio- where gas and dust temperatures are coupled is very limited., This will have some effect on parameters such as the accretion rate but probably not an important one since the region where gas and dust temperatures are coupled is very limited. On the other haud. phenomena such as depletio- of anolecular species on erain surfaces are extremely seusitive to grain temperature aud these are likely to lav different characteristics depending ou the precise grain temperature.," On the other hand, phenomena such as depletion of molecular species on grain surfaces are extremely sensitive to grain temperature and these are likely to have different characteristics depending on the precise grain temperature." This iav explain why some of the clemical characteristics of cores iu Opliuchus aud Taurus differ (long chai carbon species for example are much less prevalent iun Ophinchus) and may have consequences for the ionization degree at high densities., This may explain why some of the chemical characteristics of cores in Ophiuchus and Taurus differ (long chain carbon species for example are much less prevalent in Ophiuchus) and may have consequences for the ionization degree at high densities. One of the most useful products of this study is the analytic estimate which we have made of the temperature at the center of a splerically svuuuetric core., One of the most useful products of this study is the analytic estimate which we have made of the temperature at the center of a spherically symmetric core. We have shown that the formula which we have derived eives in many cases a reasonable fit to the radial depeudeuce of dust temperature and we believe it can be used as a useful first approximation to the eas temperature at densities above 1073., We have shown that the formula which we have derived gives in many cases a reasonable fit to the radial dependence of dust temperature and we believe it can be used as a useful first approximation to the gas temperature at densities above $10^5$. " Future studies can then perhaps cousider the hydrostatic equilibrium of ""BounorEbert spheres” for a 1nore reasonable temperature distribution.", Future studies can then perhaps consider the hydrostatic equilibrium of “Bonnor–Ebert spheres” for a more reasonable temperature distribution. A brief ΠΠ of the results presented here as well as n Inore general discussion of the pliysical properties of preprotostellar cores is given by Wahusley et al. (, A brief summary of the results presented here as well as a more general discussion of the physical properties of pre–protostellar cores is given by Walmsley et al. ( 2001).,2001). Many thanks are due to Glenn Ciolek who made available a. digital version of his model predictions for L1544 and to John Black for sending us a digital. version of his estimate for the interstellar radiation field., Many thanks are due to Glenn Ciolek who made available a digital version of his model predictions for L1544 and to John Black for sending us a digital version of his estimate for the interstellar radiation field. CMW. would like to thank the Max Planck Institut ftir Racioastronomic for its hospitality during various phases of this study., CMW would like to thank the Max Planck Institut fürr Radioastronomie for its hospitality during various phases of this study. He also wishes to acknowledge travel support from ASL Grant, He also wishes to acknowledge travel support from ASI Grant of centre frequencies for cach band: we observed. as well as 1e stronger spectral lines found within the bands.,"of centre frequencies for each band we observed, as well as the stronger spectral lines found within the bands." For the maser observations. two contiguous bancs (5 and 6) can be used together to search for masers in the velocity range of 2424 tokms.," For the maser observations, two contiguous bands (5 and 6) can be used together to search for masers in the velocity range of $-$ 2424 to." At the maser frequency. cach channel corresponds tokms.," At the maser frequency, each channel corresponds to." Bright water masers can be used. to assess the shape of the Mopra beam at €lIz., Bright water masers can be used to assess the shape of the Mopra beam at GHz. However. due to their highly variable nature. water masers are not used to determine the cllicieney of the telescope.," However, due to their highly variable nature, water masers are not used to determine the efficiency of the telescope." The bright water maser €6331.51-0.09 was mapped as part of LIOPS., The bright water maser G331.51-0.09 was mapped as part of HOPS. The strongest emission is found in the spectral channel at velocity. —89.02 ss and is shown in Figure 1.., The strongest emission is found in the spectral channel at velocity $-89.02$ $^{-1}$ and is shown in Figure \ref{beam_image}. Phis Figure shows two cillraction rings around the maser peak., This Figure shows two diffraction rings around the maser peak. We note that a secondary walter maser site (€1331.44-0.19). coincides with the outer ring [rom €1331.51-0.09 and can be seen in Figure 1.., We note that a secondary water maser site (G331.44-0.19) coincides with the outer ring from G331.51-0.09 and can be seen in Figure \ref{beam_image}. There is also a maser (€1331.56-0.12) that is located. close to the inner ring. but the maser emission is not significant at this racial velocity and is thus not seen in the Figure.," There is also a maser (G331.56-0.12) that is located close to the inner ring, but the maser emission is not significant at this radial velocity and is thus not seen in the Figure." Due to the confusion with C:331.44-0.19. we do not fit the rings around €1331.51-0.09.," Due to the confusion with G331.44-0.19, we do not fit the rings around G331.51-0.09." . Instead. the maser €2330.96-0.18.. shown in Figure Lis used. which also shows the inner beam ring and does not appear to have any other confusing masers nearby.," Instead, the maser G330.96-0.18, shown in Figure \ref{beam_image} is used, which also shows the inner beam ring and does not appear to have any other confusing masers nearby." In Figure 2. we show an azimuthally averaged histogram for €:330.96-0.09.," In Figure \ref{beam_profile}, we show an azimuthally averaged histogram for G330.96-0.09." “Phe histogram shows/— both the inner and outer beam rings., The histogram shows both the inner and outer beam rings. Phe inner ring occurs at a radius of about and contains approximately of the Iux of the main peak., The inner ring occurs at a radius of about and contains approximately of the flux of the main peak. The outer ring occurs at about and contains approximately of the Hux of the main peak., The outer ring occurs at about and contains approximately of the flux of the main peak. We estimate the ENIM of the beam from the radial profile to be2., We estimate the FWHM of the beam from the radial profile to be. 27. Recent observations by Urquhartctal.(2010). of the water masers in Orion-INL. have been used το characterise the Mopra racliotelescope., Recent observations by \citet{urquhart10} of the water masers in Orion-KL have been used to characterise the Mopra radiotelescope. We find that the positions and intensities of the rings. as well as the size of the beam that we derive above agree well with their results.," We find that the positions and intensities of the rings, as well as the size of the beam that we derive above agree well with their results." We adopt. values from Urquhartctal.(2000). for. the main beam size at C1Iz). elliciency (0.54 al 0GCGllIz) and conversion factor (12.5 at GCIIz).," We adopt values from \citet{urquhart10} for the main beam size at GHz), efficiency (0.54 at GHz) and $^{-1}$ conversion factor (12.5 at GHz)." During the course of the HOPS observations. we regularly performed. observations of a number of well known line sources in the sky. including Orion.," During the course of the HOPS observations, we regularly performed observations of a number of well known line sources in the sky, including Orion." These observations were tvpically conducted once cach night and consisted of a position-switch with 2 minutes on-source integration., These observations were typically conducted once each night and consisted of a position-switch with 2 minutes on-source integration. The standard HOPS zoom configuration was used. (Pable 1))., The standard HOPS zoom configuration was used (Table \ref{tab1}) ). The purpose of these observations is to assess the stability of the telescope system: over time and through dillerent. observing conditions., The purpose of these observations is to assess the stability of the telescope system over time and through different observing conditions. Whilst the zoom configuration includes strong maser lines. especially the maser line. we did not use this line for our calibration as the intensity is known to vary with time (bellictal. 2007).," Whilst the zoom configuration includes strong maser lines, especially the maser line, we did not use this line for our calibration as the intensity is known to vary with time \citep{felli07}." . Instead. we found the strong radio recombination emission lines (H1600 and LH620) well suited for calibration. as they are not expected to significantly vary in intensity over the timescale of our observations.," Instead, we found the strong radio recombination emission lines $\alpha$ and $\alpha$ ) well suited for calibration, as they are not expected to significantly vary in intensity over the timescale of our observations." We measure the integrated. intensity of the lines hy, We measure the integrated intensity of the lines by While 86 stars are nyore metal-rich than [Fe/H] = 40.30. most are only slightly so: half of the stars all between [Fe/H] = 0.31 and 0.35.,"While 86 stars are more metal-rich than [Fe/H] = +0.30, most are only slightly so; half of the stars fall between [Fe/H] = 0.31 and 0.35." Moreover. oreliminary analysis cemoustrated that the majority of the stars fall in ile vertical turuoll region for stars of the ok disk. making them inappropriate or comparison with stars on the unevolved main sequence.," Moreover, preliminary analysis demonstrated that the majority of the stars fall in the vertical turnoff region for stars of the old disk, making them inappropriate for comparison with stars on the unevolved main sequence." For te purpose of deriviug the cistace ο all exceptionalM7 uetal-rich cluster. the small sample could be expanded to iuclude stars with [Fe/H] as low as 425. iE reliable metallicity-depencent shifts 1 the CMD could be generated (r uievolvec inaln sedience stars.," For the purpose of deriving the distance to an exceptionally metal-rich cluster, the small sample could be expanded to include stars with [Fe/H] as low as +0.25, if reliable metallicity-dependent shifts in the CMD could be generated for unevolved main sequence stars." To derive metalicity-dependeut. CMD shifts. the field stars just be ou a common photometrNEMC system tlat is reaclily transformale to a significant cluster sample reaching the unevolved main sequence: for now. Uuis restricts the analysis to broad-baud BY data.," To derive metallicity-dependent CMD shifts, the field stars must be on a common photometric system that is readily transformable to a significant cluster sample reaching the unevolved main sequence; for now, this restricts the analysis to broad-band $BV$ data." Fortunately. fewer than of the sta* with spectroscopic abutdauces aud Aipparcos parallaxes lack reliable BV. photometry ou theTycho-2 systeur (Hogetal.2000):: the exceptions are dominated by stars that are too bright to rave been observed photouetrically or too faint tohave reliable photometry.," Fortunately, fewer than $\%$ of the stars with spectroscopic abundances and $Hipparcos$ parallaxes lack reliable $BV$ photometry on the system \citep{hog00}; the exceptions are dominated by stars that are too bright to have been observed photometrically or too faint tohave reliable photometry." TheTycho-2 BV photometry (H«ojetal.2000) lias been converted to the Cousins-Johuson system using the trausformation relatious of Mamajeketal.(2002).. derived by applying polynomial fits to a table of nea points compiled by Bessell.(2000).," The $BV$ photometry \citep{hog00} has been converted to the Cousins-Johnson system using the transformation relations of \citet{mm02}, derived by applying polynomial fits to a table of mean points compiled by \citet{be00}." . The table of Bessell(2000) was constructed by a direct. comparison of the original photometry with E-region standards composed primarily ol B-G dwarls aud IW-M giants., The table of \citet{be00} was constructed by a direct comparison of the original photometry with E-region standards composed primarily of B-G dwarfs and K-M giants. The revised relatious exhibit signilicaut structure as a function of B-—-V iu comparisoi! with the original linear relatious provided by theHipparcos catalog., The revised relations exhibit significant structure as a function of $B-V$ in comparison with the original linear relations provided by the$Hipparcos$ catalog. The uewerTycho-2 photunetry follows tlie same relatious deliued by Mamajeketal.(2002).. but with hieler internal precision.," The newer photometry follows the same relations defined by \citet{mm02}, but with higher internal precision." A systematic error iu the zero-point of the photometry and/or the slope of t1e unevolved main seceuce could cause systeLatic shifts in the distaice scale., A systematic error in the zero-point of the photometry and/or the slope of the unevolved main sequence could cause systematic shifts in the distance scale. Two basie tests of tle reliability of the transformedTyelo-.2 data are available., Two basic tests of the reliability of the transformed data are available. First. Percivaletal.(2003) defined the aj»proach of interest in this study to cotstrain the distance scale for iearby open clusters studied w Hipparcos.," First, \citet{pe03} defined the approach of interest in this study to constrain the distance scale for nearby open clusters studied by $Hipparcos$." To elsire a reliable photometric ‘comparison between the clusters aud field stars. obtained BVRE plolometry of SL cool field dwa{S over a range in [Fe/H] from —0.56 to +0.LI. as cdefinecl by interjecliate-ud photometry recaibrated to avoid the issues raised by )2)..," To ensure a reliable photometric comparison between the clusters and field stars, \citet{pe03} obtained $BVRI$ photometry of 54 cool field dwarfs over a range in [Fe/H] from $-0.56$ to +0.44, as defined by intermediate-band photometry recalibrated to avoid the issues raised by \citet{tw02}. ." The b'oad-band. photometry is ou tje. Cousins E-region system: he V uiaguituces aud B—V indices lave Mean standard deviations of d -0.007 and £0.00| mags. respectively.," The broad-band photometry is on the Cousins E-region system; the $V$ magnitudes and $B-V$ indices have mean standard deviations of $\pm$ 0.007 and $\pm$ 0.004 mags, respectively." We have taken the ho-2 BV photometry of these 51 stars auc p'Ocessed it hrough tle salue transformation relations as our catalog stars., We have taken the $BV$ photometry of these 54 stars and processed it through the same transformation relations as our catalog stars. For DL stars. the meat residuals ii B—-V axd V .in the sense (converted Tycho - PER). are +0.0007 - 0.0203 and +0.0029 + 0.030," For 54 stars, the mean residuals in $B-V$ and $V$, in the sense (converted Tycho - PER), are +0.0007 $\pm$ 0.0203 and +0.0029 $\pm$ 0.0301." Lin5— V.ifthe 2 stars with absolute residuals above 0.0|] mags are excπο. the 1jeall for the 22 stars ECOMIES +0.0003) + 0.0166.," In $B-V$ , if the 2 stars with absolute residuals above 0.04 mags are excluded, the mean for the 52 stars becomes +0.0003 $\pm$ 0.0166." In W. ifthe two stars with residuals iu V ereater tha1 0.05 mags are removect. the mean for the :52 remaining stars becomes +0.0012 += 0.(215.," In $V$, if the two stars with residuals in $V$ greater than 0.05 mags are removed, the mean for the 52 remaining stars becomes +0.0012 $\pm$ 0.0215." Note tlat inall cases the errors are coiiated by the uucertainty in the Tycho-2 photorieiry., Note that in all cases the errors are dominated by the uncertainty in the photometry. SecolncL. for reasons that will become apparent inSec.," Second, for reasons that will become apparent inSec." I.we will compare the BV photometry forstars in the Hyacles with the transformed. 2 data lor tle same stars.," 4,we will compare the $BV$ photometry forstars in the Hyades with the transformed data for the same stars." along the lines of GD98 for the ingoing energy flux of the waves excited at the top of the RZ is required.,along the lines of GD98 for the ingoing energy flux of the waves excited at the top of the RZ is required. " This estimates the tidal torque, and thus the orbital evolution of the planetary companion."," This estimates the tidal torque, and thus the orbital evolution of the planetary companion." " In this section, we perform numerical integrations of the linearised tidal response in an extensive set of stellar models of solar-type stars with masses in the range 0.5€m,/Mo<1.1, throughout their main sequence lifetimes."," In this section, we perform numerical integrations of the linearised tidal response in an extensive set of stellar models of solar-type stars with masses in the range $0.5 \leq m_{\star}/M_{\odot} \leq 1.1$, throughout their main sequence lifetimes." " We aim to determine the tidal torque numerically, and compare it with a simple model of the launching region at the top of the RZ, which was derived in GD98 and discussed in BO10."," We aim to determine the tidal torque numerically, and compare it with a simple model of the launching region at the top of the RZ, which was derived in GD98 and discussed in BO10." In this section we solve the linearised equations governing the adiabatic tidal response (Eqs., In this section we solve the linearised equations governing the adiabatic tidal response (Eqs. " 2 and 3)) throughout the star, computing the excitation of both the equilibrium and dynamical tides numerically."," \ref{eqmtideeqn} and \ref{dyntideeqn}) ) throughout the star, computing the excitation of both the equilibrium and dynamical tides numerically." " This allows us to determine the ingoing energy and angular momentum fluxes in IGWs launched at the top of the RZ, and to check the validity of approximate semi-analytic formulae for these quantities, presented in the next section."," This allows us to determine the ingoing energy and angular momentum fluxes in IGWs launched at the top of the RZ, and to check the validity of approximate semi-analytic formulae for these quantities, presented in the next section." This is important because the orbital evolution of a planetary companion is determined by the ingoing angular momentum flux absorbed at the critical layer., This is important because the orbital evolution of a planetary companion is determined by the ingoing angular momentum flux absorbed at the critical layer. We solve the following coupled ODEs for the radial and horizontal displacements: An outline of the derivation of these equations is presented in T98., We solve the following coupled ODEs for the radial and horizontal displacements: An outline of the derivation of these equations is presented in T98. " Note that we are ignoring the self-gravity of the entire tidal response, which is reasonable because most of the mass of the star is concentrated near the centre."," Note that we are ignoring the self-gravity of the entire tidal response, which is reasonable because most of the mass of the star is concentrated near the centre." " This assumption is certainly valid for the dynamical tide, and is approximately valid for the equilibrium tide."," This assumption is certainly valid for the dynamical tide, and is approximately valid for the equilibrium tide." " In these equations, we take the tidal potential in the frame rotating with € to be equal to Eq."," In these equations, we take the tidal potential in the frame rotating with $\Omega_{p}$ to be equal to Eq." " 5 with ¢=€ and w=0, so This is the amplitude of the largest tide for a circular orbit."," \ref{tidpot} with $\phi=\xi$ and $\omega=0$, so This is the amplitude of the largest tide for a circular orbit." " In this frame, the displacement field is separated into"," In this frame, the displacement field is separated into" Gravitational microlensing. observed in some multiplyimaged quasars. olfers an excellent opportunity to constrain the size and structure of the regions responsible for emitting the radiation.,"Gravitational microlensing, observed in some multiply-imaged quasars, offers an excellent opportunity to constrain the size and structure of the regions responsible for emitting the radiation." Some lensecl quasars exhibit anomalous Lux ratios between pairs of images straddling a caustic that cannot be convincinglwv. explained. using simple macrolens models., Some lensed quasars exhibit anomalous flux ratios between pairs of images straddling a caustic that cannot be convincingly explained using simple macrolens models. However microlensing models. particularly those that include a significant smooth matter component in the lens. oller a possible solution (Schechter&Wambsganss2002.hereafter SW2)..," However microlensing models, particularly those that include a significant smooth matter component in the lens, offer a possible solution \citep*[][hereafter SW02]{sw02}." The quacruply imaged quasar ALG 041410534. is one example of a lensed quasar displaving anomalous Ilux ratios., The quadruply imaged quasar MG 0414+0534 is one example of a lensed quasar displaying anomalous flux ratios. ‘These anomalies are observed in ratios between images zl». ocated at a saddle point in the time delay surface. and 24). ocated at a minimum.," These anomalies are observed in ratios between images $A_2$, located at a saddle point in the time delay surface, and $A_1$, located at a minimum." Schechter&Moore(1993). reported an elofly L-band Bux ratio of 0.45+0.06 in observations aken on 2-4 November 1991., \citet{sm93} reported an $A_2/A_1$ I-band flux ratio of $0.45 \pm 0.06$ in observations taken on 2-4 November 1991. " This result was supported by subsequent observations: slofel,=0.30.1 from CRIT in he I-band on 1 March. 1992 and ον=0.4740.01 from LST in the L-band on S November 1994 (Falco.Lehar&Shapiro1997).", This result was supported by subsequent observations: $A_2/A_1 = 0.3 \pm 0.1$ from CFHT in the I-band on 1 March 1992 and $A_2/A_1 = 0.47 \pm 0.01$ from HST in the I-band on 8 November 1994 \citep*{f97}. . Llowever. lensing theory tells αν that image magnification seales as the inverse of perpendicular distance from a critical curve (Chang&Welscal1979.. Blandford&Naravan 1986)).," However, lensing theory tells us that image magnification scales as the inverse of perpendicular distance from a critical curve \citealt{cr79}, \citealt{bn86}) )." " Models that fit the observed image positions in MG 041410534. place images 2, and elo either side of such a critical curve. and thus we would naively expect their magnification ratio. or flux ratio. to be ~1 (Witt.Mao&Schechter1995.hereafter.WMS95).."," Models that fit the observed image positions in MG 0414+0534 place images $A_1$ and $A_2$ either side of such a critical curve, and thus we would naively expect their magnification ratio, or flux ratio, to be $\sim1$ \citep*[][hereafter WMS95]{wms95}." lndeed an sS Gillz radio ιν ratio of slofel;=0.90x0.02 was observed on 2 April 1990 (Ixatz&Llewitt1993)., Indeed an 8 GHz radio flux ratio of $A_2/A_1 = 0.90 \pm 0.02$ was observed on 2 April 1990 \citep{kh93}. . This radio observation was much closer to the clefly1 ratio predicted: using lensing models (VWMS95)., This radio observation was much closer to the $A_2/A_1\sim1$ ratio predicted using lensing models (WMS95). A mix of smooth and clumped matter distributions olfers a potential explanation for the discrepancy between optical ancl radio Εις ratios., A mix of smooth and clumped matter distributions offers a potential explanation for the discrepancy between optical and radio flux ratios. Microlensing simulations that assume all matter in the lensing galaxy to be in compact objects vield. a probability of 0.068. for a tux ratio lower than clefeb;=0.4540.06 (NCMS95)., Microlensing simulations that assume all matter in the lensing galaxy to be in compact objects yield a probability of 0.068 for a flux ratio lower than $A_2/A_1 = 0.45 \pm 0.06$ (WMS95). However. the addition of a smooth matter component in the lensine galaxy can significantly increase this probability up to values as large as 0.35. for sources with a characteristic racii much smaller than an Einstein Raclius (8W02).," However, the addition of a smooth matter component in the lensing galaxy can significantly increase this probability up to values as large as 0.35, for sources with a characteristic radii much smaller than an Einstein Radius (SW02)." The most compelling alternative explanation is millilensing by CDM substructure, The most compelling alternative explanation is millilensing by CDM substructure [ast rotation requires a high.mass LIAL.) white dwarl if the period of rotation of the white dwaufis 28 s. Finally. the presence of a perioclicily al 27.86 8 in 26 keV lieht curves. along with a weaker signal in the 0.42. keV. band (one half evele out. of phase). lends considerable support for the DQ Her interpretation (Patterson οἱ al.,"fast rotation requires a high–mass $\Msun$ ) white dwarf if the period of rotation of the white dwarf is 28 s. Finally, the presence of a periodicity at 27.86 s in 2–6 keV light curves, along with a weaker signal in the 0.4–2 keV band (one half cycle out of phase), lends considerable support for the DQ Her interpretation (Patterson et al." 1998)., 1998). Lasota et al. (, Lasota et al. ( 1999) expand upon the DQ er model and suggest that the rapiclly spinning white dwarl actually ejects most of the matter transferred [rom the secondary star via a magnetic propeller.,1999) expand upon the DQ Her model and suggest that the rapidly spinning white dwarf actually ejects most of the matter transferred from the secondary star via a magnetic propeller. The P29 signal is caused by reprocessing of the P28 signal bv blobs at theouler edge of the disk., The P29 signal is caused by reprocessing of the P28 signal by blobs at the edge of the disk. " A prediction of the model is that the white dwarl cannot be massive (Z1 )). potentially a serious problem if recent estimates suggesting a massive white dwarf are correct,"," A prediction of the model is that the white dwarf cannot be massive $\gtsimeq 1$ ), potentially a serious problem if recent estimates suggesting a massive white dwarf are correct." The LIAIA model of Warner Woudt (2002) is similar in spirit to the DQ Her model of Patterson (1980). but has added flexibilitv: (he periodicities are not Ged to the white cdwarl’s rotation. but instead to a thin belt on the white dwarl," The LIMA model of Warner Woudt (2002) is similar in spirit to the DQ Her model of Patterson (1980), but has added flexibility: the periodicities are not tied to the white dwarf's rotation, but instead to a thin belt on the white dwarf." Since the belt contains much less inerlia (han the white dwarl. significant short timescale changes in rotation rate are possible.," Since the belt contains much less inertia than the white dwarf, significant short timescale changes in rotation rate are possible." In this model the belt itself amplifies the white cdwarls magnetic field. allowing a white dwarf with very low magnetic field strength to channel the accretion flow.," In this model the belt itself amplifies the white dwarf's magnetic field, allowing a white dwarf with very low magnetic field strength to channel the accretion flow." " One particularly attractive feature of the model is that Che vertical thickening at the inner disk can also explain the ""dips"" seen in WZ See's light curve.", One particularly attractive feature of the model is that the vertical thickening at the inner disk can also explain the “dips” seen in WZ Sge's light curve. While the model seems very. promising for the dwarl nova oscillations (DNOs) and QPOs seen in other cataclvsmic variables. WZ See presents more of a challenge.," While the model seems very promising for the dwarf nova oscillations (DNOs) and QPOs seen in other cataclysmic variables, WZ Sge presents more of a challenge." For all other svstems the DNOs are present only in while in WZ See the DNO signal. P28. is often present in quiescence and seems to have disappeared during the outburst.," For all other systems the DNOs are present only in while in WZ Sge the DNO signal, P28, is often present in quiescence and seems to have disappeared during the outburst." The P28 sienal is not present in outburst (e.g. Patterson οἱ al., The P28 signal is not present in outburst (e.g. Patterson et al. 1981: Ixnigge et al., 1981; Knigge et al. 2002: this work). and remained hidden for nearly 13 vears alter the 1978 outburst.," 2002; this work), and remained hidden for nearly 18 years after the 1978 outburst." In the stancard DQ Her scenario. the lack of the P28 oscillation curing outburst can be explained by the eveally enhanced mass accretion rate (see Patterson et al.," In the standard DQ Her scenario, the lack of the P28 oscillation during outburst can be explained by the greatly enhanced mass accretion rate (see Patterson et al." 1998): the ram pressure of the accreting gas overwhelms the magnetic pressure ancl effectively crushes the magnetosphere back onto the surface of the white dwarl ancl accretion takes place along the equator. nol al the magnetic poles.," 1998): the ram pressure of the accreting gas overwhelms the magnetic pressure and effectively crushes the magnetosphere back onto the surface of the white dwarf and accretion takes place along the equator, not at the magnetic poles." The magnetic field is too weak to channel the accretion flow during outburst. hence the photometric modulations vanish.," The magnetic field is too weak to channel the accretion flow during outburst, hence the photometric modulations vanish." Gebhardt et al. (,Gebhardt et al. ( 2000) inferred the projected velocity dispersion profile from —1800 mciuber stars in M15 with knuowu line-oflight velocities.,2000) inferred the projected velocity dispersion profile from $\sim$ 1800 member stars in M15 with known line-of-light velocities. Assuming isotropic velocity distribution. a constaut stellar mass-to-helt ratio (AL/L)y 11.7 aud no rotation. the best spherical dvuamical model that matches the data contaius a AMAL. black hole (see fig.15 in Cebhardt et al.," Assuming isotropic velocity distribution, a constant stellar mass-to-light ratio $_V$ 1.7 and no rotation, the best spherical dynamical model that matches the data contains a $_\odot$ black hole (see fig.15 in Gebhardt et al." 2000)., 2000). ITowever. other models also explain the data. such as the models preseuted by Gebhardt et al. (," However, other models also explain the data, such as the models presented by Gebhardt et al. (" 2000).,2000). To draw a fiui conclusion on this issue. further studies are ucecdec.," To draw a firm conclusion on this issue, further studies are needed." If the elobular clusters are eventually founcl to possess central black holes. as hiuted iu Gebhardt e al. (," If the globular clusters are eventually found to possess central black holes, as hinted in Gebhardt et al. (" 2000). it is interesting to investigate the correlation between black hole mass and velocity dispersion among elobular clusters.,"2000), it is interesting to investigate the correlation between black hole mass and velocity dispersion among globular clusters." Taking the projected velocity dispersion at cffective radius £ + and assuniue a black hole with mass of NINE... MID can be plotted into the Mp: σι diagram.," Taking the projected velocity dispersion at effective radius $\pm$ $^{-1}$ and assuming a black hole with mass of $_\odot$, M15 can be plotted into the $_{BH}$ – $\sigma_e$ diagram." In Fig., In Fig. 1. the solid line defined by is the best fit to the galaxies.," 1, the solid line defined by is the best fit to the galaxies." Within the uncertainties. MID is perfectly sitting on the lower extension of the fit!," Within the uncertainties, M15 is perfectly sitting on the lower extension of the fit!" Adding M15 to IKCC2001 data. a robust Mipy σι correlation iu a much larger range cau be eiven as which is shown by dash line in Fig.," Adding M15 to KG2001 data, a robust $_{BH}$ – $\sigma_e$ correlation in a much larger range can be given as which is shown by dash line in Fig." 1., 1. Should the globular clusters and galaxies follow simular plivsical process of black hole formation. they would exhibit the same correlation between black hole mass aud velocity dispersion.," Should the globular clusters and galaxies follow similar physical process of black hole formation, they would exhibit the same correlation between black hole mass and velocity dispersion." Based ou the data of globular clusters aud galaxies. the deteriiuation of the τομ 0 correlation would be improved significautly.," Based on the data of globular clusters and galaxies, the determination of the $_{BH}$ – $\sigma$ correlation would be improved significantly." Bearing iu nüiud that black hole mass correlates ouly with velocity dispersion or huninosity of the scl-eravitating spherical systems. a bold speculation arises that the formation aud growth of black hole cau be linked with a certain potential physical process that is universal for such systems. aud lence various sizes of sclberavitating svstenis satisfv the same correlation.," Bearing in mind that black hole mass correlates only with velocity dispersion or luminosity of the self-gravitating spherical systems, a bold speculation arises that the formation and growth of black hole can be linked with a certain potential physical process that is universal for such systems, and hence various sizes of self-gravitating systems satisfy the same correlation." With this speculation. the same Mp; 0 correlation should be found in a wide range of dimensions eoius from stellar elobular clusters to galaxies.," With this speculation, the same $_{BH}$ – $\sigma$ correlation should be found in a wide range of dimensions going from stellar globular clusters to galaxies." The black hole mass measurement bv Cebhardt et al. (, The black hole mass measurement by Gebhardt et al. ( 2000) shows that the elobular cluster MID is remarkably consistent with the Mp σ correlation derived from galaxies.,2000) shows that the globular cluster M15 is remarkably consistent with the $_{BH}$ – $\sigma$ correlation derived from galaxies. This implies that the speculation might be applicable at least for elobular clusters., This implies that the speculation might be applicable at least for globular clusters. Adopting such a universal Mpg — 0 correlation. the mass of the black hole in elobular clusters cau be estimated in terms of velocity dispersion.," Adopting such a universal $_{BH}$ – $\sigma$ correlation, the mass of the black hole in globular clusters can be estimated in terms of velocity dispersion." Iu. Table 1. the parameters of 22 Calactic aud 9 AI31 elobular clusters are tabulated.," In Table 1, the parameters of 22 Galactic and 9 M31 globular clusters are tabulated." According to the relation between the black hole mass and ceutral velocity dispersion of galaxies. given by equation (5) in Απ Forrarese (2001). the mass of black holes in those globular clusters is estimated.," According to the relation between the black hole mass and central velocity dispersion of galaxies, given by equation (5) in Merritt Ferrarese (2001), the mass of black holes in those globular clusters is estimated." The results areaud listed in cohuun (6) of Table 1., The results areand listed in column (6) of Table 1. The uncertainties are given following those of velocity dispersion data., The uncertainties are given following those of velocity dispersion data. The observations of the T Tau complex from vanBoekeletal.(2009). demonstrate that emission can also originate from shocks generated by protostellar outflows/jets.,The observations of the T Tau complex from \citet{van09} demonstrate that emission can also originate from shocks generated by protostellar outflows/jets. Because of the high ionization potential of neon atoms (21.6eeV). substantial ionization can be only produced by fast shocks with speeds > kkin/s for tvpical pre-shock densities of 10 ccm.7 (also called J shocks. Hollenbach&Mcelxee 1989)).," Because of the high ionization potential of neon atoms eV), substantial ionization can be only produced by fast shocks with speeds $\ge$ km/s for typical pre-shock densities of $^4$ $^{-3}$ (also called J shocks, \citealt{HM89}) )." For this type of strong radiative shocks the shocked gas moves at almost the shock velocity., For this type of strong radiative shocks the shocked gas moves at almost the shock velocity. argue that these high velocities may be reached in the outflow from the T Tau 9 source which has a sieht velocity of only 240 kkin/s. but it is likely to be in the plane of the sky.," \citet{van09} argue that these high velocities may be reached in the outflow from the T Tau S source which has a sight velocity of only $\sim$ km/s, but it is likely to be in the plane of the sky." We now show that it is very unlikely that jets/outflows could explain the emission of transition disks., We now show that it is very unlikely that jets/outflows could explain the emission of transition disks. First. let us consider the case of TW Ilva.," First, let us consider the case of TW Hya." Its disk is seen almost [ace-on so we would expect any jet/outllow to be almost in the direction of the observer and the sight velocity to be close to the actual shock velocity., Its disk is seen almost face-on so we would expect any jet/outflow to be almost in the direction of the observer and the sight velocity to be close to the actual shock velocity. The sight velocity of the emission from TW Ilva is just -Gkkin/s and the line is relatively narrow (deconvolved FWIIM of 710 kkimn/s)., The sight velocity of the emission from TW Hya is just km/s and the line is relatively narrow (deconvolved FWHM of $\sim$ km/s). If (his velocity is representative for (he shock velocity as precdictecl from J shock models. it would be unable to appreciably ionize neon atoms.," If this velocity is representative for the shock velocity as predicted from J shock models, it would be unable to appreciably ionize neon atoms." " Corroborating this assertion. Hollenbach&Gorti(2009) show that the line Iluminosity. produced bv the postshock region of a radiative shock depends linearly on: M,v2, where AM. is the protostellar mass wind loss rate ancl ey is the shock velocity."," Corroborating this assertion, \citet{hollenbach09} show that the line luminosity produced by the postshock region of a radiative shock depends linearly on: $\dot{M}_w\,v_s^2$, where $\dot{M}_w$ is the protostellar mass wind loss rate and $v_s$ is the shock velocity." " The wind mass loss rate scales with the stellar mass accretion rate as M,c0.01—0.1xMuse (Hartiganοἱal. 2004)."," The wind mass loss rate scales with the stellar mass accretion rate as $\dot{M}_w \simeq 0.01-0.1\times \dot{M}_{acc}$ \citep{hartigan95,WH04}." . Given the low stellar accretion rates of transition disks. the [Iuxes reported in Table 3. could be reached only. with shock velocities ranging [rom several hundreds of km/s to thousands of km/s. clearly inconsistent with the small velocity shilts and relatively small FWIIM of the observed lines.," Given the low stellar accretion rates of transition disks, the fluxes reported in Table \ref{table:results} could be reached only with shock velocities ranging from several hundreds of km/s to thousands of km/s, clearly inconsistent with the small velocity shifts and relatively small FWHM of the observed lines." Finally. line widths from shocked," Finally, line widths from shocked" wherever possible. be based upon measurements as carly as possible in the flight of tlje ejecta.,"wherever possible, be based upon measurements as early as possible in the flight of the ejecta." Finally. the observed correlation between peak radio and. X-ray Hluxes from X-rav transients (Fender Ixuiukers 2001) would be destroved if the Lorentz [actor of the radio emitting region were too large (unless the X-ray emission. were also beamed. which would however imply a huge selection ellect on observations ol X-ray binaries) wh-É.e current data may be too sparse to constrain this at present. this may be the best approach for limiting the Lorentz factors of jets [rom X-ray binaries in the future.," Finally, the observed correlation between peak radio and X-ray fluxes from X-ray transients (Fender Kuulkers 2001) would be destroyed if the Lorentz factor of the radio emitting region were too large (unless the X-ray emission were also beamed, which would however imply a huge selection effect on observations of X-ray binaries) – while current data may be too sparse to constrain this at present, this may be the best approach for limiting the Lorentz factors of jets from X-ray binaries in the future." The author would like to thank Guy Pooley and Marc IHibo for comments on this manuscript. and the anonymous referee for useful suggestions.," The author would like to thank Guy Pooley and Marc Ribo for comments on this manuscript, and the anonymous referee for useful suggestions." |]. where Αιαμ 18 the amplitude of the real (ideal) signal| and Ου the offset.,", where $A_{real\,(ideal)}$ is the amplitude of the real (ideal) signal and $O_{real\,(ideal)}$ the offset." Cy is related to the modulation efficiency. of the polarimeter. and compares the actual excursion of the llatted signal to the excursion in the ideal case (the lossless and efficient polarimeter described by eq.(1).," $C_A$ is related to the modulation efficiency of the polarimeter, and compares the actual excursion of the ted signal to the excursion in the ideal case (the lossless and efficient polarimeter described by eq.(1))." C4.«1 indicates an instrument close to ideal. thus maximizing the S/N of the measuremet.," $C_A \ll 1$ indicates an instrument close to ideal, thus maximizing the S/N of the measurement." Co is related to the offset of the modulated signal. which should be n1inimized for an optimal use of the dynamic range of the instrunent.," $C_O$ is related to the offset of the modulated signal, which should be minimized for an optimal use of the dynamic range of the instrument." A value of Co«| indicates an offset close to half of the dynamic range. 1.8. the ideal case.," A value of $C_O \ll 1$ indicates an offset close to half of the dynamic range, i.e. the ideal case." For our simulation example we have considered the measuremet of polarization of diffuse interstellar dust. which we have modeled with a temperature of K and emissivity proportional to 17. normalized to the Archeops data at GHz (1.8. we usec the spectrum plotted in 1)): it is horizontally polarized. with a degree of polarization of 10%.," For our simulation example we have considered the measurement of polarization of diffuse interstellar dust, which we have modeled with a temperature of $\,$ K and emissivity proportional to $\nu^2$, normalized to the Archeops data at $\,$ GHz (i.e. we used the spectrum plotted in $\,$ \ref{fig:0}) ); it is horizontally polarized, with a degree of polarization of $10\,\%$." We have considered the two wavelengths 240 μπι and 550um. with finite bandwidths Aul=41% and 33%. respectively.," We have considered the two wavelengths $240\,\mu$ m and $550\,\mu$ m, with finite bandwidths $\Delta \lambda/\lambda=41\%$ and $\%$, respectively." We have considered only normal incidence on the HWP., We have considered only normal incidence on the HWP. The spectral dependence of the extraordinary and ordinary refraction indices of the HWP. and of the corresponding absorption coefhicients. is given by Savini et al. (2006)).," The spectral dependence of the extraordinary and ordinary refraction indices of the HWP, and of the corresponding absorption coefficients, is given by Savini et al. \cite{Savini06}) )." We have assumed a linear decrease of the absorption coefficient with the temperature of the HWP., We have assumed a linear decrease of the absorption coefficient with the temperature of the HWP. " Small differences in the absorption coefficients of the HWP. at a level of about 1073, create a modulated polarized emission from the erystal itself."," Small differences in the absorption coefficients of the HWP, at a level of about $10^{-3}$, create a modulated polarized emission from the crystal itself." In a typical Stokes polarimeter (like e.g. MAXIPOL and PILOT) the HWP is followed by a polarizer. tilted of 45° with respect to the normal of the HWP surface.," In a typical Stokes polarimeter (like e.g. MAXIPOL and PILOT) the HWP is followed by a polarizer, tilted of $^{\circ}$ with respect to the normal of the HWP surface." In this way two independent arrays. one detecting radiation transmitted by the polarizer. the other detecting reflected radiation. can use the same focal plane of the telescope. thus observing the same area of the sky.," In this way two independent arrays, one detecting radiation transmitted by the polarizer, the other detecting reflected radiation, can use the same focal plane of the telescope, thus observing the same area of the sky." At these frequencies. metal wire grid polarizers are close to ideal.," At these frequencies, metal wire grid polarizers are close to ideal." " In our model we assume transmission coefficients p,=0.99, py=0.01 and emissivity 0.01."," In our model we assume transmission coefficients $p_x=0.99$, $p_y=0.01$ and emissivity $0.01$." The radiation is then detected by a bolometer. with emissivity 0.5. cooled at K. Due to this very low temperature. we have neglected its emission.," The radiation is then detected by a bolometer, with emissivity $0.5$, cooled at $\,$ K. Due to this very low temperature, we have neglected its emission." " The signal detected by the polarimeter. Wy,;. is given by the sum of the dust emission processed by the rotating HWP and the polarizer. the HWP emission processed by the polarizer and the polarizer emission reflected back by the HWP:"," The signal detected by the polarimeter, $W_{det}$, is given by the sum of the dust emission processed by the rotating HWP and the polarizer, the HWP emission processed by the polarizer and the polarizer emission reflected back by the HWP:" and radius. the mass of the vounger WD eives the strougest known constraint on the pre-mass-transter jnary confieuration.,"and radius, the mass of the younger WD gives the strongest known constraint on the pre-mass-transfer binary configuration." Ou the other haud. the initially OWwoer-anass conrpauionu must evolve into a white dwarf via a commnion-enuvelope process iu the last binary interaction ghase. in order to achieve the σπα} separations observed (17)...," On the other hand, the initially lower-mass companion must evolve into a white dwarf via a common-envelope process in the last binary interaction phase, in order to achieve the small separations observed \citep{IL93, Webbink08}." Tlowever. the physics underlying the evolutionary channel(s) by which DWDs form remains uncertaiu.," However, the physics underlying the evolutionary channel(s) by which DWDs form remains uncertain." A variety of explanations have been posited to explain he first stage of mass transfer (AIT). in which the initial primary loses its cuvelope.," A variety of explanations have been posited to explain the first stage of mass transfer (MT), in which the initial primary loses its envelope." ? showed that ith. CE and Roche-lobe overflow (RLOF) are possible in the first episode of the AIT., \cite{Han1998} showed that both CE and Roche-lobe overflow (RLOF) are possible in the first episode of the MT. Later. it was claimed hat this phase caunot be described by stable aud conservative RLOF (??)..," Later, it was claimed that this phase cannot be described by stable and conservative RLOF \citep{Nelemans00, Sluys2006}." The sugeestion that the first AIT episode in the formation history was a CE event also proved problematic: when formulated i terius of the binding cuerey of the envelope. it appeared to imply that the binary aust be able to eject its cuvelope with an unplivsical (often negative) οποιον 11).," The suggestion that the first MT episode in the formation history was a CE event also proved problematic: when formulated in terms of the binding energy of the envelope, it appeared to imply that the binary must be able to eject its envelope with an unphysical (often negative) efficiency \citep{Nelemans00,Nelemans05,Webbink08}." Furthermore. the majority of the discovered double-degenerate systems have components of comparable lnass. in coutracliction to the results of past uuncerical work (?)..," Furthermore, the majority of the discovered double-degenerate systems have components of comparable mass, in contradiction to the results of past numerical work \citep{Han1998}." Receutly a reconciliation was attempted by instead considering aneular-momentiu balance. re- the problem iun terms of the so-called “s-prescription (??)..," Recently, a reconciliation was attempted by instead considering angular-momentum balance, re-parametrizing the problem in terms of the so-called $\gamma$ -prescription” \citep{Nelemans00, Nelemans05}." Iu this paper. we cdemoustrate that the 5-formalisui is not stable against simall changes in the binary paraiueters 33). and that iu ecneral it too fails to provide a plivsical description of an initial. dvnamicaltimescale phase of evolution which is consistent with both energv and angular moment couservation.," In this paper, we demonstrate that the $\gamma$ -formalism is not stable against small changes in the binary parameters 3), and that in general it too fails to provide a physical description of an initial, dynamical-timescale phase of evolution which is consistent with both energy and angular momentum conservation." As an alternative. we remove the restriction to dvuamicaltimescale processes and consider the evolution of red-giaut main-sequence (RCG-MS) binaries via stable. nut Wass transter frou the primary as he first phase of mmass loss .11.55).," As an alternative, we remove the restriction to dynamical-timescale processes and consider the evolution of red-giant main-sequence (RG-MS) binaries via stable, but mass transfer from the primary as the first phase of mass loss 5)." In this paper. we Hnüt ourselves to svstenis where the initial priuary has not reached the heliuu fash.," In this paper, we limit ourselves to systems where the initial primary has not reached the helium flash." We demonstrate that. wpon the former secondary reaching RLOF. an cusuine CE phase will produce a set of DWD binaries with mass ratios and periods iu ine with the observed DWDs whose older reninant is z0.16 .66).," We demonstrate that, upon the former secondary reaching RLOF, an ensuing CE phase will produce a set of DWD binaries with mass ratios and periods in line with the observed DWDs whose older remnant is $\la 0.46\,M_\odot$ 6)." ThereforeM. the stable MT|CE channel provides a jvfural nmieans for reproducing those DWDs iu which he first phase of amass loss appears to have been accompanied by orbital expausion., Therefore the stable MT+CE channel provides a natural means for reproducing those DWDs in which the first phase of mass loss appears to have been accompanied by orbital expansion. We now outline the two canonical prescriptions for treating comlmou-cuvelope evolution. aud develop the standard formalisui for treating stable mass transfer iu the case of Roche-lobe overflow.," We now outline the two canonical prescriptions for treating common-envelope evolution, and develop the standard formalism for treating stable mass transfer in the case of Roche-lobe overflow." " Iu the standard treatment of CE outcomes. the final separation of the binary is deteriunued via the ""energy formalisuy (7).. iu which the bindiug cucrey of the (expelled) euvelope is equated to the decrease in the orbital euergv Lory: Tere a; and eg are the initial and final binary separations. mg anda, are the mitial star masses (douor and accretor. respectively) aud ig. is the final mass of the donor. after losing its envelope."," In the standard treatment of CE outcomes, the final separation of the binary is determined via the “energy formalism” \citep{Webbink84}, in which the binding energy of the (expelled) envelope is equated to the decrease in the orbital energy $E_\mathrm{orb}$: Here $a_\mathrm{i}$ and $ a_\mathrm{f}$ are the initial and final binary separations, $m_\mathrm{d}$ and $m_\mathrm{a}$ are the initial star masses (donor and accretor, respectively) and $ m_\mathrm{d,c}$ is the final mass of the donor, after losing its envelope." A paraincter À is introduced to characterise the ceutral concentration of the donor cuvelope: Tere qus is the mass of the removed (eiaut's) euvelope. rq is the radius of the eiut star at the onset of the CE and 2 is the specific internal energy.," A parameter $\lambda$ is introduced to characterise the central concentration of the donor envelope: Here $m_\mathrm{d, e}$ is the mass of the removed (giant's) envelope, $r_\mathrm{d}$ is the radius of the giant star at the onset of the CE and $\varepsilon$ is the specific internal energy." Lyne therefore consists of the potential energy. of the euvelope and its internal cuerey. and cau be fouud civectly frou the stellar structure for anv choice of core nass.," $E_\mathrm{bind}$ therefore consists of the potential energy of the envelope and its internal energy, and can be found directly from the stellar structure for any choice of core mass." Inu our calculations. we adopt to include in 5 only the thermal enerev of the eas aud the radiation energv. but nof the recombination energwv.," In our calculations, we adopt to include in $\varepsilon$ only the thermal energy of the gas and the radiation energy, but not the recombination energy." There are also alternative definitions for μια. where ionization cucrey (c.g.7) or chhanced winds (e.g.7). are taken iuto account.," There are also alternative definitions for $E_\mathrm{bind}$, where ionization energy \citep[e.g.][]{Han02} or enhanced winds \citep[e.g.][]{Soker04} are taken into account." Another parameter. og. is introduced as a measure of the efficiency. with which euergv is transferred. frou the orbit iuto envelope expansion.," Another parameter, $\alpha_\mathrm{CE}$, is introduced as a measure of the efficiency with which energy is transferred from the orbit into envelope expansion." Invoking cucrey conservation. one can then find the final orbital separation from The obvious bounds ou this paramcter are 0-formalisu and can be expressed as: where J; aud Jg are the angular momenta of the initial and the final binaries., This is known as the $\gamma$ -formalism and can be expressed as: where $J_\mathrm{i}$ and $J_\mathrm{f}$ are the angular momenta of the initial and the final binaries. Hence. the 5-parincetrization deseribes the specific fraction of the initial angular monmentun that is carried away by the euvelope as it is lost from the systeii. iu terms of a multiplicative factor (5) times the fraction of the total mass lost from the svsteni.," Hence, the $\gamma$ -parametrization describes the specific fraction of the initial angular momentum that is carried away by the envelope as it is lost from the system, in terms of a multiplicative factor $\gamma$ ) times the fraction of the total mass lost from the system." It was shown that the 2-foriialisii can reproduce the distributions of the orbital periods and mass ratios in the observed DWD svstems with a single value of +=1.5 for the firstmass-trauster event. where the range for possible," It was shown that the $\gamma$ -formalism can reproduce the distributions of the orbital periods and mass ratios in the observed DWD systems with a single value of $\gamma=1.5$ for the firstmass-transfer event, where the range for possible" source is located outside the 240x20 (8.1x8.Lb kpe) field of view].,"source is located outside the $2^{\prime}\!.0 \times 2^{\prime}\!.0$ $8.4 \times 8.4$ kpc) field of view]." Also shown in this image are the positions of the sources which have luminosities (corrected for absorption) between 5xLO ere ! and 1079 erg L| in the 0.1-8 keV band., Also shown in this image are the positions of the sources which have luminosities (corrected for absorption) between $5 \times 10^{38}$ erg $^{-1}$ and $10^{39}$ erg $^{-1}$ in the $0.4$ $8$ keV band. There are 3 sources in this luminosity range outside the field of Fig. T.., There are 3 sources in this luminosity range outside the field of Fig. \ref{fig7}. Two of these project outside the 25.0 B-magnitude (are 7 isophote of the ealactic Their hardness ratios are H4?=2.040.9 aud AR=0.33£0.06. respectively.," Two of these project outside the 25.0 B-magnitude (arc $^{-2}$ isophote of the galactic Their hardness ratios are $HR = 2.0 \pm 0.9$ and $HR = 0.33 \pm 0.06$ , respectively." For a source with a power-law spectrum of photon iudex P—2.0. typical of an ACN. AR=0.31 if we assume absorption from the Galactic column density ouly. aud HR=0.51 ifa column deusity of Ny:=4o1.28ooxaqq»1074 cm7 2eis assumed.," For a source with a power-law spectrum of photon index $\Gamma = 2.0$, typical of an AGN, $HR = 0.34$ if we assume absorption from the Galactic column density only, and $HR = 0.51$ if a column density of $N_{\rm H} = 1.28 \times 10^{21}$ $^{-2}$ is assumed." Thus. we conclude that the spectrum of. one of. these sources is Consistent with that of a typical ΑΝ. while the spectrum of the other source is consistent with that of a typical AGN only i£ it is highly absorbed.," Thus, we conclude that the spectrum of one of these sources is consistent with that of a typical AGN, while the spectrum of the other source is consistent with that of a typical AGN only if it is highly absorbed." Ifn the 5- sources withn 0.I-8] keVT luminositiesn greater than E10AC erg | are. N-rayr binariesn accreting with luminosities that are sub-Eddingtou (Le. L4S1.5x10(M/M.) erg[n] JF. where Af aud M. are the masses of the X-ray source and the Suu. respectively). theu the iuiplied source Inasses are zz 71-100AL..," If the 5 sources with $0.4$ $8$ keV luminosities greater than $10^{39}$ erg $^{-1}$ are X-ray binaries accreting with luminosities that are sub-Eddington (i.e., $L_{\rm x} \simless 1.5 \times 10^{38} \, (M/M_{\odot})$ erg $^{-1}$, where $M$ and $M_{\odot}$ are the masses of the X-ray source and the Sun, respectively), then the implied source masses are $\simgreat 7$ $100 \, M_{\odot}$." Such objects are almost certainly black holes. since the upper limit on the mass of a uou-rotatiug neutron star is 3M. (for a review see e.g.. van Paradijs MeClintock 1995).," Such objects are almost certainly black holes, since the upper limit on the mass of a non-rotating neutron star is $\sim 3 \, M_{\odot}$ (for a review see e.g., van Paradijs McClintock 1995)." The maximuau mass of a black hole formed by the collapse of a siugle. uou-zero metallicity star within the mass rauge 25-10ÀL. is commonly believed to be ~12M. due to the effects of nass loss through stellar winds.," The maximum mass of a black hole formed by the collapse of a single, non-zero metallicity star within the mass range $\sim 25$ $40 \, M_{\odot}$ is commonly believed to be $\sim 15 \, M_{\odot}$ due to the effects of mass loss through stellar winds." The black hole mass can be even lower (S10AL.) for black hole orogenitors iu close separation binary systems since. prior to collapse. the progeuitors helium core uay uidergo mass loss ina WolCBayet phase if the hydrogeu layers are renmioved by the compauiou star in a common envelope phase (Fryer&Ixalogera2001).," The black hole mass can be even lower $\simless 10 \, M_{\odot}$ ) for black hole progenitors in close separation binary systems since, prior to collapse, the progenitor's helium core may undergo mass loss in a Wolf-Rayet phase if the hydrogen layers are removed by the companion star in a common envelope phase \citep{fk01}." . However. the limit on the black hole uass nay be liigher. siuce stars more massive than 10AM. may not produce a supernova explosion aud all of the stellar material falls back onto the black hole (Fryer1999).," However, the limit on the black hole mass may be higher, since stars more massive than $\sim 40 \, M_{\odot}$ may not produce a supernova explosion and all of the stellar material falls back onto the black hole \citep{fry99}." . Moreover. the mass loss ‘ates [or low metallicity stars may be small. thus allowing the black hole progeuitors to retain most oL their original stellar mass (Vink. de Ixoter. Lamers 2001).," Moreover, the mass loss rates for low metallicity stars may be small, thus allowing the black hole progenitors to retain most of their original stellar mass (Vink, de Koter, Lamers 2001)." Stars with masses withiu the rauge 100-250AL. may uudergo explosive nuclear buruing at the end of their evolution. however. and uo remnaut is left (Woosley Weaver 1082: Clatzel. El Eid. Fricke 1985: Woosley 1956).," Stars with masses within the range $\sim 100$ $250 \, M_{\odot}$ may undergo explosive nuclear burning at the end of their evolution, however, and no remnant is left (Woosley Weaver 1982; Glatzel, El Eid, Fricke 1985; Woosley 1986)." Alternatively. black holes with mnasses zLOOAL. may originate [rom an earlier population of stars with effectively zero metallicity (i.e.. Population HIE stars) ancl massesz250AZ. (Woosley Weaver 1952: Bond. Arnett. Carr 1981: Fryer. Woosley. Heger 2001).," Alternatively, black holes with masses $\simgreat 100 \, M_{\odot}$ may originate from an earlier population of stars with effectively zero metallicity (i.e., Population III stars) and masses$\simgreat 250 \, M_{\odot}$ (Woosley Weaver 1982; Bond, Arnett, Carr 1984; Fryer, Woosley, Heger 2001)." Thesestars may not experience substantial mass loss during their lifetimes. aud a massive black bole cau form iuside the star before explosive buruiug reverses its collapse (Bondetal.198 1)..," Thesestars may not experience substantial mass loss during their lifetimes, and a massive black hole can form inside the star before explosive burning reverses its collapse \citep{bon84}. ." (Thompson&Duncan1996).., \citep{td96a}. 2-ravs (Alazetsοἱal.1979:Hurleyet1999).. (Ixouveliotouοἱal.1998:IXouveliotouet1999).. Woods&Thompson(2004)..," $\gamma$ \citep{mgi+79,hcm+99}. \citep{kds+98, ksh+99}. \citet{wt04}." (Guillot&Showman2002:Jacksonetal.2009:Batveinοἱ2011:Chabrier2007;Arras&Socrates2010).. Leconteοἱal.2009).. (Burrowsetal," \citep{Guillot02, Jackson09, Batygin2011, Chabrier07c, Arras2010}. \citep[e.g.][]{Sato05,Fortney06,Leconte2009}. \citep{Guillot06}. \citep{Burrows07}." .2007).. 10—15 M. , $10-15$ $M_{\oplus}$ "Mya, (Lacey Cole 1995. eq.","$M_{\rm halo}$ (Lacey Cole 1993, eq." 2.15). aud Mitt) is the mass of a halo whose velocity dispersion Is Chek/2.," 2.15), and $M_{\rm min}(z)$ is the mass of a halo whose velocity dispersion is $v_{\rm kick}/2$." To sunmunarize. our model for the assembly of DIIS has five parameters.," To summarize, our model for the assembly of BHs has five parameters." " Two of these. My, aud jj. describe the observed quasar SDSS 1051,|1021. and have relatively ο uucertaiunties. as discussed in the previous section."," Two of these, $M_{\rm halo}$ and $\eta$, describe the observed quasar SDSS 1054+1024, and have relatively small uncertainties, as discussed in the previous section." " The three parameters A44. €. and thc""a relate to our for theJ growtherowth ofo eth IBI.SMDII."," The three parameters $M_{\rm seed}$, $\epsilon$, and $v_{\rm kick}$ relate to our model for the growth of the SMBH." eJTh πάςdfiducial ialJvaluesvaln: quasarxu these parameters are chosen as follows., The fiducial values of these parameters are chosen as follows. Tle seed mass and Mau =LOA...the typical value for a stellar reciiuinaut clockwise.," The seed mass is $M_{\rm seed}=10~{\rm M_\odot}$, the typical value for a stellar remnant BH." VMOs (Cary. Boud & 1981) can leave lareer ferentdispersion lunamts.iSweiehiueoO 15tuins 9 100Ut vorAL(IeocrS0 otef:J alκ," VMOs (Carr, Bond Arnett 1984) can leave larger remnants, weighing up to $\sim 10^3~{\rm M_\odot}$ (Heger et al." A.2003), 2003). " ↴for radiative Defficiency.‘ is""p taken to be e =0.1.basedQn ou and he last stable orbit around a nonrotating DIT."," The radiative efficiency is taken to be $\epsilon=0.1$, based on the last stable orbit around a non–rotating BH." This value 1s consistent with a comparison of quasar light to remmaut DII inasses in nearby galaxies (Yu Tremaine 2002: Aller Richstone 2002: Tainan. Ciotti Ostriker 2001).," This value is consistent with a comparison of quasar light to remnant BH masses in nearby galaxies (Yu Tremaine 2002; Aller Richstone 2002; Haiman, Ciotti Ostriker 2004)." A uaxinallv rotating Kerr DIT would produce a larger value of e—0.12., A maximally rotating Kerr BH would produce a larger value of $\epsilon=0.42$. For auv eiven values of the above five parameters. equation 1 can be used to compute Ay=MinCMyuopeAcoεν Chick) ," For any given values of the above five parameters, equation \ref{eq:Mbh} can be used to compute $M_{\rm bh}=M_{\rm bh}( M_{\rm halo},\eta, M_{\rm seed},\epsilon, v_{\rm kick})$ ." "By requiring the predicted BIT mass to equal the value inferred frou, observations. this relation can be inverted. aud our model then vields a unique prediction for cgi as a function of the five paramctors Mas. ye Ate. € ond. My."," By requiring the predicted BH mass to equal the value inferred from observations, this relation can be inverted, and our model then yields a unique prediction for $v_{\rm kick}$ as a function of the five parameters $M_{\rm halo}$, $\eta$, $M_{\rm seed}$, $\epsilon$, and $M_{\rm bh}$." Iu our fiducial model. we fud muuerically that the maxim recoil velocity that allows the erowth of the SMDII iu the quasar SDSS 1051]1021 i Cg=6Lnis +.," In our fiducial model, we find numerically that the maximum recoil velocity that allows the growth of the SMBH in the quasar SDSS 1054+1024 is $v_{\rm kick}=64~{\rm km~s^{-1}}$ ." This value is siguificantle below the lowest values predicted dv Favata ct al. (, This value is significantly below the lowest values predicted by Favata et al. ( 2001) anc Merritt et al. (,2004) and Merritt et al. ( 2001).,2004). If actual recoil velocities are in excess of 100Jansft. this would be iucousisteut with the fiducial SMDIT erowth model preseuted here. and would require that some of the seeds grow their mass faster than the asstuned Eddington rate.," If actual recoil velocities are in excess of $100~{\rm km~s^{-1}}$, this would be inconsistent with the fiducial SMBH growth model presented here, and would require that some of the seeds grow their mass faster than the assumed Eddington rate." Iu order to illustrate the DII erowtl process in our mociel in somewhat more detail. Figure 1 shows the evolution of various quantities for SDSS 105111021 (this figure is an updated version of Figure 1 iu ITELOT. which presented simular results for the earlier SDSS quasar LO5Ll)1000 at 2= 4.8).," In order to illustrate the BH growth process in our model in somewhat more detail, Figure \ref{fig:sdss} shows the evolution of various quantities for SDSS 1054+1024 (this figure is an updated version of Figure 1 in HL01, which presented similar results for the earlier SDSS quasar 1054+1000 at $z=5.8$ )." In this figure. we have assumed ζωα=10.e=Ql. 1. aud Όμως=61kins 5.," In this figure, we have assumed $M_{\rm seed}=10, \epsilon=0.1, \eta=1$ , and $v_{\rm kick}=64~{\rm km~s^{-1}}$ ." " With this conibination. equations 1 and 2. vield the required BIT nass of Mi,=L6«109NL, at 2=613."," With this combination, equations \ref{eq:Mbh} and \ref{eq:Nprog} yield the required BH mass of $M_{\rm bh}=4.6 \times 10^9~{\rm M_\odot}$ at $z=6.43$." " The top left xuel iu Fiewe 1 shows the number of progenitors of he parent halo (Aga,28.5<1022 ML.) whose velocity dispersion exceed 32knis.", The top left panel in Figure \ref{fig:sdss} shows the number of progenitors of the parent halo $M_{\rm halo}\approx 8.5\times10^{12}~{\rm M_\odot}$ ) whose velocity dispersion exceed $32~{\rm km~s^{-1}}$. For reference. the bottom oft paucl shows the corresponding minium halo mass.," For reference, the bottom left panel shows the corresponding minimum halo mass." " CGoine towards higher redshift. the ος of progenitors Increases, peaks at zzz11. and thendecreases again as the vpical progenitors are broken up iuto halos smaller than 32lans+."," Going towards higher redshift, the number of progenitors increases, peaks at $z\approx 11$, and then decreases again as the typical progenitors are broken up into halos smaller than $32~{\rm km~s^{-1}}$." The top rightpaucl shows the coutribution of xoeenitors from each redshift to the final black hole mass. and shows that the bulk of the DIT mass is contributed by seed holes from 17x:ELs.," The top rightpanel shows the contribution of progenitors from each redshift to the final black hole mass, and shows that the bulk of the BH mass is contributed by seed holes from $17\lsim z\lsim 18$." There are no new seeds ornüue at ;zxll. aud the peak redshift is cousiderably üeher than the peak at which most progenitors form.," There are no new seeds forming at $z\lsim 11$, and the peak redshift is considerably higher than the peak at which most progenitors form." This is iniply because the increased time available between +=6.13 and increasingly ligher redshifts 2 (shown explicitly in the bottom right panel) makes the contribution frou the first —20 progenitors. fornuug at z—I8. dominant.," This is simply because the increased time available between $z=6.43$ and increasingly higher redshifts $z$ (shown explicitly in the bottom right panel) makes the contribution from the first $\sim 20$ progenitors, forming at $z\sim 18$, dominant." " We lave found above that. in order to erow au SMDIT as lnassive as LG«10""ML. iu our fiducial model. wewould need to utilize progenitors with velocity dispersions assiuall aso =32ansd."," We have found above that, in order to grow an SMBH as massive as $4.6\times10^9~{\rm M_\odot}$ in our fiducial model, wewould need to utilize progenitors with velocity dispersions assmall as $\sigma=32~{\rm km~s^{-1}}$." These κια] halos. however. should be excluded. from contributing to the final mass by the laree recoil velocities.," These small halos, however, should be excluded from contributing to the final mass by the large recoil velocities." " Another wav of stating our result is to note that in our fiducial model. but with Onin=DO.100. or 200lans1. correspouding to typical recoil velocities of 100.200. or LOOkms+. the final SMDIT mass at 2=6.13 is 5.2&LOSALL. L2&10""ALL. and 1.2«10°AL... respectively - au order of magnitude or more below the interred BIT mass of SDSS |1021."," Another way of stating our result is to note that in our fiducial model, but with $\sigma_{\rm min}=50, 100,$ or $200~{\rm km~s^{-1}}$, corresponding to typical recoil velocities of $100, 200,$ or $400~{\rm km~s^{-1}}$, the final SMBH mass at $z=6.43$ is $5.2\times10^8~{\rm M_\odot}$, $1.2\times10^7~{\rm M_\odot}$ , and $1.2\times10^5~{\rm M_\odot}$, respectively - an order of magnitude or more below the inferred BH mass of SDSS 1054+1024." lu order to assess the sensitivity 1051of the result above to our assuniptious. we here vary each of the parameters of our model.," In order to assess the sensitivity of the result above to our assumptions, we here vary each of the parameters of our model." " For cach combination of Mya. ye Maa. and e. we solve equation L with its left haud side set to My,=L6«10%+M. and the halo mass set to Mg, at 2=6.123. as discussed above."," For each combination of $M_{\rm halo}$, $\eta$, $M_{\rm seed}$, and $\epsilon$, we solve equation \ref{eq:Mbh} with its left hand side set to $M_{\rm bh}=4.6 \times 10^9\eta^{-1}~{\rm M_\odot}$, and the halo mass set to $M_{\rm halo}$ at $z=6.43$, as discussed above." We further specity ALcd and e. aud then fud een by a NewtonRhapson method.," We further specify $M_{\rm seed}$ and $\epsilon$, and then find $v_{\rm kick}$ by a Newton–Rhapson method." " We find that our results are iuseusitive to the adopted values of Mya, and i.", We find that our results are insensitive to the adopted values of $M_{\rm halo}$ and $\eta$. " IKeeping all other paramcters fixed at their fiducial values. increasing or decreasing Mi, oa factor of three vields ge,=82.2hans! and dele=19.6αν+. respectively."," Keeping all other parameters fixed at their fiducial values, increasing or decreasing $M_{\rm halo}$ by a factor of three yields $v_{\rm kick}=82.2~{\rm km~s^{-1}}$ and $v_{\rm kick}=49.6~{\rm km~s^{-1}}$, respectively." This is not surpris. and reflects the fact that the rare. massive halos at je tail of the mass function at 2=6.13 have similar uereiue histories.," This is not surprising, and reflects the fact that the rare, massive halos at the tail of the mass function at $z=6.43$ have similar merging histories." Similarly. increasing or decreasing i oa factor of three. we find ομως=SOLπάν band del=D0.6laus+. respectively.," Similarly, increasing or decreasing $\eta$ by a factor of three, we find $v_{\rm kick}=80.4~{\rm km~s^{-1}}$ and $v_{\rm kick}=50.6~{\rm km~s^{-1}}$, respectively." The sensitivity to the value of the fal DII mass is only logarithmic because of 1e exponential erowth predicted im equation 1.., The sensitivity to the value of the final BH mass is only logarithmic because of the exponential growth predicted in equation \ref{eq:Mbh}. . Thesensitivity to the adopted value of the seed mass. Aloapds the sane as tfo changing the mass of the seeds or of the final DIL is equivalent in our since the model outlined. above predicts the ratio AyMua.," Thesensitivity to the adopted value of the seed mass, $M_{\rm seed}$, is the same as to $\eta$ – changing the mass of the seeds or of the final BH is equivalent in our since the model outlined above predicts the ratio $M_{\rm bh}/M_{\rm seed}$." Towever. the seed mass is more uncertain than the inferred DII amass.," However, the seed mass is more uncertain than the inferred BH mass." Once again keeping all the other parameters fixed at their fiducial values. we find thatthe choice of Αα1. 107. and 10?AL. results iu ege=50.6. 157.5. and 332haus 1. respectively.," Once again keeping all the other parameters fixed at their fiducial values, we find thatthe choice of $M_{\rm seed}=1, 10^3$ , and $10^5~{\rm M_\odot}$ results in $v_{\rm kick}=50.6, 157.8$ , and $332~{\rm km~s^{-1}}$ , respectively." Indicatious from receut 3D simulations (Abel. Bryan Norman 2000. 2002: Dronua. Coppi Larson 1999. 2002) are that the mass of the first. ποpoor stars are a few «107AL...," Indications from recent 3D simulations (Abel, Bryan Norman 2000, 2002; Bromm, Coppi Larson 1999, 2002) are that the mass of the first, metal–poor stars are a few $\times 10^{2} \, {\rm M_\odot}$." " Nourotatiug stars with masses between ~LO110M aud above ~260M,collapse directly iuto a BIT without an explosion. whereas"," Nonrotating stars with masses between $\sim 40-140~{\rm M_\odot}$ and above $\sim 260~{\rm M_\odot}$collapse directly into a BH without an explosion, whereas" The correlation teusors are defined as where Bios. ta) are respectively the magnetic aud velocity perturbation associated with the turbulence. τι is the nonlinear decorrelation time and esscutially the cascading time of the turbulence.,"The correlation tensors are defined as where $B_{\alpha,\beta}$ , $v_{\alpha,\beta}$ are respectively the magnetic and velocity perturbation associated with the turbulence, $\tau_{k}$ is the nonlinear decorrelation time and essentially the cascading time of the turbulence." " For the balanced cascade we cousider (see discussion of our inibalanced cascade in CLVO02). Ίνοι, equal inteusity of forward aud backward waves. ΟΚ)=)."," For the balanced cascade we consider (see discussion of our imbalanced cascade in CLV02), i.e., equal intensity of forward and backward waves, $C_{ij}(\mathbf{k})=0$." The magneticOo correlatiou tensor for Alfvénnic turbulence is (CLV02). where D;—[0isa 2D tensor duong plane which is perpeudiculur to the maeuctic field. L is the clocity injection scale. V. ds —the hh3at the injection scale.," The magnetic correlation tensor for Alfvénnic turbulence is (CLV02), where $I_{ij}=\{\delta_{ij}-k_{i}k_{j}/k^{2}\}$ is a 2D tensor in $x-y$ plane which is perpendicular to the magnetic field, $L$ is the injection scale, $V$ is the velocity at the injection scale." Slow modes are passive and similar to Alfvóun modes., Slow modes are passive and similar to Alfvénn modes. The norlmalization: constant is: obtained: by assuming: equipartition:m ej=f.dh?3$774AgBGPARC/saPEROΠαπ., The normalization constant is obtained by assuming equipartition $\epsilon_{k}=\int dk^{3}\sum_{i=1}^{3}M_{ii}B_{0}^{2}/8\pi\sim B_{0}^{2}/8\pi$. The: uormalization: for the following tensors below are obtained in the same wav., The normalization for the following tensors below are obtained in the same way. " According to CLO2. fas modes are isotropic and have one dimensional euergv spectrum Lh)xk""7."," According to CL02, fast modes are isotropic and have one dimensional energy spectrum $E(k)\propto k^{-3/2}$ ." Iu low 3 medi. the corresponding correlation is (YLO3) where 0 is. the anglebetween k aud B. Γι=Αλή 2.is also à i2D teusor ine: —4g plane.," In low $\beta$ medium, the corresponding correlation is (YL03) where $\theta$ is the anglebetween $\mathbf{k}$ and $\mathbf{B}$, $H_{ij}=k_{i}k_{j}/k_{\perp}^{2}$ is also a 2D tensor in $x-y$ plane." The: factorJ cos?20 represeuts the projection as maguetic perturbation is perpeudicular to k., The factor $\cos^{2}\theta$ represents the projection as magnetic perturbation is perpendicular to $\mathbf{k}$. This teusor is different from that iu Schlickeiser Miller (1998)., This tensor is different from that in Schlickeiser Miller (1998). For isotropic turbience. the tensor of the form xEy(ó;;jL2) was obtained to satisfy the divergence free condition k:dB=0 (sce Schlickeiser 2002).," For isotropic turbulence, the tensor of the form $\propto E_{k}(\delta_{ij}-k_{i}k_{j}/k^{2})$ was obtained to satisfy the divergence free condition $\mathbf{k}\cdot\delta\mathbf{B}=0$ (see Schlickeiser 2002)." Nevertheless. the fact— kilthat 6B in fast modes is in the k-B plane places another coustraint on the eusor so that the terms à;; docsut exist.," Nevertheless, the fact that $\delta\mathbf{B}$ in fast modes is in the $\mathbf{k}$ $\mathbf{B}$ plane places another constraint on the tensor so that the term $\delta_{ij}$ doesn't exist." The motion of a charecc particle in a 1inagnetic field B cousists of the motion of the euidiug ceuter with respect to the magnetic ficld B aud the motion of the particle about the euidiug ceuter., The motion of a charged particle in a magnetic field $\Bv$ consists of the motion of the guiding center with respect to the magnetic field $\Bv$ and the motion of the particle about the guiding center. In the QLT limit. the euidiug ceuter is asstuned to follow reeular rajectory with constant pitch angle ji.," In the QLT limit, the guiding center is assumed to follow regular trajectory with constant pitch angle $\mu$." Tn MIID turbulence. B varies with respect to space and time. so 4H changes. and and ej change accordingly.," In MHD turbulence, $\Bv$ varies with respect to space and time, so $\mu$ changes, and $v_{\|}$ and $v_{\perp}$ change accordingly." Tu the NLT limit. the dispersione| of the pitch anele due to magnetic field fluctuations reads aud where By is the mean uaguctic field (W6lls 1975).," In the NLT limit, the dispersion of the pitch angle due to magnetic field fluctuations reads and, where $B_{0}$ is the mean magnetic field (Völlk 1975)." " The dispersion of parallel velocity óc| is wainly iuduced by the fluctuations of the parallel maguetic field 6B). while 92, is ouly second order effect."," The dispersion of parallel velocity $\delta v_{\|}$ is mainly induced by the fluctuations of the parallel magnetic field $\delta B_{\|}$, while $\delta B_{\perp}$ is only second order effect." Since yois constant iu the OLT. the resouance couditiouis given by ó(kjpewe| 009).,"Since $\mu$ is constant in the QLT, the resonance conditionis given by $\delta(k_{\|}\mu v-\omega+n\Omega)$ ." In the NLT. due to the fluctuations of ji (Eq. C6) ).," In the NLT, due to the fluctuations of $\mu$ (Eq. \ref{eq:dmu}) )," the resonance condition is broacened aud described by |," the resonance condition is broadened and described by + ]," to disconnect the two neighboring cells |;/] aud |;|Ly] after one timestep.,"to disconnect the two neighboring cells $[i,j]$ and $[i+1,j]$ after one timestep." " We write this condition as: Following Stone Normans notations. we finally adopt: At cach timestep. IN, values of 5; (with σον 1]. used in eq. (12))."," We write this condition as: Following Stone Norman's notations, we finally adopt: At each timestep, $N_r$ values of $n_i$ (with $i\in[0,Nr-1]$ ), used in eq. \ref{new:step7}) )," are computed using eq. (7))., are computed using eq. \ref{new:step2}) ). " These integer. values scale roughly as Πε3S""7.", These integer values scale roughly as $R_i^{-3/2}$. TheRn shift» on the ceutral parts generally. amounts to several cells over one timestep. while iu the outer parts 1; is smiadll. aud possibly zero.," The shift on the central parts generally amounts to several cells over one timestep, while in the outer parts $n_i$ is small, and possibly zero." One can wonder whether or not problems may arise κ ⋅ ↑∐↸∖⋜↧∑↕∐⋯↑∐⋜↧↕↴∖↴↕∐⋟↑↸⊳∪↥⋅↥⋅↸∖↴∖↴↻∪⋯∐∐∶↴⋁↑∪↕∐∖↑∐∐⋅≺↴∖↴∏↴⋝↴∖↴↸∖↻ ∪↕⋟↑∐↸∖⊓⋅⋜↕∐↴∖↴↻∪↥⋅↑↴∖↴↑↸∖↻↕↴∖↴↕↴∖↴↸⊳∪∐↑↕↕⋯∪∏↴∖↴⋝∙⋀∖∪↥⋅↸∖ e, One can wonder whether or not problems may arise at the radii $R_i$ where $n_i\neq n_{i-1}$ (i.e. at radii where the azimuthal shift corresponding to the third substep of the transport step is discontinuous). enerallv we want to exaumiue the question of the continuity of ay with. respect to στ)07At., More generally we want to examine the question of the continuity of $\xi^+_{ij}$ with respect to $\overline v_i^\theta\Delta t$. Tn order to check or this coutimuty. wenp) assumeyee PUC;=LL(N|5116)-\ηXE. where N ds an integer. and we work out the behavior of in the vicinity of e=0.," In order to check for this continuity, we assume $\overline v_i^\theta = \left(N+\frac{1}{2} +\epsilon\right) \frac{\Delta y_i}{\Delta t}$, where $N$ is an integer, and we work out the behavior of $\xi_{ij}^+(\epsilon)$ in the vicinity of $\epsilon=0$." Since we have to use the Gite}explicit form of the (7. uat operator. we adopt the να Leer algoritlun. (vau Leer. 1977). which is widely used.," Since we have to use the explicit form of the $*/v^{\theta a}$ ” operator, we adopt the van Leer algorithm (van Leer, 1977), which is widely used." Some straightforward algebra leads to: both for e>0 and e«0 provided [e|<4 aud where the operator “dO is the van Leer slope., Some straightforward algebra leads to: both for $\epsilon>0$ and $\epsilon<0$ provided $|\epsilon| < \frac{1}{2}$ and where the operator $d\xi$ ” is the van Leer slope. Eq. (16)), Eq. \ref{eqn:conti}) ) shows that the field {i is a contiuuous fiction of e and hence of n , shows that the field $\xi_{ij}^+$ is a continuous function of $\epsilon$ and hence of $\overline v_i^\theta$. Iu particular no special problems is to be expected from the discoutinuities of 5; across the disk., In particular no special problem is to be expected from the discontinuities of $n_i$ across the disk. As we said du section 2.. if is a conmion practice to alternate the radial 7 aud azimuthal T trausport operators every other timestep.," As we said in section \ref{sec:clas}, it is a common practice to alternate the radial $R$ and azimuthal $T$ transport operators every other timestep." Iu this modified algoritlin. R should usually be applied first. uuless the velocity field is updated just after applying the Z operator from the new momenta and new denusitv fields. or uuless special care is devoted to the jy iudices.," In this modified algorithm, $R$ should usually be applied first, unless the velocity field is updated just after applying the $T$ operator from the new momenta and new density fields, or unless special care is devoted to the $j$ indices." Indeed swapping bliudly the R aud T operators would result i moving racially the matter with the radial velocity it actually has ~4; cells upwards. and would quickly cud in a uou-plysical stagecring evervwlhnere 1;z0.," Indeed swapping blindly the $R$ and $T$ operators would result in moving radially the matter with the radial velocity it actually has $\sim n_i$ cells upwards, and would quickly end in a non-physical staggering everywhere $n_i\neq 0$." Iu order to validate this modified trausport aleorithin. we preseut some 1D tests. aud we compare the results of the standard method aud of the FARGO method ou a realistic test problem.," In order to validate this modified transport algorithm, we present some 1D tests, and we compare the results of the standard method and of the FARGO method on a realistic test problem." We solve simultaucously the continuity aud Navicr Stokes equation for an isothermal eas (which has a non-vanishiug but small kiueniatiec viscosity):, We solve simultaneously the continuity and Navier Stokes equation for an isothermal gas (which has a non-vanishing but small kinematic viscosity): NT to 934 and the contamination is reduced from. 7% to 5%.,$\sim87\%$ to $93\%$ and the contamination is reduced from $7\%$ to $5\%$. The method is illustrated in Fig. 7..," The method is illustrated in Fig. \ref{scale_power}," which jxots b against. c. averaged for⋅ the two lines.," which plots $b$ against $c$, averaged for the two lines." . As before.. the eft-hand. plot is for the WSK total sample. while the right-1and. plot shows the INSIx halo sample only.," As before, the left-hand plot is for the KSK total sample, while the right-hand plot shows the KSK halo sample only." Again the two »opulations 19112 and A/BS are clearly separated in these Mots., Again the two populations BHB and A/BS are clearly separated in these plots. The curve shown is the empirical selection boundary jiu we have chosen for this method., The curve shown is the empirical selection boundary that we have chosen for this method. Unfortunately the nmiocel curves are à very poor match to the data and therefore rave not been plotted., Unfortunately the model curves are a very poor match to the data and therefore have not been plotted. Phe problem appears to be with 16 shapes of the lines more than with than the widths., The problem appears to be with the shapes of the lines more than with than the widths. We find that the model spectra reproduce the slope of the relation between e and (21o reasonably well. but that 16 locus forthe model spectra is ollset to higher values of the parameter e.," We find that the model spectra reproduce the slope of the relation between $c$ and $(B-V)_0$ reasonably well, but that the locus forthe model spectra is offset to higher values of the parameter $c$." In other words the Balmer lines of the models are not spikey enough., In other words the Balmer lines of the models are not spikey enough. In the right-hand plot. showing the halo sample. above he line there are 31 stars classified A/BS by WKSly ancl 0 Classified DIID.," In the right-hand plot, showing the halo sample, above the line there are 31 stars classified A/BS by KSK and 0 classified BHB." Below the line there are 34 stars classified DIID ancl only 1 star classified ADS., Below the line there are 34 stars classified BHB and only 1 star classified A/BS. For reference. in the eft. hand. plot above the line there are τὸ stars classified A/BS by IxXSIx and 0 stars classified 121112. ancl below the ine there are 51 stars classified DIID and 7 stars classified A/BS.," For reference, in the left hand plot above the line there are 73 stars classified A/BS by KSK and 0 stars classified BHB, and below the line there are 51 stars classified BHB and 7 stars classified A/BS." Therclore the method appears to »e similarly effective in separating the two populations., Therefore the method appears to be similarly effective in separating the two populations. The nature of the few stars below the line. classified A/BS is discussed in 866., The nature of the few stars below the line classified A/BS is discussed in 6. Again. most appear to be anomalous by virtue of their high metallicity and can be identified: ancl removed.," Again, most appear to be anomalous by virtue of their high metallicity and can be identified and removed." We have followed the same Monte-Carlo procedure used for theColour method to establish the S/N requirements for the method., We have followed the same Monte-Carlo procedure used for the method to establish the S/N requirements for the method. Vhe results are plotted in Fig. S.., The results are plotted in Fig. \ref{bc_cont}. Here the only variable is spectroscopic S/N. The completeness and contamination for this method are slightly worse than for the method., Here the only variable is spectroscopic S/N. The completeness and contamination for this method are slightly worse than for the method. For a spectroscopic S/N of ISA ¢ the completeness is S24 (compared to A) and the contamination is 124 (compared to τά ," For a spectroscopic S/N of $15\,$ $^{-1}$ the completeness is $\sim82\%$ (compared to $87\%$ ) and the contamination is $\sim12\%$ (compared to $7\%$ )." We see that with spectroscopy alone we can separate the two populations almost as well as withtheColour method., We see that with spectroscopy alone we can separate the two populations almost as well as with the method. Because accurate photometry is not required there will clearly be circumstances where the method is preferred., Because accurate photometry is not required there will clearly be circumstances where the method is preferred. For example if the photometric accuracy of the parent catalogue from which the Atype stars are selected is significantly worse than 3% the colours ave not useful for classification., For example if the photometric accuracy of the parent catalogue from which the A–type stars are selected is significantly worse than $3\%$ the colours are not useful for classification. may then be most ellicient o simply obtain spectra of the candidate BILB stars., It may then be most efficient to simply obtain spectra of the candidate BHB stars. This savesthe time required to obtain accurate photometry. with he only penalties a small reduction in completeness. and a small increase in contamination.," This saves the time required to obtain accurate photometry, with the only penalties a small reduction in completeness and a small increase in contamination." This may well be the yest strategy for exploring the outer reaches of the Galaxy's ido using the SDSS dataset: stars at LOO kpe distance have go 21. where the error on the Sloan gior’ colour is 5% (Stoughton et al..," This may well be the best strategy for exploring the outer reaches of the Galaxy's halo using the SDSS dataset; stars at 100 kpc distance have $g^{\prime}\sim21$ , where the error on the Sloan $g^{\prime}-r^{\prime}$ colour is $5\%$ (Stoughton et al.," 2002)., 2002). Boundary conditions have often been nmupleimieuted using the so-called particles. first iutroduced. by Takeda.Mivama.&Sekiva(1991). (see also Monaghlau190 11).,"Boundary conditions have often been implemented using the so-called particles, first introduced by \citet{takeda1994} (see also \citealt{monaghan1994}) )." Ghost particles. like. SPII particles. contribute to the density of SPIT particles aud provide a pressure eradieut which prevents the latter frou approaching or penctrating the boundary.," Ghost particles, like SPH particles, contribute to the density of SPH particles and provide a pressure gradient which prevents the latter from approaching or penetrating the boundary." Clost particles can be created cyvnamically every time an ΓΗ particle ects within two smoothing leneths of the boundary., Ghost particles can be created dynamically every time an SPH particle gets within two smoothing lengths of the boundary. When this occurs. the position of cach ghost is mirrored across the boundary frou that of its parent SPIT particle (along with its mass aud deusitv).," When this occurs, the position of each ghost is mirrored across the boundary from that of its parent SPH particle (along with its mass and density)." Therefore. the need for ghosts (and a boundary) occurs only when a particle comes within reach of the boundary.," Therefore, the need for ghosts (and a boundary) occurs only when a particle comes within reach of the boundary." Tere. however. we use a slightly different approach. based on the work of Morris.Fox.&Zhu(1997) and Cunuumns&Rudman(1999).," Here, however, we use a slightly different approach, based on the work of \citet{morris1997} and \citet{cummins1999}." The approach of theseo authors differs from the mirrored-ghost technique in that the ehosts are created once. at the beeiunimg of the simulation. aud thei relative position reais fixed in time during the simulation.," The approach of these authors differs from the mirrored-ghost technique in that the ghosts are created once, at the beginning of the simulation, and their relative position remains fixed in time during the simulation." We further improve upon this techuique in order to model the outer parts of sclberavitating objects., We further improve upon this technique in order to model the outer parts of self-gravitating objects. Starting from our relaxed configurations. we identify auv particles as ghosts if they are located within three smoothing lengths inside of the boundary. which. at this poit. is arbitrarily determined.," Starting from our relaxed configurations, we identify any particles as ghosts if they are located within three smoothing lengths $\textit{inside}$ of the boundary, which, at this point, is arbitrarily determined." Particles located above the boundary are tageed as SPII particles. whereas the remaimine ones are erased and replaced by a ceutral poit mass whose total mass accouuts for both the particles romioved aud those tageed as ghosts.," Particles located above the boundary are tagged as SPH particles, whereas the remaining ones are erased and replaced by a central point mass whose total mass accounts for both the particles removed and those tagged as ghosts." Point masses interact with cach other SPII particles via the eravitational force ouly., Point masses interact with each other SPH particles via the gravitational force only. Poiut masses are also used when modelius massive or giaut brauch stars whose steep density profile iu the core is hard to resolve with SPII particles., Point masses are also used when modeling massive or giant branch stars whose steep density profile in the core is hard to resolve with SPH particles. Figure 1l illustrates how our boundary conditious are treated im our code., Figure \ref{fig:ghosts} illustrates how our boundary conditions are treated in our code. Tere. we use three smoothing leugthns of ghosts as a first safety check in order to prevent SPIT particles from penetrating the boundary.," Here, we use three smoothing lengths of ghosts as a first safety check in order to prevent SPH particles from penetrating the boundary." We also enforce that no particle goes further than one smoothing leneth inside the boundary by repositioning auv such particle above the houudary., We also enforce that no particle goes further than one smoothing length inside the boundary by repositioning any such particle above the boundary. We further ensure couscrvation of momentum bw Hupauting an equal aud opposite acceleration. to the ceutral point mnass (since the point mass aud the ghosts move together). which we write as where a; is the hydrodvuamical acceleration imparted to particle ;/ from ghost j.," We further ensure conservation of momentum by imparting an equal and opposite acceleration to the central point mass (since the point mass and the ghosts move together), which we write as where $\bfa_i$ is the hydrodynamical acceleration imparted to particle $i$ from ghost $j$." This term is added to the usual eravitational acceleration of the central point mass., This term is added to the usual gravitational acceleration of the central point mass. Ghosts are moved with the ceutral poiut mass aud are given a fixed augular velocity., Ghosts are moved with the central point mass and are given a fixed angular velocity. Note that at this point. a; has already been calculated by our code so that this calculation requires no extra CPU time.," Note that at this point, $\bfa_i$ has already been calculated by our code so that this calculation requires no extra CPU time." Cost particles are also included in the viscosity calculations to realistically iunuiec the iterface., Ghost particles are also included in the viscosity calculations to realistically mimic the interface. We now show that our new boundary condition treatinent is well suited for the modeling of stars πι lvdrostatic equilibrium., We now show that our new boundary condition treatment is well suited for the modeling of stars in hydrostatic equilibrium. We first relax a Q0.8-M. stay with rotation (c=(0.10: solar units)., We first relax a $_{\odot}$ star with rotation $\omega=0.10$; solar units). The relaxation of a star requires a fine balance between the lydrodvuamiical aud eravitational forces. aud therefore allows to assess the accuracy of our code.," The relaxation of a star requires a fine balance between the hydrodynamical and gravitational forces, and therefore allows to assess the accuracy of our code." We model our stars usine theoretical density profiles as given bv the Yale Rotational Evolution Code (YREC: Cucutheretal 1992))., We model our stars using theoretical density profiles as given by the Yale Rotational Evolution Code (YREC; \citealt{guenther1992}) ). SPII particles are first spaced equally on a hexagonal close-packed lattice extending out to the radius of the star., SPH particles are first spaced equally on a hexagonal close-packed lattice extending out to the radius of the star. The theoretical density profile is then mnatehed by iteratively assigning a lass to cach particle., The theoretical density profile is then matched by iteratively assigning a mass to each particle. Typically. particles at the ceutre of the stars are more massive than those located iu the outer reeions. bv a factor depending on the steepness of the density profile.," Typically, particles at the centre of the stars are more massive than those located in the outer regions, by a factor depending on the steepness of the density profile." As discussed by. Lombardietal.(1995). Us initial hexagonal configuration is stable against orturbations aud also tends to arise naturally during 1e relaxation of particles.," As discussed by \citet{lombardi1995}, this initial hexagonal configuration is stable against perturbations and also tends to arise naturally during the relaxation of particles." Stars are relaxed in our code Ὃν a few dyinauical times to allow for the configuration o redistribute some of its thermal energv and settle down., Stars are relaxed in our code for a few dynamical times to allow for the configuration to redistribute some of its thermal energy and settle down. Once the star has reached equilibrium. we remove he particles in the central regions and implement our )oundary conditions.," Once the star has reached equilibrium, we remove the particles in the central regions and implement our boundary conditions." We eive the star. the ghosts aud the ceutral poiut mass translational aud angular velocities.," We give the star, the ghosts and the central point mass translational and angular velocities." The final relaxed configuration of our star. with the )oundarv set to ~75% of the stays radius. is shown iu Figure 2. along with the density and pressure profiles in Fieure 3..," The final relaxed configuration of our star, with the boundary set to $\sim 75\%$ of the star's radius, is shown in Figure \ref{fig:star+ghosts1} along with the density and pressure profiles in Figure \ref{fig:star+ghosts2}." By using our initial configuration for the setup of ghosts. we ensure that the ehosts position. internal energy. aud mass are scaled to the right values and that the eusuimg pressure eradieut maintaius the elobal lydrostatic equilibrimm.," By using our initial configuration for the setup of ghosts, we ensure that the ghosts' position, internal energy, and mass are scaled to the right values and that the ensuing pressure gradient maintains the global hydrostatic equilibrium." The total energy. @vhlich includes the gravitational. kinetic. aud thermal energies) for the model of Figure 2. evolved under translation and rotation is conserved to better than 1% over the course of one full rotation.," The total energy (which includes the gravitational, kinetic, and thermal energies) for the model of Figure \ref{fig:star+ghosts1} evolved under translation and rotation is conserved to better than $1\%$ over the course of one full rotation." These results sueecst that our treatinent of boundaries is adequate for isolated stars iu translation aud rotation., These results suggest that our treatment of boundaries is adequate for isolated stars in translation and rotation. Susa~DmJy source counts.,$S_{850} \sim 5mJy$ source counts. Pherefore it would seem that at the brighter sub-nim Iluxes (2-5ni]v) we are observing the ULICG. population where as much as one third of the CIR at S50pun can be resolved into individual bright sources., Therefore it would seem that at the brighter sub-mm fluxes (2-5mJy) we are observing the ULIG population where as much as one third of the CIRB at $\umu$ m can be resolved into individual bright sources. The uncerlsing fainter population are distinct from the ULICs and are more akin to the UV Lyman Break Galaxies and. / or IUS starburst galaxies., The underlying fainter population are distinct from the ULIGs and are more akin to the UV Lyman Break Galaxies and / or IRAS starburst galaxies. In this scenario the SbOLun counts are a superposition of 2 galaxy populations. starbursts and ULICs.," In this scenario the $\umu$ m counts are a superposition of 2 galaxy populations, starbursts and ULIGs." The aim of this work has been to find an evolutionary model that can viable fit the galaxy. source counts [roni he mid-Llt to sub-mm wavelengths whilst not. violating he constraints set by the Ht. background. and. CMD nmieasurements and was not born from a fundemental ohvsical assumption., The aim of this work has been to find an evolutionary model that can viably fit the galaxy source counts from the mid-IR to sub-mm wavelengths whilst not violating the constraints set by the IR background and CMB measurements and was not born from a fundemental physical assumption. The precicament of the model discussed in this paper is how does the bimodal evolution (Lo. dual evolution) manifest itself in the evolutionary uistory of a galaxy., The predicament of the model discussed in this paper is how does the bimodal evolution (i.e. dual evolution) manifest itself in the evolutionary history of a galaxy. Are we seeing a representation of two stages of galaxy evolution of the same population or different evolutionary. paths of separate. populations?, Are we seeing a representation of two stages of galaxy evolution of the same population or different evolutionary paths of separate populations? Of the LO SCUBA sources detected at SbOtum in the Canacla-Ulx sub-mnm survey. only 2 were found to have ISO. 15tun associations implving that the ISO and SCUBA sources are in fact different. populations (or dillerent. redshift regimes) (Ealesctal.2000).," Of the 19 SCUBA sources detected at $\umu$ m in the Canada-UK sub-mm survey, only 2 were found to have ISO $\umu$ m associations implying that the ISO and SCUBA sources are in fact different populations (or different redshift regimes) \cite{eales00}." . Furthermore. what role do the ULICs play in the evolutionary history of AGN?," Furthermore, what role do the ULIGs play in the evolutionary history of AGN?" Do all QSOs go through a clusty ULIG phase secing that the space density ancl luminosities of QSOs and ULICs in the local Universe are quite similar (Soiferetal.LOST)., Do all QSOs go through a dusty ULIG phase seeing that the space density and luminosities of QSOs and ULIGs in the local Universe are quite similar \cite{soif87}. If this scenario is considered. as 2 phases of evolution then the initial Formation of the core (collapse of dark matter halo) would take place at high redshift’ accompanied. by the initial formation of a black hole and. associated star formation slowly declining towards lower redshift as the initial fuel is used up., If this scenario is considered as 2 phases of evolution then the initial formation of the core (collapse of dark matter halo) would take place at high redshift accompanied by the initial formation of a black hole and associated star formation slowly declining towards lower redshift as the initial fuel is used up. The peak in the co-moving number density of AGN is at recshifts ~2. at lower redshifts these AGN are found to be hosted. in. giant elliptical galaxies (AleClureetal.1999).," The peak in the co-moving number density of AGN is at redshifts $\sim$ 2, at lower redshifts these AGN are found to be hosted in giant elliptical galaxies \cite{mcclure99}." .. Thus the mid-LI 3-30um SED max be indicativo of the galaxies merging at lower redshifts activating / re-activating the central black hole where at, Thus the mid-IR 3-30um SED may be indicative of the galaxies merging at lower redshifts activating / re-activating the central black hole where at with J=ρατνPod5 ⋅ clui,"with $\beta \equiv \rho_g \kappa_{IR} \, T_g^4 + \sum_{i=d,c} n_i \, \pi a_i^2 \, \epsilon_i$." ssivity of a grain of type ;/ averaged over the Plauck function at temperature T;Ge). which we simply set at 1.0 (for comparison. Desch&Connolly(2002) uses values of 0.5 and O0. for Tani and μπι μίσος. grains. respectively). and £j is £the exponential iutegral of the first type.," Here, $\epsilon_i$ is the emissivity of a grain of type $i$ averaged over the Planck function at temperature $T_i (x)$, which we simply set at 1.0 (for comparison, \citet{des02} uses values of 0.8 and 0.4 for $\mm$ - and $\mum$ -sized grains, respectively), and $E_1$ is the exponential integral of the first type." Dust erains and choudrules. on the other haud. are heated both by colliding with hotter gas molecules aud by absorbing radiation from nearby smaller. muicron-sized. eraius which reach high temperatures quickly.," Dust grains and chondrules, on the other hand, are heated both by colliding with hotter gas molecules and by absorbing radiation from nearby smaller, micron-sized, grains which reach high temperatures quickly." Thev lose energy bx vacating an approximate blackbody spectrum at Z; aud I.. with cuussion efficiency of e; anc e. for dust aud choudrules. respectively.," They lose energy by radiating an approximate blackbody spectrum at $T_d$ and $T_c$, with emission efficiency of $\epsilon_d$ and $\epsilon_c$ for dust and chondrules, respectively." Therefore. As before. the index { can be either d (for dust) or € (for chonudrule).," Therefore, As before, the index $i$ can be either $d$ (for dust) or $c$ (for chondrule)." The last term in Equ. (18)), The last term in Eqn. \ref{td}) ) represents the incident flux on a given particle radiated by dust eraius in the other zoues minus its owl enission., represents the incident flux on a given particle radiated by dust grains in the other zones minus its own emission. " The experimental coustraints ou chondrule forination are (1) the erains are completely melted for a few unites: (2) the cooling timescale of gas aud dust is approximately an hour. consistent with the oft-quoted value of 102. 10° I. Ἐν and (3) small erains Cz Ο.Τ nun) are absent. possibly evaporated or destroved completely after passing through a current sheet. leacing to the observed narrow size distribution centered at 4,2: 1 nua."," The experimental constraints on chondrule formation are (1) the grains are completely melted for a few minutes; (2) the cooling timescale of gas and dust is approximately an hour, consistent with the oft-quoted value of $10^2$ $10^3$ K $^{-1}$; and (3) small grains $\lesssim$ 0.1 mm) are absent, possibly evaporated or destroyed completely after passing through a current sheet, leading to the observed narrow size distribution centered at $a_d \approx$ 1 mm." Froii the properties of current sheets described iu rofformics- 2.1. we infer that the above constraints on choudrule formation will be satisfied ouly if the following conditions are moet: ((1) In order to obtain high enough heating rate. the gas deusity has to be low (iyEz1012 οι 2) because the heating rate increases steeply as ay decreases. (," From the properties of current sheets described in \\ref{formcs}- \ref{hmech}, we infer that the above constraints on chondrule formation will be satisfied only if the following conditions are met: (1) In order to obtain high enough heating rate, the gas density has to be low $n_g \lesssim 10^{12}$ $^{-3}$ ), because the heating rate increases steeply as $n_g$ decreases. (" (2) To have “localized” heating eveuts. spatially average chondrile/dust densities should be lieh (2;71 ?).,"2) To have ""localized"" heating events, spatially averaged chondrule/dust densities should be high $n_d > 1$ $^{-3}$ )." " Otherwise. the mean free path for IR photons will excecc a few hundred kilometers aud the heating timescale wil be much more than ""a few minutes."" ("," Otherwise, the mean free path for IR photons will exceed a few hundred kilometers and the heating timescale will be much more than “a few minutes.” (" "(3) To eusure good thermal coupling between gas ik dust. either the gas deusity has to be high (vy,=Lal? cin 3) because po Yeo&Ng Which cannot be satisfiec because of the first condition. or dust grains need to be verv unall (44Z μια) κο they approach T, quickly.","3) To ensure good thermal coupling between gas and dust, either the gas density has to be high $n_g \gtrsim 10^{12}$ $^{-3}$ ) because $q_d$, $q_c \propto n_g$ which cannot be satisfied because of the first condition, or dust grains need to be very small $a_d \lesssim 1 \mum$ ) so they approach $T_g$ quickly." " Iu order to satisfv couditious (1).(3) simultaneously. the dust-to-eas mass ratio. ο, should be very large. about 50."," In order to satisfy conditions (1)–(3) simultaneously, the dust-to-gas mass ratio, $\zeta$, should be very large, about 50." " Usually ¢&0,01 is asstumed for the minima mass solar uchula. but after a few οι wears the gas deusitv is expected to have decreased due to viscous diffusion (Budeu&Lin1986) as well as the various iiechiauisuis mentioned in the last paragraph of reflunech.."," Usually $\zeta \approx 0.01$ is assumed for the minimum mass solar nebula, but after a few million years the gas density is expected to have decreased due to viscous diffusion \citep{rud86} as well as the various mechanisms mentioned in the last paragraph of \\ref{hmech}." Dust settles iuto a thin. dense laver on a timescale r4c5(algun)the Myr. indepeudent of R (Rudeu1999.C€6/97). comparable to the lifetimes of protoplauetary disks.," Dust settles into a thin, dense layer on a timescale $\tau_s \approx (a/1 \mum)^{-1} f_{\Sigma}$ Myr, independent of $R$ \citep[][CG97]{rud99}, comparable to the lifetimes of protoplanetary disks." There will still be some dust grains. particularly παπομίσος oues. that remain well above the midplane mixed with the eas.," There will still be some dust grains, particularly submicron-sized ones, that remain well above the midplane mixed with the gas." But at late times the dust deusitv outside the thin. deuse dust laver is likely to be quite small. decreasing the dust-to-gas ratio there.," But at late times the dust density outside the thin, dense dust layer is likely to be quite small, decreasing the dust-to-gas ratio there." Tusice the dust laver. however. solids may dominate the local density (Cuzz.Dobrovolskis.," Inside the dust layer, however, solids may dominate the local density \citep{cuz93}." &Champuev1993).. IIeuce. à&50 may be reached in the müdplanue. where most solids reside.," Hence, $\zeta \approx 50$ may be reached in the midplane, where most solids reside." We solve Equs. (16)). (18)), We solve Eqns. \ref{tg}) \ref{td}) ) simultaneously for Tyr.f). TuGe.f). and T.Ge.f) using a fifth-order Runee-hutta scheme appropriate for a stiff set of equations with adaptive stepsize control (Pressctal.1992).," simultaneously for $T_g(x, t)$, $T_d(x, t)$, and $T_c(x, t)$ using a fifth-order Runge-Kutta scheme appropriate for a stiff set of equations with adaptive stepsize control \citep{pre92}." ". Both gas aud dust particles begin at the same temperature. 7;,;;=500 Ix. The center of a current sheet is initially placed at w=L000 Ian aud moves to the left at ο."," Both gas and dust particles begin at the same temperature, $T_{init} = 500$ K. The center of a current sheet is initially placed at $x=1000$ km and moves to the left at $v_r$." To simplity the problem. we ignore the time evolution of 5 and Y; (sec reftcaveats)).," To simplify the problem, we ignore the time evolution of $\varepsilon$ and $\chi_i$ (see \\ref{caveats}) )." For our fiducial model. ig=1013 ci? and both vy and ny. are set to vield desired values of the ratio GC.," For our fiducial model, $n_g = 10^{12}$ $^{-3}$ and both $n_d$ and $n_c$ are set to yield desired values of the dust-to-gas ratio $\zeta$." Figure |. shows the time evolution of eas. dust. aud chondiule temperatures at a fixed position as a curent sheet moves through. for our model rams with à= (5. 50).," Figure \ref{fig4} shows the time evolution of gas, dust, and chondrule temperatures at a fixed position as a current sheet moves through, for our model runs with $\zeta=$ (5, 50)." " We also ran the code for ¢=0.05 but do not plot the result because both Fy aud T. remain practically uuchauged at Ti; for over LO’ s. We find that for ¢=5 the gas telmperature rises appreciably (above 1000 I&) but. due to poor thermal coupling between gas and dust. neither T; nor 7, chauges significantly. reaching ouly ~700 Is after 10? s. Tn the run with à= 50. however. due to the increase in optical depth. dust erains follow the gas temperature closely and the radiation field also steadily imereases im streneth."," We also ran the code for $\zeta=0.05$ but do not plot the result because both $T_d$ and $T_c$ remain practically unchanged at $T_{init}$ for over $10^3$ s. We find that for $\zeta = 5$ the gas temperature rises appreciably (above 1000 K) but, due to poor thermal coupling between gas and dust, neither $T_d$ nor $T_c$ changes significantly, reaching only $\sim 700$ K after $^3$ s. In the run with $\zeta=$ 50, however, due to the increase in optical depth, dust grains follow the gas temperature closely and the radiation field also steadily increases in strength." The erains melt after about 570 seconds aud evaporate after about 630 secouds. at which point we stop the simulation. as it docs not take iuto account the evaporation of particles.," The grains melt after about 570 seconds and evaporate after about 630 seconds, at which point we stop the simulation, as it does not take into account the evaporation of particles." " We changed the bouudiurv condition between fat at 7;,;5; aud a floating boundary condition but found the result remained qualitatively the same.", We changed the boundary condition between flat at $T_{init}$ and a floating boundary condition but found the result remained qualitatively the same. Iu au improved model that accounts for evaporation and a range of dust erain sizes. we expect the smallest erains to evaporate first. decreasing the optical depth. thus widening the heated region aud lowering the uct vohuuetric heating rate.," In an improved model that accounts for evaporation and a range of dust grain sizes, we expect the smallest grains to evaporate first, decreasing the optical depth, thus widening the heated region and lowering the net volumetric heating rate." The larger grams will therefore probably not evaporate., The larger grains will therefore probably not evaporate. This is interesting since it could naturally explain the peaking of the size distribution of chondrules around 1 nuu., This is interesting since it could naturally explain the peaking of the size distribution of chondrules around 1 mm. The fact that chondrules ect melted ouly for high values of¢ is cousistent with the FeO record in choudrules. which seclus to indicate oxveen fugacitics (relative abundance of oxveen to hydrogen) at formation that are higher than solar values by at least two or three orders of magnuitud (Wood1967).," The fact that chondrules get melted only for high values of $\zeta$ is consistent with the FeO record in chondrules, which seems to indicate oxygen fugacities (relative abundance of oxygen to hydrogen) at formation that are higher than solar values by at least two or three orders of magnitude \citep{woo67}." This is most often interpreted to mean hat chondrules were heated in regions with extremely Hel dust-to-gas ratios., This is most often interpreted to mean that chondrules were heated in regions with extremely high dust-to-gas ratios. The dust is taken to be oxides of Si. Me. Ca. AL ete.," The dust is taken to be oxides of Si, Mg, Ca, Al, etc." in chondritic proportions which ning iu a huge amount of oxvgeu., in chondritic proportions which bring in a large amount of oxygen. For this reason also. it is advantascous to evaporate the smaller eraius first ICuu then oxides will be incorporated iuto the gas and the partial pressures of condenusable elemieuts will increase locally.," For this reason also, it is advantageous to evaporate the smaller grains first because then oxides will be incorporated into the gas and the partial pressures of condensable elements will increase locally." This helps to make liquids stable at eh temperature. and also suppresses the evaporation of silicate liquids which would have caused heavy isotope chrichiment of resulting choudrules: such curichiuent is not observed. (Cally.Young.Ash.&Q'Nious 2000)..," This helps to make liquids stable at high temperature, and also suppresses the evaporation of silicate liquids which would have caused heavy isotope enrichment of resulting chondrules; such enrichment is not observed \citep{gal00}. ." coincidence if the Charming Rinelet just lBiappeued to fall at a location where both angles could be effectively coustrainect.,coincidence if the Charming Ringlet just happened to fall at a location where both angles could be effectively constrained. " A rinelet with finite free eccentricity aud [ree inclination can iu principle fori spontaneously without auy terms in the equations of motion that clepeucd explicitly on a, aud Qj. aud without auy stroug asvimuuetry in the particle's initial conditions."," A ringlet with finite free eccentricity and free inclination can in principle form spontaneously without any terms in the equations of motion that depend explicitly on $\varpi_l$ and $\Omega_l$, and without any strong asymmetry in the particle's initial conditions." Such phenomena have been cliscussecl almost exclusively ---1 the coutext of massive. cdeuse ringlets 1935).," Such phenomena have been discussed almost exclusively in the context of massive, dense ringlets \citep{BGT85}." " However. one can argue that this sort of ""spontaneous syimiuetry-breaking could also occur iu low-optical-depth clusty riugs via dissipative processes like collisions. provided that there are terius in the individual particle's equations of motion that favor the development oL a nonzero e; aud 4; comparable to those observed [or the eutire ringlet."," However, one can argue that this sort of “spontaneous symmetry-breaking” could also occur in low-optical-depth dusty rings via dissipative processes like collisions, provided that there are terms in the individual particle's equations of motion that favor the development of a nonzero $e_l$ and $i_l$ comparable to those observed for the entire ringlet." Dissipative collisious are often. invoked as a mechanism that causes narrow rings to spread in semi-major axis (GoldreichandTremaine1952).. so it might seem surprising tliat such collisions could also aligu pericenter or node locations.," Dissipative collisions are often invoked as a mechanism that causes narrow rings to spread in semi-major axis \citep{GT82}, so it might seem surprising that such collisions could also align pericenter or node locations." However. uulike tle semi-major axis. the longitudes of periceuter aud node have no direct ellect on a particles. orbital euergy.," However, unlike the semi-major axis, the longitudes of pericenter and node have no direct effect on a particles' orbital energy." Thus. while the dissipation of orbital energy requires that particles’ orbital semi-mnajor axes evolve iu a particular direction. this is not the case for pericenters or uodes.," Thus, while the dissipation of orbital energy requires that particles' orbital semi-major axes evolve in a particular direction, this is not the case for pericenters or nodes." Iustead. the evolution of pericenters and nodes should be driven primarily by the collisous’ dissipation of relative motions.," Instead, the evolution of pericenters and nodes should be driven primarily by the collisons' dissipation of relative motions." To illustrate how such collisions can aligue pericenters and nodes. cousider the followingOm simple situation: There is a riuglet composed of many particles with similar orbital properties. aud there is a single particle whose orbit is misaligned with the others.," To illustrate how such collisions can align pericenters and nodes, consider the following simple situation: There is a ringlet composed of many particles with similar orbital properties, and there is a single particle whose orbit is misaligned with the others." For simplicity. assume that both the riuglet aud the particle have zero eccentricity auc zero forced inclination.," For simplicity, assume that both the ringlet and the particle have zero eccentricity and zero forced inclination." " Furthermore. assume that both the ringlet aud the particle have the same free inclination i but different longitudes of ascending node Q, and Ορ. respectively."," Furthermore, assume that both the ringlet and the particle have the same free inclination $i$ but different longitudes of ascending node $\Omega_r$ and $\Omega_p$, respectively." " LQ,4OQ). then the particle's orbit will cross the ringlet at two longitudes A.—(0570,)/2zE/2."," If $\Omega_r\ne \Omega_p$, then the particle's orbit will cross the ringlet at two longitudes $\lambda_c=(\Omega_p+\Omega_r)/2 \pm \pi/2$." At these two lougitudes the particle will feel a force due to its collisions with the particles in the ringlet. aud the vertical component of that force Εν. will be proportional to the vertical velocity ol the particles in the ringlet. so £F.xcos(A.—ο).," At these two longitudes the particle will feel a force due to its collisions with the particles in the ringlet, and the vertical component of that force $F_z$ will be proportional to the vertical velocity of the particles in the ringlet, so $F_z \propto \cos(\lambda_c-\Omega_r)$." Luserting this into Equation 1L. we can express tlie perturbation to the particle's node position due to its interactions with the ringlet as: where D is a coustant.," Inserting this into Equation \ref{dOdt}, we can express the perturbation to the particle's node position due to its interactions with the ringlet as: where $D$ is a constant." " Substituting in the above expression for the crossing longitudes A, aud situplifvine. this expression reduces to the simple form: The forces applied to the particle’s orbit during the ringlet crossings therefore do tend to align the particle's orbital node position with that of the ringlet."," Substituting in the above expression for the crossing longitudes $\lambda_c$ and simplifying, this expression reduces to the simple form: The forces applied to the particle's orbit during the ringlet crossings therefore do tend to align the particle's orbital node position with that of the ringlet." A similar calculation, A similar calculation of ionization equilibrium (IE). we perform simulations where the chemical composition ts directly computed by integration of the corresponding differential equations. and check for differences between the two cases.,"of ionization equilibrium (IE), we perform simulations where the chemical composition is directly computed by integration of the corresponding differential equations, and check for differences between the two cases." While in many cases IE is a valid assumption. deviations from equilibrium may occur. in particular at low densities.," While in many cases IE is a valid assumption, deviations from equilibrium may occur, in particular at low densities." Furthermore we consider the role of thermal conduction., Furthermore we consider the role of thermal conduction. Heat conduction was also included by ? considering the problem of cooling pancakes with analytical methods., Heat conduction was also included by \citet{Bond84} considering the problem of cooling pancakes with analytical methods. At certain conditions very high temperature gradients are expected to occur., At certain conditions very high temperature gradients are expected to occur. This may happen particularly in the vicinity of shock fronts., This may happen particularly in the vicinity of shock fronts. Then. thermal conduction can lead to a considerable change of the temperature profiles.," Then, thermal conduction can lead to a considerable change of the temperature profiles." In the cases to be considered here. the gas is almost fully ionized and the expression for the heat conduction coetficient from ? can be used.," In the cases to be considered here, the gas is almost fully ionized and the expression for the heat conduction coefficient from \citet{Sarazin88} can be used." The distribution of the gas in the structures of the WHIM (sheets and filaments) is supposed to be very close to that of the dark matter., The distribution of the gas in the structures of the WHIM (sheets and filaments) is supposed to be very close to that of the dark matter. This is true even at late evolution stages., This is true even at late evolution stages. In order to simplify the calculations. we consider the baryonte content of the Universe only and therefore decrease the number of equations to be solved.," In order to simplify the calculations, we consider the baryonic content of the Universe only and therefore decrease the number of equations to be solved." Because this would neglect the gravitational mass of the dark matter. we assume that the dark matter obeys the same spatial distribution as. the baryons.," Because this would neglect the gravitational mass of the dark matter, we assume that the dark matter obeys the same spatial distribution as the baryons." Concordantly. we rescale the baryonic density to the total cosmic matter density when computing the gravitational potential.," Concordantly, we rescale the baryonic density to the total cosmic matter density when computing the gravitational potential." For test cases. we checked our results for deviations from the solutions including the full dark matter dynamies.," For test cases, we checked our results for deviations from the solutions including the full dark matter dynamics." For that purpose. we used the code (?) and appropriate initial conditions.," For that purpose, we used the code \citep{Teyssier02} and appropriate initial conditions." The deviation is negligible for the structures considered here. Though considering preferentially one-mode perturbations. we also investigate up to which degree small-scale perturbations may affect the results.," The deviation is negligible for the structures considered here, Though considering preferentially one-mode perturbations, we also investigate up to which degree small-scale perturbations may affect the results." For that purpose. we add Gaussian random perturbations according to the cosmological initial power-spectrum.," For that purpose, we add Gaussian random perturbations according to the cosmological initial power-spectrum." The spatial scale sizes of these fluctuations are lower compared to that of the considered large-scale single node. but much higher than the (comoving) initial Jeans length immediately after reionization.," The spatial scale sizes of these fluctuations are lower compared to that of the considered large-scale single mode, but much higher than the (comoving) initial Jeans length immediately after reionization." We will compare the various resulting density and temperature profiles., We will compare the various resulting density and temperature profiles. We use the standard approach for deseribing the baryonic component of the universe., We use the standard approach for describing the baryonic component of the universe. The assumed ideal polytropic fluid is described by the Euler equations. which may be considered as conservation laws for the quantities: the density p. the momentum densities pu (u denotes the vector of velocities) and the energy density E.," The assumed ideal polytropic fluid is described by the Euler equations, which may be considered as conservation laws for the : the density $\rho$ , the momentum densities $\rho \mathbf{u}$ $\mathbf{u}$ denotes the vector of velocities) and the energy density $E$." The latter is the sum of the kineticenergy density Εκ=1/2pul and the internal energy density Ej.The internal energy density is relatedto thepressure p by the polytropic equation of state p=(y—1)Ej. where y denotes the adiabatic index of the gas.," The latter is the sum of the kineticenergy density $E_{kin} = 1/2 \, \rho |\mathbf{u}|^2$ and the internal energy density $E_{th}$.The internal energy density is relatedto thepressure $p$ by the polytropic equation of state $p = \left( \gamma - 1 \right) E_{th}$, where $\gamma$ denotes the adiabatic index of the gas." Throughout this paper we use the adiabatic coefficient for a mono-atomic gas. Le.y-5/3.," Throughout this paper we use the adiabatic coefficient for a mono-atomic gas, i.e., $\gamma = 5/3$ ." In order to include the cosmological expansion intoour simulations we use (2).., In order to include the cosmological expansion intoour simulations we use \citep{MartelShapiro98}. This is a transformation of the physical coordinate r and the time { into the supercomoving coordinates X=(v.v.2)r/a and the conformal time dr.=dr/«. where a is the cosmological expansion factor computed from the Friedman equation.," This is a transformation of the physical coordinate $\mathbf{r}$ and the time $t$ into the supercomoving coordinates $\mathbf{x} = (x,y,z) = \mathbf{r} / a$ and the conformal time $\textrm{d}\tau = \textrm{d}t / a^2$, where $a$ is the cosmological expansion factor computed from the Friedman equation." " We use à ACDM cosmology with the parameters derived from the five-year WMAP observations (?) Q4=0.73. Q,,=0.27. and Ho=71 Mpe km! s7!."," We use a $\Lambda$ CDM cosmology with the parameters derived from the five-year WMAP observations \citep{Komatsu09} $\Omega_\Lambda = 0.73$, $\Omega_m = 0.27$, and $H_0 = 71$ Mpc $^{-1}$ $^{-1}$." " The transformed Euler-equations that are used throughout this paper are These equations already include the change in energy owing to the heating function Ε, the cooling function A. and the heat flux j caused by thermal conduction."," The transformed Euler-equations that are used throughout this paper are These equations already include the change in energy owing to the heating function $\Gamma$, the cooling function $\Lambda$, and the heat flux $\mathbf{j}$ caused by thermal conduction." The gravitational potential @ is computed using the supercomoving version of Poisson's equation where p denotes the uniform background density of the Universe and pu the total matter density (baryons + dark matter)., The gravitational potential $\phi$ is computed using the supercomoving version of Poisson's equation where $\bar{\rho}$ denotes the uniform background density of the Universe and $\rho_\mathrm{tot}$ the total matter density (baryons + dark matter). " As already mentioned. we assume similar spatial distributions for the dark matter and the baryons. and therefore compute the total matter density by po.=e/fg assuming a baryon fraction of fp=O,/0,,0.16."," As already mentioned, we assume similar spatial distributions for the dark matter and the baryons, and therefore compute the total matter density by $\rho_\mathrm{tot} = \rho / f_B$ assuming a baryon fraction of $f_B = \Omega_b / \Omega_m = 0.16$." Equation (4)) deseribes the evolution of the modified entropy density $= p/p’~!. which is necessary for the dual-energy formalism described inthe Appendix B.2...," Equation \ref{eS}) ) describes the evolution of the modified entropy density $S = p / \rho^{\gamma- 1}$ , which is necessary for the dual-energy formalism described inthe Appendix \ref{aHighMach}. ." " It can be ""Slerived from Eq.", It can be derived from Eq. (1. - 3))., \ref{eRho} - \ref{eE}) ). The only difference of Eq., The only difference of Eq. (1. - 59) with respect to the non-comoving equations is the factor a in Eq. (5)) (, \ref{eRho} - \ref{ePoisson}) ) with respect to the non-comoving equations is the factor $a$ in Eq. \ref{ePoisson}) ) ( anadditional drag term would occur in Eq. (3) ,anadditional drag term would occur in Eq. \ref{eE}) ) and Eq. (4) , and Eq. \ref{eS}) ) for yz 5/3), for $\gamma \neq 5/3$ ). An extensive derivation of the supercomoving coordinates Is given in the Appendix of ?.., An extensive derivation of the supercomoving coordinates is given in the Appendix of \citet{Doumler09}. " In order to follow the chemical network an equation of continuity for the number densities 77; is needed: where =, denotes the source term due to chemical processes.", In order to follow the chemical network an equation of continuity for the number densities $n_i$ is needed: where $\Xi_i$ denotes the source term due to chemical processes. The index / indicatesthe fivedifferent species H1. Hu. Het. i. and ur.," The index $i$ indicatesthe fivedifferent species , , , , and ." The electron number density can be computed using charge conservation: Initially. the number densities can be computed from the densityby nj=y; p/nin. where y; denotes the primordial mass fraction of Hydrogen yy=0.76 or Helium yy.= 0.24. respectively.and ju; is thecorresponding atomic mass.," The electron number density can be computed using charge conservation: Initially, the number densities can be computed from the densityby $n_i = \chi_i \, \rho / m_i$ , where $\chi_i$ denotes the primordial mass fraction of Hydrogen $\chi_\ion{H}{} = 0.76$ or Helium $\chi_\ion{He}{} = 0.24$ , respectively,and $m_i$ is thecorresponding atomic mass." The, The The degree of linear polarization p is given by The work of Μούσες(1962) aud Preiseudorler.(1965) on the interaction principle have been formalized by Crant&Hunt(1969).. ναί Hunt. (1969a) with the introduction of the internal sources which is crucial for the stellar atmospheres.,"The degree of linear polarization p is given by The work of \cite{redheffer62} and \cite{pre65} on the interaction principle have been formalized by \cite{grant69}, Grant Hunt (1969a) with the introduction of the internal sources which is crucial for the stellar atmospheres." Following this work. Ciraut aud Peraiah&ναί(1973) developed a method to obtain direct solution of the trausfer equations.," Following this work, \cite{grant72} and \cite{peraiah73} developed a method to obtain direct solution of the transfer equations." This method is called the discrete space theory of Badiative Trausfer., This method is called the discrete space theory of Radiative Transfer. In the present work the method due to Peraiah&(ανα(1973). has been employed to solve the radiative transfer equations in their vector form for linear polarization., In the present work the method due to \cite{peraiah73} has been employed to solve the radiative transfer equations in their vector form for linear polarization. " In this inethod. the entire mecitum is divided into N number of shells aud it is assumed that the specific intensities Z,ul aud J,4 are incident at the boundaries » aud à41 respectively of the shell with optical thickness 7."," In this method, the entire medium is divided into N number of shells and it is assumed that the specific intensities $I^{+}_{n}$ and $I_{n +1}^{-}$ are incident at the boundaries $n$ and $n+1$ respectively of the shell with optical thickness $\tau$." The symbols with sigus + aud - represent specific intensities of the rays travelling in opposite directious., The symbols with signs + and - represent specific intensities of the rays travelling in opposite directions. If ji represents the cosine of the angle iade by a ray with the uormal to the plane parallel layers iu the direction in which the geometrical depth decreases., If $\mu$ represents the cosine of the angle made by a ray with the normal to the plane parallel layers in the direction in which the geometrical depth decreases. " That ls. aud L,n represents the specific intensity of the ray travelling in the direction i aud 4ul represents the specific intensity of the ray travelling in the opposite direction."," That is, and $I_{n}^{+}$ represents the specific intensity of the ray travelling in the direction $\mu$ and $I^{-}_{n}$ represents the specific intensity of the ray travelling in the opposite direction." We select a finite set of values ο py:1SpSeO«mqu 0.25) or green ([Ou1]//H8« 0.25) symbols."," The region samples introduced in \ref{sec:obs} are represented by the grey dots, whilst our targets in NGC 4625 are shown either with cyan $\beta > 0.25$ ) or green $\beta < 0.25$ ) symbols." The zero-age models in Fig., The zero-age models in Fig. 6 lie on top of the ionisation sequence defined by the main extragalactic sample of giant rregions., \ref{fig:mod1} lie on top of the ionisation sequence defined by the main extragalactic sample of giant regions. " The models show that, as the rregions evolve with time after the initial burst of star formation, the eemission rapidly decreases, and the good match with the observational data quickly disappears (see earlier results by ?))."," The models show that, as the regions evolve with time after the initial burst of star formation, the emission rapidly decreases, and the good match with the observational data quickly disappears (see earlier results by )." The models also depart from the main ionisation sequence to lower, The models also depart from the main ionisation sequence to lower On the surface of the compact star and. the outer numerical bouncary the free outflow conditions are used.,On the surface of the compact star and the outer numerical boundary the free outflow conditions are used. " As initial conditions the low-clensity ambient matter (p~10 ""pg) in rest in the rotational frame is accepted.", As initial conditions the low-density ambient matter $\rho\sim10^{-6}\rho_0$ ) in rest in the rotational frame is accepted. Subsequently. this matter is forced out from the svstem by the eas injecting from mass-losing star.," Subsequently, this matter is forced out from the system by the gas injecting from mass-losing star." The main question for numerical simulation of the Ηντονπας models is the choosing of solving methoc and appropriate scheme Lor the svstem of equations., The main question for numerical simulation of the hydrodynamic models is the choosing of solving method and appropriate scheme for the system of equations. Among the large variety. of finite-dillerence schemes the so-callec CGodunov-tvpe schemes (ιομον 1959) are considered. to be the most exact ones., Among the large variety of finite-difference schemes the so-called Godunov-type schemes (Godunov 1959) are considered to be the most exact ones. In the present work. we use the modification of explicit PVD Roc scheme (oc 1986) for numerical solving of the svstem of hydrodynamic equations.," In the present work, we use the modification of explicit TVD Roe scheme (Roe 1986) for numerical solving of the system of hydrodynamic equations." Phe origina scheme (first order of spatial approximation) is mocified by monotonic Ilux limiters in the Osher's form (Chakravarthy Osher 1985) that makes the scheme of third order of approximation., The original scheme (first order of spatial approximation) is modified by monotonic flux limiters in the Osher's form (Chakravarthy Osher 1985) that makes the scheme of third order of approximation. The special model simulations show. that the given scheme permits to. describe adequately the [low structure including shock waves anc tangential discontinuities anc does not result in artificial Ductuations and smearing of features of ow.," The special model simulations show, that the given scheme permits to describe adequately the flow structure including shock waves and tangential discontinuities and does not result in artificial fluctuations and smearing of features of flow." Moreover the used scheme permits to consider the Lows with large density gradients. that of special importance for consideration of the influence of cireumbinary envelope on the How structure.," Moreover the used scheme permits to consider the flows with large density gradients, that of special importance for consideration of the influence of circumbinary envelope on the flow structure." The system of hvdrodynamie equations is solved in Cartesian coordinate system. which is predetermined: as follows: the zero of coordinate system is located in the centre of mass-losing star: X axis is clirected from the centre of mass-losing star to the accretor: Z axis is directed along the axis of orbital rotation: ) is determined to get right-handed coordinate syslem.," The system of hydrodynamic equations is solved in Cartesian coordinate system, which is predetermined as follows: – the zero of coordinate system is located in the centre of mass-losing star; – $X$ axis is directed from the centre of mass-losing star to the accretor; – $Z$ axis is directed along the axis of orbital rotation; – $Y$ is determined to get right-handed coordinate system." The computation region is a parallelepipedon AQAA0.4] (clue to symmetry about the equatorial plane calculations were conducted only in the top half-space)., The computation region is a parallelepipedon $[-A..2A]\times[-A..A]\times[0..A]$ (due to symmetry about the equatorial plane calculations were conducted only in the top half-space). Non-uniform cillerence grids (more fine near the accretor) containing 78«GO.35 gridpoints for the system X1822-371 and δε65«33 eridpoints for the svstem Z Cha is usec., Non-uniform difference grids (more fine near the accretor) containing $78\times 60\times 35$ gridpoints for the system X1822-371 and $84\times 65\times 33$ gridpoints for the system Z Cha is used. Solving of the system. of equations has been carried out [rom initial conditions up to the steady-state regime., Solving of the system of equations has been carried out from initial conditions up to the steady-state regime. To check the establishment of the steady-state. regine we have numerically monitored. Bow. parameters. (density and pressure) as a function. of time., To check the establishment of the steady-state regime we have numerically monitored flow parameters (density and pressure) as a function of time. We have checked these parameters inside the spheres around aceretor (with different radii) ancl inside the sphere closed to the outer boundary., We have checked these parameters inside the spheres around accretor (with different radii) and inside the sphere closed to the outer boundary. When the How patterns do not depend on the time we suppose that steady-state is reached., When the flow patterns do not depend on the time we suppose that steady-state is reached. To assure that the obtained solution is steady we have continued the calculations adcditionallv curing 35 orbital periods., To assure that the obtained solution is steady we have continued the calculations additionally during 3–5 orbital periods. The runs have been stopped at 12 orbital period for N1822-371. and at 20 orbital periods for Z Cha.," The runs have been stopped at 12 orbital period for X1822-371, and at 20 orbital periods for Z Cha." " Characteristic time step in both runs is approximately 10! orbital period. so the total number of steps is ~L2«10* and ~2«10"" accordingly."," Characteristic time step in both runs is approximately $10^{-4}$ orbital period, so the total number of steps is $\sim 1.2 \times 10^5$ and $\sim 2 \times 10^5$ accordingly." Rus have been conducted on NEC ALPILA computer (Alphastation 250 4/266). and CPU time per 1 eridpoint was approximately equal to S10.7 seconds.," Runs have been conducted on NEC ALPHA computer (AlphaStation 250 4/266), and CPU time per 1 gridpoint was approximately equal to $8 \times 10^{-5}$ seconds." The total CPU time for both runs is approximately 1: month., The total CPU time for both runs is approximately 1 month. Let us consider the characteristic features of the [Bow structure in. semüdetached binaries. obtained in. the framework of 3D hydrodynamic model described in Section 2.," Let us consider the characteristic features of the flow structure in semidetached binaries, obtained in the framework of 3D hydrodynamic model described in Section 2." As it was mentioned above. the calculations have been carried out. for tvpical representatives LAINBs anc CVs.," As it was mentioned above, the calculations have been carried out for typical representatives LMXBs and CVs." The obtained results testify qualitatively similar nature of he How in considered systems. that. in turn. permits to establish the general character of the steady How structures or semidetached non-magnetic binaries.," The obtained results testify qualitatively similar nature of the flow in considered systems, that, in turn, permits to establish the general character of the steady flow structures for semidetached non-magnetic binaries." ‘Taking into account the qualitative similarity of results. he general properties of How structure will be described xdow for the X1822-371 svstem.," Taking into account the qualitative similarity of results, the general properties of flow structure will be described below for the X1822-371 system." The results obtained [or he system. Z Cha will be used to discuss the quantitative characteristics., The results obtained for the system Z Cha will be used to discuss the quantitative characteristics. The general structure of the gaseous Hows. illustrating the morphology of mass transfer in the system. N1822-371. is presented in Fig.," The general structure of the gaseous flows, illustrating the morphology of mass transfer in the system X1822-371, is presented in Fig." 1l. where 3D. view of density isosurface at the level 0.005pu is shown.," 1, where 3D view of density isosurface at the level $0.005\rho_{0}$ is shown." The cross-sections of density isosurface by planes VZ and YZ passing through the accretor are also shown., The cross-sections of density isosurface by planes $XZ$ and $YZ$ passing through the accretor are also shown. The low structure presented. in Fig., The flow structure presented in Fig. lis steady-state and corresponds to a time exceeding 10 orbital periods., 1 is steady-state and corresponds to a time exceeding 10 orbital periods. " The analysis of presented. results allows o reveal the following features of the Dow structure: i) the matter of the stream is redistributed into three xwis: the first part forms a quasi-clliptic aceretion disc: the second part moves around. the aceretor bevond. the disc: 1e third. part of the stream moves towards the external Lagrangian point Ls. then a fraction of this matter leaves 10 system. while a considerable amount of the gas changes 10 direction of motion due to Coriolis force and comes back o the system: ii) the interaction between the stream ancl the clise is gajock-free: ii) the stream of matter moving from the vicinity. of Ly, changes the sizes as it spreads towards the accretor: the uckness of the stream decreases. and its width in the orbital plane increases: iv) the thickness of the accretion disce is smaller then 10 stream thickness."," The analysis of presented results allows to reveal the following features of the flow structure: i) the matter of the stream is redistributed into three parts: the first part forms a quasi-elliptic accretion disc; the second part moves around the accretor beyond the disc; the third part of the stream moves towards the external Lagrangian point $L_2$, then a fraction of this matter leaves the system, while a considerable amount of the gas changes the direction of motion due to Coriolis force and comes back to the system; ii) the interaction between the stream and the disc is shock-free; iii) the stream of matter moving from the vicinity of $L_1$ changes the sizes as it spreads towards the accretor: the thickness of the stream decreases, and its width in the orbital plane increases; iv) the thickness of the accretion disc is smaller then the stream thickness." A more detailed: analysis of the structure of gaseous —ows in the system and evaluation of linear sizes of the disc, A more detailed analysis of the structure of gaseous flows in the system and evaluation of linear sizes of the disc Recent studies suggest that the ionising radiation esca(ng from galaxies could give a substantial (possibly dominant) contribution to the ultraviolet xiekeround radiation (lVb) during a large cosmological time span (Ciallongo. Fonana Macau LOOT: Giroux 8iul. L997: Bianchi. Crisiani Wim 2001).,"Recent studies suggest that the ionising radiation escaping from galaxies could give a substantial (possibly dominant) contribution to the ultraviolet background radiation (UVB) during a large cosmological time span (Giallongo, Fontana Madau 1997; Giroux Shull 1997; Bianchi, Cristiani Kim 2001)." Also. at large redshifts. radiation from t1c first stellar objects has very ikelv driven the process of cosmic reionisation (Cinedin Ostriker 1998: Clardi 2000: Mairalda-Iscudé.. LlacAhnelt Rees 2000: Cinein 2000: Benson 2000: Clare1 2001).," Also, at large redshifts, radiation from the first stellar objects has very likely driven the process of cosmic reionisation (Gnedin Ostriker 1998; Ciardi 2000; Miralda-Escudé,, Haehnelt Rees 2000; Gnedin 2000; Benson 2000; Ciardi 2001)." In spite of this extensive. body of work « both aspects. their. predictive. power is jeopardized ny the persisting (theoretical ancl experimental) ignorance on the value of fis. the fraction of hyvdrogen-ionisinDIn photons that escapes from the parent galaxy into the interealactic medium (IGM).," In spite of this extensive body of work on both aspects, their predictive power is jeopardized by the persisting (theoretical and experimental) ignorance on the value of $f_{esc}$, the fraction of hydrogen-ionising photons that escapes from the parent galaxy into the intergalactic medium (IGM)." Obviously. this quantity enters the modeling of the UVB ancl reionisation process and the results depend quite sensibly on the assumptions mace about this poorly constrained parameter.," Obviously, this quantity enters the modeling of the UVB and reionisation process and the results depend quite sensibly on the assumptions made about this poorly constrained parameter." A promising wav to make theoretical progresses on this issue is to improve the degree of realism of the modeling and the treatment of physical processes to make predictions that can be directly. compared with available local and intermediate redsult clata., A promising way to make theoretical progresses on this issue is to improve the degree of realism of the modeling and the treatment of physical processes to make predictions that can be directly compared with available local and intermediate redshift data. Dove Shull (1994h) initially tackled the problem of determining f.EM bv assuming smoothly varving Il 1 distributions in the Galactic. disk., Dove Shull (1994b) initially tackled the problem of determining $f_{esc}$ by assuming smoothly varying H I distributions in the Galactic disk. Dhey concluded: tha about of Lyman continuum (Lyc) photons are able to escape the disk., They concluded that about of Lyman continuum (Lyc) photons are able to escape the disk. Dove. Shul Ferrara (2000) later improved the caculation by SOving the time-depencen radiation transfer problem of stellar radiation. through evolving superbubbles.," Dove, Shull Ferrara (2000) later improved the calculation by solving the time-dependent radiation transfer problem of stellar radiation through evolving superbubbles." ος main result is that the shells of the expanding superbubbles quickly trap ionising photons. πο that most of the radiation escapes shorthy alter the formation of the superbubble.," Their main result is that the shells of the expanding superbubbles quickly trap ionising photons, so that most of the radiation escapes shortly after the formation of the superbubble." This results in a value of Jf. roughv a factor of 2 lower than obtained by Dove Shull (1994b)., This results in a value of $f_{esc}$ roughly a factor of 2 lower than obtained by Dove Shull (1994b). Additional theoretical works (Ricotti Shul, Additional theoretical works (Ricotti Shull The present model has been built. for haloes formed by PA.,The present model has been built for haloes formed by PA. Not only is this kind of halo formation crucial for the inside-out growth condition. but also for the possibility to apply the peak formalism in order to derive the peak trajectory leading to a tvpical halo with a given mass at a given time.," Not only is this kind of halo formation crucial for the inside-out growth condition, but also for the possibility to apply the peak formalism in order to derive the peak trajectory leading to a typical halo with a given mass at a given time." The peak formalism itself is based. on the existence of a one-to-one correspondence between haloes and peaks inspired. in the SL model that ignores major mergers., The peak formalism itself is based on the existence of a one-to-one correspondence between haloes and peaks inspired in the SI model that ignores major mergers. This therefore raises two important questions., This therefore raises two important questions. Low do major mergers allect the tvpical spherically averaged densitv profile for haloes derived: under these conditions?, How do major mergers affect the typical spherically averaged density profile for haloes derived under these conditions? And how do they allect the peak formalism?, And how do they affect the peak formalism? As shown in Section ??.. given à seed with known spherically averaged density profile. we can. find the spherically averaged: density. profile of the virialisecl halo evolving from it by. PA. but the converse is also true.," As shown in Section \ref{model}, given a seed with known spherically averaged density profile, we can find the spherically averaged density profile of the virialised halo evolving from it by PA, but the converse is also true." " Given a halo grown by PA. we can caleulate from its mass profile Al(r) the spherical total energy. of the protohalo. £,CM) (eq. 90]]."," Given a halo grown by PA, we can calculate from its mass profile $M(r)$ the spherical total energy of the protohalo, ${\cal E}\p(M)$ (eq. \ref{vir0}] ])," and then determine its spherically averaged density. profile. £pio(r). from equations (107)) ancl (108)).," and then determine its spherically averaged density profile, $\lav\rho\p\rav(r)$ , from equations \ref{E1}) ) and \ref{M1}) )." Therefore. there is in PAprofiles.," Therefore, there is in PA." This is a well-known characteristic ofspherical SL (DelPopoloetal.2000).. extended in the present paper to non-spherical SL.," This is a well-known characteristic of SI \citep{DPea00}, extended in the present paper to non-spherical SI." Interestingly. the reconstruction of the spherically averaged. density profile for the seed of a halo having grown by PA can also be applied to à halo having sullered major mergers.," Interestingly, the reconstruction of the spherically averaged density profile for the seed of a halo having grown by PA can also be applied to a halo having suffered major mergers." This vields the spherically averaged density profile. Poir). of a putative peak that would evolve by PA into a halo with a spherically averaged density profile identical. by construction. to that of the original halo.," This yields the spherically averaged density profile, $\lav\rho\p\rav(r\p)$, of a putative peak that would evolve by PA into a halo with a spherically averaged density profile identical, by construction, to that of the original halo." Clearly. if the halo has grown by PA. such a putative peak exists and it is an ordinary peak.," Clearly, if the halo has grown by PA, such a putative peak exists and it is an ordinary peak." But if the halo has undergone major mergers. does it exist?," But if the halo has undergone major mergers, does it exist?" Is it an ordinary. peak?, Is it an ordinary peak? In which halo does it evolve?, In which halo does it evolve? To answer these questions we will make use of the rigorous treatment of the peak formalism given in MSSa and AISSh., To answer these questions we will make use of the rigorous treatment of the peak formalism given in MSSa and MSSb. As mentioned. the peak Ansatz at the base of the peak formalism states that there is a one-to-one correspondence between haloes with AZ at / and peaks in the filtered density field. at. some small enough. cosmic time ZA. [or some monotonous decreasing and increasing functions 9(/) at Ay(AL) of the respective arguments.," As mentioned, the peak Ansatz at the base of the peak formalism states that there is a one-to-one correspondence between haloes with $M$ at $t$ and peaks in the filtered density field at some small enough cosmic time $\ti$, for some monotonous decreasing and increasing functions $\delta(t)$ at $\R(M)$ of the respective arguments." " According to this Ansatz. peaks associated withacerefing haloes describe continuous trajectories in the 2, £2 diagram."," According to this Ansatz, peaks associated with haloes describe continuous trajectories in the $\delta\pk$ $\R$ diagram." Fhose peaks need not necessarily be anchored to points with fixed coordinates: they can move as the filtering scale varies (as real haloes do in the clustering process)., Those peaks need not necessarily be anchored to points with fixed coordinates; they can move as the filtering scale varies (as real haloes do in the clustering process). But. thanks to themandatory usc of the Gaussianwindow the connection can be made in a simple consistent way between peaks tracineracing one εσοῖνοῃgiven accreting accretinghalo haloat atcontiguouscontie.," But, thanks to the use of the Gaussian, the connection can be made in a simple consistent way between peaks tracing one given accreting halo at contiguous." . In a major merger. the continuous trajectorics of (connected) peaks tracing the merging halocs are interrupted. while one new continuous peak trajectory appears tracing the halo resulting from the merger. leaving a finite gap in A; due to the skip in halo mass between the merging and final objects.," In a major merger, the continuous trajectories of (connected) peaks tracing the merging haloes are interrupted, while one new continuous peak trajectory appears tracing the halo resulting from the merger, leaving a finite gap in $\R$ due to the skip in halo mass between the merging and final objects." This is the only process where peak trajectories are interrupted., This is the only process where peak trajectories are interrupted. Haloes that do not merge but are accereted by more massive haloes are traced by. peaks that do not disappear but become nested into the collapsing cloud of larger scale peaks tracing the accreting haloes., Haloes that do not merge but are accreted by more massive haloes are traced by peaks that do not disappear but become nested into the collapsing cloud of larger scale peaks tracing the accreting haloes. This leads to a complex nesting of peaks with identical 9i but cillerent δι., This leads to a complex nesting of peaks with identical $\delta\pk$ but different $\R$. " Once such a nesting is corrected. the number density of peaks with 2, at scales between A; and £y|dft and its filtering evolution recovers the mass function (and erowth rates) of virialised haloes (MSSa and ALSSh)."," Once such a nesting is corrected, the number density of peaks with $\delta\pk$ at scales between $\R$ and $\R+\der\R$ and its filtering evolution recovers the mass function (and growth rates) of virialised haloes (MSSa and MSSb)." Thanks to these results it can be shown (see MSSa) that the aff) and CA) relations defining the one-to-one correspondence between (non-nested) peaks and (non-nested) haloes stated in the peak Ansatz are necessarily of the form (119)) (120))., Thanks to these results it can be shown (see MSSa) that the $\delta\pk(t)$ and $\R(M)$ relations defining the one-to-one correspondence between (non-nested) peaks and (non-nested) haloes stated in the peak Ansatz are necessarily of the form \ref{deltat}) \ref{rm}) ). These relations can be seen as he gencralisation of those of the same form found in top-wt spherical collapse. with o(/) and q respectively equal ο 1.686 and 1.," These relations can be seen as the generalisation of those of the same form found in top-hat spherical collapse, with $\delta\co(t)$ and $q$ respectively equal to 1.686 and 1." This does not mean. of course. that these xwanmeters must take the same values in the peak formalism.," This does not mean, of course, that these parameters must take the same values in the peak formalism." On the contrary. the freedom in ὃς(1) and q makes it possible o account for the change in the filtering window (Ciaussian instead. of top-hat) ancl possibly also in the departure rom spherical collapse in the real clustering For dH)=1.93|(5.920.4720.0546:2)/(10.000568: and q=r5. the halo mass function. predicted. in. the7) ACDAL concordance cosmologyIp (after4 correction for nestinge according to AISSa) recovers the mass function derived from the excursion set formalism from z=0 up to any arbitrarily large ολ," On the contrary, the freedom in $\delta\co(t)$ and $q$ makes it possible to account for the change in the filtering window (Gaussian instead of top-hat) and possibly also in the departure from spherical collapse in the real clustering For $\delta\co[t(z)]=1.93+(5.92-0.472 z+0.0546 z^2)/(1+0.000568 z^3)$ and $q=2.75$, the halo mass function predicted in the $\Lambda$ CDM concordance cosmology (after correction for nesting according to MSSa) recovers the mass function derived from the excursion set formalism from $z=0$ up to any arbitrarily large $z$." As the halo mass function at / predicted. in the peak formalism is nothing but the filtering raclius distribution for peaks with Oyi(/) (eq. 119]., As the halo mass function at $t$ predicted in the peak formalism is nothing but the filtering radius distribution for peaks with $\delta\pk(t)$ (eq. \ref{deltat}] ]) transformed into the former by means of the relation (120)). this result implies that there is indeed. a one-to-one correspondence between peaks ancl haloes as stated by the peak Ansatz.," transformed into the former by means of the relation \ref{rm}) ), this result implies that there is indeed a one-to-one correspondence between peaks and haloes as stated by the peak Ansatz." The putative peak of a halo and. its associated: peak according to the peak Ansatz have the same (4) and RCA)., The putative peak of a halo and its associated peak according to the peak Ansatz have the same $\delta\pk(t)$ and $\R(M)$. Their. filtering. evolution may. be dillerent:: the trajectory in the ji. £2) diagram of the putative seed. can always be traced down to anv arbitrarily small filtering radius. whereas the trajectory of the associatecl peak can only be traced until reaching the filtering radius corresponding to the last major merger.," Their filtering evolution may be different: the trajectory in the $\delta\pk$ $\R$ diagram of the putative seed can always be traced down to any arbitrarily small filtering radius, whereas the trajectory of the associated peak can only be traced until reaching the filtering radius corresponding to the last major merger." " However. the values O and Ap of a peak do not allow one to tell its ""past filtering evolution because there is. in the filteringprocess. a kind of “memory loss’."," However, the values $\delta\pk$ and $\R$ of a peak do not allow one to tell its `past' filtering evolution because there is, in the filteringprocess, a kind of `memory loss'." The Gaussian window. mandatory as," The Gaussian window, mandatory as" values of VY that did not show a uoulinear P-L relation can be understood as due to the influence of outliers. because these outliers will decrease the accuracy of the determined slopes aud heuce reduce the s;guificauce of the F-test (Necowctal.2005).,"values of $X$ that did not show a nonlinear P-L relation can be understood as due to the influence of outliers, because these outliers will decrease the accuracy of the determined slopes and hence reduce the significance of the $F$ -test \citep{nge05}." . Adopting large value of X in the sigma-clipping aleorithim probably is not a good practice because some genuine outliers will not be removed (nu other words. not many outliers will be removed).," Adopting large value of $X$ in the sigma-clipping algorithm probably is not a good practice because some genuine outliers will not be removed (in other words, not many outliers will be removed)." " The cases for using sinall values of WV that do not show the uoulinearity of the P-L relation cau be ""understood as follows: the intrinsic dispersion of the P-L relation is of the order of ~20 aud sigia-clipping with (X<1.5 will remove many Cepheids. inchiding those good. Cepheids near the edees of the instability strip."," The cases for using small values of $X$ that do not show the nonlinearity of the P-L relation can be understood as follows: the intrinsic dispersion of the P-L relation is of the order of $\sim2\sigma$ and sigma-clipping with $X<1.5$ will remove many Cepheids, including those good Cepheids near the edges of the instability strip." This will make the reeression tighter and tighter along the regression linc., This will make the regression tighter and tighter along the regression line. If uoulincearitydocs exist iu the P-L relation within the iutriusie dispersion. the sigmia-clippine with simall Wo will “remove” the signature of the nonlinear P-L relation aud hence the F-test returns a non-siguificaut result.," If nonlinearity exist in the P-L relation within the intrinsic dispersion, the sigma-clipping with small $X$ will “remove” the signature of the nonlinear P-L relation and hence the $F$ -test returns a non-significant result." Therefore. too high or too low of X is not a good choice for rejecting the outlicrs.," Therefore, too high or too low of $X$ is not a good choice for rejecting the outliers." A novice choice of VW is ~2.5 which we used in this paper as well as by the OGLE teat., A novice choice of $X$ is $\sim2.5$ which we used in this paper as well as by the OGLE team. Rejection of outliers within the samples. as we demoustrate here. is more critical to detect the nonlinear P-L relatiou in the LAIC Cepheids. if aux.," Rejection of outliers within the samples, as we demonstrate here, is more critical to detect the nonlinear P-L relation in the LMC Cepheids, if any." Houce we are left with the following choices: (a) use a large value of .X (sav .X d) im sigima-clipping algorithun that will iuclude some obvious outliers iu the sample aud hence a marginal or no detection for the noulinearitv of the P-L relation: (b) use a simall value of IX. (sav X« 1) that removes a lot of the good Cephlieids. as well as the outliers. aud the nonlinear P-L relation will uot be detected: or (ο) use a reasonable value of [X (sav No— 2.5) to remove the outliers but the remaining saluple will suggest the P-L relation is nonlinear.," Hence we are left with the following choices: (a) use a large value of $X$ (say $X>4$ ) in sigma-clipping algorithm that will include some obvious outliers in the sample and hence a marginal or no detection for the nonlinearity of the P-L relation; (b) use a small value of $X$ (say $X<1$ ) that removes a lot of the good Cepheids, as well as the outliers, and the nonlinear P-L relation will not be detected; or (c) use a reasonable value of $X$ (say $X\sim2.5$ ) to remove the outliers but the remaining sample will suggest the P-L relation is nonlinear." Choice (a) is not a eood practice iu astronomy as the obvious outliers will be included iu the sample., Choice (a) is not a good practice in astronomy as the obvious outliers will be included in the sample. Choice (b) is also not a eood practice for obvious reason. Qvly remove some good data together with the outliers?)., Choice (b) is also not a good practice for obvious reason (why remove some good data together with the outliers?). Hence we left with choice (0) and couclude that the LAIC P-L relation is nouliucar after a proper rejection of the outhers., Hence we left with choice (c) and conclude that the LMC P-L relation is nonlinear after a proper rejection of the outliers. Therefore we oulv have tolincar/nonlincur., Therefore we only have to. Among the reasons that nav cause the observed nonlinear P-L relation. extinction is believed to he the most likely candidate (asstiuing that the P-L relation is imtrinsic linear).," Among the reasons that may cause the observed nonlinear P-L relation, extinction is believed to be the most likely candidate (assuming that the P-L relation is intrinsic linear)." Therefore it is important to investigate and discuss the issues related to extinction. further., Therefore it is important to investigate and discuss the issues related to extinction further. It has been suggested that the E(BV) values given by the OGLE team are generally higher (sec.e.g.Subramaniam2005).. therefore in this section we exanune the LMC P-L relation using the extinction map provided by Subramania(2005)map... who used the red chuup stars along the line of sight to estimate the extinction values.," It has been suggested that the $E(B-V)$ values given by the OGLE team are generally higher \citep[see, e.g.,][]{sub05}, therefore in this section we examine the LMC P-L relation using the extinction map provided by \citet{sub05}, who used the red clump stars along the line of sight to estimate the extinction values." Besides the lower extinction values. there is another difference between the extinction maps prescuted iu Subramaniam(2005) and by the OGLE team: the spatial resolution of the Subramaniam(2005) extinction nap. (3.56«3.56 arcu). is smaller than the OGLE extinction map (11.23«1123 arcium).," Besides the lower extinction values, there is another difference between the extinction maps presented in \citet{sub05} and by the OGLE team: the spatial resolution of the \citet{sub05} extinction map, $3.56\times3.56\ \mathrm{arcmin}^2$ ), is smaller than the OGLE extinction map $14.23\times14.23\ \mathrm{arcmin}^2$ )." Given tlic ocations of the OGLE Cepheids. the extinction map returns the corresponding ΕΤ) values and we cau convert these values to E(BVj uiug(BBV)—ΕνFY.," Given the locations of the OGLE Cepheids, the extinction map returns the corresponding $E(V-I)$ values and we can convert these values to $E(B-V)$ using$E(B-V)=E(V-I)/1.4$." However. there is a sinall fraction of he Cepheids located within the region without a reliable estimation of the L(VJ£) values 2005).," However, there is a small fraction of the Cepheids located within the region without a reliable estimation of the $E(V-I)$ values \citep[see figure 4 in][]{sub05}." . We therefore adopt/retain the original ECBV) values from the OGLE extinctio- nap for these Cepheids., We therefore adopt/retain the original $E(B-V)$ values from the OGLE extinction map for these Cepheids. The V-baud mean magnuitudes are then corrected with the new extinction values., The $V$ -band mean magnitudes are then corrected with the new extinction values. The F-test result for this OGLE sample (with log|[P?]«0. Lremoval and NV=2.5 sigma-clipping algoritlin) iρα FP= 3.76. which still iudicates a nonlinear P-L relation.," The $F$ -test result for this OGLE sample (with $\log[P]<0.4$ removal and $X=2.5$ sigma-clipping algorithm) is $F=3.76$ , which still indicates a nonlinear P-L relation." Necowetal.(2005) used a differcut extinction ma, \citet{nge05} used a different extinction map ordinary and extraordinary rays are switched between the two observations.,ordinary and extraordinary rays are switched between the two observations. The normalized Stokes parameters are given. in terms of normalized flux differences. by Jehinetal.(2005) and Patat&Romaniello(2006). as where the flux Stokes parameters are givenby Q=qi and U=uf.," The normalized Stokes parameters are given, in terms of normalized flux differences, by \citet{forsman} and \citet{2006PASP..118..146P}, as where the flux Stokes parameters are givenby $Q=qI$ and $U=uI$." The redundancy in N24 observations permits the removal of the instrumental effects that differ between the and rays., The redundancy in N=4 observations permits the removal of the instrumental effects that differ between the and rays. These differences manifest themselves as spurious polarization or depolarization., These differences manifest themselves as spurious polarization or depolarization. These instrumental effects are discussed by Patat&Romaniello(2006).., These instrumental effects are discussed by \citet{2006PASP..118..146P}. . A gain difference between the and rays for N22 observations would manifest itself às. significant polarization., A gain difference between the and rays for N=2 observations would manifest itself as significant polarization. For. spectropolarimetry. flatfields are acquired with the full polarization. optics in place. such that the observed flattields. themselves produced by scattered light. are polarized.," For spectropolarimetry, flatfields are acquired with the full polarization optics in place, such that the observed flatfields, themselves produced by scattered light, are polarized." In. addition. the optical components following the analyzer. such as grisms. filters and lenses. can also act act as linear polarizers. producing a constant additive polarization component which ts larger than effects due improper flathelding using unpolarized flats (Patat&Romaniello2006)..," In addition, the optical components following the analyzer, such as grisms, filters and lenses, can also act act as linear polarizers, producing a constant additive polarization component which is larger than effects due improper flatfielding using unpolarized flats \citep{2006PASP..118..146P}." Importantly. Patat&Romaniello also identify a non-additive polarization term. which can arise from a non-ideal Wollaston prism: for most modern dual-beam spectropolarimeters. such as FORSI. the imperfections of the Wollaston prism and the associated effects are negligible.," Importantly, \citeauthor{2006PASP..118..146P} also identify a non-additive polarization term, which can arise from a non-ideal Wollaston prism; for most modern dual-beam spectropolarimeters, such as FORS1, the imperfections of the Wollaston prism and the associated effects are negligible." In the case of N=3 observations. the instrumental polarization component cannot be removed from the Stokes parameter for which there was only a single At each retarder plate angle. the measured value of the normalized flux difference can be considered as the sum of the ideal normalized flux difference (F;) and the instrumental signature correction e: Fy’=F;+€. such that under ideal conditions (e2 0) a Stokes parameter can be measured using only one value of F at only one retarder plate position (such that the q and wv parameters are completely determined with Nz2In the same form as Eqns.," In the case of N=3 observations, the instrumental polarization component cannot be removed from the Stokes parameter for which there was only a single At each retarder plate angle, the measured value of the normalized flux difference can be considered as the sum of the ideal normalized flux difference $F_{i}$ ) and the instrumental signature correction $\epsilon$: $F_{i}^{m}=F_{i}+\epsilon$, such that under ideal conditions $\epsilon=0$ ) a Stokes parameter can be measured using only one value of $F$ at only one retarder plate position (such that the $q$ and $u$ parameters are completely determined with N=2In the same form as Eqns." 2 and 3.. the instrumental signature corrections for the g and uw Stokes parameters are. therefore. given by Another benefit of this formalism is that the instrumental signature corrections are flux normalized (such that ej and ej: are of the total flux) and are independent of the same factors as the normalized flux In the observing sequence. the primary change between each exposure is the rotation of the retarder plate.," \ref{qeqtn} and \ref{ueqtn}, the instrumental signature corrections for the $q$ and $u$ Stokes parameters are, therefore, given by Another benefit of this formalism is that the instrumental signature corrections are flux normalized (such that $\epsilon_{Q}$ and $\epsilon_{U}$ are of the total flux) and are independent of the same factors as the normalized flux In the observing sequence, the primary change between each exposure is the rotation of the retarder plate." For spectropolarimetry of a point source at the centre of the field. the only change should be the orientation. of the retarder plate. with the location of the source on the retarder plateunchanged!.," For spectropolarimetry of a point source at the centre of the field, the only change should be the orientation of the retarder plate, with the location of the source on the retarder plate." . In this case. therefore. the values of the corrections for the Q and U Stokes parameters should be approximately identical.," In this case, therefore, the values of the corrections for the $Q$ and $U$ Stokes parameters should be approximately identical." For an observing sequence with N=3. the normalized Stokes parameter with incomplete observations can be determined from the correction determined for the otherdetermined parameter. assuming ep=ει;. as The change in sign of the instrumental signature correction and F is due to switch of the polarization components observed as the and rays.," For an observing sequence with N=3, the normalized Stokes parameter with incomplete observations can be determined from the correction determined for the other parameter, assuming $\epsilon_{Q}=\epsilon_{U}$, as The change in sign of the instrumental signature correction and $F$ is due to switch of the polarization components observed as the and rays." " If the principal difference between the measured o and e rays is purely due to sensitivity. such that the difference can be expressed as a ratio of the gains between the and rays £,/g,=g. then in terms of theideal values of f, and f. (with no instrumental effects) Eqn."," If the principal difference between the measured $o$ and $e$ rays is purely due to sensitivity, such that the difference can be expressed as a ratio of the gains between the and rays $g_{o}/g_{e}=g$, then in terms of the values of $f_{o}$ and $f_{e}$ (with no instrumental effects) Eqn." 1. becomes This form assumes that there are no other effects. such as changing sky transpareney (which can become important for very large or small values of e when the flux in only ray is effectively being measured) or significant phase shift induced by the half-wavelength retarder plate.," \ref{forseqtn} becomes This form assumes that there are no other effects, such as changing sky transparency (which can become important for very large or small values of $g$ when the flux in only ray is effectively being measured) or significant phase shift induced by the half-wavelength retarder plate." For e#| the observed intensity changes at each retarder plate angle. depending on the flux and gain for each ray.," For $g \neq 1$ the observed intensity changes at each retarder plate angle, depending on the flux and gain for each ray." " The ideal values of {, and f (without instrumental effects) are given as where the ideal intensity 7=f,+f..", The ideal values of $f_{o}$ and $f_{e}$ (without instrumental effects) are given as where the ideal intensity $\overline{I}=f_{o}+f_{e}$. Using Eqns. 8..," Using Eqns. \ref{gainonly}," 9 and 10 in Eqns., \ref{fzero} and \ref{fone} in Eqns. 4 and 5 gives These equations show othat the instrumental. signature corrections are dependent on the ratio of the gains of the two rays. the total degree of polarization (see Fig. 1))," \ref{eqeqtn} and \ref{eueqtn} gives These equations show that the instrumental signature corrections are dependent on the ratio of the gains of the two rays, the total degree of polarization (see Fig. \ref{fig:model:anal}) )" and the polarization angle., and the polarization angle. In the ideal case. for e=|. Eqns.," In the ideal case, for $g=1$, Eqns." 11. give €y=ει:0., \ref{epsqu} give $\epsilon_{Q}=\epsilon_{U}=0$. The sign of the corrections are dependent on the gain ratio. with The magnitude of ej—ει; increases for g> 1. but reaches a stationary point at g= 3.85.," The sign of the corrections are dependent on the gain ratio, with The magnitude of $\epsilon_{Q}-\epsilon_{U}$ increases for $g>1$ , but reaches a stationary point at $g=3.85$ ." For g>3.85 the magnitude of e)—ei decreases due to the predominance of the signal from one ray over the other., For $g>3.85$ the magnitude of $\epsilon_{Q}-\epsilon_{U}$ decreases due to the predominance of the signal from one ray over the other. This model. therefore. has limited application for realistic. observing. conditions. for variable observing conditions between observations at different retarder," This model, therefore, has limited application for realistic observing conditions, for variable observing conditions between observations at different retarder" lens to traverse the source's disk. finite source size ellects can be neglected.,"lens to traverse the source's disk, finite source size effects can be neglected." This holds when: Unlike other methods of planet detection. gravitational lensing relies on light. [rom a more distant star.," This holds when: Unlike other methods of planet detection, gravitational lensing relies on light from a more distant star." It is therefore important (o ask what fraction of nearby dwarls will pass in front of bright sources and so can be studied with lensing., It is therefore important to ask what fraction of nearby dwarfs will pass in front of bright sources and so can be studied with lensing. Within 50 pc. there are approximately 2 dwarl stars. primarily M. dwarls. per square degree.," Within $50$ pc, there are approximately $2$ dwarf stars, primarily M dwarfs, per square degree." Consider a star with AM=03M... located at 50 pe.," Consider a star with $M=0.3\, {\rm M_\odot},$ located at $50$ pc." " For this star. 9jΠρο=0.006"". and. if its transverse velocity. ο, is 50 km +. ib traverses 0.21"" vr.1."," For this star, $\theta_E = R_E/D_L = 0.006'',$ and, if its transverse velocity, $v,$ is $50$ km $^{-1}$, it traverses $0.21''$ $^{-1}$." If the path of a more distant source star must cross within 85 of the lens in order for there to be a detectable event. the lens can generate one event per (vear. decade. century) if the density of the source field (per aarcsecond) is (16. 5.0. 1.6).," If the path of a more distant source star must cross within $\theta_E$ of the lens in order for there to be a detectable event, the lens can generate one event per (year, decade, century) if the density of the source field (per arcsecond) is (16, 5.0, 1.6)." " An accurate caleulation of the rate of detectable events must consider that. when we monitor dense source fields. even the smallest resolution element. 8,,,, is likely to contain more than one star."," An accurate calculation of the rate of detectable events must consider that, when we monitor dense source fields, even the smallest resolution element, $\theta_{mon}$ is likely to contain more than one star." In order for the magnification of a particular source star lo be detectable. the increase in the amount of light we receive [rom it must be enough to produce a certain fractional change. fp. in the amount of light received. [roma region AmonxFron:," In order for the magnification of a particular source star to be detectable, the increase in the amount of light we receive from it must be enough to produce a certain fractional change, $f_T$, in the amount of light received froma region $\theta_{mon} \times \theta_{mon}$." The rate al which a single star generates detectable events (2). is This rate is high enough that. given a dense background field and a known nearby M cwarf in front of it. we can plan observations to detect the action of the dwarl as a lens.," The rate at which a single star generates detectable events \citep{DiStefano2005} is This rate is high enough that, given a dense background field and a known nearby M dwarf in front of it, we can plan observations to detect the action of the dwarf as a lens." " For example. if the photometry can be sensitive enough (o allow fy=0.01. and if the angular resolution is good enough to allow 8,,,,=0.5"". the rate of detectable events can be comparable to one per vear. higher if fy can be made smaller."," For example, if the photometry can be sensitive enough to allow $f_T= 0.01,$ and if the angular resolution is good enough to allow $\theta_{mon} = 0.5'',$ the rate of detectable events can be comparable to one per year, higher if $f_T$ can be made smaller." " Because it is possible for the rate per lens {ο be so large. we call nearby. lenses ""high-probability. lenses” or mesolenses (7)."," Because it is possible for the rate per lens to be so large, we call nearby lenses “high-probability lenses” or \citep{DiStefano2005}." we here suggest that dust-to-gas ratio is more fundamental than metallicity in regulating the dust temperature.,we here suggest that dust-to-gas ratio is more fundamental than metallicity in regulating the dust temperature. This should be further examined with a larger sample., This should be further examined with a larger sample. " It is expected that the radiative transfer effect, tthe shielding effect of dust can be seen more clearly in submillimetre (submm) than in FIR, since the submm emission can trace dust with lower temperature (e.g.Gallianoetal.2003)."," It is expected that the radiative transfer effect, the shielding effect of dust can be seen more clearly in submillimetre (submm) than in FIR, since the submm emission can trace dust with lower temperature \citep[e.g.][]{galliano03}." ". Although the submm data of the current BCD sample are still lacking except for those of 440, future more sensitive submm facilities such as and ALMA will increase the data."," Although the submm data of the current BCD sample are still lacking except for those of 40, future more sensitive submm facilities such as and ALMA will increase the data." " We adopt A=850 jum as a representative submm wavelength, and examine the relation between (850/100)a and (60/100)a; that is, we adopt A=850 yum instead of A=140 jum, which is adopted in the rest of this paper."," We adopt $\lambda =850~\mu$ m as a representative submm wavelength, and examine the relation between $(850/100)_\mathrm{cl}$ and $(60/100)_\mathrm{cl}$; that is, we adopt $\lambda =850~\mu$ m instead of $\lambda =140~\mu$ m, which is adopted in the rest of this paper." " In reffig:clr~v0,ubmm, , wepresentthecolour− —colourrelationwithAy=0 wwithout the radiative transfer effect; 2.3)."," In \\ref{fig:clr_Av0_submm}, we present the colour--colour relation with $A_V=0$ without the radiative transfer effect; )." " We also show the nearby galaxy sample observed at A=850 yum by Dunneetal.(2000),, who also list the 60 µπι and 100 µπι fluxes."," We also show the nearby galaxy sample observed at $\lambda =850~\mu$ m by \citet{dunne00}, who also list the 60 $\mu$ m and 100 $\mu$ m fluxes." " We observe that the prediction traces the trend of the data, indicating that the submm flux is naturally explained by the natural extension of the FIR SED."," We observe that the prediction traces the trend of the data, indicating that the submm flux is naturally explained by the natural extension of the FIR SED." This means that a very cold component contributing only to the submm flux is not necessary for a major part of the nearby galaxies., This means that a very cold component contributing only to the submm flux is not necessary for a major part of the nearby galaxies. " Gallianoetal.(2003,2005) argue that a very cold component should be introduced for metal-poor dwarf galaxies."," \citet{galliano03,galliano05} argue that a very cold component should be introduced for metal-poor dwarf galaxies." " In particular, 440, which is included also in the current sample, shows a clear excess of the submm flux."," In particular, 40, which is included also in the current sample, shows a clear excess of the submm flux." " In reffig:clrAv0;ubmm, , wealsoplotthedatapointtaken f 4oh"," In \\ref{fig:clr_Av0_submm}, we also plot the data point taken from \citet{galliano05} for 40 (see also \citealt{hunt05}) )." adadéshHexiste," Indeed, we observe a clear deviation from the model prediction, which can be interpreted as a significant contribution from a very cold component." Béao£hshi&ldediéoltho 2005)) , They also propose that such very cold dust should be located in an environment where the stellar radiation is strongly shielded. "Indeed. in reffig:clr,arAv;ubmm."," In order to examine the effect of shielding radiative transfer), we show the results with $A_V>0$ in \\ref{fig:clr_varAv_submm}." .W eobservethat(850/100).1 increases even for Ay>2 while (60/100)αι is almost constant for such large Av., We observe that $(850/100)_\mathrm{cl}$ increases even for $A_V>2$ while $(60/100)_\mathrm{cl}$ is almost constant for such large $A_V$ . This confirms that 850 jum flux is also sensitive to the shielded cold dust grains., This confirms that 850 $\mu$ m flux is also sensitive to the shielded cold dust grains. " reffig:clr,ar Avsubmmalsodemonstratesthatthedatapointof 440isexp romGallianodialitt2805", \\ref{fig:clr_varAv_submm} also demonstrates that the data point of 40 is explained with $A_V\sim 5$ with $\chi\sim 300$. )BOOI TE wd dust in II Zw 40 (and in other galaxies whose data points deviate rightwards in reffig:clrAvOsubmm))., Thus we conclude the existence of shielded cold dust in II Zw 40 (and in other galaxies whose data points deviate rightwards in \\ref{fig:clr_Av0_submm}) ). Gallianoetal. (2005)alsoshowthattheUV ISRFof I1 Zw, \citet{galliano05} also show that the UV ISRF of II Zw 40is higher than that of the Milky Way by two orders of magnitude. Although our interpretation of the submm excess as a, Although our interpretation of the submm excess as a "measure) decreases by more than two orders of magnitude until £~3x10? s, is steady till t£zz2x10* s, and decreases again afterward.","measure) decreases by more than two orders of magnitude until $t\approx 3\times 10^3$ s, is steady till $t\approx 2\times 10^4$ s, and decreases again afterward." The peak X-ray luminosity of the simulated flare is consistent with the values derived for the brightest X-ray flares observed in COUP (see Table 1 in ?)) which range between 10?? ergs s! (source COUP 752) and 8x1033 ergs s! (source COUP 1568)., The peak X-ray luminosity of the simulated flare is consistent with the values derived for the brightest X-ray flares observed in COUP (see Table 1 in \citealt{2005ApJS..160..469F}) ) which range between $10^{32}$ ergs $^{-1}$ (source COUP 752) and $8\times 10^{32}$ ergs $^{-1}$ (source COUP 1568). " On the other hand, it turns out that 3/4 of the COUP flares have a peak X- luminosity approximately one order of magnitude lower than that simulated here although the total energy released during the simulated flare (namely Eg=10? ergs, see Sect. 2.3))"," On the other hand, it turns out that 3/4 of the COUP flares have a peak X-ray luminosity approximately one order of magnitude lower than that simulated here although the total energy released during the simulated flare (namely $E\rs{fl} = 10^{36}$ ergs, see Sect. \ref{sec:flare}) )" is comparable with the median total energy of the flare inferred from the COUP observations (?))., is comparable with the median total energy of the flare inferred from the COUP observations \citealt{2005ApJS..160..423W}) ). This may be due to the fact that the simulated flare lasts for a time interval significantly shorter than those typical of stellar flares and is only partially confined by the magnetic field (see discussion below)., This may be due to the fact that the simulated flare lasts for a time interval significantly shorter than those typical of stellar flares and is only partially confined by the magnetic field (see discussion below). The evolution of our simulated flare has significant differences with respect to the evolution of flares simulated with 1D models (?))., The evolution of our simulated flare has significant differences with respect to the evolution of flares simulated with 1D models \citealt{1988ApJ...328..256R}) ). " In fact, at variance with 1D models where the flare is assumed to be fully confined by the magnetic field, in our simulation the flare is only partially confined by the magnetic field at the loop footpoint anchored at the disk surface."," In fact, at variance with 1D models where the flare is assumed to be fully confined by the magnetic field, in our simulation the flare is only partially confined by the magnetic field at the loop footpoint anchored at the disk surface." " There, a substantial amount of the evaporated disk material escapes in the outer stellar magnetosphere and does not fill the post-flare loop."," There, a substantial amount of the evaporated disk material escapes in the outer stellar magnetosphere and does not fill the post-flare loop." We conclude therefore that our results could be intermediate between those found with models of fully confined flares (?)) and those of models of unconfined flares (?)) which show that the the flare evolution is much faster than that observed in the confined case., We conclude therefore that our results could be intermediate between those found with models of fully confined flares \citealt{1988ApJ...328..256R}) ) and those of models of unconfined flares \citealt{2002A&A...383..952R}) ) which show that the the flare evolution is much faster than that observed in the confined case. " On the other hand, for the purposes of this work (namely the study of the perturbation of the disk by a bright flare), we have used a simplified and idealized configuration of the initial stellar magnetic field (namely a magnetic dipole), whilst many observations indicate that the stellar atmospheres are permeated by magnetic fields with a high degree of complexity (e.g. ? and references therein)."," On the other hand, for the purposes of this work (namely the study of the perturbation of the disk by a bright flare), we have used a simplified and idealized configuration of the initial stellar magnetic field (namely a magnetic dipole), whilst many observations indicate that the stellar atmospheres are permeated by magnetic fields with a high degree of complexity (e.g. \citealt{2010RPPh...73l6901G} and references therein)." " In particular, the magnetic field in proximity of a"," In particular, the magnetic field in proximity of a" optical continuum lags on wavelength: are consistent. with this prediction (Cackettetal.2007).,optical continuum lags on wavelength are consistent with this prediction \citep{cackettetal07}. . A more stringent test. of reprocessing models. is to directly compare X-ray ancl optical variations. using multi-wavelength monitoring campaigns.," A more stringent test of reprocessing models is to directly compare X-ray and optical variations, using multi-wavelength monitoring campaigns." “Lo date. a handful of these campaigns have been carried. out. largely. facilitated by theEvrplover TE) in conjunction with various ground. based. observatories.," To date, a handful of these campaigns have been carried out, largely facilitated by the ) in conjunction with various ground based observatories." The results have been mixed. with some AGN showing good evidence [or correlated. variability. as would. be expected from reprocessing models. (e.g. NGC 4051. Peterson2000:Shemmeretal. 2003: NGC 5548. Uttlevet.al. 2003: Mrk 509. Marshalletal. 2008)). while others show more complicated: but possibly correlated: behaviour. (e.g. NGC 7469. Nandraetal.1998. 2000)) and one AGN shows no apparent correlation at all. (NGC 3516. Maozetal. 2002)).," The results have been mixed, with some AGN showing good evidence for correlated variability, as would be expected from reprocessing models (e.g. NGC 4051, \citealt{petersonetal00,shemmeretal03}; NGC 5548, \citealt{uttleyetal03}; Mrk 509, \citealt{marshalletal08}) ), while others show more complicated but possibly correlated behaviour (e.g. NGC 7469, \citealt{nandraetal98,nandraetal00}) ) and one AGN shows no apparent correlation at all (NGC 3516, \citealt{maozetal02}) )." The best case for correlated variability to cate is NGC 5548. but. Uttlevetal.(2003) note. that 1U is dillieult to reconcile the large fractional amplitude of optical variability on time-scales of months-vears with reprocessing niodels. since the X-ray variability shows smaller-amplituce variations than the optical on these lone time-scales.," The best case for correlated variability to date is NGC 5548, but \citet{uttleyetal03} note that it is difficult to reconcile the large fractional amplitude of optical variability on time-scales of months-years with reprocessing models, since the X-ray variability shows smaller-amplitude variations than the optical on these long time-scales." One would expect smaller relative variations in optical since the intrinsic. emission. due to viscous disc heating would dilute any variable reprocessed component., One would expect smaller relative variations in optical since the intrinsic emission due to viscous disc heating would dilute any variable reprocessed component. Furthermore. Gaskell (2007) notes that a simple cnerectics argument rules out reprocessing as the clominant source of optical variability in many AGN (including NGC 5548). which have chig blue bumps! dominating the total luminosity. significantly exceeding the N-rav luminosity available [or reprocessing.," Furthermore, Gaskell (2007) notes that a simple energetics argument rules out reprocessing as the dominant source of optical variability in many AGN (including NGC 5548) which have `big blue bumps' dominating the total luminosity, significantly exceeding the X-ray luminosity available for reprocessing." Detailed: reprocessing calculations. produced bv Ixazanas&Navakshin(2001). for the case of NGC 3516 show that simple reprocessing of N-ravs on their own could not produce the observed optical variability.," Detailed reprocessing calculations, produced by \citet{reprocessing} for the case of NGC 3516 show that simple reprocessing of X-rays on their own could not produce the observed optical variability." Also. in some AGN with simultaneous X-ray ancl optical monitoring. there is evidence that the optical mayfead the X-ray variations. which might be expected if at least some of the optical variability is produced. by intrinsic accretion Ductuations propagating through the disc (Shemmierctal.2008:Mar-shalletal. 2005).," Also, in some AGN with simultaneous X-ray and optical monitoring, there is evidence that the optical may the X-ray variations, which might be expected if at least some of the optical variability is produced by intrinsic accretion fluctuations propagating through the disc \citep{shemmeretal03,marshalletal08}." Clearly. no single model provides a satisfactory explanation for all the data.," Clearly, no single model provides a satisfactory explanation for all the data." Lt is possible. however. that some combination of reprocessing and intrinsic. accretion variations may explain the diverse range of optical/X-ray behaviour which is already observed in only a small sample of AGN.," It is possible, however, that some combination of reprocessing and intrinsic accretion variations may explain the diverse range of optical/X-ray behaviour which is already observed in only a small sample of AGN." The location of the optical emitting region probably plays a kev role in determining the balance of intrinsic versus reprocessed variability., The location of the optical emitting region probably plays a key role in determining the balance of intrinsic versus reprocessed variability. " Lt is governed by the. disc temperature. which scales inversely with radius £ (in units of the Gravitational radius 2,=CAL c) but also scales with black hole mass Adpy and aceretion rate (as a fraction of the Exldington rate) m as ToxGifMiyap (Irevesetal. 1988)."," It is governed by the disc temperature, which scales inversely with radius $R$ (in units of the Gravitational radius $R_g=GM/c^2$ ) but also scales with black hole mass $M_{\rm BH}$ and accretion rate (as a fraction of the Eddington rate) $\dot{m}$ as $T\propto[(\dot{m}/{M}_{\rm BH})R^{-3}]^{1/4}$ \citep{trevesetal88}." . Thus over the 3 decade range in black hole mass expected for ΑΝ. we expect the radius corresponding to a eiven temperature to change by a factor of LO (at the same fractional accretion rate). perhaps even more for cillerent accretion rates.," Thus over the 3 decade range in black hole mass expected for AGN, we expect the radius corresponding to a given temperature to change by a factor of 10 (at the same fractional accretion rate), perhaps even more for different accretion rates." Since disc temperature governs the radius where peak optical emission is produced. Uttlevetal.(2003) suggested that a diverse range of optical/N-ray. behaviour nmüsht. result. [rom the range of masses and. accretion rates expected in ACN (seealsoLi&Cao2008)..," Since disc temperature governs the radius where peak optical emission is produced, \citet{uttleyetal03} suggested that a diverse range of optical/X-ray behaviour might result from the range of masses and accretion rates expected in AGN \citep[see also][]{li}." For example. the AGN with the most massive black holes will have cool disces ancl very centrally concentrated optical-emitting regions. in terms of gravitational radii.," For example, the AGN with the most massive black holes will have cool discs and very centrally concentrated optical-emitting regions, in terms of gravitational radii." Pherelore. the disc variability time-scales will be short. comparable with the X-ray variability time-scales. so intrinsic dise variability as well as reprocessing may contribute significantly to the optical variations.," Therefore, the disc variability time-scales will be short, comparable with the X-ray variability time-scales, so intrinsic disc variability as well as reprocessing may contribute significantly to the optical variations." In contrast. AGN with lower-miass black holes will have hotter clises so optical emission will originate [rom larger radii. where dise variability time-scales are very long compared to the corresponding time-scales in the innermost regions. so that only reprocessing may contribute significantly to the rapicl variability we observe.," In contrast, AGN with lower-mass black holes will have hotter discs so optical emission will originate from larger radii, where disc variability time-scales are very long compared to the corresponding time-scales in the innermost regions, so that only reprocessing may contribute significantly to the rapid variability we observe." To test. composite models of optical variability. it is necessary to carry oul combined. optical/X-ray monitoring of AGN with widely varving masses and accretion rates.," To test composite models of optical variability, it is necessary to carry out combined optical/X-ray monitoring of AGN with widely varying masses and accretion rates." ‘To date. these campaigns have focused on Seyfert galaxies. which typically cover bolometric Iuminosities ranging [ron 1077 to 1077 erg st.," To date, these campaigns have focused on Seyfert galaxies, which typically cover bolometric luminosities ranging from $10^{43}$ to $10^{45}$ erg $^{-1}$." Here we report the first opticalX-ray correlation for a more Luminous racio-quict ACN. the quasar which we have monitored simultaneously in N-rav and optical bands for the past 2.5 vears.," Here we report the first optical/X-ray correlation for a more luminous radio-quiet AGN, the quasar which we have monitored simultaneously in X-ray and optical bands for the past 2.5 years." We describe. the data in Section. 2 and show the cross correlations in Section 3., We describe the data in Section 2 and show the cross correlations in Section 3. In Section. 4 we explore reprocessing ancl propagating Lluctuations scenarios to explain the X-ravoptical variability. in this source and discuss the implications of our results in Section 5., In Section 4 we explore reprocessing and propagating fluctuations scenarios to explain the X-ray/optical variability in this source and discuss the implications of our results in Section 5. wwas monitored in the X-ray. band. using the Rossi X-ray Timing Explorer aand in several optical bands with the δαν SALATCES telescope in Chile and the 1m. telescope at. the Wise Observatory., was monitored in the X-ray band using the Rossi X-ray Timing Explorer and in several optical bands with the 1.3m SMARTS telescope in Chile and the 1m telescope at the Wise Observatory. Below we give a brief. description. of the observational campaigns and the construction of the light Curves., Below we give a brief description of the observational campaigns and the construction of the light curves. We have monitored iin the X-rav band with Taking | ks exposure snapshot every 4.3 days., We have monitored in the X-ray band with taking 1 ks exposure snapshot every 4.3 days. In the present paper. we include X-ray. data from 2004 March 27 to 2008 January 13.," In the present paper, we include X-ray data from 2004 March 27 to 2008 January 13." Within this period. an intensive monitoring campaign was carried out with daily observations for three months. between 2007 August 2 and November 1.," Within this period, an intensive monitoring campaign was carried out with daily observations for three months, between 2007 August 2 and November 1." Data were obtained using the PProportional Counter Array (PCA). which is sensitive in the range ~2.7 keV to 60 keV and consists of 5 Proportional Counter Units (PCUs).," Data were obtained using the Proportional Counter Array (PCA), which is sensitive in the range $\sim2.7$ keV to 60 keV and consists of 5 Proportional Counter Units (PCUs)." Since. PCU 0 has lost its xenon laver leading to a changed instrumental response and high background. and PCUs 1.3 and 4 are regularly switched olf for our observations. we only extracted data from PCU 2.," Since PCU 0 has lost its xenon layer leading to a changed instrumental response and high background, and PCUs 1, 3 and 4 are regularly switched off for our observations, we only extracted data from PCU 2." We use standard &ood-time interval selection criteria (earth elevation. ELNV>10° aand source pointing OFEFSIZE« 0.027).," We use standard good-time interval selection criteria (earth elevation, $>10$ and source pointing $<0.02$ )." Background data were created using the combined faint background. moclel and the SAA history file which are all current as of 2008 Alarch., Background data were created using the combined faint background model and the SAA history file which are all current as of 2008 March. We extracted spectra in the 312 keV energy range, We extracted spectra in the 3–12 keV energy range ultraviollet radiation observed from the millisecond pulsar JO437-4715.,let radiation observed from the millisecond pulsar J0437-4715. continued collimated outflow.,continued collimated outflow. At this resolution there is little compact structure at the end of the southern jet: the ‘hot spot seen in the maps of Leahy (1985. 1993) is resolved. with ἃ size of around a second of arc.," At this resolution there is little compact structure at the end of the southern jet; the `hot spot' seen in the maps of Leahy (1985, 1993) is resolved, with a size of around a second of arc." By contrast. the northern hot spot is only just resolved. at the. full resolution of the dataset. (0.24 arcesec: maps not shown) and its brightest component has a minor axis of ~0.3 aresec.," By contrast, the northern hot spot is only just resolved at the full resolution of the dataset (0.24 arcsec; maps not shown) and its brightest component has a minor axis of $\sim 0.3$ arcsec." This use of the term ‘hot spot’ is stronger than that of ODonoghue ((19938) who only used it to indicate a brighter. broader region: the hot spot seen here is comparable in compactness with those in nearby Els BBlack 11992: Leahy 11997: Llarcleastle 11997a) and is superposed on a brighter region which corresponds to the “hot spot’ of οDonoghue et al.," This use of the term `hot spot' is stronger than that of O'Donoghue (1993), who only used it to indicate a brighter, broader region; the hot spot seen here is comparable in compactness with those in nearby FRIIs Black 1992; Leahy 1997; Hardcastle 1997a) and is superposed on a brighter region which corresponds to the `hot spot' of O'Donoghue et al." The northern jet is resolved at the bends at full resolution. and has a cross-sectional width of up to 0.8 aresec.," The northern jet is resolved at the bends at full resolution, and has a cross-sectional width of up to 0.8 arcsec." The polarization map 130.060€)). includes a correction for Riccan bias and shows all points with polarized and total intensity greater than three times the respective oll-source. nnolse values., The polarization map \\ref{3C130.060c}) ) includes a correction for Ricean bias and shows all points with polarized and total intensity greater than three times the respective off-source noise values. The position-angle vectors are perpendicular to the observed. £-eld. and so show the direction of the apparent magnetic field i£ Faraday rotation is negligible.," The position-angle vectors are perpendicular to the observed $E$ -field, and so show the direction of the apparent magnetic field if Faraday rotation is negligible." Although we expect a non-negligible rotation measure (discussed further low. section 3.4)). iese angles remain the best guess of the magnetic field. direction.," Although we expect a non-negligible rotation measure (discussed further below, section \ref{rotm}) ), these angles remain the best guess of the magnetic field direction." On this basis. the jets iive apparent magnetic field parallel to their length where »olarization is detected: the field follows the bends in the northern jet.," On this basis, the jets have apparent magnetic field parallel to their length where polarization is detected; the field follows the bends in the northern jet." Phis is as expected for a strong-IHavour jet SSaikia Salter 1988)., This is as expected for a strong-flavour jet Saikia Salter 1988). The field in the hot spot is transverse o the jet direction and parallel to the hot spot's direction of extension: this is similar to the field configuration in many IRAE hot spots (Hardcastle 11997a) but also to that in the termination knots of MST's jet (Owen. Hardee. Cornwell 1989).," The field in the hot spot is transverse to the jet direction and parallel to the hot spot's direction of extension; this is similar to the field configuration in many FRII hot spots (Hardcastle 1997a) but also to that in the termination knots of M87's jet (Owen, Hardee Cornwell 1989)." Further out. the magnetic field is parallel to the plumes. and the degree of polarization is high.," Further out, the magnetic field is parallel to the plumes, and the degree of polarization is high." This appears to be the behaviour in the best-studied WANTS T'TFavlor 11990. ODonoghue 11990. Patnaik 11984: Saikia Salter LOSS. and references therein) but is quite different from. the behaviour observed. in the weak-Ilavour jets of normal PRIs. in which the field is transverse to the jet axis. sometimes with a longitudinal sheath LULlarceastle 11996: Laing 1996: Llardeastle L1997b).," This appears to be the behaviour in the best-studied WATs Taylor 1990, O'Donoghue 1990, Patnaik 1984; Saikia Salter 1988, and references therein) but is quite different from the behaviour observed in the weak-flavour jets of normal FRIs, in which the field is transverse to the jet axis, sometimes with a longitudinal sheath Hardcastle 1996; Laing 1996; Hardcastle 1997b)." Using matched-baseline maps. E confirm earlier findings that the source is rapidly depolarized at. low frequencies.," Using matched-baseline maps, I confirm earlier findings that the source is rapidly depolarized at low frequencies." The mean depolarization between 1.5 and SA 1 (averaged over the areas with &ood signal-to-noise in both maps) of the northern plume is 0.2. and that of the southern plume 0.1.," The mean depolarization between 1.5 and 8.4 GHz (averaged over the areas with good signal-to-noise in both maps) of the northern plume is 0.2, and that of the southern plume 0.1." lt may be noteworthy that the southern lobe. with a weaker jet and no bright compact hot spot. is the more depolarized: this may be an example of a Laing-Carrington effect (Laing LOSS: Carrington 11988) in WATS. although Saripalli ((1006) suggest that there are substantial variations in the degree. of polarization with radio frequency.," It may be noteworthy that the southern lobe, with a weaker jet and no bright compact hot spot, is the more depolarized: this may be an example of a Laing-Garrington effect (Laing 1988; Garrington 1988) in WATs, although Saripalli (1996) suggest that there are substantial variations in the degree of polarization with radio frequency." Phere is weak evidence that the inner 50 aresec of both lobes is more depolarized than the outer parts. which woulc be consistent with depolarization by a medium associated with the galaxy or cluster.," There is weak evidence that the inner 50 arcsec of both lobes is more depolarized than the outer parts, which would be consistent with depolarization by a medium associated with the galaxy or cluster." Phere are no svstematic observations of depolarization in this class of source., There are no systematic observations of depolarization in this class of source. The rotation measure (RAL) distribution is not constrained by the rotation of polarization angle between S.4 and 1.5 Giz., The rotation measure (RM) distribution is not constrained by the rotation of polarization angle between 8.4 and 1.5 GHz. Rotations through all possible angles take place over the source. so there are variations in RAL of more than 36 rad 72 on aresecond scales.," Rotations through all possible angles take place over the source, so there are variations in RM of more than 36 rad $^{-2}$ on arcsecond scales." This is consisten with the RAL measurements of Leahy (1985)., This is consistent with the RM measurements of Leahy (1985). Good maps at a higher frequency are needed to constrain the RA distribution adequately., Good maps at a higher frequency are needed to constrain the RM distribution adequately. Saripalli ((1906) report measurements suggesting an integrate galactic RAL of ~300 rad = in the region. of130., Saripalli (1996) report measurements suggesting an integrated galactic RM of $\sim 300$ rad $^{-2}$ in the region of. . From the fact that the polarization vectors are well alignec with one another (ancl consistent with those in the lower-resolution maps of Saripalli al.) in the S.4-Cillz maps. ane seem to follow bends in the source where these are present. we may guess that the rotation measure towards any. poin in the source is not much greater than this value. which would. produce a 20° rotation in polarization position angle ad SA Cillz.," From the fact that the polarization vectors are well aligned with one another (and consistent with those in the lower-resolution maps of Saripalli ) in the 8.4-GHz maps, and seem to follow bends in the source where these are present, we may guess that the rotation measure towards any point in the source is not much greater than this value, which would produce a $20\dgr$ rotation in polarization position angle at 8.4 GHz." The spectral index of the source steepens rapidly with distance from the core., The spectral index of the source steepens rapidly with distance from the core. ref3C'130-spix. shows a map of spectral index: the matched baselines of the maps ensure that the steepening is not an ellect of undersampling., \\ref{3C130-spix} shows a map of spectral index; the matched baselines of the maps ensure that the steepening is not an effect of undersampling. Phis spectral behaviour is expected in the standard model in which the plumes ow slowly away [rom the source compare the spectral index maps of Hydra A by Taylor ((19905]., This spectral behaviour is expected in the standard model in which the plumes flow slowly away from the source [compare the spectral index maps of Hydra A by Taylor (1990)]. Note the comparatively [lat (az 0.5) spectral index of the jets ancl of the material they Low into., Note the comparatively flat $\alpha \approx 0.5$ ) spectral index of the jets and of the material they flow into. The northern hot spot has a spectral index Blatter than the material that surrouncds i, The northern hot spot has a spectral index flatter than the material that surrounds it. ] determined spectral ages for regions along the (straighter) southern tail. using a minimum energy for the relativistic electron distribution corresponding to 5=100. an initial clectron-cnerey power-law index of 2 to reflect the 100 spot spectral indices of 0.5. no energy contribution from relativistic protons. filling factor unity. and. equipartition magnetic fields: L took [lux measurements of regions of he plume between 30 ancl 110 aresec. measured. along the xXume. from the radio core.," I determined spectral ages for regions along the (straighter) southern tail, using a minimum energy for the relativistic electron distribution corresponding to $\gamma = 100$, an initial electron-energy power-law index of 2 to reflect the hot spot spectral indices of 0.5, no energy contribution from relativistic protons, filling factor unity, and equipartition magnetic fields; I took flux measurements of regions of the plume between 30 and 110 arcsec, measured along the plume, from the radio core." The ageing field used was 0.46 nl. which was the mean of the equipartition fields. Littec ab various points along the tail: there was little variation in equipartition field strength with distance. so that this Ποιά is à good approximation to the correct. sell-consisten value.," The ageing field used was 0.46 nT, which was the mean of the equipartition fields fitted at various points along the tail; there was little variation in equipartition field strength with distance, so that this field is a good approximation to the correct self-consistent value." “Phe model included the ellects of inverse-C'ompton, The model included the effects of inverse-Compton Iu future work. we plan ou addressing these issues.,"In future work, we plan on addressing these issues." \auy of the observational uucertaiuties in the model are at high redshift., Many of the observational uncertainties in the model are at high redshift. Modern semi-aualvytie models (egy..77). goa loug way toward clucidating these issues within the context of particular scenarios for structure formation.," Modern `semi-analytic' models \citep[\eg,][]{Cattaneo99,HaehneltKauffmann00} go a long way toward elucidating these issues within the context of particular scenarios for structure formation." Observationallv. the quasar Iqmuuinositv function (??).. OIL AMeeamascrs (2) and “N-type” radio sources (2) ave other tools for mucerstanudine the high-redshift MDBIT population.," Observationally, the quasar luminosity function \citep{Boyle2QZLF00,FanSDSSQSOLF01}, OH Megamasers \citep{Darling02} and “X-type” radio sources \citep{MerrittEkers} are other tools for understanding the high-redshift MBH population." For this work. a detailed high-resolution search for more nearby. MDII binaries themselves. perliaps in the form of double-uucleus QSOs (butsee?) and Ultra-Luimiuous Infrarec Calasies (?).. will be a crucial tool.," For this work, a detailed high-resolution search for more nearby MBH binaries themselves, perhaps in the form of double-nucleus QSOs \citep[but see][]{KochBinQSO99} and Ultra-Luminous Infrared Galaxies \citep{MurphyULIRG01}, will be a crucial tool." Analytical aud N-body studies of the dynamics and euereeties of AIBIT binaries witlin galaxies will provide population information ou MDII-MDIT mass ratios and orbit sizes crucia to future work., Analytical and N-body studies of the dynamics and energetics of MBH binaries within galaxies will provide population information on MBH-MBH mass ratios and orbit sizes crucial to future work. These will allow us to also constrain the dynamics of the MBIT binary population: if iux when do they stall prior to the DW regime?, These will allow us to also constrain the dynamics of the MBH binary population: if and when do they stall prior to the BW regime? We can. of course. use our current mocel to at least see the effect of these uncertainties;," We can, of course, use our current model to at least see the effect of these uncertainties." We can fuk a lower limit to the effect of MIBIT miass-function evolution by using a suitable initial mass function for the whole redshift range., We can find a lower limit to the effect of MBH mass-function evolution by using a suitable initial mass function for the whole redshift range. If the average AIBIT mass has increased by au order of maenitude (sav). then this woul lower the characteristic strain (eq. 2211)," If the average MBH mass has increased by an order of magnitude (say), then this would lower the characteristic strain (eq. \ref{eq:fullsimple}] ])" by no more than 10/627., by no more than $10^{5/6}\approx7$. The current experimental luit ou the low-frequeucy gravitational wave background has inuproved over the pioneering work of ?.. and will be accurately stated by Lonnaien Backer (in preparation).," The current experimental limit on the low-frequency gravitational wave background has improved over the pioneering work of \citet{Kaspi94}, and will be accurately stated by Lommen Backer (in preparation)." The new limit is lower at lower frequencies while the expected spectiua is rising., The new limit is lower at lower frequencies while the expected spectrum is rising. This new result will constraiu parameters of our model spectymu on the hieh side of the current estimate., This new result will constrain parameters of our model spectrum on the high side of the current estimate. Ougoing work with au array of millisecoucd pulsus has the prospect of significant improvement of detection capability iu the coming decade., Ongoing work with an array of millisecond pulsars has the prospect of significant improvement of detection capability in the coming decade. Techniques for optimal fitting of Pulsar Timingo Array data need to be further developed to mect the demands of the new measurements., Techniques for optimal fitting of Pulsar Timing Array data need to be further developed to meet the demands of the new measurements. We thank Jon Arons. Rav Carlbere. Ron Helliues. Yuri Levin. Andrea Lonunen. Jolin Mageorian. στο] Phinney. Philip Stark and members of the Center for Particle Astroplivsies for helpful conversations.," We thank Jon Arons, Ray Carlberg, Ron Hellings, Yuri Levin, Andrea Lommen, John Maggorian, Sterl Phinney, Philip Stark and members of the Center for Particle Astrophysics for helpful conversations." AILJ acknowledges support frou NSF NDI evant 9872979 aud NASA LTSA eraut. NACH5-6552. aud PPARC in the UK.," AHJ acknowledges support from NSF KDI grant 9872979 and NASA LTSA grant NAG5-6552, and PPARC in the UK." DCB acknowledges support from NSF evant AST-9731106 which partially supported the Pulsar Timingc» Array experiment., DCB acknowledges support from NSF grant AST-9731106 which partially supported the Pulsar Timing Array experiment. Iu this appeudix. we calculate the probability distribution of the quantity /Z(f) as given by equation (28}).," In this appendix, we calculate the probability distribution of the quantity $h_c^2(f)$ as given by equation \ref{eq:fullspec}) )." For geucralitv. consider some quantity where N(2)d eives the probability of some event happening in (2.5|dz)(ie... a Poisson rate). aud οτ} is any function.," For generality, consider some quantity where $N(z)\; dz$ gives the probability of some event happening in $(z,z+dz)$, a Poisson rate), and $g(z)$ is any function." We want to know P(y). the distribution fiction of y.," We want to know $P(y)$, the distribution function of $y$." We start with a few miportant facts from probability theory., We start with a few important facts from probability theory. First. the characteristic functiou (or moment ecnerating fiction) of a distribution is defined as the," First, the characteristic function (or moment generating function) of a distribution is defined as the" which we can identify as features of forsterite and enstatite. two abundant silicate crystals.,"which we can identify as features of forsterite and enstatite, two abundant silicate crystals." In none of the spectra is there evidence for a carbon-rich component., In none of the spectra is there evidence for a carbon-rich component. Not only are the infrared spectra of HHer and CCen very similar to each other. they also show a strong resemblance to the infrared spectrum of the solar system comet Hale-Bopp (??)..," Not only are the infrared spectra of Her and Cen very similar to each other, they also show a strong resemblance to the infrared spectrum of the solar system comet Hale-Bopp \citep{bouwman03,min05b}. ." ? model the thermal emission and degree of linear polarisation of radiation. scatterec by grains in the coma of the comet Hale-Bopp., \citet{min05b} model the thermal emission and degree of linear polarisation of radiation scattered by grains in the coma of the comet Hale-Bopp. The largest contribution in dust. about of total dust mass. is made up of amorphous silicate grains. with dust sizes from jm up to 934m. and large amorphous carbon grains (~ um).," The largest contribution in dust, about of total dust mass, is made up of amorphous silicate grains, with dust sizes from $\mu$ m up to $\mu$ m, and large amorphous carbon grains $\sim$ $\mu$ m)." Small erystalline silicates make up only of the total dust mass of Hale-Bopp but this is sufficient to have this strong spectral signature in the IR spectrum., Small crystalline silicates make up only of the total dust mass of Hale-Bopp but this is sufficient to have this strong spectral signature in the IR spectrum. The amorphous and erystalline features seen in the spectra of HHer and CCen are identified as caused by the most commonly found dust species in the circumstellar environment (2222).. namely glassy and crystalline silicates with an olivine and pyroxene stoichiometry.," The amorphous and crystalline features seen in the spectra of Her and Cen are identified as caused by the most commonly found dust species in the circumstellar environment \citep{molster02a,molster02b,molster02c,min07}, namely glassy and crystalline silicates with an olivine and pyroxene stoichiometry." " We further take the commonly used term ""amorphous and crystalline olivine and pyroxene” to describe these dust species.", We further take the commonly used term “amorphous and crystalline olivine and pyroxene” to describe these dust species. " Amorphous olivine (Mgs,Fes;-, 810,. where Oxxxl denotes the magnesium content) has very prominent broad features around um and 187m. These features (also called the μπι and μπι features) arise respectively from the Si-O stretching mode and the O-Si-O bending mode."," Amorphous olivine $_{2x}$ $_{2(1-x)}$ $_4$, where $\leq$ $\leq$ 1 denotes the magnesium content) has very prominent broad features around $\mu$ m and $\mu$ m. These features (also called the $\mu$ m and $\mu$ m features) arise respectively from the Si-O stretching mode and the O-Si-O bending mode." For large grains the jm feature gets broader and shifts to redder wavelengths., For large grains the $\mu$ m feature gets broader and shifts to redder wavelengths. " Amorphous pyroxene (Mg,Fej,SiO:;) shows a lOjmn feature. similar to that of amorphous olivine. but shifted towards. shorter wavelengths."," Amorphous pyroxene $_{x}$ $_{1-x}$ $_3$ ) shows a $\mu$ m feature similar to that of amorphous olivine, but shifted towards shorter wavelengths." Also the shape of the jim feature is slightly different., Also the shape of the $\mu$ m feature is slightly different. " Crystalline olivine and pyroxene have very distinct emission features and comparing with the features seen in the spectra of ACHHer and RUCCen. we conclude that the Mg-rich end members. forsterite (MgsSIO,) and enstatite (MgS1O1). dominate our spectra."," Crystalline olivine and pyroxene have very distinct emission features and comparing with the features seen in the spectra of Her and Cen, we conclude that the Mg-rich end members, forsterite $_2$ $_4$ ) and enstatite $_3$ ), dominate our spectra." Forsterite condenses directly from the gas-phase at high temperatures (=1500 KK) or it may form by thermal annealing of amorphous silicates. diffusing the iron out of the lattice-structure.," Forsterite condenses directly from the gas-phase at high temperatures $\approx 1500$ K) or it may form by thermal annealing of amorphous silicates, diffusing the iron out of the lattice-structure." Enstatite can form in the gas-phase from a reaction between forsterite and silica. or it may also form by a similar thermal annealing process as forsterite (??)..," Enstatite can form in the gas-phase from a reaction between forsterite and silica, or it may also form by a similar thermal annealing process as forsterite \citep{bradley83,tielens97}." The observed spectra of HHer and CCen show a shift from the amorphous 184mm feature towards μπι when comparing with synthetic spectra of amorphous olivine and pyroxene., The observed spectra of Her and Cen show a shift from the amorphous $\mu$ m feature towards $\mu$ m when comparing with synthetic spectra of amorphous olivine and pyroxene. This could point to the dominance of Mg-rich amorphous dust. which also shows this shift to redder wavelengths.," This could point to the dominance of Mg-rich amorphous dust, which also shows this shift to redder wavelengths." Photospheric depletion in iron. which we detect in CCen and HHer (??).. can be understood when the iron is locked up in the circumstellar dust (?)..," Photospheric depletion in iron, which we detect in Cen and Her \citep{maas02,vanwinckel98}, can be understood when the iron is locked up in the circumstellar dust \citep{waters92}. ." The lack of iron in the detected silicates ts therefore surprising., The lack of iron in the detected silicates is therefore surprising. If both the crystalline and amorphous silicates are devoid of iron. this could mean that iron is stored in metallic iron or iron-oxide (?)..," If both the crystalline and amorphous silicates are devoid of iron, this could mean that iron is stored in metallic iron or iron-oxide \citep{sofia06}." Metallic iron has no distinet features but still a significant contribution in opacity. especially at shorter wavelengths. making it very hard to detect directly.," Metallic iron has no distinct features but still a significant contribution in opacity, especially at shorter wavelengths, making it very hard to detect directly." Our aim is to fit the observed crystalline emission features of HHer and CCen with synthetic spectra of forsterite and enstatite., Our aim is to fit the observed crystalline emission features of Her and Cen with synthetic spectra of forsterite and enstatite. The conversion from laboratory measured optical constants of dust to mass absorption coefficients is not straightforward and is largely dependent on the adopted size. shape. structure and chemical composition of the dust (??)..," The conversion from laboratory measured optical constants of dust to mass absorption coefficients is not straightforward and is largely dependent on the adopted size, shape, structure and chemical composition of the dust \citep{min03,min05a}." These different dust approximations result in. very different emission feature profiles., These different dust approximations result in very different emission feature profiles. The spectrum produced by homogeneous spherical particles is very differentfrom that produced by moreirregular particles., The spectrum produced by homogeneous spherical particles is very differentfrom that produced by moreirregular particles. This difference i5, This difference is fixing «4-0.,fixing $w_{\lambda}$ =0. For a detailed description of see Cidnandesetal.(2004. 2005).," For a detailed description of see \citet{cid04,cid05}." As base set we take Maraston(2005) SSPs covering 14 ages. f= 0.001. 0.005. 0.01. 0.03. 0.05. 0.1. 0.2. 0.5. 0.7. 1. 2. 5. 9. 13GOGvr. and4 metallicities. namely: Z2 0.02Z.. 0.5Z.. 1Z. and 2Z..summing up 56 elements.," As base set we take \citet{maraston05} SSPs covering 14 ages, $t$ = 0.001, 0.005, 0.01, 0.03, 0.05, 0.1, 0.2, 0.5, 0.7, 1, 2, 5, 9, Gyr, and4 metallicities, namely: $Z$ = $Z_\odot$, $Z_\odot$, $Z_\odot$ and $Z_\odot$, summing up 56 elements." " To compare with ppredictions. we use the condensed population vector. which is obtained by binning the synthesis results into young. ay: ¢/5.10 yr): intermediate-age..ry (1.107ο2 I0""yr) and old. ro 02 I0""yr) components (Riffeletal.2009:CidFernandesetal. 2004)."," To compare with predictions, we use the condensed population vector, which is obtained by binning the synthesis results into young, $x_Y$ $t\leq \rm 5\times 10^7$ yr); intermediate-age, $x_I$ $1\times 10^8 \leq t\leq \rm 2\times 10^9$ yr) and old, $x_O$ $t > \rm 2\times 10^9$ yr) components \citep{riffel09,cid04}." . These components were then taken to represent the 5MMvr. 700MMyr and GGyr old populations.," These components were then taken to represent the Myr, Myr and Gyr old populations." These vectors are compared with the ppredictions in Fig. 10.., These vectors are compared with the predictions in Fig. \ref{paasp}. Clearly. our predictions are consistent with the stellar population synthesis. especially at the optical region. where the confidence level between predictions and synthesis is ~95% (1.e. almost all points fall in a region less than from the identity line).," Clearly, our predictions are consistent with the stellar population synthesis, especially at the optical region, where the confidence level between predictions and synthesis is $\sim$ (i.e. almost all points fall in a region less than from the identity line)." The confidence level drops to ~85% in the NIR., The confidence level drops to $\sim$ in the NIR. We study the panchromatic stellar population components over the Πο spectral region., We study the panchromatic stellar population components over the to spectral region. account. Our main results are: R. R. thanks to the Brazilian funding agency CAPES., Our main results are: R. R. thanks to the Brazilian funding agency CAPES. The STARLIGHT project is supported by the Brazilian agencies CNPq. CAPES and FAPESP and by the France-Brazil CAPES/Cofecub program.," The project is supported by the Brazilian agencies CNPq, CAPES and FAPESP and by the France-Brazil CAPES/Cofecub program." Such a result for a general monotone system of ODEs seeuis to be completely open.,Such a result for a general monotone system of ODEs seems to be completely open. The above estimate iu Weed is in fact related to the behavior of f iu Example 1.3... which is the worst possible regularity of f.," The above estimate in $\frac{1}{|\log \eps|}$ is in fact related to the behavior of $\o{f}$ in Example \ref{example2}, which is the worst possible regularity of $\o{f}$." Moreover. it is possible to show that under the coudition TzCe|loge|. inequality (1.7)) is sharp. see the following example whose proof will be given in the Appendix: For.=(04..0»)—CaD X7. let us considerB a vector fielda &*-=(05.05) definedÜ as followsn with a function f satistvine CÀ1)-CÀ2)-CÀ3).," Moreover, it is possible to show that under the condition $T\geq C\eps |\log \eps|$, inequality \ref{error}) ) is sharp, see the following example whose proof will be given in the Appendix: For $x=(x_{1},x_{2})\in \R^{2}$ , let us consider a vector field $a^{\eps}=(a^{\eps}_{1},a^{\eps}_{2})$ defined as follows with a function $f$ satisfying (A1)-(A2)-(A3)." We cousider the viscosity solution V*(f..c) of the following lincar transport equation: where Vy:στι)X> Sis a Lipschitz coutiuuous function.," We consider the viscosity solution $V^{\eps}(t,x)$ of the following linear transport equation: where $V_{0}:\R^{2}\rightarrow \R$ is a Lipschitz continuous function." The existenceand uniqueness of a viscosity solution V*- of EN CL.40)) is. eusured since. a?lnCΠ-(22)—2» and Vy0 roeis Lipschitz:. continuous: (see forB instance: H|21.," The existenceand uniqueness of a viscosity solution $V^{\eps}$ of \ref{transport_eqn}) ) is ensured since $a^{\eps}\in W^{1,\infty}(\R^{2})$ and $V_{0}$ is Lipschitz continuous (see for instance \cite{Barles}) )." Thei expected homogenized equation associated to (1.10)) is: with the vector field α=(04.05) defined as: As aconsequence of Theorem 1.5.. we will show in Section ?? the following result:," The expected homogenized equation associated to \ref{transport_eqn}) ) is: with the vector field $\o{a}=(\o{a}_{1},\o{a}_{2})$ defined as: As aconsequence of Theorem \ref{theo2}, , we will show in Section \ref{sec6} the following result:" The microlensing optical depth 7=fnodl is given by where @.V/dAL is the mass function of lenses.normalized by [(N/d4M)dM=1. is the number density of lenses. M=Για/ddM is the average mass and p is (he mass density of lenses.,"The microlensing optical depth $\tau=\int n\sigma dl$ is given by where $dN/dM$ is the mass function of lenses,normalized by $\int(dN/dM)dM=1$, $n(r_l)=\rho(r_l)/\bar{M}$ is the number density of lenses, $\bar{M}=\int(dN/dM)MdM$ is the average mass and $\rho$ is the mass density of lenses." From Eqn. 1..," From Eqn. \ref{thetaE}," we then have where mA.rj)=(7[AGErrr—ni).," we then have where $m(\thetaE,r_l)=(c^2/4G)\thetaE^2 r_s r_l/(r_s-r_l)$." The optical depth distribution describes the instantaneous properties of lensing events al anv given lime. but we are interested in the distribution of all events.," The optical depth distribution describes the instantaneous properties of lensing events at any given time, but we are interested in the distribution of all events." This is described by the lensing rate D= nov., This is described by the lensing rate $\Gamma=n\sigma v$ . " If the transverse velocity distribution of source stars is f.(,). and that of the lenses is f;j(v;). we can write the lensing rate as (Griest1991) where lere. o, is the observers velocity (vansverse to (he line of sight. and i—;/r;."," If the transverse velocity distribution of source stars is $f_s({\bm v}_s)$, and that of the lenses is $f_l({\bm v}_l)$, we can write the lensing rate as \citep{griest91} where Here, ${\bm v}_o$ is the observer's velocity transverse to the line of sight, and $x=r_l/r_s$." We assume all sources are bulee stars. wilh no net rotation ancl a velocity dispersion in each transverse direction of σι.," We assume all sources are bulge stars, with no net rotation and a velocity dispersion in each transverse direction of $\sigma_b$ ." Lenses are assumed to resideeither in the bulge or in the disk.," Lenses are assumed to resideeither in the bulge or in the disk," in the scaled eutropy profiles iu the central regions of he cluster Qvithin Οι ,"in the scaled entropy profiles in the central regions of the cluster (within $0.5r_{\rm \scriptscriptstyle 200}$." These cutropy profiles do not show any fat eutropy core uulike in RRBNOL (left panel in their Figure 2)., These entropy profiles do not show any flat entropy core unlike in RRBN04 (left panel in their Figure 2). Thus. this probably indicates that hermal conduction is a more plausible process in IC'M han covection for such ecutle ACN heating.," Thus, this probably indicates that thermal conduction is a more plausible process in ICM than covection for such gentle AGN heating." The amodel is constrained bv eutropy-teniperature relation., The model is constrained by entropy-temperature relation. At fixed cluster temperature this correspouds o a given density (at both radii for which the eutropv data is provided)., At fixed cluster temperature this corresponds to a given density (at both radii for which the entropy data is provided). Now. since at a eiven deusity we lave an additional coustraiut from the L-T relation (that our uodel fits reasonably well: sce below). we nuplicitelv satisty the constraints on the slope of the deusity profile.," Now, since at a given density we have an additional constraint from the L-T relation (that our model fits reasonably well; see below), we implicitely satisfy the constraints on the slope of the density profile." Thus. as the model fits both the cutropy data aud the observed L-T relation that specify the slopes of the density profiles. these slopes must also be consistent with observations that show flattening in low lass svstenis.," Thus, as the model fits both the entropy data and the observed L-T relation that specify the slopes of the density profiles, these slopes must also be consistent with observations that show flattening in low mass systems." Tudeed. this fattening is apparent in Fieure 3 that shows final density profiles for differcut masses.," Indeed, this flattening is apparent in Figure 3 that shows final density profiles for different masses." " We now discuss the permitted range in the total energy injected iuto the cluster. E,— \fio required to match the observed entropv as a function of the cluster mass."," We now discuss the permitted range in the total energy injected into the cluster, $E_{\rm \scriptscriptstyle agn} =$ $\times\, t_{\rm \scriptscriptstyle heat}$, required to match the observed entropy as a function of the cluster mass." Figure (1)) shows the permitted total injected. energy rauge as a fuuctiou of the mass of cluster for heating times between fj;—5«LOS vears aud thea=5«10? vears., Figure \ref{fig:E_Mcombined}) ) shows the permitted total injected energy range as a function of the mass of cluster for heating times between $t_{\rss heat}=5\times 10^{8}$ years and $t_{\rss heat}=5\times 10^{9}$ years. " Tere the eutropy is required to match observations at Qos, and rg."," Here the entropy is required to match observations at $0.1r_{\rm \scriptscriptstyle 200}$ and $r_{\rm \scriptscriptstyle 500}$." The thick solid line represents a relation between the total enerev injected to the cluster ly ACN and the mass of the cluster (see next section for more cletails)., The thick solid line represents a relation between the total energy injected to the cluster by AGN and the mass of the cluster (see next section for more details). Figure (5)) shows the Nav huuinositv (Ly versus cluission-weielted temperature (Ly jrelatiou in clusters., Figure \ref{fig:lum}) ) shows the X-ray luminosity $L_{\rss X}$ versus emission-weighted temperature $T_{\rss X}$ )relation in clusters. The data points have been compiled from Arnal Evrard (1999) (represented ly stars). Markevitch 1905 (represented bw open squares) and EFHelsdonu Pomman 2000 (with error bars).," The data points have been compiled from Arnaud Evrard (1999) (represented by stars), Markevitch 1998 (represented by open squares) and Helsdon Ponman 2000 (with error bars)." The XN-rav hDnuuiuositv has been caleulated within the eluster volume of 0.379599. as doue for the data.," The X-ray luminosity has been calculated within the cluster volume of $0.3r_{\rss 200}$, as done for the data." It is also seen that the XN-rav huninosity does not change much (within νο). if the yolune iincreased from 0.327599.the to rogo., It is also seen that the X-ray luminosity does not change much (within ) if the volume increased from $0.3r_{\rss 200}$ to $r_{\rss 200}$. The shaded region μα1 the plot corresponds to predicted Xrav Dhuniuositv when the cluster is heatedbv an AGN for ος105xfuae<5\LO? vears with luminosities which correspond to re two bouding lines of the shaded region in Figure (3).," The shaded region in the plot corresponds to the predicted X-ray luminosity when the cluster is heated by an AGN for $5\times 10^8\,\le t_{\rm heat}\le \,5\times 10^9$ years with luminosities which correspond to the two bouding lines of the shaded region in Figure (3)." It is seen that the predicted luminosities of the heating uodoel satisfy the data points iu the low mass cud as well as the high mass cuc., It is seen that the predicted luminosities of the heating model satisfy the data points in the low mass end as well as the high mass end. The solid Hue in the plot shows je predicted Iuninosity due to the universal temperature xofile and the default deusitv profile., The solid line in the plot shows the predicted luminosity due to the universal temperature profile and the default density profile. We note that 1ο X-ray huninosity is over-predicted by the universal cluperature profile which tudicates that the addition of ion-gravitational heating is required to lower the XN-rav iuninositv to satisty the data poiuts (see Rovchowdlauy Nath 2003. for more details).," We note that the X-ray luminosity is over-predicted by the universal temperature profile which indicates that the addition of non-gravitational heating is required to lower the X-ray luminosity to satisfy the data points (see Roychowdhury Nath 2003, for more details)." Iu Figure (6)). the ceutral SZ tempcrature decrement is plotted as a function of the cuiussion-weighted ATtemperaturexo of the cluster (75.," In Figure \ref{fig:y0_def}) ), the central SZ temperature decrement $\Delta T_{\rm \mu w 0}$ is plotted as a function of the emission-weighted temperature of the cluster $\langle T\rangle$." The data poiuts are a compilation of data sets from Zhane Wi (2000) aud AIcCarthy et al. (, The data points are a compilation of data sets from Zhang Wu (2000) and McCarthy et al. ( 0050).,2003b). " The solid line shows the predicted AT,4 from the default temperature profile aud NEW poteutial.", The solid line shows the predicted $\Delta T_{\rm \mu w 0}$ from the default temperature profile and NFW potential. The dot-dashed line shows the predicted ATxy for the same temperature profile but for zinoothed NEW potential with ο=7/20., The dot-dashed line shows the predicted $\Delta T_{\rm\mu w0}$ for the same temperature profile but for smoothed NFW potential with $r_{\rm c}=r_{\rm s}/20$. The dashed line shows the prediction from the self-similar profile (Wu Xue. 2002): Bryan 2000).," The dashed line shows the prediction from the self-similar profile (Wu Xue, 2002b; Bryan 2000)." " It has heen shown by Rovchowdhury Nath (2003) that the density profile of eas is ich. flatter in comparison to the self-3inilar profile when it assumes the ""universal teiiperature profile” aud the staudiard NEW profile is assunned.", It has been shown by Roychowdhury Nath (2003) that the density profile of gas is much flatter in comparison to the self-similar profile when it assumes the “universal temperature profile” and the standard NFW profile is assumed. es a result. the predicted. central temperature decremeutmon (ATnode ao) is lower than that predicted by the ar L," As a result, the predicted central temperature decrement $\Delta T_{\rm \mu w 0}$ ) is lower than that predicted by the self-similar model." The normalization of AT)yy for a snoothed NEW profile with a core radius re=72/20 is even lower.," The normalization of $\Delta T_{\rm \mu w 0}$ for a smoothed NFW profile with a core radius $r_{\rm c}\,= \,r_{\rm s}/20$ is even lower." This happeus because the introduction of a core radius in the dark matter profile makes the ICM density profile shallower iu the ceutral regious as conipared to the ICM density with a staudard NEW profile., This happens because the introduction of a core radius in the dark matter profile makes the ICM density profile shallower in the central regions as compared to the ICM density with a standard NFW profile. These decrements are closer to the data than predicted by earlier selfsinular models for rich clusters., These decrements are closer to the data than predicted by earlier self-similar models for rich clusters. " Next we examine the effects of the effervescent heating. radiative. cooling auc conduction on the central SZ decrement,"," Next we examine the effects of the effervescent heating, radiative cooling and conduction on the central SZ decrement." We evaluate AT)9 for clusters iun our sunple after they have been evolved for a IIbble time £j., We evaluate $\Delta T_{\rm \mu w 0}$ for clusters in our sample after they have been evolved for a Hubble time $t_{\rm H}$ . The heating source was active for treaαςty.," The heating source was active for $t_{\rss heat}\ll\,t_{\rm H}$." The values of CL; aud Frege have been chosen so as to satisfy observational constraints on ICAL eutropy after fy at OLroyy aud soy (Pomman ct al.," The values of $\langle L\rangle$ and $t_{\rss heat}$ have been chosen so as to satisfy observational constraints on ICM entropy after $t_{\rss H}$ at $0.1\,r_{\rss 200}$ and $r_{\rss 500}$ (Ponman et al." 2003: see Figure 1 and 5 in RRNDOL)., 2003; see Figure 4 and 5 in RRNB04). Iu other words. there is a range of (Lj that satisfies the eutropv observations at a l-0 uncertainty level that we used in our calculations.," In other words, there is a range of $\langle L\rangle$ that satisfies the entropy observations at a $\sigma$ uncertainty level that we used in our calculations." We used smoothed NEW profile with the core radius ry;=1/20., We used smoothed NFW profile with the core radius $r_{\rm c}=r_{\rm s}/20$. Tn Fiewre 7.. the shaded region is the expectation for the SZ ceutral decrement when the eas is heated by the central AGN.," In Figure \ref{fig:y0_heat}, , the shaded region is the expectation for the SZ central decrement when the gas is heated by the central AGN." " The shaded region represcuts the spread iu GL) which satisfies the eutropy requirenieuts at both τας, O.1rogy linoancl rsyy for b«&LOSctheapxDsLO? years."," The shaded region represents the spread in $\langle L\rangle$ which satisfies the entropy requirements at both radii, $0.1r_{\rss 200}$ and $r_{\rss 500}$ for $5\times10^8r.? originate from the wings of a realistically bell-shaped perturbation, that may be described by 6M/Mο.M~ for e exceeding 1 (e.g.,Luetal.2006)."," The cluster for $r>r_{-2}$ originate from the wings of a realistically bell-shaped perturbation, that may be described by $\delta M/M\propto M^{-\epsilon}$ for $\epsilon$ exceeding $1$ \citep[e.g.,][]{Lu2006}." ". Then the outer potential drop is shallower relative to the body value, so leading to higher values of br and values of a."," Then the outer potential drop is shallower relative to the body value, so leading to higher values of $b_R$ and values of $a$." Thus as r increases outwards we expect k(r) to deviate downward from a simple powerlaw., Thus as $r$ increases outwards we expect $k(r)$ to deviate downward from a simple powerlaw. The argument may be phrased in terms of the accretion rate M., The argument may be phrased in terms of the accretion rate $\dot M$. " A shell 6M enclosing the mass M will collapse when δΜ/Μ attains the critical threshold 1.686D-!(r) in terms of the linear growth factor D(t) (e.g.,Weinberg2008).."," A shell $\delta M$ enclosing the mass $M$ will collapse when $\delta M/M$ attains the critical threshold $1.686\, D^{-1}(t)$ in terms of the linear growth factor $D(t)$ \citep[e.g.,][]{Weinberg2008}. ." So the shape parameter e also governs the mass buildup after MοςD'/*c5: here we have represented the growth factor as D(f)ct with d ranging from 2/3 for z21 to approach 1/2 as z—0.," So the shape parameter $\epsilon$ also governs the mass buildup after $M\propto D^{1/\epsilon}\propto t^{d/\epsilon}$ ; here we have represented the growth factor as $D(t)\propto t^{d}$ with $d$ ranging from $2/3$ for $z\ga 1$ to approach $1/2$ as $z\rightarrow 0$." " So the outskirts develop from the inside-out, at accretion rates M/M~d/et that for € exceeding 1, and for d decreasing toward 1/2 at late cosmictimes?."," So the outskirts develop from the inside-out, at accretion rates $\dot M/M\approx d/\epsilon\,t$ that for $\epsilon$ exceeding $1$, and for $d$ decreasing toward $1/2$ at late cosmic." ". We add that at small accretion rates the shock position outgrows R (see 2003),, while the shock strength may weaken; both these effects will decrease a relative to Eqs. ("," We add that at small accretion rates the shock position outgrows $R$ \citep[see][]{Voit2003}, while the shock strength may weaken; both these effects will decrease $a$ relative to Eqs. (" "2) and (3), and will be discussed in detail elsewhere.","2) and (3), and will be discussed in detail elsewhere." So we see that slopes a of the entropy are to prevail for accretion rates M of DM and gas; these have a twofold origin., So we see that slopes $a$ of the entropy are to prevail for accretion rates $\dot M$ of DM and gas; these have a twofold origin. " First, the cosmological structure growth slows down at later cosmic times (low Zops), as expressed by d« 2/3."," First, the cosmological structure growth slows down at later cosmic times (low $z_{\rm obs}$ ), as expressed by $d<2/3$ ." " Second, perturbation wings marked by e>1 imply shallow gravitational wells and little available mass to accrete in average environs; the effect may be locally offset (and represented with a smaller effective €) in specifically rich environments, including adjacent filamentary large-scale structures."," Second, perturbation wings marked by $\epsilon>1$ imply shallow gravitational wells and little available mass to accrete in average environs; the effect may be locally offset (and represented with a smaller effective $\epsilon$ ) in specifically rich environments, including adjacent filamentary large-scale structures." " The decline of a from the body value and the entropy bending set in at a radius rj;~*~r5 where matter began stratifying onto the outskirts just after z,.", The decline of $a$ from the body value and the entropy bending set in at a radius $r_b\approx r_{-2}$ where matter began stratifying onto the outskirts just after $z_t$ . " Such a radius is evaluated in terms of the observed concentration in the form rp/R=r_2/Rlc, to take on values around 0.2—0.3 for typical concentrations c~6—8 of CC clusters."," Such a radius is evaluated in terms of the observed concentration in the form $r_b/R\approx r_{-2}/R\approx 1/c$, to take on values around $0.2-0.3$ for typical concentrations $c\approx 6-8$ of CC clusters." Hints to this trend loom out in the databy Prattetal.(2010) and Hoshino (2010).., Hints to this trend loom out in the databy \citet{Pratt2010} and \citet{Hoshino2010}. . " To sum up, under the accretion rates prevailing at times in average environs, we expect the entropy run to out or even into the cluster outskirts; then the temperature will decline as kgT(r)=kn??cr? or steeper, after Eq. ("," To sum up, under the accretion rates prevailing at times in average environs, we expect the entropy run to out or even into the cluster outskirts; then the temperature will decline as $k_B T(r)= k\,n^{2/3}\propto r^{-2}$ or steeper, after Eq. (" 7) of CLFF09.,7) of CLFF09. Do suchbehaviors show up in real clusters?, Do suchbehaviors show up in real clusters? " Toward an answer, we use theSM to provide profilesof density and temperature from expressing the expected entropy run in a"," Toward an answer, we use theSM to provide profilesof density and temperature from expressing the expected entropy run in a" for each target field centred on the chosen galaxy. we have an ollset field. observed immediately following the target. overlapping in area. and inclepencently processed.,"for each target field centred on the chosen galaxy, we have an offset field, observed immediately following the target, overlapping in area, and independently processed." To mitigate the effect of current uncertainty. we further choose to adopt a robust method of error estimation.," To mitigate the effect of current uncertainty, we further choose to adopt a robust method of error estimation." The independently processed overlapping field gives a reliable. processing-independent method of assessing the uncertainties in the results.," The independently processed overlapping field gives a reliable, processing-independent method of assessing the uncertainties in the results." Since the aim of this experiment is to extend. detection limits to cooler objects than can be studied. with ground-based tclescopes. we consider the capabilities of the most sensitive ISOCAM filters.," Since the aim of this experiment is to extend detection limits to cooler objects than can be studied with ground-based telescopes, we consider the capabilities of the most sensitive ISOCAM filters." Figure ??. shows the LFOCAAL system senstivity (i.e. filter transmission © detector response) superposed on a range of blackbody [lux distributions., Figure \ref{filtersandbbody} shows the ISOCAM system senstivity (i.e. filter transmission $\times$ detector response) superposed on a range of blackbody flux distributions. The ISO LW2 and L3 filters are centred. around aand rrespectivelv. and. provide the greatest sensitivity to the widest range of temperatures available.," The ISO LW2 and LW3 filters are centred around and respectively, and provide the greatest sensitivity to the widest range of temperatures available." Ehe sensitivity of the filters to very cool stellar and sub-stellar objects is shown in figure ??.., The sensitivity of the filters to very cool stellar and sub-stellar objects is shown in figure \ref{filtersens}. his additionally emphasises the important restriction. that we remain insensitive to extremely cold gas clouds.," This additionally emphasises the important restriction, that we remain insensitive to extremely cold gas clouds." Detection of very cold barvonie dark matter requires longer wavelength observations than are possible with ISOC'AM., Detection of very cold baryonic dark matter requires longer wavelength observations than are possible with ISOCAM. The ISO CAM instrument (Cesarsky ct al 1996) was used with Garesee pixels. in à somewhat non-standard observing mode.," The ISO CAM instrument (Cesarsky et al 1996) was used with 6arcsec pixels, in a somewhat non-standard observing mode." An expected detectable signal at à S/N ratio 10 is 1-3 mJy in 200s of integration., An expected detectable signal at a S/N ratio 10 is 1-3 mJy in 200s of integration. We need to ensure that this noise level does decrease with increasing integration times. and to ensure maximal reliability of any detection of low surface brightness extended emission.," We need to ensure that this noise level does decrease with increasing integration times, and to ensure maximal reliability of any detection of low surface brightness extended emission." The CAAL detector has a special feature. requiring significant time to reach a steady-state response to a stable input flux. and further having a very long decay constant back to a stable state after the Dux is removed.," The CAM detector has a special feature, requiring significant time to reach a steady-state response to a stable input flux, and further having a very long decay constant back to a stable state after the flux is removed." Although corrections for these ellects are feasible in software (see below) we ensured they were minimised by adopting relatively long stabilisation times after cach pointing prior to each integration., Although corrections for these effects are feasible in software (see below) we ensured they were minimised by adopting relatively long stabilisation times after each pointing prior to each integration. That is. we chose the tradeoll between depth and. reliability to favour reliability.," That is, we chose the tradeoff between depth and reliability to favour reliability." As the results below illustrate. sullicient sensitivity was also achieved.," As the results below illustrate, sufficient sensitivity was also achieved." We also need to define a local 7kv background. adjacent to each observation. with several criteria.," We also need to define a local “sky” background, adjacent to each observation, with several criteria." Phe olfset field must be close to the primary pointing in time — to minimise svstem drift and changing solar elongation — and in direction. to," The offset field must be close to the primary pointing in time – to minimise system drift and changing solar elongation – and in direction, to" "There are two (vpes of solutions when the value of the SP is around zero ancl we categorize them as ""mixed-partitv cases.",There are two types of solutions when the value of the SP is around zero and we categorize them as “mixed-partity” cases. One (vpe is similar to the reference case (Fig., One type is similar to the reference case (Fig. " θα),", \ref{mix}a a). The value of the SP finally converges., The value of the SP finally converges. The other (wpe is interesting in (that the value of the svnunetric parameter does nol converge and continues to oscillate between the quadrupole aud the dipole solutions (Fie., The other type is interesting in that the value of the symmetric parameter does not converge and continues to oscillate between the quadrupole and the dipole solutions (Fig. Gbb)., \ref{mix}b b). Since (he averaged value in the calculation duration is close to zero. we adopted it for the SP in such cases.," Since the averaged value in the calculation duration is close to zero, we adopted it for the SP in such cases." The results of this parameter space study are shown in Fig. 7.., The results of this parameter space study are shown in Fig. \ref{pam}. The dvnamo cycle period is also shown by the contour lines., The dynamo cycle period is also shown by the contour lines. The period is shorter when the surface depth is thicker since the transport of (he magnetic flix by the dilfusivity is more effective., The period is shorter when the surface depth is thicker since the transport of the magnetic flux by the diffusivity is more effective. Panel (a) shows the result of the slow meridional [low case (η=1000curs 1))., Panel (a) shows the result of the slow meridional flow case $u_0=1000\ \mathrm{cm\ s^{-1}}$ ). Two points can be ascertained from this ligure., Two points can be ascertained from this figure. One is that. regzuxlless of the surface depth. the strong diffusivity (>3x10Pen?s 1) can make the magnetic field to become a dipole (SP~—1).," One is that regardless of the surface depth, the strong diffusivity $> 3\times10^{12}\mathrm{\ cm^2}\ s^{-1}$ ) can make the magnetic field to become a dipole $\sim-1$ )." The other is that with the thinner surface depth. no strong diffusivitv (>1xLO’en?s 1) is needed to generate the dipole field.," The other is that with the thinner surface depth, no strong diffusivity $> 1\times10^{12}\mathrm{\ cm^2}\ s^{-1}$ ) is needed to generate the dipole field." This means that (he magnetic field is more likely to be a dipole with the thinner surface depth., This means that the magnetic field is more likely to be a dipole with the thinner surface depth. Eig., Fig. 4b shows the result of the fast meridional flow case (uy=2000cms. 1).," 4b shows the result of the fast meridional flow case $u_0=2000\ \mathrm{cm\ s^{-1}}$ )." " It dis obvious that the parameter area [or the svmietric solutions. le. 5,>0. increases."," It is obvious that the parameter area for the symmetric solutions, i.e. $S_\mathrm{p}>0$, increases." This indicates that the fast meridional How causes the magnetic field to be symmetric., This indicates that the fast meridional flow causes the magnetic field to be symmetric. We investigated the dependence of the global magnetic parity on the distribution of the diffusivity (the amplitude and the surface depth) and the amplitude of the meridional flow., We investigated the dependence of the global magnetic parity on the distribution of the diffusivity (the amplitude and the surface depth) and the amplitude of the meridional flow. Three results were obtained., Three results were obtained. First. the model shows that the stronger diffisivitv near the," First, the model shows that the stronger diffusivity near the" be somewhat wnder-resolved in the simulations (sec TSCO06 for a full discussion of this issue).,be somewhat under-resolved in the simulations (see TSC06 for a full discussion of this issue). Yot. the average SZ distortion is uot the most casily detectable quautitv.," Yet, the average SZ distortion is not the most easily detectable quantity." Rather. the majority of CMD measurements are differential in nature. and scusitive to sanall changes ou top of an overall background that is much less well measured.," Rather, the majority of CMB measurements are differential in nature, and sensitive to small changes on top of an overall background that is much less well measured." To quantity these differences. in the center and low panels of Figure 2. we plot the RAIS scatter in AT/T due to the thermal and kinetic SZ effects respectively.," To quantify these differences, in the center and low panels of Figure 2, we plot the RMS scatter in $\Delta T/T$ due to the thermal and kinetic SZ effects respectively." In both cases the changes in the amplitude of the distortions are small. indicating that ACN have a minor mipact ou the overall variauce of the teuiperature aud velocity.," In both cases the changes in the amplitude of the distortions are small, indicating that AGN have a minor impact on the overall variance of the temperature and velocity." Iu Figure 3 we directly compare maps of the thermal SZ distortions from both these runs. iutegrated down o our final simulation redshift of +=1.2. The maps clearly indicate a lack of small lot regious in the AGN eedback run relative to the comparison run.," In Figure \ref{fig:SZmap} we directly compare maps of the thermal SZ distortions from both these runs, integrated down to our final simulation redshift of $z=1.2.$ The maps clearly indicate a lack of small hot regions in the AGN feedback run relative to the comparison run." To help ming out the structure in these maps. we also plot the sale data ou a logarithiic scale in Figure L.," To help bring out the structure in these maps, we also plot the same data on a logarithmic scale in Figure \ref{fig:SZmap2}." Hore we sec hat the AGN feedback rum has a higher average level of distortions. cousistent with the (gj evolution in Figure 2..," Here we see that the AGN feedback run has a higher average level of distortions, consistent with the $\left$ evolution in Figure \ref{fig:evolution}." Furthenuore. while it is difficult to tell the overall level of he variance between the maps. it is clear that the scale of the structures is quite different.," Furthermore, while it is difficult to tell the overall level of the variance between the maps, it is clear that the scale of the structures is quite different." Ta particular. while he ACN feedback simulation has fewer small pockets of rot eas. these are compensated for by a umber of larger and more diffuse heated regions.," In particular, while the AGN feedback simulation has fewer small pockets of hot gas, these are compensated for by a number of larger and more diffuse heated regions." Finally. the kinetic SZ maps. as shown in Figure 5.. ook simular in the two siuulations.," Finally, the kinetic SZ maps, as shown in Figure \ref{fig:kSZmap}, look similar in the two simulations." The differences, The differences Owing to the monotonic decay of the eccentricity. non-linear terms are active only in the earliest. stages of the evolution.,"Owing to the monotonic decay of the eccentricity, non-linear terms are active only in the earliest stages of the evolution." Llowever. non-linear elfects will be eritieal in other applications. such as determining the outcome of the eccentric instability in superhump binaries.," However, non-linear effects will be critical in other applications, such as determining the outcome of the eccentric instability in superhump binaries." In this paper a comprehensive theory of eccentric accretion clises has been presented., In this paper a comprehensive theory of eccentric accretion discs has been presented. Starting from the basic [LIuid-dynamical equations in three dimensions. | have derived the fundamental set of. one-dimensional equations that describe how the mass. angular momentum and eccentricity vector of a thin disc evolve as a result. of internal stresses and external forcing (equations 218- 220)).," Starting from the basic fluid-dynamical equations in three dimensions, I have derived the fundamental set of one-dimensional equations that describe how the mass, angular momentum and eccentricity vector of a thin disc evolve as a result of internal stresses and external forcing (equations \ref{fundamental_mass}- \ref{fundamental_e}) )." The analysis is asvmptotically exact in the limit of a thin disc. and allows for slowly varying eccentricities of arbitrary magnitudo.," The analysis is asymptotically exact in the limit of a thin disc, and allows for slowly varying eccentricities of arbitrary magnitude." These equations are generally valid ancl therefore of funclamental interest., These equations are generally valid and therefore of fundamental interest. They are the equivalent of the Gauss perturbation equations for a continuous disc., They are the equivalent of the Gauss perturbation equations for a continuous disc. Previously. Lyubarskij et al. (," Previously, Lyubarskij et al. (" 1994) succeeded in. deriving a related set of equations lor an eccentric cise by considering the conservation of mass. angular momentum and energy.,"1994) succeeded in deriving a related set of equations for an eccentric disc by considering the conservation of mass, angular momentum and energy." llowever. their analysis is restricted to the case in which the ellipses are all aligned. ancl do not precess.," However, their analysis is restricted to the case in which the ellipses are all aligned and do not precess." Their methoe works in this case because a knowledge of the angular momentum and energy of an orbiting body is sullicicnt to determine its semi-atus rectum ancl eccentricitv. but. no its longitude of periastron.," Their method works in this case because a knowledge of the angular momentum and energy of an orbiting body is sufficient to determine its semi-latus rectum and eccentricity, but not its longitude of periastron." A closed svstem of equations is obtained only if the ellipses are artificially constrained no to precess., A closed system of equations is obtained only if the ellipses are artificially constrained not to precess. In reality. such precession is inevitable and the evolution of the longitude of periastron must be determine from a full analysis of the horizontal components. of the equation of motion.," In reality, such precession is inevitable and the evolution of the longitude of periastron must be determined from a full analysis of the horizontal components of the equation of motion." This leads to an equation for the eccentricity vector. or complex eccentricity. which is not in conservative form.," This leads to an equation for the eccentricity vector, or complex eccentricity, which is not in conservative form." The second achievement of this paper is the explicit development of the equations in the case of à. specific stress model which. it is hoped. gives a fair representation of the turbulent stress in an aceretion disc.," The second achievement of this paper is the explicit development of the equations in the case of a specific stress model which, it is hoped, gives a fair representation of the turbulent stress in an accretion disc." To obtain the coclicicnts in the evolutionary equations requires a solution of the non-linear PDEs that govern the azimuthal and. vertical structure of the disc., To obtain the coefficients in the evolutionary equations requires a solution of the non-linear PDEs that govern the azimuthal and vertical structure of the disc. Lt also requires an understanding of the relation between the turbulent stress tensor and the velocity gradient tensor., It also requires an understanding of the relation between the turbulent stress tensor and the velocity gradient tensor. The simplest plausible relation. adopted in almost all theoretical work on accretion disces. is an cllective viscosity model in which an instantaneous lincar relation is assumed. and the equation of motion therefore reduces to the Navier-Stokes equation.," The simplest plausible relation, adopted in almost all theoretical work on accretion discs, is an effective viscosity model in which an instantaneous linear relation is assumed, and the equation of motion therefore reduces to the Navier-Stokes equation." In this paper E have introduced a Maxwellian viscoelastic mocel ∪⇂⋅↿↓∐⋅⋯↓⋅∣⋡⊔↓∢⋅⊔↿⊳∖↿↓⋅∢⋅⊳∖⊳∖↕↓↕⋜⋯⋯⇍≼↛↓⋅∢⊾⇂⊲↓, In this paper I have introduced a Maxwellian viscoelastic model of the turbulent stress in an accretion disc. ∪⊔∠⇂⊀↓⊳∖≼⋱↾∐↥⊲↓⊳∖⋃⋖⋅⊔⋖⋅↓⋅⋜↧⇂⋠↓∠⋖⋅≱∖ ? the conventional alpha viscosity model. to account. for the non-zero relaxation time of the turbulence. and is physically motivated. by a consideration of the nature of AHID turbulence.," This generalizes the conventional alpha viscosity model to account for the non-zero relaxation time of the turbulence, and is physically motivated by a consideration of the nature of MHD turbulence." Phe PDEs governing the azimuthal and vertical structure of the disc. including the ellects of vertical motion. dissipation of energy and radiative (ransport. have been reduced exactly to à. set. of. dimensionless ODEs which can be solved numerically to high accuracy to vield the coefficients. required. for. the evolutionary equations.," The PDEs governing the azimuthal and vertical structure of the disc, including the effects of vertical motion, dissipation of energy and radiative transport, have been reduced exactly to a set of dimensionless ODEs which can be solved numerically to high accuracy to yield the coefficients required for the evolutionary equations." Fhis shows that the. technique of non-linear. separation of variables. applied first to warped discs (Ogilvie. 1999. 2000). is not. restricted. to. purely. viscous models but. can incorporate improved: representations of the stress as our unclerstancing of magnetorotational turbulence develops.," This shows that the technique of non-linear separation of variables, applied first to warped discs (Ogilvie 1999, 2000), is not restricted to purely viscous models but can incorporate improved representations of the stress as our understanding of magnetorotational turbulence develops." lt has been confirmed that circular disces are usually viscously unstable to short-wavelength eccentric perturbations. as found by Lyubarskij et al. (," It has been confirmed that circular discs are usually viscously unstable to short-wavelength eccentric perturbations, as found by Lyubarskij et al. (" 1994). if the conventional alpha viscosity. model is adopted.,"1994), if the conventional alpha viscosity model is adopted." It has, It has In refaQ-effects the deficiency of short wavelength flux for the model which matches the observed 2.11ju visibility of was explained by the assumption of a spherically symmetric dust distribution.,"In \\ref{a0-effects} the deficiency of short wavelength flux for the model which matches the observed $2.11\,{\rm\mu m}$ visibility of was explained by the assumption of a spherically symmetric dust distribution." However. the deficiency could be due to a different cause.," However, the deficiency could be due to a different cause." For example. the optical constants of “astronomical” silicates at wavelengths E7.5ju are not well known (Ossenkopf et citeOHMO92)) and it is possible that the optical properties of the grains around at short wavelengths differ from our assumption.," For example, the optical constants of `astronomical' silicates at wavelengths $\la 7.5\,{\rm\mu m}$ are not well known (Ossenkopf et \\cite{OHM92}) ) and it is possible that the optical properties of the grains around at short wavelengths differ from our assumption." Therefore. we have investigated the effects of different dust optical properties on the SEDand the visibility. as shown in refsed-Ow92-qext..," Therefore, we have investigated the effects of different dust optical properties on the SEDand the visibility, as shown in \\ref{sed-Ow92-qext}." " The models have been calculated with the parameters of model A (except for the value of 7,55) using the optical data from Ossenkopf et ((1992)) for ""cold"" silicates (sil-Oc). from Draine Lee (1984)) (sil-DL) and from David Péggourié (1995)) (sil-DP)."," The models have been calculated with the parameters of model A (except for the value of $\tau_{0.55}$ ) using the optical data from Ossenkopf et \cite{OHM92}) ) for `cold' silicates (sil–Oc), from Draine Lee \cite{DL84}) ) (sil–DL) and from David Péggourié \cite{DP95}) ) (sil–DP)." " The extinction coefficient per unit volume of the grains for «,,=0.1jnu is shown in refkap-Ow92-gext and the derived properties of the models are given in Table Al."," The extinction coefficient per unit volume of the grains for $a_{\rm gr} = 0.1\,{\rm \mu m}$ is shown in \\ref{kap-Ow92-qext} and the derived properties of the models are given in Table \ref{tab-Ow92-qext}." " The differences of the &4/V. resulting from the optical data sets are more or less directly translated into modifications of the SED. if the different values for 7,55 are taken into account."," The differences of the $\kappa_{\rm ext}/V_{\rm gr}$ resulting from the optical data sets are more or less directly translated into modifications of the SED, if the different values for $\tau_{0.55}$ are taken into account." " Compared to the ""warm? silicates of Ossenkopf et ((1992)) (sil-Ow). the extinction of sil-Oc grains is higher between Az1.3jan and δµια. resulting in à lower monochromatic flux of the corresponding model."," Compared to the `warm' silicates of Ossenkopf et \cite{OHM92}) ) (sil–Ow), the extinction of sil–Oc grains is higher between $\lambda \approx 1.3\,{\rm\mu m}$ and $8\,{\rm\mu m}$, resulting in a lower monochromatic flux of the corresponding model." For the sil- and sil-DP data the extinction ts lower resulting in an excess of flux., For the sil--DL and sil–DP data the extinction is lower resulting in an excess of flux. Because the shape of the silicate features at around LOjau and 18aun is similiar for the sil-Ow. sil-Oc. and sII-DP. data. except for a slightly different ratio of the peak strengths. they yield comparably good fits to width and strength of the observed feature. which has its center at 10prn.," Because the shape of the silicate features at around $10\,{\rm\mu m}$ and $18\,{\rm\mu m}$ is similiar for the sil–Ow, sil–Oc, and sil–DP data, except for a slightly different ratio of the peak strengths, they yield comparably good fits to width and strength of the observed feature, which has its center at $10\,{\rm\mu m}$." In contrast. the silicate feature from the sil-DL data peaks at 9.7jou. and it is broader than the observed one.," In contrast, the silicate feature from the sil–DL data peaks at $9.7\,{\rm\mu m}$, and it is broader than the observed one." Because the value of M depends on the adopted optical properties of the grains (see refmdoteq)). we obtain Ma for the different models ranging from 1.610[ων το 2.710“Aixο (see Table Al).," Because the value of $\dot{M}_{\rm d}$ depends on the adopted optical properties of the grains (see \\ref{mdoteq}) ), we obtain $\dot{M}_{\rm d}$ for the different models ranging from $1.6\,10^{-7}\,{\rm M_{\odot}yr^{-1}}$ to $2.7\,10^{-7}\,{\rm M_{\odot}yr^{-1}}$ (see Table \ref{tab-Ow92-qext}) )." Nevertheless. if the dust mass loss rate is derived from the match of the silicate absorption feature. its value is not very sensitive to variations of the effective temperature. dust temperature at the inner boundary and the grain radius as long as the models are calculated with the same optical constants.," Nevertheless, if the dust mass loss rate is derived from the match of the silicate absorption feature, its value is not very sensitive to variations of the effective temperature, dust temperature at the inner boundary and the grain radius as long as the models are calculated with the same optical constants." The changes of the 2.11jii visibilities are again caused by the different optical depths of the models at this wavelength.," The changes of the $2.11\,{\rm\mu m}$ visibilities are again caused by the different optical depths of the models at this wavelength." For other fixed parameters a higher optical depth produces a more extended brightness distribution and. thereby. a steeper decline of the visibility.," For other fixed parameters a higher optical depth produces a more extended brightness distribution and, thereby, a steeper decline of the visibility." The optical depth at 2.11jin has similiar values for the sil-Ow and sil-Oc models and lower. but again similiar values for the sil-DL and sil-DP models.," The optical depth at $2.11\,{\rm\mu m}$ has similiar values for the sil–Ow and sil–Oc models and lower, but again similiar values for the sil–DL and sil–DP models." Hence. the decline of visibilities from the latter models ts The optical properties from David Péggourié (1995)) yield a fit of the silicate feature. which is comparable to the fit obtained with the Ossenkopf et ((1992)) data. but they produce an excess of flux at smaller wavelengths for a grain radius of 0.1 jiu.," Hence, the decline of visibilities from the latter models is The optical properties from David Péggourié \cite{DP95}) ) yield a fit of the silicate feature, which is comparable to the fit obtained with the Ossenkopf et \cite{OHM92}) ) data, but they produce an excess of flux at smaller wavelengths for a grain radius of $0.1\,{\rm\mu m}$ ." From the investigation of the effects resulting, From the investigation of the effects resulting 2006: Dominik et al.,2006; Dominik et al. 2007: Blum et al., 2007; Blum et al. 2008)., 2008). Several recent papers have suggested. (hat (he planetesimal formation mechanism jumps over this meter size barrier and instead large objects of hundreds of kilometers in size coalesce directly. [rom over-dense clouds of em to meter sized particles in a hiehlv (turbulent. primordial solar nebula (Johansen et al., Several recent papers have suggested that the planetesimal formation mechanism jumps over this meter size barrier and instead large objects of hundreds of kilometers in size coalesce directly from over-dense clouds of cm to meter sized particles in a highly turbulent primordial solar nebula (Johansen et al. 2007: Cuzzi et al., 2007; Cuzzi et al. 2008: Morbidelli et al., 2008; Morbidelli et al. 2009: Johansen οἱ al., 2009; Johansen et al. 2009)., 2009). Numerical collisional simulations as performed lor the main asteroil belt. (Morbidelli el al., Numerical collisional simulations as performed for the main asteroid belt (Morbidelli et al. 2009) and their effect on the size distribution for the outer solar svstem small body reservoirs are warranted (ο constrain the role collisions play in helping produce the observed size distributions in (hese locations., 2009) and their effect on the size distribution for the outer solar system small body reservoirs are warranted to constrain the role collisions play in helping produce the observed size distributions in these locations. It is likely (hat the Trojans and Kuiper Delt objects have undergone less collisional evolution than (he main belt. asteroids since enplacecl in their current orbits (Xenvon et al., It is likely that the Trojans and Kuiper Belt objects have undergone less collisional evolution than the main belt asteroids since emplaced in their current orbits (Kenyon et al. 2008: Morbidelli et al., 2008; Morbidelli et al. 2009: Levison et al., 2009; Levison et al. 2009) aud if confirmed. would indicate the observed. roll-over in their size distribution is likely [rom primordial formation of the planetesimals., 2009) and if confirmed would indicate the observed roll-over in their size distribution is likely from primordial formation of the planetesimals. In addition. the outer Solar System objects are likely to have some material strength (Levison et al.," In addition, the outer Solar System objects are likely to have some material strength (Levison et al." 2009: Leinhardt S(ewart 2009). which appears to be an impediment for collisional erosion to account for (he observed roll-over in the Kuiper Belt size distribution (Pan and Sari 2005).," 2009; Leinhardt Stewart 2009), which appears to be an impediment for collisional erosion to account for the observed roll-over in the Kuiper Belt size distribution (Pan and Sari 2005)." To date the size distributions of these more distant outer solar svstem reservoirs are much more poorly characterized by observations as the main asteroid belt., To date the size distributions of these more distant outer solar system reservoirs are much more poorly characterized by observations as the main asteroid belt. Detailed in this work is the first measurement of the size distribution for the Neptune Trojans., Detailed in this work is the first measurement of the size distribution for the Neptune Trojans. The observations in (Bis work. when compared with limited collisional simulations (Morbidelli et al.," The observations in this work, when compared with limited collisional simulations (Morbidelli et al." 2009). show that the lack of objects tens of kilometers in size for all known reservoirs agrees with planetesimal formation skipping over forming significant numbers of objects in the tens of kilometer size range for all areas of the Solar System.," 2009), show that the lack of objects tens of kilometers in size for all known reservoirs agrees with planetesimal formation skipping over forming significant numbers of objects in the tens of kilometer size range for all areas of the Solar System." In (his scenario. objects smaller than about r~35JE—50 km are most likely collisional bv-products of larger primordial objects (Farinella Davis 1996: IXeinvon Dromleyv 2004; Ixenvon et al.," In this scenario, objects smaller than about $r \sim 35-50$ km are most likely collisional by-products of larger primordial objects (Farinella Davis 1996; Kenyon Bromley 2004; Kenyon et al." 2008)., 2008). It is possible that future collisional simulations using size-dependent drift due to the drag of a low turbulent solar nebular gas during accretion could account for the observed roll-over Weidenschilling 2010) in the size distributions. but this scenario would likely be much more dependent on formation location in the solar nebula unlike the primordial coalescence of large objects [rom over-dense dust. clouds.," It is possible that future collisional simulations using size-dependent drift due to the drag of a low turbulent solar nebular gas during accretion could account for the observed roll-over (Weidenschilling 2010) in the size distributions, but this scenario would likely be much more dependent on formation location in the solar nebula unlike the primordial coalescence of large objects from over-dense dust clouds." Comparing the various observed small body reservoirs shows that the Ixuiper Belt holds, Comparing the various observed small body reservoirs shows that the Kuiper Belt holds to the finding bx Sougaila Cowie (1996) of rapid evolution near ;=3.1 there is no significaut overall change in the balance of the ratio values anywhere over the whole range in redshift.,to the finding by Songaila Cowie (1996) of rapid evolution near $z = 3.1$ there is no significant overall change in the balance of the ratio values anywhere over the whole range in redshift. The use here of sinele-phase ionization cloud colmpouncuts to probe the radiation ficld must be more effective than suming over whole svstenis as doue by Sougaila Cowie. but to compare with their data the ratios of the separately totalled system values also are plotted im Figure 2: again there is no evidence for stroug evolution near ;=3.1. although at 2— the scatter iu these values seclus larger than at higher redshifts.," The use here of single-phase ionization cloud components to probe the radiation field must be more effective than summing over whole systems as done by Songaila Cowie, but to compare with their data the ratios of the separately totalled system values also are plotted in Figure 2: again there is no evidence for strong evolution near $z=3.1$, although at $z \sim 2$ the scatter in these values seems larger than at higher redshifts." This may be indicating the evolution of collapsing structures., This may be indicating the evolution of collapsing structures. Au evolving b5-value distribution. as noted above. and evident change. e.g. i NOC ID/N(GC IV) indicating a trend to higher densities at lower redshifts. also point to this.," An evolving $b$ -value distribution, as noted above, and evident change, e.g., in N(C II)/N(C IV) indicating a trend to higher densities at lower redshifts, also point to this." Such structure evolution will be investigated fully iu a later paper Gu preparation)., Such structure evolution will be investigated fully in a later paper (in preparation). More information ou the shape of the ionizing spectrum can be obtained from displavs of the ratios N(Si IV)/NCC IV) vs NCC ID/N(GC IV) than from N(Si IV)/N(C IV) alone (Songaila Cowie 1996: Caroux Shull 1997)., More information on the shape of the ionizing spectrum can be obtained from displays of the ratios N(Si IV)/N(C IV) vs N(C II)/N(C IV) than from N(Si IV)/N(C IV) alone (Songaila Cowie 1996; Giroux Shull 1997). Iu Figure 3 is such a plot from the Q1626|618 data set compared with model predictions of the CLOUDY code (Ferland 1996) for several assmuec, In Figure 3 is such a plot from the Q1626+643 data set compared with model predictions of the CLOUDY code (Ferland 1996) for several assumed Iu Figure 3 is such a plot from the Q1626|618 data set compared with model predictions of the CLOUDY code (Ferland 1996) for several assmuect, In Figure 3 is such a plot from the Q1626+643 data set compared with model predictions of the CLOUDY code (Ferland 1996) for several assumed Most. il not all. galaxies with a stellar bulge are thought to harbor a super-amassive black hole (SMBIL) in their nuclei.,"} Most, if not all, galaxies with a stellar bulge are thought to harbor a super-massive black hole (SMBH) in their nuclei." Accretion onto ancl feedback (i.e.. both radiative and mechanical enerev output) from the SMDITL is one of the fundamental astrophysical processes that govern ealaxv evolution.," Accretion onto and feedback (i.e., both radiative and mechanical energy output) from the SMBH is one of the fundamental astrophysical processes that govern galaxy evolution." Compared to their hish-redshift counterparts. most 5MDIIs in the local universe. when observed. are lound {ο be radiatively quiescent (e.g.. Zhang et al.," Compared to their high-redshift counterparts, most SMBHs in the local universe, when observed, are found to be radiatively quiescent (e.g., Zhang et al." 2009: Gallo et al., 2009; Gallo et al. 2010). and are often dubbed low-himinosity active galactic nuclei (LLAGNs: οἱ.," 2010), and are often dubbed low-luminosity active galactic nuclei (LLAGNs; cf." Ho 2008)., Ho 2008). By analogy (ο Galactic black hole binaries in a low/hard state (οἱ., By analogy to Galactic black hole binaries in a low/hard state (cf. MeClintoek. Remillard 2006). LLAGNs are generally thought to be powered by racliatively inellicient. advection-dominated accretion aud/or outflow (Naravan Yi 1994: Blancdlord Begelinan: Quataert Cruzinov 2000) that operate at very sub-Eddington accretionrates!.," McClintock Remillard 2006), LLAGNs are generally thought to be powered by radiatively inefficient, advection-dominated accretion and/or outflow (Narayan Yi 1994; Blandford Begelman; Quataert Gruzinov 2000) that operate at very sub-Eddington accretion." . Albeil often subject to instrumental limitations as a consequence of their radiative quiescence. studies of LLAGNs have important implications for accretion plivsies. Πιοας and feedback mechanisms. and black hole growth over cosmic time.," Albeit often subject to instrumental limitations as a consequence of their radiative quiescence, studies of LLAGNs have important implications for accretion physics, fueling and feedback mechanisms, and black hole growth over cosmic time." A well-known LLAGN is the SMDII in our Galaxy. Ser A (ef.," A well-known LLAGN is the SMBH in our Galaxy, Sgr $^\ast$ (cf." Melia Faleke 2001). which has an extremely. quiescent bolometric luminosity of ~3x10?Liqa (Dor its mass of 4x10°ΧΙ: Ghez et al.," Melia Falcke 2001), which has an extremely quiescent bolometric luminosity of $\sim$$3\times10^{-9} L_{\rm Edd}$ (for its mass of $\sim$$4\times10^6{\rm~M_\odot}$; Ghez et al." 2003). a factor of 10?—10° lower than the inferred values for most LLAGNs (e.g.. Zhang et al.," 2003), a factor of $10^2-10^6$ lower than the inferred values for most LLAGNs (e.g., Zhang et al." 2009: Ho 2009)., 2009; Ho 2009). More unusual about Ser À* is its flaring emission detected in X-ray. infrared and radio bands (Baganoll et al.," More unusual about Sgr $^\ast$ is its flaring emission detected in X-ray, infrared and radio bands (Baganoff et al." 2001: Genzel οἱ al., 2001; Genzel et al. 2003: Zhao et al., 2003; Zhao et al. 2003)., 2003). In particular. the N-ravy. Lares show the greatest variability. with hour-timescales," In particular, the X-ray flares show the greatest variability, with hour-timescales" "In order to illustrate the quality of the fit more clearly, we zoom in on the monochromatic amplitude plot for £= 0 in the left panel of Fig. 10..","In order to illustrate the quality of the fit more clearly, we zoom in on the monochromatic amplitude plot for $\ell=$ 0 in the left panel of Fig. \ref{zoomampphase}." " Here, we also include the uncertainty on the observed amplitudes as obtained from the least-squares fits to the light curve for each wavelength bin (thin vertical line segments shifted downwards along the y-axis for clarity)."," Here, we also include the uncertainty on the observed amplitudes as obtained from the least-squares fits to the light curve for each wavelength bin (thin vertical line segments shifted downwards along the y-axis for clarity)." " It can be seen that, while the observed amplitude behaviour in the continuum is matched nearly perfectly by the theoretical curve, there are some discrepancies in the spectral lines."," It can be seen that, while the observed amplitude behaviour in the continuum is matched nearly perfectly by the theoretical curve, there are some discrepancies in the spectral lines." " Most strikingly, the amplitude dip corresponding to the He II line at 4686 iis predicted far weaker than observed, much like what we found for the model atmosphere fit to the time-averaged spectrum in Fig. 5.."," Most strikingly, the amplitude dip corresponding to the He II line at 4686 is predicted far weaker than observed, much like what we found for the model atmosphere fit to the time-averaged spectrum in Fig. \ref{fitboth}." This is almost certainly due to the lack of metals in the model atmospheres used for the computation., This is almost certainly due to the lack of metals in the model atmospheres used for the computation. " A more puzzling feature is that the theoretical amplitudes in the Balmer line cores systematically deviate from those observed: while they are similar to, or slightly lower than the measurements for the higher Balmer lines (above He), they increasingly overestimate the observed amplitudes in the lines at higher wavelengths (for He, Hó, and especially Hy and Hf)."," A more puzzling feature is that the theoretical amplitudes in the Balmer line cores systematically deviate from those observed: while they are similar to, or slightly lower than the measurements for the higher Balmer lines (above $\epsilon$ ), they increasingly overestimate the observed amplitudes in the lines at higher wavelengths (for $\epsilon$ , $\delta$, and especially $\gamma$ and $\beta$ )." We are not sure whether this is due to some observational effect or caused by missing ingredients in our models (particularly concerning the chemical composition of the atmosphere)., We are not sure whether this is due to some observational effect or caused by missing ingredients in our models (particularly concerning the chemical composition of the atmosphere). " At the request of the referee we re-computed the Q-value of the fit taking into account only the continuum and the extended line wings (specifically, we masked out bands +6Awide centered around Hf, Hell 4686, Hy, Hó, He and H8)."," At the request of the referee we re-computed the $Q$ -value of the fit taking into account only the continuum and the extended line wings (specifically, we masked out bands $\pm$ wide centered around $\beta$, HeII 4686, $\gamma$ , $\delta$ , $\epsilon$ and H8)." " As expected, the quality-of-fit is improved, with Q=0.999 (€=0), Q=0.503 (€=1), Q=0.223 (€=2) and Q«0.001 for higher ἔ values."," As expected, the quality-of-fit is improved, with $Q$ =0.999 $\ell$ =0), $Q$ =0.503 $\ell$ =1), $Q$ =0.223 $\ell$ =2) and $Q\ll$ 0.001 for higher $\ell$ values." " This is simply associated with the fact that there are now less deviations between the predicted and observed amplitudes, and nicely illustrates the very good match achieved for a radial mode in the continuum."," This is simply associated with the fact that there are now less deviations between the predicted and observed amplitudes, and nicely illustrates the very good match achieved for a radial mode in the continuum." " While we are conviced that the dominant mode in EC 20338-1925 is radial from the amplitude data alone, we also analysed the corresponding phase data as a consistency check."," While we are conviced that the dominant mode in EC $-$ 1925 is radial from the amplitude data alone, we also analysed the corresponding phase data as a consistency check." " Given the high noise level of the measurements, we assumed a degree of ἑ= 0 from the outset, and attempted to fit the theoretical phases to those observed."," Given the high noise level of the measurements, we assumed a degree of $\ell=$ 0 from the outset, and attempted to fit the theoretical phases to those observed." " In order to be able to compute the monochromatic phases accurately, we extended our existing code for the computation of the pulsational flux perturbation by an optional radial velocity (RV) parameter."," In order to be able to compute the monochromatic phases accurately, we extended our existing code for the computation of the pulsational flux perturbation by an optional radial velocity (RV) parameter." " This parameter was not necessary for the theoretical quantities presented by ? because in that study we were interested only in wavelength-integrated phase measurements, which are dominated by the contributions from the continuum."," This parameter was not necessary for the theoretical quantities presented by \citet{randall2005} because in that study we were interested only in wavelength-integrated phase measurements, which are dominated by the contributions from the continuum." " As can be seen from Fig. 7,,"," As can be seen from Fig. \ref{ampphase}," " these yield a relatively constant phase as a function of wavelength, which is consistent with the very small phase shifts predicted from one filter bandpass to the next in ?.."," these yield a relatively constant phase as a function of wavelength, which is consistent with the very small phase shifts predicted from one filter bandpass to the next in \citet{randall2005}." " However, in a spectral line the moving matter produces significant distortions and phase delays over a pulsation cycle, and these need to be taken into account for monochromatic phase calculations."," However, in a spectral line the moving matter produces significant distortions and phase delays over a pulsation cycle, and these need to be taken into account for monochromatic phase calculations." " The distortions also affect the amplitudes in the spectral lines, but the effect is thought to be relatively small for the broader lines andwas not included in the computations presented abovefor technicalreasons."," The distortions also affect the amplitudes in the spectral lines, but the effect is thought to be relatively small for the broader lines andwas not included in the computations presented abovefor technicalreasons." It remains to be investigated whether an incorporation of the, It remains to be investigated whether an incorporation of the "lighteurves for FU Tau A. We hanel-picked a sample of 48 (1) and 45 (11) sources. including EU ""Tau A and. all other isolated stars with similar brightness in the FOV.","lightcurves for FU Tau A. We hand-picked a sample of 48 (I) and 45 (R) sources, including FU Tau A and all other isolated stars with similar brightness in the FOV." For these objects we carried out aperture photometry wine a constan aperture of ppixel and à sky annulus of ppixel., For these objects we carried out aperture photometry using a constant aperture of pixel and a sky annulus of pixel. " Duc to the poor secing. the companion FU ""Tau D is not detectec in most of the CΑΡΓΟΣ images: no photometry was possible [or this object."," Due to the poor seeing, the companion FU Tau B is not detected in most of the CAFOS images; no photometry was possible for this object." To correct. for the cllects of variable sccing anc transparency (relative. calibration’). we calculated: the average time series of non-variable stars in the field. anc subtracted it from. all lighteurves.," To correct for the effects of variable seeing and transparency ('relative calibration'), we calculated the average time series of non-variable stars in the field and subtracted it from all lightcurves." Phe non-variable stars were chosen using the procedure outlined in ?., The non-variable stars were chosen using the procedure outlined in . . Phe routine selected LS (I3) and 10 (D) stars as non-variable. based on a comparison of their lighteurve with the average lighteurve of all other stars.," The routine selected 18 (R) and 10 (I) stars as non-variable, based on a comparison of their lightcurve with the average lightcurve of all other stars." The average RAIS of the lighteurves for these non-variable stars is 0.010 (I5) ancl mmae (1). which defines the photometric accuracy.," The average RMS of the lightcurves for these non-variable stars is 0.010 (R) and mag (I), which defines the photometric accuracy." " From the BUSCA images we obtained I-band lighteurves for FU ""Tau A and all other stars in the field. again using aperture photometry with the same parameters as [or CAFOS."," From the BUSCA images we obtained I-band lightcurves for FU Tau A and all other stars in the field, again using aperture photometry with the same parameters as for CAFOS." The bright star 2\LASS 04232455|2500084 clearly looks variable. but 7 faint [eld stars show stable lighteurves.," The bright star 2MASS J04232455+2500084 clearly looks variable, but 7 faint field stars show stable lightcurves." Their average lighteurve is used for the relative calibration., Their average lightcurve is used for the relative calibration. After. subtraction of the average. lehteurve. the RALS for the 7 eld stars is 0.011-0.025. an average of mmag. confirming that they are non-variable.," After subtraction of the average lightcurve, the RMS for the 7 field stars is 0.011-0.025, an average of mag, confirming that they are non-variable." For comparison. the RATS lor 2ALASS J04232455|2500084. is mma.," For comparison, the RMS for 2MASS J04232455+2500084 is mag." The lighteurves from CAFOS and. BUSCA show. that EU Tau A is a variable star., The lightcurves from CAFOS and BUSCA show that FU Tau A is a variable star. Hs RAIS is 0.04. (I-band. CAFOS). 0.02 λος. I-band). anc 0.04 1-band). significantly more than comparison stars PM. for CAFOS. 0.02mmag for BUSCA. Sect. ShownM Figs.," Its RMS is 0.04 (R-band, CAFOS), 0.02 (CAFOS, I-band), and 0.04 (BUSCA, I-band), significantly more than comparison stars mag for CAFOS, mag for BUSCA, Sect. \ref{relcal}) )." ‘The liehteurves from CALOS and. BUSCA are in 1., The lightcurves from CAFOS and BUSCA are shown in Figs. and 2.., \ref{f1} and \ref{f4}. Most of the variability is on timescales of 71 eel: these variations are intrinsic to the source and are not seen in the reference stars., Most of the variability is on timescales of $>1$ d; these variations are intrinsic to the source and are not seen in the reference stars. In addition. the CAFOS lighteurves show intra-night variability with smaller anmplitucle.," In addition, the CAFOS lightcurves show intra-night variability with smaller amplitude." These variations. are partly seen in the reference stars as well.," These variations, however, are partly seen in the reference stars as well." EU Pau X however.is by [ar the νους object in our sample., FU Tau A is by far the reddest object in our sample. The influence of the atmospheric conditions is colour-depoencent. which is not taken into account in our correction.," The influence of the atmospheric conditions is colour-dependent, which is not taken into account in our correction." Thus. one could expect the reddest objects to show some residuals of the trends caused by atmospheric ellects.," Thus, one could expect the reddest objects to show some residuals of the trends caused by atmospheric effects." Hence. we do not consider the low-level intra-night variability in EU Tau A to be real.," Hence, we do not consider the low-level intra-night variability in FU Tau A to be real." Using all available CΑΟ datapoints for à given filter. we searched. for a period using a combination of three routines.," Using all available CAFOS datapoints for a given filter, we searched for a period using a combination of three routines." Phe R- and the Lhand dishteurves show a dominant peak in the CLIZANed. periodogram at a period. of 3.8 (1t) and 4.0dd (D., The R- and the I-band lightcurves show a dominant peak in the CLEANed periodogram at a period of 3.8 (R) and d (I). " The same peak is detected in the Scargle periodogram with a false alarm probability. below 10"" (calculated: following ?)).", The same peak is detected in the Scargle periodogram with a false alarm probability below $10^{-5}$ (calculated following ). In. the Scargle periodogram. however. the peak is very. broad. and does not permit an accurate assessment of the period.," In the Scargle periodogram, however, the peak is very broad and does not permit an accurate assessment of the period." " Finally, we compare the IMS in the original lighteurve with the RAIS after subtracting a sine function with the suspected. period using the F-test."," Finally, we compare the RMS in the original lightcurve with the RMS after subtracting a sine function with the suspected period using the F-test." Again. the period of dd is highly significant in both bands. with false alarm probabilities below 10.7.," Again, the period of d is highly significant in both bands, with false alarm probabilities below $10^{-5}$." In Fig., In Fig. 3. we show the phase-folded lighteurve assuming /?=3.8 dd. which we consider to be the best-fitting period from all three algorithms.," \ref{f3} we show the phase-folded lightcurve assuming $P=3.8$ d, which we consider to be the best-fitting period from all three algorithms." Ehe observing run covers only one M and the sampling of the period is patchy (in phase space).," The observing run covers only one period, and the sampling of the period is patchy (in phase space)." Therefore. a relatively large range of periods dd) give a decent fit to the data. ie. the uncertainty in the period is in the range of 0.3 dd. Although the coverage with BUSCA is not sullicicn ο carry out an independent period. search. we use these datapoints to check the period derived. from the CAAEOS iehteurves.," Therefore, a relatively large range of periods d) give a decent fit to the data, i.e. the uncertainty in the period is in the range of $\pm 0.3$ d. Although the coverage with BUSCA is not sufficient to carry out an independent period search, we use these datapoints to check the period derived from the CAFOS lightcurves." In Fig., In Fig. 4 we show a phaseplot for all I-baux data. assuming a period of dd. (left. panel) and. ck (right panel).," \ref{f5} we show a phaseplot for all I-band data, assuming a period of d (left panel) and d (right panel)." X good. match is achieved for a period of dd. slightly larger than the period determined from the t- and Iband οΑΕΤΟ lighteurves.," A good match is achieved for a period of d, slightly larger than the period determined from the R- and I-band CAFOS lightcurves." A period of dd only matches if a significant phase shift between the CATOS anc he BUSCA data is assumed., A period of d only matches if a significant phase shift between the CAFOS and the BUSCA data is assumed. From the Landolt standard fields observed in the last night of the CAPOS run we derived a photometric calibration., From the Landolt standard fields observed in the last night of the CAFOS run we derived a photometric calibration. In total. we observed. 45 standards fromwhich 40 eave useful photometry.," In total, we observed 45 standards fromwhich 40 gave useful photometry." These stars cover a wide range in airmass from VY=1.3 to 2.4V., These stars cover a wide range in airmass from $X=1.3$ to 2.0. For the R-band the absolute magnitudes Ho are well reproduced. with a zeropoint shift ancl an extinction term: /?=r1.6470.147.N., For the R-band the absolute magnitudes $R$ are well reproduced with a zeropoint shift and an extinction term: $R = r - 1.647 - 0.147X$. The RAIS for this transformation is 0.03. dominated by the uncertainty in the zeroterm.," The RMS for this transformation is 0.03, dominated by the uncertainty in the zeroterm." For the L-band. it turns out that an aclelitional colour term improves the IMS from 0.1 to 0.05: f=?2281]0.060X|0.1360 (," For the I-band, it turns out that an additional colour term improves the RMS from 0.1 to 0.05: $I = i - 2.281 - 0.069X + 0.136(r-i)$. (" 1n these equations. the lower case letters are instrumental magnitudes and upper case letters calibrated magnitudes.),"In these equations, the lower case letters are instrumental magnitudes and upper case letters calibrated magnitudes.)" Applying this transformation to the instrumental maenituces measured for FU Tau A “Ne R=15.39 and f=13.73 mmag for the night 2010-12-ο, Applying this transformation to the instrumental magnitudes measured for FU Tau A gives $R = 15.39$ and $I = 13.73$ mag for the night 2010-12-02. For this night the MM for EU Tlau A ux a n uncertainty of0.02 liberosmimag (see Sect. Tm adNU, For this night the lightcurve for FU Tau A indicates a photometric uncertainty of $\sim 0.02$ mag (see Sect. \ref{lc}) ). NAdding this in quadrature to the CLLOLrs. uncertainty in the absolute magnitudes is 0.04 in the R-band and 0.05 in the I-band.," Adding this in quadrature to the calibration errors, the total uncertainty in the absolute magnitudes is 0.04 in the R-band and 0.05 in the I-band." " Published photometry in ""A bands for FU Tau A is available from. CELT (CousinsiarL). Sloan (r. i). and the Carlsbere Meridian Catalog 14 close to Sloan r)."," Published photometry in similar bands for FU Tau A is available from CFHT (Cousins I), Sloan (r, i), and the Carlsberg Meridian Catalog 14 (filter close to Sloan r)." CousinsTo transform the Sloan. magnitudes to the Johnson system. we used. Equ. (," To transform the Sloan magnitudes to the Johnson/Cousins system, we used Equ. (" 2) and(8) from?.,2) and (8) from. . All calibrated photometry in the bands R Lis listed in Table 2.., All calibrated photometry in the bands R and I is listed in Table \ref{cal}. Ehe band transformations [rom Sloan to Cousins depend linearly on 24 and are only calibrated for 0«24<2. whereas FU Tau A is slightly redder (2?—2.4 2.5) in the Sloan photometry.," The band transformations from Sloan to Cousins depend linearly on $R-I$ and are only calibrated for $0 1$." The functions Wo... Yip. Yoo). and Now. Nig. NXiy are analogous to Poy. Oy. 4» from (25). respectively: they have a similar qualitative behavior and the same asvmptoties.," The functions $\Psi _{0,p} $, $\Psi _{1,p} $, $\Psi _{ - 1,p} $, and ${\rm X}_{0,q} $, ${\rm X}_{1,q} $, ${\rm X}_{ - 1,q} $ are analogous to $\Phi _0 $, $\Phi _1 $, $4\Phi _2 $ from (25), respectively; they have a similar qualitative behavior and the same asymptotics." Note that all formulas for the extended source models are transformed into that for point-source amplification (19)). as the source size tends to zero.," Note that all formulas for the extended source models are transformed into that for point-source amplification \ref{generalized Kcr}) ), as the source size tends to zero." Llere we compare our expressions for the first order corrections with that of Appendix A2 from (Ixeetonetal.2005).. further Ίνα.," Here we compare our expressions for the first order corrections with that of Appendix A2 from \citep{keeton_05}, further KGP." VPhis is especially relevant because KCP considers the 8general case of the lens equation1 without supposition on harmonic potential., This is especially relevant because KGP considers the general case of the lens equation without supposition on harmonic potential. Initial equations CXr-X8) of the lens mapping of INCIP are asfollows These equations need. tobe compared to our Las. 3--6))., Initial equations (A7-A8) of the lens mapping of KGP are asfollows These equations need tobe compared to our Eqs. \ref{eq3}- \ref{eq25}) ). " The correspondence between the coordinate notations is μυ, "," The correspondence between the coordinate notations is $\theta _i \leftrightarrow x_i ,u_i \leftrightarrow \tilde {y}_i ,\xi \leftrightarrow t^2$ ." In the general case the lens potential P(2) obevs the equation, In the general case the lens potential $\Phi \left( {\bmath x} \right)$ obeys the equation O300 exiis. respectively.,"O300 grisms, respectively." Tn these overap regions. the sensitivity fuuctious for each evisu («n each nieht) were i asaereelment.," In these overlap regions, the sensitivity functions for each grism (on each night) were in agreement." Second. we obtaiiucd a spectroscopic «XV flat hrough the standard star nask with the D600 eylsu ou the last night.," Second, we obtained a spectroscopic sky flat through the standard star mask with the B600 grism on the last night." This nask contained. two slitlets in addition to those used Kx the standard stab observations., This mask contained two slitlets in addition to those used for the standard star observations. Comparing the nigit sky spectra +wouel tjiese four slitlets indicates thedovarlations i the wavelength scusitivity between ditterent slitlets are less than (nis)., Comparing the night sky spectra through these four slitlets indicates that variations in the wavelength sensitivity between different slitlets are less than (rms). Finally. observatiois of NGC 6720 were obtai1ου through a differcut mask than the staucdare y.ars. and uo wawveleugth-depeudeut treuds are see1 in its seusitivitv calibration (see Table 3. helow).," Finally, observations of NGC 6720 were obtained through a different mask than the standard stars, and no wavelength-dependent trends are seen in its sensitivity calibration (see Table \ref{table3} below)." TheretOre. rough we did not observe the standard stars through the VAitlets used for our proerai objects. we have no reason to μονο that our scusitivity calibration is slitlet-depereent.," Therefore, though we did not observe the standard stars through the slitlets used for our program objects, we have no reason to believe that our sensitivity calibration is slitlet-dependent." We then chose the O300 observations o the plauetarv jiebulae in as our reference data set., We then chose the O300 observations of the planetary nebulae in as our reference data set. This choice was motivated by a nuuber of consideratiois., This choice was motivated by a number of considerations. First. tLOSC planetary neonilae were observed with all three exis.," First, these planetary nebulae were observed with all three grisms." Second. the O300 exisu las good seusitivitv over the IL) Ilo wavelereth range (Le Fovvre et al. 199 D).," Second, the O300 grism has good sensitivity over the $\beta$ – $\alpha$ wavelength range (Le Fèvvre et al. \cite{LeFevreetal1994}) )," which contains the strongest lines iu the specTra., which contains the strongest lines in the spectra. Third. our reddening values for tοσο planetary nebuae (see Tables G.. T.. aud 8)) were reasonable. typically E(BV)« )2umuac. aud invariadv positive.," Third, our reddening values for these planetary nebulae (see Tables \ref{table4}, \ref{table4b}, , and \ref{table4c}) ) were reasonable, typically $E(B-V)<0.2$ mag, and invariably positive." These reddeuings were consisteut wih previots observations of PN1 in (Ford et al. 1978))., These reddenings were consistent with previous observations of PN1 in (Ford et al. \cite{Fordetal1978}) ). The redClune owards is also expected ) be small fit is in front oftie disk of ο Burstein Iciles 198 1)).," The reddening towards is also expected to be small if it is in front of the disk of (e.g., Burstein Heiles \cite{BursteinHeiles1984}) )." We cusured that there were no systematic differences )etween the B6OO and O300 data sets dy comparing he inteusities of 10 Πα. [Ot11]A1959. aud. HerA5876 ueasured relative to A5007 for the planetary nebulae inM32.," We ensured that there were no systematic differences between the B600 and O300 data sets by comparing the intensities of $\beta$, $\alpha$, $\lambda$ 4959, and $\lambda$ 5876 measured relative to $\lambda$ 5007 for the planetary nebulae in." . Iu makije these comparisons. we considered only hose objects for which we had the best detections of hese lines.," In making these comparisons, we considered only those objects for which we had the best detections of these lines." For hese objects. we computec the ratio of he liιο dutensity in the D600 x)octiuu to that in the O300 SpecTru," For these objects, we computed the ratio of the line intensity in the B600 spectrum to that in the O300 spectrum." Table 2. lists he mean value of this ratio. the staidaund error in the meal. oiuk the oljjects we COisidered for cach line.," Table \ref{table2} lists the mean value of this ratio, the standard error in the mean, and the objects we considered for each line." Clearv. the main wavelougth-dependeut tre xdiu Table 2 isasystematic decrease in the D600 sensitivity relative to the OQ300. seusitivity as one COCS o longer waveleugths.," Clearly, the main wavelength-dependent trend in Table \ref{table2} is a systematic decrease in the B600 sensitivity relative to the O300 sensitivity as one goes to longer wavelengths." " Simply fittuis a line to the values in Tab o2 asa ""unction of wavelcheth. however. vields a rather poor correction at Πα."," Simply fitting a line to the values in Table \ref{table2} as a function of wavelength, however, yields a rather poor correction at $\alpha$." As a result. for waveleugthlis |votween any two lines found in Table 2.. we corrected for he differeico dn sensitivity calibratious bv interpolating lincarly heween the corrections in Table 2," As a result, for wavelengths between any two lines found in Table \ref{table2}, we corrected for the difference in sensitivity calibrations by interpolating linearly between the corrections in Table \ref{table2}." " For lines &» the blue of dor to the red of Io. we adopted the IL) or Ilo correctiois. respectively,"," For lines to the blue of $\beta$ or to the red of $\alpha$, we adopted the $\beta$ or $\alpha$ corrections, respectively." We woudered if the upturn at Πα iu Tabο 2 could be due to second order contamination. but this secs uulikelv.," We wondered if the upturn at $\alpha$ in Table \ref{table2} could be due to second order contamination, but this seems unlikely." Both the O300 aud D600 erims have very low cfiicicucy at250A.. aud a second order contamination would affect the seusitivitv calibration for both seris simnibuldw.," Both the O300 and B600 grisms have very low efficiency at, and a second order contamination would affect the sensitivity calibration for both grisms similarly." Cmsequentlv. the upturn at Io axuus to be real.," Consequently, the upturn at $\alpha$ appears to be real." The corrections 11i Table 2 were applied to he spectra of the plauctary nebulae in both aud he bulee of, The corrections in Table \ref{table2} were applied to the spectra of the planetary nebulae in both and the bulge of. The U900 data required no correction to put t10111 Ol the O300. seusiiviv scale., The U900 data required no correction to put them on the O300 sensitivity scale. We deduced this from direct conparison wit htιο D600 and 300 data (Tables 6.. 7.. and 8)). aud inelepeudeuIv using a spectruni we otained of the Calactic aretary nebula," We deduced this from direct comparison with the B600 and O300 data (Tables \ref{table4}, \ref{table4b}, and \ref{table4c}) ), and independently using a spectrum we obtained of the Galactic planetary nebula." 6720.. Table 3 lists the intensities iK reddening values for wdrogen lines in three regions of NGC 6720., Table \ref{table3} lists the intensities and reddening values for hydrogen lines in three regions of NGC 6720. The reddeiug vaTCs Wwe derive frou I5. Le. Πο. 1ο. ITLI. and 12 ave in very eood agreement in all hree apertures. dxdicatiug that our U90) seusitivity calibration 1s good to 3150A.," The reddening values we derive from $\gamma$, $\epsilon$, $9$, $10$, $11$, and $12$ are in very good agreement in all three apertures, indicating that our U900 sensitivity calibration is good to ." . Qur reddening values at Πὸ are consisteutly 16121485 lower than caklated from I2. so our U900 seusiIwitics may e under-estiniatec0 by ucarLLOOA.," Our reddening values at $\delta$ are consistently mag lower than calculated from $\gamma$, so our U900 sensitivities may be under-estimated by near." . Qur IIs reddeni-o values are conusisteutlv high. but ITS was bleuded with Πο A3889.," Our $8$ reddening values are consistently high, but $8$ was blended with He $\lambda$ 3889." We corrected. the bleud for the Πο LABSS9 coutribulon usine the Ile IALITI iutensitv assuisno radiative transfer correction. thereby removing the maxima possible Te LÀ3SSD coutributiou (oe.g.. Aler 1987)).," We corrected the blend for the He $\lambda$ 3889 contribution using the He $\lambda$ 4471 intensity assumingno radiative transfer correction, thereby removing the maximum possible He $\lambda$ 3889 contribution (e.g., Aller \cite{Aller1987}) )." Thus. it is perhaps not surprising thatOUL," Thus, it is perhaps not surprising thatour" The classic double radio sources. the FRITS (Faranoff Rilev 197L). ave thought to be powered by narrow beams or jets of οποίον cimanating from a unclear black hole in the ceuter of the host ealaxy (Rees. 1971. 1981: Longair. Ryle Scheuer 1973).,"The classic double radio sources, the FRIIs (Faranoff Riley 1974), are thought to be powered by narrow beams or jets of energy emanating from a nuclear black hole in the center of the host galaxy (Rees, 1971, 1984; Longair, Ryle Scheuer 1973)." " Tn many. though not all. of these sources, the spatial direction of the jets has remaimect nuchaneed throughout the lifetime of the radio source."," In many, though not all, of these sources, the spatial direction of the jets has remained unchanged throughout the lifetime of the radio source." Iu the most luminous sources the leugths of the jets reach up to scales of around a AIpe. aud the source lifetimes are as long as around 107 years (Alexander Leahy 1987. Liu. Pooley Riley 1992).," In the most luminous sources the lengths of the jets reach up to scales of around a Mpc, and the source lifetimes are as long as around $10^8$ years (Alexander Leahy 1987, Liu, Pooley Riley 1992)." The degree of collimatio- of the beams. often of the order of 0.1 radian or less. implies that whatever plivsical mechaisi gives rise to the joa stability is uuchaugiug in the direction it defines on comparable timescales. that is of at least LO? years.," The degree of collimation of the beams, often of the order of 0.1 radian or less, implies that whatever physical mechanism gives rise to the beam stability is unchanging in the direction it defines on comparable timescales, that is of at least $10^9$ years." In this etter. we address the question of what might eive rise to such stability.," In this letter, we address the question of what might give rise to such stability." This problem was considered by Rees (1975) who came o the conclusion that the most likely cause of the stability of the jet directions is due to the fact that it is determined x the spin of the unclear black hole., This problem was considered by Rees (1978) who came to the conclusion that the most likely cause of the stability of the jet directions is due to the fact that it is determined by the spin of the nuclear black hole. Απ accretion disk How which might power the nuclear activity is aligued with he black hole spin direction by the Bardecu-Pettersou effect (Bardeen Petterson 1975) out to a disk radius of RppB>>Ry. whore Ry is the Sclowarzschild radius.," Any accretion disk flow which might power the nuclear activity is aligned with the black hole spin direction by the Bardeen-Petterson effect (Bardeen Petterson 1975) out to a disk radius of $R_{\rm BP}\,>>\,R_s$, where $R_s$ is the Schwarzschild radius." Thus if the jet is disk powered. the jet will be strictly aligned with the spin of the hole.," Thus, if the jet is disk powered, the jet will be strictly aligned with the spin of the hole." Furthermore. this idea also fits into the current theoretical paracdiegua iu which jets are powered directly by the spin encrev of the hole (Blaudtord 1991. aud references therein: Rawlings Sauuders 1991). although this paradigui is open to debate (sec. for example. Livio. Ogilvie Pringle 1998).," Furthermore, this idea also fits into the current theoretical paradigm in which jets are powered directly by the spin energy of the hole (Blandford 1991, and references therein; Rawlings Saunders 1991), although this paradigm is open to debate (see, for example, Livio, Ogilvie Pringle 1998)." Rees (1978) pointed out however. that the couple exerted by the black hole as it aligns the disk with the spin of the hole. has bv Newtou's third law also the effect of aligning the hole with the spin of the disk.," Rees (1978) pointed out however, that the couple exerted by the black hole as it aligns the disk with the spin of the hole, has by Newton's third law also the effect of aligning the hole with the spin of the disk." Te estimated the timescale for this aliguimenut to occur by assuming that cach accreted mass clement brings with it to the hole augular momentum correspouding to its orbital angular momentum at the Bardecu-Pettersou radius App., He estimated the timescale for this alignment to occur by assuming that each accreted mass element brings with it to the hole angular momentum corresponding to its orbital angular momentum at the Bardeen-Petterson radius $R_{\rm BP}$. " Ho suggested that this aliguiment timescale is eiven by.yee, where AZ/AM is the accretion time-scale £44; aud JJ is the ratio of the augular momentum of the black hole to the maximal aneular niomoenutun of a Werr black hole."," He suggested that this alignment timescale is given by, where ${M/\dot M}$ is the accretion time-scale $t_{\rm acc}$, and ${J/J_{\rm max}}$ is the ratio of the angular momentum of the black hole to the maximal angular momentum of a Kerr black hole." Rees (LOTS) estimated ty to be of the order of 105 vears., Rees (1978) estimated $t_{\rm a}$ to be of the order of $10^8$ years. However. in recent vears there has heen considerable theoretical progress in our uudoerstaudius of how a warped (or non-planar) accretion disk commmuicates the warp aud evolves in time.," However, in recent years there has been considerable theoretical progress in our understanding of how a warped (or non-planar) accretion disk communicates the warp and evolves in time." This plivsical process has a direct bearing ou the black hole/accretiou disk alieumoent timescale., This physical process has a direct bearing on the black hole/accretion disk alignment timescale. We show below. that. using current theories. the aliguineut timescale is considerably shorter than the ages of the radio sources inferred from spectral ageing models fitted to the observations. aud is cousequeutly also less than the timescale ou which the jet direction changes.," We show below, that, using current theories, the alignment timescale is considerably shorter than the ages of the radio sources inferred from spectral ageing models fitted to the observations, and is consequently also less than the timescale on which the jet direction changes." The timescale for disk/hole aliguiment depoeuds directly ou the timescale on which an accretion disk can trausfer a warp iu the radial direction., The timescale for disk/hole alignment depends directly on the timescale on which an accretion disk can transfer a warp in the radial direction. In an accretion disk the conrponeut of angular momentum parallel to the spin of the disk is transferred at radius A in the disk in a diffusive inanner on a timescale teΠονι. where vy is the usual disk kinematic viscosity (Pringle 1981: Frank. ine Raine 1992).," In an accretion disk the component of angular momentum parallel to the spin of the disk is transferred at radius $R$ in the disk in a diffusive manner on a timescale $t_R\,\sim\,R^2/\nu_1$, where $\nu_1$ is the usual disk kinematic viscosity (Pringle 1981; Frank, King Raine 1992)." Using the dimensiouless viscosity parameter, Using the dimensionless viscosity parameter The VIRMOS (Visible and InfraRed Multi-Object Spectrographs) project is the respouse by a French-Italian Consortium of ast'onomical institutes to the ESO reques for two spectrographs with eulianced survey capabilities to ye lustalled at the Very Large Telescoye (VLT).,The VIRMOS (Visible and InfraRed Multi-Object Spectrographs) project is the response by a French-Italian Consortium of astronomical institutes to the ESO request for two spectrographs with enhanced survey capabilities to be installed at the Very Large Telescope (VLT). It consists of the twin instruments VIALOS (VIsible Multi-Object Spectrograph) aud NIBMOS (Near Infralted Object Spectrograph). wihi a Large field of view split into four quadraus and a high multiplexing factor in their Multi-Object Spectroscopy (MOS) observing modes (LeFeévreetal.1998.2000).," It consists of the twin instruments VIMOS (VIsible Multi-Object Spectrograph) and NIRMOS (Near InfraRed Multi-Object Spectrograph), with a large field of view split into four quadrants and a high multiplexing factor in their Multi-Object Spectroscopy (MOS) observing modes \citep{Lefevre98, Lefevre00}." . VIMOS is going o be olered to the European astronomical comunnity starting July 2001 at VLT-UT3. and NIRMOS is expeced to be operational at the end of 20022 at VLT-UTI.," VIMOS is going to be offered to the European astronomical community starting July 2001 at VLT-UT3, and NIRMOS is expected to be operational at the end of 2002 at VLT-UT4." In MOS mode. beAh instruments uake use of slit inasks which the astronomer cau desigu following the observatloual recuireiments.," In MOS mode, both instruments make use of slit masks which the astronomer can design following the observational requirements." Thus. he VIRMOS project includes the delivery to ESO of a complete. inclepe1ent. olL-Hiue facili¥ tO lalulacture aud banclle tle masks needed by the two Muli-object spectrograplis cu‘rently operational or fortheoming a other telescopes have adopted rachinitο solutions raugiug from laser to puuchiug to milline machines aud either aluminum or arbon fiber as masks: the MOS/OSIS instrument at CFHT (Canala France Hawaii Telescope) ses 75 un thick black anodized aluminum masks cut by a laser macune (DiBiagioetal.1990):: at the ΑΕΙἩν telescopes the LRIS instrument uses mechanically punched O.f mauu thick aluiminuiui aasks (Okeetal.1995) while the DEIMOS will use 0.25 nun masks prepared by a uilline© machine: the GALOS spectrographo for the Gemini telescopes uses 0.2 man thick carbon fiber asks cut by a laser machine (Szetoetal.1997).," Thus, the VIRMOS project includes the delivery to ESO of a complete, independent, off-line facility to manufacture and handle the masks needed by the two Multi-object spectrographs currently operational or forthcoming at other telescopes have adopted machining solutions ranging from laser to punching to milling machines and either aluminum or carbon fiber as masks: the MOS/OSIS instrument at CFHT (Canada France Hawaii Telescope) uses $75\,\mu$ m thick black anodized aluminum masks cut by a laser machine \citep{Dibiagio}; at the KECK telescopes the LRIS instrument uses mechanically punched 0.4 mm thick aluminum masks \citep{Oke} while the DEIMOS will use 0.25 mm masks prepared by a milling machine; the GMOS spectrograph for the Gemini telescopes uses 0.2 mm thick carbon fiber masks cut by a laser machine \citep{Szeto}." . Iu the VINOS case we selected the laser technique to cut the masks into 0.2 mun thick iuvar sheets., In the VIMOS case we selected the laser technique to cut the masks into 0.2 mm thick invar sheets. Iu this paper. we will describe our Mask Manulacturiung Uut (MALL). which is operational at the Paranal Observatory since August 2000.," In this paper, we will describe our Mask Manufacturing Unit (MMU), which is operational at the Paranal Observatory since August 2000." The MALU is presently used to provide the instrument FORS2 with the masks to be used iu its Mask eXchange Unit (MANU (Schinketal.2000) and will be used with VIMOS as it arrives in Paranal in early 2001., The MMU is presently used to provide the instrument FORS2 with the masks to be used in its Mask eXchange Unit (MXU) \citep{Schink} and will be used with VIMOS as it arrives in Paranal in early 2001. In section 2 we illustrate the requirements aud specifications the MALU had to satisfy aud in section 3 the adopted hardware configurations., In section 2 we illustrate the requirements and specifications the MMU had to satisfy and in section 3 the adopted hardware configurations. Sections { aud 5 respectively describe the tests aud tuiiug of he Mask Mautulacturing Machine (MMM) ancl the resulting perlormanuces., Sections 4 and 5 respectively describe the tests and tuning of the Mask Manufacturing Machine (MMM) and the resulting performances. Finally. Section 6 outlines tle MALU operational concepts.," Finally, Section 6 outlines the MMU operational concepts." The VIMOS (and NIRMOS) focal plane is divided into L quadrants. therefore [ masks (1," The VIMOS (and NIRMOS) focal plane is divided into 4 quadrants, therefore 4 masks (1" the halo angular momentum.,the halo angular momentum. " We also show some results for an ""elliptical model. where we assumed that the ellipticity of the galaxy is the same as the ellipticitv of the halo."," We also show some results for an `elliptical' model, where we assumed that the ellipticity of the galaxy is the same as the ellipticity of the halo." The relatively small number of particles in the halos leads to some uncertainty in the shape parameters of the halo. so we have therefore concentrated on the spiral mocdel.," The relatively small number of particles in the halos leads to some uncertainty in the shape parameters of the halo, so we have therefore concentrated on the spiral model." We measured the resulting projected. ellipticity correlation function arising from spin-spin correlation of 30.000LO” halos in an N-body simulations. for several CDM moclels.," We measured the resulting projected ellipticity correlation function arising from spin-spin correlation of $30,000 - 10^{5}$ halos in an N-body simulations, for several CDM models." The correlations we find lie between ~107 at small separations to ~10 on seales of 10'. and may be explicable in terms of the statistics ofthe initial gravitational potential (Catclan. Ixamionkowski ancl Blandforcl 2000).," The correlations we find lie between $\sim 10^{-4}$ at small separations to $\sim 10^{-5}$ on scales of $10'$, and may be explicable in terms of the statistics of the initial gravitational potential (Catelan, Kamionkowski and Blandford 2000)." The intrinsic correlations are generally. below the expected lensing signal for deep surveys., The intrinsic correlations are generally below the expected lensing signal for deep surveys. We note that other non-eravitational ellects could increase the correlations. through tical interactions forming tidal tails. for example.," We note that other non-gravitational effects could increase the correlations, through tidal interactions forming tidal tails, for example." However. since these effects would be confined to small separations in 3D. our feeling is that they are unlikely to be of importance in the angular correlations. especially for the deep samples.," However, since these effects would be confined to small separations in 3D, our feeling is that they are unlikely to be of importance in the angular correlations, especially for the deep samples." " For a survey with galaxies at à median redshift z,,=1. such as current weak lensing surveys. intrinsic correlations lie below the lensing signal on angular scales 6Zi 10. a scale where the lensing signal is 10.7."," For a survey with galaxies at a median redshift $z_{m}=1$, such as current weak lensing surveys, intrinsic correlations lie below the lensing signal on angular scales $\theta \la 10'$ , a scale where the lensing signal is $\sim 10^{-5}$." The elfeet appears to be too small to explain the excess power found on small scales bv Van Waerbeke et al. (, The effect appears to be too small to explain the excess power found on small scales by Van Waerbeke et al. ( 2000).,2000). While lensing produces correlations which are coherent over the depth of the survey. intrinsic shape correlations are only important over limited. physical separations.," While lensing produces correlations which are coherent over the depth of the survey, intrinsic shape correlations are only important over limited physical separations." As a result. intrinsic correlations are diluted when integrated over the depth of a deep. dedicated lensing survey.," As a result, intrinsic correlations are diluted when integrated over the depth of a deep, dedicated lensing survey." On the other hand. wider but shallower surveys such as SDSS ου 0.2) will be much more sensitive to intrinsic. correlations.," On the other hand, wider but shallower surveys such as SDSS $z_{m}\sim 0.2$ ) will be much more sensitive to intrinsic correlations." We cannot exclude the possibility that. intrinsic. correlations could. be comparable to or even dominate the weak lensing signal on all scales for such surveys., We cannot exclude the possibility that intrinsic correlations could be comparable to or even dominate the weak lensing signal on all scales for such surveys. Caution must. thus be exerted. when interpreting the weak lensing signal [ron these surveys., Caution must thus be exerted when interpreting the weak lensing signal from these surveys. With sullicicnt signal. the lensing signal can be secured. using the specific angular cependence of its induced. ellipticity. correlations. but. shot noise. will be a strong limiting factor at scales of an arcminute or less in a survev like SDSS (see Munshi and Coles 2000 for further discussion of errors)," With sufficient signal, the lensing signal can be secured using the specific angular dependence of its induced ellipticity correlations, but shot noise will be a strong limiting factor at scales of an arcminute or less in a survey like SDSS (see Munshi and Coles 2000 for further discussion of errors)." Intrinsic shape correlations are interesting in their own right. as they provide a probe to the generation of angular momentum curing galaxy formation.," Intrinsic shape correlations are interesting in their own right, as they provide a probe to the generation of angular momentum during galaxy formation." Galaxy spins can for instance be used. in principle. to measure the shear of the density field. (Lee Pen 2000).," Galaxy spins can for instance be used, in principle, to measure the shear of the density field (Lee Pen 2000)." The SuperC'OSMOS. ADPM and SDSS survevs can thus be used to measure the intrinsic correlation functions with high accuracy.," The SuperCOSMOS, APM and SDSS surveys can thus be used to measure the intrinsic correlation functions with high accuracy." Intrinsic correlations can also be constrained using 2-dimensional ealaxv-galaxw lensing to measure the alignment of mass and light in galaxies (Natarajan Itefregier 2000)., Intrinsic correlations can also be constrained using 2-dimensional galaxy-galaxy lensing to measure the alignment of mass and light in galaxies (Natarajan Refregier 2000). " ""ποσο techniques can then be used to constrain models of galaxy formation. and to secure the interpretation of deeper weak lonsing surveys."," These techniques can then be used to constrain models of galaxy formation, and to secure the interpretation of deeper weak lensing surveys." The simulations analysed in this paper were carried out using data mace available by the Virgo Supercomputing Consortium (httpi//star-www.dur.ac.uk/ frazerp/virgo/) using computers based at the Computing Centre of. the AMax-Planck Society in Garching. and at the. LEdinbureh Parallel. Computing Centre., The simulations analysed in this paper were carried out using data made available by the Virgo Supercomputing Consortium (http://star-www.dur.ac.uk/ frazerp/virgo/) using computers based at the Computing Centre of the Max-Planck Society in Garching and at the Edinburgh Parallel Computing Centre. We are very grateful to. Rob Smith for providing halos from the simulations., We are very grateful to Rob Smith for providing halos from the simulations. We thank Rachel Somerville. Priva Natarajan and Rob Crittenden for useful cliscussions. and the referee for helpful conuments.," We thank Rachel Somerville, Priya Natarajan and Rob Crittenden for useful discussions, and the referee for helpful comments." AR was supported by a EMI postdoctoral fellowship from the EEC Lensing Network. and by a Wolfson College Iesearch Fellowship.," AR was supported by a TMR postdoctoral fellowship from the EEC Lensing Network, and by a Wolfson College Research Fellowship." Some computationsused Starlink facilities., Some computationsused Starlink facilities. (Vranjes&ου»2006.2009a.,"\citep{v1,v2,v3}." b).. The former is well deseribed within the two-component [uid theory. the latter however. is a strictly kinetic ellect.," The former is well described within the two-component fluid theory, the latter however, is a strictly kinetic effect." In both cases the ions play a stabilizing role. and in some situations they may even impose a threshold for the instabilitv.," In both cases the ions play a stabilizing role, and in some situations they may even impose a threshold for the instability." Llowever. in the case of hot ions and in the presence of both the density and temperature gradients. the above mentioned reactive instability is termed. as g;-instability. where now the ions play a crucial clestabilizing role.," However, in the case of hot ions and in the presence of both the density and temperature gradients, the above mentioned reactive instability is termed as $\eta_i$ -instability, where now the ions play a crucial destabilizing role." " lere. yp=La fly. and L,=(dnoαμπο}a —(dyαμly) are the characteristic inhomogencity scale-lengths of the equilibrium quantities that are here. and further in the text. denoted by the index 0."," Here, $\eta_i=L_n/L_{\sss T}$ , and $L_n=(d n_0/dx/n_0)^{-1}$, $L_{\sss T}=(d T_0/dx/T_0)^{-1}$ are the characteristic inhomogeneity scale-lengths of the equilibrium quantities that are here, and further in the text, denoted by the index 0." The coordinate μη in the present local analysis is used to describe the changes in the radial (perpendicular) direction., The coordinate $x$ in the present local analysis is used to describe the changes in the radial (perpendicular) direction. “Phe background magnetic field is typically also inhomogeneous (ie. with a curvature and a gradient in the perpendicular direction). and this may be described by vet another characteristic scale-leneth Ly=(dBy/de/By)+.," The background magnetic field is typically also inhomogeneous (i.e., with a curvature and a gradient in the perpendicular direction), and this may be described by yet another characteristic scale-length $L_{\sss B}=(d B_0/dx/B_0)^{-1}$." " The interplay of these three egraclicnts determines the behavior of low frequency Q,Ξ Bofm;.q=Ze is the ion charge) electrostatic oscillations anc instabilities."," The interplay of these three gradients determines the behavior of low frequency $\omega \ll \Omega_i= q_i B_0/m_i$, $q_i=Z_i e$ is the ion charge) electrostatic oscillations and instabilities." This will be demonstrated. in the forthcoming text., This will be demonstrated in the forthcoming text. We apply the two-ILuid model developed in numerous works related to laboratory plasmas (Nilssonctal.1990:Nils-son&Weiland 1995).," We apply the two-fluid model developed in numerous works related to laboratory plasmas \citep{w1,w2}." . A systematic presentation of the heory that has been successfully used. in the past in the »edietion of transport. processes in tokamak plasmas can x found in Weiland(2000)., A systematic presentation of the theory that has been successfully used in the past in the prediction of transport processes in tokamak plasmas can be found in \citet{w3}. ". There. one can also see a complete agreement between this advanced [uid mocel anc he kinetic theory (that is one of the reasons for the term""advcanecd? used here)."," There, one can also see a complete agreement between this advanced fluid model and the kinetic theory (that is one of the reasons for the term used here)." Part of the basic theory of the cii wave applied to the solar plasmas is given in Vranjes'oedts (2006)., Part of the basic theory of the drift wave applied to the solar plasmas is given in \citet{v1}. It has also been used. very recently. (Vranjes&Poedts2009a.b) in order to explain some essentia ooperties of the coronal heating mechanism.," It has also been used very recently \citep{v2,v3} in order to explain some essential properties of the coronal heating mechanism." The theory is described in detail in the references mentioned above., The theory is described in detail in the references mentioned above. For completeness. we shall provide here a general description of he derivations. emphasizing some most important features of the model and providing explanations for the assumptions used in the procedure.," For completeness, we shall provide here a general description of the derivations, emphasizing some most important features of the model and providing explanations for the assumptions used in the procedure." The present analysis is restricted. to he electrostatic limit., The present analysis is restricted to the electrostatic limit. Note however. that the theory works well also in the full electromagnetic limit. CXndersson.&Welland 1988).. where it can be used. [for describing he ballooning instabilities.," Note however, that the theory works well also in the full electromagnetic limit \citep{and}, where it can be used for describing the ballooning instabilities." This domain also can be of ereat importance for the solar. plasma as it may provide a trigecring mechanism for abrupt changes in the magnetic ield topology. iin processes like magnetic reconnection and Coronal Mass Ejections (CMEs).," This domain also can be of great importance for the solar plasma as it may provide a triggering mechanism for abrupt changes in the magnetic field topology, in processes like magnetic reconnection and Coronal Mass Ejections (CMEs)." The presence of hot. ions (typical for the solar atmosphere) anc the background. temperature. gradient (that is expected in solar magnetic configurations) implies. first of all. the necessity. of including their full thermal response (the pressure and the gyro-viscosity. collision-less stress tensor) in the momenttun equation. and. second. the use of the ion energy. equation in the mathematical mocel.," The presence of hot ions (typical for the solar atmosphere) and the background temperature gradient (that is expected in solar magnetic configurations) implies, first of all, the necessity of including their full thermal response (the pressure and the gyro-viscosity collision-less stress tensor) in the momentum equation, and, second, the use of the ion energy equation in the mathematical model." For the present purpose. the later comprises the diamagnetic heat flow term only. and can be written as (Woeiland2000) Llere. 7; is in energy units. gag is the diamagnetic heat flux. and ey=B/B.," For the present purpose, the later comprises the diamagnetic heat flow term only, and can be written as \citep{w3} n_i + ) T_i + p_i = -, Here, $T_i$ is in energy units, $\bmath{ q_{*i}}$ is the diamagnetic heat flux, and $\bmath{ e_{\|}}= \bmath{ B}/B$." Vhe given form of q«i; can be obtained clirectly from the drift-kinetic theory.," The given form of $\bmath{ q_{*i}}$ can be obtained directly from the drift-kinetic theory." In the case of cilferent temperatures (pressures) in the two directions (Mondt.&Weiland1991) it is to be replaced with p;/6miQ;)]ey|(ppil)Gn;Q:)];ey(ey:V)ey.," In the case of different temperatures (pressures) in the two directions \citep{m} it is to be replaced with $[p_{i\bot}/(m_i \Omega_i)]\bmath{ e_{\|}}\times \nabla (2 T_{i\bot} + T_{i\|}/2) + [(p_{i\|} - p_{i\bot})/(m_i \Omega_i)] T_{i\|} \bmath{ e_{\|}}\times (\bmath{ e_{\|}} \cdot \nabla) \bmath{e_{\|}}$ ." A detailed analysis of the temperature anisotropy effects on the eracdient driven instability is performed by Alonelt(1996)., A detailed analysis of the temperature anisotropy effects on the gradient driven instability is performed by \citet{m2}. . The magnetic field. is inhomogeneous in the general case., The magnetic field is inhomogeneous in the general case. This implies that. in the continuity equation. the contribution of the ciamaenctic driftto the ion flux does not vanish. and the appropriate lincarizecl term is For the same reason we have also V:egz0. where ve is the E Beclrift.," This implies that, in the continuity equation, the contribution of the diamagnetic driftto the ion flux does not vanish, and the appropriate linearized term is For the same reason we have also $\nabla \cdot \bmath{ v_{\sss E}}\neq 0$, where $\bmath{ v_{\sss E}}$ is the $\bmath{ E}\times \bmath{ B}$ -drift." Hence. an additional. magnetic αμ velocity vp; appears in the description. ofthe ion motion.," Hence, an additional magnetic drift velocity $\bmath{ v_{bi}}$ appears in the description ofthe ion motion." We use standard notation from the drift wave theory where v4;=ey«Vpiftqin;D).," We use standard notation from the drift wave theory where $\bmath{ v_{*i}}=\bmath{ e_{\|}} \times \nabla p_i/(q_i n_i B)$." In the equations above we have V:q«i=SayeVIοVI;/2.," In the equations above we have $\nabla \cdot \bmath{ q_{*i}}= -5 n_i v_{*i} \nabla T_i/2 + 5 n_i \bmath{ v_{bi}}\cdot \nabla T_i/2$." " The first (non-curvature) part inthis expression cancels out in the procedure of caleulating Vea, in the ion continuity equation."," The first (non-curvature) part inthis expression cancels out in the procedure of calculating $\nabla \cdot \bmath{ v_i}$ in the ion continuity equation." " The second term comprises the ion magnetic drift. which in the general case is the sum of the curvature and the Ρας lere. fe,Wie,=&2 and RK denotes the radius of the curvature of the magnetic field. while the two velocities are in general case cdillercnt ""n= μι. οἱ24; £/m;."," The second term comprises the ion magnetic drift, which in the general case is the sum of the curvature and the $B$ drifts Here, $(\bmath{ e_{\|}} \cdot \nabla) \bmath{ e_{\|}}=- \bmath{ R}/R^2$ and $R$ denotes the radius of the curvature of the magnetic field, while the two velocities are in general case different $v_{\|}^2= T_i/m_i$ , $v_{\bot}=2 T_i/m_i$ ." lo what follows. we shall use the expression for the elective total curvature drift. (Weilancl2000) ουν—2i(qiBoey(ey⋅ Viel.," In what follows, we shall use the expression for the effective total curvature drift \citep{w3} $\bmath{ v_{bi}}\simeq [2 T_{i0}/(q_i B_0)] \bmath{ e_{\|}}\times (\bmath{e_{\|}} \cdot\nabla) \bmath{ e_{\|}}$ ." The perturbed ion. perpencicular velocity. can be obtained from the ion momentum equation by applying the vector product e. vielding | | | U," The perturbed ion perpendicular velocity can be obtained from the ion momentum equation by applying the vector product $\bmath{ e_\|} \times ...$, yielding + + + ." si llere. vg and vy; are already defined above. the third. term is the ion polarization drift. and. ez;denotes the drift. due to the ion stress tensor effects.," Here, $\bmath{ v_{\sss E}}$ and $ \bmath{ v_{*i}}$ are already defined above, the third term is the ion polarization drift, and $\bmath{ v_{\pi i}}$denotes the drift due to the ion stress tensor effects." " For. small accidental perturbations propagating predominantly in the perpendicular direction ~exp.fat|Hyg thes). [Ru]3 lhe fe] ο the linearized ion energyequation. vields (Weilanel|.2000) llere. theterms ο. ws; are the product of the perpendicular wave number component A,and the diamagnetic and magnetic drifts. respectively."," For small accidental perturbations propagating predominantly in the perpendicular direction $\sim \exp[- i \omega t + i k_y y + i k_z z]$ , $|k_y| \gg |k_z|$ , $|\omega| \ll \Omega_i$ , the linearized ion energyequation yields \citep{w3} Here, theterms $\omega_{*j}$ , $\omega_{bj}$ are the product of the perpendicular wave number component $k_y$and the diamagnetic and magnetic drifts, respectively." Note that weemyrs= Tea T= dooflio.," Note that $\omega_{*e}=k_y v_{*e}= - \tau \omega_{*i}$ , $\tau=T_{e0}/T_{i0}$ ." Using Eq. (2)), Using Eq. \ref{vel}) ) in the, in the the case of the French-hat filter we find that the diameter of the annulus. i.e./x1. may not exceed the size of the map for reliable A-variance values.,"the case of the French-hat filter we find that the diameter of the annulus, i.e.$l \times v$, may not exceed the size of the map for reliable $\Delta$ -variance values." For the Mexican hat. the parameter xv must 4ot exceed 2/3 of the map size.," For the Mexican hat, the parameter $l\times v$ must not exceed $2/3$ of the map size." From the relations between ahe effective filter length and the filter size / obtained in Sect. [L.2..," From the relations between the effective filter length and the filter size $l$ obtained in Sect. \ref{sect_effectivelength}," we see that the dynamic range of effective lags available for a fit of the A-variance spectrum grows with decreasing ciameter ratio v., we see that the dynamic range of effective lags available for a fit of the $\Delta$ -variance spectrum grows with decreasing diameter ratio $v$. Smaller v values increase the total range of lags where the A-variance can be determined without being dominated by edge effects., Smaller $v$ values increase the total range of lags where the $\Delta$ -variance can be determined without being dominated by edge effects. Moreover. Sect.," Moreover, Sect." 4.3.1 shows that lower v ratios also tend to extend the dynamic range of scales below a structure peak where the A-variance follows à power law., \ref{sect_scaledetect} shows that lower $v$ ratios also tend to extend the dynamic range of scales below a structure peak where the $\Delta$ -variance follows a power law. Thus. low ratios for a reliable slope detection.," Thus, low ratios for a reliable slope detection." To study the agreement of the measured A-variance slopes with the theoretically predicted index as a function of the filter shape we compute the spectra for fBm structures and sub-maps from fBm structures using the different filters., To study the agreement of the measured $\Delta$ -variance slopes with the theoretically predicted index as a function of the filter shape we compute the spectra for fBm structures and sub-maps from fBm structures using the different filters. Fig., Fig. 10. shows the spectra for a submap from an fBm with Z23.0 computed with four different filters., \ref{fig_cfbmdeltas} shows the spectra for a submap from an fBm with $\zeta=3.0$ computed with four different filters. None of the spectra gives an exact power law. but the French-hat filter with v=3.0 and both Mexican-hat filters provide a reasonably good reproduction of the theoretical index «=1.0.," None of the spectra gives an exact power law, but the French-hat filter with $v=3.0$ and both Mexican-hat filters provide a reasonably good reproduction of the theoretical index $\alpha=1.0$." For low v ratios. the French hat tends to overestimate the true spectral index.," For low $v$ ratios, the French hat tends to overestimate the true spectral index." The Mexican hat results in somewhat too low exponents., The Mexican hat results in somewhat too low exponents. The corresponding spectra computed by the help of the mirror-continuation method result in à spectral index which is The Mexican hat and the French hat provide almost the same slopes., The corresponding spectra computed by the help of the mirror-continuation method result in a spectral index which is The Mexican hat and the French hat provide almost the same slopes. When applying the analysis to the sine wave field with k=|. re. the equivalent of an fBm with Z=c. the longer dynamie range traced by the French-hat filter results in a measured spectral index of the A-variance which ts closer to the theoretical value of 4 than that obtained for the Mexican- filter.," When applying the analysis to the sine wave field with $k=1$, i.e. the equivalent of an fBm with $\zeta=\infty$, the longer dynamic range traced by the French-hat filter results in a measured spectral index of the $\Delta$ -variance which is closer to the theoretical value of 4 than that obtained for the Mexican-hat filter." For a systematic investigation of the accuracy in the determination of the A-variance slope as a function of the filter diameter ratio v. we analyse sets of 30 different fBm structures and 30 submaps from fBms using the two basic filter shapes varying their diameter ratio v and the fBm spectral index Z., For a systematic investigation of the accuracy in the determination of the $\Delta$ -variance slope as a function of the filter diameter ratio $v$ we analyse sets of 30 different fBm structures and 30 submaps from fBms using the two basic filter shapes varying their diameter ratio $v$ and the fBm spectral index $\zeta$ . Fig., Fig. 11. demonstrates the result for the French-hat filter applied with the filter-truncation method., \ref{fig_cfbmalphas} demonstrates the result for the French-hat filter applied with the filter-truncation method. The range of spectral indices covers the typical indices in observations of interstellar clouds (Elmegreen&Scalo.2004:Falgaroneetal.. 2004).," The range of spectral indices covers the typical indices in observations of interstellar clouds \citep{Elmegreen,Falgarone04}." .. The strongest deviations of the measured exponents from the expected values occur at low diameter ratios v. Hence. ratios below 1.7 should not be used.," The strongest deviations of the measured exponents from the expected values occur at low diameter ratios $v$ Hence, ratios below 1.7 should not be used." fBms and submapsbehave differently., fBms and submapsbehave differently. For the fBms the strongest deviations from the theoretical spectral index occur at low spectral indices: forthe, For the fBms the strongest deviations from the theoretical spectral index occur at low spectral indices; forthe matrices and effective area files have been retrieved from their web site.,matrices and effective area files have been retrieved from their web site. " In order to ease a comparison of the results between ""Sifferent instruments. the same choices of energy range and owpectral model were adopted."," In order to ease a comparison of the results between different instruments, the same choices of energy range and spectral model were adopted." Thus. only data from the HEXTE =astrument (operating in the 20-200 keV energy range) were used for the spectral fits.," Thus, only data from the HEXTE instrument (operating in the 20-200 keV energy range) were used for the spectral fits." The spectral analysis was performed with an automatic pipeline based on the same algorithm adopted for BAT (as described in Appendix AppendixA:))., The spectral analysis was performed with an automatic pipeline based on the same algorithm adopted for BAT (as described in Appendix \ref{Crab_pipeline}) ). " We ""Siscarded 53 low quality spectra. with «3.5."," We discarded 53 low quality spectra, with $<$ 3.5." As a further step. data from the PCA instrument (operating 1 the 2-60 keV energy range) were used to extract a simple light curve (ets +) in the soft (20-30 keV) energy range.," As a further step, data from the PCA instrument (operating in the 2-60 keV energy range) were used to extract a simple light curve (cts $^{-1}$ ) in the soft (20-30 keV) energy range." An analogous light curve for the hard range (30-100 keV) was also extracted from HEXTE data and an hardness ratio plot was produced., An analogous light curve for the hard range (30-100 keV) was also extracted from HEXTE data and an hardness ratio plot was produced. In addition. we downloaded public RXTE All Sky Monitor (ASM) data collected during the whole GRO J1655-40 outburst and extracted a count rate light curve in the 2-10 keV range.," In addition, we downloaded public RXTE All Sky Monitor (ASM) data collected during the whole GRO J1655-40 outburst and extracted a count rate light curve in the 2-10 keV range." The complete light curve of the outburst of GRO as seen by BAT (in erg ? ! ) is shown in Figure 6 (top panel)., The complete light curve of the outburst of GRO J1655-40 as seen by BAT (in erg $^{-2}$ $^{-1}$ ) is shown in Figure \ref{fig_GRO_flux} (top panel). HEXTE measurements are also shown. to allow for a direct comparison.," HEXTE measurements are also shown, to allow for a direct comparison." We plotted in the same figure the light curves extracted from the PCA data (count rate in 3-20 keV. central panel) and from the ASM data (count rate in 2-10 keV. bottom panel).," We plotted in the same figure the light curves extracted from the PCA data (count rate in 3-20 keV, central panel) and from the ASM data (count rate in 2-10 keV, bottom panel)." Errors are at Lo level., Errors are at $1\sigma$ level. Zooms of sections of the light-curve are shown in figures 7.. 8 and 9.. where the light-curves and hardness ratio plots obtained with the PCA instrument (taken from http:Ztahti.mit.edu/opensource/1655/) are also given.," Zooms of sections of the light-curve are shown in figures \ref{fig_GRO_flux53415_53470}, \ref{fig_GRO_flux53490_53550} and \ref{fig_GRO_flux53620_53655}, where the light-curves and hardness ratio plots obtained with the PCA instrument (taken from ) are also given." In spite of the different time coverage of such a strongly variable source. the agreement between the BAT and HEXTE light curves Is remarkably good.," In spite of the different time coverage of such a strongly variable source, the agreement between the BAT and HEXTE light curves is remarkably good." It is somewhat difficult to perform a direct quantitative comparison since BAT and HEXTE observations are. not strictly simultaneous and the source shows a large variability on short timescales., It is somewhat difficult to perform a direct quantitative comparison since BAT and HEXTE observations are not strictly simultaneous and the source shows a large variability on short timescales. Generally. BAT and HEXTE measurements appear to be fully consistent within errors.," Generally, BAT and HEXTE measurements appear to be fully consistent within errors." Considering time windows for which the BAT and HEXTE observations. are frequent and close in time. a difference not larger than ~ is apparent when the source flux is above 1-2 «10 ? ere 7s lor90 mCrab.," Considering time windows for which the BAT and HEXTE observations are frequent and close in time, a difference not larger than $\sim$ is apparent when the source flux is above 1-2 $\times$ $^{-9}$ erg $^{-2}$ $^{-1}$, or $\sim90$ mCrab." Generally. a good agreement (within errors) is found when the S/N in BAT spectra is greater than 4.," Generally, a good agreement (within errors) is found when the S/N in BAT spectra is greater than 4." The actual flux yielding such a S/N obviously depends on the position of the target within the FOV., The actual flux yielding such a S/N obviously depends on the position of the target within the FOV. Indeed. in one hour exposure. the 3c sensitivity with our approach is 1020 mCrab for an on-axis source. while it is a factor ~10 worse ata coded fraction 0.2.," Indeed, in one hour exposure, the $3\sigma$ sensitivity with our approach is $\sim10-20$ mCrab for an on-axis source, while it is a factor $\sim10$ worse at a coded fraction 0.2." " Thus. if the target lies within the half-coded region. our approach yields significant spectral measurements (consistent with HEXTE) in the 30-100 keV range down to (b.6)«101"" erg 7s +. or ~50 mCrab (see e.g. Fig 9.. around MJD 53640)."," Thus, if the target lies within the half-coded region, our approach yields significant spectral measurements (consistent with HEXTE) in the 30-100 keV range down to $(5-6) \times 10^{-10}$ erg $^{-2}$ $^{-1}$, or $\sim50$ mCrab (see e.g. Fig \ref{fig_GRO_flux53620_53655}, around MJD 53640)." The study of sources fainter than ~50 mCrab would require a different and more complex approach., The study of sources fainter than $\sim50$ mCrab would require a different and more complex approach. A good agreement between the power law photon index values as measured by BAT and HEXTE ts also apparent in Figure 10.., A good agreement between the power law photon index values as measured by BAT and HEXTE is also apparent in Figure \ref{fig_GRO_phindx}. This is particularly evident if we consider the time intervals corresponding to the highest source flux (above ~2 « ? ergs 7? +). as shown in Fig. 11..," This is particularly evident if we consider the time intervals corresponding to the highest source flux (above $\sim$ 2 $\times$ $^{-9}$ ergs $^{-2}$ $^{-1}$ ), as shown in Fig. \ref{fig_GRO_phindx_sel}," where BAT and HEXTE values agree to within ~13% with no apparent correlation between spectral shape and flux discrepancy., where BAT and HEXTE values agree to within $\sim$ with no apparent correlation between spectral shape and flux discrepancy. Fig., Fig. 6 is a clear proof of the good capabilities of our method in order to extract flux and spectral informations for bright hard X-ray sources., \ref{fig_GRO_flux} is a clear proof of the good capabilities of our method in order to extract flux and spectral informations for bright hard X-ray sources. BAT serendipitous coverage yielded a monitoring with a time coverage fully comparable to that obtained through a systematic campaign with RXTE., BAT serendipitous coverage yielded a monitoring with a time coverage fully comparable to that obtained through a systematic campaign with RXTE. We note that BAT. simply owing to its good sensitivity over a very large FOV. caught the outburst since the very beginning. while the detection of the source activity by HEXTE and PCA was due to planned observational campaign of the Galactic center region (PCA Galactic bulge scans).," We note that BAT, simply owing to its good sensitivity over a very large FOV, caught the outburst since the very beginning, while the detection of the source activity by HEXTE and PCA was due to planned observational campaign of the Galactic center region (PCA Galactic bulge scans)." Had GRO J1655-40 be located outside the galactic bulge region scanned by RXTE. its outburst would have been detected by ASM with >15 day delay with respect to BAT (see figure 7)).," Had GRO J1655-40 be located outside the galactic bulge region scanned by RXTE, its outburst would have been detected by ASM with $>$ 15 day delay with respect to BAT (see figure \ref{fig_GRO_flux53415_53470}) )." " We have developed and tested a procedure. based on public available Swift software tools. aimed at extracting flux and spectral information for bright hard X-ray sources from BAT ""survey"" data."," We have developed and tested a procedure, based on public available Swift software tools, aimed at extracting flux and spectral information for bright hard X-ray sources from BAT “survey” data." Tests performed using a large sample of Crab data have shown that our pipeline. based on the mask-weighting technique. yields reliable measurements. both in spectral shape and in flux. over the whole BAT FOV.," Tests performed using a large sample of Crab data have shown that our pipeline, based on the mask-weighting technique, yields reliable measurements, both in spectral shape and in flux, over the whole BAT FOV." Using those results as a starting point. a more comprehensive test of our method was carried out on a fainter. strongly variable source such as GRO J1655-40.," Using those results as a starting point, a more comprehensive test of our method was carried out on a fainter, strongly variable source such as GRO J1655-40." Its 9-month long outburst was systematically monitored with PCA and HEXTE instruments on board RXTE satellite and serendipitously observed by BAT., Its 9-month long outburst was systematically monitored with PCA and HEXTE instruments on board RXTE satellite and serendipitously observed by BAT. The cross-check performed by analysing indipendently the BAT and HEXTE spectra has shown a very good agreement between the two instruments when the source signal-to-noise in BAT spectrum ts greater than 4+ (750 mCrab. for a target within the half coded region). confirming the reliability of our approach for using BAT as a hard X-ray monitor for bright sources.," The cross-check performed by analysing indipendently the BAT and HEXTE spectra has shown a very good agreement between the two instruments when the source signal-to-noise in BAT spectrum is greater than 4 $\sim$ 50 mCrab, for a target within the half coded region), confirming the reliability of our approach for using BAT as a hard X-ray monitor for bright sources." Combining such good performances with the huge BAT ΕΟΝ. which covers each day ~50% of the sky. one realizes the instrument’s potential to frequently monitor the temporal and spectral evolution of numerous bright. hard-X ray sources.," Combining such good performances with the huge BAT FOV, which covers each day $\sim$ of the sky, one realizes the instrument's potential to frequently monitor the temporal and spectral evolution of numerous bright, hard-X ray sources." As shown in section ??.. BAT has been able to detect the beginning of the GRO J1655-40 outburst almost simultaneously with PCA instrument. which was luckily on target.," As shown in section \ref{GRO_results}, BAT has been able to detect the beginning of the GRO J1655-40 outburst almost simultaneously with PCA instrument, which was luckily on target." Thus. while scanning the sky waiting for GRBs. BAT can be used both for detecting emission from hard X- transients and for monitoring the temporal and spectral evolution of known sources.," Thus, while scanning the sky waiting for GRBs, BAT can be used both for detecting emission from hard X-ray transients and for monitoring the temporal and spectral evolution of known sources." of the ejecta is expected and corresponding 3D simulations have been presented bv ?..,of the ejecta is expected and corresponding 3D simulations have been presented by \citet{roepke07b}. It is possible. however. that the DDT happens at multiple locations washing out the asymmetries in the ejecta.," It is possible, however, that the DDT happens at multiple locations washing out the asymmetries in the ejecta." In an alternative scenario. the “Gravitationally Confined Detonation” (GCD) suggested by ?.. an asymmetrically ignited flame fails to unbind the star and the ash erupts from the surface.," In an alternative scenario, the “Gravitationally Confined Detonation” (GCD) suggested by \citet{plewa04}, an asymmetrically ignited flame fails to unbind the star and the ash erupts from the surface." Still gravitationally bound. it sweeps around the unburned core of the white dwarf and collides on the far side.," Still gravitationally bound, it sweeps around the unburned core of the white dwarf and collides on the far side." The resulting compression of fuel has been suggested to trigger a detonation (?) which potentially produces asymmetric ejecta compositions., The resulting compression of fuel has been suggested to trigger a detonation \citep{plewa04} which potentially produces asymmetric ejecta compositions. However. recent results by ?. indicate that triggering a detonation in this scenario is possible only with special ignition setups in two-dimensional simulations.," However, recent results by \citet{roepke07} indicate that triggering a detonation in this scenario is possible only with special ignition setups in two-dimensional simulations." Three-dimensional models seem to disfavour this mechanism. because in those models greater energy release in the deflagration stage expands the star such that a strong collision of the ashes is prevented.," Three-dimensional models seem to disfavour this mechanism, because in those models greater energy release in the deflagration stage expands the star such that a strong collision of the ashes is prevented." In some cases the energy release during deflagration is even sufficient to unbind the white dwarf (an example of one such model is discussed in Section 4 of this paper)., In some cases the energy release during deflagration is even sufficient to unbind the white dwarf (an example of one such model is discussed in Section \ref{sect:real_model} of this paper). The asymmetries produced in delayed detonation scenarios merit further investigation and will be the subject of a forthcoming study., The asymmetries produced in delayed detonation scenarios merit further investigation and will be the subject of a forthcoming study. Here. we are motivated to investigate and illustrate the possible effects of chemical asymmetries on bolometric light curves.," Here, we are motivated to investigate and illustrate the possible effects of chemical asymmetries on bolometric light curves." To this end. we will consider first a set of toy models which explore the effect of an off-centre distribution of nuclear ash.," To this end, we will consider first a set of toy models which explore the effect of an off-centre distribution of nuclear ash." We then extend the discussion to a real hydrodynamical explosion model — an asymmetrically ignited pure deflagration model that produced a weak explosion., We then extend the discussion to a real hydrodynamical explosion model – an asymmetrically ignited pure deflagration model that produced a weak explosion. The radiative transfer calculations required to obtain the light curves were performed using a 3D. fully time-dependent Monte Carlo code.," The radiative transfer calculations required to obtain the light curves were performed using a 3D, fully time-dependent Monte Carlo code." We begin. in Section 2.. by briefly describing the operation of this code.," We begin, in Section \ref{sect:code}, by briefly describing the operation of this code." Then. in Section 3.. we discuss our set of artificial toy models.," Then, in Section \ref{sect:toy}, we discuss our set of artificial toy models." In Section +. we present the results obtained with a recent hydrodynamical explosion model (2). and in Section 5. we discuss the implications of this model.," In Section \ref{sect:real_model}, we present the results obtained with a recent hydrodynamical explosion model \citep{roepke07} and in Section \ref{sect:implic} we discuss the implications of this model." Our findings are summarised in Section 6.., Our findings are summarised in Section \ref{sect:summ}. Monte Carlo methods have been successfully applied to the modelling of radiation transport in supernovae for more than two decades. ?..," Monte Carlo methods have been successfully applied to the modelling of radiation transport in supernovae for more than two decades. \citet{ambwani88}," and several subsequent studies. have used Monte Carlo simulations of 5-ray propagation to compute energy deposition rates and -ray spectra as functions of time for SN Iu. Subsequently. the Monte Carlo approach was extended to follow not only the - but also the subsequent emission and scattering of radiation in other spectral regions. thereby allowing bolometric light curves to be obtained (2)..," and several subsequent studies, have used Monte Carlo simulations of $\gamma$ -ray propagation to compute energy deposition rates and $\gamma$ -ray spectra as functions of time for SN Ia. Subsequently, the Monte Carlo approach was extended to follow not only the $\gamma$ -rays but also the subsequent emission and scattering of radiation in other spectral regions, thereby allowing bolometric light curves to be obtained \citep{cappellaro97}." Recently. ?. has presented further generalisation of the methods and demonstrated that they can be readily used for three dimensional modelling.," Recently, \citet{lucy05} has presented further generalisation of the methods and demonstrated that they can be readily used for three dimensional modelling." Following ?.. these methods have been employed in a variety of contemporary multi-dimensional radiative transfer computations of relevance to the study of SNe (see.e.g..22)..," Following \citet{lucy05}, these methods have been employed in a variety of contemporary multi-dimensional radiative transfer computations of relevance to the study of SNe \citep[see, e.g.,][]{kasen06a, maeda06}." All the light curve calculations presented in this paper were performed using the 3D Monte Carlo radiative transfer code described by ?.. which is closely based on that presented by ?..," All the light curve calculations presented in this paper were performed using the 3D Monte Carlo radiative transfer code described by \citet{sim07}, which is closely based on that presented by \citet{lucy05}." A brief description of the operation of the code is given below but we refer the reader to ?. for full details., A brief description of the operation of the code is given below but we refer the reader to \citet{sim07} for full details. The code assumes that the ejecta are in homologous expansion. an excellent approximation for the entire time span for which any significant radiative flux is able to propagate and escape.," The code assumes that the ejecta are in homologous expansion, an excellent approximation for the entire time span for which any significant radiative flux is able to propagate and escape." The supernova model is specitied on a 3D Cartesian grid which expands smoothly along with the homologous flow., The supernova model is specified on a 3D Cartesian grid which expands smoothly along with the homologous flow. For the toy models (Section 3)) a 100% grid is adopted while for the full explosion model (Section 4)) a 1287 grid is used., For the toy models (Section \ref{sect:toy}) ) a $^3$ grid is adopted while for the full explosion model (Section \ref{sect:real_model}) ) a $^3$ grid is used. The model specifies the initial density in each grid cell. the initial fractional mass of “°Ni and. when needed. the combined fractional masses of all iron group elements.," The model specifies the initial density in each grid cell, the initial fractional mass of $^{56}$ Ni and, when needed, the combined fractional masses of all iron group elements." The mass density at later times is readily deduced from the assumption of homologous expansion., The mass density at later times is readily deduced from the assumption of homologous expansion. Following ?.. the Monte Carlo quanta begin their lives as pellets of radioactive material.," Following \citet{lucy05}, the Monte Carlo quanta begin their lives as pellets of radioactive material." " These pellets are placed in the ejecta in accordance with the initial distribution of ""Ni.", These pellets are placed in the ejecta in accordance with the initial distribution of $^{56}$ Ni. " As time passes in the simulation. the pellets decay as determined by the half-lives of the ""Ni and daughter ""Co nuclei."," As time passes in the simulation, the pellets decay as determined by the half-lives of the $^{56}$ Ni and daughter $^{56}$ Co nuclei." When a pellet decays. it becomes a οταν quantum. the propagation of which is then followed in detail.," When a pellet decays, it becomes a $\gamma$ -ray quantum, the propagation of which is then followed in detail." By means of Compton scattering or photoabsorption. the ~-ray quanta are able to deposit their energy — the numerical treatment of these processes is discussed by ?..," By means of Compton scattering or photoabsorption, the $\gamma$ -ray quanta are able to deposit their energy – the numerical treatment of these processes is discussed by \citet{lucy05}." Whenever a 5-ray quantum is destroyed. it is assumed thi= its energy thermalises and is re-emitted as ultraviolet. optical or infrared VOIR) photons: it is thereafter termed an +-packet in the nomenclature used by ?..," Whenever a $\gamma$ -ray quantum is destroyed, it is assumed that its energy thermalises and is re-emitted as ultraviolet, optical or infrared ) photons; it is thereafter termed an $r$ -packet in the nomenclature used by \citet{lucy05}." Bolometric light curves are. obtained from. the behaviour of the r-packets., Bolometric light curves are obtained from the behaviour of the $r$ -packets. Currently. the code uses a simple grey- treatment to follow the propagation and scattering of the r-packets (the specitic forms of the opacity used for the models we present are discussed in Sections 3. and 4)).," Currently, the code uses a simple grey-opacity treatment to follow the propagation and scattering of the $r$ -packets (the specific forms of the opacity used for the models we present are discussed in Sections \ref{sect:toy} and \ref{sect:real_model}) )." In principle. light curves ean be obtained by angular binning of the r-packets as they emerge from the computational domain.," In principle, light curves can be obtained by angular binning of the $r$ -packets as they emerge from the computational domain." However. greater efficiency is obtained by employing volume-based Monte Carlo estimators (7) to deduce emissivities from the r-packet trajectories and then using these to perform a formal solution of the radiative transfer equation (details of the specitic Monte Carlo estimators currently used in the code are given in 2)).," However, greater efficiency is obtained by employing volume-based Monte Carlo estimators \citep{lucy99} to deduce emissivities from the $r$ -packet trajectories and then using these to perform a formal solution of the radiative transfer equation (details of the specific Monte Carlo estimators currently used in the code are given in \citealt{sim07}) )." Thus. the end products of the calculation which are used in this paper are bolometric light curves computed for distant observers who are located on specitic lines-of-sight and who are at rest relative to the centre of the supernova model.," Thus, the end products of the calculation which are used in this paper are bolometric light curves computed for distant observers who are located on specific lines-of-sight and who are at rest relative to the centre of the supernova model." " In this section. we undertake a preliminary investigation of the effects of a lop-sided ""Ni distribution on light curves using a set of simply-parameterized. artificial toy models."," In this section, we undertake a preliminary investigation of the effects of a lop-sided $^{56}$ Ni distribution on light curves using a set of simply-parameterized, artificial toy models." We begin by deseribing these models and the numerical results obtained from them (Section 3.1) and then discuss the general implications of such models (Section 3.2))., We begin by describing these models and the numerical results obtained from them (Section \ref{sect:toy-models}) ) and then discuss the general implications of such models (Section \ref{sect:toy-discuss}) ). " To explore the role of an off-centre distribution of ""Ni. a grid of simplistic toy models has been constructed."," To explore the role of an off-centre distribution of $^{56}$ Ni, a grid of simplistic toy models has been constructed." In each model. a total mass of |. M. is adopted.," In each model, a total mass of 1.4 $_{\odot}$ is adopted." " The mass density is assumed to be uniform and a maximum velocity of 4,=I kms. | is chosen.", The mass density is assumed to be uniform and a maximum velocity of $v_{\mbox{\scriptsize max}} = 10^4$ km $^{-1}$ is chosen. " This simple density distribution makes it convenient to explore off-centre distributions of ""Ni without necessitating changes in either the geometrical shape of the ""Ni blob nor the underlying total mass distributions.", This simple density distribution makes it convenient to explore off-centre distributions of $^{56}$ Ni without necessitating changes in either the geometrical shape of the $^{56}$ Ni blob nor the underlying total mass distributions. " In more sophisticated SN Ia models. the density distribution generally does extend to velocities greater than our adopted ey, (9.5. in the well-known W7 model. ?))— however. in these outer higher velocity regions. the density has typically fallen off by an order of magnitude or more compared to the inner parts which makes the outer regions relatively unimportant"," In more sophisticated SN Ia models, the density distribution generally does extend to velocities greater than our adopted $v_{\mbox{\scriptsize max}}$ (e.g. in the well-known W7 model, \citealt{nomoto84}) ) – however, in these outer higher velocity regions, the density has typically fallen off by an order of magnitude or more compared to the inner parts which makes the outer regions relatively unimportant" "The photometry of the partially crowded emission knots of the 15um ISOCAM, 24um Spitzer-MIPS and 70, 100, and 160m Herschel-PACS maps used the HIIphot package developed by D. Thilker (?)..","The photometry of the partially crowded emission knots of the $\mu$ m ISOCAM, $\mu$ m -MIPS and 70, 100, and $\mu$ m -PACS maps used the HIIphot package developed by D. Thilker \citep{thilker00}." " The standard parameter settings were applied, except a maximum source size of ppc and a background annulus of ppc were used in order to have similar source borders, taking the variation in spatial resolution into account over the considered wavelength range."," The standard parameter settings were applied, except a maximum source size of pc and a background annulus of pc were used in order to have similar source borders, taking the variation in spatial resolution into account over the considered wavelength range." PSF FWHM and the termgrad array were adjusted according to the instrument/wavelength and the flux level of the individual maps., PSF FWHM and the termgrad array were adjusted according to the instrument/wavelength and the flux level of the individual maps. " Figure 1. shows the Herschel-PACS maps at 70, 100, and 160 pum. The um map reaches farthest out, since it has twice the exposure time of the blue (703-100) bands."," Figure \ref{pacsimages} shows the -PACS maps at 70, 100, and 160 $\mu$ m. The $\mu$ m map reaches farthest out, since it has twice the exposure time of the blue $+$ 100) bands." Its faintest contours cover the optical disks FFig. 2))., Its faintest contours cover the optical disks Fig. \ref{pacs100contoursonHSTBVHalpha}) ). " There is some dust emission excess, where the optical image shows the deep cleft between the two disks."," There is some dust emission excess, where the optical image shows the deep cleft between the two disks." " The um image also indicates the base of the southern tidal arm where it shows a bulge in the optical, but there is no emission detected from the long thin tidal arms."," The $\mu$ m image also indicates the base of the southern tidal arm where it shows a bulge in the optical, but there is no emission detected from the long thin tidal arms." " The 70 and um maps show cut-off southwest of the 44039 nucleus, and this very alow flux level indicates a lack of heating sources and possibly also a depletion of dust in this area (Fig. 2))."," The 70 and $\mu$ m maps show a cut-off southwest of the 4039 nucleus, and this very low flux level indicates a lack of heating sources and possibly also a depletion of dust in this area (Fig. \ref{pacs100contoursonHSTBVHalpha}) )." " The two nuclei and the chain of HII region complexes along the northwestern wound-up spiral arm of 44038 are clearly resolved, as are several emission knots along an arc in the overlap region connecting the two nuclei (see Fig."," The two nuclei and the chain of HII region complexes along the northwestern wound-up spiral arm of 4038 are clearly resolved, as are several emission knots along an arc in the overlap region connecting the two nuclei (see Fig." 3 for the knot identification)., \ref{HIIPhotexample} for the knot identification). " Both nuclei are brighter than the HII regions in the spiral arm, but the brightest emission in all three bands comes from the overlap region."," Both nuclei are brighter than the HII regions in the spiral arm, but the brightest emission in all three bands comes from the overlap region." At 100 um the brightest emission (K1 east) lies at the southern edge of the overlap region., At 100 $\mu$ m the brightest emission (K1 east) lies at the southern edge of the overlap region. " It coincides with the prominent 15 and 24 jm emission peaks (??),, which is located at the border of an optically bright HII region complex toward the dark dust lanes (Fig. 2))."," It coincides with the prominent 15 and 24 $\mu$ m emission peaks \citep{vigroux96,mirabel98}, which is located at the border of an optically bright HII region complex toward the dark dust lanes (Fig. \ref{pacs100contoursonHSTBVHalpha}) )." This region houses the supergiant molecular cloud, This region houses the supergiant molecular cloud would produce an upward extension of the blue side of the RGB (see Williams et al.,would produce an upward extension of the blue side of the RGB (see Williams et al. 2007 for an example)., \cite{wil07} for an example). Most or all of the remainder is likely to be due to blends: we expect (see Harris et al. 2007a)), Most or all of the remainder is likely to be due to blends: we expect (see Harris et al. \cite{har07a}) ) " where N, is the number of stars in the field capable of generating a blended pair brighter than the TRGB. a is the area of one resolution element. and A is the area of the field."," where $N_{\star}$ is the number of stars in the field capable of generating a blended pair brighter than the TRGB, $a$ is the area of one resolution element, and $A$ is the area of the field." " We take A=1.42 aremin? for the area of the outer two annuli enclosed within the field: «=7.8x1077 aresec"" ;:and N,516000 for the number of stars between /=27 and 28. the top magnitude of the RGB."," We take $A = 1.42$ $^2$ for the area of the outer two annuli enclosed within the field; $a = 7.8 \times 10^{-3}$ $^2$; and $N_{\star} \simeq 16000$ for the number of stars between $I=27$ and 28, the top magnitude of the RGB." These parameters predict about 200 blends lying above the TRGB., These parameters predict about 200 blends lying above the TRGB. " In fact this estimate is only a lower limit. because (as discussed in the next section) crowding-driven incompleteness of the photometry ‘affects even the range /<28 and N, could be quite a bit larger than our directly measured count."," In fact this estimate is only a lower limit, because (as discussed in the next section) crowding-driven incompleteness of the photometry affects even the range $I < 28$ and $N_{\star}$ could be quite a bit larger than our directly measured count." Though admittedly provisional. our conclusion is that the great majority of the objects brighter than the TRGB can be accounted for by the combination of the three normal factors given above.," Though admittedly provisional, our conclusion is that the great majority of the objects brighter than the TRGB can be accounted for by the combination of the three normal factors given above." One useful comparison study of the distance to M87 is the photometry of the intracluster stars in Virgo by Williams et al. (2007))., One useful comparison study of the distance to M87 is the photometry of the intracluster stars in Virgo by Williams et al. \cite{wil07}) ). Although their target field is far from M87. it should in principle have a reasonably similar TRGB level given that M87 15 near the physical center of the Virgo environment.," Although their target field is far from M87, it should in principle have a reasonably similar TRGB level given that M87 is near the physical center of the Virgo environment." Although they do not specifically derive the TRGB. their CMD for the intracluster stars clearly shows (TRGB)=26.9—27.0. close to our value for M87 itself.," Although they do not specifically derive the TRGB, their CMD for the intracluster stars clearly shows $I(TRGB) \simeq 26.9 - 27.0$, close to our value for M87 itself." Other indirect. but still. quite. relevant. TRGB-based calibrations of the Virgo distance include studies of à small number of its dwarf ellipticals.," Other indirect, but still quite relevant, TRGB-based calibrations of the Virgo distance include studies of a small number of its dwarf ellipticals." Harris et al. (1998)), Harris et al. \cite{har98}) ) obtained Gn—ato=30.98+0.20 for VCCIIO4= 1C3388. while Caldwell (2006)) obtained Gu—M)o=31.03+0.1 for seven other dwarfs.," obtained $(m-m)_0 = 30.98 \pm 0.20$ for VCC1104 = IC3388, while Caldwell \cite{cal06}) ) obtained $(m-M)_0 = 31.03 \pm 0.1$ for seven other dwarfs." All of these are consistent with membership in the Virgo cluster. and with our result for M87.," All of these are consistent with membership in the Virgo cluster, and with our result for M87." The only other distance calibrations for M87 that rely on resolved stars are (a) the observations of two novae (Pritchet van den Bergh 19855). from which they obtain only the extremely uncertain range of 30.4 — 32.4 for the distance modulus: and (b) the planetary nebula luminosity function (PNLF) by Ciardullo et al. (1998)).," The only other distance calibrations for M87 that rely on resolved stars are (a) the observations of two novae (Pritchet van den Bergh \cite{pri85}) ), from which they obtain only the extremely uncertain range of 30.4 – 32.4 for the distance modulus; and (b) the planetary nebula luminosity function (PNLF) by Ciardullo et al. \cite{cia98}) )." " After adjustment of their adopted zeropoint M*(15007)=—4.54 upward to M*=—4.67 to reflect a change in the fiducial M31 distance (see Harris et citehar10)). the PNLF modulus ts (71—M),=30.92£0.16."," After adjustment of their adopted zeropoint $M^{\star}(\lambda 5007) = -4.54$ upward to $M^{\star} = -4.67$ to reflect a change in the fiducial M31 distance (see Harris et \\cite{har10}) ), the PNLF modulus is $(m-M)_0 = 30.92 \pm 0.16$." The modulus is 0.2 mag smaller than our TRGB value. though the two methods agree within their combined uncertainties.," The modulus is 0.2 mag smaller than our TRGB value, though the two methods agree within their combined uncertainties." The largest and most precise compilation of distances for the Virgo galaxies is by Blakeslee et al. (2009:;, The largest and most precise compilation of distances for the Virgo galaxies is by Blakeslee et al. \cite{bla09}; see also Mei et al. 2007).," see also Mei et al. \cite{mei07}) )," from the surface brightness fluctuations (SBF) technique., from the surface brightness fluctuations (SBF) technique. SBF represents a “secondary” standard-candle method because it relies for its calibratior on nearby galaxies whose distances are known beforehand from resolved-star methods. although theoretical calibratior via stellar population models is also possible.," SBF represents a “secondary” standard-candle method because it relies for its calibration on nearby galaxies whose distances are known beforehand from resolved-star methods, although theoretical calibration via stellar population models is also possible." Blakeslee et ((2009)) determine Gai—M);=31.11x0.08 for M87 i1 particular. starting from à distance modulus of 0.03 for the Virgo cluster as a whole.," Blakeslee et \cite{bla09}) ) determine $(m-M)_0 = 31.11 \pm 0.08$ for M87 in particular, starting from a distance modulus of $31.09 \pm 0.03$ for the Virgo cluster as a whole." This in turn is basec on the Cepheid calibration of the SBF method given by Tonry et ((2001)). corrected following Blakeslee et ((2002)) to the final set of Key Project Cepheid distances (Freedman et al. 2001) ," This in turn is based on the Cepheid calibration of the SBF method given by Tonry et \cite{tonry2001}) ), corrected following Blakeslee et \cite{bla02}) ) to the final set of Key Project Cepheid distances (Freedman et al. \cite{freedman2001}) )." Our TRGB distance measurement. and the earlier PNLF measurement. are gauges of the M87 distance that rely much less on Cepheids.," Our TRGB distance measurement, and the earlier PNLF measurement, are gauges of the M87 distance that rely much less on Cepheids." The PNLF zeropoint. for example. relies more heavily on the fiducial distance to ΜΟΙ. for which close agreement now holds among several standard. candles," The PNLF zeropoint, for example, relies more heavily on the fiducial distance to M31, for which close agreement now holds among several standard candles" In the following we show simulations illustrating the line profiles as could be observed with several present and future X-ray observatories.,In the following we show simulations illustrating the line profiles as could be observed with several present and future X-ray observatories. In. all cases. we assume a duration of the eclipse of 50 ks. i.e. of the same order as those already observed in NGC 1365 and in other sources (Bisaliti 2009).," In all cases, we assume a duration of the eclipse of 50 ks, i.e. of the same order as those already observed in NGC 1365 and in other sources (Risaliti 2009)." We stress again the most interesting aspect of the simulations. and the main motivation of this work. namely. that the parameters of the mocel are not chosen arbitrarily. but are obtained. from. already. observed. eclipses. and. are therefore expected to correspond. to easily. (re-)observable events.," We stress again the most interesting aspect of the simulations, and the main motivation of this work, namely that the parameters of the model are not chosen arbitrarily, but are obtained from already observed eclipses, and are therefore expected to correspond to easily (re-)observable events." We start from a complete eclipse by a Compton-thick (Nx>107 2 7) cloud with. sharp. linear. edges.," We start from a complete eclipse by a Compton-thick $N_H>10^{25}$ $^{-2}$ ) cloud with sharp, linear edges." " rp.This. is+ considered the ""perfect"" event because it would. provide a completely separate view of the approaching (“blue”) and receding (7red) halves of the accretion disc. as well as a view of the total line emission (as long as the clouds. are more or less coplanar with the disc)"," This is considered the “perfect” event because it would provide a completely separate view of the approaching (“blue”) and receding (“red”) halves of the accretion disc, as well as a view of the total line emission (as long as the clouds are more or less coplanar with the disc)." The results shown in Fig., The results shown in Fig. 2 are for observations with present. or nearly completed. observatories(VALAL-Newlon.Suzaku. Ashro-I). and for projects of possible new missions. such as or A/hena.with an assumed. cllective area at 6 keV. A420.6 n. and or Extreme Physics Explorer (Elvis 2006). with an assumed A622 m7).," 2 are for observations with present, or nearly completed, observatories, ), and for projects of possible new missions, such as or ,with an assumed effective area at 6 keV $_6$ =0.6 $^2$, and or Extreme Physics Explorer (Elvis 2006), with an assumed $_6$ =2 $^2$ )." The main results are the followingy* The case discussed. above demonstrates that the analysis of line profile variations is within the possibilities of current N-rav. observatories. if optimal conditions are met.," The main results are the following: The case discussed above demonstrates that the analysis of line profile variations is within the possibilities of current X-ray observatories, if optimal conditions are met." The observational history of NGC 1365 shows that. such conditions are (they already occurred at least once. though not during a continuous monitoring) but and dillicult to cateh (NGC 1365 has been monitored for long intervals several times. and the Ἱρωίοσ eclipse has not been observed. vet).," The observational history of NGC 1365 shows that such conditions are (they already occurred at least once, though not during a continuous monitoring) but and difficult to catch (NGC 1365 has been monitored for long intervals several times, and the “perfect” eclipse has not been observed yet)." Llere we discuss the possibility of performing a similar study. of line. profile variations during “normal” eclipses. such as the ones observed several times in NGC 1365 and in the other AGNs listed in the previous Sections.," Here we discuss the possibility of performing a similar study of line profile variations during “normal” eclipses, such as the ones observed several times in NGC 1365 and in the other AGNs listed in the previous Sections." The average properties of these eclipses are the following (Maiolino et al., The average properties of these eclipses are the following (Maiolino et al. 2010. Risaliti et al. -," 2010, Risaliti et al. -" Column density of the obscuring clouds of the order of a few 1077? - Duration of 10-15 - Partial covering of the X-ray source. with the covered fraction of the order of With these parameters. and. do not provide enough counts to perform. line variability studies.," Column density of the obscuring clouds of the order of a few $^{23}$ $^{-2}$ - Duration of 10-15 - Partial covering of the X-ray source, with the covered fraction of the order of With these parameters, and do not provide enough counts to perform line variability studies." " ""This has been confirmed. by our. simulations. and. more importantly. by the analysis of the available observations."," This has been confirmed by our simulations, and, more importantly, by the analysis of the available observations." Instead. simulations for larec-arca [uture observatories show that assuming the above parameters (with a conservative covering factor of only 25%)). one would. be able to detect line profile variations with high confidence.," Instead, simulations for large-area future observatories show that assuming the above parameters (with a conservative covering factor of only ), one would be able to detect line profile variations with high confidence." The simulations in Fig., The simulations in Fig. 3 show four possible combinations depending on the direction of the celipsing cloud. with respect to the disc axis., 3 show four possible combinations depending on the direction of the eclipsing cloud with respect to the disc axis. Clearly. we have the highest contrast between the different phases of the eclipse when the cloud covers a blue region of the disc. while the dillerence is smaller when only the red half is eclipsed.," Clearly, we have the highest contrast between the different phases of the eclipse when the cloud covers a “blue” region of the disc, while the difference is smaller when only the “red” half is eclipsed." With the exception of the unfortunate case of panel C.," With the exception of the unfortunate case of panel C," additional laver is a bouncary of the previous void boundary and exeeeds this by the given factor f.,additional layer is a boundary of the previous void boundary and exceeds this by the given factor $f$. This factor is also imposed in extending the base square laver along their for sides., This factor is also imposed in extending the base square layer along their for sides. This procedure provides almost convex empty. voids., This procedure provides almost convex empty voids. The value f is the only free parameter in our void. search algorithm., The value $f$ is the only free parameter in our void search algorithm. Hs value is chosen so às to avoid narrow tunnels that go out of the base voids into the galaxy. distribution., Its value is chosen so as to avoid narrow tunnels that go out of the base voids into the galaxy distribution. For the present. analysis. we provide only results for the base square voids.," For the present analysis, we provide only results for the base square voids." We have analysed. both 2db-cdata and simulations also including the void search with extensions. with gives similar void size distributions. scaling relations and an reproduction of the data by the simulations.," We have analysed both 2dF-data and simulations also including the void search with extensions, with gives similar void size distributions, scaling relations and an reproduction of the data by the simulations." The reason for restricting on the base voids lies in its use for looking for faint galaxies laving in central regions of large voids., The reason for restricting on the base voids lies in its use for looking for faint galaxies laying in central regions of large voids. For the analysis. a grid of resolution of 1 was chosen.," For the analysis, a grid of resolution of 1 was chosen." The void finder is useful in that it is faster than looking for the largest empty. spheres in the galaxy clistribution., The void finder is useful in that it is faster than looking for the largest empty spheres in the galaxy distribution. Although voids do not tend to be cubical. the extension along the boundaries and a sullicienthy small eid allow for realistic. void. geometries.," Although voids do not tend to be cubical, the extension along the boundaries and a sufficiently small grid allow for realistic void geometries." Comparison with the spherical void finder of ? shows. that for large voids we are mainly interested in. the void finder selects the identical void centers and sizes.," Comparison with the spherical void finder of \cite{Patiri06a} shows, that for large voids we are mainly interested in, the void finder selects the identical void centers and sizes." In our analvsis we derive the size distribution of voids up to small values. thereby covering in most cases over 90% of the space with voids.," In our analysis we derive the size distribution of voids up to small values, thereby covering in most cases over 90 of the space with voids." For the comparison with other void finder. we use and elective radius Ro=—(3V/Az)7.," For the comparison with other void finder, we use and effective radius $R = (3 V /4 \pi)^{1/3}$." As statistics we use the volume weighted void size distribution defined as the cumulative volume of the survey covered ov voids of radius larger than 2., As statistics we use the volume weighted void size distribution defined as the cumulative volume of the survey covered by voids of radius larger than $R$. This definition has the advantage of allowing a robust void size distribution over 2 ο 3 order of magnitude in Z(A)., This definition has the advantage of allowing a robust void size distribution over 2 to 3 order of magnitude in $F(>R)$. The strongly varving volumes of large voids then appear at the low abundance end of the distribution., The strongly varying volumes of large voids then appear at the low abundance end of the distribution. The more common void. probability unction. £%(2) is given. by a weighted sum. over. the dillerential size distribution f(2)=dE dl. ορ. ??..," The more common void probability function $P_0(R)$ is given by a weighted sum over the differential size distribution $f(R)= -dF/dR$ , cp. \cite{Otto86, Betancort90}." The employed. void size distribution {ος2) does not suppose a oe-specified. geometry of the voids. and it determines themarine’ empty region in the galaxy distribution. starting rom large voids and going to smaller ones.," The employed void size distribution $F(>R)$ does not suppose a pre-specified geometry of the voids, and it determines the empty region in the galaxy distribution, starting from large voids and going to smaller ones." Thus it seems to »v most sensitive to the large-scale clistribution of galaxies in the cosmic web., Thus it seems to be most sensitive to the large-scale distribution of galaxies in the cosmic web. First we investigate the void. sizes found. in the observed volume limited. samples., First we investigate the void sizes found in the observed volume limited samples. We found. maximum voids with elective radii of 24 and 22 base sizes in the sample N4 ancl S4. resp.," We found maximum voids with effective radii of 24 and 22 base sizes in the sample N4 and S4, resp." There are 156. τος ancl 2 voids over 12 base length in samples N4. 3. 2. and l. resp.:," There are 156, 70, and 2 voids over 12 base length in samples N4, 3, 2, and 1, resp.;" and. 199. 116. and 2 voids in 84. 3. and 2. resp. (," and 199, 116, and 2 voids in S4, 3, and 2, resp. (" no such large void are found in NI or S1).,no such large void are found in N1 or S1). Voids over 6 elfective radius are much more abundant. there are 9016. 1250. 321. and 66 voids in samples N4. 3. 2. and 1. resp.:," Voids over 6 effective radius are much more abundant, there are 916, 1250, 321, and 66 voids in samples N4, 3, 2, and 1, resp.;" ancl 1364. 1786. 538. and 129 voids in samples S4. 3. 2. and 1. resp.," and 1364, 1786, 538, and 129 voids in samples S4, 3, 2, and 1, resp." Fig., Fig. 1 shows the 100 largest voids as found in the sample 83., \ref{voids2df} shows the 100 largest voids as found in the sample S3. For comparison Fig., For comparison Fig. 2. shows the same for a Millenium mock catalog with the same magnitude range aud an identical survey mask (ic. NW3. see below).," \ref{voidsmill} shows the same for a Millenium mock catalog with the same magnitude range and an identical survey mask (i.e. MW3, see below)." Obviously. both 2dECGIBS- and mock samples look very similar. and they show a comparable distribution of large voids.," Obviously, both 2dFGRS- and mock samples look very similar, and they show a comparable distribution of large voids." Large voids are more abundant at [larger distances from the observer., Large voids are more abundant at larger distances from the observer. This is an effect of the survey window that strongly restricts large nearby voids., This is an effect of the survey window that strongly restricts large nearby voids. Besides this geometric ellect. large voids are evenly cistributed in data and mocel distributions. and vold sizes are comparable in both samples.," Besides this geometric effect, large voids are evenly distributed in data and model distributions, and void sizes are comparable in both samples." Alore quantitative results can be seen in the cumulative vold size distribution shown in Fig. 4.., More quantitative results can be seen in the cumulative void size distribution shown in Fig. \ref{cum2df}. Phere we combine 16 S/N samples from the 2dEGIUS to get better statistics., There we combine the S/N samples from the 2dFGRS to get better statistics. If taken separately we ect similar curves for the north and south galactic pole regions., If taken separately we get similar curves for the north and south galactic pole regions. We take the dillerence for the separate distributions as à measure of the uncertainty in the samples shown by the error bars on the binned sample., We take the difference for the separate distributions as a measure of the uncertainty in the samples shown by the error bars on the binned sample. Most obvious is the size dependence of voids on the galaxy samples. the largest voids among bright galaxies with 2;>20.21 have an effective radius over 15 sf.," Most obvious is the size dependence of voids on the galaxy samples, the largest voids among bright galaxies with $B_J > 20, 21$ have an effective radius over 15 $/h$." The statistics of such large voids is still quite restricted. but smaller voids lead. to size distribution with small error bars.," The statistics of such large voids is still quite restricted, but smaller voids lead to size distribution with small error bars." The general form of the distribution is self-similar., The general form of the distribution is self-similar. We fit it with moclified exponential distributions with 4 parameters. two length factors δι ancl 5». and two powers py and ps.," We fit it with modified exponential distributions with 4 parameters, two length factors $s_1$ and $s_2$, and two powers $p_1$ and $p_2$." The fits are by \7-minimization; and always provide excellent representations of the observational data covering more than 2 orders of magnitude in £(7AR)., The fits are by $\chi^2$ -minimization and always provide excellent representations of the observational data covering more than 2 orders of magnitude in $F(>R)$. The main scaling of the galaxy. samples is described: by the mean separation between galaxies. the scale A.," The main scaling of the galaxy samples is described by the mean separation between galaxies, the scale $\lambda$." This value and all fit parameters are given in Table 2.., This value and all fit parameters are given in Table \ref{fit}. Phe first exponential describes the statistics of small and intermediate sized. voids., The first exponential describes the statistics of small and intermediate sized voids. “This part is typically described with an linear [all-otfin the exponential function. i.e. py&1.," This part is typically described with an linear fall-off in the exponential function, i.e. $p_1 \approx 1$." For describing the eutolfof the void size distribution for large void radii. we need the second factor in the exponential distribution with a higher power of the void radius. tvpically with poz3. ie. the abundance of large voids is eut olf with the void volume entering the exponential function.," For describing the cutoff of the void size distribution for large void radii, we need the second factor in the exponential distribution with a higher power of the void radius, typically with $p_2 \approx 3$, i.e. the abundance of large voids is cut off with the void volume entering the exponential function." The length factors s; and so are both of order unity., The length factors $s_1$ and $s_2$ are both of order unity. Alter multiplication. with the mean galaxy separation they provide the void radii where the two exponential laws dominate the size clistribution., After multiplication with the mean galaxy separation they provide the void radii where the two exponential laws dominate the size distribution. There are no wavs to fit the size distribution with a single exponential distribution., There are no ways to fit the size distribution with a single exponential distribution. In Fig., In Fig. 5 we show the normalized void size distribution of the four 20ECGINS data sets. ie. we divide the void sizes ? by the mean separation between galaxies A.," \ref{cum2dfnorm} we show the normalized void size distribution of the four 2dFGRS data sets, i.e. we divide the void sizes $R$ by the mean separation between galaxies $\lambda$." Obviously. the void size distributions are self-similar in this variable.," Obviously, the void size distributions are self-similar in this variable." The scaled: void size clistributions coincide at radii &«—1.5A., The scaled void size distributions coincide at radii $R < 1.5\lambda$. This scaling is similar to the dependence of the correlation length of galaxies ancl groups as found by 2? and. 7.., This scaling is similar to the dependence of the correlation length of galaxies and groups as found by \citet{Bahcall92} and \citet{Yang05}. Note that the samples N/S4 are strongly restricted by the survey geometry., Note that the samples N/S4 are strongly restricted by the survey geometry. The mean intergalaxy separation of about IS is comparable to the thickness of the 2dECIUS slices of about45 at the far side of the selected volume. even if the length of theslices much exceeds the vold sizes.," The mean intergalaxy separation of about 18 is comparable to the thickness of the 2dFGRS slices of about45 at the far side of the selected volume, even if the length of theslices much exceeds the void sizes." Elfectively the statistics of these voids. shown by the dash-dotted lines in bie. 5. ," Effectively the statistics of these voids, shown by the dash-dotted lines in Fig. \ref{cum2dfnorm}, ," is cut olf at an volume, is cut off at an volume emplate LR 114. obtained for the purpose of spectral classification.,"template HR 114, obtained for the purpose of spectral classification." Racial velocities were extracted following the method of Tonry&Davis(1979).. where parabolic fits were »erformed to the peak of the eross-correlation functions. and he uncertainties are purely statistical.," Radial velocities were extracted following the method of \cite{ton79}, where parabolic fits were performed to the peak of the cross-correlation functions, and the uncertainties are purely statistical." The final errorbars were multiplied by a factor 2 so that the minimum reduced V of a sinewave Lit model is 1.0., The final errorbars were multiplied by a factor 2 so that the minimum reduced $\chi^{2}$ of a sinewave fit model is 1.0. Phis vields the following »ranmeters where 7i corresponds to the inferior conjunction of the donor star., This yields the following parameters where $T_{0}$ corresponds to the inferior conjunction of the donor star. ALL quoted errors are. GS per cent. confidence., All quoted errors are 68 per cent confidence. The systemic velocity 5. has been corrected. [rom the racial velocity of LUR 114. thatwe take as -10.2 40.9 km s+ (Wilson.1953).," The systemic velocity $\gamma$ has been corrected from the radial velocity of HR 114, thatwe take as -10.2 $\pm$ 0.9 km $^{-1}$ \citep{wilson53}." . Fig., Fig. 2. displays the raclial velocity points Folded on the orbital period together with the best sine fit solution., \ref{figrv} displays the radial velocity points folded on the orbital period together with the best sine fit solution. New racial velocities are marked with open circles whereas solid circles indicate velocities from. the old. 1993- database (C98)., New radial velocities are marked with open circles whereas solid circles indicate velocities from the old 1993-1997 database (C98). Our As velocity is consistent with COS within leo but not with E09 who finds A»=7943kms," Our $K_2$ velocity is consistent with C98 within $\sigma$ but not with E09 who finds $K_{2} = 79 \pm 3~ {\rm km s}^{-1}$." To ilustrate this point we also plot in dashed-line stvle the best sinewave fit for A»=79 km s.+., To ilustrate this point we also plot in dashed-line style the best sinewave fit for $K_2=79$ km $^{-1}$. This has ML=3 for 60 degrees of freedom and hence it is far less significant than our Av» value (Lamptonctal.1976)., This has $\chi^{2}_\nu=3$ for 60 degrees of freedom and hence it is far less significant than our $K_2$ value \citep{lampton76}. . E09 have suggested that the cillerence between the two A» values could be caused. by different levels of N-ray irracliation between the two observing epochs., E09 have suggested that the difference between the two $K_2$ values could be caused by different levels of X-ray irradiation between the two observing epochs. The detection of LicLL A4686 emission from the companion by E09 certainly indicates that the star is irradiated., The detection of HeII $\lambda$ 4686 emission from the companion by E09 certainly indicates that the star is irradiated. However. it. remains to be seen whether irradiation is sulliciont. not only to pump chromospheric Hell emission. but also to mocifs the surface distribution of the photospheric absorption lines.," However, it remains to be seen whether irradiation is sufficient, not only to pump chromospheric HeII emission, but also to modify the surface distribution of the photospheric absorption lines." In principle. irradiation can quench absorption lines from the inner hemisphere of the donor star. leading to an increase in the observed A» (Wade&LHlorne1988).," In principle, irradiation can quench absorption lines from the inner hemisphere of the donor star, leading to an increase in the observed $K_2$ \citep{wadehorne88}." . Lt might. be possible that. by a chance coincidence. the E09 database was obtained during an episode of lower X-ray activity than our data and we have looked for this using IUNTIZ/ASM. (ALL Sky Monitor) data.," It might be possible that, by a chance coincidence, the E09 database was obtained during an episode of lower X-ray activity than our data and we have looked for this using RXTE/ASM (All Sky Monitor) data." Contemporaneous X-ray. observations are available for the second half of the COS campaign (since 1996. when ΗΝΓΙΟ was Iaunched) our new cata from. 1999-2000 and the entire E09 database but comparable levels of X-ray activity are found. with the X-ray lux £\ oscillating between 35Jn and 50 ASAT counts ," Contemporaneous X-ray observations are available for the second half of the C98 campaign (since 1996, when RXTE was launched) our new data from 1999-2000 and the entire E09 database but comparable levels of X-ray activity are found, with the X-ray flux $F_{\rm X}$ oscillating between 35 and 50 ASM counts $^{-1}$ ." Only one velocity point in COS. obtained on the night of 5 Aug 19060. was taken during a dip in the X-ray. light curve of 5-15 counts c.," Only one velocity point in C98, obtained on the night of 5 Aug 1996, was taken during a dip in the X-ray light curve of $\simeq$ 18 counts $^{-1}$." Interestingly. its orbital phase is ó=0.63. almost identical to that of another point obtained on 3 Aug 1997 (6= 0.67). when Fx~ 50 counts + ie. almost a factor 3 higher.," Interestingly, its orbital phase is $\phi=0.63$, almost identical to that of another point obtained on 3 Aug 1997 $\phi=0.67$ ), when $F_{\rm X}\simeq$ 50 counts $^{-1}$ i.e. almost a factor 3 higher." Despite the difference in X-ray flux both velocities are consistent with our best orbital solution within em., Despite the difference in X-ray flux both velocities are consistent with our best orbital solution within $-\sigma$. And one should note that phase 0.65 is close to an orbital cquacrature. when velocity distortions from a circular orbit should be largest (e.g.Davey&Smith1992).," And one should note that phase 0.65 is close to an orbital quadrature, when velocity distortions from a circular orbit should be largest \citep[e.g.][]{davey92}." . This strongly sugeests that the elfects of X-ray irradiation in the racial velocity curve are unimportant., This strongly suggests that the effects of X-ray irradiation in the radial velocity curve are unimportant. As a matter of fact. imradiation will distort the radial velocity curve from. a simple sine wave. introducing a fictitious eccentricity which should be measurable.," As a matter of fact, irradiation will distort the radial velocity curve from a simple sine wave, introducing a fictitious eccentricity which should be measurable." Therefore. we have also attempted. to fit. elliptical. orbits to our database. following Friendetal.(1990).," Therefore, we have also attempted to fit elliptical orbits to our database, following \cite{friend90}." . Our best [it vields null eccentricity (ο=0.004+0.019) and a larger reduced. 472 than a simple circular. solution. another indication that irradiation is negligible at this level.," Our best fit yields null eccentricity $e=0.004 \pm 0.019$ ) and a larger reduced $\chi^2$ than a simple circular solution, another indication that irradiation is negligible at this level." Furthermore. Orosz&Ixuulkers(1999). finc no evidence for excess light at phase 0.5 in their optical light curves nor COS observe any. significant change of spectral type with orbital phase.," Furthermore, \cite{orosz99} find no evidence for excess light at phase 0.5 in their optical light curves nor C98 observe any significant change of spectral type with orbital phase." “Phese two results also suggest that X-ray irradiation is not enough to explain the discrepant. {νο values., These two results also suggest that X-ray irradiation is not enough to explain the discrepant $K_2$ values. The lack of irradiation signatures is probably due to the fact that the donor star is hot and the orbital separation large Orosz&Ixuulkers (1999)., The lack of irradiation signatures is probably due to the fact that the donor star is hot and the orbital separation large \cite{orosz99}. . Phe X-ray lux received. by every. surface element. on the companion star is too small to. produce any disturbance in the radial velocity curve or light curve. despite the near Eddington X-ray luminosity of (νο X-2.," The X-ray flux received by every surface element on the companion star is too small to produce any disturbance in the radial velocity curve or light curve, despite the near Eddington X-ray luminosity of Cyg X-2." Looking at the radial velocity curve of E09. (shown in fig., Looking at the radial velocity curve of E09 (shown in fig. 4) we note a large scatter in the velocity points near the phase 0.25 quadrature., 4) we note a large scatter in the velocity points near the phase 0.25 quadrature. Two datapoints seem to lio svstematically lower than the rest by ~20 km + ane this is certaintly dragging the A» velocity to lower values., Two datapoints seem to lie systematically lower than the rest by $\sim$ 20 km $^{-1}$ and this is certaintly dragging the $K_2$ velocity to lower values. The authors acit that only one are spectrum was obtainec for most of the nights., The authors admit that only one arc spectrum was obtained for most of the nights. Although sky lines were used. to correct for instrumental offsets. the fact that the stronges sky line OLLL A5577 lies at the edge of their spectral range may introduce some svstematics in the olfset correction.," Although sky lines were used to correct for instrumental offsets, the fact that the strongest sky line OIII $\lambda$ 5577 lies at the edge of their spectral range may introduce some systematics in the offset correction." Therefore. we believe that the value reported by E00 migh be alfected. by problems with the wavelength. calibration which is a critical issue given their low spectral resolution of ~160 km I.," Therefore, we believe that the value reported by E09 might be affected by problems with the wavelength calibration which is a critical issue given their low spectral resolution of $\sim$ 160 km $^{-1}$." In any case. new high resolution observations obtained at the two orbital quadratures are elearly. require to further constrain A» and confirm: our result.," In any case, new high resolution observations obtained at the two orbital quadratures are clearly required to further constrain $K_2$ and confirm our result." Since the donor star is [filling its Roche lobe anc synchronized. we can combine our updated. A» and Vsin; values to constrain the binary mass ratio through (llorne.Wade&Szkody1986). which leads to q=x 0.02.," Since the donor star is filling its Roche lobe and synchronized, we can combine our updated $K_2$ and $V \sin i$ values to constrain the binary mass ratio through \citep{hornewade86} which leads to $q=0.34\pm0.02$ ." The revised. mass function is thus f(AM)=Alisin;/(1|q=pPNSj2x0.66£0.03 and hence Adyni=1.19+0.06 M...," The revised mass function is thus $f(M)= M_{1} \sin^{3} i /(1+q)^{2} = P K_{2}^{3}/2 \pi {\rm G} = 0.66 \pm 0.03$ and hence $M_{1} \sin^{3} i = 1.19 \pm 0.06$ $_{\odot}$." " Assuming i=62.534 (Orosz&Ixuulkers1999) we find AZ,=L714021 M..", Assuming $i=62.5\pm 4^{\circ}$ \citep{orosz99} we find $M_{1}= 1.71 \pm 0.21$ $_{\odot}$ . The error budget is clearly dominated by the uncertainty in the inclination angle andthus ellipsoidal mocel fits to new light curves are urgently needed to better constraint the stellar κ..., The error budget is clearly dominated by the uncertainty in the inclination angle andthus ellipsoidal model fits to new light curves are urgently needed to better constraint the stellar masses. We have revisited the determination. of the system parameters in Cve N-2 with 21 new high-resolution spectra obtained during 1999 and 2000., We have revisited the determination of the system parameters in Cyg X-2 with 21 new high-resolution spectra obtained during 1999 and 2000. Phe new solution does not, The new solution does not nebulae at dillercnt evolutionary stages. allowing trends in the molecular abundances with age to be identified.,"nebulae at different evolutionary stages, allowing trends in the molecular abundances with age to be identified." In this paper. we trace the chemical evolution of mocel clumps. assuming them to have formed early on in the history of the PN and compare the results from those expected if the clumps Formedsii.," In this paper, we trace the chemical evolution of model clumps, assuming them to have formed early on in the history of the PN and compare the results from those expected if the clumps formed." The aim is to identify observable species that can be used as discriminants between the two scenarios., The aim is to identify observable species that can be used as discriminants between the two scenarios. Our moclel is described in Section 2. and our results are presented. discussed. ancl compared. with observations in Section 3.," Our model is described in Section 2, and our results are presented, discussed and compared with observations in Section 3." We conclude in Section 4 that molecular tracers do exist in PPNe and. PNe. and that some large molecules originating in the stellar atmosphere may survive the transition into the interstellar medium.," We conclude in Section 4 that molecular tracers do exist in PPNe and PNe, and that some large molecules originating in the stellar atmosphere may survive the transition into the interstellar medium." The cilference between a clumpy and. non-clumipy mocel is that clump interiors will have a higher extinction than rely surroundings., The difference between a clumpy and non-clumpy model is that clump interiors will have a higher extinction than their surroundings. In the harsh environment of a planetary =1ebula this can help to shield molecules so that they survive or longer than if they were in the interclump gas., In the harsh environment of a planetary nebula this can help to shield molecules so that they survive for longer than if they were in the interclump gas. The chemical difference between clumps that are formed. out of 1e planetary nebula eas ancl those that formed. earlier. is wt in the latter case. complex molecules may be shielded nel preserved. long enough to be detectable in clumps.," The chemical difference between clumps that are formed out of the planetary nebula gas and those that formed earlier is that in the latter case, complex molecules may be shielded and preserved long enough to be detectable in clumps." In 16 former case. all such molecules will have been destroved as the extinction of the gas dropped as the PN evolved.," In the former case, all such molecules will have been destroyed as the extinction of the gas dropped as the PN evolved." Lloweetal.(1992) investigated the gas-phase chemistry in a carbon-rich AGB wind cluring its transition to a planetary nebula., \citet{howe.et.al92} investigated the gas-phase chemistry in a carbon-rich AGB wind during its transition to a planetary nebula. Εις work was followed by apaper (Howeetal.1994). investigating the formation of molecules in a dense. neutral globule such as those observed. in the Lelix nebula.," This work was followed by apaper \citep{howe.et.al94} investigating the formation of molecules in a dense, neutral globule such as those observed in the Helix nebula." Howeetal.(1994). ran equilibrium chemistry models for clumps with extinctions between 0. ancl 2.0. comparable to those of the Lclx knots (Aleaburnctal. 1998)..," \citet{howe.et.al94} ran equilibrium chemistry models for clumps with extinctions between 0 and 2.0, comparable to those of the Helix knots \citep{meaburn.et.al98b}." Γον found that molecular abundances in the globule are enhanced with Coll and CN at abunclances that are possibly detectable in carbon-rich globules.," They found that molecular abundances in the globule are enhanced with ${\rm C_2H}$ and ${\rm CN}$ at abundances that are possibly detectable in carbon-rich globules." lloro. we extend the work of Howeetal.(1994). in that the time-dependent chemistry is calculated. beginning with the rich chemistry of a carbon-rich AGB atmosphere.," Here, we extend the work of \citet{howe.et.al94} in that the time-dependent chemistry is calculated, beginning with the rich chemistry of a carbon-rich AGB atmosphere." The molecular species are assumed to be locked into a clump with a density contrast with the surrounding medium., The molecular species are assumed to be locked into a clump with a density contrast with the surrounding medium. The chemistry of the clump is then traced. as both it and. the surrounding medium expand away from the star., The chemistry of the clump is then traced as both it and the surrounding medium expand away from the star. At the final stage of the calculation. the clump and medium have similar properties to those of the ος.," At the final stage of the calculation, the clump and medium have similar properties to those of the Helix." As the knots in the Helix have a low extinction. the chemistry by this stage is tending towards that expected. of a dilfuse cloud with this initial composition.," As the knots in the Helix have a low extinction, the chemistry by this stage is tending towards that expected of a diffuse cloud with this initial composition." However. at intermecliate stages. the rich initial chemistry. should. give rise to marked differences compared with that expected from a standard ISM mixture.," However, at intermediate stages, the rich initial chemistry should give rise to marked differences compared with that expected from a standard ISM mixture." some of these molecules should. be present. in detectable quantities and. if found. would. argue for an carly clump formation model.," Some of these molecules should be present in detectable quantities and if found, would argue for an early clump formation model." We follow the physical ancl chemical evolution of a parcel of gas (either clump or interclump material) as it moves out from the AGB atmosphere to the protoplanctary (PPN) ancl planetary. nebula (PN) phases. ultimately merging with the interstellar medium.," We follow the physical and chemical evolution of a parcel of gas (either clump or interclump material) as it moves out from the AGB atmosphere to the protoplanetary (PPN) and planetary nebula (PN) phases, ultimately merging with the interstellar medium." In the AGB atmosphere. the number density. and temperature are on the order of 1077.em anc LO?1. respectively.," In the AGB atmosphere, the number density and temperature are on the order of $10^{12}~{\rm cm^{-3}}$ and $10^{3}~{\rm K}$, respectively." We assume that the clumpfinterclump density ratio is about 10 (Mauron&lluggins2000— find the multiple shells in the envelope. of IRC|10216. to. have density contrasts of &10). and that the size of the clump is comparable to a stellar radius (about 104em).," We assume that the clump/interclump density ratio is about 10 \citealt{mauron&huggins00} find the multiple shells in the envelope of IRC+10216 to have density contrasts of $\la 10$ ), and that the size of the clump is comparable to a stellar radius (about $10^{13}~{\rm cm}$ )." Thus. if the eas:cust ratio is similar to that in the interstellar medium. the visual extinction associated with a clump in the atmosphere is very. large.," Thus, if the gas:dust ratio is similar to that in the interstellar medium, the visual extinction associated with a clump in the atmosphere is very large." Phe chemistry in the atmosphere is determined. under. therniocvnanica equilibrium. ancl the relative abundances are Ηχος as the envelope expands and the density falls.," The chemistry in the atmosphere is determined under thermodynamical equilibrium, and the relative abundances are fixed as the envelope expands and the density falls." At lower densities. however. thermodynamic equilibrium no longer applies anc chemistry is driven by two-bocky reactions of ion-molecule and other types. as in conventional interstellar chemistry.," At lower densities, however, thermodynamic equilibrium no longer applies and chemistry is driven by two-body reactions of ion-molecule and other types, as in conventional interstellar chemistry." " Since no chemical evolution occurs. in the initia expansion. we begin our computation of the evolution at a later stage (time /=/,100vr) at which the densities are low enough to be dominated by two-bodv reactions initiatec bv cosmic rav ionisation ancl by photoprocesses driven by the raciation field of the central star ane by the ambien interstellar medium."," Since no chemical evolution occurs in the initial expansion, we begin our computation of the evolution at a later stage (time $t = t_1 = 100~{\rm yr}$ ) at which the densities are low enough to be dominated by two-body reactions initiated by cosmic ray ionisation and by photoprocesses driven by the radiation field of the central star and by the ambient interstellar medium." For simplicity. we use a power-law description of the physical. development.," For simplicity, we use a power-law description of the physical development." We do not attempt to model the initiation and evolution of a clump., We do not attempt to model the initiation and evolution of a clump. In a steady outflow at constant velocity. the clensity should. fall olf as {7.," In a steady outflow at constant velocity, the density should fall off as $t^{-2}$." llowever. the density fall off in a clump may be slower.," However, the density fall off in a clump may be slower."