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Register a new userThe Velocity Dispersion -- Temperature Correlation from a Limited Cluster Sample
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Christina M. Bird
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Most studies of correlations between X-ray and optical properties of galaxy clusters have used the largest samples of data available, regardless of the morphological types of clusters included. Given the increasing evidence that morphology is related to a clusters degree of dynamical evolution, we approach the study of X-ray and optical correlations differently. We evaluate the relationship between velocity dispersion and temperature for a limited set of galaxy clusters taken from Bird (1994), which all possess dominant central galaxies and which have been explicitly corrected for the presence of substructure. We find that $sigma _r propto T^{0.61 pm 0.13}$. We use a Monte Carlo computer routine to estimate the significance of this deviation from the $sigma _r propto T^{0.5}$ relationship predicted by the virial theorem. We find that the simulated correlation is steeper than the observed value only 4% of the time, suggesting that the deviation is significant. The combination of protogalactic winds and dynamical friction reproduces nearly exactly the observed relationship between $sigma _r$ and $T$.
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We measure the evolution of the velocity dispersion--temperature ($sigma_{rm v}$--$T_{rm X}$) relation up to $z = 1$ using a sample of 38 galaxy clusters drawn from the textit{XMM} Cluster Survey. This work improves upon previous studies by the use of a homogeneous cluster sample and in terms of the number of high redshift clusters included. We present here new redshift and velocity dispersion measurements for 12 $z > 0.5$ clusters observed with the GMOS instruments on the Gemini telescopes. Using an orthogonal regression method, we find that the slope of the relation is steeper than that expected if clusters were self-similar, and that the evolution of the normalisation is slightly negative, but not significantly different from zero ($sigma_{rm v} propto T^{0.86 pm 0.14} E(z)^{-0.37 pm 0.33}$). We verify our results by applying our methods to cosmological hydrodynamical simulations. The lack of evolution seen in our data is consistent with simulations that include both feedback and radiative cooling.
Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object M and the velocity dispersion sigma of the host galaxy, of the form log(M/M_sun) = a + b*log(sigma/sigma_0); however, published estimates of the slope b span a wide range (3.75 to 5.3). Merritt & Ferrarese have argued that low slopes (<4) arise because of neglect of random measurement errors in the dispersions and an incorrect choice for the dispersion of the Milky Way Galaxy. We show that these explanations account for at most a small part of the slope range. Instead, the range of slopes arises mostly because of systematic differences in the velocity dispersions used by different groups for the same galaxies. The origin of these differences remains unclear, but we suggest that one significant component of the difference results from Ferrarese & Merritts extrapolation of central velocity dispersions to r_e/8 (r_e is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the measurements. A new determination of the slope using 31 galaxies yields b=4.02 +/- 0.32, a=8.13 +/- 0.06, for sigma_0=200 km/s. The M-sigma relation has an intrinsic dispersion in log M that is no larger than 0.3 dex. In an Appendix, we present a simple model for the velocity-dispersion profile of the Galactic bulge.
We present the study of a large sample of early-type dwarf galaxies in the Coma cluster observed with DEIMOS on the Keck II to determine their internal velocity dispersion. We focus on a subsample of 41 member dwarf elliptical galaxies for which the velocity dispersion can be reliably measured, 26 of which were studied for the first time. The magnitude range of our sample is $-21<M_R<-15$ mag. This paper (paper I) focuses on the measurement of the velocity dispersion and their error estimates. The measurements were performed using {it pPXF (penalised PiXel Fitting)} and using the Calcium triplet absorption lines. We use Monte Carlo bootstrapping to study various sources of uncertainty in our measurements, namely statistical uncertainty, template mismatch and other systematics. We find that the main source of uncertainty is the template mismatch effect which is reduced by using templates with a range of spectral types. Combining our measurements with those from the literature, we study the Faber-Jackson relation ($Lproptosigma^alpha$) and find that the slope of the relation is $alpha=1.99pm0.14$ for galaxies brighter than $M_Rsimeq-16$ mag. A comprehensive analysis of the results combined with the photometric properties of these galaxies is reported in paper II.
Using the DIANOGA hydrodynamical zoom-in simulation set of galaxy clusters, we analyze the dynamics traced by stars belonging to the Brightest Cluster Galaxies (BCGs) and their surrounding diffuse component, forming the intracluster light (ICL), and compare it to the dynamics traced by dark matter and galaxies identified in the simulations. We compute scaling relations between the BCG and cluster velocity dispersions and their corresponding masses (i.e. $M_mathrm{BCG}^{star}$- $sigma_mathrm{BCG}^{star}$, $M_{200}$- $sigma_{200}$, $M_mathrm{BCG}^{star}$- $M_{200}$, $sigma_mathrm{BCG}^{star}$- $sigma_{200}$), we find in general a good agreement with observational results. Our simulations also predict $sigma_mathrm{BCG}^{star}$- $sigma_{200}$ relation to not change significantly up to redshift $z=1$, in line with a relatively slow accretion of the BCG stellar mass at late times. We analyze the main features of the velocity dispersion profiles, as traced by stars, dark matter, and galaxies. As a result, we discuss that observed stellar velocity dispersion profiles in the inner cluster regions are in excellent agreement with simulations. We also report that the slopes of the BCG velocity dispersion profile from simulations agree with what is measured in observations, confirming the existence of a robust correlation between the stellar velocity dispersion slope and the cluster velocity dispersion (thus, cluster mass) when the former is computed within $0.1 R_{500}$. Our results demonstrate that simulations can correctly describe the dynamics of BCGs and their surrounding stellar envelope, as determined by the past star-formation and assembly histories of the most massive galaxies of the Universe.
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