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The Velocity Dispersion View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server The Velo city Disp ersion { Temp erature Correlation from a Limited Cluster Sample Christina M. Bird Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045 [email protected] Richard F. Mushotzky NASA/GoddardSpace Flight Center, Laboratory for High Energy Astrophysics, Code 666, Greenbelt, MD 20771 [email protected] Christopher A. Metzler metzler@ Department of Physics, University of Michigan, Ann Arbor, MI 48109 processed by the SLAC/DESY Libraries on 5 May 1995. 〉 Submitted to the Astrophysical Journal PostScript Received: ; Accepted: Abstract Most studies of correlations b etween X-ray and optical prop erties of galaxy clusters have used the largest samples of data available, regardless of the morphological typ es of clusters included. Given the increasing evidence that morphology is related to a cluster's degree of dynamical evolution, we approach the study of X-ray and optical ASTRO-PH-9505020 correlations di erently.Weevaluate the relationship b etween velo city disp ersion and temp erature for a limited set of galaxy clusters taken from Bird (1994), which all p ossess 1 dominant central galaxies and whichhave b een explicitly corrected for the presence of 0:610:13 substructure. We nd that / T .We use a Monte Carlo computer routine to r 0:5 estimate the signi cance of this deviation from the / T relationship predicted by r the virial theorem. We nd that the simulated correlation is steep er than the observed value only 4% of the time, suggesting that the deviation is signi cant. The combination of protogalactic winds and dynamical friction repro duces nearly exactly the observed relationship b etween and T . r 1 Intro duction Galaxy clusters o ccupy a unique p osition in the dynamical evolution of the universe. Unlikelower-mass systems such as galaxies, which for the most part retain little dynamical information ab out their formation, clusters of galaxies are within one or two crossing times of their formation. This suggests that they may retain valuable clues to their initial conditions (as well as hints ab out the collapse and formation of structure in the early universe). The e ect of the dense cluster environment on galaxy evolution, as well as other trends in the physical prop erties of clusters (see, for instance, Dressler 1984; Giovanelli & Haynes 1985; Edge & Stewart 1991), suggests that they are gravitationally b ound and that their galaxies no longer participate in the Hubble ow. This distinguishes clusters from sup erclusters and other large-scale structures. The study of galaxy clusters thus provides a unique opp ortunity to explore gravitational interactions and dynamical evolution in the universe. Clusters of galaxies contain two luminous comp onents, hot gas and galaxies. If a clus- ter is suciently old and unp erturb ed, these tracer particles will have equilibrated within the cluster gravitational p otential. This enables use of the equations of hydrostatic and dynamical equilibrium to explore the physical prop erties of these systems. For a hot gas in equilibrium with a spherical gravitational p otential, the equation of hydrostatic equilibrium 2 may b e written kT r dlnn dlnT gas M (r )= ( + ) (1) X Gm dlnr dlnr (e.g. Fabricant, Lecar & Gorenstein 1981), where M is the X-ray determined virial mass, X T is the temp erature of the X-ray emitting gas, n is the gas density andm is the average gas mass p er gas particle. Similarly, the Jeans equation relates the kinetic energy of the galaxies to the virial mass of the cluster: 2 Gn M (r ) d(n ) 2n gal opt gal gal r 2 2 = + (1 = ) (2) r t 2 2 r dr r r 2 d(n ) 2n gal gal r = + A 2 dr r r (Merritt 1987), where M is the optically-determined virial mass, r is the clustercentric opt radius, n is the galaxy density, and are the radial and tangential velo city disp ersions gal r t resp ectively, and A is the anisotropy parameter describing the distribution of galaxy orbits. For an isothermal cluster in dynamical equilibrium, with no source of energy other than gravity, the masses as determined by the galaxies and by the gas are exp ected to b e equal. As shown by Bahcall & Lubin (1994) among others, the ratio of the kinetic energies of the galaxies and gas is then equal to the ratio of the logarithmic slop e of the gas density pro le to that of the galaxies: 2 dlnn =d l n r gas r = : (3) kT dlnn =d l n r +2A gal m dlnn =d l n r gas = dlnn =d l n r gal (where A = 0 for an isotropic distribution of galaxy orbits). Therefore, using the assumptions that the gas and galaxies are b oth in equilibrium with the cluster gravitational p otential, and that gravity is the only source of energy, allows us to predict that the velo city disp ersion (as measured from galaxy velo cities) and the temp erature of the intracluster medium (as 0:5 determined from X-ray sp ectra) should b e correlated, with / T . The ratio of the r 3 kinetic energies is called . The ratio of the logarithmic slop es of the density pro les is spec . fit Despite the many diculties in accurately measuring cluster temp eratures and velo c- ity disp ersions, studies of X-ray and optical cluster samples reveal a well-b ehaved corre- lation b etween these quantities (Mushotzky 1984; Edge & Stewart 1991, hereafter ES91; Lubin & Bahcall 1993, hereafter LB93). The relationship b etween and T exp ected from r virial considerations is consistent with the data, although there is a large scatter ab out the 0:5 / T line. This scatter has b een attributed to incomplete gas thermalization, co oling r ows, velo city anisotropies in the galaxy orbits, foreground/background contamination, and substructure in the clusters (cf. ES91; LB93 and references therein). It is imp ortant to rememb er, however, that the predicted T correlation derives r from the virial theorem, and that in order to test it one must consider the dynamical state of the clusters in the dataset (cf. Gerbal et al. 1994). The high frequency of substructure in clusters of all morphologies, as determined by b oth X-ray and optical studies (see, e.g. Davis & Mushotzky 1993; Mohr, Fabricant & Geller 1993; Beers et al. 1991; Bird 1993, 1994), is generally b elieved to indicate that clusters are dynamically-young. If clusters are only within a few crossing times of formation, then in many cases virial equilibrium has not b een established. This certainly in uences the broad distribution of clusters ab out the 0:5 canonical / T relation. r In this pap er we will quantify the e ects of morphology and substructure on the velo city disp ersion-temp erature correlation for clusters. In Section 2 we present the limited cluster sample, in which the morphological typ e of the cluster sample has b een restricted and the e ects of substructure have b een minimized. Wehave supplemented the available published X-ray temp erature data with new, more accurate temp eratures from ASCA and Ginga.In Section 3 we present the regressions b etween the velo city disp ersion and temp erature. Section 4 4 summarizes prop osed mechanisms for mo difying the slop e of the T correlation. In r Section 5 we present a summary. 5 2 The Limited Cluster Sample The morphology of a cluster may b e describ ed by its gas and/or galaxy distribution. As our observations of clusters have improved, it has b ecome clear that morphology is re- lated to the dynamical age of a cluster. Irregular clusters are dynamically young, and tend to b e spiral-rich and gas-p o or. They tend to have non-Gaussian velo city distributions and kinematically-distinct sub concentrations of galaxies. Regular clusters are dominated by el- lipticals, have Gaussian velo city distributions and tend to b e luminous X-ray emitters (cf. Sarazin 1988 and references therein; Bird 1993,1994). Bird (1994) presents a detailed analysis of the dynamics of nearby clusters (z<0:1) with central galaxies. These clusters tend to have smo oth morphologies and X-ray co oling ows, and in the past it has b een assumed that they represent the most relaxed, dynamically- evolved clusters in the universe. However, Bird (1994) shows that these clusters also p ossess signi cant substructure. An ob jective partitioning algorithm called KMM (McLachlan & Basford 1988; Ashman, Bird & Zepf 1994) is used to remove galaxies b elonging to subsystems in the clusters, and the dynamical prop erties of the \cleaned" (i.e., substructure corrected) cluster datasets are presented. It is the 25 clusters in this \cD database" which form the optical sample of the present analysis. Of the 25 clusters used in Bird (1994), 21 have accurate X-ray temp erature measure- ments. These clusters, which will b e referred to as the limited cluster sample, are listed in Table 1. Table 1 includes the following information: column (1), the cluster name; (2), the 1-D velo city disp ersion of the cluster (estimated using the robust biweight estimator S , BI Beers, Flynn & Gebhardt 1991) without substructure correction; (3), the velo city disp ersion corrected for substructure; (4), the X-ray temp erature, (5) the source co de for the X-ray measurement. The optical redshifts are taken from the literature, with sources given in Bird (1994).
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