RESOLVING THE BETA-DISCREPANCY FOR CLUSTERS OF GALAXIES

Previous comparisons of optical and X-ray observations of clusters of galaxies have led to the so-called beta-discrepancy that has persisted for the last decade. The standard hydrostatic-isothermal model for cl usters predicts that the parameter beta(spec) = sigma(r)2/(kT/mum(p)), which describes the ratio of energy per unit mass in galaxies to that in the gas, should equal the parameter beta(fit) (where rho(gas)(r) i s-proportional-to rho(gal)(r)(beta(fit)) determined from the X-ray sur face brightness distribution. The observations suggest an apparent dis crepancy: beta(spec) approximately 1.2 (i.e., the galaxies are ''hotte r'' than the gas), while beta(fit) approximately 0.65 (i.e., the gas i s ''hotter'' and more extended than the galaxies). Here we show that t he discrepancy is resolved when the actual observed galaxy distributio n in clusters is used, rho(gal)(r) is-proportional-to r -2.4+/-0.2, in stead of the previously assumed steeper King approximation, rho(gal)(r ) is-proportional-to r-3. Using the correct galaxy profile in clusters , we show that the standard hydrostatic-isothermal model predicts beta (spec) = beta(fit)c congruent-to (1.25 +/- 0.1)beta(fit), rather than beta(spec) congruent-to beta(fit), (where beta(fit) is the standard pa rameter using the King approximation, and beta(fit)c is the corrected parameter using the proper galaxy distribution). Using a large sample of clusters, we find best-fit mean values of beta(spec) = 0.94 +/- 0.0 8 and beta(fit)c = 1.25beta(fit) = 0.84 +/- 0.1. These results resolve the beta-discrepancy and provide additional support for the hydrostat ic cluster model.