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 clusters 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) is-proportional-to rho(gal)(r)(beta(fit)) determined from the X-ray surface brightness distribution. The observations suggest an apparent discrepancy: beta(spec) approximately 1.2 (i.e., the galaxies are ''hotter'' than the gas), while beta(fit) approximately 0.65 (i.e., the gas is ''hotter'' and more extended than the galaxies). Here we show that the discrepancy is resolved when the actual observed galaxy distribution in clusters is used, rho(gal)(r) is-proportional-to r -2.4+/-0.2, instead 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 parameter 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 +/- 0.08 and beta(fit)c = 1.25beta(fit) = 0.84 +/- 0.1. These results resolve the beta-discrepancy and provide additional support for the hydrostatic cluster model.