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 β-discrepancy that has persisted for the last decade. The standard hydrostatic-isothermal model for clusters predicts that the parameter β_spec_ = σ_r_^2^/(kT/micron_p_) which describes the ratio of energy per unit mass in galaxies to that in the gas, should equal the parameter β_fit_ (where p_gas_(r) is proportional to p_gal_(r)beta_fit_^) determined from the X-ray surface brightness distribution. The observations suggest an apparent discrepancy: β_spec_~1.2 (i.e., the galaxies are "hotter" than the gas), while β_fit_ ~ 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, p_gal_(r) is proportional to r^-2.4+/-0.2^, instead of the previously assumed steeper King approximation, p_gal_(r) is proportional to r^-3^. Using the correct galaxy profile in clusters, we show that the standard hydrostatic-isothermal model predicts β_spec_ = β_fit_^c^ ~(1.25 +/- 0.1)β_fit_, rather than β_spec_ = β_fit_ (where β_fit_ is the standard parameter using the King approximation, and β_fit_^c^ is the corrected parameter using the proper galaxy distribution). Using a large sample of clusters, we find best-fit mean values of β_spec_ = 0.94 +/- 0.08 and β_fit_^c^ = 1.25β_fit_ = 0.84 +/- 0.1. These results resolve the β- discrepancy and provide additional support for the hydrostatic cluster model.