Concordance of X-Ray Cluster Data With BBN In Mixed Dark Matter Models

If the hot, X-ray emitting gas in rich clusters forms a fair sample of the universe (as in Cold Dark Matter (CDM) models), and the universe is at the critical density, $\Omega_T = 1$, then the data appears to imply a baryon fraction, $\Omega_{b,x}$ ($\Omega_{b,x}\equiv \Omega_b$ derived from X-ray cluster data), larger than that predicted by Big Bang Nucleosynthesis (BBN). While various other systematic effects such as clumping can lower $\Omega_{b,x}$, in this paper we use an elementary analysis to show that a simple admixture of Hot Dark Matter (HDM, low mass neutrinos) with CDM to yield mixed dark matter shifts $\Omega_{b,x}$ down so that significant overlap with $\Omega_b$ from BBN can occur for $H_0 \lsim 75\;{\rm km/sec/Mpc}$, even without invoking the possible aforementioned effects. The overlap interval is slightly larger for lower mass neutrinos since fewer cluster on the scale of the hot X-ray gas. We illustrate this result quantitatively in terms of a simple isothermal model. More realistic velocity dispersion profiles, with less centrally-peaked density profiles, imply that fewer neutrinos are trapped and, thus, further increase the interval of overlap. However, we also note that if future observations of light element abundances find that $\Omega_b h^2 \lsim 0.018$, the range of concordance in this simple mixed dark matter model vanishes.