Concordance of X-ray cluster data with big bang nucleosynthesis 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 appear to imply a baryon fraction Omega(bX) (Omega(b,X) = Omega(b) derived from X-ray cluster data), larger than that predicted by big bang nucleosynthesis (BBN). While 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 less than or similar to 73 km s(-1) Mpc(-1), even without invoking the possible aforementioned effects. The overlap interval is slightly larger for lower mass neutrinos since fewer of them 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.