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If the hot, X-ray emitting gas in rich clusters forms a fair sample of theuniverse (as in Cold Dark Matter (CDM) models), and the universe is at thecritical density, $\Omega_T = 1$, then the data appears to imply a baryonfraction, $\Omega_{b,x}$ ($\Omega_{b,x}\equiv \Omega_b$ derived from X-raycluster 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 asimple admixture of Hot Dark Matter (HDM, low mass neutrinos) with CDM to yieldmixed dark matter shifts $\Omega_{b,x}$ down so that significant overlap with$\Omega_b$ from BBN can occur for $H_0 \lsim 75\;{\rm km/sec/Mpc}$, evenwithout invoking the possible aforementioned effects. The overlap interval isslightly larger for lower mass neutrinos since fewer cluster on the scale ofthe hot X-ray gas. We illustrate this result quantitatively in terms of asimple isothermal model. More realistic velocity dispersion profiles, with lesscentrally-peaked density profiles, imply that fewer neutrinos are trapped and,thus, further increase the interval of overlap. However, we also note that iffuture observations of light element abundances find that $\Omega_b h^2 \lsim0.018$, the range of concordance in this simple mixed dark matter modelvanishes.

Concordance of X‐Ray Cluster Data with Big Bang Nucleosynthesis in Mixed Dark Matter Models