12.2. Clusters of Galaxies

Clusters of galaxies provide an estimate of the baryon density because most of the gas which they contain is hot and hence visible. The baryons in gas were heated up to 8 keV through fast collisions as the clusters assembled. The mass of gas in a cluster can be estimated from the observed X-ray emission, or from the scattering of CMB photons in the Sunyaev-Zel'dovich (SZ) effect. Other baryons in stars, stellar remnants and cool gas contribute about 6% to the total baryon mass.

The cosmological baryon density is obtained from the ratio of the baryonic mass to the total gravitating mass [182]. Numerical simulations show that the value of this ratio in the clusters will be similar to the cosmological average, because the clusters are so large and massive, but slightly smaller, because shock heating makes baryons more extended than dark matter [183], [184]. The total mass of a cluster, M_t, can be estimated from the velocity dispersion of the galaxies, from the X-ray emission, or from the weak lensing of background galaxies. We then use _b / _m M_b / M_t. The baryon fraction in clusters in the last factor is about 0.10 h₇₀^-1 (SZ effect: [185]), or 0.05 - 0.13 h₇₀^-3/2 (X-ray: [186]), or 0.11 h₇₀^-3/2 (X-ray: [187], [188]). Using _n = 0.3 ± 0.2 from a variety of methods [189], we get _b 0.03, with factor of two errors. These _b estimates are lower limits, since there might be additional unobserved baryons.