3.5. Cluster Baryon Fraction:

Assuming that on the scales from which clusters accrete matter during their formation, there is no segregation of baryons and DM, then the ratio of baryonic to total matter in clusters is representative of the universal value (_b / _m), something supported also by hydro-dynamical numerical simulations. Galaxies add up to only ~ 5% of the total cluster mass, while the hot gas, which fills the space between galaxies, accounts for ~ 20%.

So adding up the galactic and gas contribution to the mass of the cluster we obtain a measure of the total baryonic cluster mass, M_b and then if we can measure the total mass of the cluster, M_tot, we can estimate _m.

Assuming hydrostatic equilibrium, the gas traces the cluster total mass, and using (76) we can obtain, M_to. Most studies (cf. [186], [103], [58]) find:

(85)

From the primordial nucleosynthesis constraints (see 63) and from the recent BOMMERANG results we have that _b h² 0.020 ± 0.004), which for h = 0.72 gives _b 0.04 and therefore:

Note however that in a recent study [147], the application of various corrections to account for the clumping of gas and the gas fraction gradients, within the virial radius of a cluster, resulted in significantly lower values of the baryon fraction and thus higher values of _m.