**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}
*h*^{2}
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}.