**2.3. Baryons in Clusters of Galaxies**

The cluster mass function is approximated as (Bahcall & Cen 1993)

where *M*^{*} = (1.8 ± 0.3) x 10^{14}
*h*^{-1} *M*_{}, and *M* is the total
gravitational mass within a sphere of a radius of
1.5*h*^{-1} Mpc (the Abell radius) centered on the cluster.
At the Abell radius the mass distribution is close to dynamical
equilibrium. The envelope of matter around the cluster at greater
distances merges into the ``large-scale structure'' and we take
this matter to be included in the field (as discussed in
Section 2.4).
We define clusters as objects with mass *M* > 10^{14}
*h* *M*_{}.
The integral
*dM M dn*_{cl} / *dM* gives the mean mass
density in clusters,

The contribution of this gravitational mass to the density parameter is

Intracluster plasma masses are well determined from X-ray observations (Fabricant et al. 1986; Hughes 1989; White et al. 1993). The ratio of X-ray emitting gas mass to gravitational mass within the Abell radius from the survey by White & Fabian (1995) is

In the White & Fabian
(1995)
sample this ratio shows no correlation with cluster mass.
The value (18) is independently verified by
Myers et al. (1997),
(*M*_{HII} / *M*_{grav})_{cl} =
(0.061 ± 0.011) *h*^{-1}
from the measurement of the Sunyaev-Zeldovich effect in three clusters.
The product of equations (17) and (18) is

This is the contribution to the baryon budget by intracluster plasma.

Let us estimate the baryons in stars in galaxies in clusters.
Although these stars
are included in the estimate for stars in Section 2.1,
it is useful to compare their mass with the plasma mass, which we
can derive from the cluster mass-to-light ratio. In the discussion of the
Coma cluster by
White et al. (1993),
straightforward applications of galaxy velocity dispersions or
the X-ray pressure gradient give
(*M*_{grav} / *L _{B}*)

For cluster galaxies (Dressler 1980) we adopt the composition within the Abell radius

(This is somewhat richer in early-type galaxies than the
estimate given by
Schechter & Dressler (1987),
but their sample
extends beyond the Abell radius.) The mass-to-light ratios
in equations (7) and (8) and the bulge-to-disk
ratios in Table 1 give
(*M/L*)_{star} = 4.5 ± 1.
The ratio to equation (20) gives
*h M*_{stars} / *M*_{grav} =
0.010^{+0.005}_{-0.004}.
The product with equation (17) is the contribution to
the density parameter by stars in clusters,

about ten percent of the total in equations (10)-(12).