**3.1.4. Baryon Fractions**

A cluster is a virialised object with the cooling time scale longer
than the dynamical time scale, and hence the physics is governed only by
gravity (except for cooling flows in high density regions).
The gas in clusters is shock heated
to the virial temperature
*T* 7 x 10^{7}
(/1000 km
s^{-1})^{2} K, and thus emits
X rays by thermal bremsstrahlung.
From the luminosity and temperature of X rays one can
infer the mass of the X ray emitting gas. It has been known that the
gas amounts to a substantial fraction of the dynamical mass, which
means that baryons reside more in the gas than in stars by an order
of magnitude
(Forman & Jones
1982).
The argument was then elaborated by
White et
al. (1993b)
based on ROSAT observations. From 19 clusters
White & Fabian
(1995)
obtained *M*_{gas} / *M*_{grav} =
0.056*h*^{-2/3}, where *M*_{grav}
is the dynamical mass. By requiring that the cluster
baryon fraction agrees with
_{B} /
in the field, we have
= 0.066*h*^{-1/2}
_{10} =
0.39(_{10}/5),
where _{10}
is the baryon to photon ratio in units
of 10^{-10} and the last number assumes *h* = 0.7.

An independent estimate
is made from the Zeldovich-Sunyaev effect observed
in clusters
(Myers et al. 1997;
Grego et al. 1999):
*M*_{gas} / *M*_{grav} = 0.082*h*^{-1}
is translated to =
0.044*h*^{-1}
_{10} =
0.31(_{10}/5).

If we insert a probable value of the baryon to photon ratio
from primordial nucleosynthesis calculations,
_{10} = 3-5, we have
= 0.2-0.4.