2.3 Cluster Baryon Fraction

This issue was discussed in detail by White et al. (1993) for the Coma cluster, and has been addressed now in many contexts by a number of authors (e.g., White & Frenk 1991; White & Fabian 1995; Steigman & Felten 1995). The calculation goes as follows: First, the number density of baryons (_b) can be determined based on the observed densities of light elements from big-bang nucleosynthesis. Hence, the fraction of baryons (f_b) measured in clusters of galaxies can be used to estimate of the overall matter density assuming

There are four explicit assumptions made:

1) The gas is in hydrostatic equilibrium.

2) There is a smooth potential.

3) Most of the baryons in the clusters are in the X-ray gas.

4) The cluster baryon fraction is representative of the Universe.

If the gas is clumped or there is another source of pressure (magnetic fields or turbulence) in addition to the thermal pressure, the baryon fraction would be decreased and the matter density would be increased (Steigman & Felten 1995).

Recent measurements of X-ray clusters (e.g., Loewenstein & Mushotsky 1996; White & Fabian 1995) indicate that the baryon fraction has a range of values from about 10 -> 20%. The values for f_b tend to be smaller for small groups and in the inner regions of larger clusters. These results underscore the importance of ensuring that such measurements are made on large enough scales to be truly representative of the large-scale Universe as a whole.

Taken at face value, the cluster-baryon method estimates again favor low values of _m. For _b h² = 0.024 ± 12% (Tytler, this conference) relatively low values of _m < 0.5 are favored for the range of baryon fractions observed. The Tytler et al. 1997 baryon determination is at the high end of recent measures of this quantity (low end of the deuterium abundance measurements); lower baryon densities only serve to decrease the _m estimates. (However, see the discussion by Bothun, Impey and McGaugh 1997; these authors suggest that perhaps low-surface-brightness galaxies could be source of most of the baryons in the Universe and that rich clusters are not representative of the overall baryon density.)