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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 appeq 7 x 107 (sigma/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 Mgas / Mgrav = 0.056h-2/3, where Mgrav is the dynamical mass. By requiring that the cluster baryon fraction agrees with OmegaB / Omega in the field, we have Omega = 0.066h-1/2 eta10 = 0.39(eta10/5), where eta10 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): Mgas / Mgrav = 0.082h-1 is translated to Omega = 0.044h-1 eta10 = 0.31(eta10/5).

If we insert a probable value of the baryon to photon ratio from primordial nucleosynthesis calculations, eta10 = 3-5, we have Omega = 0.2-0.4.