8. The baryon mass fraction in clusters of galaxies

Abell (1958) made the first useful catalog of the rich clusters considered here and in the next test. A typical value of the Abell cluster mass within the Abell radius r_a = 1.5h^-1 Mpc is 3 × 10¹⁴h^-1 M. The cluster masses are reliably measured (within Newtonian gravity) from consistent results from the velocities of the galaxies, the pressure of the intracluster plasma, and the gravitational deflection of light from background galaxies.

White (1992) and White et al. (1993) point out that rich clusters likely are large enough to contain a close to fair sample of baryons and dark matter, meaning the ratio of baryonic to total mass in a cluster is a good measure of _B0 / _M0. With _B0 from the model for light elements (Eqs. [62]), this gives a measure of the mean mass density. The baryon mass fraction in clusters is still under discussion.⁽⁸³⁾ We adopt as the most direct and so maybe most reliable approach the measurement of the baryonic gas mass fraction of clusters, f_gas, through the Sunyaev-Zel'dovich microwave decrement caused by Thomson-Compton scattering of cosmic microwave background radiation by the intracluster plasma. The Carlstrom et al. (2001) value for f_gas gives _M0 ~ 0.25, ⁽⁸⁴⁾ in the range of Eq. (59). This test does not directly constrain _K0, ₀, or the dynamics of the dark energy.

⁸³ See Hradecky et al. (2000), Roussel, Sadat, and Blanchard (2000), Allen, Schmidt, and Fabian (2002), and references therein. Back.

⁸⁴ This assumes _B0 h² = 0.014 from Eqs. (62). For the full range of values in Eqs. (6) and (62), 0.1 _M0 0.4 at two standard deviations. Back.