© CAMBRIDGE UNIVERSITY PRESS 1999

2.10. Mass, Luminosity, and Mass-to-Luminosity Ratio

The typical dynamical mass of rich clusters within 1.5h^-1 Mpc radius sphere (determined from the virial theorem for an isothermal distribution) is

(24)

The approximate range of masses for R 0 clusters (within 1.5h^-1 Mpc) is

(25)

Comparable masses are obtained using the X-ray temperature and distribution of the hot intracluster gas (Hughes 1989; Bahcall and Cen 1993; Lubin and Bahcall 1993; Section 3).

The typical (median) blue luminosity of rich clusters (within 1.5h^-1 Mpc) is

(26)

The approximate range of rich cluster blue luminosities is

(27)

The typical mass-to-luminosity ratio of rich clusters is thus

(28)

The inferred mass-density in the universe based on cluster dynamics is

(29)

(if mass follows light, M L, on scales 1h^-1 Mpc). = 1 corresponds to the critical mass-density needed for a closed universe and / L_B ( = 1) 1500h.