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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

Equation 24 (24)

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

Equation 25 (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

Equation 26 (26)

The approximate range of rich cluster blue luminosities is

Equation 27 (27)

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

Equation 28 (28)

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

Equation 29 (29)

(if mass follows light, M propto L, on scales gtapprox 1h-1 Mpc). Omega = 1 corresponds to the critical mass-density needed for a closed universe and curlyM / LB (Omega = 1) appeq 1500h.

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