| © CAMBRIDGE UNIVERSITY PRESS 1999 |

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

The typical dynamical mass of rich clusters within
1.5*h*^{-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 1.5*h*^{-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
1.5*h*^{-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
1*h*^{-1} Mpc).
= 1 corresponds to
the critical mass-density needed for a closed
universe and /
*L*_{B}
( = 1)
1500*h*.