Velocity dispersion:this is a total-mass indicator, and is generally largest for rich, regular, relaxed clusters. An unbiased (or maybe only slightly biased) virial mass estimator is given by Heisler et al 1985 (ApJ 298, 8) aswhere Viis the radial velocity of galaxy iwith respect to the cluster mean, R⊥is the projected distance from the cluster center, α~1.5 is a fudge factor accounting for the fact the the center must be determined from the galaxy positions themselves, and fPMdepends on the typical orbital shape; it has values 32/πfor isotropically distributed orbits and 64/πfor purely radial orbits. See also the discussion of mass estimators by Postman, Huchram and Geller 1988 (AJ 95, 267).One might well ask whether and how clusters blend into groups and any larger structure. Peebles championed the use of a correlation functionas a statistical probe for this (see his book Large-Scale Structure of the Universe, Princeton 1980). The correlation function ξmeasures the
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