Velocity dispersion:
this is a totalmass 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) as
where
V
i
is the radial velocity of galaxy
i
with 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
f
PM
depends on the typical orbital
shape; it has values 32/
π
for isotropically distributed orbits and 64/
π
for 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 function
as a statistical probe for this (see his book
Large
Scale Structure of the Universe
, Princeton 1980). The correlation function
ξ
measures the
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 Fall '10
 EmilyHoward
 Astronomy, correlation function

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