Y. Suto et Yp. Jing, THE FINITE-SIZE EFFECT OF GALAXIES ON THE COSMIC VIRIAL-THEOREM AND THE PAIRWISE PECULIAR VELOCITY DISPERSIONS, The Astrophysical journal. Supplement series, 110(2), 1997, pp. 167-175
We discuss the effect of the finite size of galaxies on estimating sma
ll-scale relative pairwise peculiar velocity dispersions from the cosm
ic virial theorem (CVT). Specifically, we evaluate the effect by incor
porating the finite core radius r(c) in the two-point correlation func
tion of mass, i.e., xi(rho)(r) proportional to (r + r(c))-(gamma), and
the effective gravitational force softening r(s) on small scales. We
analytically obtain the lowest order correction term for gamma < 2, wh
ich is in quantitative agreement with the full numerical evaluation. W
ith a nonzero r(s) and/or r(c), the cosmic virial theorem is no longer
limited to the case of gamma < 2. We present accurate fitting formula
e for the CVT-predicted pairwise velocity dispersion for the case of g
amma > 2. Compared with the idealistic point-mass approximation (r(s)
= r(c) = 0), the finite-size effect can significantly reduce the small
-scale velocity dispersions of galaxies at scales much larger than r,
and r,. Even without considering the finite size of galaxies, nonzero
values for r(c) are generally expected, for instance, for cold dark ma
tter (CDM) models with a scale-invariant primordial spectrum. For thes
e CDM models, a reasonable force softening r(s) less than or equal to
100 h(-1) kpc would have a rather tiny effect. We present the CVT pred
ictions for the small-scale pairwise velocity dispersion in the CDM mo
dels normalized by the COBE observations. The implications of our resu
lts for confrontation of observations of galaxy pairwise velocity disp
ersions and theoretical predictions of the CVT are also discussed.