[astro-ph/9812387] Dynamics of pairwise motions

Authors:  Roman Juszkiewicz, Volker Springel, Ruth Durrer
Abstract:  We derive a simple closed-form expression, relating $\vs(r)$ -- the mean relative velocity of pairs of galaxies at fixed separation $r$ -- to the two-point correlation function of mass density fluctuations, $\xi(r)$. We compare our analytic model for $\vs(r)$ with N-body simulations, and find excellent agreement in the entire dynamical range probed by the simulations ($0.1 \lsim \xi \lsim 1000$). Our results can be used to estimate the cosmological density parameter, $\Om$, directly from redshift-distance surveys, like Mark III.
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Anze Slosar
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Affiliation: Brookhaven National Laboratory
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[astro-ph/9812387] Dynamics of pairwise motions

Post by Anze Slosar » January 30 2005

Pair conservation in the universe implies that the evolution of correlation function must be accompanied by the flow of galaxies in the right direction. Thus, the mean pairwise velocity is given by

[tex]
\frac{a}{3\left(1+\xi\right)} \frac{\partial \bar{\xi}}{\partial a} = -\frac{v_{12}}{Hr}
[/tex]

In my understanding, there is nothing special in this equation, it just says that one can calculate the evolution of [tex]\xi[/tex] if one knows the mean pairwise motions and vice versa, but since [tex]v_{12}[/tex] contains no information on dispersion it is useless for predicting fingers of god and similar.

The authors of this paper find a good ansatz to this equation (their equations 11 and 12). However, in my understanding the [tex]\xi[/tex] in their ansatz are the actual correlation function, not the linear correlation function. Could anybody confirm this? If this is the case, it severly limits the usefulness of their approximation. On the other hand, the approximation they mention that relies on linear correlation function only ([tex]-2/3 H r f \xi[/tex]) is fairly inaccurate. Is there a more recent paper that has a better approximation to this?

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