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Abstract
We propose a simple closed-form expression relating v12(r)—the mean relative velocity of pairs of galaxies at fixed separation r—to the two-point correlation function of mass density fluctuations, ξ(r). Our Ansatz is an interpolation between the perturbative and stable clustering expressions for v12. We compare our analytic model for v12(r) with N-body simulations and find excellent agreement in the entire dynamical range probed by the simulations (0.1 ξ 1000). Our results can be used to estimate the cosmological density parameter, Ω, directly from redshift-distance surveys.
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