The Mean Pairwise Peculiar Velocity in Cosmological [ITAL]N[/ITAL]-Body Simulations: Time Variation, Scale Dependence, and the Stable Condition

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Abstract
We report on the detailed analysis of the mean pairwise peculiar velocity profile in high-resolution cosmological N-body simulations (N = 8.8 × 106 particles in a sphere of 50-200 Mpc radius). In particular, we examine the validity and limitations of the stable condition, which states that the mean physical separation of particle pairs is constant on small scales. We find a significant time variation (an irregular oscillatory behavior) in the mean pairwise peculiar velocity in nonlinear regimes. We argue that this behavior is not due to any numerical artifact but is a natural consequence of the continuous merging processes in the hierarchical clustering universe. While such a time variation is significant in a relatively local patch of the universe, the global average over a huge spatial volume of 200 Mpc3 does not reveal any systematic departure from the stable condition. Thus, we conclude that the mean pairwise peculiar velocity is rather unstable statistically but that it still satisfies the stable condition when averaged over the cosmological volume.
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