Linear theory and velocity correlations of clusters

TL;DR

This paper refines linear theory predictions for velocity correlations of biased tracers by incorporating pair-weighted measurement effects, revealing that previous discrepancies were due to neglecting an important term.

Contribution

It introduces a correction to linear theory for velocity correlations that accounts for pair-weighted statistics, improving accuracy for biased tracers.

Findings

Linear theory accurately describes velocity correlations when pair-weighted effects are included.

Neglecting pair-weighted effects leads to significant errors in parallel velocity component predictions.

The correction is especially important for highly biased tracers.

Abstract

Linear theory provides a reasonable description of the velocity correlations of biased tracers both perpendicular and parallel to the line of separation, provided one accounts for the fact that the measurement is almost always made using pair-weighted statistics. This introduces an additional term which, for sufficiently biased tracers, may be large. Previous work suggesting that linear theory was grossly in error for the components parallel to the line of separation ignored this term.