Deriving accurate peculiar velocities (even at high redshift)

TL;DR

This paper analyzes the inaccuracies in common methods of deriving peculiar velocities from redshift and distance measurements, proposing exact calculation techniques to improve accuracy especially at higher redshifts.

Contribution

It identifies the limitations of the standard approximation for peculiar velocities and provides a detailed method for exact calculation to reduce systematic errors.

Findings

The standard approximation overestimates peculiar velocities by ~100 km/s at z~0.04.

The paper demonstrates the breakdown point of the approximation at higher redshifts.

It offers a corrected calculation method for more accurate peculiar velocity estimates.

Abstract

The way that peculiar velocities are often inferred from measurements of distances and redshifts makes an approximation, v_p = cz-H_0 D, that gives significant errors even at relatively low redshifts (overestimates peculiar velocity by ~ 100 km/s at z~0.04). Here we demonstrate where the approximation breaks down, the systematic offset it introduces, and how the exact calculation should be implemented.