An Unbiased Estimator of Peculiar Velocity with Gaussian Distributed Errors for Precision Cosmology

TL;DR

This paper presents a new unbiased estimator for galaxy peculiar velocities that ensures Gaussian errors, improving the accuracy of large-scale velocity field analyses in precision cosmology.

Contribution

The paper introduces a novel estimator that produces unbiased, Gaussian-distributed velocity errors, enhancing the reliability of peculiar velocity measurements.

Findings

Improved accuracy of peculiar velocity estimates.

Elimination of systematic biases in velocity analyses.

Enhanced validation of large velocity catalog statistics.

Abstract

We introduce a new estimator of the peculiar velocity of a galaxy or group of galaxies from redshift and distance estimates. This estimator results in peculiar velocity estimates which are statistically unbiased and that have errors that are Gaussian distributed, thus meeting the assumptions of analyses that rely on individual peculiar velocities. We apply this estimator to the SFI++ and the Cosmicflows-2 catalogs of galaxy distances and, using the fact that peculiar velocity estimates of distant galaxies are error dominated, examine their error distributions, The adoption of the new estimator significantly improves the accuracy and validity of studies of the large-scale peculiar velocity field and eliminates potential systematic biases, thus helping to bring peculiar velocity analysis into the era of precision cosmology. In addition, our method of examining the distribution of velocity errors should provide a useful check of the statistics of large peculiar velocity catalogs, particularly those that are compiled out of data from multiple sources.