Improved Methods for Estimating Peculiar Velocity Correlation Functions Using Volume Weighting

TL;DR

This paper introduces a novel weighted maximum-likelihood method for estimating peculiar velocity correlation functions, reducing bias from survey inhomogeneity and improving their utility for cosmological analysis.

Contribution

The paper develops a position-dependent weighting scheme for velocity correlation functions, enhancing bias reduction and comparability across surveys and with linear theory.

Findings

Weighted correlation functions are less biased by local galaxy overrepresentation.

Parallel velocity correlation function is a promising cosmological probe.

Weighting reduces cosmic variance despite increased statistical uncertainty.

Abstract

We present an improved method for calculating the parallel and perpendicular velocity correlation functions directly from peculiar velocity surveys using weighted maximum-likelihood estimators. A central feature of the new method is the use of position-dependent weighting scheme that reduces the influence of nearby galaxies, which are typically overrepresented relative to the more distant galaxies in most surveys. We demonstrate that the correlation functions calculated this way are less susceptible to biases due to our particular location in the Universe, and thus are more easily comparable to linear theory and between surveys. Our results suggest that the parallel velocity correlation function is a promising cosmological probe, given that it provides a better approximation of a Gaussian distribution than other velocity correlation functions and that its bias is more easily minimized by weighting. Though the position weighted parallel velocity correlation function increases the statistical uncertainty, it decreases the cosmic variance and is expected to provide more stable and tighter cosmological parameter constraints than other correlation methods in conjunction with more precise velocity surveys in the future.