On methods of estimating cosmological bulk flows

TL;DR

This paper compares different estimators for cosmological bulk flows derived from galaxy peculiar velocities, analyzing their assumptions, differences, and potential biases, and proposes two new estimators for improved accuracy.

Contribution

It provides a detailed comparison of existing bulk flow estimators and introduces two novel methods to enhance estimation robustness and reduce biases.

Findings

WF and CMV estimators are mathematically related under certain conditions.

CMV may be more susceptible to observational biases in noisy or limited data.

Two new estimators are proposed for better bulk flow measurement accuracy.

Abstract

We explore similarities and differences between several estimators of the cosmological bulk flow, $\bf B$, from the observed radial peculiar velocities of galaxies. A distinction is made between two theoretical definitions of $\bf B$ as a dipole moment of the velocity field weighted by a radial window function. One definition involves the three dimensional (3D) peculiar velocity, while the other is based on its radial component alone. Different methods attempt at inferring $\bf B$ for either of these definitions which coincide only for a constant velocity field. We focus on the Wiener Filtering (WF, Hoffman et al. 2015) and the Constrained Minimum Variance (CMV,Feldman et al. 2010) methodologies. Both methodologies require a prior expressed in terms of the radial velocity correlation function. Hoffman et al. compute $\bf B$ in Top-Hat windows from a WF realization of the 3D peculiar velocity field. Feldman et al. infer $\bf B$ directly from the observed velocities for the second definition of $\bf B$. The WF methodology could easily be adapted to the second definition, in which case it will be equivalent to the CMV with the exception of the imposed constraint. For a prior with vanishing correlations or very noisy data, CMV reproduces the standard Maximum Likelihood (ML, Kaiser 1988) estimation for $\bf B$ of the entire sample independent of the radial weighting function. Therefore, this estimator is likely more susceptible to observational biases that could be present in measurements of distant galaxies. Finally, two additional estimators are proposed.