Testing the minimum variance method for estimating large-scale velocity moments

TL;DR

This paper evaluates the robustness of a minimum variance method for estimating large-scale velocity moments in peculiar velocity surveys, demonstrating its unbiased nature and resilience to non-linear flows through simulation tests.

Contribution

It introduces and tests the robustness of an optimal minimum variance estimator for large-scale velocity moments using numerical simulations.

Findings

MV estimators are unbiased in simulations.

Estimators are minimally affected by non-linear flows.

Method provides consistent bulk flow estimates across different mock catalogues.

Abstract

The estimation and analysis of large-scale bulk flow moments of peculiar velocity surveys is complicated by non-spherical survey geometry, the non-uniform sampling of the matter velocity field by the survey objects and the typically large measurement errors of the measured line-of-sight velocities. Previously, we have developed an optimal `minimum variance' (MV) weighting scheme for using peculiar velocity data to estimate bulk flow moments for idealized, dense and isotropic surveys with Gaussian radial distributions, that avoids many of these complications. These moments are designed to be easy to interpret and are comparable between surveys. In this paper, we test the robustness of our MV estimators using numerical simulations. Using MV weights, we estimate the bulk flow moments for various mock catalogues extracted from the LasDamas and the Horizon Run numerical simulations and compare these estimates to the moments calculated directly from the simulation boxes. We show that the MV estimators are unbiased and negligibly affected by non-linear flows.