Observational biases in Lagrangian reconstructions of cosmic velocity fields

TL;DR

This paper analyzes observational biases affecting Lagrangian reconstructions of cosmic velocity fields, using mock catalogues to develop correction recipes and propose an improved Bayesian method for estimating cosmological parameters.

Contribution

It provides a comprehensive analysis of systematic effects in Lagrangian velocity reconstructions and introduces correction strategies and an unbiased Bayesian estimator for Omega_m.

Findings

Biases can be corrected with specific recipes using mock catalogues.

Reconstructed velocities have about 25% of the velocity dispersion as error.

A nearly unbiased estimator of Omega_m can be achieved with MAK reconstruction.

Abstract

Lagrangian reconstruction of large-scale peculiar velocity fields can be strongly affected by observational biases. We develop a thorough analysis of these systematic effects by relying on specially selected mock catalogues. For the purpose of this paper, we use the MAK reconstruction method, although any other Lagrangian reconstruction method should be sensitive to the same problems. We extensively study the uncertainty in the mass-to-light assignment due to luminosity incompleteness, and the poorly-determined relation between mass and luminosity. The impact of redshift distortion corrections is analyzed in the context of MAK and we check the importance of edge and finite-volume effects on the reconstructed velocities. Using three mock catalogues with different average densities, we also study the effect of cosmic variance. In particular, one of them presents the same global features as found in observational catalogues that extend to 80 Mpc/h scales. We give recipes, checked using the aforementioned mock catalogues, to handle these particular observational effects, after having introduced them into the mock catalogues so as to quantitatively mimic the most densely sampled currently available galaxy catalogue of the nearby universe. Once biases have been taken care of, the typical resulting error in reconstructed velocities is typically about a quarter of the overall velocity dispersion, and without significant bias. We finally model our reconstruction errors to propose an improved Bayesian approach to measure Omega_m in an unbiased way by comparing the reconstructed velocities to the measured ones in distance space, even though they may be plagued by large errors. We show that, in the context of observational data, a nearly unbiased estimator of Omega_m may be built using MAK reconstruction.