Reconstructing dark matter distribution with peculiar velocities: Bayesian forward modelling with corrections for inhomogeneous Malmquist bias

TL;DR

This paper introduces a Bayesian forward-modeling method for reconstructing the dark matter distribution using peculiar velocity data, effectively correcting for inhomogeneous Malmquist bias and validating results with simulations and real data.

Contribution

The paper presents a novel Bayesian velocity field reconstruction algorithm that accounts for Malmquist bias and demonstrates its effectiveness on simulated and real peculiar velocity data.

Findings

Unbiased velocity field reconstruction achieved in simulations.

Good agreement with independent galaxy catalogue reconstructions.

Model outperforms adaptive kernel smoothing with the same data.

Abstract

We present a forward-modelled velocity field reconstruction algorithm that performs the reconstruction of the mass density field using only peculiar velocity data. Our method consistently accounts for the inhomogeneous Malmquist bias using analytic integration along the line-of-sight. By testing our method on a simulation, we show that our method gives an unbiased reconstruction of the velocity field. We show that not accounting for the inhomogeneous Malmquist bias can lead to significant biases in the forward-modelled reconstructions. We applied our method to a peculiar velocity data set consisting of the SFI++ and 2MTF Tully-Fisher catalogues and the A2 supernovae compilation, thus obtaining a novel velocity reconstruction in the local Universe. Our velocity reconstructions have a cosmological power spectrum consistent with the theoretical expectation. Furthermore, we obtain a full description of the uncertainties on reconstruction through samples of the posterior distribution. We validate our velocity reconstruction of the local Universe by comparing it to an independent reconstruction using the 2M++ galaxy catalogue, obtaining good agreement between the two reconstructions. Using Bayesian model comparison, we find that our velocity model performs better than the adaptive kernel smoothed velocity with the same peculiar velocity data. However, our velocity model does not perform as well as the velocity reconstruction from the 2M++ galaxy catalogue, due to the sparse and noisy nature of the peculiar velocity tracer samples. The method presented here provides a way to include peculiar velocity data in initial condition reconstruction frameworks.