Unbiased Bayesian Inference of Peculiar Motions of Galaxies from Type Ia Supernovae Observations

TL;DR

This paper introduces an unbiased Bayesian method for estimating galaxy peculiar velocities from Type Ia supernova data, avoiding assumptions of local linearity and fixed cosmology, and validated with simulations.

Contribution

It presents a novel Bayesian approach that provides unbiased peculiar velocity estimates without assuming local linearity or a fixed cosmology, improving accuracy over standard methods.

Findings

The new estimator has lower bias than the standard linearized estimator.

It remains consistent for larger peculiar velocities.

Validation with simulated data confirms its effectiveness.

Abstract

The peculiar motions of galaxies are powerful cosmological probes that trace the growth of structures and the distribution of matter in the universe, providing a means to investigate the nature of dark energy and test gravity on cosmological scales. However, their direct observation is extremely challenging, as it requires independent and precise distance measurements to galaxies. We present a Bayesian approach to estimate the radial component of peculiar velocities of galaxies hosting Type Ia supernovae (SNe Ia), relying solely on the background cosmological model and the precision of the SNe Ia data. Unlike other peculiar velocity estimators based on Hubble residuals, our method does not assume local linearity of the magnitude-redshift relation or a fixed cosmology, making it unbiased even for large peculiar velocities and self-consistently avoiding bias due to a wrong cosmology. We validate our method using simulated supernova data with the precision of current and upcoming surveys, and further compare it with the linearized estimator to test its efficacy. We show that our estimator has lower bias than the standard estimator and remains consistent even for larger values of $v_{\rm p}/cz$. We also present a Bayesian derivation for the linearized estimator generalized to include the supernova magnitude covariance.