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

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.

Figures (10)

• Figure 1: 1D and 2D marginalized posterior distribution for the cosmological parameters and peculiar velocities for the three lowest redshift supernovae in the sample obtained from simulated data with $\sigma_m=0.02$. The black-dashed lines show the true values of the parameters.
• Figure 2: Estimated peculiar velocities along with $1\sigma$ error bars at different redshifts obtained using the general method from simulated data with $\sigma_m = 0.02$.
• Figure 3: The root mean square errors (RMSE) of estimation as a function of redshifts for two different supernovae magnitude precision shown by different marker shapes. The color bar on the right shows the contribution of variance.
• Figure 4: Estimated peculiar velocities along with $1\sigma$ error bars versus the true values used in the simulation for simulated data with $\sigma_m = 0.02$. Different colors represent the methods used.
• Figure 5: Comparison of bias due to breakdown of linear approximation and wrong cosmology. The solid lines are polynomial fits to the scatter used to better represent the trend. The general method remains statistically unbiased within a $68\%$ credible region, even for $v_{\rm true}\approx cz$, where the linear approximation is not valid.