Statistically bias-minimized peculiar velocity catalogs from Gibbs point processes and Bayesian inference

Galaxy peculiar velocities are excellent cosmological probes provided that biases inherent to their measurements are contained before any study. This paper proposes a new algorithm based on an object point process model whose probability density is built to statistically reduce the effects of Malmquist biases and uncertainties due to lognormal errors in radial peculiar velocity catalogs. More precisely, a simulated annealing algorithm permits maximizing the probability density describing the point process model. The resulting configurations are bias-minimized catalogs. Tests are conducted on synthetic catalogs mimicking the second and third distance modulus catalogs of the Cosmicflows project from which peculiar velocity catalogs are derived. By reducing the local peculiar velocity variance in catalogs by an order of magnitude, the algorithm permits recovering the expected one while preserving the small-scale velocity correlation. It also permits retrieving the expected clustering. The algorithm is then applied to the observational catalogs. The large-scale structure reconstructed with the Wiener-filter technique applied to the bias-minimized observational catalogs matches with great success the local cosmic web as depicted by redshift surveys of local galaxies. These new bias-minimized versions of peculiar velocity catalogs can be used as a starting point for several studies from possibly estimating the most probable Hubble constant, H0, value to the production of simulations constrained to reproduce the local Universe.