An unbiased estimator of peculiar velocity with Gaussian distributed errors for precision cosmology

We introduce a new estimator of the peculiar velocity of a galaxy or group of galaxies from redshift and distance estimates. This estimator results in peculiar velocity estimates which are statistically unbiased and have Gaussian distributed errors, thus complying with the assumptions of analyses that rely on individual peculiar velocities. We apply this estimator to the SFI++ and the Cosmicflows-2 catalogues of galaxy distances and, since peculiar velocity estimates of distant galaxies are error dominated, examine their error distributions. The adoption of the new estimator significantly improves the accuracy and validity of studies of the large-scale peculiar velocity field that assume Gaussian distributed velocity errors and eliminates potential systematic biases, thus helping to bring peculiar velocity analysis into the era of precision cosmology. In addition, our method of examining the distribution of velocity errors should provide a useful check of the statistics of large peculiar velocity catalogues, particularly those that are compiled out of data from multiple sources.