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

Abstract

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 that have errors that are Gaussian distributed, thus meeting the assumptions of analyses that rely on individual peculiar velocities. We apply this estimator to the SFI++ and the Cosmicflows-2 catalogs of galaxy distances and, using the fact that 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 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 catalogs, particularly those that are compiled out of data from multiple sources.

Cosmicflows-3

“…Objects within 3000 km s −1 of the supergalactic equator drawn from the groups catalog are plotted at positions given by velocities in the CMB frame with colors indicative of peculiar velocities. The peculiar velocities represented in the plots are calculated using the formulation by Watkins & Feldman (2015) that are statistically unbiased and have Gaussian distributed errors: given by Equation (9) as V LS runs from zero to 3000 km s −1 . The most evident feature of Figure 19 is the prominence of blue shades at positive SGX, negative SGY and red shades at negative SGX, positive SGY.…”

The 6dF Galaxy Survey: bulk flows on 50-70h-1Mpc scales

“…A further effect may come from the fact that the distribution of measured velocities themselves will be affected by the lognormal uncertainties. A possible solution to this problem was recently suggested by Watkins & Feldman (2015). We leave investigation of this for 6dFGSv to future work.…”

The redshift-space momentum power spectrum – II. Measuring the growth rate from the combined 2MTF and 6dFGSv surveys

“…'Log-distance' ratios are the preferred method for presenting peculiar velocity data as they have measurement errors which are closer to Gaussian. We use the estimator of Watkins & Feldman (2015) to convert these to pseudo peculiar velocity measurements which preserve Gaussianity, as demonstrated for the 2MTF dataset by Howlett et al (2017b).…”

“…3 is the definition of the galaxy density field, while the second one is the definition of the galaxy momentum field as presented in Paper I. In this paper, the line-ofsight peculiar velocity v(r), is estimated from the measured log-distance ratios of galaxies using the estimator of Watkins & Feldman (2015).…”