Peculiar velocities in the local Universe: comparison of different models and the implications for $H_0$ and dark matter

When measuring the value of the Hubble parameter, $H_0$, it is necessary to know the recession velocity free of the effects of peculiar velocities. In this work, we study different models of peculiar velocity in the local Universe. In particular, we compare models based on density reconstruction from galaxy redshift surveys and kernel smoothing of peculiar velocity data. The velocity field from the density reconstruction is obtained using the 2M++ galaxy redshift compilation, which is compared to two adaptive kernel-smoothed velocity fields: the first obtained from the 6dF Fundamental Plane sample and the other using a Tully-Fisher catalogue obtained by combining SFI++ and 2MTF. We highlight that smoothed velocity fields should be rescaled to obtain unbiased velocity estimates. Comparing the predictions of these models to the observations from a few test sets of peculiar velocity data, obtained from the Second Amendment Supernovae catalogue and the Tully-Fisher catalogues, we find that 2M++ reconstruction provides a better model of the peculiar velocity in the local Universe than the kernel-smoothed peculiar velocity models. We study the impact of peculiar velocities on the measurement of $H_0$ from gravitational waves and megamasers. In doing so, we introduce a probabilistic framework to marginalize over the peculiar velocity corrections along the line-of-sight. For the megamasers, we find $H_0 = 69^{+2.9}_{-2.8}$ km s^{-1} Mpc^{-1} using the 2M++ velocity field. We also study the peculiar velocity of the the galaxy NGC1052-DF2, concluding that a short $\sim$ 13 Mpc distance is not a likely explanation of the anomalously low dark matter fraction of that galaxy.