Determination of the large scale volume weighted halo velocity bias in simulations

A profound assumption in peculiar velocity cosmology is $b_v=1$ at sufficiently large scales, where $b_v$ is the volume weighted halo(galaxy) velocity bias with respect to the matter velocity field. However, this fundamental assumption has not been robustly verified in numerical simulations. Furthermore, it is challenged by structure formation theory (BBKS, 1986, ApJ; Desjacques and Sheth, 2010, PRD), which predicts the existence of velocity bias (at least for proto-halos) due to the fact that halos reside in special regions (local density peaks). The major obstacle to measure the volume weighted velocity from N-body simulations is an unphysical sampling artifact. It is entangled in the measured velocity statistics and becomes significant for sparse populations. With recently improved understanding of the sampling artifact (Zhang, Zheng and Jing, 2015, PRD; Zheng, Zhang and Jing, 2015, PRD), for the first time we are able to {\it appropriately correct this sampling artifact and then robustly measure the volume weighted halo velocity bias}. (1) We verify $b_v=1$ within $2\%$ model uncertainty at $k\lesssim 0.1h/$Mpc and $z=0$-$2$ for halos of mass $\sim 10^{12}$-$10^{13} h^{-1} M_\odot$, and, therefore, consolidates a foundation of the peculiar velocity cosmology. (2) We also find statistically significant signs of $b_v\neq 1$ at $k\gtrsim 0.1h/$Mpc. Unfortunately, whether this is real or caused by residual sampling artifact requires further investigation. Nevertheless, cosmology based on $k\gtrsim 0.1h/$Mpc velocity data shall be careful this potential velocity bias.