Accurate Determination of Halo Velocity Bias in Simulations and Its Cosmological Implications

A long-standing issue in peculiar velocity cosmology is whether the halo/galaxy velocity bias b _v = 1 at large scale. The resolution of this important issue must resort to high-precision cosmological simulations. However, this is hampered by another long-standing “sampling artifact” problem in volume-weighted velocity measurement. We circumvent this problem with a hybrid approach. We first measure the statistics free of sampling artifacts, then link them to volume-weighted statistics in theory, and finally solve for the velocity bias. b _v (determined by our method) is not only free of sampling artifacts but also free of cosmic variance. We apply this method to a ΛCDM N-body simulation of 3072³ particles and 1200 {Mpc}/h box size. For the first time, we determine the halo velocity bias to 0.1%-1% accuracy. Our major findings are as follows: (1) {b}_v\ne 1 at k> 0.1 h/{Mpc}. The deviation from unity (| {b}_v-1| ) increases with k. Depending on halo mass and redshift, it may reach { \mathcal O }(0.01) at k=0.2 h/{Mpc} and { \mathcal O }(0.05) at k∼ 0.3 h/{Mpc}. The discovered {b}_v\ne 1 has a statistically significant impact on the structure growth rate measurement by spectroscopic redshift surveys, including DESI, Euclid, and SKA. (2) Both the sign and the amplitude of b _v - 1 depend on mass and redshift. These results disagree with the peak model prediction in that b _v has much weaker deviation from unity, varies with redshift, and can be bigger than unity. (3) Most of the mass and redshift dependences can be compressed into a single dependence on the halo density bias. Based on this finding, we provide an approximate two-parameter fitting formula.