Kriging interpolating cosmic velocity field

Volume-weighted statistics of large-scale peculiar velocity is preferred by peculiar velocity cosmology, since it is free of the uncertainties of galaxy density bias entangled in observed number density-weighted statistics. However, measuring the volume-weighted velocity statistics from galaxy (halo/simulation particle) velocity data is challenging. Therefore, the exploration of velocity assignment methods with well-controlled sampling artifacts is of great importance. For the first time, we apply the Kriging interpolation to obtain the volume-weighted velocity field. Kriging is a minimum variance estimator. It predicts the most likely velocity for each place based on the velocity at other places. We test the performance of Kriging quantified by the E-mode velocity power spectrum from simulations. Dependences on the variogram prior used in Kriging, the number n_k of the nearby particles to interpolate, and the density n_P of the observed sample are investigated. First, we find that Kriging induces 1% and 3% systematics at k ∼0.1 h Mpc^-1 when n_P∼6 ×1 0^-2(h^-1 Mpc )^-3 and n_P∼6 ×1 0^-3(h^-1 Mpc )^-3 , respectively. The deviation increases for decreasing n_P and increasing k . When n_P≲6 ×1 0^-4(h^-1 Mpc )^-3 , a smoothing effect dominates small scales, causing significant underestimation of the velocity power spectrum. Second, increasing n_k helps to recover small-scale power. However, for n_P≲6 ×1 0^-4(h^-1 Mpc )^-3 cases, the recovery is limited. Finally, Kriging is more sensitive to the variogram prior for a lower sample density. The most straightforward application of Kriging on the cosmic velocity field does not show obvious advantages over the nearest-particle method [Y. Zheng, P. Zhang, Y. Jing, W. Lin, and J. Pan, Phys. Rev. D 88, 103510 (2013)] and could not be directly applied to cosmology so far. However, whether potential improvements may be achieved by more delicate versions of Kriging is worth further investigation.