Sampling artifact in volume weighted velocity measurement. II. Detection in simulations and comparison with theoretical modeling

Measuring the volume weighted velocity power spectrum suffers from a severe systematic error due to imperfect sampling of the velocity field from the inhomogeneous distribution of dark matter particles/halos in simulations or galaxies with velocity measurement. This "sampling artifact" depends on both the mean particle number density (n) over bar (P) and the intrinsic large scale structure (LSS) fluctuation in the particle distribution. (1) We report robust detection of this sampling artifact in N-body simulations. It causes similar to 12% underestimation of the velocity power spectrum at k = 0.1 h/Mpc for samples with (n) over bar (P) = 6 x 10(-3) (Mpc/h)(-3). This systematic underestimation increases with decreasing (n) over bar (P) and increasing k. Its dependence on the intrinsic LSS fluctuations is also robustly detected. (2) All of these findings are expected based upon our theoretical modeling in paper I [P. Zhang, Y. Zheng, and Y. Jing, Sampling artifact in volume weighted velocity measurement. I. Theoretical modeling, arXiv: 1405.7125.]. In particular, the leading order theoretical approximation agrees quantitatively well with the simulation result for (n) over bar (P) greater than or similar to 6 x 10(-4) (Mpc/h)(-3). Furthermore, we provide an ansatz to take high order terms into account. It improves the model accuracy to less than or similar to 1% at k less than or similar to 0.1 h/Mpc over 3 orders of magnitude in (n) over bar (P) and over typical LSS clustering from z = 0 to z = 2. (3) The sampling artifact is determined by the deflection D field, which is straightforwardly available in both simulations and data of galaxy velocity. Hence the sampling artifact in the velocity power spectrum measurement can be self-calibrated within our framework. By applying such self-calibration in simulations, it is promising to determine the real large scale velocity bias of 10(13)M(circle dot) halos with similar to 1% accuracy, and that of lower mass halos with better accuracy. (4) In contrast to suppressing the velocity power spectrum at large scale, the sampling artifact causes an overestimation of the velocity dispersion. We prove that a correlation between the signal field (v) and the sampling field (D) is a major cause. This complexity, among other issues, is carefully investigated to further improve understanding of the sampling artifact