Sampling Artifact in Volume Weighted Velocity Measurement.--- II. Detection in simulations and comparison with theoretical modelling

Measuring the volume weighted velocity power spectrum suffers from a severe systematic error, due to imperfect sampling of the velocity field from 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 $\bar{n}_P$ 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 $\sim 12$% underestimation of the velocity power spectrum at $k=0.1$h/Mpc for samples with $\bar{n}_P=6\times10^{-3}$ (Mpc/h)$^{-3}$. This systematic underestimation increases with decreasing $\bar{n}_P$ and increasing $k$. Its dependence on the intrinsic LSS fluctuations is also robustly detected. (2) All these findings are expected by our theoretical modelling in paper I \cite{Zhang14}. In particular, the leading order theoretical approximation agrees quantitatively well with simulation result for $\bar{n}_P\gtrsim6\times 10^{-4}$(Mpc/h)$^{-3}$. Furthermore, we provide an ansatz to take high order terms into account. It improves the model accuracy to $\lesssim1$% at $k\lesssim0.1$h/Mpc over 3 orders of magnitude in $\bar{n}_P$ and over typical LSS clustering from $z=0$ to $z=2$. (3) The sampling artifact is determined by the deflection ${\bf D}$ 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 becomes promising to determine the {\it real} large scale velocity bias of $10^{13}M_\odot$ halos with $\sim 1$% accuracy, and that of lower mass halos by better accuracy. ...[abridged]