Measuring the Galaxy Power Spectrum with Multiresolution Decomposition. III. Velocity Field Analysis

Abstract

In this paper we develop the method of analyzing the velocity field of cosmic matter with a multiresolution decomposition. This is necessary in calculating the redshift distortion of the power spectrum in the discrete wavelet transform (DWT) representation. We show that, in the DWT analysis, the velocity field can be described by discrete variables, which are given by assignment of the number density and velocity into the DWT modes. These DWT variables are complete and not redundant. In this scheme, the peculiar velocity and pairwise velocity of galaxies or particles are given by field variables. As a consequence, the velocity dispersion (VD) and pairwise velocity dispersion (PVD) are no longer measured by number-counting or pair-counting statistic, but with the ensemble of the field variables, and therefore they are free from the bias due to the number counting and pair counting. We analyzed the VD and PVD of the velocity fields given by the N-body simulation for models of the standard cold dark matter (SCDM), τCDM, and ΛCDM. The spectrum (scale dependence) of the VD and PVD shows that the length scale of the two-point correlation of the velocity field is as large as a few tens h^-1 Mpc. Although the VD and PVD show similar behavior in some aspects, they are substantially different from each other. The VD-to-PVD ratio shows the difference between the scale dependencies of the VD and PVD. More prominent difference between the VD and PVD is shown by the probability distribution function. The one-point distribution of peculiar velocity is approximately exponential, while that of the pairwise velocity is lognormal, i.e., of long tail. This difference indicates that the cosmic velocity field is typically intermittent.