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

In this paper, we develop the method of analyzing the velocity field ofcosmic matter with a multiresolution decomposition. This is necessary incalculating the redshift distortion of power spectrum in the discrete wavelettransform (DWT) representation. We show that, in the DWT analysis, the velocityfield can be described by discrete variables, which are given by assignment ofthe number density and velocity into the DWT modes. These DWT variables arecomplete and not redundant. In this scheme, the peculiar velocity and pairwisevelocity of galaxies or particles are given by field variables. As aconsequence, the velocity dispersion (VD) and pairwise velocity dispersion(PVD) are no longer measured by number-counting or pair-counting statistic, butwith the ensemble of the field variables, and therefore, they are free from thebias due to the number-counting and pair-counting. We analyzed the VD and PVDof the velocity fields given by the N-body simulation for models of the SCDM,$\tau$CDM and $\Lambda$CDM. The spectrum (scale-dependence) of the VD and PVDshow that the length scale of the two-point correlation of the velocity fieldis as large as few tens h$^{-1}$ Mpc. Although the VD and PVD show similarbehavior in some aspects, they are substantially different from each other. TheVD-to-PVD ratio shows the difference between the scale-dependencies of the VDand PVD. More prominent difference between the VD and PVD is shown byprobability distribution function. The one-point distribution of peculiarvelocity is approximately exponential, while the pairwise velocity's islognormal, i.e. of long tail. This difference indicates that the cosmicvelocity field is typically intermittent.Comment: AAS LaTeX file, 46 pages, 15 figures included, accepted for publication in Ap