Measuring the galaxy power spectrum with multiresolution decomposition. III. Velocity field analysis

In this paper we develop the method of analyzing the velocity field of cosm ic matter with a multiresolution decomposition. This is necessary in calcul ating the redshift distortion of the power spectrum in the discrete wavelet transform (DWT) representation. We show that, in the DWT analysis, the vel ocity field can be described by discrete variables, which are given by assi gnment of the number density and velocity into the DWT modes. These DWT var iables are complete and not redundant. In this scheme, the peculiar velocit y and pairwise velocity of galaxies or particles are given by field variabl es. As a consequence, the velocity dispersion (VD) and pairwise velocity di spersion (PVD) are no longer measured by number-counting or pair-counting s tatistic, 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 ana lyzed the VD and PVD of the velocity fields given by the N-body simulation for models of the standard cold dark matter (SCDM), tau CDM, and Lambda CDM . The spectrum (scale dependence) of the VD and PVD shows that the length s cale of the two-point correlation of the velocity field is as large as a fe w tens h(-1) Mpc. Although the VD and PVD show similar behavior in some asp ects, they are substantially different from each other. The VD-to-PVD ratio shows the difference between the scale dependencies of the VD and PVD. Mor e prominent difference between the VD and PVD is shown by the probability d istribution function. The one-point distribution of peculiar velocity is ap proximately exponential, while that of the pairwise velocity is lognormal, i.e., of long tail. This difference indicates that the cosmic velocity fiel d is typically intermittent.