Power Spectrum of Velocity Fluctuations in the Universe

We investigate the power spectrum of velocity fluctuations in the universe,$V^2(k)$, starting from four different measures of velocity: (1) the powerspectrum of velocity fluctuations from peculiar velocities of galaxies; (2) therms peculiar velocity of galaxy clusters; (3) the power spectrum of velocityfluctuations from the power spectrum of density fluctuations in the galaxydistribution; (4) and the bulk velocity from peculiar velocities of galaxies.We show that measures (1) and (2) are not consistent with each other and eitherthe power spectrum from peculiar velocities of galaxies is overestimated or therms cluster peculiar velocity is underestimated. The amplitude of velocityfluctuations derived from the galaxy distribution (measure 3) depends on theparameter $\beta$. We estimate the parameter $\beta$ on the basis of measures(2) and (4). The power spectrum of velocity fluctuations from the galaxydistribution in the Stromlo-APM redshift survey is consistent with the observedrms cluster velocity and with the observed large-scale bulk flow when theparameter $\beta$ is in the range 0.4-0.5. In this case the value of thefunction $V(k)$ at wavelength $\lambda=120h^{-1}$Mpc is $\sim 350$ km s$^{-1}$and the rms amplitude of the bulk flow at the radius $r=60h^{-1}$ Mpc is $\sim340$ km s$^{-1}$. The velocity dispersion of galaxy systems originates mostlyfrom the large-scale velocity fluctuations with wavelengths $\lambda>100h^{-1}$ Mpc.Comment: Astrophysical Journal, Vol. 493, in press: 23 pages, uses AAS Latex, and 14 separate postscript figure