Power spectrum of velocity fluctuations in the universe

We investigate the power spectrum of velocity fluctuations in the universe starting from four different measures of velocity: the power spectrum of velocity fluctuations from peculiar velocities of galaxies, the rms peculiar velocity of galaxy clusters, the power spectrum of velocity fluctuations from the power spectrum of density fluctuations in the galaxy distribution, and the bulk velocity from peculiar velocities of galaxies. There are various way of interpreting the observational data. (1) The power spectrum of velocity fluctuations follows a power law V-2(k) similar to k(2) on large scales, achieves a maximum V(k) similar to 500 km s(-1) at a wavelength of lambda similar to 120 h(-1) Mpc, and declines as V-2(k) proportional to k(-0.8) on small scales. This type of power spectrum is predicted by a mixed dark matter model with density parameter Omega(0) = 1. This model is consistent with all data observed, except the rms peculiar velocity of galaxy clusters. (2) The shape of the power spectrum of velocity fluctuations is similar to that in (1), but the amplitude is lower (similar to 300 km s(-1) at lambda similar to 120 h(-1) Mpc). This power spectrum is predicted by a low-density cold dark matter model with a density parameter Omega(0) similar or equal to 0.3. (3) There is a peak in the power spectrum of velocity fluctuations at a wavelength of lambda similar or equal to 120 h(-1) Mpc on larger scales the power spectrum decreases with an index n similar or equal to 1.0. The maximum value of the function V(k) is similar to 420 km s(-1). This power spectrum is consistent with the power spectrum of the galaxy distribution in the Stromlo-APM redshift survey provided that the parameter beta is in the range 0.5-0.6. (4) There is a peak in the power spectrum as in (3), but on larger scales the amplitude of fluctuations is higher than that estimated starting from the observed power spectrum of galaxies. For the parameter beta in the range 0.4-0.5, the observed rms cluster peculiar velocity is consistent with the rms amplitude of the bulk flow of similar to 340 km s(-1) at a scale of 60 h(-1) Mpc. In this case, the value of the function V(k) at wavelength lambda = 120 h(-1) Mpc is similar to 350 km s(-1). In the future, larger redshift surveys and more accurate observations of peculiar velocities of galaxies and clusters will help to constrain the power spectrum of velocity fluctuations in the universe.