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 (k) ∼ k, on large scales, achieves a maximum V (k) ∼ 500 km s at a wavelength λ ∼ 120h Mpc, and declines as V (k) ∝ k on small scales. This type of power spectrum is predicted by a mixed dark matter model with density parameter Ω0 = 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 model (1), but the amplitude is lower (∼ 300 km s at λ ∼ 120h Mpc). This power spectrum is predicted by a low-density cold dark matter model with density parameter Ω0 ≃ 0.3. (3) There is a peak in the power spectrum of velocity fluctuations at a wavelength λ ≃ 120h Mpc and on larger scales the power spectrum decreases with an index n ≃ 1.0. The maximum value of the function V (k) is ∼ 420 km s. This power spectrum is consistent with the power spectrum of the galaxy distribution in the Stromlo-APM redshift survey provided the parameter β is in the range 0.5− 0.6. (4) There is a peak in the power spectrum as in model (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 β in the range 0.4− 0.5, the observed rms cluster peculiar velocity is consistent with the rms amplitude of the bulk flow ∼ 340 km s at the scale 60h Mpc. In this case the value of the function V (k) at wavelength λ = 120h Mpc is ∼ 350 km s.