Large‐Scale Power Spectrum from Peculiar Velocities

The power spectrum (PS) of mass density fluctuations, in the range$0.05 \leq k \leq 0.2 \ihmpc$, is derived from the Mark III catalog of peculiarvelocities of galaxies, independent of ``biasing". It is computed from thedensity field as recovered by POTENT with Gaussian smoothing of $12\hmpc$,within a sphere of radius $\sim 60\hmpc$ about the Local Group. The density isweighted inversely by the square of the errors. The PS is corrected for theeffects of smoothing, random errors, sparse sampling and finite volume usingmock catalogs that mimic in detail the Mark III catalog and the dynamics of ourcosmological neighborhood. The mock catalogs are also used for error analysis.The PS at $k = 0.1 \ihmpc$ (for example) is $(4.6 \pm 1.4) \times 10^3\Omega^{-1.2} \3hmpc$, with a local logarithmic slope of $-1.45 \pm 0.5$. Anitegration yields $\sigma_8 \Omega^{0.6} \simeq 0.7-0.8$, depending on wherethe PS peak is. Direct comparisons of the mass PS with the galaxy PS derivedfrom sky and redshift surveys show a similarity in shape and yield for $\beta\equiv \Omega^{0.6}/b$ values in the range $0.77-1.21$, with a typical error of$\pm 0.1$ per galaxy sample. A comparison of the mass PS at $\sim 100\hmpc$with the large-angle CMB fluctuations by COBE provides constraints oncosmological parameters and on the slope of the initial PS ($n$). The``standard" CDM model is marginally rejected at the $\sim 2\sigma$ level, whileeach of the following modifications leads to a good fit: $n \lsim 1$,$\Omega_\nu \sim 0.3$, or $\Omega \lsim 1$. Values of $\Omega$ as low as $\sim0.2$ are ruled out with high confidence (independent of $\Lambda$).