LARGE-SCALE POWER SPECTRUM FROM PECULIAR VELOCITIES VIA LIKELIHOOD ANALYSIS

The power spectrum (PS) of mass density fluctuations, independent of ' 'biasing,'' is estimated from the Mark III catalog of peculiar velocit ies using Bayesian statistics. A parametric model is assumed for the P S, and the free parameters are determined by maximizing the probabilit y of the model given the data. The method has been tested using detail ed mock catalogs. It has been applied to generalized CDM models with a nd without COBE normalization. The robust result for all the models is a relatively high PS, with P(k)Omega(1.2) = (4.8 +/- 1.5) x 10(3)(h(- 1) Mpc)(3) at k = 0.1 h Mpc(-1). An extrapolation to smaller scales us ing the different CDM models yields sigma(8) Omega(0.6) = 0.88 +/- 0.1 5. The peak is weakly constrained to the range 0.02 less than or equal to k less than or equal to 0.06 h Mpc(-1). These results are consiste nt with a direct computation of the PS. When compared to galaxy-densit y surveys, the implied values for beta (=Omega(0.6)/b) are of order un ity to within 25%. The parameters of the COBE-normalized, flat CDM mod el are confined by a 90% likelihood contour of the sort Omega h(50)(mu )n(nu) = 0.8 +/- 0.2 where mu = 1.3 and nu = 3.4, 2.0 for models with and without tensor fluctuations, respectively. For open CDM the powers are mu = 0.95 and nu = 1.4 (no tensor fluctuations). A Gamma-shape mo del free of COBE normalization yields only a weak constraint: Gamma = 0.4 +/- 0.2.