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Monthly Notices of the Royal Astronomical Society


We estimate the mass density fluctuations power spectrum (PS) on large scales by applying a maximum likelihood technique to the peculiar velocity data of the recently completed redshift—distance survey of early-type galaxies (hereafter ENEAR). Parametric cold dark matter (CDM)-like models for the PS are assumed, and the best-fitting parameters are determined by maximizing the probability of the model given the measured peculiar velocities of the galaxies, their distances and estimated errors. The method has been applied to CDM models with and without COBE normalization. The general results are in agreement with the high-amplitude power spectra found from similar analyses of other independent all-sky catalogue of peculiar velocity data such as MARK III and SFI, in spite of the differences in the way these samples were selected, the fact that they probe different regions of space and galaxy distances are computed using different distance relations. For example, at k = 0.1 h Mpc−1 the power spectrum value is P(k1.2 = (6.5 ± 3) × 103(h−1 Mpc)3 and η8σ8Ω0.6 = 1.1−0.35+0.2; the quoted uncertainties refer to 3σ error level. We also find that, for ΛCDM and OCDM COBE-normalized models, the best-fitting parameters are confined by a contour approximately defined by Ω h1.3 = 0.377 ± 0.08 and Ω h0.88 = 0.517±0.083 respectively. Γ-shape models, free of COBE normalization, result in the weak constraint of Γ≥0.17 and in the rather stringent constraint of η8 = 1.0 ± 0.25. All quoted uncertainties refer to 3σ confidence level (c.l.).

The calculated PS has been used as a prior for Wiener reconstruction of the density field at different resolutions and the three-dimensional velocity field within a volume of radius ≈80 h−1 Mpc. All major structures in the nearby Universe are recovered and are well matched to those predicted from all-sky redshift surveys. The robustness of these features has been tested with constrained realizations (CR). Analysis of the reconstructed three-dimensional velocity field yields a small bulk-flow amplitude (∼160±60 km s−1 at 60 h−1 Mpc) and a very small rms value of the tidal field (∼60 km s−1). The results give further support to the picture that most of the motion of the Local Group arises from mass fluctuations within the volume considered.