Wiener Reconstruction of Large-Scale Structure from Peculiar Velocities

We present an alternative, Bayesian method for large-scale reconstruction from observed peculiar velocities. The method stresses a rigorous treatment of the random errors, and it allows extrapolation into poorly sampled regions in real space or in k-space. A likelihood analysis is used in a preliminary stage to determine the fluctuation power spectrum, followed by a Wiener filter (WF) analysis to obtain the minimum-variance mean fields of velocity and mass density. Constrained realizations (CRs) are then used to sample the statistical scatter about the WF mean field. The method is tested using mock catalogs of the Mark III data, drawn from a simulation that mimics our local cosmological neighborhood. The success of the reconstruction is evaluated quantitatively. With low-resolution Gaussian smoothing of radius 1200 km s-1, the reconstruction is of high signal-to-noise ratio (S/N) in a relatively large volume, with small variance about the mean field. A high-resolution reconstruction, of 500 km s-1 smoothing, is of reasonable S/N only in limited nearby regions, where interesting new substructure is resolved. The WF/CR method is applied as a demonstration to the Mark III data. The reconstructed structures are consistent with those extracted from the same velocity data by the POTENT method, and with the structures seen in the distribution of IRAS 1.2 Jy galaxies. The reconstructed velocity field is decomposed into its divergent and tidal components relative to a cube of side ±8000 km s-1 centered on the Local Group. The divergent component is similar to the velocity field predicted from the distribution of IRAS galaxies. The tidal component is dominated by a bulk flow of 194 ± 32 km s-1 in the general direction of the Shapley concentration, and it also indicates a significant quadrupole.