A redshift survey of IRAS galaxies. III. Reconstruction of the velocity and density fields in N-body model universes

In previous papers in this series, we have used a full-sky flux-limited sample of IRAS galaxies and linear gravitational theory to predict the velocity field within 8000 km s^-1 of the Local Group. In this paper we use N-body simulations of a Cold Dark Matter universe to calibrate the accuracy and understand the limitations of our procedure. The true acceleration and velocity of points with properties close to that of the Local Group are typically aligned within 7°, and are strongly correlated in amplitude. The rms difference between the one-dimensional acceleration and velocity of field particles is an increasing function of local density. For a particle in positions of average density, linear theory can account for all but one-sixth of its kinetic energy. We construct a series of artificial IRAS catalogs that closely match the real sample in space density and clustering amplitude, centered on a random sample of Local Group candidates. Peculiar velocities are estimated from the redshift data using linear theory in a self-consistent way. We can reproduce the true density field smoothed on a scale of 1000 km s^-1 with a scatter of roughly 0.05 in δρ/ρ, but with systematic offsets caused by inaccuracies in the mean density and selection function estimation. The amplitude of the acceleration of the Local Groups computed from these dilute IRAS realizations has rms scatter of roughly 30% relative to the velocity, typically making an angle with the peculiar velocity vector of 7°-35°. The comparison of acceleration induced by the galaxy distribution with the microwave dipole amplitude allows an estimate of Ω good to within a factor of 1.5, assuming that galaxies trace the mass. Our estimates of the peculiar velocities for galaxies other than our own are good in regions of low density. However in higher density zones, the solutions are frequently multivalued, and the reconstruction process can lead to serious errors. Without secondary estimates of distance for each object, this multivalued behavior sets a fundamental limit to our ability to reconstruct the true space distribution. Using velocity correlation functions we demonstrate that the predicted velocity fields, although fraught with error on scales smaller than ≈1000 km s^-1 are in good agreement with the true velocity field on large scales, where linear theory is more valid and dilute sampling is less of a problem. On the largest scales in the simulations, shot noise can cause significant residual large-scale bulk motions; they are minimized by working in a reference frame at rest with respect to the Local Group.