Toward an Optimal Sampling of Peculiar Velocity Surveys For Wiener
  Filter Reconstructions
  The Wiener Filter (WF) technique enables the reconstruction of density and
velocity fields from observed radial peculiar velocities. This paper aims at
identifying the optimal design of peculiar velocity surveys within the WF
framework. The prime goal is to test the dependence of the quality of the
reconstruction on the distribution and nature of data points. Mock datasets,
extending to 250 Mpc/h, are drawn from a constrained simulation that mimics the
local Universe to produce realistic mock catalogs. Reconstructed fields
obtained with these mocks are compared to the reference simulation.
Comparisons, including residual distributions, cell-to-cell and bulk
velocities, imply that the presence of field data points is essential to
properly measure the flows. The fields reconstructed from mocks that consist
only of galaxy cluster data points exhibit poor quality bulk velocities. In
addition, the quality of the reconstruction depends strongly on the grouping of
individual data points into single points to suppress virial motions in high
density regions. Conversely, the presence of a Zone of Avoidance hardly affects
the reconstruction. For a given number of data points, a uniform sample does
not score any better than a sample with decreasing number of data points with
the distance. The best reconstructions are obtained with a grouped survey
containing field galaxies: Assuming no error, they differ from the simulated
field by less than 100 km/s up to the extreme edge of the catalogs or up to a
distance of three times the mean distance of data points for non-uniform
catalogs. The overall conclusions hold when errors are added.
