# Toward an Optimal Sampling of Peculiar Velocity Surveys For Wiener Filter Reconstructions

## TL;DR

This study investigates how the design of peculiar velocity surveys affects the accuracy of Wiener Filter reconstructions of cosmic density and velocity fields, emphasizing the importance of data distribution, grouping, and survey coverage.

## Contribution

It identifies optimal survey strategies for Wiener Filter reconstructions, highlighting the importance of data point grouping and distribution in achieving accurate cosmic flow reconstructions.

## Key findings

- Field data points are essential for accurate flow measurements.
- Grouped surveys with field galaxies yield the best reconstructions.
- Uniform and decreasing-distance samples perform similarly in reconstruction quality.

## Abstract

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.