Kriging interpolating cosmic velocity field. II. Taking anistropies and multistreaming into account

TL;DR

This paper enhances Kriging interpolation for cosmic velocity fields by incorporating anisotropic correlations and multi-streaming effects, significantly improving accuracy in sparse data scenarios.

Contribution

The study introduces two physically motivated extensions to Kriging interpolation, improving velocity field reconstruction by accounting for anisotropies and multi-streaming effects.

Findings

Extended reliable velocity power spectrum measurement scale by ~1.6 times.

Reduced dependence on velocity correlation prior by a factor of ~2.

Significant improvement in sparse sampling conditions.

Abstract

Measuring the volume-weighted peculiar velocity statistics from inhomogeneously and sparsely distributed galaxies/halos, by existing velocity assignment methods, suffers from a significant sampling artifact. As an alternative, the Kriging interpolation based on Gaussian processes was introduced and evaluated [Y. Yu, J. Zhang, Y. Jing, and P. Zhang, Phys. Rev. D 92, 083527 (2015)]. Unfortunately, the most straightforward application of Kriging does not perform better than the existing methods in the literature. In this work, we investigate two physically motivated extensions. The first takes into account of the anisotropic velocity correlations. The second introduces the nugget effect, on account of multi-streaming of the velocity field. We find that the performance is indeed improved. For sparsely sampled data [$n_P\lesssim 6\times 10^{-3}(h^{-1} {\rm Mpc})^{-3}$] where the sampling artifact is the most severe, the improvement is significant and is two-fold: 1) The scale of reliable measurement of the velocity power spectrum is extended by a factor $\sim 1.6$, and 2) the dependence on the velocity correlation prior is weakened by a factor of $\sim 2$. We conclude that such extensions are desirable for accurate velocity assignment by Kriging.