A comparison of the galaxy peculiar velocity field with the PSCz gravity field-- A Bayesian hyper-parameter method

TL;DR

This paper introduces a Bayesian hyper-parameter method to compare galaxy velocity predictions from the PSCz survey with observed peculiar velocities, confirming the model's accuracy within 70 Mpc/h and estimating the growth rate of structure.

Contribution

The paper develops a novel Bayesian hyper-parameter approach to quantify differences between predicted and observed galaxy velocities, improving analysis of local velocity fields.

Findings

Model-data comparison reliable within 70 Mpc/h

PSCz gravity field accurately models local peculiar velocities

Estimated growth rate fσ8(z~0) = 0.42 ± 0.033

Abstract

We constructed a Bayesian hyper-parameter statistical method to quantify the difference between predicted velocities derived from the observed galaxy distribution in the \textit{IRAS}-PSC$z$ redshift survey and peculiar velocities measured using different distance indicators. In our analysis we find that the model--data comparison becomes unreliable beyond $70 \hmpc$ because of the inadequate sampling by \textit{IRAS} survey of prominent, distant superclusters, like the Shapley Concentration. On the other hand, the analysis of the velocity residuals show that the PSC$z$ gravity field provides an adequate model to the local, $\le 70 \hmpc$, peculiar velocity field. The hyper-parameter combination of ENEAR, SN, A1SN and SFI++ catalogues in the Bayesian framework constrains the amplitude of the linear flow to be $\beta=0.53 \pm 0.014$. For an rms density fluctuations in the PSC$z$ galaxy number density $\sigma_8^{\rm gal}=0.42\pm0.03$, we obtain an estimate of the growth rate of density fluctuations $f\sigma_{8}(z\sim0) = 0.42 \pm 0.033$, which is in excellent agreement with independent estimates based on different techniques.