Local Gravity versus Local Velocity: Solutions for $\beta$ and nonlinear bias

TL;DR

This study compares observed and predicted large-scale cosmic flows using galaxy data to estimate the growth rate of structure, biasing, and fluctuation amplitude, providing constraints consistent with WMAP findings.

Contribution

It introduces a method to compare velocity fields from galaxy surveys using orthonormal basis functions, avoiding error covariance issues and calibrating predictions with mock data.

Findings

Estimated $eta$ between 0.28 and 0.37 at 68% CL.

Derived $eta$ constraints consistent with previous measurements.

Found $\sigma_8 = 0.73 imes ext{(uncertainty)}$, aligning with WMAP results.

Abstract

(abridged) We perform a reconstruction of the cosmological large scale flows in the nearby Universe using two complementary observational sets. The first, the SFI++ sample of Tully-Fisher (TF) measurements of galaxies, provides a direct probe of the flows. The second, the whole sky distribution of galaxies in the 2MASS redshift survey (2MRS), yields a prediction of the flows given the cosmological density parameter, $\Omega$, and a biasing relation between mass and galaxies. We aim at an unbiased comparison between the peculiar velocity fields extracted from the two data sets and its implication on the cosmological parameters and the biasing relation. We expand the fields in a set of orthonormal basis functions, each representing a plausible realization of a cosmological velocity field. Our analysis completely avoids the strong error covariance in the smoothed TF velocities by the use of orthonormal basis functions and employs elaborate realistic mock data sets to extensively calibrate the errors in 2MRS predicted velocities. We relate the 2MRS galaxy distribution to the mass density field by a linear bias factor, $b$, and include a luminosity dependent, $\propto L^\alpha$, galaxy weighting. We assess the agreement between the fields as a function of $\alpha$ and $\beta=f(\Omega)/b$, where $f$ is the growth factor of linear perturbations. The agreement is excellent with a reasonable $\chi^2$ per degree of freedom. For $\alpha=0$, we derive $0.28<\beta<0.37$ and $0.24<\beta<0.43$, respectively, at the 68.3% and 95.4% confidence levels (CLs). For $\beta=0.33$, we get $\alpha<0.25$ and $\alpha<0.5$, respectively, at the 68.3% and 95.4% CLs. We set a constraint on the fluctuation normalization, finding $\sigma_8 = 0.73 \pm 0.1$, in very good agreement with the latest WMAP results.