Three-Point Correlation Functions of SDSS Galaxies: Constraining Galaxy-Mass Bias

TL;DR

This study uses the three-point correlation function of SDSS galaxies to measure galaxy bias parameters, finding that bright galaxies are significantly biased tracers of mass and that a linear bias model suffices for current data.

Contribution

It provides the first detailed analysis of galaxy-mass bias using 3PCF measurements from SDSS, demonstrating the effectiveness of eigenmode analysis in error estimation.

Findings

Bright galaxies are biased tracers with 4.5 sigma significance.

A linear bias model adequately explains galaxy-mass bias.

Eigenmode analysis mitigates covariance estimation issues.

Abstract

We constrain the linear and quadratic bias parameters from the configuration dependence of the three-point correlation function (3PCF) in both redshift and projected space, utilizing measurements of spectroscopic galaxies in the Sloan Digital Sky Survey (SDSS) Main Galaxy Sample. We show that bright galaxies (M_r < -21.5) are biased tracers of mass, measured at a significance of 4.5 sigma in redshift space and 2.5 sigma in projected space by using a thorough error analysis in the quasi-linear regime (9-27 Mpc/h). Measurements on a fainter galaxy sample are consistent with an unbiased model. We demonstrate that a linear bias model appears sufficient to explain the galaxy-mass bias of our samples, although a model using both linear and quadratic terms results in a better fit. In contrast, the bias values obtained from the linear model appear in better agreement with the data by inspection of the relative bias, and yield implied values of sigma_8 that are more consistent with current constraints. We investigate the covariance of the 3PCF, which itself is a measurement of galaxy clustering. We assess the accuracy of our error estimates by comparing results from mock galaxy catalogs to jackknife re-sampling methods. We identify significant differences in the structure of the covariance. However, the impact of these discrepancies appears to be mitigated by an eigenmode analysis that can account for the noisy, unresolved modes. Our results demonstrate that using this technique is sufficient to remove potential systematics even when using less-than-ideal methods to estimate errors.