Three-Point Correlation Functions of SDSS Galaxies: Luminosity and Color Dependence in Redshift and Projected Space

TL;DR

This study measures the three-point correlation function of SDSS galaxies, revealing its configuration dependence, sensitivity to galaxy properties, and the impact of systematic effects, thus providing insights into galaxy clustering beyond two-point statistics.

Contribution

It presents the largest analysis of the reduced 3PCF in SDSS galaxies, highlighting its dependence on configuration, luminosity, and color, and discusses the influence of redshift distortions and systematics.

Findings

Significant configuration dependence of the 3PCF at 3-27 Mpc/h.

Redshift space 3PCF shows weaker amplitude and dependence below 6 Mpc/h.

3PCF is more sensitive to galaxy color than luminosity on small scales.

Abstract

The three-point correlation function (3PCF) provides an important view into the clustering of galaxies that is not available to its lower order cousin, the two-point correlation function (2PCF). Higher order statistics, such as the 3PCF, are necessary to probe the non-Gaussian structure and shape information expected in these distributions. We measure the clustering of spectroscopic galaxies in the Main Galaxy Sample of the Sloan Digital Sky Survey (SDSS), focusing on the shape or configuration dependence of the reduced 3PCF in both redshift and projected space. This work constitutes the largest number of galaxies ever used to investigate the reduced 3PCF, using over 220,000 galaxies in three volume-limited samples. We find significant configuration dependence of the reduced 3PCF at 3-27 Mpc/h, in agreement with LCDM predictions and in disagreement with the hierarchical ansatz. Below 6 Mpc/h, the redshift space reduced 3PCF shows a smaller amplitude and weak configuration dependence in comparison with projected measurements suggesting that redshift distortions, and not galaxy bias, can make the reduced 3PCF appear consistent with the hierarchical ansatz. The reduced 3PCF shows a weaker dependence on luminosity than the 2PCF, with no significant dependence on scales above 9 Mpc/h. On scales less than 9 Mpc/h, the reduced 3PCF appears more affected by galaxy color than luminosty. We demonstrate the extreme sensitivity of the 3PCF to systematic effects such as sky completeness and binning scheme, along with the difficulty of resolving the errors. Some comparable analyses make assumptions that do not consistently account for these effects.