Our non-Gaussian universe: Higher order correlation functions in the Sloan Digitial Sky Survey

Modern galaxy surveys, such as the Sloan Digital Sky Survey (SDSS), provide a wealth of information about large scale structure, galaxy evolution and cosmology. Even if initial density fluctuations were extremely Gaussian, gravitational collapse predicts the growth of non-Gaussianities in the galaxy distribution. Higher order clustering statistics, such as the three-point correlation function (3PCF), are necessary to probe the non-Gaussian structure and shape information in these distributions. We measure the clustering of spectroscopic galaxies in the SDSS Main Galaxy Sample, focusing on the shape or configuration dependence of the 3PCF in redshift and projected space. This work constitutes the largest observational dataset ever used to investigate the 3PCF, and the only known projected measurement for SDSS galaxies. The 3PCF exhibits extreme sensitivity to systematic effects such as sky completeness, binning scheme and insufficient error resolution. We show these systematics can dramatically affect our results, which are not consistently accounted for in comparable analyses. We find significant configuration dependence of the 3PCF on intermediate to large scales (3--27 h -1Mpc), in agreement with predictions from ΛCDM and disagreement with the hierarchical ansatz. Below 6 h-1Mpc, the redshift space 3PCF shows reduced power and weak configuration dependence in comparison with projected measurements. Our results indicate that redshift distortions, and not galaxy bias, can make the 3PCF appear consistent with the hierarchical ansatz. Compared to the lower order 2PCF, the 3PCF shows a weaker dependence on luminosity with no significant dependence on scales above 9 h-1Mpc. On scales less than 9 h-1Mpc, the 3PCF shows a greater dependence on color than on luminosity. We conclude that galaxies remain a biased tracer of the mass with a stronger bias associated with greater luminosity. Using a thorough error analysis in the linear regime (9--27 h -1Mpc), we show bright galaxies (Mr < -21.5) are a biased realization of mass clustering at greater than 4.5sigma in redshift space and 2.5sigma in projected space. The strong degeneracy between linear and quadratic bias terms naturally explains the weak luminosity dependence of the 3PCF. Contrary to some claims, we find linear bias is sufficient to explain galaxy-mass bias of our samples.