Three-Point Statistics from a New Perspective

Abstract

The multipole expansion of spatial three-point statistics is introduced as a tool for investigating and displaying configuration dependence. The novel parameterization renders the relation between bispectrum and three-point correlation function especially transparent as a set of two-dimensional Hankel transforms. It is expected on theoretical grounds that three-point statistics can be described accurately with only a few multipoles. In particular, we show that in the weakly nonlinear regime, the multipoles of the reduced bispectrum, Ql, are significant only up to quadrupole. Moreover, the nonlinear bias in the weakly nonlinear regime only affects the monopole order of these statistics. As a consequence, a simple, novel set of estimators can be constructed to constrain galaxy bias. In addition, the quadrupole to dipole ratio is independent of the bias; thus, it becomes a novel diagnostic of the underlying theoretical assumptions: weakly nonlinear gravity and perturbative local bias. To illustrate the use of our approach, we present predictions based on both power-law and cold dark matter models. We show that the presently favored Sloan Digital Sky Survey/Wilkinson Microwave Anisotropy Probe concordance model displays strong baryon bumps in the Ql's. Finally, we sketch out three practical techniques to estimate these novel quantities: they amount to new, and for the first time edge-corrected, estimators for the bispectrum.