Three-Point Statistics from a New Perspective

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, Q_l, 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 Q_l'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.