The Three-Point Correlation Function for Spin-2 Fields

Abstract

The three-point correlation function (3PCF) of the spin-2 fields, the cosmic shear and cosmic microwave background polarization fields, is a statistical measure of non-Gaussian signals. At each vertex of a triangle, the shear field has two independent components. The resulting eight possible 3PCFs were recently investigated by Schneider & Lombardi (2002) and Zaldarriaga & Scoccimarro (2002). Using rotation and parity transformations they addressed the question: how many non-zero components for the shear 3PCF exist? We address this question using an analytical model and measurements from ray-tracing simulations. We show that all the eight 3PCFs are generally non-zero and have comparable amplitude. These eight 3PCFs can be used to improve the signal-to-noise from survey data and their configuration dependence can be used to separate the contribution from E and B-modes. We estimate the signal-to-noise for measuring the shear 3PCF from weak lensing surveys using simulated maps that include the noise due to intrinsic ellipticities. A deep lensing survey with area exceeding 10 square degrees would allow for the detection of the shear 3PCFs, but a survey area of order 100 square degrees is needed for accurate measurements.