Projected Three‐Point Correlation Functions and Galaxy Bias

Abstract

The three-point correlation function (3PCF) can now be measured in large galaxy redshift surveys, but in three dimensions its interpretation is complicated by the presence of redshift-space distortions. I investigate the projected 3PCF, where these distortions are eliminated by integrating over the redshift dimension, as is commonly done for the two-point correlation function. The calculation of the projected 3PCF from the real-space, three-dimensional bispectrum is greatly simplified by expanding both quantities in Fourier components, analogous to Szapudi's expansion of the three-dimensional quantities in multipole components. In the weakly nonlinear regime, the bispectrum can be well represented by the first few Fourier components. There is a well-known relation between the reduced 3PCFs of matter and galaxies in the weakly nonlinear regime, which can be used to infer galaxy bias factors if the real-space three-dimensional galaxy correlation functions (two-point and three-point) can be measured. I show that the same relation holds for the reduced projected 3PCFs if these are properly defined. These results should aid determinations of galaxy bias from large redshift surveys by eliminating the complication of redshift-space distortions.