Non-local bias contribution to third-order galaxy correlations

Abstract

We study halo clustering bias with second- and third-order statistics of halo and matter density fields in the MICE Grand Challenge simulation. We verify that two-point correlations deliver reliable estimates of the linear bias parameters at large scales, while estimations from the variance can be significantly affected by non-linear and possibly non-local contributions to the bias function. Combining three-point auto- and cross-correlations we find, for the first time in configuration space, evidence for the presence of such non-local contributions. These contributions are consistent with predicted second-order non-local effects on the bias functions originating from the dark matter tidal field. Samples of massive haloes show indications of bias (local or non-local) beyond second order. Ignoring non-local bias causes $20-30$\% and $5-10$\% overestimation of the linear bias from three-point auto- and cross-correlations respectively. We study two third-order bias estimators which are not affected by second-order non-local contributions. One is a combination of three-point auto- and cross- correlation. The other is a combination of third-order one- and two-point cumulants. Both methods deliver accurate bias estimations of the linear bias. Furthermore their estimations of second-order bias agree mutually. Ignoring non-local bias causes higher values of the second-order bias from three-point correlations. Our results demonstrate that third-order statistics can be employed for breaking the growth-bias degeneracy.