Signatures of cosmic reionization on the 21-cm two- and three-point correlation function I: quadratic bias modelling

Abstract

The three-point correlation function (3PCF) of the 21cm brightness temperature from the Epoch of Reionization (EoR) probes complementary information to the commonly studied two-point correlation function (2PCF) about the morphology of ionized regions. We investigate the 21cm 2PCF and 3PCF in configuration space using semi-numerical simulations and test whether they can be described by the local quadratic bias model. We find that fits of bias model predictions for the 2PCF and 3PCF deviate from our measurements by $\sim 20\%$ at scales above the typical size of ionized regions ($\simeq 30$ Mpc) and at early times with global neutral fractions of $\langle x_{\rm HI} \rangle \gtrsim 0.7$. At later times and smaller scales these deviations increase strongly, indicating a break down of the bias model. The 2PCF and 3PCF fits of the linear bias parameter agree at the $10\%$ level for different EoR model configurations. This agreement holds, when adding redshift space distortions to the simulations. The relation between spatial fluctuations in the matter density and the 21cm signal, as predicted by the bias model, is consistent with direct measurements of this relation in simulations for large smoothing scales ($\gtrsim 30$ Mpc). From this latter test we conclude that negative amplitudes of the 21cm 3PCF result from negative bias parameters, which describe the anti-correlation between the matter over-densities and the 21cm signal during the EoR. However, a more detailed interpretation of the bias parameters may require a description of non-local contributions to the bias model.