Signatures of Cosmic Reionization on the 21cm 2- and 3-point Correlation Function I: Quadratic Bias Modeling

Constraints on reionization models from future 21cm observations will rely on the statistical characterization of the spatial fluctuations in the observed 21cm brightness temperature. Three-point correlation functions (3PCF) of this 21cm signal probe information about the shape of ionized regions and can therefore improve constraints on reionization model from the power spectrum which is not sensitive to such shape information. We study the 21cm two-point correlation functions (2PCF) and 3PCF in configuration space, using semi-numerical simulations. These measurements are compared to leading order predictions from the local quadratic bias model, which is commonly used for modeling the galaxy 3PCF. Fits of the bias model predictions to the 2PCF and 3PCF measurements show an $\simeq 20\%$ accuracy for scales above the typical size of of ionizes regions ($\simeq 30$ Mpc) and at early times for global neutral fractions of $\langle x_{\rm HI} \rangle\gtrsim 0.7$, while deviations between the predictions and measurements increase strongly for smaller scales and later reionization stages. In the regime in which the bias model performs well, the 2PCF and 3PCF fits of the linear bias parameter agree at the $10\%$ level. The relation between fluctuations in the matter density and the 21cm signal, as predicted by the bias model, is consistent with simulations for large smoothing scales. Our results suggest that measurements of the 3PCF in upcoming radio observations can constrain astrophysical processes driving the reionization. Combining the 21cm 2PCF and 3PCF can further break the degeneracy between the linear growth function of matter fluctuations and the reionization bias parameters, and hence constrain cosmological models during the epoch of reionization.