Analysing the Epoch of Reionization with three-point correlation functions and machine learning techniques

Abstract

Three-point and high-order clustering statistics of the high-redshift 21cm signal contain valuable information about the Epoch of Reionization. We present 3PCF-Fast, an optimised code for estimating the three-point correlation function of 3D pixelised data such as the outputs from numerical and semi-numerical simulations. After testing 3PCF-Fast on data with known analytic three-point correlation function, we use machine learning techniques to recover the mean bubble size and global ionisation fraction from correlations in the outputs of the publicly available 21cmFAST code. We assume that foregrounds have been perfectly removed and negligible instrumental noise. Using ionisation fraction data, our best MLP model recovers the mean bubble size with a median prediction error of around 10%, or from the 21cm differential brightness temperature with median prediction error of around 14%. A further two MLP models recover the global ionisation fraction with median prediction errors of around 4% (using ionisation fraction data) or around 16% (using brightness temperature). Our results indicate that clustering in both the ionisation fraction field and the brightness temperature field encode useful information about the progress of the Epoch of Reionization in a complementary way to other summary statistics. Using clustering would be particularly useful in regimes where high signal-to-noise ratio prevents direct measurement of bubble size statistics. We compare the quality of MLP models using the power spectrum, and find that using the three-point correlation function outperforms the power spectrum at predicting both global ionisation fraction and mean bubble size.