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

Abstract

ABSTRACT Three-point and high-order clustering statistics of the high-redshift 21 cm signal contain valuable information about the Epoch of Reionization (EoR). We present 3PCF-fast, an optimized code for estimating the three-point correlation function (3PCF) of 3D pixelized data such as the outputs from numerical and seminumerical simulations. After testing 3PCF-fast on data with known analytical 3PCF, we use machine learning techniques to recover the mean bubble size and global ionization 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 ionization fraction data, our best multilayer perceptron (MLP) model recovers the mean bubble size with a median prediction error of around $10 {{\ \rm per\ cent}}$, or from the 21 cm differential brightness temperature with median prediction error of around $14 {{\ \rm per\ cent}}$. A further two MLP models recover the global ionization fraction with median prediction errors of around $4 {{\ \rm per\ cent}}$ (using ionization fraction data) or around $16 {{\ \rm per\ cent}}$ (using brightness temperature). Our results indicate that clustering in both the ionization fraction field and the brightness temperature field encode useful information about the progress of the EoR 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 3PCF outperforms the power spectrum at predicting both global ionization fraction and mean bubble size.