Extracting the Optical Depth to Reionization τ from 21 cm Data Using Machine Learning Techniques

Abstract Upcoming measurements of the high-redshift 21 cm signal from the Epoch of Reionization (EoR) are a promising probe of the astrophysics of the first galaxies and of cosmological parameters. In particular, the optical depth τ to the last scattering surface of the cosmic microwave background (CMB) should be tightly constrained by direct measurements of the neutral hydrogen state at high redshift. A robust measurement of τ from 21 cm data would help eliminate it as a nuisance parameter from CMB estimates of cosmological parameters. Previous proposals for extracting τ from future 21 cm data sets have typically used the 21 cm power spectra generated by semi-numerical models to reconstruct the reionization history. We present here a different approach which uses convolution neural networks (CNNs) trained on mock images of the 21 cm EoR signal to extract τ. We construct a CNN that improves upon on previously proposed architectures, and perform an automated hyperparameter optimization. We show that well-trained CNNs are able to accurately predict τ, even when removing Fourier modes that are expected to be corrupted by bright foreground contamination of the 21 cm signal. Typical random errors for an optimized network are less than 3.06%, with biases factors of several smaller. While preliminary, this approach could yield constraints on τ that improve upon sample-variance limited measurements of the low-ℓ EE observations of the CMB, making this approach a valuable complement to more traditional methods of inferring τ.