Deep Learning the Intergalactic Medium using Lyman-alpha Forest at 4 ≤ z ≤ 5

Unveiling the thermal history of the intergalactic medium (IGM) at 4 ≤ z ≤ 5 holds the potential to reveal early onset HeII reionization or lingering thermal fluctuations from HI reionization. We set out to reconstruct the IGM gas properties along simulated Lyman-alpha forest data on pixel-by-pixel basis, employing deep Bayesian neural networks. Our approach leverages the Sherwood-Relics simulation suite, consisting of diverse thermal histories, to generate mock spectra. Our convolutional and residual networks with likelihood metric predicts the Lyα optical depth-weighted density or temperature for each pixel in the Lyα forest skewer. We find that our network can successfully reproduce IGM conditions with high fidelity across range of instrumental signal-to-noise. These predictions are subsequently translated into the temperature-density plane, facilitating the derivation of reliable constraints on thermal parameters. This allows us to estimate temperature at mean cosmic density, T_ 0 with one sigma confidence δ T_ 0∼ 1000 K using only one 20Mpc/h sightline (Δ z≃ 0.04) with a typical reionization history. Existing studies utilize redshift pathlength comparable to Δ z≃ 4 for similar constraints. We can also provide more stringent constraints on the slope (1σ confidence interval δγ≲ 0.1) of the IGM temperature-density relation as compared to other traditional approaches. We test the reconstruction on a single high signal-to-noise observed spectrum (20 Mpc/h segment), and recover thermal parameters consistent with current measurements. This machine learning approach has the potential to provide accurate yet robust measurements of IGM thermal history at the redshifts in question.