Deep learning the intergalactic medium using Lyman-alpha forest at 4 ≤ z ≤ 5

ABSTRACT Unveiling the thermal history of the intergalactic medium (IGM) at $4 \le z \le 5$ holds the potential to reveal early onset He ii reionization or lingering thermal fluctuations from H i reionization. We set out to reconstruct the IGM gas properties along simulated Lyman-alpha (Lyα) forest data on pixel-by-pixel basis, employing deep 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 predict the Ly$\rm {\alpha }$ optical depth-weighted density or temperature for each pixel in the Ly$\rm {\alpha }$ forest skewer. We find that our network can successfully reproduce IGM conditions with high fidelity across range of instrumental signal-to-noise ratio. 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, $T_{\rm 0}$, with 1σ confidence, $\delta {T_{\rm 0}} \lesssim 1000 \ {\rm K}$, using only one $20 \ h^{-1} \, {\rm cMpc}$ sightline ($\Delta z\simeq 0.04$) with a typical reionization history. Existing studies utilize redshift path-length comparable to $\Delta z\simeq 4$ for similar constraints. We can also provide more stringent constraints on the slope ($1\sigma$ confidence interval, $\delta {\rm \gamma } \lesssim 0.1$) 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 ($20 \ h^{-1}\,{\rm cMpc}$ 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.