Cosmic Ly$\alpha$ Emission from Diffuse Gas

The Ly$\alpha$ emission has emerged as a powerful tool for probing diffuse gas within the large-scale structure of the universe. In this paper, we investigate cosmic Ly$\alpha$ emission by post-processing cosmological simulations from \texttt{IllustrisTNG} and \texttt{THESAN} project. Specifically, we calculate the Ly$\alpha$ emission from galaxies, circum-galactic medium (CGM) and inter-galactic medium (IGM) across various redshifts. Our results show that IGM alone is significantly under the current observational upper limits. Meanwhile, CGM overshoots the observed galaxy contribution at $z \lesssim 0.5$ indicating that either the escape fraction for the inner CGM is less than unity or the current photoionization equilibrium treatment with an approximate self-shielding prescription is less accurate. The galaxy component also overshoots at low redshift, indicating that the escape fraction has strong evolution caused by an evolving halo mass function and dust growth distribution, that agrees with observationally inferred escape fractions. Furthermore, our findings suggest that the Ly$\alpha$ emission from diffuse gas (CGM+IGM) peaked at $z \sim 4$ and diminishes toward lower redshift. The Ly$\alpha$ emission from diffuse gas mainly originates through the collisional excitation of hot plasma. By comparing models with observation, our predicted Ly$\alpha$ emission from diffuse gas remains $\sim 6$ times fainter than the observed cosmic Ly$\alpha$ emission at $z=1-3$. However, future large telescopes may hold great promise to detect Ly$\alpha$ emission from diffuse gas toward $z>3$.