21 cm Signal from the Thermal Evolution of Lyman-$\alpha$ during Cosmic Dawn

TL;DR

This paper models the thermal evolution of neutral hydrogen during cosmic dawn by solving coupled Lyman-$eta$-HI and X-ray heating systems, revealing how photon intensities influence temperature and the observable 21 cm signal.

Contribution

It introduces a comprehensive model of Lyman-$eta$ and X-ray heating effects on hydrogen during cosmic dawn, highlighting the conditions for temperature equilibrium and signal features.

Findings

Temperature reaches a quasi-static state independent of photon intensity.

High Lyman-$eta$ photon density dominates the temperature evolution.

Global HI signal is frozen in the large photon density limit.

Abstract

The Lyman-$\alpha$ photons couple the spin temperature of neutral hydrogen (HI) to the kinetic temperature during the era of cosmic dawn. During this process, they also exchange energy with the medium, heating and cooling the HI. In addition, we expect X-ray photons to heat the mostly neutral gas during this era. We solve this coupled system (Lyman-$\alpha$-HI system along with X-ray heating) for a period of 500 Myr (redshift range $8 <z < 25$). Our main results are: (a) Without X-ray heating, the temperature of the gas reaches an equilibrium which is nearly independent of photon intensity and only weakly dependent on the expansion of the universe. The main determinant of the quasi-static temperature is the ratio of injected and continuum Lyman-$\alpha$ photons. (b) While X-ray photons provide an additional source of heating at initial times, for large enough Lyman-$\alpha$ photon intensity, the system tends to reach the same quasi-static temperature as expected without additional heating. This limit is reached when the density of photons close to the Lyman-$\alpha$ resonance far exceeds the HI number density. (c) We compute the global HI signal for these scenarios. In the limit of the large density of Lyman-$\alpha$ photons, the spin temperature of the hyperfine line is fixed. This freezes the global HI signal from the era of cosmic dawn and the cross-over redshift from absorption to emission. This feature depends only on the ratio of injected to continuum Lyman-$\alpha$ photons, and the global HI signal can help us determine this ratio.