21 cm Signal from the Thermal Evolution of Ly <i>α</i> during Cosmic Dawn

Abstract The Ly α photons couple the spin temperature of neutral hydrogen (H I ) to the kinetic temperature during the era of cosmic dawn (CD). During this process, they also exchange energy with the medium, heating and cooling the H I . In addition, we expect X-ray photons to heat the mostly neutral gas during this era. We solve this coupled system (Ly α –H I system along with X-ray heating) for a period of 500 Myr (redshift range 8 &lt; z &lt; 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 Ly α photons. (b) While X-ray photons provide an additional source of heating at initial times, for large enough Ly α 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 Ly α resonance far exceeds the H I number density. (c) We compute the global H I signal for these scenarios. In the limit of the large density of Ly α photons, the spin temperature of the hyperfine line is fixed. This freezes the global H I signal from the era of CD and the crossover redshift from absorption to emission. This feature depends only on the ratio of injected to continuum Ly α photons, and the global H I signal can help us determine this ratio.