Thermal Evolution of the Intergalactic Medium due to Lyα Photons during the Cosmic Dawn

The first star-forming objects that formed at high redshifts during the cosmic dawn (CD) also emitted photons between Ly alpha and Lyman-limit frequencies. These photons are instrumental in coupling the spin temperature of the neutral hydrogen (H i) atoms with the kinetic temperature of the intergalactic medium (IGM). Along with this coupling effect, these photons also impact the kinetic temperature by exchanging energy with the H i atoms. The injected Ly alpha photons in general cool the medium, while the continuum photons heat the medium. While studying this effect in the literature, a quasi-static profile around the Ly alpha frequency is assumed. In this paper, we solve the time-dependent coupled dynamics of the photon intensity profile along with the evolution of the thermal state of the IGM and H i spin temperature. It is expected that, during the CD era, the IGM has a mix of continuum photons with 10%-20% of injected photons. For this case, we show that the system reaches thermal equilibrium in around 1 Myr, with the final temperature in the range 50-100 K. This timescale is comparable to the source lifetime of Population III stars at high redshifts. One impact of switching off short-lived sources is that it can keep the system heated above the temperature of the quasi-static state. We also show that the quasi-static equilibrium for the continuum photons is only achieved on timescales of 100 Myr at z similar or equal to 20, comparable to the age of the Universe. We also briefly discuss how the Ly alpha induced heating can impact the 21 cm signal from CD.