Analytical Formalism to Study the 21 cm Signal from Cosmic Dawn and Epoch of Reionization

Abstract

The epoch of Cosmic Dawn and Reionization is one of the most important time periods of the universe when first sources of radiation like stars and galaxies were formed, and they changed the properties of their surrounding medium. 21 cm radiation emitted due to the hyperfine splitting of ground state of neutral hydrogen is one of the most important probes to study the state and dynamics of neutral medium during this epoch. I present an analytical formalism to compute the fluctuating component of the 21 cm signal from CD/EoR. I have used excursion set formalism to calculate the size distribution of randomly distributed selfionized regions, and calculate the isotropic spin temperature profiles around them, taking into account the effect of X‐rays and Ly‐alpha photons. I present an analytical formalism to compute the two‐point correlation function for this topology, where small ionization bubbles are surrounded by large and shallow spin temperature profiles, which can overlap with one another and merge with a background value far away from any source. Using geometric and probabilistic arguments, I compute the global 21 cm signal, its auto‐correlation and power spectrum in the redshift range 10 < z < 30. Our results from this analytical formalism agree reasonably well with existing results in the literature from N‐body simulations