Analytical formalism to study the 21 cm signal from cosmic dawn and epoch of reionization

Abstract

The epoch of cosmic dawn and reionization (CD/EoR) is one of the most important time periods of the history of the universe when the first sources of radiation like stars and galaxies were formed. These sources emitted a wide spectrum of radiation and changed the properties of their surrounding medium. This epoch is not completely understood theoretically and is poorly constrained with observations. 21 cm radiation emitted due to the hyperfine splitting of neutral hydrogen (HI) is one of the most important probes to study the state and dynamics of the neutral medium during this epoch. In this thesis, we present an analytical formalism to study the fluctuating component of the HI signal from the epoch of cosmic dawn and reionization. We use excursion set formalism to calculate the size distribution of randomly distributed self-ionized regions. These ionization bubbles are surrounded by isotropically heated neutral regions. The spin temperature (TS) of HI in these regions might be fully or partially coupled to the kinetic temperature of the medium. We model the ionization, X-ray heating, and Lyman-a coupling using five parameters: efficiency of ionization (z ), number of X-ray photons emitted per stellar baryon (Nheat), the spectral index of X-ray photons (a), minimum frequency of X-ray photons (nmin), and the ratio of source luminosity of Lyman-a to ionizing photon ( fL). We develop a formalism to compute the two-point correlation function for this topology, taking into account the autocorrelation of the ionization field and spin temperature field, and cross-correlation between ionization and spin temperature. Using geometric and probabilistic arguments, we compute the global HI signal, its autocorrelation and power spectrum in the redshift range 10 z 30 for the LCDM model. We check the validity of this formalism for various limits and simplified cases and develop a few toy models to explore the results more intuitively. Our results agree reasonably well with existing results from N-body simulations in spite of following an entirely different approach and requiring orders of magnitude less computational power and time. We further apply our formalism to study the fluctuating component corresponding to the recent EDGES observation that shows an unexpectedly deep absorption trough in global HI signal in the redshift range 15 < z < 19. We show that, generically, this observation predicts larger signal in this redshift range, but smaller signal at higher redshifts. We also explore the possibility of negative real-space auto-correlation of spin temperature in the early universe.