Analytic Formulation of 21 cm Signal from Cosmic Dawn: Lyα Fluctuations

Abstract

We present an analytic formalism to compute the fluctuating component of the H i signal and extend it to take into account the effects of partial Ly α coupling during the era of cosmic dawn. We use excursion set formalism to calculate the size distribution of randomly distributed self-ionized regions. These ionization bubbles are surrounded by partially heated and Ly α coupled regions, which create spin temperature T S fluctuations. We use the ratio of number of Ly α to ionizing photons ( f L ) and number of X-ray photons emitted per stellar baryon ( N heat ) as modeling parameters. Using our formalism, we compute the global H i signal, its autocorrelation, and its power spectrum in the redshift range 10 ≤  z  ≤ 30 for the ΛCDM model. We check the validity of this formalism for various limits and simplified cases. Our results agree reasonably well with existing results from N -body simulations, in spite of following a different approach and requiring orders of magnitude less computation power and time. We further apply our formalism to study the fluctuating component corresponding to the recent observation by the Experiment to Detect the Global Epoch of reionization Signature (EDGES) that shows an unexpectedly deep absorption trough in the global H i signal in the redshift range 15 <  z  < 19. We show that, generically, the EDGES observation predicts a larger signal in this redshift range but a smaller signal at higher redshifts. We also explore the possibility of negative real-space autocorrelation of spin temperature and show that it can be achieved for partial Ly α coupling in many cases corresponding to simplified models and a complete model without density perturbations.