Radiative Transfer Effect on Ultraviolet Pumping of the 21cm Line in the High Redshift Universe

TL;DR

This paper investigates how radiative transfer effects influence the ultraviolet photon scattering rate near sources during reionization, revealing a faster decline with distance and an increased 21cm signal brightness.

Contribution

It introduces a detailed calculation of the photon scattering rate profile including natural broadening, showing significant deviations from previous models.

Findings

Photon scattering rate drops faster than 1/r^2 with distance.

Near the source, the scattering rate scales as r^{-7/3}.

Total Ly_alpha photon scattering rate is higher by ~30% at certain redshifts.

Abstract

During the epoch of reionization the 21cm signal is sensitive to the scattering rate of the ultraviolet photons, redshifting across the Lyman_alpha resonance. Here we calculate the photon scattering rate profile for a single ultraviolet source. After taking into account previously neglected natural broadening of the resonance line, we find that photons approach the resonance frequency and experience most scatterings at a significantly smaller distance from the source than naively expected r=(dnu/nu_0)(c/H), where dnu=nu-nu_0 is the initial frequency offset, and the discrepancy increases as the initial frequency offset decreases. As a consequence, the scattering rate P(r) drops much faster with increasing distance than the previously assumed 1/r^2 profile. Near the source (r<1Mpc comoving), the scattering rate of photons that redshift into the Ly_alpha resonance converges to P(r) \propto r^{-7/3}. The scattering rate of Ly_alpha photons produced by splitting of photons that redshift into a higher resonance (Ly_gamma, Ly_delta, etc.) is only weakly affected by the radiative transfer, while the sum of scattering rates of Ly_alpha photons produced from all higher resonances also converges to P(r) \propto r^{-7/3} near the source. At 15<z<35, on scales of ~0.01-20Mpc/h (comoving), the total scattering rate of Ly_alpha photons from all Lyman resonances is found to be higher by a factor of ~1+0.3[(1+z)/20]^{2/3} than obtained without full radiative transfer. Consequently, during the early stage of reionization, the differential brightness of 21cm signal against the cosmic microwave background is also boosted by a similar factor.