Local burst model of CMB temperature fluctuations: Scattering in the resonance lines of primordial hydrogen and helium

Abstract

The propagation of an instantaneous burst of isotropic radiation from the time of its onset at some redshift z ₀ to the time of its detection at the present epoch (at z = 0) is considered within the framework of a flat Universe. The Thomson scattering by free electrons and the scattering in the primordial hydrogen Lα and Lβ lines and in the He I 1s2–1s2p, 1s3p (¹S–¹P*) lines are taken into account. It is shown that the relative amplitude of the spectral distortions due to the scattering in these lines at the corresponding frequencies can be a factor of 10³−10⁴ greater than the maximum possible amplitude from the scattering in the subordinate hydrogen lines considered previously (Dubrovich and Grachev 2015). In the linear approximation in optical depth, the distortion profiles in the resonance lines turn out to be purely absorption ones and depend neither on the direction nor on the distance to the burst center, in contrast to the profiles in the subordinate lines. The profiles contain jumps at frequencies corresponding to the instant the source (burst) appears at a given redshift z ₀. For example, at z ₀ = 5000 the jumps in the hydrogen Lα and Lβ lines lie at frequencies of 493 and 584 GHz, respectively, while in the above two helium lines they lie at frequencies of 855 and 930 GHz at z ₀ = 6000. The relative magnitude of the jumps ranges from 10−4 to 3 × 10−3.