Local burst model of CMB temperature fluctuations: scattering in primordial hydrogen lines

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. Thomson scattering by free electrons and scattering in primordial hydrogen lines (H α , H β , P α , and P β ) are believed to be the sources of opacity, with the single-scattering albedo in the lines being calculated by taking into account the deexcitation of the upper levels of the transitions being considered under the action of background blackbody radiation. The profiles of these lines in the burst spectrum at the present epoch have been constructed for various z0 at various distances from the burst center. To a first approximation, these profiles do not depend on the burst radiation spectrum and intensity. It is shown that the lines are purely absorption ones at a sufficiently large distance, but an emission component can appear with decreasing distance, which strengthens as the distance decreases, while the absorption component weakens. The absorption depth in the combined profile can reach 2 ×10 −4 for the H α and H β lines and 7 × 10 −6 for the P α and P β lines. In this case, the relative amplitude of the temperature fluctuations lies within the range 10 −7 −10 −9 . The calculations have been performed for bursts with different characteristic initial sizes. At the same z 0 , the hydrogen line profiles essentially coincide for sizes smaller than some value, and the contrast of the lines decreases with increasing burst size for greater ones.