Effect of radiative feedbacks for resonant transitions during cosmological recombination

Abstract

The inhibition of the total HI $n\ensuremath{\leftrightarrow}1$ transition rate by delayed resonant reabsorption of HI $(n+1)\ensuremath{\rightarrow}1$ photons by HI $n\ensuremath{\rightarrow}1$ line which is possible due to cosmological redshift is considered semianalytically. The method taking into account this effect in the frame of simple three-level approximation model of recombination is suggested. It is confirmed that the resonant feedbacks affect ionization fraction at the level about 0.2% for the epoch of last scattering. Similar consideration of $\mathrm{HeI}\text{ }\text{ }2^{1}P\ensuremath{\leftrightarrow}1^{1}S\ensuremath{\Rightarrow}\mathrm{HeI}\text{ }\text{ }2^{3}P\ensuremath{\leftrightarrow}1^{1}S$ feedback for helium is provided. It is confirmed that allowance of this feedback leads to an increase of predicted free electron fraction by 0.12% at $z\ensuremath{\simeq}2300$. It is shown that taking into account absorption and thermalization of HeI $2^{1}P\ensuremath{\leftrightarrow}1^{1}S$ resonant superequilibrium photons (during their redshifting to the HeI $2^{3}P\ensuremath{\leftrightarrow}1^{1}S$ frequency) by a small amount of neutral hydrogen (${10}^{\ensuremath{-}7}--{10}^{\ensuremath{-}4}$ of total number of hydrogen atoms and ions) existing in the helium recombination epoch is important for correct consideration of this helium feedback.