Molecular hydrogen in the cosmic recombination epoch

Abstract

The advent of precise measurements of the CMB anisotropies has motivated correspondingly precise calculations of the cosmic recombination history. Cosmic recombination proceeds far out of equilibrium because of a “bottleneck” at the n=2 level of hydrogen: atoms can only reach the ground state via slow processes—two-photon decay or Lyman-α resonance escape. However, even a small primordial abundance of molecules could have a large effect on the interline opacity in the recombination epoch and lead to an additional route for hydrogen recombination. Therefore, this paper computes the abundance of the H_2 molecule during the cosmic recombination epoch. Hydrogen molecules in the ground electronic levels X^1Σ_g+ can either form from the excited H_2 electronic levels B^1Σ_u^+ and C^1Π_u or through the charged particles H_2^+, HeH^+, and H^-. We follow the transitions among all of these species, resolving the rotational and vibrational sublevels. Since the energies of the X^1Σ_g^+-B^1Σ_u^+ (Lyman band) and X^1Σ_g^+-C^1Π_u (Werner band) transitions are near the Lyman-α energy, the distortion of the CMB spectrum caused by escaped H Lyman-line photons accelerates both the formation and the destruction of H_2 due to this channel relative to the thermal rates. This causes the populations of H_2 molecules in X^1Σ_g^+ energy levels to deviate from their thermal equilibrium abundances. We find that the resulting H_2 abundance is 10^(-17) at z=1200 and 10^(-13) at z=800, which is too small to have any significant influence on the recombination history.