The KramersHeisenberg Formula and the GunnPeterson Trough from the First Objects in the Universe
Abstract
Recent cosmological observations indicate that the reionized universe may have started at around z=6, where a significant suppression around Ly alpha has been observed from the neutral intergalactic medium. The associated neutral hydrogen column density is expected to exceed 10^{21}cm^{2}},where it is very important to use the accurate scattering cross section known as the KramersHeisenberg formula that is obtained from the fully quantum mechanical timedependent second order perturbation theory. We present the KramersHeisenberg formula and compare it with the formula introduced in a heuristic way by Peebles (1993) treating the hydrogen atom as a twolevel atom, from which we find a devitaion by a factor of two in the red wing region far from the line center. Adopting simple cosmological models, we compute the GunnPeterson optical depths and the trough profiles. Our results are compared with the works performed by Madau & Rees (2000), who adopted the cross section introduced by Peebles. We find deviations up to 5 per cent in the GunnPeterson transmission coefficient for an accelerated expanding universe in the red offresonance wing part with the rest wavelength Delta_lambda~10{AA}.
 Publication:

arXiv eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:astroph/0110234
 Bibcode:
 2001astro.ph.10234B
 Keywords:

 Astrophysics
 EPrint:
 3 pages, 2 figures