The Spin–Kinetic Temperature Coupling and the Heating Rate due to Lyα Scattering before Reionization: Predictions for 21 Centimeter Emission and Absorption

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Abstract
We investigate the interaction of Lyman alpha photons produced by the first stars in the universe with the intergalactic medium (IGM) prior to reionization. The background Lyman alpha spectral profile is obtained by solving a Fokker-Planck equation. Accurate values of the heating and scattering rates, and the spin-kinetic temperature coupling coefficient, are presented. We show that the heating rate induced by the Lyman alpha scatterings is much lower than found previously, and is basically negligible. The dominant heating source is most likely the X-rays from the first ionizing sources, which are able to penetrate into the atomic medium. The scattering of Lyman alpha photons couples the hydrogen spin temperature to the kinetic temperature. If the first ionizing sources in the universe did not emit significant X-rays, the spin temperature would be rapidly brought down to the very low gas kinetic temperature, and a 21cm absorption signal against the CMB larger than 100 mK would be predicted. However, we argue that sufficient X-rays are likely to have been emitted by the first stellar population, implying that the gas kinetic temperature should rapidly increase, turning a reduced and brief absorption signal into emission, with a smaller amplitude of about 10 mK. The detection of the 21cm absorption and emission feature would be a hallmark in unravelling the history of the ``dark age'' before reionization.Comment: AASTEX 5.02, 23 pages with 8 figures, submitted to ApJ. Our code for solving the Lyman alpha line profile and calculating the scattering and heating rates can be downloaded from http://theory.itp.ucsb.edu/~xuelei/LAST/index.html replaced with revised version, added more discussion on the physical process of heating and coolin