Identifier: 2008-25
Author(s): I. Roy, W. Xu, J.-M. Qiu , C.-W. Shu, and L.-Z. Fang
Title: Time evolution of Wouthuysen-Field coupling
Page count: 21 pp.
Date: 2008-01-01
Abstract:
We study the Wouthuysen-Field coupling at early universe with numerical solutions of the integrodifferential equation describing the kinetics of photons undergoing resonant scattering. The numerical solver is developed based on the weighted essentially non-oscillatory (WENO) scheme for the Boltzmann-like in- tegrodifferential equation. This method has perfectly passed the tests of analytic solution and conservation property of the resonant scattering equation. We focus on the time evolution of the Wouthuysen-Field (W-F) coupling in relation to the 21 cm emission and absorption at the epoch of reionization. We especially pay attention to the formation of the local Boltzmann distribution, e−(ν −ν0 )/kT , of photon frequency spectrum around resonant frequency ν0 within width νl , i.e. |ν − ν0 | ≤ νl . We show that a local Boltzmann distribution will be formed if photons with frequency ∼ ν0 have undergone a thousand or more times of scattering, which corresponds to the order of 102 yrs for neutral hydrogen den- sity of the concordance ΛCDM model. The time evolution of the shape and width of the local Boltzmann distribution actually is independent of the details of atomic recoil, photon sources, or initial conditions. However, the intensity of photon flux at the local Boltzmann distribution is substantially time-dependent. The time scale of approaching the saturated intensity can be as long as about 105 yrs for typical parameters of the ΛCDM model. The intensity of the local Boltzmann distribution at time less than 105 yrs is significantly lower than that of the saturation state. Therefore, it may not be always reasonable to assume that the deviation of the spin temperature of 21 cm energy states from cosmic background temperature is mainly due to the W-F coupling if first stars or their emission/absorption regions evolved with a time scale equal to or less than Myrs.
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