The Wouthuysen-Field effect in a clumpy intergalactic medium

Abstract

We show that, due to the high optical depth of the intergalactic medium to Lyman-alpha photons before the Epoch of Reionization, the Lyman-alpha scattering rate responsible for the Wouthuysen-Field effect from an isolated source will be negligible unless (1) there is sufficient time for the scattering photons to establish a steady state, or (2) the scattering gas is undergoing internal expansion or has a peculiar motion of tens to hundreds of km/s away from the source. We present steady-state solutions in the radiative diffusion approximation for the radiation field trapped in a clump of gas and show that this may result in an enhancement, by a factor of up to 10^6, of the strength of the Wouthuysen-Field effect over that obtained from the free-streaming limit. Solutions to the time-dependent diffusion equation, however, suggest that the timescales required to reach such a steady state will generally exceed the source lifetimes. In the presence of internal expansion, a steady state may be established as photons are redshifted into the red wing, and significant enhancement in the scattering rate may again be produced. Alternatively, a substantial scattering rate may arise in systems with a peculiar motion away from the source that redshifts the received radiation into the resonance line centre. As a consequence, at epochs z<30, when collisional decoupling is small except in dense regions, and prior to the establishment of any large-scale diffuse radiation field of resonance line photons, the 21cm signature from the Intergalactic Medium produced by the Wouthuysen-Field effect will in general trace the peculiar velocity field of the gas in addition to its density structure.

11 pages, 7 figures. Accepted for publication in MNRAS

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• Constraining the unexplored period between reionization and the dark ages with observations of the global 21 cm signal
• Lyman-$\alpha$ coupling and heating at Cosmic Dawn
• The scattering of LyA radiation in the intergalactic medium: numerical methods and solutions
• The impact of Lyman-$\alpha$ emission line heating and cooling on the cosmic dawn 21-cm signal
• Time-Dependent Behavior of Lyman$\alpha$ Photon Transfer in High Redshift Optically Thick Medium
• Lyman-alpha Heating of Inhomogeneous High-redshift Intergalactic Medium
• Infra-red emission line tomography of the intergalactic medium during the Epoch of Reionization