The Wouthuysen-Field effect in a clumpy intergalactic medium

TL;DR

This paper investigates how the Wouthuysen-Field effect in a clumpy intergalactic medium is influenced by optical depth, gas motion, and steady-state conditions, revealing potential enhancements or delays in the effect's strength before reionization.

Contribution

It provides new steady-state and time-dependent diffusion solutions showing conditions for significant Wouthuysen-Field effect enhancement in a clumpy IGM.

Findings

Steady-state solutions can enhance the effect by up to 10^6 times.

Timescales to reach steady state often exceed source lifetimes.

Peculiar velocities can induce significant scattering rates.

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.