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The Wouthuysen-Field effect in a clumpy intergalactic medium

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Original languageEnglish
Pages (from-to)949-958
Number of pages10
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
Publication statusPublished - 2009


We show that the high optical depth of the intergalactic medium to Lyα photons before the Epoch of Re-ionization results in a negligible magnitude for the Wouthuysen-Field effect produced by a radiation source on its distant surroundings, unless (i) the scattering medium has sufficient time for the impinging resonance line photons to establish a steady-state frequency distribution or (ii) the scattering gas is undergoing internal expansion or has a peculiar motion of tens to hundreds of kms-1 away from the source. Because of the intergalactic attenuation, discrete structures will receive only radiation from a source displaced from the resonance line frequency by typically hundreds to thousands of Doppler widths. The incident radiation must diffuse across the resonance line to produce a substantial scattering rate. 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 of the strength of the Wouthuysen-Field effect by as much as a factor of 106 over the free-streaming (single-scattering) limit. Solutions to the time-dependent diffusion equation, however, show that the time-scales required to establish a steady state will generally exceed the lifetime of the sources, resulting in a substantially reduced scattering rate. In the presence of internal expansion, a steady state may be established as photons are redshifted across the resonance line and into the red wing, and significant enhancement in the scattering rate over the free-streaming limit 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 of the hyperfine structure of hydrogen from the cosmic microwave background is small except in dense regions, and prior to the establishment of any large-scale diffuse radiation field of resonance line photons, the 21-cm 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.

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