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.Comment: 11 pages, 7 figures. Accepted for publication in MNRA

The impact of Lyman series photons on the intergalactic medium during the Epoch of Reionization

“…The differential proper line element evolves according to d l p /d z = c /[ H ( z )(1 + z )]≃ ( c / H 0 )Ω −1/2 m (1 + z ) −5/2 in a flat universe at redshifts for which Ω m (1 + z ) 3 dominates the contribution from the vacuum energy, where H ( z ) is the Hubble parameter at redshift z . In the limit of scattering in the blue wing, the optical depth along the path of a photon emitted at frequency x e from a source at redshift z s and received at frequency x (provided it has not passed through any resonance line centre en route) is given at large separations by (Furlanetto & Pritchard 2006; Higgins & Meiksin 2009), where λ lu is the wavelength of the resonance transition.…”

“…The source function describing the injection of Lyman series photons following the initial scattering of continuum photons by the IGM is given by (Higgins & Meiksin 2009), where n inc, n ν is the specific number density of incident continuum photons near the resonance line frequency ν n and R n (ν′, ν) is the frequency redistribution function for the scattered photons. The incident photon number density near Ly‐ n is given by n inc, n ν = (4π/ c ) L ν exp(−τ ν )/[(4π r L ) 2 h ν] for a source of specific luminosity L ν and at a luminosity distance from the source r L .…”

“…Multiplying by the number of scatters gives for the scattering rate per hydrogen atom P direct α = n inc,α ν (0) c σ α since ( a α /π)(τ α / x 1 ) = 1. Thus, the scattering rate is simply given by the scattering rate of the incident photons assuming no scattering losses en route (Field 1959a; Madau et al 1997; Higgins & Meiksin 2009).…”

“…The direct Ly‐ n scattering rate is given by integrating n direct, n ν over the Ly‐ n cross‐section. Noting that , the integrals in contract, resulting in the direct scattering rate where is the scattering rate for an optically thin IGM, and describes the scattering suppression factor due to the scattering out of source photons by the intervening IGM out to the distance r L (Dijkstra et al 2008; Higgins & Meiksin 2009). Values of are tabulated in Table 2 for some typical situations.…”

“…It is emphasized that radiative transfer effects for Lyα photons involving spatial diffusion, which may enhance the density of Lyα photons near a source (Loeb & Rybicki 1999; Chuzhoy & Zheng 2007; Semelin, Combes & Baek 2007), or recoils, which may suppress the density near line centre and so reduce the scattering rate (Chen & Miralda‐Escudé 2004; Higgins & Meiksin 2009) have not been included. It is presumed that the Lyα photons produced in cascades will be subject to the same radiative transfer processes as the directly incident photons so that the enhancements here reflect the fractional increase due to cascades alone.…”