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The Spin-Resolved Atomic Velocity Distribution and 21-cm Line Profile of Dark-Age Gas

Christopher M. Hirata·Kris Sigurdson
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Abstract

The 21-cm hyperfine line of atomic hydrogen (HI) is a promising probe of the cosmic dark ages. In past treatments of 21-cm radiation it was assumed the hyperfine level populations of HI could be characterized by a velocity-independent ``spin temperature'' T_s determined by a competition between 21-cm radiative transitions, spin-changing collisions, and (at lower redshifts) Lyman-alpha scattering. However we show here that, if the collisional time is comparable to the radiative time, the spin temperature will depend on atomic velocity, T_s=T_s(v), and one must replace the usual hyperfine level rate equations with a Boltzmann equation describing the spin and velocity dependence of the HI distribution function. We construct here the Boltzmann equation relevant to the cosmic dark ages and solve it using a basis-function method. Accounting for the actual spin-resolved atomic velocity distribution results in up to a 2 per cent suppression of the 21-cm emissivity, and a redshift and angular-projection dependent suppression or enhancement of the linear power spectrum of 21-cm fluctuations of up to 5 per cent. The effect on the 21-cm line profile is more dramatic -- its full-width at half maximum (FWHM) can be enhanced by up to 60 per cent relative to the velocity-independent calculation. We discuss the implications for 21-cm tomography of the dark ages.

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Christopher M. Hirata, Kris Sigurdson. 2006-05-02. The Spin-Resolved Atomic Velocity Distribution and 21-cm Line Profile of Dark-Age Gas. https://doi.org/10.1111/j.1365-2966.2006.11321.x

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