This paper presents theoretical models of H I Lyα emission from the extended solar corona, taking into account various plasma kinetic effects that induce departures from Maxwellian velocity distributions. Such phenomena as suprathermal tails, strong temperature anisotropies, and skewed or double-peaked distributions have been observed in the solar wind, and UV spectroscopy is beginning to be able to detect their signatures in the corona. For resonantly scattered lines like H I Lyα, most of the physics is contained in the frequency-dependent redistribution function. The dependence of this function on the local plasma parameters is presented analytically for four different non-Maxwellian distributions, and optically thin line intensities are computed for a representative model of the fast solar wind. Isotropic power-law "κ" tails in the velocity distribution should be detectable between 2 and 5 ? from line center. Although existing observations that appear to have broad tails do not resemble those arising from κ-distributions, their presence is still possible. Anisotropic bi-Maxwellian distributions affect line profile shapes and total intensities via both their parallel and perpendicular components, and it is important to include an accurate description of the photon redistribution for large anisotropies. Skewness caused by a Chapman-Enskog expansion in the conductive heat flux is detectable as a unique non-Gaussian profile shape, but other types of collisionally beamed or skewed distributions may not noticeably affect the emission lines.
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