Asymptotic expansions of the kernel functions for line formation with continuous absorption

Abstract

Asymptotic expressions are obtained for the kernel functions M̃ 2(τ, α, β) and K̃ 2(τ, α, β) appearing in the theory of line formation with complete redistribution over a Voigt profile with damping parameter α, in the presence of a source of continuous opacity parameterized by β. For α > 0, each coefficient in the asymptotic series is expressed as the product of analytic functions of α and η ≡ βτ separately. For Doppler broadening, only the leading term can be evaluated analytically.