Recombination Lines and Free-Free Continua formed in Asymptotic Ionized Winds: Analytic solution for the radiative transfer

TL;DR

This paper extends an analytic model of radiative transfer in dense, ionized stellar winds to include line blends and clumping effects, providing insights into emission line profiles and continua in hot star winds.

Contribution

It develops an extended analytic solution for radiative transfer in ionized winds, incorporating radius-dependent clumping and line blends, which was not previously available.

Findings

Line widths and equivalent widths depend on clumping steepness.

The model successfully fits Spitzer/IRS spectra of WR 90.

Clumping influences emission line profiles and continuum shapes.

Abstract

In dense hot star winds, the infrared and radio continua are dominated by free-free opacity and recombination emission line spectra. In the case of a spherically symmetric outflow that is isothermal and expanding at constant radial speed, the radiative transfer for the continuum emission from a dense wind is analytic. Even the emission profile shape for a recombination line can be derived. Key to these derivations is that the opacity scales with only the square of the density. These results are well-known. Here an extension of the derivation is developed that also allows for line blends and the inclusion of an additional power-law dependence beyond just the density dependence. The additional power-law is promoted as a representation of a radius dependent clumping factor. It is shown that differences in the line widths and equivalent widths of the emission lines depend on the steepness of the clumping power-law. Assuming relative level populations in LTE in the upper levels of He {\sc ii}, an illustrative application of the model to {\em Spitzer}/IRS spectral data of the carbon-rich star WR 90 is given.