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

<div class="line" id="line-5"> In dense hot star winds, the infrared and radio continua are dominated by free&hyphen;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&hyphen;known. Here an extension of the derivation is developed that also allows for line blends and the inclusion of an additional power&hyphen;law dependence beyond just the density dependence. The additional power&hyphen;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&hyphen;law. Assuming relative level populations in LTE in the upper levels of He II, an illustrative application of the model to Spitzer/IRS spectral data of the carbon&hyphen;rich star WR 90 is given (&copy; 2009 WILEY&hyphen;VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</div>