\begin{center}{\Large\bf 
Recombination Lines and Free-Free Continua Formed in Asymptotic Ionized
Winds: Analytic solution for the radiative transfer}\end{center} 

\centerline{\bf Richard Ignace
}{\footnotesize Physics and Astronomy, East Tennessee State University
}
 
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.

{\bf Reference: to appear in Astronomische Nachrichten} \\{\it Status:} Manuscript has been accepted
 \\ {\it Comments:} 

{\it On the web at:} {\tt http://arxiv.org/abs/0803.4507} 

{\it Preprints from:} {\tt  ignace@etsu.edu} 
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