*Astron. Astrophys. 325, 677-684*
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## Inference of steady stellar wind *v*(*r*) laws from optically thin
emission lines
### I. Idealised analysis for the profile of a single line
**J.C. Brown**^{1}, L.L. Richardson^{1}, J.P. Cassinelli^{2}, and R. Ignace^{1}
^{1}Department of Physics and Astronomy, University of Glasgow,
Glasgow, UK
^{2}Department of Astronomy, University of
Wisconsin-Madison, USA
*Received 28 August 1996 / Accepted 21 November 1996*
**Abstract**
The form of the profile
of an emission line from a steady spherical wind of velocity
profile *v*(*r*) is derived for the case when optical depths
are small, when stellar occultation of the wind is neglected,
and when *v*(*r*) is highly supersonic. It is shown how the
resulting integral equation for *v*(*r*), given , can be inverted to yield *v*(*r*) if the line
emissivity function *j*(*r*) is known.
Solutions are demonstrated for simulated data in
the case of a recombination line for various
trial forms of *v*(*r*). The solution is unique provided
does not change sign anywhere and is remarkably stable
against noise in the data.
The analysis is idealised in the sense that the stellar mass
loss rate and distance *D* are assumed known, the solution
being then carried out in scaled dimensionless variables. The
absolute *r*-scale of the solution for given
scales as . If this
quantity is known the method also yields the stellar radius.
**Key words: **lines: profile - stars: mass loss - numerical methods
*Send offprint requests to:* J.C. Brown
© European Southern Observatory (ESO) 1997
Online publication: September 9, 1997
Last change: April 28, 1998
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