Inference of steady stellar wind v(r) laws from optically thin emission lines I. Idealised analysis for the profile of a single line

The form of the profile Fλ0 (∆λ) 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 thewind is neglected, andwhen v(r) is highly supersonic. It is shown how the resulting integral equation for v(r), given Fλ0 (∆λ), 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 (j ∝ n2) for various trial forms of v(r). The solution is unique provided dv/dr does not change sign anywhere and is remarkably stable against noise in theFλ0 (∆λ) data. The analysis is idealised in the sense that the stellar mass loss rate Ṁ 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 Fλ0 (∆λ) scales as (Ṁ/D)2. If this quantity is known the method also yields the stellar radius.