INFERENCE OF STEADY STELLAR WIND V(R) LAWS FROM OPTICALLY THIN EMISSION-LINES .1. IDEALIZED ANALYSIS FOR THE PROFILE OF A SINGLE LINE

The form of the profile F-lambda 0 (Delta lambda) of an emission line from a steady spherical wind of velocity profile v(r) is derived for t he case when optical depths are small, when stellar occultation of the wind is neglected, and when v(r) is highly supersonic. It is shown ho w the resulting integral equation for v(r), given F-lambda 0(Delta lam bda), 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 proportional to n(2)) for various trial fo rms of v(r). The solution is unique provided dv/dr does not change sig n anywhere and is remarkably stable against noise in the F-lambda 0(De lta lambda) data. The analysis is idealised in the sense that the stel lar mass loss rate (M) over dot 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 F-lambda 0(Delta lambda) s cales as ((M) over dot/D)(2). If this quantity is known the method als o yields the stellar radius.