Determination of mass-loss rates from the first order moment W1 of unsaturated Cygni line profiles

The relationship between the first order moment and the mass loss rate is investigated within the framework of the Sobolev approximation (1947, 1957, 1958) under various physical and geometrical conditions. By assuming that the size of the expanding envelope from which the observed P Cygni profiles arise is large with respect to the central stellar core, a general expression for the n-th order moment is obtained for the case of a point-like source in terms of the usual parameters inherent to Sobolev-type theories. It is then shown how the first result is altered when considering separately the effects due to collisions and rotation, the presence of the underlying photospheric absorption line, the finite size of the central core, and the limb-darkening of the stellar core. It is concluded that the total uncertainty of the mass loss rate determination made with the approach proposed here should be less than 60 percent.