## A consistent solution for the velocity field and mass-loss rate of massive stars

**Patrick E. Mueller (1), Jorick S. Vink (2)**

(1) Keele University, UK

(2) Armagh Observatory, Northern Ireland, UK

Stellar winds are an important aspect of our understanding of the evolution of massive stars

and their input into the interstellar medium. Here we present solutions for the velocity

field and mass-loss rates for stellar outflows as well as for the case of mass accretion

through the use of the so-called Lambert W-function. For the case of a radiation-driven

wind, the velocity field is obtained analytically using a parameterised description for

the line acceleration that only depends on radius, which we obtain from Monte-Carlo multi-

line radiative transfer calculations. In our form of the equation of motion the critical

point is the sonic point. We also derive an approximate analytical solution for the

supersonic flow which closely resembles our exact solution. For the simultaneous solution of

the mass-loss rate and velocity field, we describe a new iterative method. We apply our

theoretical expressions and our iterative method to the stellar wind from a typical O5-V main

sequence star, and find good agreement with empirical values. Our computations represent the

first self-consistent mass-loss calculations including the effect of multi-line scattering for

an O-type star, opening up the possibility of applying Monte Carlo mass-loss calculations in

regions of the Universe for which empirical constraints cannot be readily obtained.

**Reference: **A&A, in press

Status: Manuscript has been accepted

**Weblink: **http://arXiv.org/abs/0810.1901

**Comments: **

**Email: **pmueller@astro.keele.ac.uk