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

TL;DR

This paper presents an analytical and iterative approach to determine the velocity field and mass-loss rates of stellar winds in massive stars, incorporating multi-line scattering effects for more accurate modeling.

Contribution

It introduces a self-consistent method combining Lambert W-function solutions and Monte Carlo radiative transfer to improve stellar wind modeling, especially for O-type stars.

Findings

Good agreement with empirical mass-loss rates for O5-V stars

Analytical solutions closely match numerical results

Method enables application to regions lacking empirical data

Abstract

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 a self-consistent mass-loss calculation 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.