Analytical Solutions for Radiation-Driven Winds in Massive Stars. I: The Fast Regime

TL;DR

This paper derives an analytical solution for radiation-driven stellar winds in massive stars, facilitating easier and faster calculations of mass-loss rates by expressing the equations in terms of force multipliers.

Contribution

It introduces an analytical expression for the wind equation of motion using force multiplier parameters, based on Villata's line acceleration and Mueller and Vink's methodology.

Findings

Analytical solution for wind equations derived

Relationships between line acceleration parameters and force multipliers established

Simplifies calculations of stellar wind properties

Abstract

Accurate massloss rate estimates are crucial keys to study wind properties of massive stars and test different evolutionary scenarios. From a theoretical point of view, this implies to solve a complex set of differential equations in which the radiation field and the hydrodynamics are strong coupled. The use of analytical expression to represent the radiation force and the solution of the equation of motion have many advantages over numerical integrations. Therefore, in this work, we present an analytical expression as solution of the equation of motion for radiation driven winds, in terms of the force multipliers parameters. This analytical expression is obtained by employing the line acceleration expression given by Villata (1992) and the methodology proposed by Mueller and Vink (2008). On the other hand, we find useful relationships to determine the parameters for the line acceleration given by Mueller and Vink (2008) in terms of the force multiplier parameters.