# Self-consistent solutions for line-driven winds of hot massive stars. The m-CAK procedure

## TL;DR

This paper introduces a self-consistent method coupling hydrodynamics and line-force calculations to accurately determine mass-loss rates and wind parameters in hot massive stars, improving stellar evolution models.

## Contribution

The novel approach integrates detailed atomic transition data and NLTE effects to produce self-consistent stellar wind solutions with fewer free parameters.

## Key findings

- Line-force parameters depend on effective temperature and gravity.
- Terminal velocities scale with escape velocity, explaining observed scatter.
- Self-consistent mass-loss rates agree well with empirical data.

## Abstract

Massive stars present strong stellar that which are described by the radiation driven wind theory. Accurate mass-loss rates are necessary to properly describe the stellar evolution across the Hertzsprung--Russel Diagram. We present a self-consistent procedure that coupled the hydrodynamics with calculations of the line-force, giving as results the line-force parameters, the velocity field, and the mass-loss rate. Our calculations contemplate the contribution to the line-force multiplier from more than $\sim 900,000$ atomic transitions, an NLTE radiation flux from the photosphere and a quasi-LTE approximation for the occupational numbers. A full set of line-force parameters for $T_\text{eff}\ge 32,000$ K, surface gravities higher than 3.4 dex for two different metallicities are presented, with their corresponding wind parameters (terminal velocities and mass-loss rates). The already known dependence of line-force parameters on effective temperature is enhanced by the dependence on $\log g$. The terminal velocities present a stepper scaling relation with respect to the escape velocity, this might explain the scatter values observed in the hot side of the bistability jump. Moreover, a comparison of self-consistent mass-loss rates with empirical values shows a good agreement. Self-consistent wind solutions are used as input in FASTWIND to calculate synthetic spectra. We show, comparing with the observed spectra for three stars, that varying the clumping factor, the synthetic spectra rapidly converge into the neighbourhood region of the solution. It is important to stress that our self-consistent procedure significantly reduces the number of free parameters needed to obtain a synthetic spectrum.