CMF models of hot star winds I. Test of the Sobolev approximation in the case of pure line transitions

TL;DR

This study assesses the accuracy of the Sobolev approximation in hot star wind models by comparing it with detailed CMF radiative transfer calculations, finding it reliable under certain conditions and highlighting factors affecting mass-loss rates.

Contribution

It provides the first detailed comparison of CMF radiative transfer with Sobolev approximation in hot star winds, including effects of line overlaps and broadening.

Findings

Sobolev approximation is reliable without line overlaps.

Line overlaps reduce radiative force by ~40%.

Additional line broadening can lower mass-loss rates.

Abstract

We provide hot star wind models with radiative force calculated using the solution of comoving frame (CMF) radiative transfer equation. The wind models are calculated for the first stars, O stars, and the central stars of planetary nebulae. We show that without line overlaps and with solely thermal line broadening the pure Sobolev approximation provides a reliable estimate of the radiative force even close to the wind sonic point. Consequently, models with the Sobolev line force provide good approximations to solutions obtained with non-Sobolev transfer. Taking line overlaps into account, the radiative force becomes slightly lower, leading to a decrease in the wind mass-loss rate by roughly 40%. Below the sonic point, the CMF line force is significantly lower than the Sobolev one. In the case of pure thermal broadening, this does not influence the mass-loss rate, as the wind mass-loss rate is set in the supersonic part of the wind. However, when additional line broadening is present (e.g., the turbulent one) the region of low CMF line force may extend outwards to the regions where the mass-loss rate is set. This results in a decrease in the wind mass-loss rate. This effect can at least partly explain the low wind mass-loss rates derived from some observational analyses of luminous O stars.