Oscillatory Line-Driven Winds: The Role of Atmospheric Stratification

TL;DR

This paper investigates the origin of oscillations in line-driven stellar winds, revealing that the line force amplifies acoustic waves near the Lamb cut-off frequency, leading to self-excited variability rooted in atmospheric stratification.

Contribution

The study combines simulations and perturbation analysis to identify how line forces amplify waves and cause oscillations, emphasizing the need to go beyond the Sobolev approximation in wind models.

Findings

Line force amplifies waves near the Lamb cut-off frequency.

Oscillations originate from non-linear effects in the exponential atmosphere.

Self-excitation occurs due to the velocity gradient dependence in the line force.

Abstract

Time-dependent numerical studies of line-driven winds using the Sobolev approximation have a history spanning over three decades. In many of these studies, the wind solutions display notorious oscillations. Two clues suggest the oscillations originate at the wind base: (i) simulations reach a steady state without oscillations when the base density is sufficiently low and (ii) the oscillation dominant frequency is comparable to the Lamb cut-off frequency, {\omega}c, of acoustic waves propagating in a stratified hydrostatic atmosphere. Recently, Dannen et al. observed another clue: when the line force significantly weakens due to ionization, the winds become increasingly sensitive to the self-excited oscillations. Here, we present a set of simulations and perturbation analyses that further elucidate the source and characteristics of oscillations. We found that the line force adds wave energy and amplifies perturbations with frequencies near {\omega}c. This selective amplification results from the coupling between the natural tendency of velocity perturbations to grow in a stratified atmosphere and from the line force dependence on the velocity gradient, per the Castor-Abbott-Klein line-driven wind theory. We also found that the variability stems from self-excitation that occurs in the exponential atmosphere due to the non-linearity introduced by the absolute value of the velocity gradient in the line force prescription. We conclude that self-consistently calculating ionization is insufficient for modeling the dynamics in the subsonic atmosphere. Instead, future wind or unified models should relax the Sobolev approximation, or model the radiative transfer to properly capture the resulting radiation-induced instabilities and dynamics at the wind base.