Wave-Driven Shocks in Stellar Outbursts: Dynamics, Envelope Heating, and Nascent Blastwaves

TL;DR

This paper develops a theoretical framework for understanding shock dynamics in stellar outbursts, predicting shock evolution, energy transfer, and mass ejection, with validation from numerical simulations.

Contribution

It generalizes classical shock analysis techniques to wave trains in stellar environments, providing new expressions for shock heating and insights into energy preservation and mass ejection.

Findings

Internal shocks significantly heat the stellar envelope.

Head and tail shocks retain more wave energy at large radii.

Waveform shape critically influences shock dynamics and matter ejection.

Abstract

We address the shocks from acoustic pulses and wave trains in general one-dimensional flows, with an emphasis on the application to super-Eddington outbursts in massive stars. Using approximate adiabatic invariants, we generalize the classical equal-area technique in its integral and differential forms. We predict shock evolution for the case of an initially sinusoidal but finite wave train, with separate solutions for internal shocks and head or tail shocks, and demonstrate detailed agreement with numerical simulations. Our internal shock solution motivates improved expressions for the shock heating rate. Our solution for head and tail shocks demonstrates that these preserve dramatically more wave energy to large radii and have a greater potential for the direct ejection of matter. This difference highlights the importance of the waveform for shock dynamics. Our weak-shock analysis predicts when shocks will become strong and provides a basis from which this transition can be addressed. We use it to estimate the mass ejected by sudden sound pulses and weak central explosions.