Shock Dynamics in Stellar Outbursts: I. Shock formation

TL;DR

This paper investigates the nonlinear wave dynamics leading to shock formation in stellar outbursts, providing analytical conditions and numerical verification, emphasizing shock formation's role in super-Eddington phenomena.

Contribution

It introduces a general analytical condition for shock formation applicable to various stellar environments and verifies it through numerical experiments.

Findings

Shock formation radius can be accurately predicted by crossing characteristics.

Super-Eddington acoustic waves always produce shocks, not damped by radiative diffusion.

Shock formation is fundamental to super-Eddington stellar outbursts.

Abstract

Wave-driven outflows and non-disruptive explosions have been implicated in pre-supernova outbursts, supernova impostors, LBV eruptions, and some narrow-line and superluminous supernovae. To model these events, we investigate the dynamics of stars set in motion by strong acoustic pulses and wave trains, focusing here on nonlinear wave propagation, shock formation, and an early phase of the development of a weak shock. We identify the shock formation radius, showing that a heuristic estimate based on crossing characteristics matches an exact expansion around the wave front and verifying both with numerical experiments. Our general analytical condition for shock formation applies to one-dimensional motions within any static environment, including both eruptions and implosions, and can easily be extended to non-stationary flows. We also consider the early phase of shock energy dissipation. We find that waves of super-Eddington acoustic luminosity always create shocks, rather than damping by radiative diffusion. Therefore, shock formation is integral to super-Eddington outbursts.