Stability of a Spherical Accretion Shock with Nuclear Dissociation

TL;DR

This study investigates how nuclear dissociation affects the stability and oscillations of a spherical accretion shock in core-collapse supernovae, combining simulations and linear analysis to reveal key influences on the instability.

Contribution

It introduces a simplified model with nuclear dissociation to analyze its impact on shock stability, extending previous work that used more complex physics.

Findings

Nuclear dissociation lowers the growth rate and amplitude of the instability.

A negative Bernoulli parameter reduces the shock oscillation frequency.

The growth rate peaks when advection time matches sound wave period.

Abstract

We examine the stability of a standing shock wave within a spherical accretion flow onto a gravitating star, in the context of core-collapse supernova explosions. Our focus is on the effect of nuclear dissociation below the shock on the linear growth, and non-linear saturation, of non-radial oscillations of the shocked fluid. We combine two-dimensional, time-dependent hydrodynamic simulations using FLASH2.5 with a solution to the linear eigenvalue problem, and demonstrate the consistency of the two approaches. Previous studies of this `Standing Accretion Shock Instability' (SASI) have focused either on zero-energy accretion flows without nuclear dissociation, or made use of a detailed finite-temperature nuclear equation of state and included strong neutrino heating. Our main goal in this and subsequent papers is to introduce equations of state of increasing complexity, in order to isolate the various competing effects. In this work we employ an ideal gas equation of state with a constant rate of nuclear dissociation below the shock, and do not include neutrino heating. We find that a negative Bernoulli parameter below the shock significantly lowers the real frequency, growth rate, and saturation amplitude of the SASI. A decrease in the adiabatic index has similar effects. The non-linear development of the instability is characterized by an expansion of the shock driven by turbulent kinetic energy at nearly constant internal energy. Our results also provide further insight into the instability mechanism: the rate of growth of a particular mode is fastest when the radial advection time from the shock to the accretor overlaps with the period of a standing lateral sound wave. The fastest-growing mode can therefore be modified by nuclear dissociation.