Analytic insight into the physics of the standing accretion shock instability

I. Shock instability in a non-rotating stellar core

Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France

^⋆ Corresponding author; foglizzo@cea.fr

Received: 18 September 2024
Accepted: 23 October 2024

Abstract

Context. During the core collapse of a massive star, and immediately before its supernova explosion, there is amplification of asymmetric motions by the standing accretion shock instability (SASI). This imprints a frequency signature on the neutrino flux and the gravitational waves that carries direct information about the explosion process.

Aims. The physical interpretation of this multi-messenger signature requires a detailed understanding of the instability mechanism.

Methods. We carried out a perturbative analysis to characterise the properties of SASI and assess the effect of the region of neutronization above the surface of the proto-neutron star. We compared the eigenfrequencies of the most unstable modes to those obtained in an adiabatic approximation where neutrino interactions are neglected above the neutrinosphere. We solved the differential system analytically using a Wronskian method and approximated it asymptotically for a large shock radius.

Results. The oscillation period of SASI is well fitted with a simple analytic function of the shock radius, the radius of maximum deceleration, and the mass of the proto-neutron star. The oscillation period is weakly dependent on the parameterised cooling function, but this latter does affects the SASI growth rate. We describe the general properties of SASI eigenmodes using an adiabatic model. In this approximation, the eigenvalue problem is formulated as a self-forced oscillator. The forcing agent is the radial advection of baroclinic vorticity perturbations and entropy perturbations produced by the shock oscillation. We reduced the differential system defining the eigenfrequencies to a single integral equation. Its analytical approximation sheds light on the radially extended character of the region of advective-acoustic coupling. The simplicity of this adiabatic formalism opens new perspectives for the investigation of the effect of stellar rotation and non-adiabatic processes on SASI.