Three-dimensional Hydrodynamic Instabilities in Stellar Core Collapses

TL;DR

This paper investigates three-dimensional hydrodynamic instabilities, especially g-modes, during stellar core collapse, revealing their potential impact on supernova dynamics and neutron star formation.

Contribution

It introduces a more general model for 3D perturbations in collapsing stellar cores, including internal gravity modes and unstable vortical disturbances.

Findings

g(-)-modes and high-order g(+)-modes are unstable

Acoustic p-modes and surface f-modes remain stable

Unstable g-modes can influence supernova and neutron star properties

Abstract

A spherically symmetric hydrodynamic stellar core collapse under gravity is time-dependent and may become unstable once disturbed. Specifically for a homologously collapse of stellar core characterized by a polytropic exponent \Gamma=4/3, we examine oscillations and/or instabilities of three dimensional (3D) general polytropic perturbations. For compressible 3D perturbations, the polytropic index \gamma of perturbations can differ from \Gamma=4/3 of the general polytropic hydrodynamic background flow. Our model formulation here is more general and allows the existence of internal gravity g(-)-modes and/or g(+)-modes. Eigenvalues and eigen-functions of various oscillatory and unstable perturbation modes are computed. As studied in several specialized cases of Goldreich & Weber and of Cao & Lou, we further confirm that acoustic p-modes and surface f-modes remain stable in the current more general situations. In comparison, g(-)-modes and sufficiently high radial order g(+)-modes are unstable, leading to inevitable convective motions within the collapsing stellar interior. Unstable growths of 3D g-mode disturbances are governed dominantly by the angular momentum conservation and modified by the gas pressure restoring force. We note in particular that unstable temporal growths of 3D vortical perturbations exist even when the specific entropy distribution becomes uniform and \gamma=\Gamma=4/3. Conceptually, unstable g-modes might bear conceivable physical consequences on supernova explosions, the initial kicks of nascent proto-neutron stars (PNSs) and break-ups of the collapsing core, while unstable growths of vortical perturbations can lead to fast spins of compact objects and other relevant results.