Three-dimensional Hydrodynamic Instabilities in Stellar Core Collapses

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 Γ=4/3, we examine oscillations and/or instabilities of three dimensional (3D) general polytropic perturbations. For compressible 3D perturbations, the polytropic index γof perturbations can differ from Γ=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 γ=Γ=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.

16 pages, MNRAS(to be published)

References in corpus (14)

• The gravitational wave burst signal from core collapse of rotating stars
• Pulsar spins from an instability in the accretion shock of supernovae
• Dimension as a Key to the Neutrino Mechanism of Core-Collapse Supernova Explosions
• Supernova Shock Breakout Through a Wind
• Theoretical Support for the Hydrodynamic Mechanism of Pulsar Kicks
• Linear growth of spiral SASI modes in core-collapse supernovae
• Multi-Dimensional Explorations in Supernova Theory
• Induced Rotation in 3D Simulations of Core Collapse Supernovae: Implications for Pulsar Spins
• New Self-Similar Solutions of Polytropic Gas Dynamics
• Magnetohydrodynamic Rebound Shocks of Supernovae
• Dynamic Evolution of a Quasi-Spherical General Polytropic Magnetofluid with Self-Gravity
• Self-Similar Dynamics of a Magnetized Polytropic Gas
• Self-Similar Dynamics of a Relativistically Hot Gas
• Rebound Shock Breakouts of Exploding Massive Stars: A MHD Void Model

Cited by in corpus (3)

• Scale-free gravitational collapse as the origin of $\rho \sim r^{-2}$ density profile -- a possible role of turbulence in regulating gravitational collapse
• Gravo-thermal catastrophe in gravitational collapse and energy progenitor of Gamma-Ray Bursts
• On the emergence of a new instability during core-collapse of very massive stars