Nonaxisymmetric instability and fragmentation of general relativistic quasitoroidal stars

Abstract

In a recent publication, we have demonstrated that differentially rotating stars admit new channels of black hole formation via fragmentation instabilities. Since a higher order instability of this kind could potentially transform a differentially rotating supermassive star into a multiple black hole system embedded in a massive accretion disk, we investigate the dependence of the instability on parameters of the equilibrium model. We find that many of the models constructed exhibit nonaxisymmetric instabilities with corotation points, even for low values of T=jWj, which lead to a fission of the stars into one, two, or three fragments, depending on the initial perturbation. At least in the models selected here, an m 1 mode becomes unstable at lower values of T=jWj, which would seem to favor a scenario where one black hole with a massive accretion disk forms. In this case, we have gained evidence that low values of compactness of the initial model can lead to a stabilization of the resulting fragment, thus preventing black hole formation in this scenario.

Stiffness effects on the dynamics of the bar-mode instability of neutron stars in full general relativity

“…(20) do not correspond to proper oscillation eigenmodes of the star but to global characteristics that are selected in terms of their spatial azimuthal shape. Eqs.…”

“…The investigations in the literature into its dependence on the stiffness of EOSs usually focused on values of Γ (i.e. the adiabatic index of a polytropic EOS) in the range from 1 to 2 [9,10,20], while the expected value for a real neutron star is more likely higher, between 2 and 3, and probably around Γ = 2.75 (at least in large portions of the interior). Such a choice for the EOS was already implemented in [21], and also quite recently in [11,22].…”

Gravitational wave burst signal from core collapse of rotating stars

“…Recently, a new kind of dynamical rotational nonaxisymmetric instability at a value of β much lower than the classical threshold has been discovered both in numerical and perturbative studies (see, e.g., [17,22,25,[79][80][81][82][83][84][85] and references therein). This low-β instability (making the classical MacLaurin instability a "high"-β instability) appears to amplify nonaxisymmetric modes at points where their pattern speed σ m (the eigenfrequency ω m divided by the azimuthal mode order m) coincides with the local angular velocity of the fluid [22,[81][82][83].…”

AMR, stability and higher accuracy

“…On one hand higher derivative operators are being introduced [3,4,5,6,7] and on the other AMR techniques within a second order accurate implementation have been adopted for over a decade [30]. (For recent efforts implementing second order AMR/FMR see for instance [8]/ [9])…”