Accurate simulations of the dynamical bar-mode instability in full general relativity

Abstract

We present accurate simulations of the dynamical bar-mode instability in full general relativity focusing on two aspects which have not been investigated in detail in the past, namely, on the persistence of the bar deformation once the instability has reached its saturation and on the precise determination of the threshold for the onset of the instability in terms of the parameter T=jWj. We find that generic nonlinear mode-coupling effects appear during the development of the instability and these can severely limit the persistence of the bar deformation and eventually suppress the instability. In addition, we observe the dynamics of the instability to be strongly influenced by the value and on its separation from the critical value c marking the onset of the instability. We discuss the impact these results have on the detection of gravitational waves from this process and provide evidence that the classical perturbative analysis of the bar-mode instability for Newtonian and incompressible Maclaurin spheroids remains qualitatively valid and accurate also in full general relativity.

Gravitational wave burst signal from core collapse of rotating stars

“…Although Newtonian MacLaurin spheroids are highly idealized configurations, numerical studies (see, e.g., [77] and references therein) have shown that the above insta- bility threshold β dyn for the dynamical instability holds approximately even when differentially rotating compressible fluid configurations in general relativity are considered. The situation may be different for the gravitational radiation back-reaction driven secular instability, since perturbative studies (see, e.g., [78]) predict an onset at significantly lower β in general relativity than in the Newtonian case.…”

Sources of Gravitational Waves: Theory and Observations

“…The hypermassive NS is expected to be a non-axisymmetric ellipsoid supported against collapse by a combination of thermal pressure and differential rotation [305] and can delay BH formation for 1 ms to 1 s [305,307]. This phase could wit-ness quite a lot of rotational energy emitted as GWs, with a spectrum that is characteristic of the NS EoS [308,309]. A BH without an accretion disk is not a very likely outcome, but it can happen if M > ∼ 3 M [303, 304,310].…”

“…Analytical and semi-analytical models of NS-NS and NS-BH mergers will be crucial for parameter esti-mation and Bayesian hypothesis testing. This will be a huge challenge for the bar-mode instability regime where the signal does not seem to have any phase coherence (see, e.g., simulations in [308,309]). Even so, accurate modeling of the expected spectrum or time-frequency content of the signal can be useful in understanding the physics of dynamical instabilities.…”

Nonaxisymmetric instability and fragmentation of general relativistic quasitoroidal stars

“…Nonaxisymmetric dynamical instabilities in general relativistic, self-gravitating fluid stars have been studied by several authors [25,[61][62][63][64][65]. Some evidence of fragmentation has been found in [25] in a ring resulting from a ''supra-Kerr'' collapse with J=M 2 > 1 (here J denotes the total angular momentum, and M the Arnowitt-DeserMisner (ADM) mass), but no black hole was identified, although the pressure in the initial data was artificially reduced by a large factor in order to induce collapse.…”