Gravitational-Wave Emission from Rotating Gravitational Collapse in three Dimensions

TL;DR

This paper presents the first three-dimensional simulations of gravitational wave emission from rotating neutron stars collapsing into black holes, revealing waveform features linked to initial stellar properties and black hole quasi-normal modes.

Contribution

It introduces a fully three-dimensional simulation approach with mesh refinement and gauge-invariant waveform extraction for rotating stellar collapse.

Findings

Waveforms reflect initial stellar oscillations and black hole modes.

Amplitude is about ten times smaller than previous 2D results.

Detectability estimates suggest marginal signals for current detectors.

Abstract

We present the first calculation of gravitational wave emission produced in the gravitational collapse of uniformly rotating neutron stars to black holes in fully three-dimensional simulations. The initial stellar models are relativistic polytropes which are dynamically unstable and with angular velocities ranging from slow rotation to the mass-shedding limit. An essential aspect of these simulations is the use of progressive mesh-refinement techniques which allow to move the outer boundaries of the computational domain to regions where gravitational radiation attains its asymptotic form. The waveforms have been extracted using a gauge-invariant approach in which the numerical spacetime is matched with the non-spherical perturbations of a Schwarzschild spacetime. Overall, the results indicate that the waveforms have features related to the properties of the initial stellar models (in terms of their w-mode oscillations) and of the newly produced rotating black holes (in terms of their quasi-normal modes). While our waveforms are in good qualitative agreement with those computed by Stark and Piran in two-dimensional simulations, our amplitudes are about one order of magnitude smaller and this difference is mostly likely due to our less severe pressure reduction. For a neutron star rotating uniformly near mass-shedding and collapsing at 10 kpc, the signal-to-noise ratio computed uniquely from the burst is S/N ~ 0.25, but this grows to be S/N <~ 4 in the case of LIGO II.