Gravitational waves from axisymmetric rotating stellar core collapse to a neutron star in full general relativity

TL;DR

This paper presents axisymmetric simulations of rotating stellar core collapse to neutron stars in full general relativity, analyzing gravitational waveforms and validating the approximation methods used.

Contribution

It demonstrates the effectiveness of the Cartoon method in full GR simulations of core collapse and compares gravitational waveforms with previous approximate models.

Findings

Central density evolution matches previous approximate models.

Waveforms are qualitatively similar but quantitatively differ from prior results.

Full GR simulations validate the approximation methods used in earlier studies.

Abstract

Axisymmetric numerical simulations of rotating stellar core collapse to a neutron star are performed in the framework of full general relativity. The so-called Cartoon method, in which the Einstein field equations are solved in the Cartesian coordinates and the axisymmetric condition is imposed around the $y=0$ plane, is adopted. The hydrodynamic equations are solved in the cylindrical coordinates (on the $y=0$ plane in the Cartesian coordinates) using a high-resolution shock-capturing scheme with the maximum grid size $(2500,2500)$. A parametric equation of state is adopted to model collapsing stellar cores and neutron stars following Dimmelmeier et al. It is found that the evolution of central density during the collapse, bounce, and formation of protoneutron stars agree well with those in the work of Dimmelmeier et al. in which an approximate general relativistic formulation is adopted. This indicates that such approximation is appropriate for following axisymmetric stellar core collapses and subsequent formation of protoneutron stars. Gravitational waves are computed using a quadrupole formula. It is found that the waveforms are qualitatively in good agreement with those by Dimmelmeier et al. However, quantitatively, two waveforms do not agree well. Possible reasons for the disagreement are discussed.