Axisymmetric general relativistic hydrodynamics: Long-term evolution of neutron stars and stellar collapse to neutron stars and black holes

TL;DR

This paper introduces a new axisymmetric general relativistic hydrodynamics simulation method, capable of long-term neutron star evolution and stellar collapse modeling, with successful tests demonstrating robustness and accuracy for various astrophysical scenarios.

Contribution

The paper presents a novel implementation combining the Nakamura-Shibata formulation with the cartoon method and high-resolution shock-capturing scheme for axisymmetric GR hydrodynamics simulations.

Findings

Successfully simulated long-term evolution of neutron stars.

Captured shock formation during stellar collapse.

Accurately computed black hole masses after collapse.

Abstract

We report a new implementation for axisymmetric simulation in full general relativity. In this implementation, the Einstein equations are solved using the Nakamura-Shibata formulation with the so-called cartoon method to impose an axisymmetric boundary condition, and the general relativistic hydrodynamic equations are solved using a high-resolution shock-capturing scheme based on an approximate Riemann solver. As tests, we performed the following simulations: (i) long-term evolution of non-rotating and rapidly rotating neutron stars, (ii) long-term evolution of neutron stars of a high-amplitude damping oscillation accompanied with shock formation, (iii) collapse of unstable neutron stars to black holes, and (iv) stellar collapses to neutron stars. The tests (i)--(iii) were carried out with the $\Gamma$-law equation of state, and the test (iv) with a more realistic parametric equation of state for high-density matter. We found that this new implementation works very well: It is possible to perform the simulations for stable neutron stars for more than 10 dynamical time scales, to capture strong shocks formed at stellar core collapses, and to accurately compute the mass of black holes formed after the collapse and subsequent accretion. In conclusion, this implementation is robust enough to apply to astrophysical problems such as stellar core collapse of massive stars to a neutron star and black hole, phase transition of a neutron star to a high-density star, and accretion-induced collapse of a neutron star to a black hole. The result for the first simulation of stellar core collapse to a neutron star started from a realistic initial condition is also presented.