Simulation of merging binary neutron stars in full general relativity: $\Gamma=2$ case

TL;DR

This paper presents 3D numerical simulations of binary neutron star mergers in full general relativity with a $b3=2$ equation of state, revealing how the final product depends on initial compactness and rotation, including black hole and neutron star outcomes.

Contribution

First detailed simulation of binary neutron star mergers with b3=2 in full GR, analyzing the dependence of the merger outcome on initial conditions and compactness.

Findings

Black holes form for sufficiently compact stars within dynamical timescales.

Less compact mergers produce differentially rotating massive neutron stars.

Disk masses around black holes are estimated, with larger disks for corotational cases.

Abstract

We have performed 3D numerical simulations for merger of equal mass binary neutron stars in full general relativity. We adopt a $\Gamma$-law equation of state in the form $P=(\Gamma-1)\rho\epsilon$ where P, $\rho$, $\varep$ and $\Gamma$ are the pressure, rest mass density, specific internal energy, and the adiabatic constant with $\Gamma=2$. As initial conditions, we adopt models of corotational and irrotational binary neutron stars in a quasi-equilibrium state which are obtained using the conformal flatness approximation for the three geometry as well as an assumption that a helicoidal Killing vector exists. In this paper, we pay particular attention to the final product of the coalescence. We find that the final product depends sensitively on the initial compactness parameter of the neutron stars : In a merger between sufficiently compact neutron stars, a black hole is formed in a dynamical timescale. As the compactness is decreased, the formation timescale becomes longer and longer. It is also found that a differentially rotating massive neutron star is formed instead of a black hole for less compact binary cases, in which the rest mass of each star is less than 70-80% of the maximum allowed mass of a spherical star. In the case of black hole formation, we roughly evaluate the mass of the disk around the black hole. For the merger of corotational binaries, a disk of mass $\sim 0.05-0.1M_*$ may be formed, where M_* is the total rest mass of the system. On the other hand, for the merger of irrotational binaries, the disk mass appears to be very small : < 0.01M_*.