Simulation of merging binary neutron stars in full general relativity:Γ=2case

We perform 3D numerical simulations for the merger of equal mass binary neutron stars in full general relativity. We adopt a $\Gamma$-law equation of state in the form $P=\left(\Gamma -1\right)\rho \varepsilon$ where P, $\rho ,$ $\varepsilon$ and $\Gamma$ are the pressure, rest mass density, specific internal energy, and the adiabatic constant with $\Gamma =2.\mathrm{}$ As initial conditions, we adopt models of corotational and irrotational binary neutron stars in a quasiequilibrium state which are obtained using the conformal flatness approximation for the three geometry as well as the 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 time scale. As the compactness is decreased, the formation time scale 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: $<{0.01M}_{*}.$