Binary neutron star mergers: Dependence on the nuclear equation of state

We perform a numerical-relativity simulation for the merger of binary neutron stars with 6 nuclear-theory-based equations of states (EOSs) described by piecewise polytropes. Our purpose is to explore the dependence of the dynamical behavior of the binary neutron star merger and resulting gravitational waveforms on the EOS of the supernuclear-density matter. The numerical results show that the merger process and the first outcome are classified into three types: (i) a black hole is promptly formed, (ii) a short-lived hypermassive neutron star (HMNS) is formed, (iii) a long-lived HMNS is formed. The type of the merger depends strongly on the EOS and on the total mass of the binaries. For the EOS with which the maximum mass is larger than $2M_{\odot }$, the lifetime of the HMNS is longer than 10 ms for a total mass $m_0=2.7M_{\odot }$. A recent radio observation suggests that the maximum mass of spherical neutron stars is $M_{\max }\ge 1.97\pm 0.04M_{\odot }$ in one $\sigma$ level. This fact and our results support the possible existence of a HMNS soon after the onset of the merger for a typical binary neutron star with $m_0=2.7M_{\odot }$. We also show that the torus mass surrounding the remnant black hole is correlated with the type of the merger process; the torus mass could be large, $\ge 0.1M_{\odot }$, in the case that a long-lived HMNS is formed. We also show that gravitational waves carry information of the merger process, the remnant, and the torus mass surrounding a black hole.

Figure 1

Color map of the density, $\log \rho$ ($\mathrm{g}/{\mathrm{cm}}^3$). Top, middle, and bottom rows show the snapshots for APR4-29, H3-27, and H4-27, respectively. The black filled circle denotes the region inside apparent horizon. Note that the density range of the color bar for APR4-29 is different from the other models.

Figure 2

The evolution of the maximum baryon rest-mass density, ${\rho }_{\max }$, for three models. The solid, dashed, dash-dotted, and dotted curves denote the results for models APR4-29 (type I), H3-27 (type II), H4-27 (type III), and APR4-27 (type III), respectively.

Figure 3

Type of the merger process and the remnants for each model. The vertical axis shows the total mass of two neutron stars. The horizontal axis shows the EOSs together with their radii for $M=1.4M_{\odot }$, $R_{1.4}\mathrm{km}$.

Figure 4

The evolution of the torus mass, $M_{\mathrm{torus}}$, for three models. The solid, dashed, and dash-dotted curves denote the results for models APR4-29 (type I), H3-27 (type II), and H4-27 (type III), respectively. The time at the black hole formation is set to be $t=0$.

Figure 5

Gravitational waveforms and their spectra. The solid and dashed curves in the left panels denote the waveforms calculated by the simulation and Taylor T4 formula, respectively. The solid and dashed curves in the right panels denote the spectra calculated by the simulation, and spectrum calculated by Taylor T4 formula, respectively, at a hypothetical source distance of 100 Mpc. The effective amplitude for the most optimistic direction of the source is shown. Here the noise levels of advanced LIGO (Optimal NSNS version), LCGT (Broadband version), and Einstein Telescope are shown together. (1a) and (1b) for APR4-27 (type III), (2a) and (2b) for H3-27 (type II), (3a) and (3b) for H4-27 (type III), (4a) and (4b) for PS-27 (type III).

Figure 6

The same as Fig. 5 but for $m_0=2.9M_{\odot }$. (5a) and (5b) for APR4-29 (type I), (6a) and (6b) for H4-29 (type II).