Constraining Nuclear Equations of State Using Gravitational Waves from Hypermassive Neutron Stars

Latest general relativistic simulations for the merger of binary neutron stars with realistic equations of states (EOSs) show that a hypermassive neutron star of an ellipsoidal figure is formed after the merger if the total mass is smaller than a threshold value which depends on the EOSs. The effective amplitude of quasiperiodic gravitational waves from such hypermassive neutron stars is $\sim 6–7\times {10}^{-21}$ at a distance of 50 Mpc, which may be large enough for detection by advanced laser interferometric gravitational wave detectors although the frequency is high, $\sim 3\mathrm{kHz}$. We point out that the detection of such signals may lead to constraining the EOSs for neutron stars.

Figure 1

The density contour curves for $\rho$ in the equatorial plane at $t=10.138\mathrm{ms}$. (The initial condition is set at $t=0$ and the merger sets in at $t\sim 2\mathrm{ms}$.) The solid contour curves are drawn for $\rho =2\times {10}^{14}\times i\mathrm{g}/{\mathrm{cm}}^3(i=2\sim 10)$ and for $2\times {10}^{14}\times {10}^{-0.5i}\mathrm{g}/{\mathrm{cm}}^3(i=1\sim 7)$. The dotted curves denote $2\times {10}^{14}\mathrm{g}/{\mathrm{cm}}^3$. Vectors indicate the local velocity field $(v^x,v^y)$, and the scale is shown in the upper right-hand corner.

Figure 2

$h_{+}$ and $h_{\times }$ modes of gravitational waves observed along the rotational axis of the binary neutron stars at a hypothetical distance of 50 Mpc. Mass of two neutron stars is identical and $1.3M_{\odot }$. The SLy EOS is adopted.

Figure 3

The (nondimensional) effective amplitude $h_{\mathrm{eff}}(f)$ of gravitational waves observed along the rotational axis of the binary neutron stars at a distance of 50 Mpc. The solid curve is the spectrum computed from gravitational waveforms shown in Fig. 2. The dashed curve denotes an expected peak amplitude computed for a long term integration. The dotted line denotes the planned noise level of the advanced LIGO.