Abstract
We report results of numerical relativity simulations for {\it new} 26 non-spinning binary neutron star systems with 6 grid resolutions using an adaptive mesh refinement numerical re\ lativity code {\tt SACRA-MPI}. The finest grid spacing is $\approx 64$--$85$ m, depending on the systems. First, we derive long-term high-precision inspiral gravitational waveforms and show that the accumulated gravitational-wave phase error due to the finite grid resolution is less than $0.5$ rad during more than $200$ rad phase evolution irrespective of the systems. We also find that the gravitational-wave phase error for a binary system with a tabulated equation of state (EOS) is comparable to that for a piecewise polytropic EOS. Then we validate the SACRA inspiral gravitational waveform template, which will be used to extract tidal deformability from gravitational wave observation, and find that accuracy of \ our waveform modeling is $\lesssim 0.1$ rad in the gravitational-wave phase and $\lesssim 20 \%$ in the gravitational-wave amplitude up to the gravitational-wave frequency $1000$ Hz.\ Finally, we calibrate the proposed universal relations between a post-merger gravitational wave signal and tidal deformability/neutron star radius in the literature and show that th\ ey suffer from systematics and many relations proposed as universal are not very universal. Improved fitting formulae are also proposed.
Highlights
On August 17, 2017, advanced LIGO [1] and advanced Virgo [2] detected gravitational waves from a binary neutron star (BNS) merger, GW170817, for the first time [3]
To derive high-precision gravitational waveforms in a large parameter space, we systematically vary the equation of state (EOS) of NS, the chirp mass, and the mass ratio
To assess gravitationalwave phase error stemming from a finite grid resolution, we change the grid spacing by a factor of two for simulating each binary system
Summary
On August 17, 2017, advanced LIGO [1] and advanced Virgo [2] detected gravitational waves from a binary neutron star (BNS) merger, GW170817, for the first time [3]. Numerical relativity simulation is the unique tool to derive high-precision gravitational waveforms in the late inspiral stage during which the gravitational-wave phase shift due to the tidal deformation becomes prominent. During this stage, any analytic techniques break down. We derive a number of gravitational waveforms from BNS mergers by performing numerical-relativity simulations in a wider parameter space for EOSs, binary total mass, and mass ratio than that in the previous papers [46,51]. The signal could bring us information of the EOS complementary to that imprinted in the late inspiral signal To extract such information, we should explore a heuristic relation between postmerger signals and the tidal deformability/NS radius in numerical relativity simulations. Throughout this paper, we employ the geometrical units of c 1⁄4 G 1⁄4 1, where c and G are the speed of light and the gravitational constant, respectively
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