Sub-radian-accuracy gravitational waves from coalescing binary neutron stars II: Systematic study on the equation of state, binary mass, and mass ratio

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 $\lesssim 20\mathrm{\%}$ 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.