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

## TL;DR

This study performs high-precision numerical relativity simulations of binary neutron star mergers, validating gravitational waveform templates and examining universal relations, with implications for gravitational wave data analysis.

## Contribution

It provides systematic, high-resolution simulations of binary neutron star mergers, validating waveform templates and critically assessing universal relations for tidal deformability.

## Key findings

- Phase error less than 0.5 rad over 200 rad phase evolution
- Waveform accuracy within 0.1 rad in phase and 20% in amplitude up to 1000 Hz
- Universal relations for post-merger signals show significant systematics

## 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.