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Abstract

We report results of numerical relativity simulations of binary neutron star
mergers. We perform simulations for {\it new} 26 non-spinning binary models
with 6 grid resolutions using an adaptive mesh refinement numerical relativity
code {\tt SACRA-MPI}. The finest grid spacing is $\approx 64$ m. First, we
derive long-term high-precision inspiral gravitational waveforms for
calibrating the SACRA gravitational waveform template. We find that the
accumulated gravitational-wave phase error due to the finite grid resolution is
less than $0.5$ radian during more than $200$ radian phase evolution
irrespective of the models. We also find that the gravitational-wave phase
error for a model with a tabulated equation of state is comparable to that for
a piece-wise polytropic equation of state. Then we calibrate the proposed
universal relations between a post-merger gravitational wave signal and tidal
deformability/neutron star radius in the literature. We find that they suffer
from systematics and many relations proposed as universal are not very
universal. We also propose improved fitting formulae. Finally, we validate\ the
SACRA gravitational waveform template which will be used to extract tidal
deformability from gravitational wave observation and find that accuracy of our
waveform modeling is $\lesssim 0.1$ radian in the gravitational-wave phase and
$\lesssim 20 \%$ in the gravitational-wave amplitude up to the
gravitational-wave frequency $1000$ Hz.