Sub-radian-accuracy gravitational waveforms of coalescing binary neutron stars in numerical relativity

Extending our previous studies, we perform high-resolution simulations of inspiraling binary neutron stars in numerical relativity. We thoroughly carry through a convergence study in our currently available computational resources with the smallest grid spacing of $\ensuremath{\approx}63--86$ meter for the neutron-star radius 10.9--13.7 km. The estimated total error in the gravitational-wave phase is of order 0.1 rad for the total phase of $\ensuremath{\gtrsim}210\text{ }\text{ }\mathrm{rad}$ in the last $\ensuremath{\sim}15--16$ inspiral orbits. We then compare the waveforms (without resolution extrapolation) with those calculated by the latest effective-one-body formalism (tidal SEOBv2 model referred to as TEOB model). We find that for any of our models of binary neutron stars, the waveforms calculated by the TEOB formalism agree with the numerical-relativity waveforms up to $\ensuremath{\approx}3\text{ }\text{ }\mathrm{ms}$ before the peak of the gravitational-wave amplitude is reached: For this late inspiral stage, the total phase error is $\ensuremath{\lesssim}0.1\text{ }\text{ }\mathrm{rad}$. Although the gravitational waveforms have an inspiral-type feature for the last $\ensuremath{\sim}3\text{ }\text{ }\mathrm{ms}$, this stage cannot be well reproduced by the current TEOB formalism, in particular, for neutron stars with large tidal deformability (i.e., lager radius). The reason for this is described.