Efficient magnetic-field amplification due to the Kelvin-Helmholtz instability in binary neutron star mergers

We explore magnetic-field amplification due to the Kelvin-Helmholtz instability during binary neutron star mergers. By performing high-resolution general relativistic magnetohydrodynamics simulations with a resolution of 17.5 m for 4--5 ms after the onset of the merger on the Japanese supercomputer ``K'', we find that an initial magnetic field of moderate maximum strength ${10}^{13}\text{ }\text{ }\mathrm{G}$ is amplified at least by a factor of $\ensuremath{\approx}{10}^{3}$. We also explore the saturation of the magnetic-field energy and our result shows that it is likely to be $\ensuremath{\gtrsim}4\ifmmode\times\else\texttimes\fi{}{10}^{50}\text{ }\text{ }\mathrm{erg}$, which is $\ensuremath{\gtrsim}0.1%$ of the bulk kinetic energy of the merging binary neutron stars.