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Abstract

Long-term ideal and resistive magnetohydrodynamics (MHD) simulations in full
general relativity are performed for a massive neutron star formed as a remnant
of binary neutron star mergers. Neutrino radiation transport effects are taken
into account as in our previous papers. The simulation is performed in axial
symmetry and without considering dynamo effects as a first step. In the ideal
MHD, the differential rotation of the remnant neutron star amplifies the
magnetic-field strength by the winding in the presence of a seed poloidal field
until the electromagnetic energy reaches $\sim 10\%$ of the rotational kinetic
energy, $E_{\rm kin}$, of the neutron star. The timescale until the maximum
electromagnetic energy is reached depends on the initial magnetic-field
strength and it is $\sim 1$ s for the case that the initial maximum
magnetic-field strength is $\sim 10^{15}$ G. After a significant amplification
of the magnetic-field strength by the winding, the magnetic braking enforces
the initially differentially rotating state approximately to a rigidly rotating
state. In the presence of the resistivity, the amplification is continued only
for the resistive timescale, and if the maximum electromagnetic energy reached
is smaller than $\sim 3\%$ of $E_{\rm kin}$, the initial differential rotation
state is approximately preserved. In the present context, the post-merger mass
ejection is induced primarily by the neutrino irradiation/heating and the
magnetic winding effect plays only a minor role for the mass ejection.