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Strong magnetic fields play an important role in powering the emission ofneutron stars. Nevertheless a full understanding of the interior configurationof the field remains elusive. In this work, we present General RelativisticMagnetoHydroDynamics simulations of the magnetic field evolution in neutronstars lasting 500 ms (5 Alfven crossing times) and up to resolutions of 0.231km using Athena++. We explore two different initial conditions, one with purelypoloidal magnetic field and the other with a dominant toroidal component, andstudy the poloidal and toroidal field energies, the growth times of the variousinstability-driven oscillation modes and turbulence. We find that the purelypoloidal setup generates a toroidal field which later decays exponentiallyreaching 1% of the total magnetic energy, showing no evidence of reachingequilibrium. The initially stronger toroidal field setup, on the other hand,loses up to 20% of toroidal energy and maintains this state till the end of oursimulation. We also explore the hypothesis, drawn from previous MHDsimulations, that turbulence plays an important role in the quasi equilibriumstate. An analysis of the spectra in our higher resolution setups reveal,however, that in most cases we are not observing turbulence at small scales,but rather a noisy velocity field inside the star. We also observe that themajority of the magnetic energy gets dissipated as heat increasing the internalenergy of the star, while a small fraction gets radiated away aselectromagnetic radiation.

Long-term GRMHD simulation of magnetic field in isolated neutron stars