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Abstract:
Magnetar flares excite strong Alfvén waves in the magnetosphere of a neutron star. The wave energy can (1)
dissipate in the magnetosphere, (2) convert to “fast modes” and possibly escape, and (3) penetrate the neutron star
crust and dissipate there. We examine and compare the three options. Particularly challenging are nonlinear
interactions between strong waves, which develop a cascade to small dissipative scales. This process can be studied
in the framework of force-free electrodynamics (FFE). We perform three-dimensional FFE simulations to
investigate Alfvén wave dissipation in a constant background magnetic field, how long it takes, and how it depends
on the initial wave amplitude on the driving scale. In the simulations, we launch two large Alfvén wave packets
that keep bouncing in a periodic computational box and collide repeatedly until the full turbulence spectrum
develops. Besides dissipation due to the turbulent cascade, we find that in some simulations spurious energy losses
occur immediately in the first collisions. This effect occurs in special cases where the FFE description breaks. It is
explained with a simple one-dimensional model, which we examine in both FFE and full magnetohydrodynamic
settings. Our results suggest that magnetospheric dissipation through nonlinear wave interactions is relatively slow,
and more energy is drained into the neutron star. The wave energy deposited into the star is promptly dissipated
through plastic crustal flows induced at the bottom of the liquid ocean, and a fraction of the generated heat is
radiated from the stellar surface.
