Alfv\'en Wave Conversion to Low Frequency Fast Magnetosonic Waves in Magnetar Magnetospheres
Abstract
Rapid shear motion of magnetar crust can launch Alfv\'en waves into the magnetosphere. The dissipation of the Alfv\'en waves has been theorized to power the X-ray bursts characteristic of magnetars. However, the process by which Alfv\'en waves convert their energy to X-rays is unclear. Recent work has suggested that energetic fast magnetosonic (fast) waves can be produced as a byproduct of Alfv\'en waves propagating on curved magnetic field lines; their subsequent dissipation may power X-ray bursts. In this work, we investigate the production of fast waves by performing axisymmetric force-free simulations of Alfv\'en waves propagating in a dipolar magnetosphere. For Alfv\'en wave trains that do not completely fill the flux tube confining them, we find a fast wave dominated by a low frequency component with a wavelength defined by the bouncing time of the Alfv\'en waves. In contrast, when the wave train is long enough to completely fill the flux tube, and the Alfv\'en waves overlap significantly, the energy is quickly converted into a fast wave with a higher frequency that corresponds to twice the Alfv\'en wave frequency. We investigate how the energy, duration, and wavelength of the initial Alfv\'en wave train affect the conversion efficiency to fast waves. For modestly energetic star quakes, we see that the fast waves that are produced will become non-linear well within the magnetosphere, and we comment on the X-ray emission that one may expect from such events.
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