Alfv\'en Wave Conversion to Low Frequency Fast Magnetosonic Waves in Magnetar Magnetospheres

TL;DR

This study uses simulations to explore how Alfvén waves in magnetar magnetospheres convert into fast magnetosonic waves, potentially powering X-ray bursts, with the conversion efficiency depending on wave properties.

Contribution

It provides the first detailed simulation-based analysis of Alfvén to fast wave conversion in magnetar magnetospheres, highlighting the dependence on wave filling and energy.

Findings

Fast waves dominate when Alfvén waves do not fill the flux tube completely.

Complete filling of the flux tube leads to higher frequency fast waves at twice the Alfvén frequency.

Conversion efficiency depends on initial wave energy, duration, and wavelength.

Abstract

Rapid shear motion of magnetar crust can launch Alfv\'{e}n waves into the magnetosphere. The dissipation of the Alfv\'{e}n waves has been theorized to power the X-ray bursts characteristic of magnetars. However, the process by which Alfv\'{e}n 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\'{e}n 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\'{e}n waves propagating in a dipolar magnetosphere. For Alfv\'{e}n 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\'{e}n waves. In contrast, when the wave train is long enough to completely fill the flux tube, and the Alfv\'{e}n waves overlap significantly, the energy is quickly converted into a fast wave with a higher frequency that corresponds to twice the Alfv\'{e}n wave frequency. We investigate how the energy, duration, and wavelength of the initial Alfv\'{e}n 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.