Magnetars, highly magnetized neutron stars, can have crustal quakes that disrupt their magnetic fields, causing X-ray and fast radio bursts (FRBs). This study uses simulations to model plasma waves in magnetar magnetospheres and understand the transport of magnetic energy. We found that Alfvén waves can transform into fast magnetosonic (FMS) waves, especially when opposite-moving Alfvén waves interact in the equatorial region. When propagating along curved field lines, Alfvén waves generate FMS waves with twice their frequency at early times. About half of the converted FMS wave energy can be stored in a slowly decaying tail of FMS waves. Feedback of the magnetar crust only minimally affects the mode conversion. Our findings provide important clues for where magnetic energy is converted into radiation like FRBs, for example in electric zones of electrically dominated fields outgoing FMS waves develop naturally.
Research summary
Alfvén wave propagation along curved field lines can inject both high-frequency and low-frequency fast magnetosonic (FMS) waves into the inner magnetar magnetosphere. As Alfvén waves bounce along dipolar field lines, they generate a tail of FMS waves with decaying amplitudes that stores up to half of the total induced FMS wave energy.
If counter-propagating Alfvén waves interact, the conversion efficiency can be enhanced.
Plastic damping of Alfvén waves at the stellar surface has marginal effects on the outgoing FMS wave luminosity.
We present a thorough analysis of the numerical challenges of resolving Alfvén wave interactions in simplified models of dipolar magnetospheres. The constraints we show are universal for comparable numerical methods and relevant for the design of future computational work on this topic.
Visualizing science
Mode conversion of an Alfvén wave envelope: The initially linear Alfvénic perturbation propagates along magnetic field lines. Interaction with the curved magnetic field lines converts part of the Alfvén wave energy into fast magnetosonic modes propagating across field lines. Alfvén waves are strongly sheared due to the different lengths of magnetic field lines and bounce in the inner magnetosphere after reflection from the stellar surface. The fast wave amplitude relative to the magnetic field becomes significant as the generated pulses propagate outwards. Electric zones can develop (green contour).
Mode conversion of a half-wavelength Alfvén pulse: The initially linear Alfvénic perturbation propagates along magnetic field lines. Interaction with the curved magnetic field lines converts part of the Alfvén wave energy into fast magnetosonic modes propagating across field lines. Alfvén waves are strongly sheared due to the different lengths of magnetic field lines and bounce in the inner magnetosphere after reflection from the stellar surface. The fast wave amplitude relative to the magnetic field becomes significant as the generated pulses propagate outwards. Electric zones can develop (green contour).
Interaction of two half-wavelength out-of-phase Alfvén pulses: Two Alfvén waves launched symmetrically and out-of-phase are injected in both hemispheres. The Alfvén waves interact in the equatorial region and increase the efficiency of fast wave generation. The fast wave amplitude relative to the magnetic field becomes significant as the generated pulses propagate outwards. Electric zones can develop (green contour).
Interaction of two half-wavelength in-phase Alfvén pulses: Two Alfvén waves launched symmetrically and in phase are injected in both hemispheres. The Alfvén waves interact in the equatorial region and increase the efficiency of fast wave generation. The fast wave amplitude relative to the magnetic field becomes significant as the generated pulses propagate outwards. Electric zones can develop (green contour).
Collaborative results
Mahlmann, J. F., Aloy, M. Á. & Li, X. (2024), Force-free wave interaction in magnetar magnetospheres: Computational modeling in axisymmetry, arXiv:2405.12272
Jens Mahlmann 