Force-free wave interaction in magnetar magnetospheres: Computational modeling in axisymmetry

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Magnetars, highly magnetized neutron stars, can experience crustal quakes that disrupt their magnetic fields and cause X-ray and fast radio bursts (FRBs). This study uses simulations to model plasma waves in magnetar magnetospheres and to understand how magnetic energy is transported. We find that Alfvén waves can transform into fast magnetosonic (FMS) waves, especially when counter-propagating Alfvén waves interact in the equatorial region. When propagating along curved field lines, Alfvén waves initially generate FMS waves with twice their frequency. About half of the converted FMS wave energy is carried by a slowly decaying tail of FMS waves. Feedback from the magnetar crust only minimally affects the mode conversion. Our findings provide important clues about where magnetic energy is converted into radiation such as FRBs. For example, outgoing FMS waves naturally develop electric zones, regions where the electric field dominates over the magnetic field.

Research summary

  • Alfvén waves propagating 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 carries up to half of the total induced FMS wave energy.
  • The interaction of counter-propagating Alfvén waves can enhance the conversion efficiency by up to a factor of three.
  • Plastic damping of Alfvén waves at the stellar surface has only 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 identify apply to comparable numerical methods and are relevant for the design of future computational work on this topic.

Visualizing science

Mode conversion of an Alfvén wave envelope: An initially linear Alfvénic perturbation propagates along magnetic field lines. Interaction with the curved field converts part of the Alfvén wave energy into fast magnetosonic modes that propagate across field lines. Because the field lines differ in length, the Alfvén waves become strongly sheared and bounce through the inner magnetosphere after reflecting off the stellar surface. As the generated pulses propagate outward, the fast wave amplitude becomes significant relative to the magnetic field. Green contours mark regions where electric zones develop.
Mode conversion of a half-wavelength Alfvén pulse: An initially linear Alfvénic perturbation propagates along magnetic field lines. Interaction with the curved field converts part of the Alfvén wave energy into fast magnetosonic modes that propagate across field lines. Because the field lines differ in length, the Alfvén wave becomes strongly sheared and bounces through the inner magnetosphere after reflecting off the stellar surface. As the generated pulses propagate outward, the fast wave amplitude becomes significant relative to the magnetic field. Green contours mark regions where electric zones develop.
Interaction of two half-wavelength out-of-phase Alfvén pulses: Two Alfvén waves are launched symmetrically and out of phase, one in each hemisphere. Their interaction in the equatorial region increases the efficiency of fast wave generation. As the generated pulses propagate outward, the fast wave amplitude becomes significant relative to the magnetic field. Green contours mark regions where electric zones develop.
Interaction of two half-wavelength in-phase Alfvén pulses: Two Alfvén waves are launched symmetrically and in phase, one in each hemisphere. Their interaction in the equatorial region increases the efficiency of fast wave generation. As the generated pulses propagate outward, the fast wave amplitude becomes significant relative to the magnetic field. Green contours mark regions where electric zones develop.

Collaborative results

Mahlmann, J. F., Aloy, M. Á., & Li, X. (2024). Force-free wave interaction in magnetar magnetospheres: Computational modeling in axisymmetry. The Astrophysical Journal, arXiv:2405.12272