Dynamics of Strongly Twisted Relativistic Magnetospheres

TL;DR

This paper uses time-dependent simulations to explore how strongly twisted relativistic magnetospheres, such as those around magnetars, evolve, become unstable, and release energy through magnetic reconnection, affecting stellar spin-down rates.

Contribution

It provides the first detailed time-dependent analysis of the evolution and instability of strongly twisted relativistic magnetospheres, including the effects of differential rotation and magnetic reconnection.

Findings

Magnetospheres become tearing-mode unstable at a critical twist angle.

Rapid shearing can stabilize the magnetosphere beyond the critical point.

Shearing increases the star's spindown torque and causes measurable rate spikes.

Abstract

Magnetar magnetospheres are believed to be strongly twisted, due to shearing of the stellar crust by internal magnetic stresses. We present time-dependent axisymmetric simulations showing in detail the evolution of relativistic force-free magnetospheres subjected to slow twisting through large angles. When the twist amplitude is small, the magnetosphere moves quasi-statically through a sequence of equilibria of increasing free energy. At some twist amplitude the magnetosphere becomes tearing-mode unstable to forming a resistive current sheet, initiating large-scale magnetic reconnection in which a significant fraction of the magnetic free energy can be dissipated. This "critical" twist angle is insensitive to the resistive length scale. Rapid shearing temporarily stabilizes the magnetosphere beyond the critical angle, allowing the magnetosphere of a rapidly differentially rotating star to store, and dissipate, more free energy. In addition to these effects, shearing the surface of a rotating star increases the spindown torque applied to the star. If shearing is much slower than rotation, the resulting spikes in spindown rate can occur on timescales anywhere from the long twisting timescale to the stellar spin period or shorter, depending both on the stellar shear distribution and the existing distribution of magnetospheric twists. A model in which energy is stored in the magnetosphere, and released by a magnetospheric instability, therefore predicts large changes in the measured spindown rate before SGR giant flares.