Instability of twisted magnetar magnetospheres

Abstract

We present 3D force-free electrodynamics simulations of magnetar magnetospheres that demonstrate the instability of certain degenerate, high energy equilibrium solutions of the Grad–Shafranov equation. This result indicates the existence of an unstable branch of twisted magnetospheric solutions and allows us to formulate an instability criterion. The rearrangement of magnetic field lines as a consequence of this instability triggers the dissipation of up to 30 per cent of the magnetospheric energy on a thin layer above the magnetar surface. During this process, we predict an increase of the mechanical stresses on to the stellar crust, which can potentially result in a global mechanical failure of a significant fraction of it. We find that the estimated energy release and the emission properties are compatible with the observed giant flare events. The newly identified instability is a candidate for recurrent energy dissipation, which could explain part of the phenomenology observed in magnetars.

Computational general relativistic force-free electrodynamics

“…The following sections as well as the code implementation in the Einstein Toolkit employ units where M = G = c = 1, which sets the respective time and length scales to be 1M ≡ 4.93 × 10 −6 s ≡ 1477.98 m. This unit system is a variation of the so-called system of geometrized units (as introduced in appendix F of Wald 2010), with the additional normalization of the mass to 1M (see also Mahlmann et al 2019, on unit conversion in the Einstein Toolkit). In the following, Latin indices denote spatial indices, running from 1 to 3; Greek indices denote space-time indices, running from 0 to 3 (0 is the time coordinate).…”

“…Such nonconservative splitting -chipping off parts of the flux terms -requires diligent attention and is prone to have a significant impact on the quality of the numerical evolution. We dedicate section 3.4 and a large part of Paper II (Mahlmann et al 2020a) to the implementation of current closure. In practice, the combination of the force-free current (49) as a source-term to Eq.…”

“…The discussion of techniques to ensure a physical (cf. McKinney 2006) evolution of numerical force-free codes is a recurrent topic that can be found throughout the literature (e.g., Lyutikov 2003;Komissarov 2004;Palenzuela et al 2010;Alic et al 2012;Paschalidis & Shapiro 2013;Carrasco & Reula 2017;Parfrey et al 2017;Mahlmann et al 2019). We review one of these techniques in Sect.…”

“…We demonstrate that our code correctly reproduces the features of the force-free magnetosphere inside of the pulsar light cylinder r LC = c/Ω p . We transparently point out the consequences of the emerging equatorial current sheet in ideal FFE, to which we ultimately dedicate paper II of this series (Mahlmann et al 2020a). This test sets up the initial data of Eq.…”

Striped Blandford/Znajek jets from advection of small-scale magnetic field

“…Lyutikov 2003;Komissarov 2004;Palenzuela et al 2010;Alic et al 2012;Paschalidis & Shapiro 2013;Carrasco & Reula 2016;Parfrey et al 2017). A review of the employed conservative system of equations, and techniques to minimise numerical errors is given in appendix A1, as well as Mahlmann et al (2019).…”