Resistive Tearing Instability in Electron-MHD: Application to Neutron Star Crusts

Abstract

We study a resistive tearing instability developing in a system evolving through the combined effect of Hall drift in the Electron-MHD limit and Ohmic dissipation. We explore first the exponential growth of the instability in the linear case and we find the fastest growing mode, the corresponding eigenvalues and dispersion relation. The instability growth rate scales as $\gamma \propto B^{2/3}{\sigma }^{-1/3}$ where $B$ is the magnetic field and $\sigma$ the electrical conductivity. We confirm the development of the tearing resistive instability in the fully non-linear case, in a plane parallel configuration where the magnetic field polarity reverses, through simulations of systems initiating in Hall equilibrium with some superimposed perturbation. Following a transient phase, during which there is some minor rearrangement of the magnetic field, the perturbation grows exponentially. Once the instability is fully developed the magnetic field forms the characteristic islands and X-type reconnection points, where Ohmic decay is enhanced. We discuss the implications of this instability for the local magnetic field evolution in neutron stars' crusts, proposing that it can contribute to heating near the surface of the star, as suggested by models of magnetar post-burst cooling. In particular, we find that a current sheet a few meters thick, covering as little as $1\%$ of the total surface can provide $10^{42}$erg in thermal energy within a few days. We briefly discuss applications of this instability in other systems where the Hall effect operates such as protoplanetary discs and space plasmas.

Accepted by MNRAS, 10 pages, 10 Figures

References in corpus (13)

• Magnetic field dissipation in neutron star crusts: from magnetars to isolated neutron stars
• Three-dimensional numerical simulations of the pulsar magentoshere: Preliminary results
• Three-dimensional simulations of the magnetic stress in a neutron star crust
• Tearing instability in relativistic magnetically dominated plasmas
• A new code for the Hall-driven magnetic evolution of neutron stars
• Hall drift and the braking indices of young pulsars
• Thermoplastic waves in magnetars
• Creation of magnetic spots at the neutron star surface
• Repeated, Delayed Torque Variations Following X-ray Flux Enhancements in the Magnetar 1E1048.1$-$5937
• Forward and inverse cascades in decaying two-dimensional electron magnetohydrodynamic turbulence
• Hall drift of axisymmetric magnetic fields in solid neutron-star matter
• Density-shear instability in electron MHD
• Stability of Hall equilibria in neutron star crusts

Cited by in corpus (10)

• Magnetic-field evolution in a plastically-failing neutron-star crust
• Magnetic Axis Drift and Magnetic Spot Formation in Neutron Stars with Toroidal Fields
• Powering Central Compact Objects with a Tangled Crustal Magnetic Field
• Magnetic Field Evolution in Neutron Star Crusts: Beyond the Hall Effect
• Combined magnetic field evolution in neutron star cores and crusts: Ambipolar diffusion, Hall effect and Ohmic dissipation
• Nonaxisymmetric Hall instability: A key to understanding magnetars
• Interlinking internal and external magnetic fields of relativistically rotating neutron stars
• Hall instability: origin, properties, and asymptotic theory for its tearing mode
• Magnetic Field Evolution in the Crust of Neutron Stars: Crust Failure and Plastic Flow
• Stratified Resistive Tearing Instability