Hall cascades versus instabilities in neutron star magnetic fields

Abstract

The Hall effect is an important nonlinear mechanism affecting the evolution of magnetic fields in neutron stars. Studies of the governing equation, both theoretical and numerical, have shown that the Hall effect proceeds in a turbulent cascade of energy from large to small scales. We investigate the small-scale Hall instability conjectured to exist from the linear stability analysis of Rheinhardt and Geppert. Identical linear stability analyses are performed to find a suitable background field to model Rheinhardt and Geppert's ideas. The nonlinear evolution of this field is then modelled using a three-dimensional pseudospectral numerical MHD code. Combined with the background field, energy was injected at the ten specific eigenmodes with the greatest positive eigenvalues as inferred by the linear stability analysis. Energy is transferred to different scales in the system, but not into small scales to any extent that could be interpreted as a Hall instability. Any instabilities are overwhelmed by a late-onset turbulent Hall cascade, initially avoided by the choice of background field, but soon generated by nonlinear interactions between the growing eigenmodes. The Hall cascade is shown here, and by several authors elsewhere, to be the dominant mechanism in this system.

7 pages, 3 figures, accepted to Astronomy & Astrophysics

References in corpus (3)

• Magnetic field dissipation in neutron star crusts: from magnetars to isolated neutron stars
• Simulations of Electron Magnetohydrodynamic Turbulence
• Forward and inverse cascades in decaying two-dimensional electron magnetohydrodynamic turbulence

Cited by in corpus (13)

• Hall Effect in Neutron Star Crusts: Evolution, Endpoint and Dependence on Initial Conditions
• Hall Attractor in Axially Symmetric Magnetic Fields in Neutron Star Crusts
• Global Crustal Dynamics of Magnetars in Relation to their Bright X-ray Outbursts
• Stability and instability of hydromagnetic Taylor-Couette flows
• Magnetic Helicity Conservation and Inverse Energy Cascade in Electron Magnetohydrodynamic Wave Packets
• Post fall-back evolution of multipolar magnetic fields and radio pulsar activation
• Confirmation of the occurrence of the Hall instability in the non-linear regime
• Magnetic Field Evolution in Neutron Star Crusts: Beyond the Hall Effect
• Magnetic field configurations in neutron stars from MHD simulations
• Nonaxisymmetric Hall instability: A key to understanding magnetars
• The shear-Hall instability in newborn neutron stars
• Approximative Analytic Study of Fermions in Magnetar's Crust; Ultra-relativistic Plane Waves, Heun and Mathieu Solutions and Beyond
• Reality of inverse cascading in neutron star crusts