Magnetar activity via the density–shear instability in Hall-MHD

Abstract

We investigate the density-shear instability in Hall-MHD via numerical simulation of the full non-linear problem, in the context of magnetar activity. We confirm the development of the instability of a plane-parallel magnetic field with an appropriate intensity and electron density profile, in accordance with analytic theory. We find that the instability also appears for a monotonically decreasing electron number density and magnetic field, a plane-parallel analogue of an azimuthal or meridional magnetic field in the crust of a magnetar. The growth rate of the instability depends on the Hall properties of the field (magnetic field intensity, electron number density and the corresponding scale-heights), while being insensitive to weak resistivity. Since the Hall effect is the driving process for the evolution of the crustal magnetic field of magnetars, we argue that this instability is critical for systems containing strong meridional or azimuthal fields. We find that this process mediates the formation of localised structures with much stronger magnetic field than the average, which can lead to magnetar activity and accelerate the dissipation of the field and consequently the production of Ohmic heating. Assuming a 5 × 10 14 G magnetic field at the base of crust, we anticipate that magnetic field as strong as 10 15 G will easily develop in regions of typical size of a few 10 2 meters, containing magnetic energy of 10 43 erg, sufficient to power magnetar bursts. These active regions are more likely to appear in the magnetic equator where the tangential magnetic field is stronger.

Modelling neutron star magnetic fields

“…Of particular interest is the speed at which such instabilities could develop, the total amount of energy liberated, and whether this could be related to observations of magnetar bursts. Numerical calculations in local box geometry (Gourgouliatos et al 2015, Gourgouliatos & Hollerbach 2016 indicate that localized spots with fields up to 10 15 G can develop, and can release up to 10 42 erg via ohmic heating within a few days, consistent with observed outbursts.…”

Magnetic field evolution in magnetar crusts through three-dimensional simulations

“…These features are well above the resolution of the simulation and appear both in the low and high resolution runs. This behaviour is indicative of the density-shear instability in Hall-MHD, where, based on analytical arguments [21,22], the wavelength of the dominant mode is 2πL where L is the scale height of the electron density and the magnetic field, which can be approximated by the thickness of the crust.…”

Evolution of Neutron Star Magnetic Fields

“…Further work in Hall instabilities has also considered more local aspects, such as instabilities that can develop in small-scale current sheets [80][81][82][83][84]. The depth-dependence of the electron number density n e plays an important role in many of these instability modes.…”