Magnetic field dissipation in neutron star crusts: from magnetars to isolated neutron stars

Abstract

Context. We study the non-linear evolution of magnetic fields in neutron star crusts with special attention to the influence of the Hall drift. Aims. Our goal is to understand the conditions for fast dissipation due to the Hall term in the induction equation. We study the interplay of Ohmic dissipation and Hall drift in order to find a timescale for the overall crustal field decay. Methods. We solve numerically the Hall induction equation by means of a hybrid method (spectral in angles but finite differences in the radial coordinate). The microphysical input consists of the most modern available crustal equation of state, composition and electrical conductivities.Results. We present the first long term simulations of the non-linear magnetic field evolution in realistic neutron star crusts with a stratified electron number density and temperature dependent conductivity. We show that Hall drift influenced Ohmic dissipation takes place in neutron star crusts on a timescale of 10 6 years. When the initial magnetic field has magnetar strength, the fast Hall drift results in an initial rapid dissipation stage that lasts ∼ 10 4 years. The interplay of the Hall drift with the temporal variation and spatial gradient of conductivity tends to favor the displacement of toroidal fields toward the inner crust, where stable configurations can last for ∼ 10 6 years. We show that the thermally emitting isolated neutron stars, as the Magnificent Seven, are very likely descendants of neutron stars born as magnetars.

Is SGR 0418+5729 Indeed a Waning Magnetar?

“…The first attempts in this direction used a split approach. Pons & Geppert (2007) studied the evolution of the field by solving the complete induction equation in an isothermal crust, but assuming a prescribed time dependence for the temperature. They found that crustal magnetic fields in NSs suffer significant decay during the first ≈10 6 yr and that the Hall drift, although inherently conservative (i.e., alone it cannot dissipate magnetic energy), plays an important role since it may reorganize the field from the larger to the smaller (spatial) scales where Ohmic dissipation proceeds faster.…”

Magnetic field evolution in superconducting neutron stars

“…The actual mechanisms, causing the magnetic field to change on these rather short timescales, are only poorly understood and there is no definitive answer to the question of which part of the neutron star dominates the magnetic field evolution. Most theoretical studies and numerical simulations focus on the crust as the source of the field decay and neglect the core contribution (Pons & Geppert 2007;Viganò et al 2013;Gourgouliatos & Cumming 2014). However, one could argue that the core, which carries the majority of the star's inertia and magnetic energy, should also play a role in the magnetic field evolution.…”

Confirmation of the occurrence of the Hall instability in the non-linear regime

“…In that case, the Meissner-Ochsenfeld effect prevents the magnetic field from penetrating into the superconducting matter. This requires that the normal component of the magnetic field and the tangential components of the electric field have to vanish (Pons & Geppert 2007), i.e., we assume that B z = E x = E y = 0 at that interface. At the transition to a vacuum (z = +1), the analog to the toroidal component B y has to vanish, but the boundary conditions for the other components are not so simple.…”

“…They correctly pointed out that Hall currents are able to create current sheets (which are sites for efficient dissipation) and that the evolution of the toroidal field resembles the Burgers equation. The same Burgers-like equation is applicable even to non-stratified media, but in a spherical shell (Pons & Geppert 2007), in which the Hall term in the induction equation tends to create current sheets instead of ordinary turbulence. Rheinhardt & Geppert (2002, hencefort RG) showed by a linear analysis that, in a one-component (electron) plasma, a large-scale background magnetic field may become unstable to smaller scale perturbations.…”

“…An important component of their study was their estimate of the response of the crust to the magnetic stresses induced by Hall waves. Pons & Geppert (2007) performed 2D simulations by solving the non-linear Hallinduction equation in a realistic NS crust and found some evidence for a rapid reorganization of the field during a relatively short period, but no clear confirmation of the Hi could be concluded. The code again had numerical limitations that avoided additional exploration of extreme limits to confirm or rule out the existence of the Hi.…”