We derive general equations for axisymmetric Newtonian MHD and use these as the basis of a code for calculating equilibrium configurations of rotating magnetised neutron stars in a stationary state. We investigate the field configurations that result from our formalism, which include purely poloidal, purely toroidal and mixed fields. For the mixed-field formalism the toroidal component appears to be bounded at less than 7%. We calculate distortions induced both by magnetic fields and by rotation. From our non-linear work we are able to look at the realm of validity of perturbative work: we find for our results that perturbative-regime formulae for magnetic distortions agree to within 10% of the nonlinear results if the ellipticity is less than 0.15 or the average field strength is less than $10^{17}$ G. We also consider how magnetised equilibrium structures vary for different polytropic indices.Comment: 19 pages, 11 figures; typos removed, one paragraph of Discussion rewritte

The problem of the stability of magnetic fields in stars has a long history and has been investigated in detail in perturbation theory. Here we consider the nonlinear evolution of a nonrotating neutron star with a purely poloidal magnetic field, in general relativity. We find that an instability develops in the region of the closed magnetic field lines and over an Alfvén timescale, as predicted by perturbation theory. After the initial unstable growth, our evolutions show that a toroidal magnetic field component is generated, which increases until it is locally comparable in strength with the poloidal one. On longer timescales the system relaxes to a new non-axisymmetric configuration with a reorganization of the stellar structure and large-amplitude oscillations, mostly in the fundamental mode. We discuss the energies involved in the instability and the impact they may have on the phenomenology of magnetar flares and on their detectability through gravitational-wave emission.

Crustquake events may be connected with both rapid spin-up 'glitches' within the regular slowdown of neutron stars, and high-energy magnetar flares. We argue that magnetic field decay builds up stresses in a neutron star's crust, as the elastic shear force resists the Lorentz force's desire to rearrange the global magnetic-field equilibrium. We derive a criterion for crust-breaking induced by a changing magnetic-field configuration, and use this to investigate strain patterns in a neutron star's crust for a variety of different magnetic-field models. Universally, we find that the crust is most liable to break if the magnetic field has a strong toroidal component, in which case the epicentre of the crustquake is around the equator. We calculate the energy released in a crustquake as a function of the fracture depth, finding that it is independent of field strength. Crust-breaking is, however, associated with a characteristic local field strength of 2.4 × 10 14 G for a breaking strain of 0.001, or 2.4 × 10 15 G at a breaking strain of 0.1. We find that even the most luminous magnetar giant flare could have been powered by crustal energy release alone.

In the current work we explore the applicability of standard theoretical models of accretion to the observed properties of M51 ULX-7. The spin-up rate and observed X-ray luminosity are evidence of a neutron star with a surface magnetic field of 2 − 7 × 10 13 G, rotating near equilibrium. Analysis of the X-ray light-curve of the system (Swift/XRT data) reveals the presence of a ∼39 d super-orbital period. We argue that the super-orbital periodicity is due to disc precession, and that material is accreted onto the neutron star at a constant rate throughout it. Moreover, by attributing this modulation to the free precession of the neutron star we estimate a surface magnetic field strength of 3 − 4 × 10 13 G. The agreement of these two independent estimates provide strong constraints on the surface polar magnetic field strength of the neutron star.

The presence of superconducting and superfluid components in the core of mature neutron stars calls for the rethinking of a number of key magnetohydrodynamical notions like resistivity, the induction equation, magnetic energy and flux-freezing. Using a multi-fluid magnetohydrodynamics formalism, we investigate how the magnetic field evolution is modified when neutron star matter is composed of superfluid neutrons, type-II superconducting protons and relativistic electrons. As an application of this framework, we derive an induction equation where the resistive coupling originates from the mutual friction between the electrons and the vortex/fluxtube arrays of the neutron and proton condensates. The resulting induction equation allows the identification of two timescales that are significantly different from those of standard magnetohydrodynamics. The astrophysical implications of these results are briefly discussed.

We construct barotropic stellar equilibria, containing magnetic fields with both poloidal and toroidal field components. We extend earlier results by exploring the effect of different magnetic field and current distributions. Our results suggest that the boundary treatment plays a major role in whether the poloidal or toroidal field component is globally dominant. Using time evolutions we provide the first stability test for mixed poloidal-toroidal fields in barotropic stars, finding that all these fields suffer instabilities due to one of the field components: these are localised around the pole for toroidal-dominated equilibria and in the closed-field line region for poloidal-dominated equilibria. Rotation provides only partial stabilisation. There appears to be very limited scope for the existence of stable magnetic fields in barotropic stars. We discuss what additional physics from real stars may allow for stable fields.Comment: 16 pages, 11 figures. Some minor revision from v1, including a new figure; results unchanged. Now published in MNRA

Under normal conditions in a neutron-star crust, ions are locked in place in the crustal lattice and only electrons are mobile, and magnetic-field evolution is thus directly related to the electron velocity. The evolution, however, builds magnetic stresses that can become sufficiently large for the crust to exceed its elastic limit, and to flow plastically. We consider the nature of this plastic flow and the back-reaction on the crustal magnetic field evolution. We formulate a plane-parallel model for the local failure, showing that surface motions are inevitable once the crust yields, in the absence of extra dissipative mechanisms. We perform numerical evolutions of the crustal magnetic field under the joint effect of Hall drift and Ohmic decay, tracking the build-up of magnetic stresses, and diagnosing crustal failure with the von Mises criterion. Beyond this point we solve for the coupled evolution of the plastic velocity and magnetic field. Our results suggest that to have a coexistence of a magnetar corona with small-scale magnetic features, the viscosity of the plastic flow must be roughly 10 36 − 10 37 g cm −1 s −1 . We find significant motion at the surface at a rate of 10 − 100 centimetres per year, and that the localised magnetic field is weaker than in evolutions without plastic flow. We discuss astrophysical implications, and how our local simulations could be used to build a global model of field evolution in the neutron-star crust.

We investigate the oscillation spectrum of rotating Newtonian neutron stars endowed with purely toroidal magnetic fields, using a time‐evolution code to evolve linear perturbations in the Cowling approximation. The background star is generated by numerically solving the magnetohydrodynamics equilibrium equations and may be non‐spherical by virtue of both rotation and magnetic effects; hence, our perturbations and background are fully consistent. Whilst the background field is purely toroidal, the perturbed field is mixed poloidal–toroidal. From Fourier analysis of the perturbations, we are able to identify a number of magnetically restored Alfvén (or a) modes. We show that in a rotating star pure inertial and a‐modes are replaced by hybrid magneto‐inertial modes, which reduce to a‐modes in the non‐rotating limit and inertial modes in the non‐magnetic limit. We show that the r‐mode instability is suppressed by magnetic fields in sufficiently slowly rotating stars. In addition, we determine magnetic frequency shifts in the f‐mode. We discuss the astrophysical relevance of our results, in particular for magnetar oscillations.