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Register a new userHall cascade with fractional magnetic helicity in neutron star crusts
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Authors
Axel Brandenburg
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The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time $t$: $propto t^{-2/5}$ instead of $propto t^{-2/3}$ in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber $k$ is compatible with earlier findings for the forced Hall cascade, i.e., proportional to $k^{-7/3}$, but in the decaying cases, the subinertial range spectrum steepens to a novel $k^5$ slope instead of the $k^4$ slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the root-mean square (rms) magnetic field. For neutron star conditions with an rms magnetic field of a few times $10^{14},$G, the large-scale magnetic field might only be $10^{11},$G, while still producing magnetic dissipation of $10^{33},$erg$,$s$^{-1}$ for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries.
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In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which Ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are Hall equilibria, i.e., field configurations that are unaffected by Hall drift. Here, we address the crucial question of the stability of these equilibria through axially symmetric (2D) numerical simulations of Hall drift and Ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D-stability of a purely poloidal equilibrium, for which Ohmic dissipation makes the field evolve towards an attractor state through adjacent stable configurations, around which damped oscillations occur. For this field, the decay scales with the Ohmic timescale. We also study the case of an unstable equilibrium consisting of both poloidal and toroidal field components that are confined within the crust. This field evolves into a stable configuration, which undergoes damped oscillations superimposed on a slow evolution towards an attractor, just as the purely poloidal one.
We report results from a convection dynamo simulation of proto-neutron star (PNS), with a nuclear equation of state (EOS) and the initial hydrodynamic profile taken from a neutrino radiation-hydrodynamics simulation of a massive stellar core-collapse. A moderately-rotating PNS with the spin period of $170$ ms in the lepton-driven convection stage is focused. We find that large-scale flow and thermodynamic fields with north-south asymmetry develop in the turbulent flow, as a consequence of the convection in the central part of the PNS, which we call as a deep core convection. Intriguingly, even with such a moderate rotation, large-scale, $10^{15}$ G, magnetic field with dipole symmetry is spontaneously built up in the PNS. The turbulent electro-motive force arising from rotationally-constrained core convection is shown to play a key role in the large-scale dynamo. The large-scale structures organized in the PNS may impact the explosion dynamics of supernovae and subsequent evolution to the neutron stars.
We calculate for the first time the phonon excitation rate in the outer crust of a neutron star due to scattering from light dark matter (LDM) particles gravitationally boosted into the star. We consider dark matter particles in the sub-GeV mass range scattering off a periodic array of nuclei through an effective scalar-vector interaction with nucleons. We find that LDM effects cause a modification of the net number of phonons in the lattice as compared to the standard thermal result. In addition, we estimate the contribution of LDM to the ion-ion thermal conductivity in the outer crust and find that it can be significantly enhanced at large densities. Our results imply that for magnetized neutron stars the LDM-enhanced global conductivity in the outer crust will tend to reduce the anisotropic heat conduction between perpendicular and parallel directions to the magnetic field.
Magnetic field evolution in neutron-star crusts is driven by the Hall effect and Ohmic dissipation, for as long as the crust is sufficiently strong to absorb Maxwell stresses exerted by the field and thus make the momentum equation redundant. For the strongest neutron-star fields, however, stresses build to the point of crustal failure, at which point the standard evolution equations are no longer valid. Here, we study the evolution of the magnetic field of the crust up to and beyond crustal failure, whence the crust begins to flow plastically. We perform global axisymmetric evolutions, exploring different types of failure affecting a limited region of the crust. We find that a plastic flow does not simply suppress the Hall effect even in the regime of a low plastic viscosity, but it rather leads to non-trivial evolution -- in some cases even overreacting and enhancing the impact of the Hall effect. Its impact is more pronouced in the toroidal field, with the differences on the poloidal field being less substantial. We argue that both the nature of magnetar bursts and their spindown evolution will be affected by plastic flow, so that observations of these phenomena may help to constrain the way the crust fails.
Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudo-vacuum condition on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha^2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, most of the magnetic helicity losses occur at large scales. Whether this changes at even larger magnetic Reynolds numbers, as required for alleviating the catastrophic dynamo quenching problem, remains still unclear.
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