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Register a new userStability of Hall equilibria in neutron star crusts
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Pablo Marchant Campos
Publication date
2014
fields
Physics
and research's language is
English
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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.
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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fields, however, stresses build to the point of crustal failure, at which point the standard evolution equations are no longer valid.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.
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.
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.
A systematic search for multicomponent crystal structures is carried out for five different ternary systems of nuclei in a polarizable background of electrons, representative of accreted neutron star crusts and some white dwarfs. Candidate structures are bred by a genetic algorithm, and optimized at constant pressure under the assumption of linear response (Thomas-Fermi) charge screening. Subsequent phase equilibria calculations reveal eight distinct crystal structures in the $T=0$ bulk phase diagrams, five of which are complicated multinary structures not before predicted in the context of compact object astrophysics. Frequent instances of geometrically similar but compositionally distinct phases give insight into structural preferences of systems with pairwise Yukawa interactions, including and extending to the regime of low density colloidal suspensions made in a laboratory. As an application of these main results, we self-consistently couple the phase stability problem to the equations for a self-gravitating, hydrostatically stable white dwarf, with fixed overall composition. To our knowledge, this is the first attempt to incorporate complex multinary phases into the equilibrium phase layering diagram and mass-radius-composition dependence, both of which are reported for He-C-O and C-O-Ne white dwarfs. Finite thickness interfacial phases (interphases) show up at the boundaries between single-component bcc crystalline regions, some of which have lower lattice symmetry than cubic. A second application -- quasi-static settling of heavy nuclei in white dwarfs -- builds on our equilibrium phase layering method. Tests of this nonequilibrium method reveal extra phases which play the role of transient host phases for the settling species.
X-ray observations of transiently accreting neutron stars during quiescence provide information about the structure of neutron star crusts and the properties of dense matter. Interpretation of the observational data requires an understanding of the nuclear reactions that heat and cool the crust during accretion, and define its nonequilibrium composition. We identify here in detail the typical nuclear reaction sequences down to a depth in the inner crust where the mass density is 2E12 g/cm^3 using a full nuclear reaction network for a range of initial compositions. The reaction sequences differ substantially from previous work. We find a robust reduction of crust impurity at the transition to the inner crust regardless of initial composition, though shell effects can delay the formation of a pure crust somewhat to densities beyond 2E12 g/cm^3. This naturally explains the small inner crust impurity inferred from observations of a broad range of systems. The exception are initial compositions with A >= 102 nuclei, where the inner crust remains impure with an impurity parameter of Qimp~20 due to the N = 82 shell closure. In agreement with previous work we find that nuclear heating is relatively robust and independent of initial composition, while cooling via nuclear Urca cycles in the outer crust depends strongly on initial composition. This work forms a basis for future studies of the sensitivity of crust models to nuclear physics and provides profiles of composition for realistic crust models.
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