Multi-fluid simulation of the magnetic field evolution in neutron stars (original) (raw)
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Magnetic field evolution in neutron stars: one-dimensional multi-fluid model
2008
Aims. This paper is the first in a series that aims to understand the long-term evolution of neutron star magnetic fields. Methods. We model the stellar matter as an electrically neutral and lightly-ionized plasma composed of three moving particle species: neutrons, protons, and electrons; these species can be converted into each other by weak interactions (beta decays), suffer binary collisions, and be affected by each other's macroscopic electromagnetic fields. Since the evolution of the magnetic field occurs over thousands of years or more, compared to dynamical timescales (sound and Alfvén) of milliseconds to seconds, we use a slow-motion approximation in which we neglect the inertial terms in the equations of motion for the particles. This approximation leads to three nonlinear partial-differential equations describing the evolution of the magnetic field, as well as the movement of two fluids: the charged particles (protons and electrons) and the neutrons. These equations are first rather than second order in time (involving the velocities of the three species but not their accelerations). Results. In this paper, we restrict ourselves to a one-dimensional geometry in which the magnetic field points in one Cartesian direction, but varies only along an orthogonal direction. We study the evolution of the system in three different ways: (i) estimating timescales directly from the equations, guided by physical intuition; (ii) a normal-mode analysis in the limit of a nearly uniform system; and (iii) a finite-difference numerical integration of the full set of nonlinear partial-differential equations. We find good agreement between our analytical normal-mode solutions and the numerical simulations. We show that the magnetic field and the particles evolve through successive quasi-equilibrium states, on timescales that can be understood by physical arguments. Depending on parameter values, the magnetic field can evolve by ohmic diffusion or by ambipolar diffusion, the latter being limited either by interparticle collisions or by relaxation to chemical quasi-equilibrium through beta decays. The numerical simulations are further validated by verifying that they satisfy the known conservation laws in highly nonlinear situations.
Monthly Notices of the Royal Astronomical Society, 2017
As another step towards understanding the long-term evolution of the magnetic field in neutron stars, we provide the first simulations of ambipolar diffusion in a spherical star. Restricting ourselves to axial symmetry, we consider a charged-particle fluid of protons and electrons carrying the magnetic flux through a motionless, uniform background of neutrons that exerts a collisional drag force on the former. We also ignore the possible impact of β decays, proton superconductivity and neutron superfluidity. All initial magnetic field configurations considered are found to evolve on the analytically expected timescales towards 'barotropic equilibria' satisfying the 'Grad-Shafranov equation', in which the magnetic force is balanced by the degeneracy pressure gradient, so ambipolar diffusion is choked. These equilibria are so-called 'twisted torus' configurations, which include poloidal and toroidal components, the latter restricted to the toroidal volumes in which the poloidal field lines close inside the star. In axial symmetry, they appear to be stable, although they are likely to undergo non-axially symmetric instabilities.
Ambipolar diffusion in superfluid neutron stars
Monthly Notices of the Royal Astronomical Society, 2011
In this paper we reconsider the problem of magnetic field diffusion in neutron star cores. We model the star as consisting of a mixture of neutrons, protons and electrons, and allow for particle reactions and binary collisions between species. Our analysis is in much the same spirit as that of , and we content ourselves with rough estimates of magnetic diffusion timescales, rather than solving accurately for some particular field geometry. However, our work improves upon previous treatments in one crucial respect: we allow for superfluidity in the neutron star matter. We find that the consequent mutual friction force, coupling the neutrons and charged particles, together with the suppression of particles collisions and reactions, drastically affect the ambipolar magnetic field diffusion timescale. In particular, the addition of superfluidity means that it is unlikely that there is ambipolar diffusion in magnetar cores on the timescale of the lifetimes of these objects, contradicting an assumption often made in the modelling of the flaring activity commonly observed in magnetars. Our work suggests that if a decaying magnetic field is indeed the cause of magnetar activity, the field evolution is likely to take place outside of the core, and might represent Hall/Ohmic diffusion in the stellar crust, or else that a mechanism other than standard ambipolar diffusion is active, e.g. flux expulsion due to the interaction between neutron vortices and magnetic fluxtubes.
Hydromagnetic Equilibria and their Evolution in Neutron Stars
Proceedings of the International Astronomical Union, 2013
The strongest known magnetic fields are found in neutron stars. I briefly discuss how they are inferred from observations, as well as the evidence for their time-evolution. I go on to show how these extremely strong fields are actually weak in terms of their effects on the stellar structure. This is also the case for magnetic stars on the upper main sequence and magnetic white dwarfs, which have similar total magnetic fluxes, perhaps pointing to an evolutionary connection. I suggest that a stable hydromagnetic equilibrium (containing a poloidal and a toroidal field component) could be established soon after the birth of the neutron star, aided by the strong compositional stratification of neutron star matter, and this state is slowly eroded by non-ideal magnetohydrodynamic processes such as beta decays and ambipolar diffusion in the core of the star and Hall drift and breaking of the solid in its crust. Over sufficiently long time scales, the fluid in the neutron star core will beha...
Magnetic field evolution in neutron stars
Astronomische Nachrichten, 2007
Neutron stars contain persistent, ordered magnetic fields that are the strongest known in the Universe. However, their magnetic fluxes are similar to those in magnetic A and B stars and white dwarfs, suggesting that flux conservation during gravitational collapse may play an important role in establishing the field, although it might also be modified substantially by early convection, differential rotation, and magnetic instabilities. The equilibrium field configuration, established within hours (at most) of the formation of the star, is likely to be roughly axisymmetric, involving both poloidal and toroidal components. The stable stratification of the neutron star matter (due to its radial composition gradient) probably plays a crucial role in holding this magnetic structure inside the star. The field can evolve on long time scales by processes that overcome the stable stratification, such as weak interactions changing the relative abundances and ambipolar diffusion of charged particles with respect to neutrons. These processes become more effective for stronger magnetic fields, thus naturally explaining the magnetic energy dissipation expected in magnetars, at the same time as the longer-lived, weaker fields in classical and millisecond pulsars.
Magnetic field decay in isolated neutron stars
The Astrophysical Journal, 1992
We investigate three mechanisms that promote the loss of magnetic flux from an isolated neutron star. Ohmic decay produces a diffusion of the magnetic field with respect to the charged particles. It proceeds at a rate that is inversely proportional to the electric conductivity and independent of the magnetic field strength. Ohmic decay occurs in both the fluid core and solid crust of a neutron star, but it is too slow to directly affect magnetic fields of stellar scale. Ambipolar diffusion involves a drift of the magnetic field and charged particles relative to the neutrons. The drift speed is proportional to the second power of the magnetic field strength if the protons form a normal fluid. Variants of ambipolar diffusion include both the buoyant rise and the dragging by superfluid neutron vortices of magnetic flux tubes. Ambipolar diffusion operates in the outer part of the fluid core where the charged particle composition is homogeneous, protons and electrons being the only species. The charged particle flux associated with ambipolar diffusion decomposes into a solenoidal and an irrotational component. Both components are opposed by frictional drag. The irrotational component perturbs the chemical equilibrium between neutrons, protons, and electrons, thus generating pressure gradients that effectively choke it. The solenoidal component is capable of transporting magnetic flux from the outer core to the crust on a short time scale. Magnetic flux that threads the inner core, where the charged particle composition is inhomogeneous, would be permanently trapped unless particle interactions could rapidly smooth departures from chemical equilibrium. Magnetic fields undergo a Hall drift related to the Hall component of the electric field. The drift speed is proportional to the magnetic field strength. Hall drift occurs throughout a neutron star. Unlike ohmic decay and ambipolar diffusion which are dissipative, Hall drift conserves magnetic energy. Thus, it cannot by itself be responsible for magnetic field decay. However, it can enhance the rate of ohmic dissipation. In the solid crust, only the electrons are mobile and the tangent of the Hall angle is large. There, the evolution of the magnetic field resembles that of vorticity in an incompressible fluid at large Reynolds number. This leads us to speculate that the magnetic field undergoes a turbulent cascade terminated by ohmic dissipation at small scales. The small-scale components of the magnetic field are also transported by Hall drift waves from the inner crust where ohmic dissipation is slow to the outer crust where it is rapid. The diffusion of magnetic flux through the crust takes-5 x 10 8 /B 12 yr, where B 12 is the crustal magnetic field strength measured in units of 10 12 G.
Long-term GRMHD simulation of magnetic field in isolated neutron stars
2021
Strong magnetic fields play an important role in powering the emission of neutron stars. Nevertheless, a full understanding of the interior configuration of the field remains elusive. In this work, we present General Relativistic MagnetoHydroDynamics simulations of the magnetic field evolution in neutron stars lasting∼880ms (∼6.5 Alfvén crossing periods) and up to resolutions of 0.1155km using Athena++. We explore two different initial conditions, one with purely poloidal magnetic field and the other with a dominant toroidal component, and study the poloidal and toroidal field energies, the growth times of the various instability-driven oscillation modes and turbulence. We find that the purely poloidal setup generates a toroidal field which later decays exponentially reaching 1% of the total magnetic energy, showing no evidence of reaching equilibrium. The initially stronger toroidal field setup, on the other hand, loses up to 20% of toroidal energy and maintains this state till the...
Long-term GRHMD simulation of magnetic field in isolated neutron stars
2021
Strong magnetic fields play an important role in powering the emission of neutron stars. Nevertheless a full understanding of the interior configuration of the field remains elusive. In this work, we present General Relativistic MagnetoHydroDynamics simulations of the magnetic field evolution in neutron stars lasting ∼500ms (∼5 Alfvén crossing times) and up to resolutions of 0.231km using Athena++. We explore two different initial conditions, one with purely poloidal magnetic field and the other with a dominant toroidal component, and study the poloidal and toroidal field energies, the growth times of the various instability-driven oscillation modes and turbulence. We find that the purely poloidal setup generates a toroidal field which later decays exponentially reaching 1% of the total magnetic energy, showing no evidence of reaching equilibrium. The initially stronger toroidal field setup, on the other hand, loses up to 20% of toroidal energy and maintains this state till the end ...
2015
Neutron stars are compact objects remaining of supernova explosions. Astronomical observations suggest that surface star magnetic fields decay over long dissipative time scales. Although it is well known that the diffusive time scales are much longer than the age of the universe, non linear processes such as ambipolar diffusion or Hall effect can generate small-scale structures that shorten the time scales [1]. In this paper we calculate the magnetic diffusion modes confined in spherical neutron star crusts with axial symmetry (2D). The solution of the partial differential equations is based on a spectral method that expands the angular functions in Legendre polynomials while the radial and temporal part are solved by separation of variables.
Many Aspects of Magnetic Fields in Neutron Stars
Universe, 2018
In this work, we explore different aspects in which strong magnetic fields play a role in the composition, structure and evolution of neutron stars. More specifically, we discuss (i) how strong magnetic fields change the equation of state of dense matter, alter its composition, and create anisotropies, (ii) how they change the structure of neutron stars (such mass and radius) and the formalism necessary to calculate those changes, and (iii) how they can affect neutron stars' evolution. In particular, we focus on how a time-dependent magnetic field modifies the cooling of a special group known as X-ray dim neutron stars.