Ambipolar diffusion in superfluid neutron stars (original) (raw)
Related papers
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.
Multi-fluid simulation of the magnetic field evolution in neutron stars
AIP Conference Proceedings, 2008
Using a numerical simulation, we study the effects of ambipolar diffusion and ohmic diffusion on the magnetic field evolution in the interior of an isolated neutron star. We are interested in the behavior of the magnetic field on a long time scale, over which all Alfvén and sound waves have been damped. We model the stellar interior as an electrically neutral plasma composed of neutrons, protons and electrons, which can interact with each other through collisions and electromagnetic forces. Weak interactions convert neutrons and charged particles into each other, erasing chemical imbalances. As a first step, we assume that the magnetic field points in one fixed Cartesian direction but can vary along an orthogonal direction. We start with a uniformdensity background threaded by a homogeneous magnetic field and study the evolution of a magnetic perturbation as well as the density fluctuations it induces in the particles. We show that the system evolves through different quasi-equilibrium states and estimate the characteristic time scales on which these quasi-equilibria occur.
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.
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.
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.
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.
Dissipative processes in superfluid neutron stars
2011
We present some results about a novel damping mechanism of r-mode oscillations in neutron stars due to processes that change the number of protons, neutrons and electrons. Deviations from equilibrium of the number densities of the various species lead to the appearance in the Euler equations of the system of a dissipative mechanism, the so-called rocket effect. The evolution of the r-mode oscillations of a rotating neutron star are influenced by the rocket effect and we present estimates of the corresponding damping timescales. In the description of the system we employ a two-fluid model, with one fluid consisting of all the charged components locked together by the electromagnetic interaction, while the second fluid consists of superfluid neutrons. Both components can oscillate however the rocket effect can only efficiently damp the countermoving r-mode oscillations, with the two fluids oscillating out of phase. In our analysis we include the mutual friction dissipative process between the neutron superfluid and the charged component. We neglect the interaction between the two r-mode oscillations as well as effects related with the crust of the star. Moreover, we use a simplified model of neutron star assuming a uniform mass distribution.
Ambipolar decay of magnetic field in magnetars and the observed magnetar activities
arXiv: High Energy Astrophysical Phenomena, 2020
Magnetars are comparatively young neutron stars with ultra-strong surface magnetic field in the range 1014−1610^{14-16}1014−16 G. The old neutron stars have surface magnetic field some what less sim108\sim 10^8sim108 G which clearly indicates the decay of field with time. One possible way of magnetic field decay is by ambipolar diffusion. We describe the general procedure to solve for the ambipolar velocity inside the star core without any approximation. With a realistic model of neutron star we determine the ambipolar velocity configuration inside the neutron star core and hence find the ambipolar decay rate and time scale which is consistent with the magnetar observations.
Submergence and re-diffusion of the neutron star magnetic field after the supernova
Astronomy & Astrophysics, 1999
We consider the effect of post core-collapse accretion on the magnetic field of the new-born neutron star. If this accretion is hypercritical then the ram pressure overwhelms the magnetic field pressure and we show that in this case the accretion induced flow time scale in the upper layers of the neutron star is shorter, by orders of magnitude, than the magnetic field ohmic diffusion time scale. This means that the magnetic field is frozen in the matter and any initial magnetic field of the neutron star is rapidly submerged beneath the accreted matter. If the accreting matter is weakly, or non, magnetized, this implies that neutron stars produced by supernovae in which hypercritical accretion occurred are born with weak, or even vanishing, surface magnetic field. Later diffusion of the magnetic field back to the surface could produce a delayed switch-on of a pulsar (Muslimov & Page 1995): We model this re-diffusion in detail for a wide range of submergence depths and discuss the consequences for pulsar observables, such as the period P and its time derivativeṖ . As a result of the field submergence, the spin-down age τ sd can be much larger than the real age of the pulsar. Moreover, we show that if the field submergence is deep enough the magnetic field will be hidden for many millions of years. This mechanism of field submergence may explain the lack of evidence for the presence of a pulsar in all recent supernovae and may also contribute to the discrepancy between the estimated pulsar birth rate and type Ib+II supernova rate. In particular, we predict that a pulsar will never turn-on in the remnant of SN 1987A.