Magnetic field evolution in neutron stars: one-dimensional multi-fluid model (original) (raw)
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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.
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.
Time-dependent magnetic annihilation at a stagnation point
Journal of Geophysical Research, 1993
Magnetic reconnection is a fundamental process that can take place in astrophysical or laboratory plasmas. It occurs within regions of large magnetic gradient where the magnetic field is no longer frozen to the plasma but instead diffuses through it, releasing magnetic energy and causing a change in the connectivity of the field lines. In particular, on the Sun, magnetic reconnection is believed to play an important role in coronal heating, X ray bright points, solar flares and canceling magnetic features. Here, an exact time-dependent solution of the MHD equations for magnetic annihilation in response to a time-varying stagnation point flow is presented. The main assumptions in this model are that the magnetic field lines are straight (so that there is no magnetic tension acting on the plasma) and the flow that carries the field lines together is of stagnation point type. This is a reasonable model for the resistive MHD behaviour near the X point of a reconnecting field, especially when the central diffusion region is long, as in the flux pile up regime (Priest and Forbes 1986). The general solution is used to conduct a series of numerical experiments, namely, the evolution of different initial magnetic profiles in a steady flow; the effect of a sudden change in magnetic diffusivity on an initially steady state; the effects of a velocity that either increases linearly in time or ramps up from one steady value to another. The results exhibit the effects of subtle irabalances in diffusion and advection but have the following general features: (1) a diffusion layer is created, the thickness of which is determined by the nature of the plasma flow; (2) the magnetic field outside the diffusion region is determined by advection and will either exponentially increase, exponentially decay or remain in a steady state, depending on whether the initial magnetic profile B (y) ~ y-n has n < 1, n > 1, or n = 1, respectively; and (3) the magnetic field within the diffusion layer tends to respond to the advected magnetic field at its edge. 1. INTRODUCTION In an astrophysical environment the global magnetic Reynolds number (the ratio of magnetic advection to magnetic diffusion) is extremely large, implying that the magnetic field is "frozen" to the plasma. Exceptions to this occur where there are large magnetic gradients, usually in thin current sheets. Here, the magnetic field lines may diffuse and be reconnected, releasing magnetic energy. Many models of this process focus on the large-scale field and flows, which are external to the current sheet, and on how they affect the rate of magnetic reconnection [e.g., Petschek 1964; Priest and Forbes 1986]. They assume that the exact nature of the diffusion region is of secondary importance and that its behaviour is controlled by the inflows or boundary conditions at large distances. If the diffusion region is considered at all, then it is usually treated in an approximate manner and patched to the external region. However, one exact solution of the MHD equations for steady magnetic energy release is known: Sonnerup and Priest [1975] followed Parker [1973] in examining magnetic annihilation in a current sheet formed between two regions of oppositely directed field lines. By reconnection we simply mean the breaking and rejoining of magnetic field lines, whereas "annihilation" refers to the bringing together and cancelation of straight field lines. The main assumptions in the Sonnerup-and Priest model were that (1) the magnetic field lines are straight, so that there is no magnetic tension Copyright 1993 by the American Geophysical Union. Paper number 92JA02723. 0148-0227/93/92JA-02723505.00 acting on the plasma; this means that there can be no localized reconnection of the field lines as all the magnetic field is destroyed so that no magnetic flux is ejected from the diffusion region; (2) the flow that carries the field lines together is of stagnation point type; (3) the flow and magnetic field are steady state. Models of this sort are amenable to analytical solution and can be adapted to study a wide range of phenomena.
IEEE Transactions on Plasma Science, 2018
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The initial evolution of millisecond magnetars: an analytical solution
Monthly Notices of the Royal Astronomical Society, 2020
Millisecond magnetars are often invoked as the central engine of some gamma-ray bursts (GRBs), specifically the ones showing a plateau phase. We argue that an apparent plateau phase may not be realized if the magnetic field of the nascent magnetar is in a transient rapid decay stage. Some GRBs that lack a clear plateau phase may also be hosting millisecond magnetars. We present an approximate analytical solution of the coupled set of equations describing the evolution of the angular velocity and the inclination angle between rotation and magnetic axes of a neutron star in the presence of a corotating plasma. We also show how the solution can be generalized to the case of evolving magnetic fields. We determine the evolution of the spin period, inclination angle, magnetic dipole moment, and braking index of six putative magnetars associated with GRB 091018, GRB 070318, GRB 080430, GRB 090618, GRB 110715A, and GRB 140206A through fitting, via Bayesian analysis, the X-ray afterglow ligh...
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.
Astronomy & Astrophysics, 2009
Context. Long-lived, large-scale magnetic field configurations exist in upper main sequence, white dwarf, and neutron stars. Externally, these fields have a strong dipolar component, while their internal structure and evolution are uncertain but highly relevant to several problems in stellar and high-energy astrophysics. Aims. We discuss the main properties expected for the stable magnetic configurations in these stars from physical arguments and the ways these properties may determine the modes of decay of these configurations. Methods. We explain and emphasize the likely importance of the non-barotropic, stable stratification of matter in all these stars (due to entropy gradients in main-sequence envelopes and white dwarfs, due to composition gradients in neutron stars). We first illustrate it in a toy model involving a single, azimuthal magnetic flux tube. We then discuss the effect of stable stratification or its absence on more general configurations, such as axisymmetric equilibria involving poloidal and toroidal field components. We argue that the main mode of decay for these configurations are processes that lift the constraints set by stable stratification, such as heat diffusion in main-sequence envelopes and white dwarfs, and beta decays or particle diffusion in neutron stars. We estimate the time scales for these processes, as well as their interplay with the cooling processes in the case of neutron stars. Results. Stable magneto-hydrostatic equilibria appear to exist in stars whenever the matter in their interior is stably stratified (not barotropic). These equilibria are not force-free and not required to satisfy the Grad-Shafranov equation, but they do involve both toroidal and poloidal field components. In main sequence stars with radiative envelopes and in white dwarfs, heat diffusion is not fast enough to make these equilibria evolve over the stellar lifetime. In neutron stars, a strong enough field might decay by overcoming the compositional stratification through beta decays (at the highest field strengths) or through ambipolar diffusion (for somewhat weaker fields). These processes convert magnetic energy to thermal energy, and they occur at significant rates only once the latter is less than the former; therefore, they substantially delay the cooling of the neutron star, while slowly decreasing its magnetic energy.
Evolution of magnetic fields in a transversely expanding highly conductive fluid
Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018), 2019
Due to the absence of a transverse expansion with respect to the beam direction, the Bjorken flow is unable to describe certain observables in heavy ion collisions. This caveat has motivated the introduction of analytical relativistic hydrodynamics (RH) solutions with transverse expansion, in particular, the 3+1 self-similar (SSF) and Gubser flows. Inspired by recent generalizations of the Bjorken flow to the relativistic magnetohydrodynamics (RMHD), we present a procedure for a generalization of RH solutions to RMHD. Our method is mainly based on symmetry arguments. Using this method, we find the relation between RH degrees of freedom and the magnetic field evolution in the ideal limit for an infinitely conductive fluid, and determine the proper time dependence of the magnetic field in aforementioned flows. In the case of SSF, a family of solutions are found that are related through a certain differential equation. To find the magnetic field evolution in the Gubser flow, we solve RMHD equations for a stationary fluid in a conformally flat dS 3 × E 1 spacetime. The result is then Weyl transformed back into the Minkowski spacetime. In this case, the temporal evolution of the magnetic field exhibits a transmission between 1/t to 1/t 3 near the center of the collision. The longitudinal component of the magnetic field is found to be sensitive to the transverse size of the fluid. We also find the radial evolution of the magnetic field for both flows. The radial domain of validity in the case of SSF is highly restricted, in contrast to the Gubser flow. A comparison of the results suggests that the Gubser RMHD may give a more appropriate qualitative picture of the magnetic field decay in the quark-gluon plasma (QGP).
Magnetic field decay in neutron stars: Analysis of general relativistic effects
Physical Review D, 2000
An analysis of the role of general relativistic effects on the decay of a neutron star's magnetic field is presented. At first, a generalized induction equation on an arbitrary static background geometry has been derived and, secondly, by a combination of analytical and numerical techniques, a comparison of the time scales for the decay of an initial dipole magnetic field