Field Evolution In Neutron Stars Research Articles

Long-term general relativistic magnetohydrodynamics simulations of magnetic field in isolated neutron stars

ABSTRACT 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 (MHD) simulations of the magnetic field evolution in neutron stars lasting ${\sim } {880}\,$ms (∼6.5 Alfvén crossing periods) and up to resolutions of $0.1155\,$km 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 $1{{\ \rm per\ cent}}$ 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 per cent of toroidal energy and maintains this state till the end of our simulation. We also explore the hypothesis, drawn from previous MHD simulations, that turbulence plays an important role in the quasi-equilibrium state. An analysis of the spectra in our higher resolution setups reveals, however, that in most cases we are not observing turbulence at small scales, but rather a noisy velocity field inside the star. We also observe that the majority of the magnetic energy gets dissipated as heat increasing the internal energy of the star, while a small fraction gets radiated away as electromagnetic radiation.

Fast magnetic field evolution in neutron stars: The key role of magnetically induced fluid motions in the core

In [Gusakov et al.\ PRD, 96, 103012, (2017)], we proposed a self-consistent method to study the quasistationary evolution of the magnetic field in neutron-star cores. Here we apply it to calculate the instantaneous particle velocities and other parameters of interest, which are fixed by specifying the magnetic field configuration. Interestingly, we found that the magnetic field can lead to generation of a macroscopic fluid motion with the velocity, significantly exceeding the diffusion particle velocities. This result calls into question the standard view on the magnetic field evolution in neutron stars and suggests a new, shorter timescale for such evolution.

Looking for Hall attractor in astrophysical sources

Recently, numerical calculations of the magnetic field evolution in neutron stars demonstrated the possible existence of a Hall attractor, a stage at which the evolution of the field driven by the Hall cascade ends. The existence of such a stage in neutron star magnetic evolution is very important, and can be potentially probed by observations. Here we discuss three types of objects which could have reached this stage. First, we briefly describe the evolution of normal radio pulsars with ages about a few hundred thousand years. Then we analyse in more detail observations of RX J1856.5-3754, one of the Magnificent Seven, focusing on the surface temperature distribution and comparing model predictions with the temperature map inferred from X-ray observations. Finally, we discuss the necessity of the Hall attractor stage to explain the hypothetical existence of accreting magnetars. We conclude that at the moment there is no direct confirmation of the Hall attractor stage in known sources. However, more detailed observations in the near future can demonstrate existence (or absence) of this stage of the crustal magnetic field evolution.

Magnetic field evolution of neutron stars – I. Basic formalism, numerical techniques and first results

In this work we explore the evolution of magnetic fields inside strongly magnetized neutron stars in axisymmetry. We model numerically the coupled field evolution in the core and the crust. Our code models the Hall drift and Ohmic effects in the crust, the back-reaction on the field from magnetically-induced elastic deformation of the crust, the magnetic twist exchange between the crust and the core, and the drift of superconducting flux tubes inside the core. The correct hydromagnetic equilibrium is enforced in the core. We find that i) The Hall attractor found by Gourgouliatos and Cumming in the crust exists also for configurations when the B-field penetrates into the core. However, the evolution timescale for the core-penetrating fields is dramatically different than that of the fields confined to the crust. ii) The combination of Jones' flux tube drift and Ohmic dissipation in the crust can deplete the pulsar magnetic fields on the timescale of $150$ Myr if the crust is hot ($T\sim2\times10^8$ K), but acts on much slower timescales for cold neutron stars, such as recycled pulsars ($\sim 1.8 $ Gyr, depending on impurity levels). iii) The outward motion of superfluid vortices during the rapid spin-down of a young highly magnetized pulsar, can result in a partial expulsion of flux from the core when $B\lesssim 10^{13}$ G. However for $B\gtrsim2\times 10^{13}$ G, the combination of a stronger magnetic field and a longer spin period implies that the core field cannot be expelled.

Resistive tearing instability in electron MHD: application to neutron star crusts

We study a resistive tearing instability developing in a system evolving through the combined effect of Hall drift in the Electron-MHD limit and Ohmic dissipation. We explore first the exponential growth of the instability in the linear case and we find the fastest growing mode, the corresponding eigenvalues and dispersion relation. The instability growth rate scales as $\gamma \propto B^{2/3} \sigma^{-1/3}$ where $B$ is the magnetic field and $\sigma$ the electrical conductivity. We confirm the development of the tearing resistive instability in the fully non-linear case, in a plane parallel configuration where the magnetic field polarity reverses, through simulations of systems initiating in Hall equilibrium with some superimposed perturbation. Following a transient phase, during which there is some minor rearrangement of the magnetic field, the perturbation grows exponentially. Once the instability is fully developed the magnetic field forms the characteristic islands and X-type reconnection points, where Ohmic decay is enhanced. We discuss the implications of this instability for the local magnetic field evolution in neutron stars' crusts, proposing that it can contribute to heating near the surface of the star, as suggested by models of magnetar post-burst cooling. In particular, we find that a current sheet a few meters thick, covering as little as $1\%$ of the total surface can provide $10^{42}~$erg in thermal energy within a few days. We briefly discuss applications of this instability in other systems where the Hall effect operates such as protoplanetary discs and space plasmas.

Magnetic field evolution in neutron stars: one-dimensional multi-fluid model

This paper is the first in a series aimed at understanding the long-term evolution of neutron star magnetic fields. We model the stellar matter as an electrically neutral and lightly ionized plasma composed of three moving particle species: neutrons, protons, and electrons, which 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 time scales (sound and Alfv\'en) 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. 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 time scales 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 equations of motion. 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 time scales that can be understood by physical arguments. Depending of the 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 equilibrium through beta decays. The numerical simulations are further validated by verifying that they satisfy the known conservation laws also in highly non-linear situations.

Flux Expulsion and Field Evolution in Neutron Stars

Models for the evolution of magnetic fields of neutron stars are constructed, assuming the field is embedded in the proton superconducting core of the star. The rate of expulsion of the magnetic flux out of the core, or equivalently the velocity of outward motion of flux-carrying proton-vortices is determined from a solution of the Magnus equation of motion for these vortices. A force due to the pinning interaction between the proton-vortices and the neutron-superfluid vortices is also taken into account in addition to the other more conventional forces acting on the proton-vortices. Alternative models for the field evolution are considered based on the different possibilities discussed for the effective values of the various forces. The coupled spin and magnetic evolution of single pulsars as well as those processed in low-mass binary systems are computed, for each of the models. The predicted lifetimes of active pulsars, field strengths of the very old neutron stars, and distribution of the magnetic fields versus orbital periods in low-mass binary pulsars are used to test the adopted field decay models. Contrary to the earlier claims, the buoyancy is argued to be the dominant driving cause of the flux expulsion, for the single as well as the binary neutron stars. However, the pinning is also found to play a crucial role which is necessary to account for the observed low field binary and millisecond pulsars.

Magnetic field evolution of accreting neutron stars * III

We investigate the evolution of the magnetic field of isolated pulsars and of neutron stars in different kinds of binary systems, assuming the field to be originally confined to the crust. Our results for the field evolution in isolated neutron stars helps us to constrain the physical parameters of the crust. Modelling the full evolution of a neutron star in a binary system through several stages of interaction we compare the resulting final field strength with that observed in neutron stars in various types of binary systems. One of the interesting aspects of our result is a positive correlation between the rate of accretion and the final field strength, for which some observational indication already exists. Our results also match the overall picture of the field evolution in neutron stars derived from observations.

Magnetic field evolution of accreting neutron stars -- II

We investigate the evolution of the magnetic fields of isolated pulsars and neutron stars in different kinds of binary systems, assuming the field to be originally confined to the crust. Our results for the field evolution in isolated neutron stars help us to constrain the physical parameters of the crust. By modelling the full evolution of a neutron star in a binary system through several stages of interaction, we can compare the resulting final field strength with that observed in neutron stars in various types of binary systems. One of the interesting aspects of our results is a positive correlation between the rate of accretion and the final field strength, for which some observational indication already exists. Our results also match the overall picture of the field evolution in neutron stars derived from observations.

On the Magnetic Field Evolution in Isolated Neutron Stars

We examine the discrepancy between the theoretically expected number of detectable isolated old neutron stars (102-103), and the actually detected number of candidates (2-3). We argue that this discrepancy is explicable in terms of the suppression of accretion from the interstellar medium onto the old neutron stars. We show that for such a suppression to occur, a specific pattern for the magnetic field evolution in neutron stars is required. Strong magnetic fields (B 1012 G) are required to decay rapidly, while fields of the order of 1010 G are required to remain constant in the absence of accretion. The required pattern agrees with recent theoretical models for magnetic field decay in neutron stars.

Pulsar Velocities – Revisions & Ramifications

AbstractThe recent shift of opinion concerning the distribution of pulsar velocities at birth with a mean value of 400-500 km/s has several ramifications for our understanding of the origin and evolution of pulsars. From the present data, there is no convincing evidence for a causal correlation between velocity and magnetic field, any magnetic field evolution in neutron stars or that galactic neutron stars once active as radio pulsars are the sources ofγ-ray bursts. Asymmetric kicks seem the most plausible origin for the high velocities.

The evolution of the magnetic fields of neutron stars

Observational evidence, and theoretical models of the magnetic field evolution of neutron stars is discussed. Observational data indicates that the magnetic field of a neutron star decays significantly only if it has been a member of a close interacting binary. Theoretically, the magnetic field evolution has been related to the processing of a neutron star in a binary system through the spin evolution of the neutron star, and also through the accretion of matter on the neutron star surface. I describe two specific models, one in which magnetic flux is expelled from the superconducting core during spin-down, via a copuling between Abrikosov fluxoids and Onsager-Feynman vortices; and another in which the compression and heating of the stellar crust by the accreted mass drastically reduces the ohmic decay time scale of a magnetic field configuration confined entirely to the crust. General remarks about the behaviour of the crustal field under ohmic diffusion are also made.

Magnetic field evolution in neutron stars: coupling between poloidal and toroidal components in the crust

We calculate the decay of the magnetic field in a neutron star crust, with allowance for the Hall effect. The magnetic field is represented by the large-scale (dipole and quadrupole) poloidal modes initially confined to the outer crust, as well as the toroidal component wound around the core of the neutron star. We perform our calculations using rapid and relatively slow cooling histories, both implying the possibility of a direct Urca process in the core. At the late stages, after ∼10 8 yr, the poloidal modes become strongly coupled (due to the Hall term in the conductivity tensor) to each other via the toroidal component. We show that this coupling may strongly affect the subsequent evolution of poloidal modes

Pulsar demography and neutron star astrophysics

Pulsars, in particular, millisecond and binary pulsars offer new and unique tests of physics. The explosive birth of neutron stars and coalescence of binary neutron stars are prime targets for planned gravitational wave interferometers. All these applications require a thorough understanding of the statistics of pulsars to reliably estimate detection frequencies and thresholds. There are many aspects of the origin and evolution of neutron stars that benefit from an appreciation of pulsar phenomenology and statistics. Theoretical understanding of the magnetic field evolution of neutron stars is, at the present, poor. Statistical studies continue to play an important role in guiding us empirically in this area. The shortest spin period of a neutron star directly constrains the equation of state of dense matter. The limitations of current millisecond pulsar searches in this regard is thoroughly reviewed. The prospects and problems of searchers for pulsars with periods below a millisecond are reviewed.