Magnetic field evolution and equilibrium configurations in neutron star cores: the effect of ambipolar diffusion

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 beta decays, proton superconductivity, and neutron superfluidity. All initial magnetic field configurations considered are found to evolve on the analytically expected time-scales 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.Comment: MNRAS, accepte

Internal Heating of Old Neutron Stars: Contrasting Different Mechanisms

Context: The standard cooling models of neutron stars predict temperatures $T10^{7}$ yr. However, the likely thermal emission detected from the millisecond pulsar J0437-4715, of spin-down age $t_s \sim 7\times10^9$ yr, implies a temperature $T\sim 10^5$ K. Thus, a heating mechanism needs to be added to the cooling models in order to obtain agreement between theory and observation. Aims: Several internal heating mechanisms could be operating in neutron stars, such as magnetic field decay, dark matter accretion, crust cracking, superfluid vortex creep, and non-equilibrium reactions ("rotochemical heating"). We study these mechanisms in order to establish which could be the dominant source of thermal emission from old pulsars. Methods: We show by simple estimates that magnetic field decay, dark matter accretion, and crust cracking mechanism are unlikely to have a significant effect on old neutron stars. The thermal evolution for the other mechanisms is computed using the code of Fern\'andez and Reisenegger. Given the dependence of the heating mechanisms on the spin-down parameters, we study the thermal evolution for two types of pulsars: young, slowly rotating "classical" pulsars and old, fast rotating millisecond pulsars. Results: We find that magnetic field decay, dark matter accretion, and crust cracking do not produce detectable heating of old pulsars. Rotochemical heating and vortex creep can be important both for classical pulsars and millisecond pulsars. More restrictive upper limits on the surface temperatures of classical pulsars could rule out vortex creep as the main source of thermal emission. Rotochemical heating in classical pulsars is driven by the chemical imbalance built up during their early spin-down, and therefore strongly sensitive to their initial rotation period.Comment: 7 pages, 5 figures, accepted version to be published in A&

Search for Stable Magnetohydrodynamic Equilibria in Barotropic Stars

It is now believed that magnetohydrodynamic equilibria can exist in stably stratified stars due to the seminal works of Braithwaite & Spruit (2004) and Braithwaite & Nordlund (2006). What is still not known is whether magnetohydrodynamic equilibria can exist in a barotropic star, in which stable stratification is not present. It has been conjectured by Reisenegger (2009) that there will likely not exist any magnetohydrodynamical equilibria in barotropic stars. We aim to test this claim by presenting preliminary MHD simulations of barotropic stars using the three dimensional stagger code of Nordlund & Galsgaard (1995).Comment: 4 pages, 2 figures, to appear in the proceedings of IAUS 302: "Magnetic Fields Throughout Stellar Evolution

Neutrino emission rates in highly magnetized neutron stars revisited

Magnetars are a subclass of neutron stars whose intense soft-gamma-ray bursts and quiescent X-ray emission are believed to be powered by the decay of a strong internal magnetic field. We reanalyze neutrino emission in such stars in the plausibly relevant regime in which the Landau band spacing of both protons and electrons is much larger than kT (where k is the Boltzmann constant and T is the temperature), but still much smaller than the Fermi energies. Focusing on the direct Urca process, we find that the emissivity oscillates as a function of density or magnetic field, peaking when the Fermi level of the protons or electrons lies about 3kT above the bottom of any of their Landau bands. The oscillation amplitude is comparable to the average emissivity when the Landau band spacing mentioned above is roughly the geometric mean of kT and the Fermi energy (excluding mass), i. e., at fields much weaker than required to confine all particles to the lowest Landau band. Since the density and magnetic field strength vary continuously inside the neutron star, there will be alternating surfaces of high and low emissivity. Globally, these oscillations tend to average out, making it unclear whether there will be any observable effects.Comment: 7 pages, 2 figures; accepted for publication in Astronomy & Astrophysic

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.Comment: Paper Accepted in Astronomy & Astrophysics: 24 April 2008, Paper Reference Number: AA/2008/09466. Paper contains 8 Figures. In this version the section: Summary and Conclusions has been expande