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

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

Multi-Fluid Simulation of the Magnetic Field Evolution in Neutron Stars

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 Alfven 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 uniform-density 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.Comment: It will be published in AIP Proceedings of the Conference '40 Years of Pulsars: Milisecond Pulsars, Magnetars and More' held at University of McGill, Montreal, Canada, August 2007. Contributed Talk at Conference '40 Years of Pulsars: Milisecond Pulsars, Magnetars and More

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&

Old but still warm: Far-UV detection of PSR B0950+08

We report on a Hubble Space Telescope detection of the nearby, old pulsar B0950+08 ($d\simeq 262$ pc, spin-down age 17.5 Myr) in two far-ultraviolet (FUV) bands. We measured the mean flux densities $\bar{f}_\nu = 109\pm 6$ nJy and $83\pm 14$ nJy in the F125LP and F140LP filters (pivot wavelengths 1438 and 1528 \AA). Using the FUV data together with previously obtained optical-UV data, we conclude that the optical-FUV spectrum consists of two components -- a nonthermal (presumably magnetospheric) power-law spectrum ($f_\nu\propto \nu^\alpha$) with slope $\alpha\sim -1.2$ and a thermal spectrum emitted from the bulk of the neutron star surface with a temperature in the range of $(1-3)\times 10^5$ K, depending on interstellar extinction and neutron star radius. These temperatures are much higher than predicted by neutron star cooling models for such an old pulsar, which means that some heating mechanisms operate in neutron stars. A plausible mechanism responsible for the high temperature of PSR B0950+08 is the interaction of vortex lines of the faster rotating neutron superfluid with the slower rotating normal matter in the inner neutron star crust (vortex creep heating).Comment: 9 pages, 5 figures. Accepted by the Astrophysical Journa

Redshift-space limits of bound structures

An exponentially expanding Universe, possibly governed by a cosmological constant, forces gravitationally bound structures to become more and more isolated, eventually becoming causally disconnected from each other and forming so-called "island universes". This new scenario reformulates the question about which will be the largest structures that will remain gravitationally bound, together with requiring a systematic tool that can be used to recognize the limits and mass of these structures from observational data, namely redshift surveys of galaxies. Here we present a method, based on the spherical collapse model and N-body simulations, by which we can estimate the limits of bound structures as observed in redshift space. The method is based on a theoretical criterion presented in a previous paper that determines the mean density contrast that a spherical shell must have in order to be marginally bound to the massive structure within it. Understanding the kinematics of the system, we translated the real-space limiting conditions of this "critical" shell to redshift space, producing a projected velocity envelope that only depends on the density profile of the structure. From it we created a redshift-space version of the density contrast that we called "density estimator", which can be calibrated from N-body simulations for a reasonable projected velocity envelope template, and used to estimate the limits and mass of a structure only from its redshift-space coordinates.Comment: Contains 12 pages, 12 figures and 8 table

The glitch activity of neutron stars

We present a statistical study of the glitch population and the behaviour of the glitch activity across the known population of neutron stars. An unbiased glitch database was put together based on systematic searches of radio timing data of 898 rotation-powered pulsars obtained with the Jodrell Bank and Parkes observatories. Glitches identified in similar searches of 5 magnetars were also included. The database contains 384 glitches found in the rotation of 141 of these neutron stars. We confirm that the glitch size distribution is at least bimodal, with one sharp peak at approximately $20\, \rm{\mu\,Hz}$, which we call large glitches, and a broader distribution of smaller glitches. We also explored how the glitch activity $\dot{\nu}_{\rm{g}}$, defined as the mean frequency increment per unit of time due to glitches, correlates with the spin frequency $\nu$, spin-down rate $|\dot{\nu}|$, and various combinations of these, such as energy loss rate, magnetic field, and spin-down age. It is found that the activity is insensitive to the magnetic field and that it correlates strongly with the energy loss rate, though magnetars deviate from the trend defined by the rotation-powered pulsars. However, we find that a constant ratio $\dot\nu_{\rm{g}}/|\dot\nu| = 0.010 \pm 0.001$ is consistent with the behaviour of all rotation-powered pulsars and magnetars. This relation is dominated by large glitches, which occur at a rate directly proportional to $|\dot{\nu}|$. The only exception are the rotation-powered pulsars with the highest values of $|\dot{\nu}|$, such as the Crab pulsar and PSR B0540$-$69, which exhibit a much smaller glitch activity, intrinsically different from each other and from the rest of the population. The activity due to small glitches also shows an increasing trend with $|\dot\nu|$, but this relation is biased by selection effects.Comment: Accepted for publication in A&