Core and crust contributions in overshooting glitches: the Vela pulsar 2016 glitch

During the spin-up phase of a large pulsar glitch - a sudden decrease of the rotational period of a neutron star - the angular velocity of the star may overshoot, namely reach values greater than that observed for the new post-glitch equilibrium. These transient phenomena are expected on the basis of theoretical models for pulsar internal dynamics, and their observation has the potential to provide an important diagnostic for glitch modelling. In this article, we present a simple criterion to assess the presence of an overshoot, based on the minimal analytical model that is able to reproduce an overshooting spin-up. We employed it to fit the data of the 2016 glitch of the Vela pulsar, obtaining estimates of the fractional moments of inertia of the internal superfluid components involved in the glitch, of the rise and decay timescales of the overshoot, and of the mutual friction parameters between the superfluid components and the normal one. We studied the cases with and without strong entrainment in the crust: in the former, we found an indication of a large inner core strongly coupled to the observable component, and of a reservoir of angular momentum extending into the core to densities below nuclear saturation; while in the latter, a large reservoir extending above nuclear saturation and a standard normal component without inner core were found

Axially symmetric equations for differential pulsar rotation with superfluid entrainment

In this article we present an analytical two-component model for pulsar rotational dynamics. Under the assumption of axial symmetry, implemented by a paraxial array of straight vortices that thread the entire neutron superfluid, we are able to project exactly the 3D hydrodynamical problem to a 1D cylindrical one. In the presence of density dependent entrainment the superfluid rotation is non-columnar: we circumvent this by using an auxiliary dynamical variable directly related to the areal density of vortices. The main result is a system of differential equations that take consistently into account the stratified spherical structure of the star, the dynamical effects of non-uniform entrainment, the differential rotation of the superfluid component and its coupling to the normal crust. These equations represent a mathematical framework in which to test quantitatively the macroscopic consequences of the presence of a stable vortex array, a working hypothesis widely used in glitch models. Even without solving the equations explicitly, we are able to draw some general quantitative conclusions; in particular, we show that the reservoir of angular momentum (corresponding to recent values of the pinning forces) is enough to reproduce the largest glitch observed in the Vela pulsar, provided its mass is not too large

Incompressible analytical models for spinning-down pulsars

We study a class of Newtonian models for the deformations of non-magnetized neutron stars duringtheir spin-down. The models have all an analytical solution, and thus allow to understand easily thedependence of the strain on the star\u2019s main physical quantities, such as radius, mass and crust thickness.In the first \u201chistorical\u201d model the star is assumed to be comprised of a fluid core and an elastic crustwith the same density. We compare the response of stars with different masses and equations of stateto a decreasing centrifugal force, finding smaller deformations for heavier stars: the strain angle ispeaked at the equator and turns out to be a decreasing function of the mass.We introduce a second,more refined, model in which the core and the crust have different densities and the gravitationalpotential of the deformed body is self-consistently accounted for. Also in this case the strain angle isa decreasing function of the stellar mass, but its maximum value is at the poles and is always largerthan the corresponding one in the one-density model by a factor of two. Finally, within the presentanalytic approach, it is possible to estimate easily the impact of the Cowling approximation: neglectingthe perturbations of the gravitational potential, the strain angle is 40% of the one obtained with thecomplete model

Systematic thermal reduction of neutronization in core-collapse supernovae

We investigate to what extent the temperature dependence of the nuclear symmetry energy can affect the neutronization of the stellar core prior to neutrino trapping during gravitational collapse. To this end, we implement a one-zone simulation to follow the collapse until beta equilibrium is reached and the lepton fraction remains constant. Since the strength of electron capture on the neutron-rich nuclei associated to the supernova scenario is still an open issue, we keep it as a free parameter. We find that the temperature dependence of the symmetry energy consistently yields a small reduction of deleptonization, which corresponds to a systematic effect on the shock wave energetics: the gain in dissociation energy of the shock has a small yet non-negligible value of about 0.4 foe (1 foe = 10^51 erg) and this result is almost independent from the strength of nuclear electron capture. The presence of such a systematic effect and its robustness under changes of the parameters of the one-zone model are significative enough to justify further investigations with detailed numerical simulations of supernova explosions.Comment: 15 pages, 2 tables, 3 figure

The r-modes in accreting neutron stars with magneto-viscous boundary layers

We explore the dynamics of the r-modes in accreting neutron stars in two ways. First, we explore how dissipation in the magneto-viscous boundary layer (MVBL) at the crust-core interface governs the damping of r-mode perturbations in the fluid interior. Two models are considered: one assuming an ordinary-fluid interior, the other taking the core to consist of superfluid neutrons, type II superconducting protons, and normal electrons. We show, within our approximations, that no solution to the magnetohydrodynamic equations exists in the superfluid model when both the neutron and proton vortices are pinned. However, if just one species of vortex is pinned, we can find solutions. When the neutron vortices are pinned and the proton vortices are unpinned there is much more dissipation than in the ordinary-fluid model, unless the pinning is weak. When the proton vortices are pinned and the neutron vortices are unpinned the dissipation is comparable or slightly less than that for the ordinary-fluid model, even when the pinning is strong. We also find in the superfluid model that relatively weak radial magnetic fields ~ 10^9 G (10^8 K / T)^2 greatly affect the MVBL, though the effects of mutual friction tend to counteract the magnetic effects. Second, we evolve our two models in time, accounting for accretion, and explore how the magnetic field strength, the r-mode saturation amplitude, and the accretion rate affect the cyclic evolution of these stars. If the r-modes control the spin cycles of accreting neutron stars we find that magnetic fields can affect the clustering of the spin frequencies of low mass x-ray binaries (LMXBs) and the fraction of these that are currently emitting gravitational waves.Comment: 19 pages, 8 eps figures, RevTeX; corrected minor typos and added a referenc

Fully consistent semi-classical treatment of vortex-nucleus interaction in rotating neutron stars

We present the first realistic and fully consistent model to study the vortex-nucleus interaction in the inner crust of a rotating neutron star, where a gas of unbound superfluid neutrons threaded by vortex lines coexists with a lattice of neutron-rich nuclei. Within the framework of the local density approximation, the model determines unambiguously the structure and radius of the vortex core along the crust, and takes into account all energy contributions to evaluate the vortex-nucleus configuration with lowest energy. The results show that, quite independent from the pairing interaction used, pinning of vortices on nuclei occurs only in the deepest layers of the crust and even there the average pinning forces are quite weak. If confirmed by complete quantum calculations, such a limited region of weak nuclear pinning may be relevant to the explanation of pulsar glitches

Realistic energies for vortex pinning in intermediate-density neutron star matter

Realistic values for the pinning energies of vortices in the neutron superfluid expected in the inner crust of neutron stars are crucial for the theory of pulsar glitches. To this end, we supplement our consistent semi-classical model for the vortex-nucleus interaction with general properties of intermediate-d. fermion systems with large neg. scattering lengths, such as neutron matter at the densities corresponding to the inner crust. We also implement the redn. of pairing expected from the polarization of the strongly correlated neutron medium, although allowing for the present large theor. uncertainties on the amt. of redn. Finally, we better evaluate the kinetic contributions to pinning accounting also for the quantum structure of the vortex core, which sustains divergenceless flow. When compared to existing results, we find weaker values for the pinning energies per site (EP < 3.5 MeV); moreover, significant nuclear pinning occurs only in a restricted d. range (about 2 * 1013 .ltorsim. r .ltorsim. 5 * 1013 g/cm3 or 0.07 r0 .ltorsim. r .ltorsim. 0.2 r0, with r0 the nuclear satn. d.). The rest of the crust presents either interstitial pinning (r < 0.07 r0) or collective super-weak pinning (r &rt; 0.2 r0), both negligible at the macroscopic scale relevant to vortex unpinning and glitches

Investigating superconductivity in neutron star interiors with glitch models

The high-density interior of a neutron star is expected to contain superconducting protons and superfluid neutrons. Theoretical estimates suggest that the protons will form a type II superconductor in which the stellar magnetic field is carried by flux tubes. The strong interaction between the flux tubes and the neutron rotational vortices could lead to strong "pinning," i.e., vortex motion could be impeded. This has important implications especially for pulsar glitch models as it would lead to a large part of the vorticity of the star being decoupled from the "normal" component to which the electromagnetic emission is locked. In this Letter, we explore the consequences of strong pinning in the core on the "snowplow" model for pulsar glitches, making use of realistic equations of state and relativistic background models for the neutron star. We find that, in general, a large fraction of the pinned vorticity in the core is not compatible with observations of giant glitches in the Vela pulsar. Thus, the conclusion is that either most of the core is in a type I superconducting state or the interaction between vortices and flux tubes is weaker than previously assumed