Constraining the Origin of Magnetar Flares

Sudden relaxation of the magnetic field in the core of a magnetar produces mechanical energy primarily in the form of shear waves which propagate to the surface and enter the magnetosphere as relativistic Alfv\'en waves. Due to a strong impedance mismatch, shear waves excited in the star suffer many reflections before exiting the star. If mechanical energy is deposited in the core and is converted {\em directly} to radiation upon propagation to the surface, the rise time of the emission is at least seconds to minutes, and probably minutes to hours for a realistic magnetic field geometry, at odds with observed rise times of \lap 10 ms for both and giant flares. Mechanisms for both small and giant flares that rely on the sudden relaxation of the magnetic field of the core are rendered unviable by the impedance mismatch, requiring the energy that drives these events to be stored in the magnetosphere just before the flare. ends, unless the waves are quickly damped.Comment: Final version in Monthly Notices of the Royal Astronomical Society. 13 pages, 5 figure

Thermally-Activated Post-Glitch Response of the Neutron Star Inner Crust and Core. I: Theory

Pinning of superfluid vortices is predicted to prevail throughout much of a neutron star. Based on the idea of Alpar et al., I develop a description of the coupling between the solid and liquid components of a neutron star through {\em thermally-activated vortex slippage}, and calculate the the response to a spin glitch. The treatment begins with a derivation of the vortex velocity from the vorticity equations of motion. The activation energy for vortex slippage is obtained from a detailed study of the mechanics and energetics of vortex motion. I show that the "linear creep" regime introduced by Alpar et al. and invoked in fits to post-glitch response is not realized for physically reasonable parameters, a conclusion that strongly constrains the physics of post-glitch response through thermal activation. Moreover, a regime of "superweak pinning", crucial to the theory of Alpar et al. and its extensions, is probably precluded by thermal fluctuations. The theory given here has a robust conclusion that can be tested by observations: {\em for a glitch in spin rate of magnitude $\Delta\nu$, pinning introduces a delay in the post-glitch response time}. The delay time is t_d=7 (t_{sd}/10^4\mbox{yr})((\Delta\nu/\nu)/10^{-6}) d where $t_{sd}$ is the spin-down age; $t_d$ is typically weeks for the Vela pulsar and months in older pulsars, and is independent of the details of vortex pinning. Post-glitch response through thermal activation cannot occur more quickly than this timescale. Quicker components of post-glitch response as have been observed in some pulsars, notably, the Vela pulsar, cannot be due to thermally-activated vortex motion but must represent a different process, such as drag on vortices in regions where there is no pinning. I also derive the mutual friction force for a pinned superfluid at finite temperature for use in other studies of neutron star hydrodynamics.Comment: Final version appearing in the Astrophysical Journa

Vortex Pinning in Neutron Stars, Slip-stick Dynamics, and the Origin of Spin Glitches

We study pinning and unpinning of superfluid vortices in the inner crust of a neutron star using 3-dimensional dynamical simulations. Strong pinning occurs for certain lattice orientations of an idealized, body-centered cubic lattice, and occurs generally in an amorphous or impure nuclear lattice. The pinning force per unit length is $\sim 10^{16}$ dyn cm$^{-1}$ for a vortex-nucleus interaction that is repulsive, and $\sim 10^{17}$ dyn cm$^{-1}$ for an attractive interaction. The pinning force is strong enough to account for observed spin jumps (glitches). Vortices forced through the lattice move with a slip-stick character; for a range of superfluid velocities, the vortex can be in either a cold, pinned state or a hot unpinned state, with strong excitation of Kelvin waves on the vortex. This two-state nature of vortex motion sets the stage for large-scale vortex movement that creates an observable spin glitch. We argue that the vortex array is likely to become tangled as a result of repeated unpinnings and repinnings. We conjecture that during a glitch, the Kelvin-wave excitation spreads rapidly along the direction of the mean superfluid vorticity and slower in the direction perpendicular to it, akin to an anisotropic deflagration.Comment: 12 pages, 7 figures (two animations

Simulations of Glitches in Isolated Pulsars

Many radio pulsars exhibit glitches wherein the star's spin rate increases fractionally by $\sim 10^{-10} - 10^{-6}$. Glitches are ascribed to variable coupling between the neutron star crust and its superfluid interior. With the aim of distinguishing among different theoretical explanations for the glitch phenomenon, we study the response of a neutron star to two types of perturbations to the vortex array that exists in the superfluid interior: 1) thermal motion of vortices pinned to inner crust nuclei, initiated by sudden heating of the crust, (e.g., a starquake), and 2) mechanical motion of vortices, (e.g., from crust cracking by superfluid stresses). Both mechanisms produce acceptable fits to glitch observations in four pulsars, with the exception of the 1989 glitch in the Crab pulsar, which is best fit by the thermal excitation model. The two models make different predictions for the generation of internal heat and subsequent enhancement of surface emission. The mechanical glitch model predicts a negligible temperature increase. For a pure and highly-conductive crust, the thermal glitch model predicts a surface temperature increase of as much as $\sim$ 2%, occurring several weeks after the glitch. If the thermal conductivity of the crust is lowered by a high concentration of impurities, however, the surface temperature increases by $\sim$ 10% about a decade after a thermal glitch. A thermal glitch in an impure crust is consistent with the surface emission limits following the January 2000 glitch in the Vela pulsar. Future surface emission measurements coordinated with radio observations will constrain glitch mechanisms and the conductivity of the crust.Comment: 21 pages, 10 figures, submitted to MNRA