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

Abstract

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 $t_d=7 (t_{sd}/10^4\mbox{yr})((Δν/ν)/10^{-6})$ 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.

Final version appearing in the Astrophysical Journal

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Cited by in corpus (23)

• Models of Pulsar Glitches
• Superfluidity and Superconductivity in Neutron Stars
• The impact of glitches on young pulsar rotational evolution
• Higher-order symmetry energy and neutron star core-crust transition with Gogny forces
• The unusual glitch recoveries of the high magnetic field pulsar J1119$-$6127
• Peculiar Glitch of PSR J1119-6127 and Extension of the Vortex Creep Model
• Microscopic Vortex Velocity in the Inner Crust and Outer Core of Neutron Stars
• Observational constraints on neutron star crust-core coupling during glitches
• Structures of the Vela pulsar and the glitch crisis from the Brueckner theory
• Nuclear fourth-order symmetry energy and its effects on neutron star properties in the relativistic Hartree-Fock theory
• Superfluid vortex-mediated mutual friction in non-homogeneous neutron star interiors
• Vortex Pinning in Neutron Stars, Slip-stick Dynamics, and the Origin of Spin Glitches
• The effect of non-linear mutual friction on pulsar glitch sizes and rise times
• Anti-glitches within the standard scenario of pulsar glitches
• Pinned vortex hopping in a neutron star crust
• Effects of the equation of state on the core-crust interface of slowly rotating neutron stars
• Hydrodynamic Stability Analysis of the Neutron Star Core
• Measuring the vortex-nucleus pinning force from pulsar glitch rates
• Rapid rotational crust-core relaxation in magnetars
• $M/R$ estimates for two neutron stars in LMXBs with possible r-mode frequencies detected
• Oscillatory superfluid Ekman pumping in Helium II and neutron stars
• Glitches in neutron stars with magnetically decoupled core
• Dissipative superfluid relativistic magnetohydrodynamics of a multicomponent fluid: the combined effect of particle diffusion and vortices