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 thermally activated vortex slippage, and calculate 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 a 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: for a glitch in the spin rate of magnitude Δν, pinning introduces a delay in the post-glitch response time. The delay time is t_d = 7(t_sd/10⁴ 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.