Neutron-superfluid vortices and proton-superconductor flux tubes: Development of a minimal model for pulsar glitches

We develop a theoretical framework that allows us to explore the coupled motion of neutron-superfluid vortices and proton-superconductor flux tubes in a gravitationally collapsed condensate, which describe neutron stars that form pulsars. Our framework uses the 3D Gross-Pitaevskii-Poisson-equation for neutron Cooper pairs, the real-time-Ginzburg-Landau equation for proton Cooper pairs, the Maxwell equations for the vector potential A, and Newtonian gravity and interactions, both direct and induced by the Poisson equation, between the neutron and proton subsystems. For a pulsar we include a crust potential, characterized by an angle θ, and frictional drag. By carrying out extensive direct numerical simulations of this model, we obtain a variety of interesting results. We show that a rotating proton superconductor generates a uniform London magnetic field and the field distribution around flux tubes changes. In the absence of any direct interaction between the two species, they interact through the gravitational Poisson equation. The inclusion of the current-current interaction and the complete Maxwell equations allows us to quantify the entrainment effect that leads to induced magnetization of neutron vortices. We demonstrate that, with a strong external magnetic field Bext, proton flux tubes are anchored to the crust, whereas neutron vortices leave the condensate and lead to abrupt changes of the crust angular momentum Jc. The frictional term in the dynamical equation for θ yields stick-slip dynamics that leads, in turn, to glitches in the time series of Jc. By calculating various statistical properties of this time series, we demonstrate that they display self-organized criticality that has been found in observations for several pulsars. We compare our results with those of earlier explorations of pulsar-glitch statistics in Gross-Pitaevskii equation-based minimal models for pulsars. © 2024 American Physical Society.