We show that the short spin-up time observed for the Vela pulsar during the 1988 "Christmas" glitch implies that the coupling time of the pulsar core to its crust is less than ~10 s. Ekman pumping cannot explain the fast core-crust coupling and a more effective coupling is necessary. The internal magnetic field of the Vela pulsar can provide the necessary coupling if the field threads the core with a magnitude that exceeds 10 13 G for a normal interior and 10 11 G for a superconducting interior. These lower bounds favor the hypothesis that the interior of neutron stars contains superfluid neutrons and protons and challenge the notion that pulsar magnetic fields decay over million year timescales or that magnetic flux is expelled from the core as the star slows.
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