Theoretical Constraints on Neutron Star Superfluidity from Her X-1 Precession

Recent IXPE observations of Her X-1 reveal correlations between flux, polarization degree, and polarization angle across its 35-day superorbital cycle. These measurements have been interpreted as strong evidence that the 35-day period is driven by nearly free precession of the neutron star. We show that this interpretation carries far-reaching implications for the dynamics of the crustal superfluid. In particular, maintaining precession over the $\sim 50$-year observational baseline of Her X-1 would require that superfluid vortices remain unpinned for centuries and experience extremely weak mutual friction while traversing the heavy-ion lattice of the inner crust -- conditions that challenge conventional wisdom and standard models of glitch dynamics. Under the condition of weak pinning, nearly free precession of the crust may be sustained by a balance between the internal and external torques.