Glitch Rises as a Test for Rapid Superfluid Coupling in Neutron Stars

Pulsar glitches provide a unique way to study neutron star microphysics because short post-glitch dynamics are directly linked to strong frictional processes on small scales. To illustrate this connection between macroscopic observables and microphysics, we review calculations of vortex interactions focusing on Kelvin wave excitations and determine the corresponding mutual friction strength for realistic microscopic parameters in the inner crust. These density-dependent crustal coupling profiles are combined with a simplified treatment of the core coupling and implemented in a three-component neutron star model to construct a predictive framework for glitch rises. As a result of the density-dependent dynamics, we find the superfluid to transfer angular momentum to different parts of the crust and the core on different timescales. This can cause the spin frequency change to become non-monotonic in time, allowing for a maximum value much larger than the measured glitch size, as well as a delay in the recovery. The exact shape of the calculated glitch rise is strongly dependent on the relative strength between the crust and core mutual friction, providing the means to probe not only the crustal superfluid but also the deeper neutron star interior. To demonstrate the potential of this approach, we compare our predictive model with the first pulse-to-pulse observations recorded during the December 2016 glitch of the Vela pulsar. Our analysis suggests that the glitch rise behavior is relatively insensitive to the crustal mutual friction strength as long as $\mathcal{B} \gtrsim 10^{-3}$, while being strongly dependent on the core coupling strength, which we find to be in the range $3 \times 10^{-5} \lesssim \mathcal{B}_{\rm core} \lesssim 10^{-4}$.