Superfluid $^3$He aerogel experiments as a laboratory neutron star analogue

Neutron stars make a unique astrophysical test bench for our understanding of quantum physics at kilometre scales. The rotation of a neutron star features glitches, sudden spin-ups that interrupt the otherwise regular stellar spin-down, which are often attributed to the dynamics of pinned quantised vortices in one or several of the superfluid phases inside the star. Laboratory experiments probing superfluid vortices have inspired neutron star theory and simulations from the beginning. Here we argue that vortex experiments in superfluids contained in aerogels show phenomenology that offers a highly appealing but vastly unexplored analogue for neutron star physics. We build a point-vortex simulation that allows analysing experiments in a crust-like and a core-like aerogel, extracting two different regimes of pinned vortex (non-)dynamics and validating a microscopic picture of very strong vortex pinning. In the crust-like aerogel, vortices get depinned once the ambient superflow is fast enough, while in the core-like aerogel pinned vortices are never released and rotational velocity changes are accommodated by the avalanche-like production of new vortices instead. Finally, we show that these concepts should apply also in neutron stars and may thus revolutionise the analysis of neutron star observations.