  We study the motion of superfluid vortices with filled massive cores.
Previous point-vortex models already pointed out the impact of the core mass on
the vortex dynamical properties, but relied on an assumption that is
questionable in many physical systems where the immiscibility condition is
barely satisfied: the fact that the massive core always lays at the very bottom
of the effective confining potential constituted by the hosting vortex. Here,
we relax this assumption and present a new point-vortex model where quantum
vortices are harmonically coupled to their massive cores. We thoroughly explore
the new dynamical regimes offered by this improved model; we then show that the
functional dependence of the system normal modes on the microscopic parameters
can be correctly interpreted only within this new generalized framework. Our
predictions are benchmarked against the numerical simulations of coupled
Gross-Pitaevskii equations for a realistic mixture of atomic Bose-Einstein
condensates.
