  We consider the mean-field vortex solutions and their stability within a
two-component Bose Einstein condensate in the immiscible limit. A variational
approach is employed to study a system consisting of a majority component which
contains a single quantised vortex and a minority component which fills the
vortex core. We show that a super-Gaussian function is a good approximation to
the two-component vortex solution for a range of atom numbers of the in-filling
component, by comparing the variational solutions to the full numerical
solutions of the coupled Gross-Pitaevskii equations. We subsequently examine
the stability of the vortex solutions by perturbing the in-filling component
away from the centre of the vortex core, thereby demonstrating their stability
to small perturbations.
