Convex Cocompact Subgroups of $\mathrm{Out}(F_n)$

Call a finitely generated subgroup $\Gamma$ of $\mathrm{Out}(F_n)$ convex cocompact if its orbit map into the free factor graph is a quasi-isometric embedding. We develop a characterization of convex cocompact subgroups of $\mathrm{Out}(F_n)$ via their action on Outer space similar to one of convex cocompact subgroups of mapping class groups.