Centralisers of linear growth automorphisms of free groups

In this note we investigate the centraliser of a linearly growing element of Out(Fₙ) (that is, a root of a Dehn twist automorphism), and show that it has a finite index subgroup mapping onto a direct product of certain “equivariant McCool groups” with kernel a finitely generated free abelian group. In particular, this allows us to show it is VF and hence finitely presented.