  In this note we investigate the centraliser of a linearly growing element of
$\mathrm{Out}(F_n)$ (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.
