  We prove that the mapping torus group $\FN \rtimes_{\alpha} \Z$ of any
automorphism $\alpha$ of a free group $\FN$ of finite rank $n \geq 2$ is weakly
hyperbolic relative to the canonical (up to conjugation) family $\mathcal
H(\alpha)$ of subgroups of $\FN$ which consists of (and contains
representatives of all) conjugacy classes that grow polynomially under
iteration of $\alpha$. Furthermore, we show that $\FN \rtimes_{\alpha} \Z$ is
strongly hyperbolic relative to the mapping torus of the family $\mathcal
H(\alpha)$. As an application, we use a result of Drutu-Sapir to deduce that
$\FN \rtimes_{\alpha} \Z$ has Rapic Decay.
