Self-interaction spin effects in inspiralling compact binaries

Gravitational radiation drives compact binaries through an inspiral phase towards a final coalescence. For binaries with\textit{spin, mass quadrupole and magnetic dipole moments}, various contributions add to this process, which is characterized by the rate of increase $df/dt$ of the gravitational wave frequency and the accumulated number $\mathcal{N}$ of gravitational wave cycles. We present here all contributions to $df/dt$ and $$ up to the second post-Newtonian order. Among them we give for the first time the contributions due to the \textit{self-interaction of individual spins}. These are shown to be commensurable with the proper spin-spin contributions for the recently discovered J0737-3039 double pulsar, and argued to represent the first corrections to the radiation reaction in the Lense-Thirring approach.