A model for periodic blazars

We describe a scenario to explain blazar periodicities with timescales of $\sim$ few years. The scenario is based on a binary super-massive black hole (SMBH) system in which one of the two SMBH carries a jet. We discuss the various mechanisms that can cause the jet to precess and produce corkscrew patterns through space with a scale of $\sim$ few pc. It turns out that the dominant mechanism responsible for the precession is simply the imprint of the jet-carrying SMBH orbital speed on the jet. Gravitational deflection and Lense-Thirring precession (due to the gravitational field of the other SMBH) are second order effects. We complement the scenario with a kinematical jet model which is inspired to the spine-sheath structure observed in M87. One of the main advantages of such a structure is that it allows the peak of the synchrotron emission to scale with frequency according to $\nu F\propto \nu^{\xi}$ as the viewing angle is changed, where $\xi$ is not necessarily 3 or 4 as in the case of jets with uniform velocity, but can be $\xi \sim 1$. Finally, we apply the model to the source PG1553+113, which has been recently claimed to show a $T_{\rm obs}=(2.18\pm 0.08)\text{ yr}$ periodicity. We are able to reproduce the optical and gamma-ray light curves and multiple synchrotron spectra simultaneously. We also give estimates of the source mass and size.