Shock-in-jet model for quasars and microquasars

We present the theoretical background and detailed equations for the synchrotron emission of a shock wave propagating in a relativistic jet. We then show how the evolution of an outburst in this shock-in-jet scenario can be analytically described and parameterized to be fitted to multi-frequency lightcurves of galactic and extragalactic sources. This is done here for the first time with a completely physical description of the jet and the shocked gas, while previous studies used a more phenomenological approach based on the observed properties of the outbursts. Another interesting addition to previous work is the introduction of a low-energy cut of the electron energy distribution that allows for much more diverse synchrotron spectral shapes. To demonstrate and illustrate the new methodology, we present results of infrared-to-radio lightcurve fitting of a succession of outbursts observed in 1994 in the microquasar Cyg X-3. We find that the diversity of outbursts in shape, amplitude, frequency range and timescale can be fairly described by varying only the strength of the shock and its build-up distance from the apex of the jet. A rapid build-up results in high-frequency outbursts evolving on short timescales, while slowly evolving, low-frequency outbursts form and evolve further out in the jet. We conclude by outlining future developments, in particular the inclusion of the associated synchrotron self-Compton emission at X-rays and gamma-rays.