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Blazars are among the most powerful extragalactic objects, as a sub-class ofactive galactic nuclei. They launch relativistic jets and their emittedradiation shows strong variability across the entire electro-magnetic spectrum.The mechanisms producing the variability are still controversial and differentmodels have been proposed to explain the observed variations in multi-frequencyblazar light curves.We investigate the capabilities of the classicalshock-in-jet model to explain and reconstruct the observed evolution of flaresin the turnover frequency turnover flux density plane and theirfrequency-dependent light curve parameters. With a detailed parameter spacestudy we provide the framework for future, detailed comparisons of observedflare signatures with the shock-in-jet scenario. Based on the shock model wecompute synthetic single-dish light curves at different radio frequencies (2.6to 345 GHz) and for different physical conditions in a conical jet (e.g.magnetic field geometry and Doppler factor). From those we extract the slopesof the different energy loss stages within the $\nu_\mathrm{m}$-$S_\mathrm{m}$plane and deduce the frequency-dependence of different light curve parameterssuch as flare amplitude, time scale and cross-band delays. The evolution of theDoppler factor along the jet has the largest influence on the evolution of theflare and on the frequency-dependent light curve parameters. The synchrotronstage can be hidden in the Compton or in the adiabatic stage, depending mainlyon the evolution of the Doppler factor, which makes it difficult to detect itssignature in observations. In addition, we show that the time lags betweendifferent frequencies can be used as an efficient tool to better constrain thephysical properties of these objects.

Multi-frequency properties of synthetic blazar radio light curves within the shock-in-jet scenario