2018ApJ...854...59V

We present in this article a new method to derive the observed properties of outbursts in relativistic jets. We use the VLBI MOJAVE maps to obtain the light curves, based on the principle that the variability of extragalactic sources, in this case 3C 279 and 4C +29.45, should appear in high resolution observations since 1996 until 2016. The use of the cross entropy method (CE) can accurately determine the ranges of parameters for a sequence of outbursts based on the shock-wave model, where the decay/rise timescale ratio has a small spread and the use of a unique index 1.3 generates a good fit modeled by functions of outbursts and by the model of the three stages. By the CE method, one can automatically get the start epochs as well as the occurrence of rise and decline times of the outbursts in the light curves. The values found are in agreement with the power-law distribution of energy, which shows that the cooling of electrons is a predominant process during the initial phase of the shock model evolution. The results of the decomposition show that the outbursts match the VLBI components observed in jets in addition to showing strong evidence of the peaks in the frequencies of 15.3 GHz. With this, we can model the shock waves with reference to the distance at the core of AGN to obtain the Doppler factor and the Lorentz factor.