A Small-scale Structure Model of a Jet Based on Observations of Microvariability

We developed a multiregion radiation model for the evolution of flux and spectral index with time. In this model, each perturbation component in the jet produces an independent flare. The model can be used to study the decomposition of microvariability, the structural scale of the perturbed components, and the physical parameters of the acceleration processes. Based on the shock acceleration model for a relativistic jet, the influence of the acceleration parameters on multiband flare parameters is calculated. We present the results of multiband optical microvariability of the blazar BL Lacertae observed during 89 nights in the period from 2009 to 2021, and use them as a sample for model fitting. The results show that both the amplitude and duration of flares decomposed from the microvariability light curves conform to a log-normal distribution. The time delays between the optical bands follow a normal distribution and amount to several minutes, which corroborate with both predictions from the theoretical model and the calculation of the discrete correlation function. Using the spectral index evolution and the simultaneous fitting of the multiband variability curves, we obtain the acceleration and radiation parameters to constrain and distinguish the origins of different flares. Based on the flare decomposition, we can effectively reproduce the time-domain evolution trends of the optical variations and energy spectrum, and explain the various redder-when-brighter and bluer-when-brighter behaviors.