Universal Stochastic Process in Blazar Gamma-Ray Variability Revealed by Bayesian Kernel Comparison

Abstract Although Gaussian processes have been widely applied in modeling the high-energy light curves of blazars, a systematic comparison of the performances of different kernel functions within Gaussian processes has remained lacking. Based on a Bayesian inference framework, we systematically compare the performances of three Gaussian process kernel functions in modeling blazars’ long-term gamma-ray light curves. The results indicate that, among the tested kernel functions, the Matérn 1/2 kernel performs best for both types of blazars—BL Lacertae objects (BL Lacs) and flat-spectrum radio quasars (FSRQs)—suggesting that a universal stochastic process likely governs the high-energy variability of the blazar population. Statistically, this kernel is equivalent to the “shot-noise” model, supporting the scenario that the gamma-ray variability in blazars originates from the random superposition of numerous independent flares. A statistical analysis of hyperparameters reveals that the variability amplitude of FSRQs is significantly higher than that of BL Lacs, which may be related to their radiation being more strongly modulated by external photon fields. The intrinsic correlation timescales of both sources are similar and show no dependence on black hole mass or intrinsic luminosity. This indicates that the timescale is primarily determined by local physical conditions within the jet, rather than by the global properties of the central engine.