Variability Signatures of a Burst Process in Flaring Gamma-Ray Blazars

Blazars exhibit stochastic flux variability across the electromagnetic spectrum, often exhibiting heavy-tailed distributions, commonly modeled as lognormal. However, Tavecchio et al. (2020) and Adams (2022) found that high-energy gamma-ray distributions of several brightest flaring Fermi-LAT flat spectrum radio quasars (FSRQs) are well by an even heavier-tailed distribution, which we show is inverse gamma distribution. We propose autoregressive model in distribution arises a consequence shot-noise process. In this model, discrete bursts individually unresolved averaged over within time bins, analysis data. Stochastic on timescales longer than bin duration using first-order structure. The becomes approximately lognormal limiting case many weak bursts. fractional predicted to decrease increases. Using simulated light curves, proposed consistent with typical properties FSRQs BL Lac objects. parameters can be physically interpreted average burst rate, fluence, timescale long-term fluctuations.