An Inverse Gamma Model for Interpreting the Gamma-ray Variability of Flaring Blazars

Blazars have been observed to exhibit stochastic flux variability across the electromagnetic spectrum, at essentially all measurable time scales, but the mechanisms that drive this variability are not yet well understood. The light curves of these sources often have heavy-tailed flux distributions which are commonly modeled as lognormal and taken to indicate evidence of multiplicative processes. However, we find that several bright flaring blazars, especially flat spectrum radio quasars, have high-energy gamma-ray light curves exhibiting extremely heavy-tailed flux distributions that are better described by the inverse gamma distribution than by the lognormal distribution. We propose a simple model in which an inverse gamma flux distribution may arise as a consequence of a shot-noise process in which discrete bursts are individually unresolved within time bins, as in the analysis of Fermi-LAT data. In the limiting case of many small bursts, the flux distribution becomes approximately lognormal. Using simulated light curves, we show how the proposed model can reproduce the variability properties of different blazar source classes, and demonstrate how the model parameters can be extracted and interpreted in terms of physical quantities, such as the fluence of flares powered by relativistic magnetic reconnection.