On the distribution of fluxes of gamma-ray blazars: hints for a stochastic process?

Abstract

We examine a model for the observed temporal variability of powerful blazars in the $\gamma$-ray band in which the dynamics is described in terms of a stochastic differential equation, including the contribution of a deterministic drift and a stochastic term. The form of the equation is motivated by the current astrophysical framework, accepting that jets are powered through the extraction of the rotational energy of the central supermassive black hole mediated by magnetic fields supported by a so-called \emph{magnetically arrested} accretion disk. We apply the model to the $\gamma$-ray light curves of several bright blazars and we infer the parameters suitable to describe them. In particular, we examine the differential distribution of fluxes ($dN/dF_{\gamma}$) and we show that the predicted probability density function for the assumed stochastic equation naturally reproduces the observed power law shape at large fluxes $dN/dF_{\gamma} \propto F_{\gamma}^{-\alpha}$ with $\alpha>2$.