Gamma-ray blazar variability: new statistical methods of time-flux distributions

Variable γ-ray emission from blazars, one of the most powerful classes of astronomical sources featuring relativistic jets, is a widely discussed topic. In this work, we present the results of a variability study of a sample of 20 blazars using γ-ray (0.1-300 GeV) observations from Fermi/LAT telescope. Using maximum likelihood estimation (MLE) methods, we find that the probability density functions that best describe the γ-ray blazar flux distributions use the stable distribution family, which generalizes the Gaussian distribution. The results suggest that the average behaviour of the γ-ray flux variability over this period can be characterized by log-stable distributions. For most of the sample sources, this estimate leads to standard lognormal distribution (α = 2). However, a few sources clearly display heavy tail distributions (MLE leads to α < 2), suggesting underlying multiplicative processes of infinite variance. Furthermore, the light curves were analysed by employing novel non-stationarity and autocorrelation analyses. The former analysis allowed us to quantitatively evaluate non-stationarity in each source - finding the forgetting rate (corresponding to decay time) maximizing the log-likelihood for the modelled evolution of the probability density functions. Additionally, evaluation of local variability allows us to detect local anomalies, suggesting a transient nature of some of the statistical properties of the light curves. With the autocorrelation analysis, we examined the lag dependence of the statistical behaviour of all the {(y_t, y_{t + l})} points, described by various mixed moments, allowing us to quantitatively evaluate multiple characteristic time scales and implying possible hidden periodic processes.