Gamma-ray Blazar variability: New statistical methods of time-flux distributions

TL;DR

This study introduces new statistical methods to analyze gamma-ray flux variability in blazars, revealing that their flux distributions are best described by stable distributions, with some sources showing heavy tails indicating complex underlying processes.

Contribution

The paper applies maximum likelihood estimation with stable distributions to gamma-ray blazar flux data and introduces novel non-stationarity and autocorrelation analyses to characterize variability.

Findings

Flux distributions are best modeled by stable distributions, often log-normal.

Some sources exhibit heavy-tailed distributions, indicating infinite variance processes.

Analysis reveals multiple characteristic time scales and potential hidden periodicities.

Abstract

Variable \gama-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 \gama-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 $\gamma$-ray blazar flux distributions use the stable distribution family, which generalizes the Gaussian distribution. The results suggest that the average behavior of the \gama-ray flux variability over this period can be characterized by log-stable distributions. For most of the sample sources, this estimate leads to standard log-normal distribution ($\alpha=2$). However, a few sources clearly display heavy tail distributions (MLE leads to $\alpha<2$), suggesting underlying multiplicative processes of infinite variance. Furthermore, the light curves were analyzed 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 modeled 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 behavior 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.