Comprehensive Study of the Blazars from Fermi-LAT LCR: The Log-Normal Flux Distribution and Linear rms-Flux Relation

Fermi-LAT LCR provides continuous and regularly sampled gamma-ray light curves, spanning about 14 yr, for a large sample of blazars. The log-normal flux distribution and linear rms-flux relation of the light curves for a few Fermi blazars have been examined in previous studies. However, the probability that blazars exhibit the log-normal flux distribution and linear rms-flux relation in their gamma-ray light curves has not been systematically explored. In this study, we comprehensively research the distribution of gamma-ray flux and the statistical characteristics on a large sample of 1414 variable blazars from the Fermi-LAT LCR catalog, including 572 FSRQs, 477 BL Lacs, and 365 BCUs, and statistically compare their flux distributions with normal and log-normal distributions. The results indicate that the probability of not rejecting log-normal is 42.05% for the large sample, and there is still a 2.05% probability of not rejecting normality, based on the joint of Kolmogorov-Smirnov, Shapiro-Wilk, and Normality tests. We further find that the probability that BL Lacs conform to the log-normal distribution is higher than that of FSRQs. Besides, after removing sources with less than 200 data points from this large sample, a sample of 549 blazars, which is still a large sample compared to the previous studies, was obtained. Based on dividing the light curves into segments every 20 points (or 40 points, or one year), we fitted the linear rms-flux relation of these three different sets and found that the Pearson correlation coefficients are all close to 1 for most blazars. This result indicates a strong linear correlation between the rms and the flux of these 549 blazars. The log-normal distribution and linear rms-flux relation indicate that the variability of the gamma-ray flux for most blazars is a non-linear and multiplicative process.