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Despite numerous detections of individual flares, the physical origin of the rapid variability observed from blazars remains uncertain. Using Bayesian blocks and the Eisenstein-Hut HOP algorithm, we characterize flux variations of high significance in the $\gamma$-ray light curves of two samples of blazars. Daily binned long-term light curves of TeV-bright blazars observed with the First G-APD Cherenkov Telescope (FACT) are compared to those of GeV-bright blazars observed with the Large Area Telescope on board the $Fermi$ Gamma-ray Space Telescope ($Fermi$-LAT). We find no evidence for systematic asymmetry of the flux variations based on the derived rise and decay time scales. Additionally, we show that the daily-binned blazar light curves can be described by an exponential stochastic Ornstein-Uhlenbeck (OU) process with parameters depending on energy. Our analysis suggests that the flux variability in both samples is a superposition of faster fluctuations. This is, for instance, challenging to explain by shock-acceleration but expected for magnetic reconnection., Comment: for associated HOP algorithm, see https://github.com/swagner-astro/lightcurves and for associated OU algorithm, see https://github.com/PRBurd/astro-wue

On 2019 October 25, the Fermi-Large Area Telescope observed the first gamma-ray flare from the radio-loud narrow-line Seyfert 1 (NLSy 1) galaxy PKS 2004$-$447 ($z=0.24$). We report on follow-up observations in the radio, optical-UV, and X-ray bands that were performed by ATCA, the Neil Gehrels Swift observatory, XMM-Newton, and NuSTAR, respectively, and our multi-wavelength analysis. We study the variability across all energy bands and additionally produce $\gamma$-ray light curves with different time binnings to study the variability on short timescales during the flare. We examine the X-ray spectrum from 0.5$-$50 keV by describing the spectral shape with an absorbed power law. We analyse multi-wavelength datasets before, during, and after the flare and compare these with a low activity state of the source by modelling the respective SEDs with a one-zone synchrotron inverse Compton radiative model. Finally, we compare our results to gamma-ray flares previously observed from other $\gamma$-loud NLSy 1 galaxies. At gamma-ray energies (0.1$-$300 GeV) the flare reached a total maximum flux of $(2.7\pm0.6)\times10^{-6}$~ph~cm$^{-2}$~s$^{-1}$ in 3-hour binning. With a photon index of $\Gamma_{0.1-300\mathrm{GeV}}=2.42\pm0.09$ during the flare, this corresponds to an isotropic gamma-ray luminosity of $(2.9\pm0.8)\times10^{47}\,\mathrm{erg}\,\mathrm{s}^{-1}$. The $\gamma$-ray, X-ray, and optical-UV light curves covering the end of September to the middle of November show significant variability, and we find indications for flux-doubling times of $\sim 2.2$~hours at $\gamma$-ray energies. During the flare, the SED exhibits large Compton dominance. While the increase in the optical-UV range can be explained by enhanced synchrotron emission, the elevated $\gamma$-ray flux can be accounted for by an increase in the bulk Lorentz factor of the jet, similarly observed for flaring gamma-ray blazars., Comment: 17 pages, 7 figures. Accepted for publication in Astronomy & Astrophysics

Context. Monthly-binned gamma-ray light curves of 236 bright gamma-ray sources, particularly blazars, selected from a sample of 2278 high-galactic latitude objects observed with Fermi-LAT, show flux variability characterized by power spectral densities consisting of a single power-law component, ranging from Brownian to white noise. Aims. The main goal here is to assess the Ornstein-Uhlenbeck (OU) model by studying the range of its three parameters that reproduces these statistical properties. Methods. We develop procedures for extracting values of the three OU model parameters (mean flux, correlation length, and random amplitude) from time series data, and apply them to compare numerical integrations of the OU process with the Fermi-LAT data. Results. The OU process fully describes the statistical properties of the flux variations of the 236 blazars. The distributions of the extracted OU parameters are narrowly peaked about well-defined values (sigma, mu, theta) = (0.2, -8.4, 0.5) with variances (0.004, 0.07, 0.13). The distributions of rise and decay time scales of flares in the numerical simulations, i.e. major flux variations fulfilling pre-defined criteria, are in agreement with the observed ones. The power spectral densities of the synthetic light curves are statistically indistinguishable from those of the measured light curves. Conclusions. Long-term gamma-ray flux variability of blazars on monthly time scales is well described by a stochastic model involving only three parameters. The methods described here are powerful tools to study randomness in light curves and thereby constrain the physical mechanisms responsible for the observed flux variations., Comment: 13 pages, 9 figures