Multiwavelength variability and broad-band SED modelling of BL Lac during a bright flaring period MJD 59000-59943

We carried out a detailed temporal and spectral study of the BL Lacertae (BL Lac) by using the long-term Fermi-Large Area Telescope (LAT) and Swift-X-ray Telescope (XRT)/Ultraviolet Optical Telescope (UVOT) observations, during the period MJD 59000-59943. The daily-binned γ-ray light curve displays a maximum flux of $1.74\pm 0.09\times 10^{-5} \,\rm photons\, cm^{-2}\, s^{-1}$ on MJD 59868, which is the highest daily γ-ray flux observed from BL Lac. The γ-ray variability is characterized by power spectral density (PSD), rms-flux relation, and flux distribution study. We find that the power-law model fits the PSD with index ~1, which suggests a long-memory process at work. The observed rms-flux relation exhibits a linear trend, which indicates that the γ-ray flux distribution follows a lognormal distribution. The skewness/Anderson-Darling test and histogram fit reject the normality of flux distribution, and instead suggest that the flux distribution is a lognormal distribution. The fractional variability amplitude shows that the source is more variable in the X-ray band than in optical/ultraviolet/γ-ray bands. In order to obtain an insight into the underlying physical process, we extracted broad-band spectra from different time periods of the light curve. The broad-band spectra are statistically fitted with the convolved one-zone leptonic model with different forms of the particle energy distribution. We found that spectral energy distribution during different flux states can be reproduced well with the synchrotron, synchrotron self-Compton, and external Compton emissions from a broken power-law electron distribution, ensuring equipartition condition. A comparison between the best-fitting physical parameters shows that the variation in different flux states is mostly related to an increase in the bulk Lorentz factor and spectral hardening of the particle distribution.