Multi-wavelength variability and broadband SED modeling of BL Lac during a bright flaring period MJD 59000-59943

Abstract: We carried a detailed temporal and spectral study of the BL\,Lac by using the long-term \emph{Fermi}-LAT and \emph{Swift}-XRT/UVOT observations, during the period MJD\,59000-59943. The daily-binned $\gamma$-ray light curve displays a maximum flux of $1.74\pm 0.09\times 10^{-5} \rm ph\,cm^{-2}\,s^{-1}$ on MJD\,59868, which is the highest daily $\gamma$-ray flux observed from BL\,Lac. The $\gamma$-ray variability is characterised by power-spectral-density (PSD), r.m.s-flux relation and flux-distribution study. We find that power-law model fits the PSD with index $\sim 1$, which suggest for long memory process at work. The observed r.m.s.-flux relation exhibits a linear trend, which indicates that the $\gamma$-ray flux distribution follows a log-normal distribution. The skewness/Anderson-Darling test and histogram-fit reject the normality of flux distribution, and instead suggest that the flux distribution is log-normal distribution. The fractional-variability amplitude shows that source is more variable in X-ray band than in optical/UV/$\gamma$-ray bands. In order to obtain an insight into the underlying physical process, we extracted broadband spectra from different time periods of the lightcurve. The broadband 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 fit physical parameters show that the variation in different flux-states are mostly related to increase in the bulk-Lorentz factor and spectral hardening of the particle distribution.