Optical flux and spectral variability of BL Lacertae during its historical high outburst in 2020

BL Lacertae had undergone a series of historical high flux activity over a year, from August 2020 in the optical to VHE $\gamma$-rays. In this paper, we report on optical flux and spectral variability of the first historical maxima outburst event during October-November in g, r and i bands with the 1.26m telescope at Xinglong observatory, China. We detected significant intranight variations with amplitude rising up to $\sim 30$%, when the fastest variability timescale is found to be a few tens of minutes, giving an emitting region size of the order $10^{-3}$ pc, which corresponds to $\sim 100$ Schwarzschild radius of the central black hole, likely coming from some jet mini-structures. Unlike on intranight timescale, a clear frequency dependent pattern along with symmetric timescales ($\sim$ 11d) of flux variation are detected on long timescale. The spectral evolution was predominated by flattening of the spectra with increasing brightness i.e., a bluer-when-brighter trend in 96% of the cases. On the night before the outburst peak, the color indices clustered in two distinct branches in color--magnitude diagram within a period of $\sim$ 6 hours that is connected to a hard-soft-hard spectral evolution trend extracted from time-resolved spectra. Such trend has never seen in BL Lac or any other blazars before to the best of our knowledge. The results obtained in this study can be explained in the context of shock induced particle acceleration or magnetic re-connection in the jet where turbulent processes most likely resulted the asymmetric flux variation on nightly timescale.