Intraday Optical Variability of BL Lacertae during its Highly Active 2020-2024 Phase

We present an analysis of the intraday flux and spectral variability of BL Lacertae from 2020 September 30 to 2024 December 7, covering its highest recorded brightness and low, intermediate, and high flux states. Our study involved 62 nights of multi-band (BVRI) optical monitoring using four ground-based telescopes located in Egypt, T\"urkiye, and Bulgaria. We assessed intraday flux variability using the power-enhanced F-test and the nested ANOVA test. Significant variability was detected in 88 out of 117 light curves, consistent with previous studies of this object during active epochs. The maximum variability amplitude is 44.5 per cent in the B band. Spectral analysis reveals a bluer-when-brighter trend during intraday flares, supporting a synchrotron origin for the variable emission. For a subset of well-sampled flares, we model their profiles with a double exponential function, deriving rise and decay time-scales, thereby constraining the characteristic times of particle acceleration and cooling processes within the relativistic jet. Assuming a turbulent jet model, we determined limits on the radii and magnetic field strengths of the emitting regions. We detected soft time lags for a multi-band flare and from their analysis, derived the Doppler factor and magnetic field strength of the corresponding emitting region. Our long-term, high-cadence study confirms that BL Lacertae was in an exceptionally active phase during the 2020-2024 period, with intraday variability being a common phenomenon. The results underscore the dynamic nature of the jet emission region and provide valuable observational constraints for models of blazar variability and jet physics.