The eponymous BL Lac object BL Lacertae is one of the most well-monitored active galactic nuclei, frequently observed from radio to gamma rays. Its relatively soft γ -ray spectrum peaks near 500~MeV, and since 2020 it has undergone an exceptional series of flaring episodes. The observed emission is well described by synchrotron self-Compton (SSC) models, with negligible contribution from external seed photons. We investigate the physical origin of BL~Lacertae's γ-ray temporal and spectral variability using data from the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope, and show that this variability can be explained by a single varying parameter, namely the electrons' peak energy, γₚ, under a single-zone SSC scenario with a log-parabolic electron distribution. We use a Markov chain Monte Carlo to estimate the spectral parameters of BL Lacertae over time, selected from an adaptive-binned gamma-ray light curve. We then study the correlation between the inverse Compton peak luminosity, Lᵢ꜀, and the position of this peak on the SED energy axis, Eₚ, and compare it with what is expected for a single-zone SSC scenario when only one parameter is free to vary. We find a correlation Lᵢ꜀ = 10 superscript (42. 33±0. 15±0. 18) ₛᵧₛ Eₚ superscript (0. 98±0. 05±0. 06) ₛᵧₛ consistent, within the errors, with the linear relation Lᵢ꜀∝Eₚ, expected when γₚ is the only free parameter in the assumed SSC model. This result supports a minimalist SSC scenario in which changes in γₚ dominate the observed temporal and spectral variability of BL~Lacertae.
Menezes et al. (Mon,) studied this question.