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 $\gamma$-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 $\gamma$-ray temporal and spectral variability using data from the Large Area Telescope 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 ${\gamma }_p$, 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 $L_{\mathrm{IC}}$ and the position of this peak on the spectral energy distribution energy axis, $E_p$, 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 $L_{\mathrm{IC}}={10}^{42.33\pm 0.15\pm 0.18_{\mathrm{sys}}}{E}_p^{0.98\pm 0.05\pm 0.06_{\mathrm{sys}}}$, consistent, within the errors, with the linear relation $L_{\mathrm{IC}}\propto E_p$, expected when ${\gamma }_p$ is the only free parameter in the assumed SSC model. This result supports a minimalist SSC scenario in which changes in ${\gamma }_p$ dominate the observed temporal and spectral variability of BL Lacertae.

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• Gamma ray astronomy