Comparative analysis of BL Lacertae in flaring and non-flaring states: Timing and spectral studies

Abstract Context: BL Lacertae is a blazar known for its high flux variability and occasional broadband flares, the origins of which remain unknown. BL Lacertae was found to be in an extended flaring state in July 2020 which continued until the end of 2021. Aims: The long-term flaring activity makes it an ideal candidate to study its spectral and temporal properties during different flux states. This study explores the X-ray temporal and spectral variability of BL Lacertae. Methods: We analysed five observations of BL Lacertae with the XMM-Newton EPIC instrument taken up to the end of 2021. Temporal properties were investigated using the fractional variability method, minimum variability timescale, and the discrete correlation function. Detailed spectral modelling was performed on the two most variable observations, including an investigation of correlations between the soft (0.3–2.0 keV) and hard (2.0–10.0 keV) energy bands. Results: Out of five observations, two observations were found to be highly variable with $F_\mathrm{var}=19.16 \pm 0.32$ and 6.27 $\pm$ 0.43. The observation taken in 2021 corresponds to the highest flux state. The shortest variability timescale in the 0.3–10 keV band is estimated as 1.24 ks. Assuming the X-ray emission is dominated by the synchrotron process, this variability timescale constrains the size of the emission region. Under the assumption of equipartition between the magnetic field and radiating particles, this implies a magnetic field strength of $B \approx 0.4$ G. The spectral analysis reveals a softer-when-brighter trend, which is commonly seen in blazars. We modelled the X-ray spectra with single power-law, log-parabola, and broken power-law models. In most cases, a broken power-law provided the best fit based on corrected Akaike Information Criterion (AICc) statistics, and a strong correlation was observed between the break energy and the source flux. When a thermal blackbody component was added to the model, its temperature also showed a positive correlation with flux in some observations. Conclusions: Our work indicates the complex spectral evolution of BL Lacertae during this flare. The spectral break, interpreted as the cooling break within the synchrotron component, shifts to higher energies with increasing flux. The source consistently displayed softer-when-brighter behaviour. In only one observation were the soft and hard bands found to be significantly correlated. The data suggest a scenario where the peak of the synchrotron emission moves into or across the X-ray band as the source brightens.