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

Abstract

BL Lacertae is a blazar known for its high flux variability and occasional broadband flares of unknown origin. It was in an extended flaring state from July 2020 until the end of 2021, making it an ideal candidate to study spectral and temporal properties during different flux states. We analysed five XMM--Newton EPIC observations of BL Lacertae taken up to the end of 2021. Temporal properties were investigated using fractional variability, minimum variability timescale, and the discrete correlation function. Detailed spectral modeling was performed on the two most variable observations, including correlation analysis between the soft (0.3--2.0 keV) and hard (2.0--10.0 keV) bands. Two of five observations were found to be highly variable with $F_{\mathrm{var}} = 19.16 \pm 0.32$ and $6.27 \pm 0.43$. The 2021 observation corresponds to the highest flux state. The shortest variability timescale in the 0.3--10 keV band is 1.24 ks. Assuming synchrotron-dominated X-ray emission, this timescale constrains the emission region size. Under equipartition between the magnetic field and radiating particles, this implies $B \approx 0.4\,\mathrm{G}$. A softer-when-brighter spectral trend was found, as commonly seen in blazars. Spectra were modeled with single power-law, log-parabola, and broken power-law models; the broken power-law gave the best fit by Akaike Information Criterion in most cases, with a strong break energy--flux correlation. A thermal blackbody component showed a positive temperature--flux correlation in some observations. The spectral break, interpreted as the synchrotron cooling break, shifts to higher energies with increasing flux. The source consistently showed softer-when-brighter behavior. Only one observation showed significant soft--hard band correlation. The data suggest the synchrotron peak moves into or across the X-ray band as the source brightens.