BL Lacertae produced its strongest daily-averaged gamma-ray output of the analyzed period on MJD 60588, or 5 October 2024: (1.03 ± 0.05) × 10−5 ph cm−2 s−1. Its photon index was 1.93 ± 0.04, with a reported test statistic of 3792.
The result comes from a multi-wavelength examination of two flaring episodes in BL Lacertae between MJD 60500 and 60800, corresponding to 9 July 2024 through 5 May 2025. The researchers used Fermi-LAT, Swift-XRT/UVOT, ZTF and Mephisto observations to build quasi-simultaneous broadband SEDs for the F1 and F2 flare epochs, with a low-flux quiet state included in the model comparison.
A clear signal at hour scale
At the longer timescale, both active periods showed significant changes. The shortest doubling time in F1 was 1.47 ± 0.30 hours at MJD 60587.20, reported at 6.0σ significance. In F2, the shortest halving time was 1.33 ± 0.29 hours at MJD 60718.40, at 5.9σ.
Those measurements were used to set conditional upper limits on the size of the emitting region. Taking bulk Lorentz factors of 14.9 for F1 and 14.8 for F2, and assuming the Doppler factor was approximately equal to the corresponding Lorentz factor, the authors obtained size limits of 2.2 × 10¹⁵ cm and 2.0 × 10¹⁵ cm. The corresponding upper limits on distance from the black hole were 6.6 × 10¹⁶ cm and 5.9 × 10¹⁶ cm.
The faster signal is still a question
An attempt to resolve a shorter event produced a more cautious result. A 2-minute light curve around MJD 60588.6 gave only marginal evidence for minute-scale variability, with p = 0.03 and χ²/dof = 26.70/15 under the study’s adopted p ≤ 0.05 threshold. Flares I and III, by contrast, were consistent with constant flux.
Using the tentative shortest doubling time of 0.7 ± 0.2 minutes on MJD 60588, the paper inferred an upper limit of 1.8 × 10¹³ cm for the variable region. That estimate depends on treating the marginal signal as real, so it is a conditional constraint rather than a direct measurement.
The fitted flare profiles also differed in shape. Flare I was nearly symmetric, with an asymmetry value of 0.2, while Flares II and III were moderately asymmetric, at −0.5 and −0.7. Their fitted peaks came at MJD 60587.35 ± 0.02, 60588.64 ± 0.06 and 60718.43 ± 0.03, respectively.
Brighter did not mean harder
During the fast episode around MJD 60588.6, brighter gamma-ray flux went with a higher photon index, a softer-when-brighter pattern. Spearman correlations were r = 0.74 for 2-minute bins (p = 9.5 × 10−4), r = 0.66 for 3-minute bins (p = 0.02), and r = 0.96 for 5-minute bins (p = 4.5 × 10−4). The strongest reported association was therefore in the 5-minute grouping, but this within-source correlation does not establish what produced it.
What the broadband fit suggests
To describe the emission across the observed bands, the researchers used a one-zone leptonic JetSet model. It treated the source as a homogeneous spherical emission region and used a broken-power-law distribution for the electrons.
In the fitted picture, synchrotron radiation represented the low-energy peak, the SSC component accounted mainly for the X-rays, and the EC component represented the high-energy peak. Reduced χ² values were 1.1 for F1, 0.9 for F2 and 1.6 for the low state, although the two highest-energy gamma-ray points in F2 and in the low state were not well reproduced.
The fitted low-energy electron index p1 was 2.5 in the low state, 1.2 in F1 and 1.5 in F2. The modeled magnetic field was 2.3 G in the low state, 0.5 G in F1 and 0.4 G in F2. Both sets of values are model best fits, not direct measurements.
One source, one preprint
The evidence remains narrow. This was a study of one blazar observed across two flaring episodes, with comparisons among its active and quiet states. Its direct empirical conclusions apply to BL Lacertae during the analyzed period; the region sizes, distances and spectral components are inferred within the stated variability and SED assumptions. The study does not by itself establish how other blazars behave.
The document is an arXiv version-1 preprint. Its acknowledgements report support from the National Key Research and Development Program of China and the Yunnan Key Laboratory of Survey Science.
Paper data and sources
Original title: Rapid Variability and Broadband Spectral Modeling in the Flaring Activity of BL Lacertae
Authors: Xin Chang, Dingrong Xiong, Chenxu Liu et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text