Systematic Search for and Study of Short-timescale Flare Structures in BL Lac Object Gamma-Ray Emission

We present here the first systematic search of short-timescale γ -ray flares from 29 high Galactic latitude BL Lac objects over 14 yr of Fermi Large Area Telescope data. Using a combined Bayesian Blocks and HOP algorithm, we identified seven high-quality orbital timescale flare segments from three sources and quantified 24 short-timescale flare structures. We then performed a comprehensive analysis of flare symmetry, power spectral density (PSD) of variability, and flux–photon index relation. The main results are as follows. (1) The flare symmetry parameter A shows a “U-shaped” distribution. Short-timescale flares are symmetric while long-timescale flares are asymmetric. The number of fast-rise, slow-decay and slow-rise, fast-decay type flares are equal. No correlation is found between A and peak/integral flux. No parameter evolution is seen between consecutive flares, either. The observations support a scenario where longer-timescale flares originate from the superposition of short, symmetric subhour flares. (2) PSD from yearly to hourly timescales is modeled using the CARMA process. At lower frequencies, the PSD follows the typical broken power-law form. The high-frequency region of the PSD exhibits a continuous power-law shape, indicating that γ -ray variability originates from a single physical process across all probed timescales. (3) The flux–photon index distribution shows a pattern of “harder-when-brighter” or “softer-when-brighter,” but becomes flat above a certain critical flux, with Γ ≈ 2. This behavior cannot be simply explained by a two-component or blazar sequence model, and we speculate it may be related to complex interplay between electron acceleration and cooling.