A systematic search for spectral hardening in blazar flares with the

Context. Blazars, a subclass of active galactic nuclei (AGNs), are among the most powerful and variable γ-ray sources in the universe. They emit non-thermal radiation across the electromagnetic spectrum in the form of relativistic jets, characterized by rapid flux and polarization variability. High synchrotron-peaked blazars (HSPs) and extreme high synchrotron-peaked blazars (EHSPs), with synchrotron peaks exceeding 1015 Hz and 1017 Hz, respectively, are crucial for understanding the full range of blazar phenomena and testing models of jet physics. Yet, their understanding remains challenging. Aims. This work aims to systematically identify and characterize the most extreme γ-ray blazars using data from the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope. The focus is on spectral hardening, where the γ-ray spectrum becomes harder at higher energies, particularly during flaring episodes. This represents the first dedicated analysis of spectral hardening, as previous studies have only explored this phenomenon in a few individual sources. Methods. We analyzed a sample of 138 blazars selected from the 4FGL-DR2 catalog with high synchrotron peak frequencies and well-sampled light curves. Flaring periods were selected using Bayesian Block analysis. Each flare was then analyzed through γ-ray spectral fitting with both power-law and broken power-law models to identify potential spectral hardening. The significance of spectral hardening was assessed using a test statistic, TShardening, based on the likelihood ratio of the two spectral models. Results. We identified two flaring episodes with indications of spectral hardening, one in 4FGL J0238.4−3116 and another in PKS 2155−304, the latter detected independently by both selection methods but referring to the same flaring period. This number of candidate events is consistent with expectations from statistical fluctuations, suggesting that spectral hardening is, at most, a rare occurrence in γ-ray blazars. These results provide the first population-level constraint on the frequency of such events (< 0.1%). The scarcity of events reinforces the notion that the dominant blazar emission mechanism is well described by smoothly varying power-law spectra across the Fermi-LAT range, with sharp spectral hardenings representing rare deviations likely tied to exceptional jet conditions or transient physical processes. Although these flares show notable spectral changes, their statistical significance remains modest and motivates future multi-wavelength studies to assess whether these rare flares reflect genuinely distinct physical processes within blazar jets.