Evidence for a bursty $\gamma$-ray QPO in the neutrino-associated FSRQ PKS 1424$-$418 using Fast Template Periodograms and Machine Learning

Abstract

Standard frequency-domain searches for quasi-periodic oscillations (QPOs) in active galactic nuclei generally assume sinusoidal variability. However, $\gamma$-ray blazar emission often shows asymmetric flares and localized bursts, causing spectral leakage that can reduce the sensitivity of conventional methods to non-sinusoidal periodic signals. We analyze a blind sample of 100 high-cadence (7-day binned) Fermi-LAT blazar light curves. After baseline detrending with Singular Spectrum Analysis, we apply the Fast Template Periodogram using three template families: a sinusoid, a Gaussian burst, and an empirical asymmetric template derived from PG 1553+113. Candidate signals are then evaluated with a Random Forest classifier trained on $5\times10^4$ simulated light curves to distinguish genuine periodic phase structure from stochastic red noise. We identify nine $>3\sigma$ periodicity candidates. Three persistent QPOs, including PG 1553+113, are recovered by all template models, whereas six additional candidates are strongly suppressed under the standard sinusoidal assumption but become detectable with morphology-aware templates. Machine learning validation rejects five of these as lacking stable phase coherence. The remaining candidate, PKS 1424$-$418, shows a structurally stable 4.8-year periodicity with a source-specific significance of $3.76\sigma$ (approximately $2.4\sigma$ after accounting for the trial factor of the 100-source sample). These results demonstrate that morphology-aware periodograms, combined with structural machine learning validation, improve the detection of burst-dominated QPOs that are difficult to identify with traditional harmonic searches.