A multi-technique search for year-scale $γ$-ray quasi-periodic modulation in the high-redshift FSRQ PKS~2052$-$47

Abstract

We investigate year-scale quasi-periodic oscillations in the $γ$-ray emission of the high-redshift flat-spectrum radio quasar PKS~2052$-$47 using monthly binned \emph{Fermi}-LAT data spanning MJD~54727.99--58507.99. To assess the statistical significance of periodic features embedded in red-noise-dominated variability, we apply several complementary timing techniques, including the Lomb--Scargle periodogram, weighted wavelet $Z$-transform, date-compensated discrete Fourier transform, REDFIT assuming an AR(1) process, and damped random walk modelling. The analyses reveal a dominant quasi-periodic modulation on a timescale of $\sim600$--630~d, together with a secondary longer-timescale feature near $\sim1050$--1110~d. Monte Carlo simulations show that the shorter-period signal exceeds the highest local confidence levels, while the longer modulation reaches $\gtrsim99$ per cent local significance in several tests; independent DRW-based simulations place both peaks above the $4σ$ envelope in the Lomb--Scargle analysis. Spectral-window diagnostics indicate that the detected periodicities are not artefacts of uneven sampling, and a sliding-window analysis shows that the QPO power is episodic across the $\sim11$~yr baseline. We discuss possible physical interpretations in terms of geometric Doppler modulation associated with jet precession or helical motion, accretion-driven instabilities, and SMBBH-induced dynamics.