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

TL;DR

PKS 2052-47 exhibits year-scale gamma-ray quasi-periodic modulation investigated with 11 years of monthly-binned Fermi-LAT data. A multi-method timing framework (LSP, WWZ, REDFIT, DCDFT, DRW) with Emmanoulopoulos-type significance testing reveals a robust ~600–630 d QPO and a secondary ~1050–1110 d feature, with the shorter period consistently detected across methods and the longer one more tentative yet significant in several tests. The QPOs appear episodic in sliding-window analyses, suggesting non-stationary drivers, and interpretations point to geometric Doppler modulation from jet precession/helical motion or, less likely, SMBBH-driven dynamics and accretion instabilities. The study demonstrates a rigorous approach to testing long-term QPOs in red-noise-dominated blazar light curves and highlights the need for continued, coordinated multiwavelength monitoring to discriminate among potential physical mechanisms and assess recurrence.

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.

Figures (7)

• Figure 1: (a) LSP computed from the monthly binned Fermi-LAT data over MJD 54727.99--58507.99. The two most prominent peaks occur at frequencies of $0.000920$ and $0.001655~\mathrm{day^{-1}}$, corresponding to periods of $P_1 = 1087.2 \pm 80.4$ d and $P_2 = 604.2 \pm 23.4$ d, respectively. Horizontal lines mark the false-alarm-probability (FAP) levels of 10% (blue dotted), 5% (orange dashed), and 1% (green dash-dotted). (b) $\gamma$-ray light curve overlaid with the best-fitting sinusoidal models corresponding to the two LSP periods. (c,d) Phase-folded light curves for $P_1$ and $P_2$, respectively, shown over two full cycles (phase 0–2). In each panel, the data points are plotted in black, the best-fit sinusoidal model is shown by the red dashed curve, and the horizontal blue dashed line indicates the mean flux level. The folding highlights the quasi-periodic modulation present in the $\gamma$-ray emission.
• Figure 2: Top: LSP of the monthly binned $\gamma$-ray light curve of PKS 2052$-$47, showing two dominant peaks at frequencies of $0.000920$ and $0.001655~\mathrm{d^{-1}}$ (periods of $\sim1087$ and $\sim604$ d), both exceeding the 99.5% confidence level derived from $10^{5}$ Monte Carlo simulations following the method of emmanoulopoulos2013generating. Bottom: Left: WWZ map of the $\gamma$-ray light curve showing the evolution of power as a function of time (MJD) and frequency. Right: The average WWZ power spectrum with confidence levels derived from $10^{5}$ Monte Carlo simulations. The dashed green and red lines represent the 97.0% and 99.5% confidence levels, respectively. The dotted and dashed cyan lines mark the two most prominent peaks at frequencies of 0.000947 and 0.001606 day$^{-1}$, corresponding to periods of $\sim1056$ and $\sim623$ d; the shorter-period feature exceeds the 99.5% level, while the longer-timescale peak reaches the $\sim97$% level.
• Figure 3: Red-noise-corrected REDFIT power spectrum of the $\gamma$-ray light curve of PKS 2052$-$47. The black curve shows the observed spectrum, while the blue and cyan curves correspond to the theoretical and ensemble-averaged AR(1) models, respectively. The brown, green, and red horizontal lines indicate the 90%, 95%, and 99% Monte Carlo confidence levels. Two dominant peaks are present, both exceeding the 99% significance threshold.
• Figure 4: Modified periodogram $H(\omega)$ obtained using the DCDFT method for the $\gamma$-ray light curve of PKS 2052$-$47. Two dominant peaks are detected at periods of $\sim1111$ and $\sim625$ d, consistent with the timescales inferred from the other timing techniques. The associated uncertainties were estimated by fitting Gaussian profiles to the corresponding features in the periodogram. The black dash--dotted curve denotes the 99% confidence level, which is exceeded by both peaks, indicating that they are statistically significant.
• Figure 5: PSDs derived from the DRW modeling of the $\gamma$-ray light curve. Left: PSD obtained using the maximum-likelihood DRW parameters together with the posterior-median solution. Right: Corresponding PSD representation derived from the MCMC posterior samples. Both panels exhibit the characteristic low-frequency flattening and a steep high-frequency decline expected for a DRW process. The inferred parameters are $\ln\sigma_{\rm DRW}=-16.35$ and $\ln\tau_{\rm DRW}=4.55^{+0.33}_{-0.28}$ (days), consistent with the maximum-likelihood values $\ln\sigma_{\rm DRW}=-16.37$ and $\ln\tau_{\rm DRW}=4.49$.