Indication of gamma-Ray Quasi-periodicity in GB6 J1037+5711 from Multi-technique Timing Analysis
We report the indication of a long-term quasi-periodic oscillation (QPO) in the $\gamma$-ray emission of the BL Lac object 4FGL J1037.7+5711 (GB6 J1037+5711) using more than 17 years of monthly binned Fermi-LAT observations. Since blazar $\gamma$-ray variability is typically dominated by stochastic red-noise processes from turbulent jet activity and accretion fluctuations, we applied multiple independent timing techniques to test periodic modulation. These include the Lomb--Scargle periodogram (LSP), weighted wavelet $Z$-transform (WWZ), first-order autoregressive red-noise modeling (REDFIT), and epoch-folding analysis. The LSP reveals a significant periodic signal at $478.74 \pm 17.55$ days, exceeding the $99.99\%$ confidence level from Monte Carlo simulations. The WWZ analysis independently recovers a comparable period of $474.72 \pm 27.24$ days at $99.7\%$ significance, while the REDFIT analysis identifies a similar periodic feature at $481.67 \pm 35.41$ days above the $99\%$ confidence level. The epoch-folding analysis further confirms the same modulation timescale. The small differences in period estimates across methods are expected given the distinct mathematical frameworks and sensitivity functions. The long-term flux distribution of the source is better described by a lognormal profile than a Gaussian, suggesting that the underlying variability arises from multiplicative processes. The indication of a $\sim$478 day QPO, independently confirmed across all four timing techniques, may be associated with the orbital dynamics of a supermassive binary black hole system driving Newtonian jet precession or periodic Doppler-factor modulation, Lense--Thirring precession of the inner accretion disk around a rapidly spinning SMBH, or accretion-driven instabilities at the disk--jet interface amplified through relativistic beaming.