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Gaussian Process Modeling $\it{Fermi}$-LAT $γ$-ray Blazar Variability: A Sample of Blazars with $γ$-ray Quasi-periodicities

Blazar variability may be driven by stochastic processes. On the other hand, quasi-periodic oscillation (QPO) behaviors are recently reported to be detected in $\it{Fermi}$-LAT data of blazars. However, the significances of these QPO signals given by traditional Fourier-like methods are still questioned. We analyze $γ$-ray light curves of the QPO blazars with two Gaussian process methods, CARMA and $\it{celerite}$, to examine the appropriateness of Gaussian processes for characterizing $γ$-ray light curves of blazars and the existence of the reported QPOs. We collect a sample of 27 blazars with possible $γ$-ray periodicity and generate their $\sim11$ years $\it{Fermi}$-LAT light curves. We apply the Gaussian process models to the $γ$-ray light curves, and build their intrinsic power spectral densities (PSDs). The results show that in general the $γ$-ray light curves can be characterized by CARMA and $\textit{celerite}$ models, indicating that $γ$-ray variabilities of blazars are essentially Gaussian processes. The resulting PSDs are generally the red noise shapes with slopes between $-0.6$ and $-1.7$. Possible evidence for the $γ$-ray QPOs in PKS 0537$-$441 and PG 1553$+$113 are found in the Gaussian process modelings.