Two Transient Quasi-periodic Oscillations in -Ray Emission from the Blazar S4 0954+658

In this work, we report periodicity search analyses in the gamma-ray light curve of the blazar S4 0954+658 in monitoring undertaken by the Fermi Large Area Telescope. Four analytical methods and a tool are adopted to detect any periodic flux modulation and corresponding significance level, revealing: (i) a quasi-periodic oscillation (QPO) of 66 days with a significance level of >5 sigma spanning over 600 days from 2015 to 2016 (MJD 57,145-57,745), resulting in continuous observation of nine cycles, which is one of the longest cycles discerned in blazar gamma-ray light curves; (ii) a possible QPO of 210 days at a moderate significance of similar to 3.5 sigma, which lasted for over 880 days from 2020 to 2022 (MJD 59,035-59,915) and for four cycles. In addition, we discuss several physical models to explain the origin of the two transient QPOs and conclude that a geometrical scenario involving a plasma blob moving helically inside the jet can explain the timescale of the QPO.