Blazar Mrk 501 shows rhythmic oscillations in its $\gamma$-ray emission

Quasi-periodic oscillations (QPO) originating from innermost regions of blazars can provide unique perspective of some of the burning issues in blazar studies including disk-jet connection, launch of relativistic jets from the central engine, and other extreme conditions near the fast rotating supermassive black holes. However, a number of hurdles associated with searching QPOs in blazars e.g., red-noise dominance, modest significance of the detection and periodic modulation lasting for only a couple of cycles, make it difficult to estimate the true significance of the detection. In this work, we report a $\sim$ 330-day QPO in the Fermi/LAT observations of the blazar Mrk 501 spanning nearly a decade. To establish consistency of the result, we adopted multiple approaches to the time series analysis and employed four widely known methods. Among these, Lomb-Scargle periodogram and weighted wavelet z-transform represent frequency domain based methods whereas epoch folding and z-transformed discrete auto-correlation function are time-domain based analysis. Power spectrum response method was followed to properly account for the red-noise, largely inherent in blazar light curves. Both local and global significance of the signal were found to be above 99\% over possible spurious detection. In the context where not many $\gamma$-ray QPOs have been reported to last more than 5 cycles, this might be one of the few instances where we witness a sub-year timescale $\gamma$-ray QPO persisting nearly 7 cycles. A number of possible scenarios linked with binary supermassive black hole, relativistic jets, and accretion disks can be invoked to explain the transient QPO.

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