Discovery of a 310-day Period from the Enshrouded Massive System NaSt1 (WR 122).

We present optical and infrared (IR) light curves of NaSt1, also known as Wolf-Rayet (WR) 122, with observations from Palomar Gattini-IR (PGIR), the Zwicky Transient Facility (ZTF), the Katzman Automatic Imaging Telescope (KAIT), the Asteroid Terrestrial-impact Last Alert System (ATLAS), and the All-Sky Automated Survey for Supernovae (ASAS-SN). We identify a $P=309.7\pm0.7$ d photometric period from the optical and IR light curves that reveal periodic, sinusoidal variability between 2014 July and 2021 July. We also present historical IR light curves taken between 1983 July and 1989 May, which show variability consistent with the period of the present-day light curves. In the past, NaSt1 was brighter in the $J$ band with larger variability amplitudes than the present-day PGIR values, suggesting that NaSt1 exhibits variability on longer ($\gtrsim$ decade) timescales. Sinusoidal fits to the recent optical and IR light curves show that the amplitude of NaSt1's variability differs at various wavelengths and also reveal significant phase offsets of $17.0\pm2.5$ d between the ZTF $r$ and PGIR $J$ light curves. We interpret the $310$ d photometric period from NaSt1 as the orbital period of an enshrouded massive binary. We suggest that the photometric variability of NaSt1 may arise from variations in the line-of-sight optical depth toward circumstellar optical/IR emitting regions throughout its orbit due to colliding-wind dust formation. We speculate that past mass transfer in NaSt1 may have been triggered by Roche-lobe overflow (RLOF) during an eruptive phase of an Ofpe/WN9 star. Lastly, we argue that NaSt1 is no longer undergoing RLOF mass transfer.