A Face-on Accretion Disk Geometry Revealed by Millimeter-wave Periodicity in Sgr A ^∗

Abstract We analyzed 77 epochs of Atacama Large Millimeter/submillimeter Array archival data to investigate flux variability in Sagittarius A ∗ , the supermassive black hole at the Galactic center. Among these, we identified a rare but unusually clear and coherent ∼52 minute sinusoidal modulation at 230 GHz, with a statistical significance exceeding 5 σ . Modeling with a Doppler-boosted hotspot scenario yields an orbital radius of ∼4 Schwarzschild radii and a disk inclination of 8°(or 172°), providing the first direct millimeter wavelength constraint on the inner accretion flow geometry. This nearly face-on inclination is in good agreement with previous constraints from GRAVITY and Event Horizon Telescope observations. These findings provide robust, independent evidence that millimeter-wave periodicity can directly probe the innermost accretion flow geometry, offering a powerful complement to variability studies at infrared and X-ray wavelengths.