The Galactic center hosts several hundred early-type stars, about 20% of which lie in the so-called clockwise disk, while the remaining 80% do not belong to any disks. The circumnuclear ring (CNR), a ring of molecular gas that orbits the supermassive black hole (SMBH) with a radius of 1.5 pc, has been claimed to induce precession and Kozai-Lidov oscillations onto the orbits of stars in the innermost parsec. We investigate the perturbations exerted by a gas ring on a nearly-Keplerian stellar disk orbiting a SMBH by means of combined direct N-body and smoothed particle hydrodynamics simulations. We simulate the formation of gas rings through the infall and disruption of a molecular gas cloud, adopting different inclinations between the infalling gas cloud and the stellar disk. We find that a CNR-like ring is not efficient in affecting the stellar disk on a timescale of 3 Myr. In contrast, a gas ring in the innermost 0.5 pc induces precession of the longitude of the ascending node Omega, significantly affecting the stellar disk inclination. Furthermore, the combined effect of two-body relaxation and Omega-precession drives the stellar disk dismembering, displacing the stars from the disk. The impact of precession on the star orbits is stronger when the stellar disk and the inner gas ring are nearly coplanar. We speculate that the warm gas in the inner cavity might have played a major role in the evolution of the clockwise disk.
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