Effects of a disk structure on stellar motion at the Galactic Center

Abstract

Stellar orbits are key for probing the environment of the supermassive black hole at the Galactic Center, Sagittarius A$^*$. So far, the mass around SgrA$^*$ has been assumed to be spherically distributed. However, the extended mass may instead be flattened, creating disk-like structures. We investigate the effects that a thin disk structure would have on stars at the Galactic Center, focusing on star S2 and S301 and the clockwise stellar disk. We derive analytically the acceleration exerted by a disk with power law density $\Sigma \propto r^{-\gamma}$. We use this acceleration to compute the osculating equations and the variations of the orbital elements, showing how the latter depend on the orientation of the disk with respect to the orbital plane. We find that the disk structure induces a secular shift in the semi-latus rectum, an extra in-plane precession and an out-of-plane precession. The former is neither present at the low-order post Newtonian description that we use for the black hole, nor when a spherical mass distribution is considered. The latter can be competitive with the Lense-Thirring precession induced by the spin of SgrA$^*$ on S301 motion, depending on the mass, the radial extent and the orientation of the disk. Since the Lense-Thirring precession is negligible in S2 motion, the out-of-plane precession can be used to place upper limits on the non luminous mass of disk-like structures at the Galactic Center. The limits might significantly differ from those obtained for spherical distributions and depend on the disk parameters. These results highlight the importance of constraining disk-like structures when using stellar orbits to probe the central black hole, in particular its spin. Once mass estimates are at hand, one can quantify the disk's effect on S301 motion and the resulting degeneracy with a future measurement of SgrA$^*$ spin.