Kozai-driven mass loss of the circumbinary disk in D9 in orbit around the supermassive black hole Sgr A*

Abstract

The supermassive black hole (Sgr A*) in the Galactic center is surrounded by the S-star cluster consisting of young stars on eccentric orbits. Recently, the S-star binary, called D9, was found to be orbited by a circumbinary disk. Due to the gravitational interaction between Sgr A* and the binary, the disk could be short-lived. We investigate the evolution of the disk around a stellar binary while orbiting Sgr A*. We use the \texttt{AMUSE} framework for coupling a gravity solver (for the binary and Sgr. A*) with a hydrodynamics solver (for the disk). We find that, the disk eventually settles between 5.2$a_{\rm in}$ and 0.28 Hill radii of the binary. Here, $a_{\rm in}$ is the semi-major axis of D9. The inclination of the circumbinary disk follows the binary's, which evolves due to the von Zeipel-Lidov-Kozai (vZLK) mechanism induced by Sgr A*. The mean eccentricity of the disk is approximately in anti-phase with the eccentricity evolution of the binary. We find a vZLK timescale of $T_\text{vZLK}\approx62.5\,$kyr, which is two orders of magnitude shorter than the value reported by Peisker etal. (2024). As a consequence, D9 has undergone multiple vZLK oscillations in its lifetime of 2.7 Myr. We find the disk shows periodic bursts of mass loss on the vZLK timescale, suggesting that the mass loss itself is in part driven by the vZLK mechanism. The secular evolution observed in both the binary and the disk are consistent with theoretical predictions. We find the disk loses $\sim$7\% $\pm$ 2\% of its mass every vZLK cycle. If we extrapolate this mass loss, the disk will have 1\% of its current mass left after another $\sim$4 Myr. D9 will then be $\sim$6.7 Myr old, which is on the same order as the current average age of S cluster members. The vZLK-driven mass loss could, therefore, explain the absence of Br$γ$ emission from other S cluster members.