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Evolution of eccentric stellar disks around supermassive black holes: the complex disk disruption dynamics and the milliparsec stars

We study the 10 Myr evolution of parsec-scale stellar disks with initial masses of $M_{\mathrm{disk}} = 1.0$ - $7.5 \times 10^4 M_\odot$ and eccentricities $e_\mathrm{init}=0.1$-$0.9$ around supermassive black holes (SMBHs). Our disk models are embedded in a spherical background potential and have top-heavy single and binary star initial mass functions (IMF) with slopes of $0.25$-$1.7$. The systems are evolved with the N-body code $\texttt{BIFROST}$ including post-Newtonian (PN) equations of motion and simplified stellar evolution. All disks are unstable and evolve on Myr timescales towards similar eccentricity distributions peaking at $e_\star \sim 0.3$-$0.4$. Models with high $e_\mathrm{init}$ also develop a very eccentric $(e_\star\gtrsim0.9)$ stellar population. For higher disk masses $M_\mathrm{disk} \gtrsim3 \times10^4\;\mathrm{M_\odot}$, the disk disruption dynamics is more complex than the standard secular eccentric disk instability with opposite precession directions at different disk radii - a precession direction instability. We present an analytical model describing this behavior. A milliparsec population of $N\sim10$-$100$ stars forms around the SMBH in all models. For low $e_\mathrm{init}$ stars migrate inward while for $e_\mathrm{init}\gtrsim0.6$ stars are captured by the Hills mechanism. Without PN, after $6$ Myr the captured stars have a sub-thermal eccentricity distribution. We show that including PN effects prevents this thermalization by suppressing resonant relaxation effects and cannot be ignored. The number of tidally disrupted stars is similar or larger than the number of milliparsec stars. None of the simulated models can simultaneously reproduce the kinematic and stellar population properties of the Milky Way center clockwise disk and the S-cluster.