Two-body relaxation driven evolution of the young stellar disc in the Galactic Centre

The centre of our Galaxy hosts almost two hundreds of very young stars, a subset of which is orbiting the central supermassive black hole (SMBH) in a relatively thin disc-like structure. First analyses indicated a power-law surface density profile of the disc, $\Sigma \propto R^\beta$ with $\beta = -2$. Recently, however, speculations about this profile arose. In particular, it now seems to be better described by a sort of broken power-law. By means of both analytical arguments and numerical N-body modelling, we show that such a broken power-law profile is a natural consequence of the two-body relaxation of the disc which is, due to small relative velocities of stars on nearby co-planar Keplerian orbits around the SMBH, effective enough to affect the evolution of the disc on time-scales comparable to its estimated age. In the inner, densest part of the disc, the profile becomes rather flat ($\beta ~ -1$) while the outer parts keep imprints of the initial state. Our numerical models show that the observed projected surface density profile of the young stellar disc can result from two-body relaxation driven evolution of a disc with initial single power-law profile with $-2 < \beta < -1.5$. In addition, we suggest that two-body relaxation may have caused a significant radial migration of the S-stars towards the central SMBH, thus playing an important role in their formation scenario.