Research Note

On highly eccentric stellar trajectories interacting with a self-gravitating disc in Sgr A

¹ Charles University, Faculty of Mathematics and Physics, V Holešovičkách 2, 180 00 Prague, Czech Republic e-mail: vladimir.karas@cuni.cz
² Astronomical Institute, Academy of Sciences, Boční II, 141 31 Prague, Czech Republic

Received: 29 September 2004
Accepted: 30 December 2004

Abstract

We propose that Kozai's phenomenon is responsible for the long-term evolution of stellar orbits near a supermassive black hole. We pursue the idea that this process may be driven by a fossil accretion disc in the centre of our Galaxy, causing the gradual orbital decay of stellar trajectories, while setting some stars on highly elliptic orbits. We evolve model orbits that undergo repetitive transitions across the disc over the period of ≈10⁷ years. We assume that the disc mass is small compared to the central black hole, and its gravitational field comparatively weak, yet non-zero, and we set the present values of orbital parameters of the model star consistent with those reported for the S2 star in Sagittarius A. We show how a model trajectory decays and circularizes, but at some point the mean eccentricity is substantially increased by Kozai's resonance. In consequence the orbital decay of highly eccentric orbits is accelerated. A combination of an axially symmetric gravitational field and dissipative environment can provide a mechanism explaining the origin of stars on highly eccentric orbits tightly bound to the central black hole. In the context of other S-stars, we can conclude that an acceptable mass of the disc (i.e.,  per cent of the black hole mass) is compatible with their surprisingly young age and small pericentre distances, provided these stars were formed at gravitational radii.