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 \approx 10 ^ { 7 } 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 ^ { \ast } .
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. , M _ { \mathrm { d } } \lesssim 1 per cent of the black hole mass ) is compatible with their surprisingly young age and small pericentre distances , provided these stars were formed at r \lesssim 10 ^ { 5 } gravitational radii .