Punctuated chaos and the unpredictability of the Galactic Centre S-star orbital evolution

Abstract

We investigate the chaotic behaviour of the S-star cluster in the Galactic Centre using precise N-body calculations, free from round-off or discretization errors. Our findings reveal that chaos among the Galactic Centre S-stars arises from close encounters, particularly among pairs and near the massive central body. These encounters induce perturbations, causing sudden changes in the orbital energies of the interacting stars. Consequently, neighbouring solutions experience roughly exponential growth in separation. We propose a theory of ‘punctuated chaos’ that describes the S-star cluster’s chaotic behaviour. This phenomenon results from nearly linear growth in the separation between neighbouring orbits after repeated finite perturbations. Each participating star’s orbit experiences discrete, abrupt changes in energy due to the perturbations. The cumulative effect of these events is further amplified by the steady drift in orbital phase. In the Galactic Centre, perturbations originate from coincidental encounters occurring within a distance of ≲100 au between at least two stars (in some cases, three stars). Our model satisfactorily explains the observed exponential growth in the 27 S-stars cluster. We determine that the S-star system has a Lyapunov time-scale of approximately 462 ± 74 yr. For the coming millennium, chaos in the S-star cluster will be driven mainly by a few of the closest orbiting stars: S2, S5, S6, S8, S9, S14, S18, S31, S21, S24, S27, S29, and S38.