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

TL;DR

This paper introduces the concept of punctuated chaos to explain the unpredictable orbital evolution of S-stars in the Galactic center, highlighting the role of close encounters and perturbations in driving exponential divergence of orbits.

Contribution

It presents a new theory of punctuated chaos that accounts for the chaotic behavior of S-stars caused by discrete perturbations from close encounters.

Findings

Chaos arises mainly from close stellar encounters within 100 au.

The Lyapunov time scale for the S-star cluster is approximately 462 years.

A few close orbiting stars dominate the chaos in the next millennium.

Abstract

We investigate the chaotic behavior of the S-star cluster in the Galactic center using precise $N$-body calculations, free from round-off or discretization errors. Our findings reveal that chaos among the Galactic center 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, neighboring solutions experience roughly exponential growth in separation. We propose a theory of "punctuated chaos" that describes the S-star cluster's chaotic behavior. This phenomenon results from nearly linear growth in the separation between neighboring 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 center, perturbations originate from coincidental encounters occurring within a distance of $\aplt 100$\,au between at least two stars (in some cases, three stars). Our model satisfactorily explains the observed exponential growth in the 27 S-star cluster. We determine that the S-star system has a Lyapunov time scale of approximately 462 +/-74 years. 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.