The Effectiveness of the Kozai Mechanism in the Galactic Centre

TL;DR

This paper investigates the impact of the Galactic centre's stellar bulge and relativistic effects on Kozai oscillations induced by stellar discs, finding that a spherical bulge suppresses these oscillations, challenging previous assumptions.

Contribution

It provides a detailed analysis of how the spherical stellar bulge influences Kozai oscillations, highlighting suppression effects relevant to the Galactic centre dynamics.

Findings

Spherical stellar bulge suppresses Kozai oscillations.

Kozai oscillations are unlikely due to stellar discs in the Galactic centre.

Suppression depends on the bulge's enclosed mass relative to stellar discs.

Abstract

I examine the effectiveness of Kozai oscillations in the centres of galaxies and in particular the Galactic centre using standard techniques from celestial mechanics. In particular, I study the effects of a stellar bulge potential and general relativity on Kozai oscillations, which are induced by stellar discs. Lockmann et al (2008) recently suggested that Kozai oscillations induced by the two young massive stellar discs in the Galactic centre drives the orbits of the young stars to large eccentricity ($e\approx 1$). If some of these young eccentric stars are in binaries, they would be disrupted near pericentre, leaving one star in a tight orbit around the central SMBH and producing the S-star population. I find that the {\it spherical} stellar bulge suppresses Kozai oscillations, when its enclosed mass inside of a test body is of order the mass in the stellar disc(s). Since the stellar bulge in the Galactic centre is much larger than the stellar discs, Kozai oscillations {\it due to the stellar discs} are likely suppressed. Whether Kozai oscillations are induced from other nonspherical components to the potential (for instance, a flattened stellar bulge) is yet to be determined.