Probabilistic eccentricity bifurcation for stars around shrinking massive black hole binaries

TL;DR

This paper investigates how stars around a shrinking massive black hole binary can experience sudden eccentricity changes due to probabilistic bifurcations, impacting phenomena like tidal disruptions and gravitational waves.

Contribution

It introduces the concept of probabilistic eccentricity bifurcation caused by separatrix crossing in the orbital phase space, advancing understanding of stellar dynamics near black hole binaries.

Findings

Eccentricities can undergo sharp transitions depending on initial conditions.

Separatrix crossings are linked to high stellar eccentricities.

Probabilistic bifurcation influences astrophysical phenomena like tidal disruptions.

Abstract

Based on the secular theory, we discuss the orbital evolution of stars in a nuclear star cluster to which a secondary massive black hole is infalling with vanishing eccentricity. We find that the eccentricities of the stars could show sharp transitions, depending strongly on their initial conditions. By examining the phase-space structure of an associated Hamiltonian, we show that these characteristic behaviors are partly due to a probabilistic bifurcation at a separatrix crossing, resulting from the retrograde apsidal precession by the cluster potential. We also show that separatrix crossings are closely related to realization of a large eccentricity and could be important for astrophysical phenomena such as tidal disruption events or gravitational wave emissions.