Ejection and Capture Dynamics in Restricted Three-Body Encounters

TL;DR

This paper analyzes the dynamics of binary star disruptions by massive objects, revealing how mass and orbit parameters influence which member is ejected or captured, with implications for hypervelocity stars and satellites.

Contribution

It provides a simple, analytical framework using the restricted three-body approximation to predict ejection and capture outcomes based on binary and encounter parameters.

Findings

Heavier binary members are more likely to be ejected or captured depending on orbit energy.

The probability distributions for ejection and capture are derived for various orbital energies.

The model explains the dynamics of hypervelocity stars and irregular satellites.

Abstract

We study the tidal disruption of binaries by a massive point mass (e.g. the black hole at the Galactic center), and we discuss how the ejection and capture preference between unequal-mass binary members depends on which orbit they approach the massive object. We show that the restricted three-body approximation provides a simple and clear description of the dynamics. The orbit of a binary with mass m around a massive object M should be almost parabolic with an eccentricity |1-e| < (m/M)^{1/3} << 1 for a member to be captured, while the other is ejected. Indeed, the energy change of the members obtained for a parabolic orbit can be used to describe non-parabolic cases. If a binary has an encounter velocity much larger than (M/m)^{1/3} times the binary rotation velocity, it would be abruptly disrupted, and the energy change at the encounter can be evaluated in a simple disruption model. We evaluate the probability distributions for the ejection and capture of circular binary members and for the final energies. In principle, for any hyperbolic (elliptic) orbit, the heavier member has more chance to be ejected (captured), because it carries a larger fraction of the orbital energy. However, if the orbital energy is close to zero, the difference between the two members becomes small, and there is practically no ejection and capture preference. The preference becomes significant when the orbital energy is comparable to the typical energy change at the encounter. We discuss its implications to hypervelocity stars and irregular satellites around giant planets.