Levy Flights of Binary Orbits due to Impulsive Encounters

TL;DR

This paper models how impulsive encounters with unbound objects cause binary orbits to evolve via Levy flights, providing an analytic framework that explains observed eccentricities in Kuiper belt systems and has broader astrophysical applications.

Contribution

It introduces an analytic solution to a Boltzmann equation describing eccentricity evolution due to impulsive encounters, revealing Levy flight behavior in binary orbit perturbations.

Findings

Eccentricity and inclination evolve as Levy flights rather than normal random walks.

The mass spectrum of perturbers influences the importance of close scatterings.

Model matches observed eccentricities of Kuiper belt binaries and moons.

Abstract

We examine the evolution of an almost circular Keplerian orbit interacting with unbound perturbers. We calculate the change in eccentricity and angular momentum that results from a single encounter, assuming the timescale for the interaction is shorter than the orbital period. The orbital perturbations are incorporated into a Boltzmann equation that allows for eccentricity dissipation. We present an analytic solution to the Boltzmann equation that describes the distribution of orbital eccentricity and relative inclination as a function of time. The eccentricity and inclination of the binary do not evolve according to a normal random walk but perform a Levy flight. The slope of the mass spectrum of perturbers dictates whether close gravitational scatterings are more important than distant tidal ones. When close scatterings are important, the mass spectrum sets the slope of the eccentricity and inclination distribution functions. We use this general framework to understand the eccentricities of several Kuiper belt systems: Pluto, 2003 EL 61, and Eris. We use the model of Tholen et al (2007) to separate the non-Keplerian components of the orbits of Pluto's outer moons Nix and Hydra from the motion excited by interactions with other Kuiper belt objects. Our distribution is consistent with the observations of Nix, Hydra, and the satellites of 2003 EL 61 and Eris. We address applications of this work to objects outside of the solar system, such as extrasolar planets around their stars and millisecond pulsars.