# Effect of orbital eccentricity on the dynamics of precessing compact binaries

## TL;DR

This paper investigates how orbital eccentricity influences the precession dynamics and spin morphology transitions of binary black holes during inspiral, using an effective potential formalism and post-Newtonian evolution.

## Contribution

It introduces a classification of binary black hole spin morphologies in eccentric orbits and analyzes their evolution, demonstrating eccentricity's sub-dominant role in morphology transitions.

## Key findings

- Eccentricity can monotonically increase, decrease, or rise after a minimum during inspiral.
- Spin morphology transition probabilities are similar in eccentric and circular orbits.
- Eccentricity evolution patterns are influenced by 2PN spin-spin coupling.

## Abstract

We study precession dynamics of generic binary black holes in eccentric orbits using an effective potential based formalism derived in [M. Kesden et al., PRL {\bf 114}, 081103 (2015)]. This effective potential is used to classify binary black holes into three mutually exclusive spin morphologies. During the inspiral phase, binaries make transitions from one morphology to others. We evolve a population of binary black holes from an initial separation of $1000\mathbf{M}$ to a final separation of $10\mathbf{M}$ using post-Newtonian accurate evolution equations. We find that, given suitable initial conditions, a binary's eccentricity can follow one of three distinct evolutionary patterns: (i) eccentricity monotonically increasing until final separation, (ii) eccentricity rising after decaying to a minimum value, and (iii) eccentricity monotonically decreasing throughout the inspiral. The monotonic growth or growth after reaching a certain minimum of eccentricity is due to the effect of 2PN spin-spin coupling. Further, we investigate the morphology transitions in eccentric binaries and find that the probability of such binaries transiting from one to other is similar to those in circular orbits, implying that eccentricity plays a sub-dominant role in spin morphology evolution of a precessing binary black hole. We, hence, argue that the morphological classification of spin precession dynamics is a robust tool to constrain the formation channels of binaries with arbitrary eccentricity as well.