Long-Term Stability of Planets in the $\alpha$ Centauri System, II: Forced Eccentricities

TL;DR

This study investigates how minimizing initial forced eccentricities affects the long-term orbital stability of planets in the alpha Centauri system, revealing that certain initial conditions significantly expand stable regions, especially for retrograde orbits.

Contribution

It introduces models for forced eccentricity as a function of semimajor axis and demonstrates the impact of initial eccentricity states on planetary stability in the alpha Centauri system.

Findings

Retrograde orbits have larger stable regions when initial eccentricity is minimized.

Planets near their forced eccentricity are stable for up to a billion years.

Stability boundaries are more sensitive in multi-planet systems on prograde, circular orbits.

Abstract

We extend our study of the extent of the regions within the $\alpha$ Centauri AB star system where small planets are able to orbit for billion-year timescales (Quarles & Lissauer 2016, AJ 151, 111) to investigate the effects of minimizing the forced eccentricity of initial trajectories. We find that initially prograde, circumstellar orbits require a piecewise quadratic function to accurately approximate forced eccentricity as a function of semimajor axis, but retrograde orbits can be modeled using a linear function. Circumbinary orbits in the $\alpha$ Centauri AB system are less affected by the forced eccentricity. {Planets on circumstellar orbits that begin with eccentricity vectors near their forced values are generally stable, up to $\sim$$10^9$ yr, out to a larger semimajor axis than are planets beginning on circular orbits. The amount by which the region of stability expands is much larger for retrograde orbits than it is for prograde orbits. The location of the stability boundary for two planet systems on prograde, circular orbits is much more sensitive to the initial eccentricity state than it is for analogous single planet systems.