Evolution of Planetary Systems with Time Dependent Stellar Mass Loss

TL;DR

This paper analyzes how planetary orbits evolve under time-dependent stellar mass loss, providing analytic models for bound/unbound outcomes and exploring chaos in multi-planet systems, enhancing understanding of planetary system dynamics during stellar evolution.

Contribution

It introduces analytic approximations for orbital evolution with variable mass loss rates and examines chaos in multi-planet systems, extending previous constant-rate studies.

Findings

Bound planets can remain so even as stellar mass approaches zero.

Lyapunov time decreases with increasing stellar mass loss rate.

Chaotic behavior is amplified by stellar mass loss, reducing predictability.

Abstract

Observations indicate that intermediate mass stars, binary stars, and stellar remnants often host planets; a complete explanation of these systems requires an understanding of how planetary orbits evolve as their central stars lose mass. Motivated by these dynamical systems, this paper generalizes in two directions previous studies of orbital evolution in planetary systems with stellar mass loss: [1] Many previous treatments focus on constant mass loss rates and much of this work is carried out numerically. Here we study a class of single planet systems where the stellar mass loss rate is time dependent. The mass loss rate can be increasing or decreasing, but the stellar mass always decreases monotonically. For this class of models, we develop analytic approximations to specify the final orbital elements for planets that remain bound after the epoch of mass loss, and find the conditions required for the planets to become unbound. We also show that for some mass loss functions, planets become unbound only in the asymptotic limit where the stellar mass vanishes. [2] We consider the chaotic evolution for two planet systems with stellar mass loss. Here we focus on a model consisting of analogs of Jupiter, Saturn, and the Sun. By monitoring the divergence of initially similar trajectories through time, we calculate the Lyapunov exponents of the system. This analog solar system is chaotic in the absence of mass loss with Lyapunov time in the range 5 - 10 Myr; we find that the Lyapunov time decreases with increasing stellar mass loss rate, with a nearly linear relationship between the two time scales. Taken together, the results of this paper help provide an explanation for a wide range of dynamical evolution that occurs in solar systems with stellar mass loss.