Stability of a cluster-disrupted mean-motion resonance (chain) in HR 8799 and PDS 70

TL;DR

This study investigates the stability of mean-motion resonances in the HR 8799 and PDS 70 planetary systems under external perturbations, finding that resonance enhances long-term stability and is likely preserved from formation.

Contribution

It demonstrates through simulations that mean-motion resonance significantly increases planetary system stability and suggests these systems were likely born in resonance.

Findings

Resonant systems are more stable over hundreds of thousands of years.

Non-resonant systems dissolve within about 0.3 to 1.3 million years.

Resonance preservation is probable from formation, enhancing system longevity.

Abstract

HR~8799 is a planetary system with four planets potentially in a mean-motion resonance chain. It is unclear from the observations if they are in mean-motion resonance. Similarly, PDS~70 has two observed planets also potentially in mean-motion resonance. We simulate HR~8799 and PDS~70 under external perturbations to study their responds if in resonance or mean-motion resonance. We integrate the equations of motion for HR~8799 and PDS~70 starting with either in resonance or in mean-motion resonance and study their in isolation and in a star cluster. In the star cluster, we take the effects of passing stars into account. The dynamics of the star cluster is resolved using the Lonely Planets module in AMUSE. HR~8799 and PDS~70 in mean-motion resonance are stable, whereas in non-resonance they dissolve in $0.303\pm0.042$Myr and $1.26\pm0.25$Myr, respectively. In a cluster, the non-resonant HR~8799 is slightly more stable than in isolation, but still dissolves in $0.300\pm0.043$Myr, whereas the resonant planetary system remains stable for at least $0.71$Myr. In contrast, a non-resonant PDS~70 system is approximately equally stable in a cluster compared to isolation, and dissolves in $1.03\pm0.20$Myr, whereas the resonant PDS~70 system remains stable for at least $0.83$Myr. Considering the more stable solutions of mean-motion resonance for HR~8799, we argue that the planetary system was born in mean-motion resonance and that the mean-motion resonance was preserved. If HR~8799 was not born in resonance, the probability that it survived until the present day is negligible. Similarly, we argue that PDS~70 was probably born in mean-motion resonance and that its state was preserved. We also find that it is almost possible for planetary systems with a broken mean-motion resonance chain to survive longer in a perturbing cluster environment compared to isolation.