High-resolution resonant portraits of a single-planet white dwarf system

TL;DR

This study uses high-performance computing and semi-analytical methods to analyze how mean motion resonances influence asteroid stability during stellar evolution, revealing key resonances that can destabilize or stabilize asteroid orbits around white dwarfs.

Contribution

It introduces a combined computational and semi-analytical approach to quantify resonant stability and effects during stellar evolution, focusing on a single-planet system with asteroids.

Findings

Resonant instability can be predicted using main-sequence parameters.

Certain resonances efficiently destabilize or stabilize asteroid orbits.

Specific resonances like 4:1, 3:1, and 2:1 are key in white dwarf pollution.

Abstract

The dynamical excitation of asteroids due to mean motion resonant interactions with planets is enhanced when their parent star leaves the main sequence. However, numerical investigation of resonant outcomes within post-main-sequence simulations is computationally expensive, limiting the extent to which detailed resonant analyses have been performed. Here, we combine the use of a high-performance computer cluster and the general semianalytical libration width formulation of Gallardo et al. (2021) in order to quantify resonant stability, strength and variation instigated by stellar evolution for a single-planet system containing asteroids on both crossing and non-crossing orbits. We find that resonant instability can be accurately bound with only main-sequence values by computing a maximum libration width as a function of asteroid longitude of pericentre. We also quantify the relative efficiency of mean motion resonances of different orders to stabilize versus destabilize asteroid orbits during both the giant branch and white dwarf phases. The 4:1, 3:1 and 2:1 resonances represent efficient polluters of white dwarfs, and even when in the orbit-crossing regime, both the 4:3 and 3:2 resonances can retain small reservoirs of asteroids in stable orbits throughout giant branch and white dwarf evolution. This investigation represents a preliminary step in characterising how simplified extrasolar Kirkwood gap structures evolve beyond the main-sequence.