Three-body Mean Motion Resonance Chains as a Delivery Mechanism for White Dwarf Pollution

In this work, we used numerical integration of the four-body problem to study three-body resonance chains (two planets and an asteroid in the innermost orbit) as a possible mechanism for white dwarf pollution. Two three-body resonance chains were selected for study: the 6:3:2 and the 4:2:1. Asteroids in both a dynamically colder initial orbit in the 6:3:2 resonance and hotter initial orbits in both resonances were studied. An asteroid had up to a 1.08% chance of being delivered to the stellar Roche limit of the white dwarf. This probability was strongly linearly correlated with the mass of the inner planet but was not correlated with the mass of the outer planet for both colder and hotter orbits. Average dynamical lifetimes ranged from 23 to 1137 kyr for the dynamically colder orbit and from 12.9 to 89.2 kyr and 10.8 to 793.4 kyr for the dynamically hotter orbits in the 6:3:2 and 4:2:1 resonances, respectively. Average dynamical lifetime was exponentially anticorrelated with the outer planet mass and usually with the inner planet mass except in one case. The hotter 4:2:1 resonance delivered 1.1 times more asteroids to the stellar Roche limit than the hotter 6:3:2 resonance. The hotter 6:3:2 resonance delivered 1.2 times more asteroids to the stellar Roche limit than the colder 6:3:2 resonance. A typical accretion rate for a white dwarf star of 10 8 g s −1 could be explained by the accretion of an equivalent mass of one of our simulated asteroids every 13.8 Myr.