Instability mechanisms for the Uranus-Neptune Belt

We have implemented a highly-optimised integrator (called GLISSE) on GPU hardware that integrates huge numbers of test particle orbits in the the gravitational field caused by a set of massive planets, terminating particles upon their first close approach to a planet. GLISSE (GPU Long-term Integrator for Solar System Evolution) can easily integrate tens or even hundreds of thousands of particles for hundreds of millions of orbits and is well adapted to exploring the multi-dimensional nature of stable phase spaces (where statistics is thus very important). In this talk I illustrate two initial applications of GLISSE, in which our benchmarks showed factors of 100 to 300 speedup compared to using a CPU alone.

In the first application, we map the stability boundaries of the known small stable band between Uranus and Neptune near 26 au from Gladman and Duncan 1990, and Holman 1997. With the enormously improved statistics, we are able to delineate the dynamical details of very sharp boundaries and identify the mechanisms which cause them. We confirm that this region would be able to harbour leftover planetesimals if any had been present at the end of giant planet formation.

In the second application, we explore the 4 Gyr stability of the transneptunian 5:2 and 3:1 resonances. Assuming a “filled phase space” initial model, we map the resonance boundaries and show that long-term evolution removes almost all the Neptune crossing population, despite such large-e librators being stable initially.