Simulations of two-planet systems through all phases of stellar evolution: implications for the instability boundary and white dwarf pollution

Exoplanets have been observed at many stages of their host star's life, including the main-sequence (MS), subgiant and red giant branch stages. Also, polluted white dwarfs (WDs) likely represent dynamically active systems at late times. Here, we perform three-body simulations which include realistic post-MS stellar mass-loss and span the entire lifetime of exosystems with two massive planets, from the endpoint of formation to several Gyr into the WD phase of the host star. We find that both MS and WD systems experience ejections and star-planet collisions (Lagrange instability) even if the planet-planet separation well-exceeds the analytical orbit-crossing (Hill instability) boundary. Consequently, MS-stable planets do not need to be closely packed to experience instability during the WD phase. This instability may pollute the WD directly through collisions, or, more likely, indirectly through increased scattering of smaller bodies such as asteroids or comets. Our simulations show that this instability occurs predominately between tens of Myr to a few Gyr of WD cooling.