Exploring the Origin of Metastability in Multi-Planet Systems Through Angular Momentum Deficit Accumulation

Numerical studies have shown that multi-planet systems on initially nearly circular, co-planar tend to auto-excite dynamically, eventually leading to systemic instability. The timescale of this instability grows exponentially with mean planet spacing and may not be reached for billions of orbits. Various competing explanations have been proposed to explain the origins of this eventual instability, and it is not known whether all multi-planet systems are metastable and will eventually destabilize or a critical spacing exists beyond which the system is expected to be perpetually stable. We present numerical simulations testing prior hypotheses for the pathway to instability: we examine the challenges faced by the two-body and three-body MMR overlap models in accurately predicting encounter times as the number of planets in a system increases. We find that although two-body MMR overlap theory traditionally favors equal spacing to minimize the optical depth of MMRs, systems with a more significant number of planets and varied planetary masses tend to destabilize more rapidly under such conditions, compared with an unequal spacing regime where planets with higher angular momentum are packed more tightly. Our results suggest that global transport of AMD facilitated by secular interactions may play a key role. We present a novel mode diffusion theory to illustrate how mild and bounded aperiodicity in planet semimajor axes can cause planet systems to accumulate global AMD. If this theory is correct, it suggests that all planet systems are only metastable but have a long instability time dispersion.