We investigated the dynamical stability of high-multiplicity Kepler and K2 planetary systems .
Our numerical simulations find instabilities in \sim 20 \% of the cases on a wide range of timescales ( up to 5 \times 10 ^ { 9 } orbits ) and over an unexpectedly wide range of initial dynamical spacings .
To identify the triggers of long-term instability in multi-planet systems , we investigated in detail the five-planet Kepler-102 system .
Despite having several near-resonant period ratios , we find that mean motion resonances are unlikely to directly cause instability for plausible planet masses in this system .
Instead , we find strong evidence that slow inward transfer of angular momentum deficit ( AMD ) via secular chaos excites the eccentricity of the innermost planet , Kepler-102 b , eventually leading to planet-planet collisions in \sim 80 \% of Kepler-102 simulations .
Kepler-102 b likely has a mass \gtrsim 0.1 M _ { \earth } , hence a bulk density exceeding about half Earth ’ s , in order to avoid dynamical instability .
To investigate the role of secular chaos in our wider set of simulations , we characterize each planetary system ’ s AMD evolution with a ‘ ‘ spectral fraction '' calculated from the power spectrum of short integrations ( \sim 5 \times 10 ^ { 6 } orbits ) .
We find that small spectral fractions ( \lesssim 0.01 ) are strongly associated with dynamical stability on long timescales ( 5 \times 10 ^ { 9 } orbits ) and that the median time to instability decreases with increasing spectral fraction .
Our results support the hypothesis that secular chaos is the driver of instabilities in many non-resonant multi-planet systems , and also demonstrate that the spectral analysis method is an efficient numerical tool to diagnose long term ( in ) stability of multi-planet systems from short simulations .