Stable lifetime of compact, evenly spaced planetary systems with non-equal masses

Abstract

ABSTRACT Compact planetary systems with more than two planets can undergo orbital crossings from planet–planet perturbations. The time for which the system remains stable without orbital crossings has an exponential dependence on the initial orbital separations in units of mutual Hill radii. However, when a multiplanet system has period ratios near mean-motion resonances, its stability time differs from the time determined by planet separation. This difference can be up to an order of magnitude when systems are set-up with chains of equal period ratios. We use numerical simulations to describe the stability time relationship in non-resonant systems with equal separations but non-equal masses which breaks the chains of equal period ratios. We find a deviation of 30 per cent in the masses of Earth-mass planets that creates a large enough deviation in the period ratios where the average stability time of a given spacing can be predicted by the stability time relationship. The mass deviation where structure from equal period ratios is erased increases with planet mass but does not depend on planet multiplicity. With a large enough mass deviation, the distribution of stability time at a given spacing is much wider than in equal-mass systems where the distribution narrows due to period commensurabilities. We find the stability time distribution is heteroscedastic with spacing – the deviation in stability time for a given spacing increases with said spacing.