The stability of tightly-packed, evenly-spaced systems of Earth-mass planets orbiting a Sun-like star

Abstract

Many of the multi-planet systems discovered to date have been notable for their compactness, with neighbouring planets closer together than any in the Solar System. Interestingly, planet-hosting stars have a wide range of ages, suggesting that such compact systems can survive for extended periods of time. We have used numerical simulations to investigate how quickly systems go unstable in relation to the spacing between planets, focusing on hypothetical systems of Earth-mass planets on evenly-spaced orbits (in mutual Hill radii). In general, the further apart the planets are initially, the longer it takes for a pair of planets to undergo a close encounter. We recover the results of previous studies, showing a linear trend in the initial planet spacing between 3 and 8 mutual Hill radii and the logarithm of the stability time. Investigating thousands of simulations with spacings up to 13 mutual Hill radii reveals distinct modulations superimposed on this relationship in the vicinity of first and second-order mean motion resonances of adjacent and next-adjacent planets. We discuss the impact of this structure and the implications on the stability of compact multi-planet systems. Applying the outcomes of our simulations, we show that isolated systems of up to five Earth-mass planets can fit in the habitable zone of a Sun-like star without close encounters for at least $10^9$ orbits.

arXiv comment31 pages, 5 figures. Updates to figures and table 2

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