Title: 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.