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.

Stability of Compact Multi-Planet Systems: A Numerical Investigation

This paper presents a comprehensive study on the stability of densely packed, equally spaced systems of Earth-mass planets orbiting a Sun-like star, utilizing numerical simulations to explore the dynamics and longevity of these systems. The focus is on understanding how initial spacing affects the stability time, defined as the duration before a pair of planets experiences a close encounter.

The authors conducted extensive simulations, analyzing 17,500 five-planet systems under varied initial conditions. These systems were configured with circular, coplanar orbits and were evenly spaced in units of the mutual Hill radius. By systematically varying the initial interplanetary spacing between two and thirteen mutual Hill radii, the study reveals both a linear correlation that had been noted in past research and significant modulations superimposed on this trend.

Key findings recover previous results, where the logarithm of stability time increases linearly with the initial spacing in mutual Hill radii, particularly observable for spacings between 3 and 8 Hill radii. Beyond a spacing of approximately 8.4 Hill radii, there is a notable increase in stability time, suggesting that these systems have the potential to remain stable for billions of orbits. Yet, the study importantly highlights regular, strong variations in this stability time, associated with mean motion resonances (MMRs). The presence of first and second-order MMRs plays a crucial role in driving chaotic diffusion and impacting stability, evidenced by the sharp dips in survivability at nominal resonant period ratios.

The implications of these findings are profound for the study of exoplanet systems. Systems of five Earth-mass planets could be stable within the habitable zone of a Sun-like star for durations comparable to the star's main-sequence lifetime. This supports the possibility of detecting long-lived multi-planet systems in upcoming observational missions like TESS, which targets transiting exoplanets around F5-M5 type stars.

Future studies could aim to refine our understanding of the resonant mechanisms governing these dynamics. The influence of varied initial conditions, such as planet masses and eccentricities, could elucidate the extent to which these general patterns hold in more complex scenarios. Given the prevalence of compact systems in exoplanet surveys, understanding their stability characteristics is vital for improving models of planetary system formation and evolution.

In conclusion, the paper's results underscore the nuanced and intricate nature of tightly packed planetary systems, illustrating the delicate balance between gravitational interactions and orbital resonances. This study offers valuable insights into the dynamical stability of compact multi-planet systems, contributing to the broader discourse on planetary dynamics. It highlights potential pathways for future investigation, suggesting that with advanced computational techniques and observational tools, further elucidation of these systems' long-term behavior is attainable.