How Close are Compact Multi-Planet Systems to the Stability Limit?

TL;DR

This study compares observed eccentricities of compact multi-planet systems with stability limits, finding that real systems are less eccentric than predicted by giant impact formation models, implying additional damping processes.

Contribution

The paper introduces a novel comparison between observed eccentricities and stability limits using machine learning, challenging the assumption that such systems are maximally packed.

Findings

Observed systems have eccentricities 2-10 times lower than stability limits.

Median observed eccentricity is about 4 times lower than giant impact predictions.

Additional eccentricity damping mechanisms are likely involved in system formation.

Abstract

Transit surveys have revealed a significant population of compact multi-planet systems, containing several sub-Neptune-mass planets on close-in, tightly-packed orbits. These systems are thought to have formed through a final phase of giant impacts, which would tend to leave systems close to the edge of stability. Here, we assess this hypothesis, comparing observed eccentricities in systems exhibiting transit-timing variations (TTVs), with the maximum eccentricities compatible with long-term stability. We use the machine-learning classifier SPOCK (Tamayo et al. 2020) to rapidly classify the stability of numerous initial configurations and hence determine these stability limits. While previous studies have argued that multi-planet systems are often maximally packed, in the sense that they could not host any additional planets, we find that the existing planets in these systems have measured eccentricities below the limits allowed by stability by a factor of 2--10. We compare these results against predictions from the giant impact theory of planet formation, derived from both $N$-body integrations and theoretical expectations that in the absence of dissipation, the orbits of such planets should be distributed uniformly throughout the phase space volume allowed by stability. We find that the observed systems have systematically lower eccentricities than this scenario predicts, with a median eccentricity about 4 times lower than predicted. These findings suggest that if such systems formed through giant impacts, then some dissipation must occur to damp their eccentricities. This may take place during formation, perhaps through interactions with the natal gas disk or a leftover population of planetesimals, or over longer timescales through the coupling of tidal and secular processes.