How Close are Compact Multiplanet Systems to the Stability Limit?

Transit surveys have revealed a significant population of compact multiplanet 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 versus the maximum eccentricities compatible with long-term stability. We use the machine-learning classifier SPOCK (Tamayo et al.) to rapidly classify the stability of numerous initial configurations and hence determine these stability limits. While previous studies have argued that multiplanet 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 four times lower than predicted. This suggests that, if these systems formed through giant impacts, then some dissipation must occur to damp their eccentricities. This may occur 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.