65 Transit-timing variation planets properties

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.