Abstract:

We developed a new analytical method to identify potential missed planets in multi-planet systems found via transit surveys such as those conducted by Kepler and TESS. Our method depends on quantifying a system’s dynamical packing in terms of the dynamical spacing Δ, the number of mutual Hill radii between adjacent planets (“planet pair”). The method determines if a planet pair within a multi-planet system is dynamically unpacked and thus capable of hosting an additional intermediate planet. If a planet pair is found to be unpacked, our method constrains the potential planet’s mass and location. Our method was tested using three well-characterized multi-body systems: the Galilean satellites, the solar system, and TRAPPIST-1. The analysis was run with three previously proposed values for minimum Δ required for planet pair orbital stability (Δ = 10, 12.3, and 21.7). The method was then applied to the Kepler primary mission multi-candidate systems, first via direct calculations and then via Monte Carlo (MC) analysis. Direct calculations show that as many as 560 planet pairs in Kepler multi-candidate systems could contain additional planets (Δ = 12.3). The MC analysis shows that 164 of these pairs have a probability ≥ 0.90 of being unpacked. Furthermore, according to calculated median mass efficiencies, 28.2% of these potential planets could be Earths and Sub-Earths. If these planets exist, the masses and semimajor axes predicted here could facilitate detection by characterizing expected detection signals. Ultimately, understanding the dynamical packing of multi-planet systems could help contribute to our understanding of their architectures.