Predicting Missing Planets in Multiplanet System Populations via Analytical Assessments of Dynamical Packing

We present 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 D, 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. We apply our method to the Kepler primary mission multi-candidate systems, first via direct calculations and then via Monte Carlo (MC) analysis. The analysis was repeated with three proposed values from the literature for minimum Delta required for planet pair orbital stability (D = 10, 12.3, and 21.7). Direct calculations show that as many as 560 planet pairs in Kepler multi-candidate systems could contain additional planets (D = 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 calculated from packed Kepler systems, 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 and formation.