Finding Exoplanets by Assessing the Dynamical Packing of Kepler Multi-Candidate Systems
Barnes’ and Raymond’s Packed Planetary System (PPS) hypothesis postulates that planetary formation is efficient and creates dynamically packed planetary systems that cannot contain additional planets. Here we look for unpacked spaces in Kepler multi-candidate systems that should, according to a PPS corollary, contain planets. In doing so, we create a “roadmap” to potentially find as-of-yet unidentified planets and test the validity of PPS using observation-based data. Gladman and Chambers proposed that a system’s dynamical packedness can be quantified using the dynamical spacing ∆, the number of mutual Hill radii between adjacent planets (a “planet pair”). Using previously proposed values for minimum ∆ required for planet pair orbital stability, we determine whether planet pairs in Kepler multi-candidate systems could host an intermediate body (an “unpacked pair”). For each Kepler unpacked pair, we calculate the maximum mass of an intermediate body that the pair could host while remaining in stable orbits (“mass capacity”) and the semimajor axis at which this mass could be hosted. Next, we determine the probable masses of the unpacked pairs’ potential intermediate planets. Packed planet triplets were surveyed in Kepler multi-candidate systems to determine how much mass capacity each middle planet uses. Ultimately, the predicted mass and semimajor axis for a potential intermediate planet could facilitate its detection by characterizing its expected transit and radial velocity signals. Such observation-based evidence of whether or not these intermediate planets exist also could support or dispute PPS.