In the outer solar system there is a gap in perihelion between the Extreme Trans-Neptunian Objects (ETNOs; q>40, a>150) and the Inner Oort Cloud objects (IOCs; q>65, a>250). These two populations are among the most distant objects in the solar system and the apparent alignment of their eccentric orbits serves as one of the primary evidences for the existence of a hypothesized distant giant planet, often referred to as Planet 9 or Planet X.
Using a suite of observational simulations, we explore the relationship between the perihelion gap and the surrounding populations. First, we randomly draw particles from a range of orbital element distributions near the ETNOs and IOCs. Then, we apply observational limits to these synthetic particles to determine their detectability. We find that the gap is very unlikely to arise from a realistic single continuous distribution of objects and that a bimodal distribution is a better fit to the observed ETNO/IOC population by several orders of magnitude. This indicates that the perihelion gap is a separation between two distinct populations in the outer solar system, the ETNOs and the IOCs.
To examine the possibility of a connection between the perihelion gap and the hypothesized Planet X, we ran hundreds of dynamical simulations using the REBOUND mercurius integrator. For these simulations, we included the Sun, the giant planets, hundreds to thousands of test particles, and some parameter combination for Planet X. The test particles were initialized in a Kuiper belt-like distribution and we make the assumptions that these particles are acted on by Planet X after giant planet migration and in the absence of stellar encounters and galactic tides. The simulations were run for 4.5 Gyrs using a 0.2 yr timestep.
We find that in the absence of Planet X, the ETNOs, perihelion gap, and IOCs do not form through interactions with Neptune alone. However, when Planet X is present, as particles are scattered from the Kuiper belt to high eccentricity by Neptune, they are captured into secular resonances with Planet X and have their perihelia increased. Once these particles reach a perihelion of roughly 50 au (the outer boundary of the ETNO population), they quickly cross the perihelion gap and begin to oscillate in perihelion and eccentricity along lines of roughly constant semi-major axis over hundreds of kyrs. Hence, the gap serves as a transition region between the ETNOs and the IOCs (including more distant objects we have yet to observe). As these objects return to lower perihelia within this oscillation cycle, many of them reach minimum perihelia within the IOC region. This causes an increase in the number density of the IOCs compared to objects transitioning through the gap by roughly a factor of 5. Thus, we predict that objects will be discovered within the transitory perihelion gap, but that they will be only about 20% as numerous as the IOCs.