Very wide-orbit planets from dynamical instabilities during the stellar birth cluster phase

Gas giant planets have been detected on eccentric orbits several hundreds of astronomical units in size around other stars. The Sun itself has been proposed to host a wide-orbit planet of 5-10 Earth-masses (often called Planet Nine) that dynamically sculpts the orbits of distant Trans-Neptunian objects. Here we show that very wide-orbit planets are a natural byproduct of dynamical instabilities in planetary systems that happen while their host stars are still embedded within their natal clusters. On the pathway to ejection, a planet undergoes repeated gravitational scattering by other planets and its orbit becomes nearly parabolic. Once the scattered planet’s apoastron grows to several hundred au, perturbations by passing stars can lift its periastron distance and decouple it from the other planets, stranding it on a wide, eccentric orbit. Planets were ejected from the young Solar System during two epochs: the growth of Uranus and Neptune from a population of ~5 M_Earth planetary embryos, and the giant planet instability. If any of these events happened while the Sun was still embedded in its birth cluster, the likelihood that any given scattered planet was trapped on a wide eccentric orbit around the Sun is 5-10%, depending on the star cluster properties; put together, the probability may be as high as 40%. Among gas giant exoplanets, which undergo near-ubiquitous dynamical instabilities, the trapping efficiency is ~5%. For ice giant systems and circumbinary gas giants, the efficiency is significantly lower. Our results imply the existence of a vast population of planets on wide, eccentric orbits with an occurrence rate of at least ~10^-3 per star.