Interaction Cross Sections and Survival Rates for Proposed Solar System Member Planet Nine

Motivated by the report of a possible new planetary member of the Solar System, this work calculates cross sections for interactions between passing stars and this proposed Planet Nine. Evidence for the new planet is provided by the orbital alignment of Kuiper Belt objects, and other Solar System properties, which suggest a Neptune-mass object on an eccentric orbit with semimajor axis a9 ≈ 400− 1500 AU. With such a wide orbit, Planet Nine has a large interaction cross section, and is susceptible to disruption by passing stars. Using a large ensemble of numerical simulations (several million), and Monte Carlo sampling, we calculate the cross sections for different classes of orbit-altering events: [A] scattering the planet into its proposed orbit from a smaller orbit, [B] ejecting it from the Solar System from its current orbit, [C] capturing the planet from another system, and [D] capturing a free-floating planet. Results are presented for a range of orbital elements with planetary mass m9 = 10M⊕. Removing Planet Nine from the Solar System is the most likely outcome. Specifically, we obtain ejection cross sections σ = 4.2×10 AU (4.3×10 AU) for environments corresponding to the birth cluster (field). With these cross sections, Planet Nine is likely to be ejected if the Sun resides within its birth cluster longer than t>∼ 100 Myr. The probability of ejecting Planet Nine due to passing field stars is ∼ 10 − 50% over the age of the Sun. Probabilities for producing the inferred Planet Nine orbit are significantly lower (<∼ 5%). Subject headings: planets and satellites: dynamical evolution and stability — planet-star interactions ar X iv :1 60 2. 08 49 6v 1 [ as tr oph .E P] 2 6 Fe b 20 16