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

TL;DR

This study calculates the likelihood of a proposed Planet Nine being ejected or captured due to stellar interactions, using extensive simulations to assess its stability and origin within the Solar System over billions of years.

Contribution

It provides the first detailed cross section calculations for various interaction outcomes of Planet Nine with passing stars, considering different orbital scenarios and environments.

Findings

Planet Nine is most likely to be ejected from the Solar System.

Ejection probability exceeds 50% if the Sun remains in its birth cluster longer than 100 Myr.

Probability of capturing Planet Nine from another system is less than 5%.

Abstract

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 $a_9\approx400-1500$ 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 $m_9=10M_{earth}$. Removing Planet Nine from the Solar System is the most likely outcome. Specifically, we obtain ejection cross sections $\sigma_{int}\sim5\times10^6$ AU$^2$ ($5\times10^4$ AU$^2$) 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 $\Delta{t} \gtrsim 100$ Myr. The probability of ejecting Planet Nine due to passing field stars is $\lesssim 3\%$ over the age of the Sun. Probabilities for producing the inferred Planet Nine orbit are low $(\lesssim 5\%)$.