Interaction Cross Sections and Survival Rates for Proposed Solar System Member Planet Nine (1602.08496v2)

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 $(\lesssim 5\%)$.

• The paper quantifies Planet Nine’s dynamical evolution using Monte Carlo simulations, revealing a high ejection cross section (~5×10^6 AU²) in stellar clusters.
• It demonstrates that capture probabilities from other systems or as rogue planets are under 1%, indicating these scenarios are unlikely.
• Scattering from an inner orbit yields a modest success rate (~25% for a 600 AU initial orbit), challenging traditional formation models.

An Analysis of Interaction Cross Sections and Survival Probabilities for the Hypothetical Planet Nine

The paper "Interaction Cross Sections and Survival Rates for Proposed Solar System Member Planet Nine" by Gongjie Li and Fred C. Adams explores the dynamical fate and the potential origin scenarios for Planet Nine—a hypothetical yet intriguing member of our Solar System. The motivation arises from anomalies in the trajectories of Kuiper Belt objects, which suggest the gravitational influence of an unseen, Neptune-mass planet on a highly eccentric orbit.

Key Results and Analysis

The paper primarily investigates four types of orbit-altering events that Planet Nine could experience due to gravitational perturbations from passing stars:

1. Scattering from a smaller initial orbit to its proposed orbit.
2. Ejection from the Solar System.
3. Capture from another star system.
4. Capture as a free-floating planet.

To simulate these interactions, the authors employ a vast ensemble of numerical simulations supported by Monte Carlo methods, examining a wide parameter space of initial orbital conditions and environmental interactions.

Ejection and Capture

The research finds that Planet Nine's susceptibility to ejection by stellar interactions is significant, especially within a stellar birth cluster environment compared to the field star environment of the Solar neighborhood. The ejection cross section is found to be large, approximately $5 \times 10^6$ AU$^2$ in a cluster environment, suggesting a considerable likelihood of ejection if the Sun remains in its birth cluster for longer than about 100 million years. In contrast, the likelihood of ejection in the current Solar neighborhood is less than 3% over the life of the Sun.

The probability of capturing Planet Nine from another stellar system or as a rogue planet is relatively low, under 1%. These results emphasize the challenge in explaining the current orbit of Planet Nine through capture scenarios, given the improbability dictated by the calculated interaction cross sections.

Formation by Scattering

Achieving the currently hypothesized orbit of Planet Nine via dynamical scattering from an initial orbit within the Solar System is also deemed unlikely. The paper's results imply that such formation events have a modest probability unless Planet Nine's initial semi-major axis was quite large ($\sim 400-800$ AU). Even in these optimal conditions, the success probability remains relatively low (around 25% for $a_0 = 600$ AU), highlighting the difficulty of the formation through traditional in-situ or scattering models.

Implications and Future Considerations

The findings present a significant challenge to prevailing models of Planet Nine's origin and stability. While capturing a planet from another star or as a rogue planet seems plausible, the low probability of these events occurring naturally is a hurdle. Consequently, these results necessitate further exploration into the dynamical history and formation mechanisms within planetary systems.

Future work may explore the detailed parameter space of interactions between small, close-in orbits and the massive external perturbers that might provide alternative clues for forming or ejecting such planetary bodies. It also raises questions about the potential for extended dynamical effects over secular time scales, perhaps involving interactions with the known Solar System giants, which have not been fully resolved within the scope of this current work.

Overall, the research enriches our understanding of the dynamical processes contributing to planetary system architecture and provides a foundation for subsequent investigations into the enigmatic Planet Nine.