Constraints on Planet Nine's Orbit and Sky Position within a Framework of Mean Motion Resonances (1612.07774v1)

Abstract: A number of authors have proposed that the statistically significant orbital alignment of the most distant Kuiper Belt Objects (KBOs) is evidence of an as-yet undetected planet in the outer solar system, now referred to colloquially a "Planet Nine". Dynamical simulations by Batygin & Brown (2016) have provided constraints on the range of the planet's possible orbits and sky locations. We extend these investigations by exploring the suggestion of Malhotra et al. (2016) that Planet Nine is in small integer ratio mean-motion resonances (MMRs) with several of the most distant KBOs. We show that the observed KBO semi-major axes present a set of commensurabilities with an unseen planet at $\sim 654 \ \mathrm{AU}$ ($P \sim 16,725 \ \mathrm{yr}$) that has a greater than $98\%$ chance of stemming from a sequence of MMRs rather than from a random distribution. We describe and implement a Monte-Carlo optimization scheme that drives billion-year dynamical integrations of the outer solar system to pinpoint the orbital properties of perturbers that are capable of maintaining the KBOs' apsidal alignment. This optimization exercise suggests that the unseen planet is most consistently represented with mass, $m \sim 6-12 M_{\oplus}$, semi-major axis, $a \sim 654 \ \mathrm{AU}$, eccentricity, $e\sim0.45$, inclination, $i \sim 30^{\circ}$, argument of periastron, $\omega \sim 150^{\circ}$, longitude of ascending node, $\Omega \sim 50^{\circ}$, and mean anomaly, $M \sim 180^{\circ}$. A range of sky locations relative to this fiducial ephemeris are possible. We find that the region $30^{\circ}\, \lesssim \mathrm{RA} \lesssim 50^{\circ}$, $-20^{\circ}\, \lesssim \mathrm{Dec} \lesssim 20^{\circ}$ is promising.

• The paper demonstrates that mean-motion resonances can explain the clustering of distant KBOs, supporting a high-probability existence of Planet Nine.
• It employs numerical simulations and a Monte Carlo optimization to derive specific orbital parameters, including a ~654 AU semi-major axis and 6–12 Earth masses.
• The findings narrow Planet Nine's sky location to a targeted region between RA 30°–50° and Dec -20°–20°, guiding future observational strategies.

Examining Constraints on Planet Nine's Orbital Features Through Mean Motion Resonances

The paper by Millholland and Laughlin explores the enigmatic concept of "Planet Nine," a hypothetical celestial body hypothesized to exist in the outer solar system. The paper aims to place constraints on the potential orbit and sky position of this planet by adopting a framework that incorporates mean-motion resonances (MMRs) with Kuiper Belt Objects (KBOs).

The prospect of a ninth planet emerges from observed clustering in the orbits of distant KBOs, which cannot be fully explained by known solar system dynamics. The authors build on groundwork laid by previous research, particularly that of Batygin and Brown (2016), by exploring MMRs as plausible mechanisms responsible for this clustering. They hypothesize that Planet Nine is situated at approximately 654 AU, with evidence showing over a 98% probability that the KBOs' semi-major axes result from a sequence of MMRs rather than from a random distribution.

Millholland and Laughlin employ detailed numerical simulations, notably a Monte Carlo optimization scheme, to derive orbital properties that could support the apsidal alignment of the KBOs over billion-year timescales. The results suggest that Planet Nine is best characterized by a mass between 6 and 12 Earth masses ($M_\oplus$), a semi-major axis of approximately $a \sim 654$ AU, eccentricity $e \sim 0.45$, inclination $i \sim 30^{\circ}$, argument of periastron $\omega \sim 150^{\circ}$, longitude of ascending node $\Omega \sim 50^{\circ}$, and mean anomaly $M \sim 180^{\circ}$.

A crucial aspect of their analysis is the observation that the proposed orbit of Planet Nine may align with small-integer ratio mean-motion resonances with multiple detached KBOs, such as Sedna, which appears in a 3:2 resonance. These findings not only suggest a potential semi-major axis but also focus observations on particular sky locations, making the search for Planet Nine more practical.

The research provides theoretical implications by supporting the presence of additional massive planets beyond Neptune, as well as demonstrating the utility of dynamical methods in parsing the complex gravitational architecture of the solar system. The proposed MMR framework informs future observational strategies and iterative refinements of celestial models.

Practical implications relate to the astronomical search for Planet Nine. The suggested sky region, particularly between RA 30° and 50° and Dec -20° to 20°, can streamline observational campaigns. This localization aligns with constraints from other methodologies, such as those based on the Cassini spacecraft's gravitational influences, enhancing the confidence in these models.

The paper's constraints and findings contribute to a deeper understanding of MMRs, shedding light on dynamic processes in intensely sustained multi-body systems far from the Sun. While direct observational verification remains pending, the theoretical scaffolding presented provides a well-reasoned basis for ongoing and future searches for Planet Nine, drawing a step closer to either confirming its existence or prompting the need for alternative explanations for KBO alignments.

The paper invites further examinations and methodologies that could harness the resonant dynamics more exhaustively, seeking firmer constraints that guide empirical astronomical observations. The research posits that a targeted search can significantly narrow the parameters further, meritoriously advancing the quest for understanding the outermost realms of our solar system.