Constraints on Planet Nine’s Orbit and Sky Position within a Framework of Mean-motion Resonances

Abstract

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 as “Planet Nine.” Dynamical simulations by Batygin & Brown 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. 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 semimajor axes present a set of commensurabilities with an unseen planet at ∼654 au (P ∼ 16,725 years) 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 ∼ 6–12 M ⊕, semimajor axis, a ∼ 654 au, eccentricity, e ∼ 0.45, inclination, i ∼ 30°, argument of periastron, ω ∼ 150°, longitude of ascending node, Ω ∼ 50°, and mean anomaly, M ∼ 180°. A range of sky locations relative to this fiducial ephemeris are possible. We find that the region 30° ≲ R.A. ≲ 50°, −20° ≲ decl. ≲ 20° is promising.