Mean plane of the Kuiper belt beyond 50 AU in the presence of Planet 9

¹ School of Astronomy and Space Science & Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University, 163 Xianlin Road, Nanjing 210023, PR China
e-mail: ljian@nju.edu.cn
² Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA
e-mail: xia@math.northwestern.edu

Received: 14 February 2020
Accepted: 7 April 2020

Abstract

Context. A recent observational census of Kuiper belt objects (KBOs) has unveiled anomalous orbital structures. This has led to the hypothesis that an additional ∼5 − 10 m_⊕ planet exists. This planet, known as Planet 9, occupies an eccentric and inclined orbit at hundreds of astronomical units. However, the KBOs under consideration have the largest known semimajor axes at a >  250 AU; thus they are very difficult to detect.

Aims. In the context of the proposed Planet 9, we aim to measure the mean plane of the Kuiper belt at a >  50 AU. In a comparison of the expected and observed mean planes, some constraints would be put on the mass and orbit of this undiscovered planet.

Methods. We adopted and developed the theoretical approach of Volk & Malhotra (2017, AJ, 154, 62) to the relative angle δ between the expected mean plane of the Kuiper belt and the invariable plane determined by the eight known planets. Numerical simulations were constructed to validate our theoretical approach. Then similar to Volk & Malhotra (2017, AJ, 154, 62), we derived the angle δ for the real observed KBOs with 100 <  a <  200 AU, and the measurement uncertainties were also estimated. Finally, for comparison, maps of the theoretically expected δ were created for different combinations of possible Planet 9 parameters.

Results. The expected mean plane of the Kuiper belt nearly coincides with the said invariable plane interior to a = 90 AU. But these two planes deviate noticeably from each other at a >  100 AU owing to the presence of Planet 9 because the relative angle δ could be as large as ∼10°. Using the 1σ upper limit of δ <  5° deduced from real KBO samples as a constraint, we present the most probable parameters of Planet 9: for mass m₉ = 10 m_⊕, orbits with inclinations i₉ = 30°, 20°, and 15° should have semimajor axes a₉ >  530 AU, 450 AU, and 400 AU, respectively; for m₉ = 5 m_⊕, the orbit is i₉ = 30° and a₉ >  440 AU, or i₉ <  20° and a₉ >  400 AU. In this work, the minimum a₉ increases with the eccentricity e₉ (∈[0.2, 0.6]) but not significantly.