http://iopscience.iop.org/article/10.3847/0004-6256/151/2/22/pdf
Recent analyses have shown that distant orbits within the scattered disk population of the Kuiper Belt exhibit an
unexpected clustering in their respective arguments of perihelion. While several hypotheses have been put forward
to explain this alignment, to date, a theoretical model that can successfully account for the observations remains
elusive. In this work we show that the orbits of distant Kuiper Belt objects (KBOs) cluster not only in argument of
perihelion, but also in physical space. We demonstrate that the perihelion positions and orbital planes of the objects
are tightly confined and that such a clustering has only a probability of 0.007% to be due to chance, thus requiring a
dynamical origin. We find that the observed orbital alignment can be maintained by a distant eccentric planet with
mass 10 m⊕ whose orbit lies in approximately the same plane as those of the distant KBOs, but whose perihelion
is 180° away from the perihelia of the minor bodies. In addition to accounting for the observed orbital alignment,
the existence of such a planet naturally explains the presence of high-perihelion Sedna-like objects, as well as the
known collection of high semimajor axis objects with inclinations between 60° and 150° whose origin was
previously unclear. Continued analysis of both distant and highly inclined outer solar system objects provides the
opportunity for testing our hypothesis as well as further constraining the orbital elements and mass of the distant
planet.
Key words: Kuiper Belt: general – planets and satellites: dynamical evolution and stability
1. INTRODUCTION
The recent discovery of 2012VP113, a Sedna-like body and
a potential additional member of the inner Oort cloud,
prompted Trujillo & Sheppard (2014) to note that a set of
Kuiper Belt objects (KBOs) in the distant solar system exhibits
unexplained clustering in orbital elements. Specifically, objects
with a perihelion distance larger than the orbit of Neptune and
semimajor axis greater than 150 AU—including 2012VP113
and Sedna—have arguments of perihelia, ω, clustered approximately
around zero. A value of ω = 0 requires that the object’s
perihelion lies precisely at the ecliptic, and during eclipticcrossing
the object moves from south to north (i.e., intersects
the ascending node). While observational bias does preferentially
select objects with perihelia (where they are closest and
brightest) at the heavily observed ecliptic, no possible bias
could select only for objects moving from south to north.
Recent simulations (de la Fuente Marcos & de la Fuente
Marcos 2014) confirmed this lack of bias in the observational
data. The clustering in ω therefore appears to be real.
Orbital grouping in ω is surprising because gravitational
torques exerted by the giant planets are expected to randomize
this parameter over the multi-Gyr age of the solar system. In
other words, the values of ω will not stay clustered unless some
dynamical mechanism is currently forcing the alignment. To
date, two explanations have been proposed to explain the data.
Trujillo & Sheppard (2014) suggest that an external
perturbing body could allow ω to librate about zero via the
Kozai mechanism.
1 As an example, they demonstrate that a
five-Earth-mass body on a circular orbit at 210 AU can drive
such libration in the orbit of 2012VP113. However, de la
Fuente Marcos & de la Fuente Marcos (2014) note that the
existence of librating trajectories around ω = 0 requires the
ratio of the object to perturber semimajor axis to be nearly
unity. This means that trapping all of the distant objects within
the known range of semimajor axes into Kozai resonances
likely requires multiple planets, finely tuned to explain the
particular data set.
Further problems may potentially arise with the Kozai
hypothesis. Trujillo & Sheppard (2014) point out that the Kozai
mechanism allows libration about both ω = 0 as well as
ω = 180, and the lack of ω ∼ 180 objects suggests that some
additional process originally caused the objects to obtain
ω ∼ 0. To this end, they invoke a strong stellar encounter to
generate the desired configuration. Recent work (Jílková
et al. 2015) shows how such an encounter could, in principle,
lead to initial conditions that would be compatible with this
narrative. Perhaps a greater difficulty lies in that the dynamical
effects of such a massive perturber might have already been
visible in the inner solar system. Iorio (2014) analyzed the
effects of a distant perturber on the precession of the apsidal
lines of the inner planets and suggests that, particularly for lowinclination
perturbers, objects more massive than the Earth with
a ∼ 200–300 AU are ruled out from the data (see also
Iorio 2012).
As an alternative explanation, Madigan & McCourt (2015)
have proposed that the observed properties of the distant
Kuiper Belt can be attributed to a so-called inclination
instability. Within the framework of this model, an initially
axisymmetric disk of eccentric planetesimals is reconfigured
into a cone-shaped structure, such that the orbits share an
approximately common value of ω and become uniformly
distributed in the longitude of ascending node, Ω. While an
intriguing proposition, additional calculations are required to
assess how such a self-gravitational instability may proceed
when the (orbit-averaged) quadrupolar potential of the giant
planets, as well as the effects of scattering, are factored into the
simulations. Additionally, in order to operate on the appropriate
timescale, the inclination instability requires 1–10 Earth masses
The Astronomical Journal, 151:22 (12pp), 2016 February doi:10.3847/0004-6256/151/2/22
© 2016. The American Astronomical Society. All rights reserved.
1 Note that the invoked variant of the Kozai mechanism has a different phasespace
structure from the Kozai mechanism typically discussed within the
context of the asteroid belt (e.g., Thomas & Morbidelli 1996).
1
