The Planet Nine Hypothesis (Part 1)

 

July 29, 2021

Constantin Batygin,¹ Fred C. Adams,^2,3 Michael E. Brown,¹ and Juliette C. Becker³¹Division of Geological and Planetary Sciences California Institute of Technology, Pasadena, CA 91125, USA

²Physics Department, University of Michigan, Ann Arbor, MI 48109, USA

³Astronomy Department, University of Michigan, Ann Arbor, MI 48109, USA

 Abstract

Over the course of the past two decades, observational surveys have unveiled the intri- cate orbital structure of the Kuiper Belt, a field of icy bodies orbiting the Sun beyond Neptune. In addition to a host of readily-predictable orbital behavior, the emerging census of trans-Neptunian objects displays dynamical phenomena that cannot be ac- counted for by interactions with the known eight-planet solar system alone. Specifi- cally, explanations for the observed physical clustering of orbits with semi-major axes in excess of 250 AU, the detachment of perihelia of select Kuiper belt objects from Neptune, as well as the dynamical origin of highly inclined/retrograde long-period or- bits remain elusive within the context of the classical view of the solar system. This

newly outlined dynamical architecture of the distant solar system points to the exis- tence of a new planet with mass of m₉ 5 10 M_⊕, residing on a moderately inclined orbit (i₉ 15 25 deg) with semi-major axis a₉ 400 800 AU and eccentricity between e₉ 0.2 0.5. This paper reviews the observational motivation, dynamical constraints, and prospects for detection of this proposed object known as Planet Nine.

Introduction

Understanding the solar system’s large-scale architecture embodies one of human- ity’s oldest pursuits and ranks among the grand challenges of natural science. Histor- ically, the first attempts to astronomically map the imperceptible structure of the solar system trace back to Galileo himself, and his adoption of the telescope as a scientific instrument some four centuries ago. In terms of sheer numbers, however, the quest to unveil new planets in the solar system has been strikingly inefficient: only two large objects that were not already known to ancient civilizations – Uranus and Neptune – have been discovered to date, with no significant updates to the solar system’s planetary catalogue since 1930.

While countless astronomical surveys aimed at discovering new solar system plan- ets have consistently resulted in non-detections, the solar system’s vast collection of minor bodies has slowly come into sharper focus. Particularly, the past quarter-century witnessed the discovery and characterization of a diverse collection of small icy objects residing in the outer reaches of our solar system, extending from the immediate vicinity

Preprint submitted to Physics Reports February 27, 2019

of Neptune’s orbit to far beyond the heliosphere¹ (Jewitt & Luu, 1993). Intriguingly, rather than the planets themselves, it is this population of scattered debris that holds the key to further illuminating the solar system’s intricate dynamical structure and to unraveling its dramatic evolutionary history.

The vast majority of trans-Neptunian small bodies, collectively known as the Kuiper belt, reside on orbits that are consistent with known dynamical properties of the so- lar system. The most extreme members of this population, however, trace out highly elongated orbits with periods measured in millennia, and display a number of curious orbital patterns. These anomalies include the striking alignment in the orientations of eccentric orbits in physical space, a common tilt of the orbital planes, perihelion dis- tances that stretch far beyond the gravitational reach of Neptune, as well as excursions of trans-Neptunian objects into highly inclined, and even retrograde orbits. All of these otherwise mysterious orbital features can be readily understood if the solar system con- tains an additional – as yet undetected – large planet, residing hundreds of astronomical units away from the sun.

The existence of this particular solar system object, colloquially known as Planet Nine, has only recently been proposed (Batygin and Brown, 2016a). Nonetheless, the discoveries in the outer solar system that ultimately led to the Planet Nine Hypothesis (Brown et al. 2004; Trujillo and Sheppard 2014 and the references therein) represent a veritable revolution in the scientific understanding of our home planetary system. This review will explore these developments, and will provide a status update on the Planet Nine hypothesis. Before delving into specifics, however, we note that despite being characterized by a unique combination of observational evidence and dynamical mechanisms, the Planet Nine hypothesis is by no means the first inference of a new solar system member that is based upon anomalous orbital behavior of known objects. Moreover, it is important to recognize that this general class of scientific proposals has a long and uneven history, with results varying from the stunning success of Neptune (Le Verrier, 1846a; Galle, 1846; Adams, 1846) to the regrettable failure of Nemesis (Davis et al., 1984). Accordingly, it is instructive to begin this manuscript with a brief historical review of past claims.

The Discovery of Neptune

The mathematical determination of the existence of Neptune represents the only successful example of a new planetary discovery motivated by dynamical evidence within the solar system, and epitomizes one of the most sensational stories in the his- tory of astronomy (see Krajnovic´ 2016 for a recent review). The saga begins with the official discovery of the planet Uranus (then called Georgium Sidus) in 1781 by William Herschel. Although Herschel was the first to record the proper motion of the object and present his results to the Royal Astronomical Society (for further details, see the historical accounts of Alexander 1965; Miner 1998), numerous recorded obser- vations of Uranus already existed, which mistook the planet for a background star.

¹Data collected by the Voyager 1 and 2 spacecraft suggest that the heliosphere nominally extends to a heliocentric distance of approximately 120 AU.

Figure 1: Predicted orbit of Neptune. This diagram shows the outer solar system viewed from the north ecliptic pole, including the orbits of Uranus (gray) and Neptune (black), as well as the predicted Neptunian orbits (purple) from Le Verrier (1846a) and Adams (1846). Note that although the predicted physical location of Neptune was in close agreement with the actual location of Neptune in 1846, the derived orbits are considerably wider and more eccentric than Neptune’s true orbit.

Over the next six decades, astronomers continued to monitor the motion of Uranus along its 84 year orbit and computed ephemerides of its position over time based on the then-known properties of the giant planets (e.g., Bouvard 1824). The calculations and the observations were not in perfect agreement, with thedifferences between the theoretical longitudes and the observed longitudes of the orbit growing by approxi- mately 2^jj per year (see page 150 of Adams 1846). These data led Le Verrier (1846a,b)

and then Adams (1846)² to propose an additional planet to account for the differences.

It is worth noting that the inferred physical and orbital properties of Le Verrier’s and Adams’ putative planet differ considerably from those of the real Neptune (Figure 1). Specifically, instead of the modern value a₈ ≈ 30 AU, the orbit of the proposed planet

had a semi-major axis (reported as the ‘assumed mean distance’) of ~ 36 AU (Le

Verrier, 1846b) and ~ 37 AU (Adams, 1846). Meanwhile, the estimated orbital eccen- tricity was e₈ ~ 0.11 (Le Verrier, 1846b) and e₈ ~ 0.12 (Adams, 1846), significantly larger than the modern value of e₈ ≈ 0.008. Finally, the mass estimate for the new planet was reported as m₈ ~ 36 M_⊕ (Le Verrier, 1846b) and m₈ ~ 50 M_⊕ (Adams, 1846), two to three times larger than Neptune’s actual mass of m₈ 17 M_⊕. The pre- dicted properties of Neptune were thus somewhat larger in both mass and semi-major

²Although Le Verrier’s calculations famously predate Galle & d’Arrest’s astronomical detection of Nep- tune, Adams’s orbital predictions were only published after Neptune’s location was already known.axis than the observed body.

We note that resolution of the irregularities found in the orbit of Uranus required rather extensive calculations (Le Verrier, 1846a; Adams, 1846). The analysis had to include perturbations of all the previously known planets, the error budget for the es- timated orbital elements of Uranus, and the assumed orbital elements (and mass) of the proposed new planet (an overview of the difficulties is outlined in Lyttleton 1958). The discrepancies between Le Verrier’s and Adams’ theoretical expectations and the observed properties of Neptune therefore constitutes a gold standard for dynamically motivated planetary predictions. Moreover, it is worth pointing out that the most sig- nificant quantity in perturbing the orbit of Uranus was the anomalous acceleration in the radial direction produced by the new body, m₈/r² – a ratio that was predicted with much higher accuracy than the individual values of mass and semi-major axis. As we discuss below, comparable degeneracies between mass and orbital parameters exist within the framework of the Planet Nine hypothesis as well.

1. Planet X and the Discovery of Pluto

Following Le Verrier’s triumphant mathematical discovery of Neptune, unexplained behavior in the motions of objects in the solar system continued to inspire predictions of the existence, and sometimes locations of new planets beyond the boundaries of the known solar system. Some of the early trans-Neptunian planetary proposals include Jacques Babinet’s 1848 claim of a 12 M_⊕ planet beyond Neptune (Grosser, 1964),

David P. Todd’s 1877 speculation about a planet at 52 AU (Hoyt, 1976), Camille Flam-

marion’s inference of a planet at 48 AU (Flammarion, 1884), as well as the prediction of two planets at 100 and 300 AU by George Forbes, whose calculations were mo- tivated by an apparent grouping of orbital elements of long-period comets (Forbes, 1880). An expansive set of planetary hypotheses was later put forth by W. H. Picker- ing, who predicted seven different planets between 1909 and 1932, with masses rang-

ing from 0.045 M_⊕ to 20, 000 M_⊕ (see Hoyt 1976 for an excellent historical overview). Arguably, the most emblematic planetary prediction, however, can be attributed to Per-

cival Lowell, who championed the search for what he called “Planet X” and founded Lowell Observatory in Arizona in hopes of finding it.

The story of the search for Planet X is well documented in the literature (e.g., Levy 1991). Briefly: despite the addition of Neptune to the solar system’s ledger of planets, small apparent discrepancies in the orbits of the giant planets remained. With the ob- servations and analysis available at the time, the inferred orbital anomalies in the orbit of Uranus implied a planetary object with a mass of m_X 7 M_⊕, about half the mass

of Neptune. Lowell died suddenly in 1916, without having found the elusive planet.

Nevertheless, the search continued. The new director, Vesto Slipher (who used the ob- servatory to measure the recession velocities of galaxies; see Appendix A), handed off the search for Planet X to Clyde Tombaugh. By 1930, Tombaugh had examined countless photographic plates containing millions of point sources for possible plane- tary motion and finally discovered a moving object (Tombaugh,1946, 1996). Because it was found in the approximate location on the sky where Planet X was envisioned to be, and because Planet X was the object of the original search, the newly found body was initially considered to be the long-sought-after Planet X (Slipher, 1930).

1

₁₀-1

₁₀-2

₁₀-3

1920 1940 1960 1980 2000 2020

Year

Figure 2: Estimated mass of Pluto as a function of time. The first (and largest) estimate is from the dynamical calculations that inpired the initial search. The subsequent estimates are based on observations (as labeled) and show a steady downward trend until relatively recently. The particularly steep decline of Pluto’s mass in 1978 is marked by the discovery of its largest moon, Charon.

Immediately there was a problem. An object with physical size comparable to Nep- tune should have been resolved with the observational facilities of the era, but the new planet appeared point-like. It was also dim, coming in about six times fainter than the estimates. It soon became clear that the newly found member of the solar system was not the Planet X, as it was not massive enough to account for the perceived perturba- tions in the orbit of Uranus. The new body was subsequently named Pluto, after the Greek god of the underworld³. In the end, the observed irregularities in Uranus’ and Neptune’s motion turned out to be spurious, and were fully resolved by a 0.5% revision of Neptune’s mass, following the Voyager 2 flyby (Standish, 1993).

Figure 2 shows the estimated mass of Pluto as a function of time. The initial es- timate (m_X 7 M_⊕) is the mass required to account for the perceived perturbations of the giant planet orbits (Tombaugh, 1946). The first observational estimate for the mass of Pluto (Nicholson and Mayall, 1931) was already down toM_LP 1 M_⊕, and subsequent observations led to steadily lower values as shown in the Figure. Note that

a precipitous drop in the mass estimate that came in 1978, with the discovery of the moon Charon and the first clean measurement of Pluto’s mass (Christy and Harring- ton, 1978). The current mass estimate is only M_LP 0.00218 M_⊕ (Buie et al., 2006), roughly 3200 times smaller than the original mass estimate that inspired the search. In spite of its diminutive size, Pluto was considered as the ninth planet of the solar system

until 2006, when it was demoted to the status of a dwarf planet (IAU Resolution B5, 2006).

³As a bonus, the first two letters of the planet’s name were coincident with the initials of Percival Lowell, although W. H. Pickering was evidently under the impression that it stood for Pickering-Lowell (Hoyt, 1976).

1. The False Alarm of Vulcan

By the mid 19th century, observations of the planet Mercury became precise enough to detect variations in its orbital parameters, lending a handle on the gravitational per- turbations exerted by the terrestrial planets upon one-another. By making precise mea- surements of transits of Mercury across the Sun, 19th century astronomers thus realized that the orbit of Mercury was precessing forward at a rate that could not be fully ac- counted for by known bodies. This determination inspired Le Verrier (1843, 1859) to propose that an additional planet interior to Mercury is responsible for the extra perihe- lion precession necessary to fit the observations. This hypothetical new planet become known as Vulcan, the god of fire, volcanoes, and metal working in Roman mythology. In order to generate the anomalous (da/dt) = 43”/century perihelion advance of Mercury, the parameters of the unseen planet (m_v, a_v) would have been constrained by

(see section 3.1)_da

3 ^, G M_s 1

m_v a²

_da

^, G M_s G M_s 3

 where G is the gravitational constant and c is the speed of light. Coincidentally, the above expression is satisfied by a m_v 3 M_⊕ Super-Earth type planet with an orbital period of approximately 3 days, analogues of which are now known to be very com-

mon around sun-like stars (Borucki et al., 2010; Batalha et al., 2013). In the early 20th century, however, Einstein developed his theory of General Relativity, which self- consistently resolved the ancillary precession problem (yielding a rate of apsidal ad- vance given by the RHS of the above equation; Einstein 1916). This alleviated the need for intra-Mercurian planets within the solar system. Accordingly, unlike the case of Uranus (discussed in section 1.1), dynamical anomalies in the inner solar system paved the way to the discovery of fundamentally new physics rather than a planet.

1. The Nemesis Affair

The 1980s witnessed the proposal that the Sun was actually part of a binary star system. This time, the motivation for the proposed stellar companion stemmed from paleontology: approximately 65 Myr ago, a mass extinction event wiped out three quar- ters of the species then living on Earth. This cataclysm, which famously included the removal of (non-avian) dinosaurs from the biosphere, occurred at what is known as the Cretaceous-Tertiary (K-T) boundary. At the layer of rock corresponding to this geological age, sediments are observed to contain high levels of iridium, an element that is relatively rare in crustal rocks on Earth, but is much more plentiful in asteroids. The association of the iridium layer with the extinction boundary led to the hypothesis that the event was caused by a collision of a large ( 10 15 km) asteroid with Earth (Alvarez et al., 1980). The resulting impact would have catastrophic consequences on the climate, and would, in turn, explain the mass extinction event.

Although the K-T extinction event is often seen as being the most dramatic, it is far from unique: the geologic record unequivocally shows that the biosphere of Earth has experienced a series of mass extinction events. Moreover, although the data are sparse, with 12 events distributed over a time span of ~ 250 Myr, some analyses have

Figure 1: Predicted orbit of Neptune. This diagram shows the outer solar system viewed from the north ecliptic pole, including the orbits of Uranus (gray) and Neptune (black), as well as the predicted Neptunian orbits (purple) from Le Verrier (1846a) and Adams (1846). Note that although the predicted physical location of Neptune was in close agreement with the actual location of Neptune in 1846, the derived orbits are considerably wider and more eccentric than Neptune’s true orbit.

Over the next six decades, astronomers continued to monitor the motion of Uranus along its 84 year orbit and computed ephemerides of its position over time based on the then-known properties of the giant planets (e.g., Bouvard 1824). The calculations and the observations were not in perfect agreement, with the