The planet nine hypothesis

Abstract

Over the course of the past two decades, observational surveys have unveiled the intricate 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 accounted for by interactions with the known eight-planet solar system alone. Specifically, explanations for the observed physical clustering of orbits with semi-major axes in excess of $\sim 250$ AU, the detachment of perihelia of select Kuiper belt objects from Neptune, as well as the dynamical origin of highly inclined/retrograde long-period orbits 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 existence of a new planet with mass of $m_9\sim 5\text{–}10M_{\oplus }$, residing on a moderately inclined orbit ($i_9\sim 15\text{–}25deg$) with semi-major axis $a_9\sim 400\text{–}800$ AU and eccentricity between $e_9\sim 0.2\text{–}0.5$. 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 humanity’s oldest pursuits and ranks among the grand challenges of natural science. Historically, 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 planets 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 of Neptune’s orbit to far beyond the heliosphere¹  (Jewitt and 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 solar 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 distances 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 contains 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, 1846b, 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 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 history of astronomy (see Krajnović 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 observations of Uranus already existed, which mistook the planet for a background star.

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 differences between the theoretical longitudes and the observed longitudes of the orbit growing by approximately $2^{\prime \prime }$ per year (see page 150 of Adams 1846). These data led Le Verrier, 1846a, Le Verrier, 1846b and then [2]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 (Fig. 1). Specifically, instead of the modern value $a_8\approx 30$ AU, the orbit of the proposed planet had a semi-major axis (reported as the ‘assumed mean distance’) of $\sim 36$ AU (Le Verrier, 1846a) and $\sim 37$ AU (Adams, 1846). Meanwhile, the estimated orbital eccentricity was $e_8\sim 0.11$ (Le Verrier, 1846a) and $e_8\sim 0.12$ (Adams, 1846), significantly larger than the modern value of $e_8\approx 0.008$. Finally, the mass estimate for the new planet was reported as $m_8\sim 36M_{\oplus }$ (Le Verrier, 1846a) and $m_8\sim 50M_{\oplus }$ (Adams, 1846), two to three times larger than Neptune’s actual mass of $m_8\approx 17M_{\oplus }$. The predicted properties of Neptune were thus somewhat larger in both mass and semi-major axis than the observed body.

We note that resolution of the irregularities found in the orbit of Uranus required rather extensive calculations (Le Verrier, 1846b, Adams, 1846). The analysis had to include perturbations of all the previously known planets, the error budget for the estimated 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 constitute a gold standard for dynamically motivated planetary predictions. Moreover, it is worth pointing out that the most significant quantity in perturbing the orbit of Uranus was the anomalous acceleration in the radial direction produced by the new body, $\mathcal{A}\propto m_8∕r_8^2$ — 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.

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 $\sim 12M_{\oplus }$ planet beyond Neptune (Grosser, 1964), David P. Todd’s 1877 speculation about a planet at $52$ AU (Hoyt, 1976), Camille Flammarion’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 motivated 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. Pickering, who predicted seven different planets between 1909 and 1932, with masses ranging from $0.045M_{\oplus }$ to $20,000M_{\oplus }$ (see Hoyt 1976 for an excellent historical overview). Arguably, the most emblematic planetary prediction, however, can be attributed to Percival 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 observations and analysis available at the time, the inferred orbital anomalies in the orbit of Uranus implied a planetary object with a mass of $m_X\sim 7M_{\oplus }$, 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 observatory 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 planetary motion and finally discovered a moving object (Tombaugh, 1946, Tombaugh, 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).

Immediately there was a problem. An object with physical size comparable to Neptune 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 perturbations in the orbit of Uranus. The new body was subsequently named Pluto, after the Greek god of the underworld.³ 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).

Fig. 2 shows the estimated mass of Pluto as a function of time. The initial estimate ($m_X\approx 7M_{\oplus }$) 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 to $M_{\mathrm{P}\mathrm{L}}$ $\approx 1M_{\oplus }$, and subsequent observations led to steadily lower values as shown in the Figure. Note that a precipitous drop in the mass estimate came in 1978, with the discovery of the moon Charon and the first clean measurement of Pluto’s mass (Christy and Harrington, 1978). The current mass estimate is only $M_{\mathrm{P}\mathrm{L}}$ $\approx 0.00218M_{\oplus }$ (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).

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 perturbations exerted by the terrestrial planets upon one-another. By making precise measurements 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 accounted for by known bodies. This determination inspired Le Verrier, 1843, Le Verrier, 1859 to propose that an additional planet interior to Mercury is responsible for the extra perihelion precession necessary to fit the observations. This hypothetical new planet became known as Vulcan, the god of fire, volcanoes, and metal working in Roman mythology.

In order to generate the anomalous $(d\varpi ∕dt)=43”$/century perihelion advance of Mercury, the parameters of the unseen planet ($m_{\mathrm{v}},a_{\mathrm{v}}$) would have been constrained by (see Section 3.1)

$${\left(\frac{d\varpi }{dt}\right)}_{\mathrm{v}}\approx \frac{3}{4}\sqrt{\frac{\mathcal{G}{M}_{\odot }}{a_1^3}}\frac{1}{{\left(1-e_1^2\right)}^2}\frac{m_{\mathrm{v}}{a}_{\mathrm{v}}^2}{M_{\odot }{a}_1^2}\iff {\left(\frac{d\varpi }{dt}\right)}_{\mathrm{gr}}=3\sqrt{\frac{\mathcal{G}{M}_{\odot }}{a_1^3}}\frac{\mathcal{G}{M}_{\odot }}{a_1{c}^2}\frac{3}{{\left(1-e_1^2\right)}^2},$$

where $\mathcal{G}$ is the gravitational constant and $c$ is the speed of light. Coincidentally, the above expression is satisfied by a $m_{\mathrm{v}}\sim 3M_{\oplus }$ Super-Earth type planet with an orbital period of approximately 3 days, analogues of which are now known to be very common 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 advance 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.

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 quarters 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 ($\sim 10\text{–}15$ 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 $\sim 250$ Myr, some analyses have suggested that these extinction events are periodic, and recur every $\sim 26$ Myr (Raup and Sepkoski, 1984). One way to achieve a periodic signal in the extinction events is for the Sun to have an eccentric stellar companion, which perturbs comets in the Oort cloud on the necessary time interval (Davis et al., 1984). The envisaged red/brown dwarf companion would therefore have an orbital period of about 26 Myr and hence a semi-major axis of $a_{\mathrm{nem}}\sim 88,000$  AU. This hypothetical body became known as Nemesis, named after the Greek goddess of retribution. Although the orbital stability of the proposed companion was inconclusively analyzed by Hills, 1984, Hut, 1984, Torbett and Smoluchowski, 1984, more recent work indicates that the probability of the ejection for Nemesis from the solar system by passing stars is of order unity over the age of the Sun (Li and Adams, 2016).

A number of searches for Nemesis have come up empty, starting with a University of California search (Perlmutter, 1986), and continuing with infrared surveys carried out by IRAS (Beichman, 1987) and 2MASS (Sykes et al., 2002). Moreover, the evidence for periodic extinction events itself is tenuous, meaning that the Nemesis hypothesis may simply be unnecessary. A more modest proposal, motivated by the distribution of aphelion directions of comets, has been subsequently put forward, where the Sun has a Jovian mass companion (referred to as Tyche) on a distant orbit that perturbs comets in the Oort cloud (Matese et al., 1999, Matese and Whitmire, 2011). However, the Wide-field Infrared Survey Explorer (WISE) has placed stringent limits on the existence of such bodies in the distant solar system. Specifically, objects with the mass of Saturn and Jupiter are ruled out to distances of 28,000 AU and 82,000 AU, respectively (Luhman, 2014). Taken together, these observational surveys leave little parameter space for any putative binary companion to the Sun.

Since the discovery of the Kuiper belt (Jewitt and Luu, 1993), the orbital architecture of this population has often been examined in hope that it can provide insight into massive astrophysical objects that may reside beyond the current observational frontier of the solar system. The first suggestion that the observed distribution of objects in the Kuiper belt pointed to the presence of a perturbing planet came from Brunini and Melita (2002), who argued that the dramatic drop-off in the numbers of Kuiper belt objects (KBOs) with semi-major axes beyond $a\gtrsim 48$ AU could be explained by an approximately Mars-sized body with a semi-major axis of $a\sim 60$ AU. Melita et al. (2004), however, quickly determined that such an object was incapable of reproducing the observations.

The idea of a sub-Earth-sized outer planet was revisited by Lykawka and Mukai (2008) who suggested that such a body could explain many of the detailed properties of the main region of the Kuiper belt. The next suggestions of a planetary perturber came after the discovery of objects with high eccentricities and with perihelia beyond the immediate reach of strong Neptunian perturbations. Particularly, the KBO 2000 CR₁₀₅ inspired speculation that its large perihelion distance of $q=44.3$ AU can most readily be attributed to the current or former presence of an external perturber, although slow chaotic diffusion driven by the known planets also constitutes a viable explanation for this seemingly unusual trajectory (Gladman et al., 2002, Gladman and Chan, 2006). The orbit of the distant object Sedna (2003 VB₁₂), on the other hand, which has perihelion distance of $q=76$ AU, can only be explained by perturbations from an external agent. To this end, Brown et al. (2004) suggested that even though an approximately Earth mass object at $\sim 70$ AU could in principle be responsible, perturbations arising from stars within the birth cluster constitute a more plausible explanation for Sedna’s detachment from Neptune (Adams and Laughlin, 2003, Morbidelli and Levison, 2004). Nevertheless, Gomes et al. (2006) carried out an extensive series of numerical simulations showing that the orbits of both 2000 CR₁₀₅ and Sedna could be explained by a Neptune-to-Jupiter mass planet with a semi-major axis of $100$s to $1000$s of AU.

A separate suggestion of a planetary perturber surfaced when Trujillo and Sheppard (2014) discovered an additional outer solar system object, 2012 VP₁₁₃, with a perihelion well beyond the planetary region, and noted that all known KBOs in the outer solar system with perihelion distance beyond Neptune and semi-major axis greater than $a>150$ AU have argument of perihelion,⁴ $\omega$, clustered around zero. Orbits with $\omega =0$ or $\omega =180deg$ come to perihelion at the heavily observed ecliptic, so observational bias could naturally facilitate a clustering around both of those values, particularly for the highest eccentricity objects. However, no conceivable bias could lead to only observing objects clustered around $\omega =0$, implying that Trujillo and Sheppard (2014)’s result is both statistically robust and not a product of survey strategy.

To explain the observations, Trujillo and Sheppard (2014) speculated that a several Earth mass planet at approximately $200$ AU could maintain the arguments of perihelion alignment through the Kozai–Lidov effect (see Section 4.1 for a short discussion). In particular, Trujillo and Sheppard (2014) demonstrated that a $5M_{\oplus }$ body on a circular orbit at $a=210$ AU could cause Kozai–Lidov oscillations of 2012 VP₁₁₃, thereby maintaining its argument of perihelion in libration around zero. Nevertheless, they also pointed out two difficulties with this scenario. First, in their simulations, they failed to find a single planet that can cause all of the KBOs – which have semi-major axes between 150 and 500 AU – to undergo Kozai–Lidov oscillations. This difficultly is not surprising; objects librate about $\omega =0$ or $180deg$ only for an interior perturber with a semi-major axis relatively close to the semi-major axis of the object being perturbed (Thomas and Morbidelli, 1996). Thus, Kozai–Lidov libration of all objects with semi-major axes between 150 and 500 AU would likely require a special configuration of several carefully placed planets (see de la Fuente Marcos and de la Fuente Marcos 2016 for further discussion). Second, internal perturbers can cause affected objects to have Kozai–Lidov oscillations about either $\omega =0$ or $\omega =180deg$, and as already stated above, the evidence for clustering about only $\omega =0$ is robust. Trujillo and Sheppard (2014) suggested that this dilemma might be overcome if a close stellar encounter had previously aligned the arguments of perihelia, a process demonstrated by Feng and Bailer-Jones (2015). The Trujillo and Sheppard (2014) planetary proposal thus requires multiple external planets and a close stellar flyby to explain the argument of perihelion clustering, along with some additional mechanism to explain the high perihelia of many of the distant objects.

Even more recently, Volk and Malhotra (2017) examined the observational census of long-period KBOs, and argued that the mean orbital plane of the Kuiper belt in the $a\sim 50\text{–}80$ AU domain is inclined with respect to the ecliptic in an unexpected manner. This led the authors to suggest that the observed warping may be facilitated by a small (e.g. $\sim$Mars-mass) planet, residing in the solar system on an appreciably inclined orbit with $a\sim 65\text{–}80$ AU. The possibility that a body of this type may indeed exist in the solar system is bolstered by the recent simulations of Silsbee and Tremaine (2018), who find a significant probability that sub-Earth-mass planetary embryos can become trapped on orbits with $a\lesssim 200$ AU and $q\sim 40\text{–}70$ AU early in the solar system’s lifetime. Given that the expected visual magnitude of such an object would be of order $\sim 17$ or less, the most likely location on the sky where this body could have avoided being discovered to date is the galactic plane, which remains relatively unexplored by solar system surveys.

This brief overview of gravitationally motivated planetary proposals illuminates the fact that over the course of the last 170 years, numerous variants of trans-Neptunian perturbers have been considered (and subsequently abandoned), with the aim to explain a broad range of dynamical phenomena at the outskirts of the solar system. In light of this multiplicity, a natural question emerges: what distinguishes the different planetary proposals and the models that accompany them? A simple answer may be that each proposition of a trans-Neptunian planet is characterized by the unique combination of the anomalous data it seeks to explain, and the specific dynamical mechanism through which the putative planet generates its observational signatures. With an eye towards characterizing the Planet Nine hypothesis specifically within this framework, in the text below we will present an up-to-date account of the orbital architecture of the trans-Neptunian region of the solar system, and outline a theoretical description of the dynamical mechanisms through which Planet Nine sculpts the small body population of the distant solar system.

The remainder of this review is structured as follows. In Section 2, we sketch out the various sub-categories of objects residing in the trans-Neptunian solar system, and summarize the relevant nomenclature. In Section 3, we provide a detailed account of the anomalous structure of the distant solar system, including a brief discussion of the characteristic timescales and observational biases. Section 4 outlines a theoretical description of the dynamical mechanisms through which Planet Nine sculpts the population of small bodies in the distant solar system and thereby accounts for these anomalies. In Section 5 we present results from a large ensemble of numerical simulations that fully capture the non-linear and chaotic nature of Planet Nine-induced dynamics. These integrations conform to the expectations of the analytical theory from the previous section and constrain the allowed properties of Planet Nine. The prospects for detecting this as-yet-unseen planet are described in Section 6. Given its requisite large distance from the Sun, the formation of Planet Nine poses a challenging problem, and various scenarios are discussed in Section 7. The review concludes in Section 8 with a summary of results, possible alternative explanations, and a brief outline of questions that remain open within the broader framework of the Planet Nine hypothesis.