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Register a new userOrbital precession in the distant solar system; further constraining the Planet Nine hypothesis with numerical simulations
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The longitudes of perihelia and orbital poles of the solar systems dozen or so most remote detected objects are clustered in a manner inconsistent with that of a random sample of uniformly distributed orbits. While small number statistics and observational biases may explain these features, the statistical significance of the clustering has led to the recent development of the Planet Nine hypothesis. In the proposed scenario, orbits in the distant solar system are shepherded via secular perturbations from an undetected massive planet on an eccentric orbit. However, the precession of perihelia and nodes in the outer Kuiper Belt and inner Oort Cloud are also affected by the the giant planets, passing stars, and the galactic tide. We perform a large suite of numerical simulations designed to study the orbital alignment of Extreme Trans-Neptunian Objects (ETNOs) and Inner Oort Cloud Objects (IOCOs). In our various integrations that include Planet Nine, we consistently find that >60% of ETNOs and IOCOs that are detectable after 4 Gyr are also anti-aligned in perihelia with the distant massive perturber. However, when we randomly select 17 objects from this sample of remaining orbits, there is significant scatter in the degree of longitude of perihelion and orbital pole clustering that might be observed. Furthermore, we argue that, in the absence of Planet Nine, 17 randomly drawn orbits should still exhibit some clustering even if the underlying distribution is uniform. Thus, we find that still more ETNO and IOCO detections are required to confidently infer the presence of Planet Nine.
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We evaluate the dynamical stability of a selection of outer solar system objects in the presence of the proposed new Solar System member Planet Nine. We use a Monte Carlo suite of numerical N-body integrations to construct a variety of orbital elements of the new planet and evaluate the dynamical stability of eight Trans-Neptunian objects (TNOs) in the presence of Planet Nine. These simulations show that some combinations of orbital elements ($a,e$) result in Planet Nine acting as a stabilizing influence on the TNOs, which can otherwise be destabilized by interactions with Neptune. These simulations also suggest that some TNOs transition between several different mean-motion resonances during their lifetimes while still retaining approximate apsidal anti-alignment with Planet Nine. This behavior suggests that remaining in one particular orbit is not a requirement for orbital stability. As one product of our simulations, we present an {it a posteriori} probability distribution for the semi-major axis and eccentricity of the proposed Planet Nine based on TNO stability. This result thus provides additional evidence that supports the existence of this proposed planet. We also predict that TNOs can be grouped into multiple populations of objects that interact with Planet Nine in different ways: one population may contain objects like Sedna and 2012 VP$_{113}$, which do not migrate significantly in semi-major axis in the presence of Planet Nine and tend to stay in the same resonance; another population may contain objects like 2007 TG$_{422}$ and 2013 RF$_{98}$, which may both migrate and transition between different resonances.
The observed physical clustering of the orbits of small bodies in the distant Kuiper Belt (TNOs) has recently prompted the prediction of an additional planet in the outer solar system. Since the initial posing of the hypothesis, the effects of Planet Nine on the dynamics of the main cluster of TNOs - the objects anti-aligned with its orbit - have been well-studied. In particular, numerical simulations have revealed a fascinating phenomenon, referred to as resonance hopping, in which these objects abruptly transition between different mean-motion commensurabilities with Planet Nine. In this work, we explore this effect in greater detail, with the goal of understanding what mechanism prompts the hopping events to occur. In the process, we elucidate the often underestimated role of Neptune scattering interactions, which leads to diffusion in the semi-major axes of these distant TNOs. In addition, we demonstrate that although some resonant interactions with Planet Nine do occur, the anti-aligned objects are able to survive without the resonances, confirming that the dynamics of the TNOs are predominantly driven by secular, rather than resonant, interactions with Planet Nine.
The existence of a giant planet beyond Neptune -- referred to as Planet Nine (P9) -- has been inferred from the clustering of longitude of perihelion and pole position of distant eccentric Kuiper belt objects (KBOs). After updating calculations of observational biases, we find that the clustering remains significant at the 99.6% confidence level. We thus use these observations to determine orbital elements of P9. A suite of numerical simulations shows that the orbital distribution of the distant KBOs is strongly influenced by the mass and orbital elements of P9 and thus can be used to infer these parameters. Combining the biases with these numerical simulations, we calculate likelihood values for discrete set of P9 parameters, which we then use as input into a Gaussian Process emulator that allows a likelihood computation for arbitrary values of all parameters. We use this emulator in a Markov Chain Monte Carlo analysis to estimate parameters of P9. We find a P9 mass of $6.2^{+2.2}_{-1.3}$ Earth masses, semimajor axis of $380^{+140}_{-80}$ AU, inclination of $16pm5^circ$ and perihelion of $300^{+85}_{-60}$ AU. Using samples of the orbital elements and estimates of the radius and albedo of such a planet, we calculate the probability distribution function of the on-sky position of Planet Nine and of its brightness. For many reasonable assumptions, Planet Nine is closer and brighter than initially expected, though the probability distribution includes a long tail to larger distances, and uncertainties in the radius and albedo of Planet Nine could yield fainter objects.
Most known trans-Neptunian objects (TNOs) gravitationally scattering off the giant planets have orbital inclinations consistent with an origin from the classical Kuiper belt, but a small fraction of these scattering TNOs have inclinations that are far too large (i > 45 deg) for this origin. These scattering outliers have previously been proposed to be interlopers from the Oort cloud or evidence of an undiscovered planet. Here we test these hypotheses using N-body simulations and the 69 centaurs and scattering TNOs detected in the Outer Solar Systems Origins Survey and its predecessors. We confirm that observed scattering objects cannot solely originate from the classical Kuiper belt, and we show that both the Oort cloud and a distant planet generate observable highly inclined scatterers. Although the number of highly inclined scatterers from the Oort Cloud is ~3 times less than observed, Oort cloud enrichment from the Suns galactic migration or birth cluster could resolve this. Meanwhile, a distant, low-eccentricity 5 Earth-mass planet replicates the observed fraction of highly inclined scatterers, but the overall inclination distribution is more excited than observed. Furthermore, the distant planet generates a longitudinal asymmetry among detached TNOs that is less extreme than often presumed, and its direction reverses across the perihelion range spanned by known TNOs. More complete models that explore the dynamical origins of the planet are necessary to further study these features. With observational biases well-characterized, our work shows that the orbital distribution of detected scattering bodies is a powerful constraint on the unobserved distant solar system.
The gravitational interaction between a protoplanetary disc and planetary sized bodies that form within it leads to the exchange of angular momentum, resulting in migration of the planets and possible gap formation in the disc for more massive planets. In this article, we review the basic theory of disc-planet interactions, and discuss the results of recent numerical simulations of planets embedded in protoplanetary discs. We consider the migration of low mass planets and recent developments in our understanding of so-called type I migration when a fuller treatment of the disc thermodynamics is included. We discuss the runaway migration of intermediate mass planets (so-called type III migration), and the migration of giant planets (type II migration) and the associated gap formation in the disc. The availability of high performance computing facilities has enabled global simulations of magnetised, turbulent discs to be computed, and we discuss recent results for both low and high mass planets embedded in such discs.
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