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Circularizing Planet Nine Through Dynamical Friction with an Extended, Cold Planetesimal Belt

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Circularizing Planet Nine Through Dynamical Friction with an Extended, Cold Planetesimal Belt MNRAS 000,1{9 (2017) Preprint 6 November 2018 Compiled using MNRAS LATEX style file v3.0 Circularizing Planet Nine through dynamical friction with an extended, cold planetesimal belt Linn E.J. Eriksson,1? Alexander J. Mustill,1 Anders Johansen1 1Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, SE-221 00 Lund, Sweden Accepted XXX. Received YYY; in original form ZZZ ABSTRACT Unexpected clustering in the orbital elements of minor bodies beyond the Kuiper belt has led to speculations that our solar system actually hosts nine planets, the eight established plus a hypothetical \Planet Nine". Several recent studies have shown that a planet with a mass of about 10 Earth masses on a distant eccentric orbit with perihelion far beyond the Kuiper belt could create and maintain this clustering. The evolutionary path resulting in an orbit such as the one suggested for Planet Nine is nevertheless not easily explained. Here we investigate whether a planet scattered away from the giant-planet region could be lifted to an orbit similar to the one suggested for Planet Nine through dynamical friction with a cold, distant planetesimal belt. Recent simulations of planetesimal formation via the streaming instability suggest that planetesimals can readily form beyond 100 au. We explore this circularisation by dynamical friction with a set of numerical simulations. We find that a planet that is scattered from the region close to Neptune onto an eccentric orbit has a 20-30% chance of obtaining an orbit similar to that of Planet Nine after 4:6 Gyr. Our simulations also result in strong or partial clustering of the planetesimals; however, whether or not this clustering is observable depends on the location of the inner edge of the planetesimal belt. If the inner edge is located at 200 au the degree of clustering amongst observable objects is significant. Key words: Kuiper belt: general | planets and satellites: dynamical evolution and stability | planets and satellites: formation | planet{disc interactions 1 INTRODUCTION tant eccentric orbit that is inclined and anti-aligned with the ETNOs. They found in their simulations that orbits Trujillo & Sheppard(2014) discovered an unexpected clus- outside the parameter region bounded by semimajor axis tering in the argument of perihelion of minor planets with a ∼ 400 − 1500 au and eccentricity e ∼ 0:5 − 0:8 were dis- semimajor axis beyond 150 au and perihelion beyond the favoured. In this incarnation, the undetected planet has be- orbit of Neptune, objects referred to as extreme trans- come known as "Planet Nine". This region was refined in a Neptunian objects (ETNOs). Subsequent orbital element later paper by Brown & Batygin(2016), who identified a analysis performed by Batygin & Brown(2016) showed that region with a ∼ 380 − 980 au, e ∼ 0:1 − 0:8, masses between arXiv:1710.08295v2 [astro-ph.EP] 10 Jan 2018 the orbits of these clustered ETNOs are physically aligned. 5−20 M and an inclination (i) of approximately 30◦ relative The authors of both papers demonstrated that this cluster- ⊕ to the ecliptic. Other authors (Malhotra et al. 2016; Becker ing could be explained by the presence of a distant eccentric et al. 2017; Millholland & Laughlin 2017) have studied the planet. dynamical stability of the clustered ETNOs and used reso- Trujillo & Sheppard(2014) demonstrated that a planet nance considerations to constrain the orbital parameters of with mass between 2 and 15 M and a semimajor axis be- ⊕ Planet Nine, which yield solutions within the region identi- yond 200 au could have created the clustering of ETNOs, fied by Brown & Batygin(2016). and maintained it for billions of years. Stronger constraints were placed by Batygin & Brown(2016), who showed that Various mechanisms have been proposed to explain the the clustering of longitude of perihelion and ascending node origin of Planet Nine, e.g. capture from another star during could be maintained by a planet of mass ≥ 10 M⊕ on a dis- a close encounter in the Sun's birth cluster (Li & Adams 2016; Mustill et al. 2016; Parker et al. 2017), or in-situ for- mation by slow coagulation within a distant ring of planetes- ? E-mail: [email protected] imals (Kenyon & Bromley 2015, 2016). A third option is that © 2017 The Authors 2 L. E. J. Eriksson, A. J. Mustill and A. Johansen Planet Nine is a scattered ice giant, originating in the outer ditional simulations with smaller tolerance parameters were giant-planet region. Planets with masses in the predicted executed in order to check that the outcome was not affected. regime for Planet Nine can be scattered onto large semima- A planet of mass 10 M⊕ was initiated on an eccentric jor axis orbits by giant protoplanets growing in the ice-giant orbit with a perihelion distance of 30 au, mimicking a re- region that are clearing their respective orbital domains (e.g. cent scattering by Neptune. The initial inclination was set Thommes et al. 1999; Levison & Morbidelli 2007). Outward to be 5 degrees, since preliminary integrations showed that scattering can also occur during instabilities in mature sys- smaller initial inclinations resulted in systems with high ec- tems (see e.g. Tsiganis et al. 2005; Nesvorn´y 2011). However, centricities of Uranus and Neptune. Following the results unless such scattered planets somehow circularize their or- from Carrera et al.(2017), we introduce a massive cryobelt bits, subsequent scattering near perihelion eventually leads that has a surface density distribution following 1/a. We set to ejection. One potential mechanism for circularizing the the width of the cryobelt to be 500 au, and perform sim- orbit is through dynamical friction with an extended mas- ulations for inner edges at 100 and 200 au. The models of sive disc of gas (Bromley & Kenyon 2016). Carrera et al.(2017) produce cryobelts of masses down to In this work we propose a new mechanism for circular- & 60 M⊕. We use the lower mass limit since it results in a izing the orbit of a scattered Planet Nine, namely through lower limit on the effect on the orbit of the scattered planet. dynamical friction with a massive planetesimal belt beyond We also perform a small set of simulations with a less mas- 100 au. Formation at these large distances is a result of FUV sive cryobelt, to represent the scenario when mass is stripped photoevaporation, which reduces gas mass and triggers plan- from the solar system during its time in the birth cluster, or etesimal formation through the streaming instability. In re- if planetesimal formation is less efficient than in our fiducial cent simulations of planetesimal formation via the stream- model. The cryobelt is represented by either 1000 or 10000 ing instability performed by Carrera et al.(2017), a massive massive small bodies in mercury (see discussion in 3.1). (60 − 130 M⊕) planetesimal belt forms beyond 100 au. We At an initial semimajor axis of 30 au, Planet Nine is will refer to such an ultracold belt of planetesimals as a cry- unlikely to suffer any close encounters with Jupiter or Sat- obelt. The amount of planetesimals formed interior to 100 au urn, and so for the sake of computational time we chose to is heavily dependent on the model and parameters that are only include three big bodies in the simulations (Uranus, being used, whilst the formation of a cryobelt by FUV pho- Neptune and Planet Nine). However, even though close en- toevaporation is a robust result of the simulations and does counters between Planet Nine and the gas giants might be not require particular fine tuning of any parameters (except unlikely, the gas giants could dominate the orbital evolution for the assumption that FUV radiation indeed leads to ef- of some close-in cryobelt objects. As this is the part of the ficient photoevaporation in the first place, as pointed out cryobelt that is most likely to be observable, we choose to by Ercolano et al. 2017). Since this cryobelt forms early it use the same trick as Batygin & Brown(2016) and include should be present at the time of the giant planet forma- the gravitational potential of the gas giants in a manner tion, when Planet Nine is most likely to have been scat- that does not demand a decreased time-step. We incorpo- tered out. An additional result from Carrera et al.(2017) rated the acceleration due to the gas giants by increasing is that the streaming instability together with FUV photoe- the radius of the Sun out to the orbit of Saturn (R∗ = aS) vaporation does not form enough planetesimals in the giant and adding a J2 moment to its potential. The magnitude of planet region to form the cores of giant planets, suggesting the J2 moment due to Jupiter and Saturn is (Burns 1976) that the planetesimals taking part in the formation of giant i=2 2 planet cores form through some other process, e.g. particle 1 Õ mia J = i (1) pile-ups near ice lines (Sirono 2011a,b; Ida & Guillot 2016; 2 2 2 i=1 M∗R∗ Dra_zkowska, & Alibert 2017; Schoonenberg & Ormel 2017). In this paper we investigate whether dynamical friction where mi is the mass of planet i and M∗ is the mass of the with a massive planetesimal belt beyond 100 au can put a Sun. scattered ice giant on an orbit similar to that which is ex- The aim of the simulations was to investigate whether pected for the hypothetical Planet Nine. In Section 2 we it is possible to circularize the orbit of Planet Nine enough briefly describe the numerical methods that have been used; to be within the region of parameters identified by Brown in Section 3 we present results from the preliminary inte- & Batygin(2016), without considerably exciting the outer grations; in Section 4 we present results from the final sim- giant-planet region.
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