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Shaping of the Inner Oort Cloud by Planet Nine 3 MNRAS 000, 1–9 (2017) Preprint 25 October 2017 Compiled using MNRAS LATEX style file v3.0 Shaping of the inner Oort cloud by Planet Nine Erez Michaely and 1⋆, Abraham Loeb2 1Physics Department, Technion - Israel Institute of Technology, Haifa 3200004, Israel 2Department of Astronomy, Harvard University, 60 Garden St., Cambridge, MA 02138, USA Accepted XXX. Received YYY; in original form ZZZ ABSTRACT We present a numerical simulation of the dynamical interaction between the proposed Planet Nine and a debris disk around the Sun for 4Gyr, accounting for the secular perturbation of the four giant planets in two scenarios: (a) an initially thin circular disk around the Sun (b) inclined and eccentric disk. We show, in both scenarios, that Planet Nine governsthe dynamics in between 1000−5000AU and forms spherical structure in the inner part (∼ 1000AU) and inclined disk. This structure is the outcome of mean motion resonances and secular interaction with Planet Nine. We compare the morphologyof this structurewith the outcomefrom a fly-by encounter of a star with the debris disk and show distinct differences between the two cases. We predict that this structure serves as a source of comets and calculate the resulting comet production rate to be detectable. Key words: Kuiper belt: general– Oort Cloud – planets and satellites: dynamical evolution and stability 1 INTRODUCTION (Batygin & Brown 2016; Trujillo & Sheppard 2014). The proposed Planet Nine has a mass of m = 10m , sma of a = 700AU, The structure of the outer solar system is complex and interest- 9 ⊕ 9 eccentricity e = 0.6, inclination to the ecliptic, i = 30◦, and ing. Oort (1950) explained the isotropic distribution of long-period 9 9 argument of the periapsis, ω = 130◦. Several other follow up comets, by conjecturing with the existence of a Sun-centred spheri- 9 studies supported the existence of Planet Nine by different meth- cal cloud with inner semi-major axis (sma) of 2×104AU and an outer ods (Fienga et al. 2016; Holman & Payne 2016; Bailey et al. 2016; sma of 2 × 105AU. Later work by Marsden et al. (1978) extended Gomes et al. 2017; Lai 2016). Additionally, Li & Adams (2016) the inner sma to 1 × 104AU. Oort showed that the comet reservoir calculated the survival rates and the interaction cross section of the can easily be perturbed by frequent distant stellar encounter and the proposed planet, and Lawler et al. (2016) investigated the impact Galactic tides. These perturbations can drive the objects in the Oort of Planet Nine of the Kuiper belt objects. Perets & Kouwenhoven cloud to the inner-solar system with eccentricities close to unity, (2012) described a mechanism of a planet captured from a different yielding the constant rate of Sun grazing comets. star system or a rouge planet, and predicted a wide, eccentric and Hills (1981) suggested that the inner boundary of the Oort inclined orbit of the captured planet. cloud reflects an observational bias, and the actual inner boundary is 4 In this work we explore the interaction of a captured Planet closer than 2×10 AU. He found that the critical sma ac that satisfies Nine with a debris disk in two scenarios: (a) an initially flat ecliptic arXiv:1609.08614v2 [astro-ph.EP] 24 Oct 2017 both the rate of stellar encounters and a typical comet lifetime is 4 disk around the Sun and (b) an initially inclined and eccentric disk. ac = 2×10 AU. In this model, the inner Oort cloud (“Hills cloud”) continues inward of 2 × 104AU but stellar encounters that on this The disk we consider represents the early debris disk, remnant scale occur on a longer timescale than the typical lifetime of comets. from the Sun’s formation era. For a short-term interaction of a Therefore, on these scales there should be a burst of comet showers planet with a ring of debris around it, see Lee & Chiang (2016). after each stellar encounter. We show that Planet Nine, due to its large sma, dominates the Duncan et al. (1987) studied numerically how the Oort and evolution of the outer disk between 1000−5000AU. This results in a Hills clouds were formed. They focused on scattering by the planets spheroidal structure at 1100AU . aTAUS . 1500AU where TAUS to high sma and the interaction with the Galactic tides and stellar stands for “Thousand AU Sphere”. For scenario (a) this structure is perturbations and found that the inner part of the Hills cloud is surrounded by an inclined disk aligned with Planet Nine’s orbital ∼ 3 × 103AU. plane and a warped disk towards the ecliptic plane. For scenario Recently Batygin & Brown (2016) reported intriguing evi- (b) the TAUS and inclined disk are created but less visible due to dence for the existence of a ninth planet in our solar system the initial conditions. This structure serves as a new source of Sun grazing comets, penetrating the inner solar system by long term secular evolution and dynamical interaction with Planet Nine. ⋆ E-mail: [email protected] Our paper is organized as follows: in section 2 we describe the © 2017 The Authors 2 Erez Michaely and Abraham Loeb numerical simulation. In section 3 we describe the results of the scenario (a) i.e. flat and circular initial disk. In subsection 3.2 we numerical runs in comparison to the standard Hills cloud formation present the results for scenario (b), namely for initially inclined and mechanism, i.e. a fly-by event in the early stages of the solar system. eccentric disk. Both subsection present the results after integrating In section 4 we present the implications of TAUS to the morphology the system for 4Gyr, and in both we find three qualitatively different of the outer solar system as well as the rate and orientation of comets regions of the disk: (i) The most inner stable part of the disk has originating from this region. Finally, we summarize the results and a spheroidal structure (TAUS); (ii) beyond the sphere there is an their implications in section 5. inclined disk with respect to the ecliptic; and (iii) beyond the inclined part of the disk, reside a disk warped back to the ecliptic plane. 2 NUMERICAL EXPERIMENTS We used the code MERCURY6 (Chambers 1999), N-body code 3.1 Scenario (a) with a the Bulirsch-Stoer algorithm. The timestep used was 185 days which is one thousandth of the period of Planet Nine around the Figure 1 presents several snapshots from the scenario (a) at an −3 −12 edge-on view relative to the ecliptic plane in the outer solar sys- Sun ∼ 10 P9 and accuracy parameter of 10 . Only the Sun tem at different times, with the x-direction chosen arbitrarily and and Planet Nine were treated explicitly while the rest of the four the y-direction is aligned with the orbital angular momentum of giant planets (Jupiter, Saturn, Uranus and Neptune) were included the ecliptic plane. Figure 2 presents an edge-on view from Planet J secularly via their 2 moment term Nine’s orbital plane. At this orientation, Planet Nine’s orbital angu- 4 2 lar momentum is pointing in the y-direction and the line of nodes is 1 miai J2 = (1) perpendicular to the origin. The spheroidal structure is visible from 2 MR2 Õi=1 both perspectives. The structure of the disk is complex. Figure 3 presents the where mi and ai are the mass and its sma of planet number i eccentricity, inclination, argument of pericentre and the longitude of respectively. R = a4 is the effective radius of the inner solar system which was set to be the orbital sma of Neptune. Any particle that the ascending node of the test particles as a function of the sma. The crossed R (from outside) was removed from the integration. We results exhibit a spread in inclination, eccentricity and the longitude can neglect the Galactic tides effects up to the scale of ∼ 104AU the ascending nodes. This implies a spherical like structure up to (Veras & Evans 2013). 1500AU which decline gradually with distance. The complexity For scenario (a) we simulated an initially flat and circular originates from mean motion resonances (MMRs) with Planet Nine debris disk around the Sun with 32, 000 massless particles of surface and secular interaction with Planet Nine’s orbit (Murray & Dermott density profile σ ∝ a−γ, with γ = −1 and a being the massless 1999). MMRs are caused when the ratio of the orbital periods P1 particle sma (Andrews et al. 2010). Larwood & Kalas (2000) and and P2 is a rational number, Kalas et al. (2000) use a different power-law index, γ = −3/2; this α P a 3/2 value has only a minor effect on the results presented in section 3. = 1 = 1 , (2) The region of the disk encompasses 700AU < a < 7000AU, with β P2 a2 eccentricity chosen from a flat distribution in the range e ∈ {0, 0.1}. α β φ The initial inclination i = 0, so that the longitude of the ascending with and being (small) integers. In MMRs the resonant angle nodes, Ω, and the argument of the periapsis, ω, are ill defined. The defined as mean anomaly M was drawn from a flat distribution of angles in φ = j λ + j λ + j ̟ + j ̟ + j Ω + j Ω, (3) the range M ∈ {0, 360◦ }. For senario (b) we simulated 32, 000 1 9 2 3 9 4 5 9 6 massless particles with surface density and sma distribution as in where λ is the mean longitude, ̟ is the longitude of pericentre and senario (a). We used thermal distribution for the eccentricity and Ω is the longitude of the ascending node.
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