1

******* This paper was published in Advances in Geosciences 15 (Eds. Anil Bhardwaj et al., World Scientific, Singapore.), 293-304 (2009). [email protected] http://sites.google.com/site/patryksofialykawka/ *******

Trans-Neptunian Region Architecture: Evidence for a Planet Beyond Pluto* PATRYK SOFIA LYKAWKA† Kobe University, Graduate School of Science, Department of Earth and Planetary Sciences, 1-1 rokkodai-cho, nada-ku, Kobe, 6578501, Japan TADASHI MUKAI Kobe University, Graduate School of Science, Department of Earth and Planetary Sciences, 1-1 rokkodai-cho, nada-ku, Kobe, 6578501, Japan Trans-Neptunian objects (TNOs) orbiting in the Edgeworth-Kuiper Belt carry precious information about the origin and evolution of the Solar System1–5. The Kuiper Belt has a very complex orbital structure. Indeed, TNOs exhibit surprisingly large eccentricities, e, and inclinations, i, and are classified in distinct dynamical classes2,4,6. Here we propose that the Kuiper Belt orbital structure can be explained by a massive scattered planetesimal with tenths of the Earth’s mass, which later remained in the system in a distant stable orbit (an outer planet). Near the end of planet formation, the outer planet was firstly scattered by one of the icy giant planets, then it dynamically excited the primordial planetesimal disk over at least tens of Myr, reproducing the levels observed at 40–50 AU and the truncation of the disk at about 48 AU before planet migration. Later, the outer planet was captured by a distant resonance with Neptune of the type r:1 or r:2 (e.g., 6:1, 7:1, ...), acquiring an inclined stable orbit (≥100 AU; 20–40°), thus preserving the Kuiper Belt over ~4 Gyr. Our model explains the following: 1) Depletion of the inner Kuiper Belt; 2) The entire currently known resonant populations in the Kuiper Belt, including Neptune Trojans and resonant TNOs in distant resonances (>50 AU); 3) Formation of scattered and detached TNOs, including analogues of (136199) Eris, 2004 XR190, (148209) 2000 CR105, and (90377) Sedna; 4) Classical TNOs and their dual nature of cold and hot populations; 5) Orbital excitation of classical TNOs; 6) The Kuiper Belt outer edge at about 48 AU; 7) Loss of ~99% of the initial total mass of the Kuiper Belt through dynamical depletion and enhanced collisional grinding; 8) Neptune’s current orbit at 30.1 AU. In summary, our scenario consistently reproduces all main aspects of Kuiper Belt architecture with unprecedented detail. The best constraints obtained from the model for the outer planet are: aP=100–175 AU (currently near or inside an r:1 or r:2 resonance), qP>80 AU, iP=20–40°, and apparent magnitude mP~15–17mag at perihelion (assuming an albedo of 0.1–0.3 and qP=80–90 AU).

1. Introduction Trans-Neptunian objects (TNOs) represent the relics of the primordial planetesimal disk that originated the Solar System1–4,7. The study of physical properties and dynamical evolution of these icy/rocky bodies can provide valuable information about the origin of the Solar System, planet formation, and other important properties of the disk. Today, more than 1000 TNOs have been observed thus far, revealing a surprisingly complex orbital distribution6 (Fig. 1d). Several scenarios have been proposed to explain the Kuiper Belt structure4,7–10, but none has satisfied uniquely all main observational constraints. Ongoing detection of bodies in the Kuiper Belt has revealed four main classes of TNOs: resonant, scattered, detached, and classical2,6. Resonant TNOs are locked in mean motion resonances with Neptune, and their origin is associated with Neptune’s outward migration (resonance sweeping)9,11. Scattered TNOs originated from gravitational scattering by Neptune, and maintain a perihelion distance, q, close to the giant planet12. Detached TNOs, located beyond 48 AU (usually q>40 AU), never encounter Neptune for longer than 4–5 Gyr6,13; this population could not have been formed solely by the presence of the giant planets14. Classical TNOs are non-resonant objects that orbit around 37–48 AU and exhibit intriguing orbital excitation (Fig. 1d); these bodies are subdivided into cold (i≤5°) and hot (i>5°) populations4, and possess different physical properties2. Other important constraints include the outer edge of the Kuiper Belt at about 48 AU15,16 and the Belt’s small total mass, which is only ~1% of that required for TNOs to grow via accretion1,5. Although this suggests the Kuiper Belt was more massive in the past3,5,17, standard scenarios cannot explain the loss of ~99% of its mass2. Based on accretion models, planet formation is an inefficient process: giant planets scatter remaining disk planetesimals that move in their vicinity (e.g., around 10–20 AU). Worth noting, several of these planetesimals are massive (0.1–1.0 Earth masses, M⊕)18–20. This is presently evidenced in the Solar System by Pluto and other TNO multiple systems, the tilts of Uranus and Neptune, and the retrograde orbit of Triton. These examples can be well *

This work is supported by “The 21st Century COE Program of the Origin and Evolution of Planetary Systems” of the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) and the Japan Society for the Promotion of Science (JSPS). † P. S. Lykawka is supported by a JSPS fellowship.

2

explained by giant impact/close encounter events of massive planetesimals. However, these objects must have had large populations to enable such events17,19. In this paper, we argue that a massive scattered body acquired a resident trans-Plutonian orbit after planet migration. We refer to this body as the ‘outer planet’ or ‘planetoid’, denoted by a subscript P.

Figure 1. Orbital evolution of a planetesimal disk with an outer planet. In this reference simulation, the planetesimal disk was initially cold (e~0.001 and i~0.2°), and extended from 17 to 51 AU following a distribution falling inversely with heliocentric distance. The disk was modelled with 2125 small mass bodies (seeds). In runs of planet migration and long-term evolution (4 Gyr), the disks were composed of ~15000 massless particles after cloning the seeds that remained in the system. We placed Jupiter, Saturn, Uranus, and Neptune at 5.4, 8.7, 15, and 20 AU, respectively, and a 0.4-M⊕ scattered planetoid at ~65 AU with iP~10° (big circle). Objects above the long-dashed curve could encounter the outer planet. The dotted curves represent the perihelion distances of 30, 37, and 40 AU. Vertical lines indicate resonance positions with Neptune. Panels a–c represent three stages of our scenario, where black circles represent disk objects. Panel d presents current observations for comparison. a) After 60 Myr, before planet migration. Objects did not exhibit appreciable radial changes. Non-resonant TNOs are illustrated for reference (open circles). The enclosed region defines the eccentricities needed in a stirred planetesimal disk to reproduce long-term TNOs in resonances beyond 50 AU26; b) After planet migration, performed within 100 Myr. This migration timescale is in line with previous models9,11,25. The outer planet was transported to semimajor axis aP~100 AU (iP~30°), following the location of the 6:1 resonance; c) After evolving the system to 4 Gyr; d) Orbital distribution of TNOs. Only objects with more reliable orbits are plotted (with long-arc). Because observational biases favour discovery of TNOs at close distances16, 3:2 resonants are overrepresented.

2. Methods and initial conditions We performed almost 1000 simulations using many thousands of disk planetesimals. The gravitational influence of the Sun, the four giant planets, and this outer planet (0.1–1.0 M⊕) was taken into account in all simulations. We focussed on planetoids with medium mass, MP=0.3–0.7 M⊕. The giant planets were initially in compact orbital configurations (within ~17–20 AU, before planet migration), whilst the planetoids were on Neptune-scattered orbits (initial aP~40–160 AU), and with iP=10–40°. Initially, these systems evolved over tens of millions of years before planet migration. A delayed migration is in line with recent models21. Planet migration was implemented as described in previous studies9,11. The giant planets and the planetoid were forced to migrate outwards, with the latter typically following the position of a distant and strong resonance with Neptune, in particular r:1 resonances (6:1, 7:1, ...). Because these resonances commonly trap objects in Kozai mechanism (KM)14, the outer planet probably exhibited KM orbital behaviour, decreasing eP (increasing qP) and increasing iP conserving vertical angular momentum, sqrt(1 – eP2)·cos(iP). This effect was implemented in our migration code. At the end, the outer planet acquired a distant and highly inclined orbit, which satisfies several observational constraints10,22. All simulations were conducted using the EVORB23 and MERCURY24 symplectic integrators. The dependence of results on the initial planetoid’s angular elements or the integrator used was negligible.

3

3. Results An outer planet can obviously threaten the stability of resonant TNOs over 4 Gyr; their depletion and maximum eccentricity are essentially dependent on qP. Thus, long-term 3:2, 2:1, and 5:2 resonant TNOs require qP≥80 AU. This rules out the resident planets as proposed in previous modern models10,23 because they cannot satisfy the constraints on the Kuiper Belt without destroying the 2:1 and 5:2 resonant populations. Our model is able to reproduce all identified resonant populations, including eccentricities, inclinations, libration amplitudes (a measure of Neptune–TNOs relative distance during resonant motion), and TNOs in KM. After 4 Gyr, the main occupied resonances are 1:1, 5:4, 4:3, 7:5, 3:2, 8:5, 5:3, 7:4, 9:5, 11:6, 2:1, 13:6, 11:5, 9:4, 7:3, 5:2, 8:3, 11:4, and 3:1 (62.6 AU). Some 1:1 resonant bodies acquired e<0.14 and i<20°, suggesting that the observed Neptune Trojans could have formed within this framework. Pluto-like objects were obtained in the 3:2 resonance, and orbital elements and resonant properties were fully reproduced. However, no analogues of 2003 EL61 appeared in the 12:7 resonance6,17. Finally, the maximum eccentricity of distant resonant bodies stable over 4 Gyr was conditioned to Q≤qP, where Q is the aphelion distance. The scattered and detached populations obtained using the model are compatible with observations (Fig. 2). The model produced scattered bodies with large eccentricities and i<50°, including analogues of Eris (i~44°). The majority of detached bodies were initially Neptune-scattered objects, which later acquired larger perihelia and/or inclinations due to the perturbation from the outer planet. The bulk detached population resulted in q=40–60 AU and i<60° (both quantities were weakly correlated). The model also produced analogues of 2004 XR190, 2000 CR105, and Sedna. The fractions of detached to scattered populations, 0.7–2.5, agree with intrinsic estimates based on observations4,13. Unlike standard models6,12, our scenario also yielded a non-negligible fraction of TNOs with i>40°, the first members of which appear to be Eris, 2004 XR190, and 2004 DG77 (ref. 6).

Figure 2. Comparison of orbital distributions between the model and observations. In this reference simulation, initial conditions were very similar to those shown in Figure 1, except that the disk extended from 17 to 53 AU, and the giant planets started within ~18 AU. Vertical lines indicate resonance position with Neptune. Dotted curves represent the perihelia of 30, 37, and 40 AU. The results represent outcomes after 4 Gyr (black circles). The outer planet (0.4 M⊕) acquired semimajor axis aP~100 AU, eccentricity eP~0.2, and inclination iP~45° (large circle). Objects above the long-dashed curve could encounter the outer planet. Only TNOs with more reliable orbits are plotted (with long-arc; grey circles). Triangles represent detached TNOs6. Another detached body, Sedna, is out of the range of this figure (a=525.6 AU; e=0.855; i=11.9°). Observational biases severely limit discovery of detached TNOs13, hence this population is underrepresented.

4

In our simulations, the classical bodies yielded final eccentricities very similar to observed values (see Fig. 1). In addition, we obtained hot classical bodies (i=10–35°) using a method similar to the standard model11, but our model yielded an important distinction: some initially cold classical bodies acquired i~5–15°. Thus, part of the local classical population was promoted to the hot component. Consequently, classical TNOs with low inclinations and those with i>10–15° will possibly reveal clearer different physical properties. In fact, this predicted feature is apparent in the distribution of inclinations with spectral slopes of classical TNOs4. During the pre-migration stage, the early perturbation of a scattered planetoid resulted in disks with orbital distributions quite similar to those observed in the 40–50 AU region. In addition, the outer planet effectively truncated the Kuiper Belt at ~48 AU (Fig. 1a,b). Since these outcomes were intrinsically dependent on the planetoid’s initial location, planetoids at 60–80 AU yielded the best excited orbital distributions before migration. Thus, if Neptune was initially located at 14–20 AU9,25, the best candidate r:1 resonances to capture the planetoid are the 6:1, 7:1, …, 14:1. The probability for capture is low amongst these resonances9,26. Nevertheless, strong r:1 (and r:2) resonances were mutually nearer each other and large populations of massive planetesimals existed in the past19, supporting the likelihood of this scenario. Another finding was that the ancient Kuiper Belt appeared to have a radius of at least ~50–53 AU. This not only supports the formation of distant resonant TNOs26, but also suggests that detached TNOs at 49–53 AU (e.g., 2003 UY291 and 1995 TL8) were members of the primordial planetesimal disk prior to eccentricity pumping. Could Neptune stop at 30 AU in a 50–60 AU-sized disk with embedded planetoids? We evolved pre-migration systems of massive disks (10000-20000 bodies): 1, 0.9, 0.8, 0.5, 0.3, 0.25, and 0.1 times the minimum mass solar nebula2 (MMSN), with surface densities falling with heliocentric distance, R, as R–3/2±1/2. The results of state-of-the-art collisional models indicate that less massive disks are expected during the pre-migration epoch3. We found that in most 0.9–0.5 MMSN disks, Neptune stopped migrating at ~25–30 AU after a few hundred million years. Therefore, Neptune’s current orbit at 30.1 AU can be explained without requiring the disk to be truncated at similar distances25. This scenario could solve the problem of the loss in the Kuiper Belt’s total mass. First, 15–40% of objects remained in the system after 4 Gyr. Second, because a large fraction of planetesimals acquired excited orbits at early stages, their random velocities (that vary with (e2+i2)1/2) rendered fragmentation rather than accretion5,27, thus enabling the Kuiper Belt to experience quite intense collisional grinding. The combination of dynamical depletion (60–85%) and collisional grinding (92–97%)27 suggests the original Belt’s mass was reduced to only ~0.5–3% after billions of years, thus comparable to the observed estimate (~1%). It is noteworthy that our estimate is an upper limit. That is, stable resonant populations are overrepresented (i.e., underestimating dynamical depletion fractions) in our simulations because stochastic migration25 was not modelled. Furthermore, collisional grinding estimates could reach higher values if the planetesimal disks obtained here were taken into account in collisional evolution models. Finally, the planetoid dynamically excited the eccentricities of a substantial fraction of disk planetesimals during the first hundred million years. Because several of these objects acquired unstable orbits due to perturbations from Neptune and the other giant planets, a non-negligible fraction of those objects penetrated the inner Solar System. Therefore, the terrestrial planets and the Moon likely experienced an enhanced impact flux of bodies from the outskirts of the planetesimal disk during this early period of solar system history. 4. Observational constraints on trans-Plutonian planets How is it possible to detect such a massive outer planet? The possible capture in one of the best candidate resonances (6:1–14:1) suggests aP~100–175 AU. For plausible initial conditions, KM dynamics point to qP>80 AU and iP=20–40°. Figure 3 illustrates that the outer planet would be quite bright, hence rare in the sky16, so only wide area surveys could find it. Nevertheless, the majority of surveys have adopted the strategy of finding TNOs that move at apparent sky motions of 2–5 arcsec/h (R=60–30 AU), being sensible at most to ~1.5 arcsec/h.

5

Figure 3. Apparent magnitudes of an outer planet in distant orbits. To determine apparent magnitudes, we estimated the planetoid’s diameter assuming spherical shape, MP=0.3–0.5 M⊕, and a mean density of 2–3 gcm–3 (e.g., Pluto’s mean density is ~2 gcm–3), and obtained a result of ~10000–14000 km. We also assumed an albedo within 0.1–0.3, which agrees with that expected for hypothetical distant planetoids19, and with Sedna’s albedo31, the best known representative of the latter. Solid, dashed, and dotted curves represent outer planets with 0.3, 0.4, and 0.5 M⊕, respectively (mean density ρ=2 gcm–3). Different set of curves indicate assumed albedos of 0.1, 0.2, and 0.3. When ρ=3 gcm–3, the apparent magnitudes become ~0.3 mag darker. A decreasing curve represents the apparent sky motion of an outer planet as a function of heliocentric distance. The variation in the planet’s heliocentric distance for a final orbit at ~100 AU, as exemplified in reference simulations shown in Figures 1 and 2, is plotted as a horizontal grey line. In this case, the apparent magnitude varies within ~15.2–18.5 mag because of uncertainties in physical properties. Notice that the planetoid’s aphelion distance could reach ~270 AU for other plausible orbital configurations, (i.e., near the 14:1 resonance location, ~175 AU, and a perihelion distance equal to 80 AU). In addition, the outer planet will spend more time near aphelion during its orbit (moving at smaller apparent rates), because of its possible moderate–large eccentricity.

For example, the most distant TNOs discovered thus far, Eris and Sedna, were moving at similar critical rates near the detection limits28. In addition, high-i objects are more likely to be discovered at ecliptic latitudes, β~i, than in the ecliptic (β=0°) (~4 times greater probability). Moreover, a high-i object with 20–40° spends only ~1.5–4% of its orbit near the ecliptic (β=0–10°)16. All wide area surveys to date have essentially searched near the ecliptic. Consequently, high-i objects have been severely discriminated against discovery28–30. Thus, a massive planet beyond Pluto has likely escaped detection because it is currently moving with sky motion below survey sensibility, or its current orbital position is away from the ecliptic. Finally, because these surveys avoid the region near the Galactic Plane28, the probability of non-detection should be ~10–15% regardless of the planetoid’s properties. 5. Conclusions Our model naturally accounts for the Kuiper Belt’s resonant structure, its outer edge, the loss of ~99% of its initial total mass, scattered and detached TNOs, classical TNOs and their dual character, and Neptune’s current orbit at 30.1 AU. We conclude that the observed orbital excitation in the 40–50 AU region and the truncation near 48 AU were caused by the perturbation from the outer planet during its pre-migration scattered orbit, thus representing fossilised signatures of this planet. Because the formation of prominent populations of detached and TNOs with i>40° apparently requires the existence of a resident outer planet, we believe these populations represent current signatures of the planetoid’s perturbation over billions of years. In summary, the scenario presented here can explain all main characteristics of Kuiper Belt architecture and offers insightful predictions, especially the existence of a massive distant outer planet within the Solar System.

Acknowledgments We would like to thank the reviewer for comments and suggestions. This study was supported by “The 21st Century COE Program of the Origin and Evolution of Planetary Systems” of the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT), and a MEXT scholarship. P. S. Lykawka is also grateful to a fellowship from the Japan Society for the Promotion of Science.

6

References 1. 2. 3.

4. 5. 6. 7.

8. 9. 10. 11. 12. 13. 14.

15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

Luu, J. X. & Jewitt, D. C. Kuiper belt objects: relics from the accretion disk of the Sun. Annu. Rev. Astron. Astrophys. 40, 63-101 (2002). Morbidelli, A. & Brown, M. E. The Kuiper belt and the primordial evolution of the Solar System, in Comets II (eds Festou, M. C., Keller, H. U. & Weaver, H. A.) 175-191 (Univ. of Arizona Press, Tucson, 2004). Kenyon, S. J., Bromley, B. C., O’Brien, D. P. & Davis, D. R. Formation and collisional evolution of Kuiper belt objects, in The Kuiper Belt (eds Barucci, M. A., Boehnhardt, H., Cruikshank, D. & Morbidelli, A.) 293-313 (Univ. of Arizona Press, Tucson, 2008). Chiang, E. et al. A Brief History of Trans-Neptunian Space, in Protostars and Planets V (eds Reipurth, B., Jewitt, D. & Keil, K) 895-911 (Univ. of Arizona Press, Tucson, 2007). Stern, S. A. & Colwell, J. E. Accretion in the Edgeworth-Kuiper belt: forming 100-1000km radius bodies at 30AU and beyond. Astron. J. 114, 841-849; 881-884 (1997). Lykawka, P. S. & Mukai, T. Dynamical classification of trans-neptunian objects: Probing their origin, evolution and interrelation. Icarus 189, 213-232. Morbidelli, A., Levison, H. F. & Gomes, R. The Dynamical Structure of the Kuiper Belt and its Primordial Origin, in The Kuiper Belt (eds Barucci, M. A., Boehnhardt, H., Cruikshank, D. & Morbidelli, A.) 275-292 (Univ. of Arizona Press, Tucson, 2008). Kobayashi, H., Ida, S. & Tanaka, H. The evidence of an early stellar encounter in Edgeworth-Kuiper belt. Icarus 177, 246-255 (2005). Hahn, J. M. & Malhotra, R. Neptune’s Migration into a Stirred-up Kuiper Belt: A Detailed Comparison of Simulations to Observations. Astron. J. 130, 2392-2414 (2005). Melita, M. D., Williams, I. P., Brown-Collander, S. J. & Fitzsimmons, A. The edge of the Kuiper belt: the Planet X scenario. Icarus 171, 516-524 (2004). Gomes, R. S. The origin of the Kuiper belt high-inclination population. Icarus 161, 404-418 (2003). Duncan, M. J. & Levison, H. F. A disk of scattered icy objects and the origin of Jupiter-family comets. Science 276, 1670-1672 (1997). Gladman, B. et al. Evidence for an extended scattered disk. Icarus 157, 269-279 (2002). Gomes, R. S., Fernandez, J. A., Gallardo, T. & Brunini, A. The Scattered Disk: Origins, Dynamics and End States, in The Kuiper Belt (eds Barucci, M. A., Boehnhardt, H., Cruikshank, D. & Morbidelli, A.) 259-273 (Univ. of Arizona Press, Tucson, 2008). Allen, R. L., Bernstein, G. M. & Malhotra, R. The edge of the solar system. Astrophys. J. 549, L241-L244 (2001). Trujillo, C. A., Jewitt, D. C. & Luu, J. X. Properties of the Trans-Neptunian belt: statistics from the Canada-FranceHawaii Telescope survey. Astron. J. 122, 457-473 (2001). Brown, M. E. et al. Satellites of the largest Kuiper belt objects. Astrophys. J. 639, L43-L46 (2006). Goldreich, P., Lithwick, Y. & Sari, R. Final stages of planet formation. Astrophys. J. 614, 497-507 (2004). Stern, S. A. On the Number of Planets in the Outer Solar System: Evidence of a Substantial Population of 1000-km Bodies. Icarus 90, 271-281 (1991). Pollack, J. B. et al. Formation of the Giant Planets by Concurrent Accretion of Solids and Gas. Icarus 124, 62-85 (1996). Gomes, R., Levison, H. F., Tsiganis, K. & Morbidelli, A. Origin of the Cataclysmic Late Heavy Bombardment period of the Terrestrial Planets. Nature 435, 466-469 (2005). Morbidelli, A., Jacob, C. & Petit, J. -M. Planetary embryos never formed in the Kuiper belt. Icarus 157, 241-248 (2002). Brunini, A. & Melita, M. D. The existence of a planet beyond 50AU and the orbital distribution of the classical Edgeworth-Kuiper belt objects. Icarus 160, 32-43 (2002). Chambers, J. E. A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304, 793-799 (1999). Levison, H. F., Morbidelli, A., Gomes, R. & Backman, D. Planet migration in planetesimal disks, in Protostars and Planets V (eds Reipurth, B., Jewitt, D. & Keil, K) 669-684 (Univ. of Arizona Press, Tucson, 2007). Lykawka, P. S. & Mukai, T. Origin of scattered disk resonant TNOs: Evidence for an ancient excited Kuiper belt of 50 AU radius. Icarus 186, 331-341 (2007). Kenyon, S. J. & Bromley, B. C. Collisional Cascades in Planetesimal Disks. II. Embedded Planets. Astron. J. 127, 513-530 (2004). Trujillo, C. A. & Brown, M. E. The Caltech Wide Area Sky Survey. Earth, Moon, and Planets 92, 99-112 (2003). Larsen, J. A. et al. The Search for Distant Objects in the Solar System Using Spacewatch. Astron. J. 133, 12471270 (2007). Sheppard, S. S., Jewitt, D. C., Trujillo, C. A., Brown, M. J. I. & Ashley, M. C. B. A Wide-Field CCD Survey for Centaurs and Kuiper Belt Objects. Astron. J. 120, 2687-2694 (2000). Emery, J. P., Dalle Ore, C. M., Cruikshank, D. P., Fernández, Y. R., Trilling, D. E. & Stansberry, J. A. Ices on (90377) Sedna: confirmation and compositional constraints. Astron. Astrophys. 466, 395-398 (2007).