1. Dynamics of comets and the origin of the solar system Origin of solar systems - 30/06/2009 Jean-Baptiste Vincent Max-Planck-Institut für Sonnensystemforschung

2. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 2/24 Introduction Because of their random apparitions, comets were considered as atmospheric events during many centuries until Tycho Brahe proved that comets are celestial objects by measuring parallaxes in 1577. The study of comet dynamics started then with E. Halley 1705 : Edmund Halley calculates the period of a comet 1758 : Observations confirm Halley’s predictions

3. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 3/24 Comets follow keplerian orbits. => For any observed comet, we can calculate its orbital parameters and estimate its orbit. This will allow us to sort the comets into different groups, the study of these groups leading to important insights on the early ages of our solar system. Introduction

4. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 4/24 Classification The classification is mainly based on the orbital parameters of the comets like orbital period or aphelion distance. We distinguish three main groups: 1. short period comets 2. long period comets 3.non-periodic comets Jupiter Family Comets (JFC) Halley Type Comets (HTC) Main Belt Comets (MBC)

5. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 5/24 Short Period Comets 1/5 of the catalogued comets Coming mainly from the Kuiper Belt region (beyond Neptune’s orbit). Orbits affected by perturbations from the giant planets (especially Jupiter) Examples: 1P/Halley (p = 76 yrs), 2P/Encke (p = 3.3 yrs) Period< 200 years a< 100 AU i± 10º

6. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 6/24 Tisserand’s Parameter Tisserand’s parameter is a dynamic number which is conserved (or only slightly modified) during an encounter between two objects in a restricted 3-bodies system. T J = a J a + 2 ¢ r a a J ( 1 ¡ e 2 ) ¢ cos ( i ) a J = semi-major axis of Jupiter = 5.20 AU a = semi-major axis of the comet e = eccentricity i = inclination

7. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 7/24 JFC: 2.5 < T J < 3 Period < 20 years Aphelion ~ Jupiter distance from the Sun (5.2 AU) 2P/Halley, 9P/Tempel 1 HTC: T J < 2 20 < Period < 200 years Aphelion ~ Neptune distance from the Sun (30 AU) 1P/Halley, 8P/Tuttle Short Period Comets

8. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 8/24 The Tisserand’s parameter is very different for JFC and HTC. Besides, some of the HTC have a retrograd orbit which can not be explained if they were formed were they are now. HTC are believed to be long period comets captured by the giant planets and trapped in the inner solar system, whereas JFC were “born” as short period comets. Short Period Comets

9. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 9/24 Main belt comets ? Asteroids pretending to be comets ? or Comets pretending to be asteroids ?

10. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 10/24 Long Period Comets Period> 200 years a< 10 5 AU i± 90º 4/5 of the catalogued comets Examples: Hale-Bopp, Comet McNaught None of these parameters can be explained by simple gravitational interaction of short period comets with giant planets.

11. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 11/24 Long Period Comets This let Oort to conlude (1950) about the existence of ~10 11 comets orbiting in a spherical “cloud” at distances of 10 4 -10 5 AU. This structure, called the Oort cloud, is the source of the long-period comets that appear today. Distribution of 1/a shows a peak around 5.10 -3, typical of orbits which have not been affected by interactions with the giant planets. => Most of the comets enter the inner solar system for the first time.

12. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 12/24 Non-periodic comets These comets have an eccentricity >=1. Their orbit is a parabola or an hyperbola, thus they do not come back after the perihelion passage. Spectrometric measurements have shown that they come from the solar system (same isotope ratio). We expect similar comets coming from other solar system (~6/century) but unfortunately none has been observed so far.

13. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 13/24 Summary Short Period comets come from the Kuiper belt (30 – 55 AU) Long period & non-periodic comets come from the Oort cloud (50 000 AU) as a reference : α – Centauri (277 600 AU)

14. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 14/24 We have a problem... Comets show a 12 C/ 13 C ratio ~ 100, close to the solar system value (89) and quite different from the interstellar one (~30-50) => comets must have formed in the solar system Comets share a similar composition, => they must have formed in the same region of the early solar system, more or less beyond Neptune’s orbit.

15. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 15/24 But... => radius of accretion disk ~ 200-1000 AU => radius of Oort cloud ~ 50 000 AU Comets come from the solar system, but cannot be formed where they are now... we need a dynamical model. => The “Nice” Model We have a problem...

16. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 16/24 The “Nice” Model R. Gomes, H. F. Levison, K. Tsiganis & A. Morbidelli

17. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 17/24 The “Nice” Model Still not perfect but best model available so far. Main scenario: Original solar system much more compact than now, with the four giant planets orbiting between 5.45 and 14.2 AU, surrounded by a disk of planetesimals at 30-35 AU. ( now Jupiter is at 5.2, Neptune at 30.1, and the Kuiper Belt between 30 and 50 AU)

18. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 18/24 The “Nice” Model Planetesimals are dragged inwards by Neptune, which move then outwards to keep the angular momentum of the Solar system constant. The same process continues as the icy bodies reach Uranus and Saturn. The situation is different for Jupiter. As its gravitational force is much stronger, most of the small bodies are accelerated and ejected out of the inner solar system, which causes Jupiter to move inwards to balance the loss of angular momentum.

19. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 19/24 The “Nice” Model This slow migration goes on for ~800 Myrs, until Jupiter and Saturn cross their 1:2 mean-motion resonance orbit. The gravitational interaction between the two bodies causes an increase in Saturn eccentricity, which then affects the 2 other giant planets, eventually switching their orbits. In 4 Myrs, planets move from their original position to the current one. The disk of planetesimals “explodes” and loses 97% of it’s mass. Small bodies are ejected inwards (Late Heavy Bombardment), and outwards (Oort Cloud).

20. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 20/24 The “Nice” Model 100 Myr, beginning of planetary migration 879 Myr, just before reaching 1:2 MMR 882 Myr, just after reaching 1:2 MMR 1082 Myr, final state, only 3% of initial disk mass remains.

21. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 21/24 The “Nice” Model

22. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 22/24 Any evidence ? Source: Alessandro Morbidelli

23. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 23/24 Summary The Nice model explains the actual position of the giant planets and the Kuiper belt, explains the origin of the Oort cloud, solves the mystery of the missing mass in the Kuiper belt, explains the LHB. but... everything is based on the assumption of a more compact solar system at the beginning... Giant exoplanets have been observed very close to their star so... why not ?

24. Jean-Baptiste Vincent – Dynamics of comets 30/06/09 24/24 References: Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets. R. Gomes, H. F. Levison, K. Tsiganis & A. Morbidelli Nature Vol. 435, May 2005 Origin and dynamical evolution of comets and their reservoirs. A. Morbidelli. Lecture book available on arXiv.org + all articles written by these authors