N-body Simulationen. Gas aus dem System entwichen. Gasplaneten und eine Scheibe von Planetesimalen

Transcription

1 N-body Simulationen Gas aus dem System entwichen Gasplaneten und eine Scheibe von Planetesimalen Störende Wechselwirkung zwischen Planeten und den Planetesimalen Migration

2 The Kuiper Belt - 3 Populations Classical (stable) Belt Resonant Objects, 3/4, 2/3, 1/2 with Neptune Scattered Disk Objects Orbital distribution cannot be explained by present planetary perturbations planetary migration

3 Fernandez & Ip (1984) Standard migration model: - Semi-major axes of the planets - ~ Kuiper-belt structure - constrains the size of the initial disc (<30-35 AU, m~35-50 M Ε )

4 Problem #1: The final orbits of the planets are circular Problem #2: If everything ended <10 8 yr, what caused the

5 Ein neues Migration Modell Sind die Planeten weiter auseinander (Neptun bei ~20 AU) - leichte Migration Ein kompaktes System kann instabil werden aufgrund von Resonanzen zwischen den Planeten (und nicht close encounters)!

6 Tsiganis et al. (2005), Nature 435, p. 459 Morbidelli et al. (2005), Nature 435, p. 462 Gomes et al. (2005), Nature 435, p. 466 Alessandro Morbidelli (OCA, France) Kleomenios Tsiganis (Thessaloniki, Greece) Hal Levison (SwRI, USA) Rodney Gomes (ON-Brasil) Nice Model

7 N-body simulations: Sun + 4 giant planets + Disc of planetesimals 43 simulations t~100 My: ( e, sinι ) ~ a J =5.45 AU, a S =a J 2 2/3 - Δa, Δa < 0.5 AU U and N initially with a < 17 AU ( Δa > 2 AU ) Disc: M E, edge at AU (1,000 5,000 bodies) 8 simulations for t ~ 1 Gy with a S = AU

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9 Evolution of the planetary system A slow migration phase with (e,sini) < 0.01, followed by Jupiter and Saturn crossing the 1:2 resonance eccentricities are increased chaotic scattering of U,N and S (~2 My) inclinations are increased Rapid migration phase: 5-30 My for 90% Δa

10 Crossing the 1:2 resonance

11 The final planetary orbits Statistics: 14/43 simulations (~33%) failed (one of the planets left the system) 29/43 67% successful simulations: all 4 planets end up on stable orbits, very close to the observed ones Red (15/29) U N scatter Blue (14/29) S-U-N scatter Better match to real solar system data

12 Jupiter Trojans Trojans = asteroids that share Jupiter s orbit but librate around the Lagrangian points, δλ ~ ± 60 o We assume a population of Trojans with the same age as the planet A simulation of 1.3 x 10 6 Trojans all escape from the system when J and S cross the resonance!!! Is this a problem for our new migration model?

13 No! Chaotic capture in the 1:1 resonance The total mass of captured Trojans depends on migration speed For 10 My < T mig < 30 My we trap M Tro This is the first model that explains the distribution of Trojans in the space of proper elements ( D, e, I )

14 The timing of the instability What was the initial distribution of planetesimals like? 1 My < Τ inst < 1 Gyr Depending on the density (or inner edge) of the disc LHB timing suggests an external disc of planetesimals in agreement with the short dynamical lifetimes of particles in the proto-solar nebula

15 Late Heavy Bombardment A brief but intense bombardment of the inner solar system, presumably by asteroids and comets ~ (3.9±0.1) Gyrs ago, i.e. ~ 600 My after the formation of the planets Petrological data (Apollo, etc.) show: Same age for 12 different impact sites Total projectile mass ~ 6x10 21 g Duration of ~ 50 My We need a huge source of small bodies, which stayed intact for ~600 My and some sort of instability, leading to the bombardment of the inner solar system

16 1 Gyr simulation of the young solar system

17 The Lunar Bombardment Two types of projectiles: asteroids / comets ~ 9x10 21 g comets ~ 8x10 21 g asteroids (crater records 6x10 21 g) The Earth is bombarded by ~1.8x10 22 g comets (water) 6% of the oceans Compatible with D/H measurements!

18 The NICE model assumes: Conclusions An initially compact and cold planetary system with P S / P J < 2 and an external disc of planetesimals 3 distinct periods of evolution for the young solar system: 1. Slow migration on circular orbits 2. Violent destabilization 3. Calming (damping) phase Main observables reproduced: 1. The orbits of the four outer planets (a,e,i) 2. Time delay, duration and intensity of the LHB 3. The orbits and the total mass of Jupiter Trojans

19 Solar system architecture Inner (terrestrial) planets: Mercury Venus Earth - Mars (1.5 AU) Main Asteroid Belt (2 4 AU) Gas giants: Jupiter (5 AU), Saturn (9.5 AU) Ice giants: Uranus (19 AU), Neptune (30 AU) Kuiper Belt (36 50 AU) + Pluto +...

20 Are there Planets outside the Solar System? First answer : 1992 Discovery of the first Extra- Solar Planet around the pulsar PSR (Wolszczan &Frail) Are there Planets moving around other Sun-like stars?

21 The EXO Planet: 51 Peg b Mass: M sin i = m_jup semi-major axis: a = AU period: p = 4.23 days eccentricity: e = 0 Discovered by: Michel Mayor Didier Queloz a of Mercury: AU

22 Status of Observations 452 Extra-solar planets 43 Mulitple planetary systems 43 Planets in binaries

23 Questions How frequent are other planetary systems? Are they like our Solar System? (no. of planets, masses, radii, albedos, orbital paramenters,. ) What type of environments do they have? (atmospheres, magnetosphere, rings, ) How do they form and evolve? How do these features depend on the type of the central star (mass, chemical composition, age, binarity, )?

24 Extra-solare Planeten ca. 130 Planeten entdeckt massereich (~M jup ) enge Umlaufbahnen Radialgeschwindigkeitsmessungen

25 Distribution of the detected Extra-Solar Planets Mercury Earth Mars Venus Jupiter

26 Mass distribution

27 55 Cancri 5 Planeten bei 55 Cnc: 55Cnc d -- the only known Jupiter-like planet in Jupiterdistance Binary: a_binary= 1000 AU

28 Facts about Extra-Solar Planetary Systems: Only 28% of the detected planets have masses < 1 Jupitermass About 33% of the planets are closer to the host-star than Mercury to the Sun Nearly 60% have eccentricities > 0.2 And even 40% have eccentricities > 0.3

29 Sources of uncertainty in parameter fits: the unknown value of the orbital line-of-sight inclination i allows us to determine from radial velocities measurements only the lower limit of planetary masses; the relative inclination i r between planetary orbital planes is usually unknown. In most of the mulitple-planet systems, the strong dynamical interactions between planets makes planetary orbital parameters found using standard two-body keplerian fits unreliable (cf. Eric Bois) All these leave us a substantial available parameter space to be explored in order to exclude the initial conditions which lead to dynamically unstable configurations

30 Multi-planetary systems Binaries Single Star and Single Planetary Systems

31 SEMI-MAJOR AXIS Major catastrophe in less than years TIME (yr) (S. Ferraz-Mello,

32 Chaos Indicators: Fast Lyapunov Indicator (FLI) Numerical Methods Long-term numerical integration: C. Froeschle, R.Gonczi, E. Lega (1996) MEGNO RLI Helicity Angle Stability-Criterion: No close encounters within the Hill sphere (i)escape time (ii) Study of the eccentricity: maximum eccentricity LCE

33 The Fast Lyapunov Indicator (FLI) (see Froeschle et al., CMDA 1997) a fast tool to distinguish between regular and chaotic motion length of the largest tangent vector: FLI(t) = sup_i v_i(t) i=1,...,n (n denotes the dimension of the phase space) it is obvious that chaotic orbits can be found very quickly because of the exponential growth of this vector in the chaotic region. For most chaotic orbits only a few number of primary revolutions is needed to determine the orbital behavior.

34 Multi-planetary systems Binaries Single Star and Single Planetary Systems

35 ExoStab appropriate for single-star single-planet system - Stability of an additional planet - Stability of the habitable zone (HZ) - Stability of an additional planet with repect to the HZ

36 Stability maps Inner region (Solar system type) Outer region (Hot-Jupiter-type)

37 Computations distance star-planet: 1 AU variation of - a_tp:[0.1,0.9] [1.1,4] AU - e_gp: M_gp: 0 and 180 deg - M_tp: [0, 315] deg Dynamical model: restricted 3 body problem Methods: (i) Chaos Indicator: - FLI (Fast Lyapunov) - RLI (Relative Lyapunov) (ii) Long-term computations - e-max

38 ANIMATION

39 How to use the catalogue HD114729: m_p=0.82 [Mjup] (0.93 [Msun]) a_p= 2.08 AU e_p=0.31 m=0.001 HZ: AU

40 m = HD10697: m_p= 6.12 [Mjup] (1.15 Msun) a_p = 2.13 AU e_p = 0.11 HZ: AU

41 Multi-planetary systems:

42 Multi-Planeten Systeme Stabiliät des Planetensystems muss überprüft werden

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44 Gliese 876 d c b a [AU] P[days] e m sin i

45 CoRoT Exo 7 b

46 Spacing of Planets -- Hill criterion Convenient rough proxy for the stability of planetary systems In its simpliest form for planets of equal mass on circular orbits around a sun-like star

47 Two adjacent orbits with separation Dai=ai+1 ai have to fullfill:

48 mass-dependency closer spacing for smaller mass planets

49 Determination of Planetary Periods: Using Kepler s third law in its log-differential Form (d ln(p) = 3/2 d ln(a)) obtain the periods Pi -1 (D Pi / Pi) gives the periodic scaling for the planets

50 Numerical Study Fictitious compact planetary systems: Sun-mass star up to 10 massive planets (4/17/30 Earthmasses) ap= 0.01AU 0.26 AU e, incl, omega, Omega, M: 0

51 Compact planetary system using the Hill- Criterion: mp=1earth-mass

52 Class Ia -- Planets in mean-motion resonance This class contains planet pairs with large masses and eccentric orbits that are relatively close to each other, where strong gravitational interactions occur. Such systems remain stable if the two planets are in mean motion resonance (MMR).

53 Star Planet mass_p a_p e_p Period [M_Sun] [M_Jup] [AU] [days] GJ 876 b (0.32) c Cnc b (1.03) c HD82942 b (1.15) c HD b (1.15) c

54 How important are the resonances for the long term stability of multi-planet systems?

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56 Systems in 2:1 resonance GJ876 b GJ876c HD82 b HD82 c HD160 b HD160 c A [AU]: e: M.sin i: [M_jup] Gliese 876 HD82943 HD160691

57 SEMI-MAJOR AXIS Major catastrophe in less than years TIME (yr) (S. Ferraz-Mello,

58 . HD c,b : A case study (S.Ferraz-Mello)

59 HD82943 Aligned Anti-aligned

60 Periastra in opposite directions Equivalent pairs, depending on the resonance A2 A1 S P1 P2 Periastra in the same direction A P S P 2 A Periastra in the same direction S - P 1 - P 2 S - A 1 - A 2 A 1 - S - P 2 P 1 - S - A 2 Periastra in opposite directions S - P 1 - A 2 S - A 1 - P 2 P 1 - S P 2 A 1 - S A 2