Extrasolar Planets: Dynamics and Formation - Numerical Simulations for Terrestrial Planet Formation

Transcription

1 Extrasolar Planets: Dynamics and Formation - Numerical Simulations for Terrestrial Planet Formation Jianghui JI 1, 3 Collaborators: Lin LIU 2, H. Kinoshita 4, H. Nakai 4, G. LI 1, 3 J. E. Chambers 5, R. P. Butler 5, S. Ou 6 jijh@pmo.ac.cn (1) Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing , China (2) Department of Astronomy, Nanjing University, Nanjing , China (3) National Astronomical Observatory, Chinese Academy of Sciences, Beijing , China (4) National Astronomical Observatory, Mitaka, Tokyo , Japan (5) Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Road, NW, Washington DC (6) High Performance Computing, Center for Computation and Technology, Louisiana State University, Baton Rouge, LA , Winter Workshop on Planetary Astrophysics, KIAA-PKU

2 Outline Brief Introduction on background Disk-planet interaction Dynamics of the Planetary Systems Terrestrial Planets Formation

3 Nebular Hypothesis the Sun and planets formed together out of a rotating cloud of gas (the solar nebula ) gravitational instabilities in the gas disk condense into planets (Kant 1755) or maybe the protosun cools and contracts and sheds rings of gas that condense into planets (Laplace 1796) variations might work to form Jupiter, Saturn, extrasolar gas giants but not Uranus, Neptune, terrestrial planets

4 Extrasolar planets : a e diagram Inward Migration: Three-body interaction (Weidenschilling &Marzari 1996; Rasio & Ford 1996) Resonant interactions between the planet and planetesimals (Murray et al. 1998) Disk-planet interaction (Goldreich & Tremaine 1978; Lin et al. 1996) As of Dec. 16, 2009, 412 planets, over 40 multiple systems

5 Extrasolar planets: a mass diagram As of Dec. 16, 2009, 412 planets, over 40 multiple systems

6 Young Stars have Protoplanetary Disks Typical Disk lifetime are 3 Myr or less, Haisch et al. ApJ, 2001

7 The problem: Dynamics of Planetary Systems A point mass is surrounded by N much smaller masses on nearly circular, nearly coplanar orbits. Is the configuration stable over very long times (up to orbits)? The issues: how do planetary embryos evolve into planets? why are there so few planets? Are there more low-mass (terrestrial) planets? why are the regions between the planets so clean (asteroidal structure)? what is the fate of the Earth? Other Earths? where do comets, meteors, and Centaurs, KBOs come from? what can extrasolar planetary systems look like? Similar to ours (solar system analogs)? are properties of planetary systems determined at creation or by evolution? how do dynamical systems behave over very long times? What s the importance of the resonance in the secular evolution? How the planets evolved into the resonance?

8 The Planetesimal (Safronov) Hypothesis Forming Sun is surrounded by a gas disk (like nebular hypothesis) Planets form by multi-stage process: 1. as the disk cools, rock and ice grains condense out and settle to the midplane of the disk 2. small solid bodies grow from the thin dust layer to form km-sized bodies ( planetesimals ) - gas drag and solar gravity are dominant processes 3. planetesimals collide and grow to become planets or planetary cores gravitational scattering and solar gravity are dominant processes. Molecular chaos applies and evolution is described by statistical mechanics 4. a few planetesimals grow large enough to dominate evolution. Orbits become regular or weakly chaotic and are described by celestial mechanics rather than statistical mechanics ( planetary embryos ) 5. on much slower timescales, planetary embryos collide and grow into planetary cores 6. cores of intermediate and giant planets accrete gas envelopes Tremaine

9 Planet Formation Lissauer Chambers (1998, 2001, 2006) Core-accretion model Lin Gravitational Instability model Boss Note: Core-accretion model is unable to explain the gaseous planet formed about M Dwarf stars

10 Core-accretion model Core accretion scenario 1. Coalescence of solid particles. Growth from dust to rocky planets. 2. Large rocky planets (>= 10 M ) accrete gas and form gas planets

11 Formation of Jovian planets Existence of Uranus and Neptune prove that solid cores can form These might accrete gas from the disk to form Jupiter/Saturn - like of planets. Bottle necks: Should be able to form a core quickly enough Should accrete gas fast, before disk disperses Timescale of gas dissipates?

12 Type I migration Planet s gravity launches spiral waves in disk These spiral waves exert torque on planet: Inner spiral wave pushes planet outward Outer spiral wave pushes planet inward Outer spiral wave wins: inward migration

13 Type II migration Massive planet opens a gap Accretion in the disk is stopped by the gap If the disk is massive enough: accretion continues, simply by pushing the planet inward. Planet is locked to the disk accretion. Type II migration If the disk is not massive enough: planet will not migrate. Inner disk will deplete

14 Disk-planet interaction

15 Basic Equations, Methods and Initial Setup To study the interaction between a disk and an embedded planet requires coupling hydrodynamics and orbital dynamics together. Here, we follow Nelson et al. (2000) and many previous investigations to reduce the problem to a two-dimensional (2D) one since the disk is considered to be very thin. Three dimensional (3D) investigations will be postponed to future. The fluid motion inside the disk is described by the vertically integrated continuity equation (1), radial and azimuthal components of the Navier-Stokes equation (2) and (3), ( v) 0 t (1) 2 ( vr ) v P ( vrv) fr t r r r (2) ( v ) vrv 1 P ( v v ) f t r r r (3) See Ou, Ji, et al. 2007, ApJ, for details

16 HD Simulations: (I) Test Run a Jupiter-mass planet Fig. 1 The top and bottom panels show, respectively, (R) and x(r) of a viscous disk with a Jupiter-mass planet averaged azimuthally at t 0 (solid line), 100 (dotted line), and 200 (dashed line) orbits for the higher resolution run (256 x 512). See also Kley s talk Fig. 2 Logarithmic color map of surface density distribution for a viscous disk with a Jupiter-mass planet at t 200 orbits for the higher resolution run (256 x 512). The horizontal axis is the radial axis ranging from 0.4 to 2.5, the vertical axis is the azimuthal direction spanning over 2p range with the planet shifted to around the middle. A letter P" is labeled next to the location of the planet. The color bar represents relative rather than absolute values

17 (II) Case of a Neptunian-mass planet on a circular orbit Fig. 4 The top and bottom panels show, respectively, (R) and x(r) of the disk with a Neptune-mass planet averaged azimuthally at t 0 (solid line), 60 (dotted line), and 120 (dashed line) orbits for the higher resolution run (400x 1600). Fig. 5 The same as Fig. 2 but in linear scale for an inviscid disk with a Neptune-mass planet at t 150 orbits. A letter ``P" is labeled next to the location of the planet, with a resolution run (400x 1600).

18 III. The migration of a Neptune-mass planet Fig. 12 Time evolutions of the total torque (top) exerted on a Neptune mass planet by the disk and the radius of the planet (bottom) for the run in which the planet is allowed to move. A nonmonotonic behavior for the migration speed is observed. Fig. 13 The same as Fig. 5 but at t 103 orbits for a run, in which a Neptune mass planet is allowed to move. The planet is penetrating the high density region around r ~ 0.88 and a fairly large density blob forms (green arc-like structure at the edge of inner disk

19 Dynamics of the Planetary Systems

20 Quantitative analysis on planetary stability Wisdom, Malhotra, Chiang,... Wu, Murray Ji, Liu, Kinoshita,et al. Beauge, Hadjidemetriou Zhou, Sun...

21 Laplace-Lagrange theory and numerical reults Ji et al. ApJ, 2007

22 Multi-planet systems Marcy et al. (2005) Resonant systems P 1 / P 2 < 5:1 2:1 MMR: 4, GJ 876, HD 82943, HD128311, HD :1 MMR: 2, 55 Cancri, Hierachical systems P 1 / P 2 >> 5:1 HD168443, HD 38529

23 Resonant systems: three types of stable orbits for 2:1 MMR Ji et al., 2003a, ApJ

24 Expanding of Disturbing Potential

25 Coplanar analytical model for the eccentricity Ji, Kinoshita, Liu et al. 2003, Cel. Mech., 87, 113

26 Hamiltonian Contour for HD Type III Type II Numerical results

27 Convergent migration - Damped N-body model Lee & Peale (2002), ApJ

28 Convergent migration - Hydrodynamical model Kley et al. (2004), A&A See also Kley s review talk

29 Habitable Zones for Earth-like Planets Provide a suitable environment for ex-biological life evolution Kasting et al. (1993) found the following values for the present HZ in the solar system: 1. most conservative case: 0.95 AU AU, 2. least conservative case: 0.75 AU AU, 3. intermediate case : 0.84 AU AU. Condition: Kasting et al The zero age main sequence HZ as a function of central star mass (in solar masses M) for the intermediate case of climatic constraints. The long-dashed lines delineate the probable terrestrial planet accretion zone. The dotted line is the orbital distance, for which an Earth-like planet in a circular orbit would be locked into synchronous rotation (tidal locking). Water (liquid state) 273K -373K Temperature constraint Atmosphere presensence, composition (CO2 /H2O/N2 ), greenhouse Obliquity (the tilt angle of the spin axis to its orbit) Rotation rate Stellar luminosity Stable orbits in the HZ

30 Case study: 47 Uma Planetary System Doppler measurements exhibiting the two planets, Fischer et al. (2002) Name : 47 Uma Distance : 13.3 pc Spectral Type: G0V Apparent Magnitude: V = 5.10 Mass : 1.03 Msun Metallicity [Fe/H] Right Asc. Coord Decl. Coord

31 Numerical simulations Masses of the terretrial planets : 0.1 Me < M < 10 Me Orbital parameters : 0.05 AU <= a <= 2.0 AU, spaced 0.01 AU 0.0 <= e <= < I < 5.0 Typical integration time: 1 Myr - 10 Myr, Over 3000 simulations carried out Purpose : understand the dynamical structure or Habitable zones in 47 Uma Questions: the presence of the inner low-mass terrestrial planets, the asteroidal belts or Kuiper belts (e.g. Spitzer Mission) around central stars? Ji et al. (2005), ApJ

32 Habitable Zones in 47 UMa (I) 0.05 <= a < 0.40 AU 0.40 < = a < 1.0 AU v1 v2 The contour of status of the final eccentricities for Earth-like planets, the vertical axis for the initial e. Left: 0.05 <= a < 0.40 AU for 1 Myr. Notice v1 secular resonance at ~ 0.30 AU pumps up the eccentricities. Right: 0.40 <= a < 1.0 AU for 5 Myr. The e of the orbits with 0.70 AU < a < 0.78 AU can be excited and in the 2:9 MMR at ~ 0.76 AU, e can reach ~ Ji et al. (2005), ApJ Two secular resonances: v1 and v2, similar to v5 and v6, for Jupiter and Saturn

33 Secular resonances excite eccentricity Possible to form close-in Earth-like planets? Ji et al., in prep.

34 Habitable Zones in 47 UMa (II) 1.00 <= a < 1.30 AU 1.30 <= a < 1.60 AU 3:1 5:2 2:1 3:2 The surviving time for Earth-like planets for the integration of 10 Myr, the vertical axis is the same as Fig.2. Left: for 1.0 AU <= a < 1.3 AU, see the gap for the 5:2 MMR at ~ 1.13 AU. Right: for 1.3 AU <= a < = 1.6 AU, a population of the terrestrial planets is about 9:5 MMR at ~ 1.40 AU for low eccentricities.

35 Dynamical structure in 55 Cancri Ji et al. 2009

36 Summay on dynamics works of extrasolar planets We studied the dynamics of the resonant planetary systems as GJ 876 (Ji et al. 2002, ApJ), HD (Ji et al., 2003a, ApJ), 55 Cancri (Ji et al., 2003b, ApJ) and other multi-planet systems. We showed the evidence that the two inner planets of 55 Cnc can be locked into a 3:1 mean motion resonance (MMR) and found that the crossing stable orbit for HD (Ji et al., 2003, CeMDA) both in a 2:1 MMR and apsidal resonance, then presented the theoretical models to explain the orbital motions of the planets; further revealed an important phenomenon to characterize the multiple systems that a pair of planets in most extrasolar systems are inclined to be in an apsidal alignment or antialignment, which can be considered as a vital dynamical mechanism of stabilizing the exosystems. We also studied the potential habitable Earth-like planets in the extrasolar systems (e.g. 47UMa, Ji et al. 2005, ApJ ; Ji et al. 2007, ApJ) and found the secular resonance will significantly influence their motion.

37 Terrestrial Planets Formation

38 Formation of the inner solar system

39 Planetesimal growing to planetary embryos Kokubo & Ida (2002), ApJ

40 Embryos collide to form Terrestrial Planets Relative velocities are high so growth is slow. Embryos rarely escape Sun so they eventually form planets. Chambers 2001

41 Late stage terrestrial planets formation Consider one giant, Jupiter Raymond (2004)

42 Our model Jupiter-Saturn model Saturn mass varies Initial data for embryos and planetesimals 0.5 AU <= a <=4.2 AU, both 6.2 AU <= a <=9.6 AU, simply planetesimals e(0-0.02), i( ) 1a, 2a, 3a, self-gravity 1b, 2b, 3b, no self-gravity among planetesimals Simulation Time: 400 Myr see Zhang & Ji (2009) In the late stage of planetary formation, massive protoplanets grow slowly than the smaller ones (oligarchic growth), and most planetesimals remain small. The final stage of terrestrial planet formation would be giant impacts among massive protoplanets.

43 Initial Setup Use the model 1.5 MMSN,the surface density profile as follows: where The mass of a planetary embryo increases as : The planetesimals equal masses,the number distribution follows (Kokubo et al. 2000; Raymond et al. 2004; Stevenson et al. 1988)

44 Simulation 2a

45 Simulation 2b

46 Table 1 The properties of the terrestrial planets from simulations 2a and 2b Planets a (AU) e i ( ) m (M ) Water mass (%) 2a b a c a d b b b c b d b e

47 Mass accretion

48 Habitable Zone

49 Statistics properties Table 2 Properties of terrestrial planets from different systems. system accretion rate n concentration 1a % b % a % b % a % b % a-3b % solar

50 Mechanisms of forming close-in super-earths Most of the discovered super-earth planets so far are shortperiod planets, with orbits extremely close to its parent star. Migration and scattering are two possible formation mechanisms for such planets, while migration are most common around low-mass star (Kennedy & Kenyon, 2008). Close-in earth-like planet may have formed during the inward migration of a giant planet ( Raymond et al, 2006 ), with (1) short-period or (2) solitary eccentric giants and (3) systems that contain intermediate-period resonant giants, based on the sequential accretion model (Zhou et al, 2005). Any new mechanism?

51 Earths can form after Giant Planets Migrate Migrating giant removes embryos & planetesimals from inner disk. Ice-rich material moves into inner disk afterwards. Prediction: Hot Jupiters associated with water-rich terrestrial planets. Raymond et al. 2006, Science

52 Numerical Setup The simulation using a hybrid symplectic algorithm provided by the MERCURY integration package (Chambers, 1998). Selfgravity among planetesimals. Simulation 1: 648 planetary embryos ( e < 0.02; 0.4 AU < a < 1.6 AU ) with total 5.14 Earth-mass, and two giants [ (M, a, e) = (2.9 MJ,2.08 AU,0.05), and (1.1 MJ,3.97 AU,0.001) ], 100 Myr. Simulation 2: 500 planetary embryos ( e < 0.02; 0.3 AU < a < 5.2 AU ) with total 10 Earth-mass, and two giants simulate the OGLE BLG-109L system [ (M,a,e) = (0.71 MJ, 2.3 AU,0.001), and (0.27 MJ, 4.6 AU,0.11) ], 400 Myr. Ji & Jin, in prep.

53 Close-in Earth-like planets formed by violent collision In the late stage, the giant impacts occur, the orbital crossing and collisions, merges (the craters on the larger planets, their moons, the asteroids), last for long time. Here, we present a potential mechanism to form close-in Earth-like planets by collision. In the late stage of planet formation, without the migration of giant planets, one planetary embryo could be shifted to close-in orbit immediately after a collision with another embryo, then seize by the central star, tidally interact. We present two examples that out of about 20 simulations of late stage planetary accretion.

54 Case 1, a collision occured at 2.2 Myr, the embryo was shifted into 0.06 AU.

55 Case 2, a collision occured at 0.71 Myr, the embryo was shifted into AU.

56 Snapshot of simulation 2

57 Final configuration of two simulations

58 Summary The dynamical structure of the planetary system is related with mean motion resonances and secular resonance with respect to giant planets. Several terrestrial planets can be formed in the habitable zones in the planetary systems, similar to our solar system. This may imply the solar system may be common. Earth-like planets with close-in orbits may be formed in the late stage formation due to a collision. Such process may be relevant to the number and total mass of the planetesimals or embryos in the inner region.

59 Future Prospects The Era for ELTs: Giant Magellan Telescope (GMT, 25m), the Thirty Meter Telescope (TMT, 30m), and the European Extremely Large Telescope (E-ELT, 42m): direct imaging of gas giants, the characterization of their atmospheres. probe the earliest stages of the formation of planetary systems detect water and organic molecules in protoplanetary discs around stars, discovery Earth-like planets in the habitable zones Space missions: GAIA, SIM, Are we alone? Solar system common or uncommon?

60 Thank you!