Planetesimal Dynamics Formation of Terrestrial Planets from Planetesimals

Transcription

1 Planetesimal Dynamics Formation of Terrestrial Planets from Planetesimals Protoplanetary disk Gas/Dust Planetesimals yr yr Protoplanets yr Terrestrial planets Eiichiro Kokubo National Astronomical Observatory of Japan

2 Outline Basic Dynamics of Planetesimals (e.g., Stewart & Wetherill 1988; Ida 1990; Ida & Makino 1992a, b) Runaway Growth of Planetesimals Oligarchic Growth of Protoplanets (e.g., Wetherill & Stewart 1989; Kokubo & Ida 1996) (e.g., Kokubo & Ida 1998, 2002; Thommes+ 2003; Chambers 2006) Giant Impacts of Protoplanets (e.g., Chambers & Wetherill 1998; Agnor+ 1999; Kominami & Ida 2002; Raymond+ 2004; Kokubo+ 2006) Formation of Terrestrial Planets: The Movie (Miura & Kokubo 2007)

3 Basic Hypotheses of Planet Formation Disk Hypothesis A planetary system forms from a light circumstellar disk (protoplanetary disk) that is a by-product of star formation. A protoplanetary disk consists of gas and dust. Planetesimal Hypothesis Planetesimals are formed from dust. Solid planets are formed by accretion of planetesimals. Gaseous planets are formed by gas accretion onto solid planets ( core accretion model). (Safronov 1969; Hayashi+ 1985)

4 Terrestrial Planet Formation Scenario Protoplanetary disk Gas/Dust Planetesimals yr yr Protoplanets yr Terrestrial planets Act 1 Dust to planetesimals (gravitational instability/binary coagulation) Act 2 Planetesimals to protoplanets (runaway-oligarchic growth) Act 3 Protoplanets to terrestrial planets (giant impacts)

5 Terrestrial Planet Formation Scenario Protoplanetary disk Gas/Dust Planetesimals yr yr Protoplanets yr Terrestrial planets Act 1 Dust to planetesimals (gravitational instability/binary coagulation) Act 2 Planetesimals to protoplanets (runaway-oligarchic growth) Act 3 Protoplanets to terrestrial planets (giant impacts)

6 Terminology Random Velocity Deviation velocity from a non-inclined circular orbit v ran e 2 + i 2 v K e : eccentricity, i : inclination, v K : Kepler velocity σ R σ e, σ z σ i Hill (Roche/Tidal) Radius Radius of the potential well of an orbiting body r H = ( m 3M ) 1/3 a m : body mass, a : semimajor axis

7 Planetesimals planetesimals Surface density distribution ( a ) α Σ solid = Σ 1 gcm 2 1 AU Assumptions no radial migration perfect accretion 1 Σ 1 100, 1/2 α 5/2 standard protosolar disk: Σ 1 10, α = 3/2

8 Equation of Motion dv i dt = GM x i x i 3 } {{ } solar gravity + N x j x i Gm j x j x i 3 j i } {{ } mutual interaction + f gas }{{} + f }{{} col gas drag collision effect solar gravity (dominant) nearly Kepler orbits mutual interaction random velocity gas drag random velocity collision random velocity mutual interaction + gas drag equilibrium random velocity

9 Two-Body Relaxation of Planetesimals Elementary Process Two-body gravitational scattering Viscous Stirring (Disk Heating) increase of random velocity v ran (e and i) Dynamical Friction equiparation of random energy mv 2 ran m(e 2 + i 2 )

10 Viscous Stirring increase of e and i (σ e > σ i ) diffusion in a

11 Viscous Stirring Two-body relaxation in a differentially rotating disk σ e, σ i t 1/4 (two-body relaxation timescale) σ e /σ i 2 (anisotropic velocity dispersion) (Ida 1990; Ida, Kokubo &Makino 1993)

12 Dynamical Friction decrease of e M and i M ( increase of local e and i) almost constant a M

13 Dynamical Friction Two-body relaxation in a differentially rotating disk e M, i M 0 (non-inclined circular orbit) (sufficient condition for runaway growth)

14 Growth Mode d dt ( M1 M 2 ) = M 1 M 2 ( 1 dm 1 M 1 dt 1 M 2 dm 2 dt ) relative growth rate: 1 M dm dt M p orderly growth runaway growth p<0 p>0

15 Collisional Cross-Section v rel R gf M R v esc Gravitational focusing ( R gf = R 1 + 2GM rvrel 2 ) 1/2 ( ) 1/2 = R 1 + v2 esc vrel 2 Collisional cross-section ( ) S gf = πrgf 2 = πr2 1 + v2 esc vrel 2

16 Growth Rate M R m Test body: Field bodies: M, R, v esc n, m dm dt ( ) nπr v2 esc vrel 2 v rel m 1 M dm dt M 1 3 v 2 ran ( v rel v ran, n v 1 ran, v esc M 1/3, R M 1/3, v rel < v esc ) Random velocity controls the growth mode the growth timescale

17 Runaway Growth of Planetesimals yr e yr yr self-gravity of planetesimals dominates 1 M dm dt v ran f(m) M 1 3 v 2 ran M 1 3 runaway growth! a (AU) (Kokubo & Ida 2000)

18 Runaway Growth of Planetesimals 23 M max,<m>(10 g) t (yr) solid: M max, dashed: m (Kokubo & Ida 2000)

19 Oligarchic Growth of Protoplanets y y Slowdown of runaway scattering of planetesimals by a protoplanet with M > 100m e y y 1 M v ran r H M 1/3 dm dt M 1 3 v 2 ran M 1 3 orderly growth! y Orbital repulsion a(au) (Kokubo & Ida 2002) orbital separation: b 10r H (Kokubo & Ida 1998)

20 Protoplanets protoplanets Isolation mass M iso 2πabΣ solid = 0.16 ( ) 3/2 ( ) 3/2 b Σ1 ( a ) (3/2)(2 α) M AU b : orbital separation, b = b/r H Growth time T grow ( b 10 ) 1/10 ( Σ1 10 ) 9/10 ( a ) (9α+16)/10 yr 1 AU (Kokubo & Ida 2002)

21 Isolation Mass of Protoplanets snow line J Standard protosolar disk Σ 1 = 10, α = 3/2 Terrestrial Planet Zone M iso 0.1M large planets: impacts among protoplanets small planets: protoplanet mass [Earth mass] Me V E Ma S U N leftover protoplanets heliocentric distance[au] (Kokubo & Ida 2000)

22 Protoplanets to Terrestrial Planets Giant Impacts among Protoplanets Protoplanets gravitationally perturb each other to become orbitally unstable after gas dispersal log T inst c 1 (b/r H ) + c 2 (e.g., Chambers+ 1996; Yoshinaga+ 1999) protoplanets giant impacts terrestrial planets

23 Timescale of Orbital Instability Chambers+ (1996) log T inst c 1 (b ini /r H ) + c 2 (Yoshinaga, Kokubo & Makino 1999)

24 Giant Impacts of Protoplanets (Kokubo, Kominami & Ida 2006)

25 Total Mass-Planet Mass Σ 1 = 3( ), 10( ), 30( ), r in = 0.5AU, r out = 1.5, 2.0, 2.5, 3.0AU M 1 :, M 2 : M 1 0.4M tot, M 2 0.3M tot (global accretion!) (Kokubo & Ida 2009)

26 Spin Parameters dotted line: critical ω for rotational breakup dotted line: isotropic distribution ( ) 1/2 ρ ω ω cr = 3.3 3gcm 3 hr 1 isotropic : ndε = 1 2 sin εdε (Kokubo & Ida 2007)

27 Mass large planets: M M tot Terrestrial Planets small planets: leftover protoplanets Orbital elements e, i 0.1 (higher than the solar system values!) Spin parameters angular velocity: breakup velocity ω cr obliquity: isotropic distribution (ε 90 ) Radial mixing terrestrial planet zone wide (Kokubo+ 2006; Kokubo & Ida 2007, 2009)

28 Oligarchic Growth Stage Important Effects Type I migration (e.g., Daisaka+ 2005; McNeil+ 2005) Collisional disruption Giant Impact Stage Perturbation by gas giants (e.g., Chambers 2001) Gravitational gas drag (e.g., Kominami & Ida 2002) Dynamical friction from residual planetesimals (e.g., Agnor+ 1999; O Brien+ 2006) Sweeping secular resonance due to gas disk dispersal (e.g., Nagasawa+ 2005) Hit-and-run collisions (Agnor & Asphang 2004; Kokubo & Genda 2009)

29 Summary Orbital Dynamics Viscous stirring Dynamical friction Orbital instability Accretionary Dynamics Runaway growth Oligarchic growth Giant impacts

30 Movie Formation of Terrestrial Planets: The Movie Simulations: Kokubo & Ida (2002) Kokubo, Kominami & Ida (2006) Kokubo & Ida (2007) Genda, Kokubo & Ida (2009) Visualization: Miura & Kokubo (A 4D2U NAOJ Production)