Dynamics of Extra-solar Planetary Systems with Hot Jupiters

1. Dynamics of Extra-solar Planetary Systems with Hot Jupiters USP-UNC team on Exoplanets: C. Beaugé (UNC) S. Ferraz-Mello (USP) T. A. Michtchenko (USP)

2. Why do we study the Dynamics of Extrasolar Planetary Systems ? To know how stable they are ! Ref: Brasil CoRoT week, Natal2004

3. 3 (4) classes Ia – Planets in mean-motion resonances Ib – Low-eccentricity Non-resonant Planet Pairs II – Non-resonant Planets with a Significant Secular Dynamcis III – Weakly interacting Planet Pairs

4. Period ratio of consecutive planets in a system III II I

5. Class Ia – Planet pairs in Mean-Motion Resonance

6. GJ 876 (0,0) apsidal corotation resonance

7. SYMMETRIC APSIDAL COROTATIONS  (0,0) Ref:Beaugé et al., Lee and Peale Hadjidemetriou et al. 2002-2003-2004

8. M0=1.15 Msun m1=1.7 Mjup/sin i m2=1.8 Mjup/sin i

9. The orbits of the least-squares solution are bound to a catastrophic event in less than 100,000 years. Ref: Ferraz-Mello et al. (ApJ 2005)

10. The planets of 47 UMa M = 2.9 M M = 1.1 M 1 Jup 2 Jup

11. Class Ib – Low-eccentricity Near-resonant pairs Outer Solar System

12. Solar System with Saturn initialized on a grid of different initial conditions 2/17/3 5/2 8/3 . 50 Myr Collision Chaos Order Grid: 33x251 Ref: Michtchenko (unpub.)

13. Class Ib – Low-eccentricity Near-resonant pairs Near Resonant Pulsar Planets

14. Neighborhood of the 3rd planet of pulsar B1257 +12 collision Grid: 21x101 Pulsar system initialized with planet C on a grid of different initial conditions. The actual position of planet C is shown by a cross. (N.B. I=90 degrees)

15. One question: (Brasil CoRoT week, Natal 2004) Is it possible to find a system of two close-in planets with period ratio close to 2.5?

16. Dynamical Map of the Neighborhood of the 5:2 MMR e1 e2=0.04 26x40 px cf TAM

17. TIDAL EVOLUTION OF SYSTEMS OF HOT JUPITERS DIVERGENT MIGRATION If the star rotation is slower than the orbital motion of the inner planet, the migration is divergent.

18. INTERACTION WITH RESONANCES Consequences: Enhancement of eccentricities and inclinations, semi-major axis discontinuities, but no capture into the resonance.

19. Example (highly hypothetical) Masses 0.82 Sun 1.1e-4 star 7.2e-4 star --2:1-- ----crossing Time units ~ 2 x 10 4to 5 x 10 5 years t41227.dat

20. (same example as before) 2:1 7:4 --- 3:1---- 5:2----

21. (same example as before)

22. One more realistic example Masses 0.82 Sun 1.1e-4 star 7.2e-4 star Time units ~ 2 x 10 4to 5 x 10 5 years t41223.dat

23. (same example as before) 3:1 ------ t23e

24. (same example as before)

25. SCALING: Adopted value of k2 / Q ~ 2 x 10-3 Actual values cf. Paetzold & Rauer, 2002 7 x 10-8 < k2 / Q < 2 x 10-6 Hence, the scaling is in the range 10 3to 3 x 10 4

26. Synchronization (due to tides raised on the planet) Scaling ~ 10 3 t41231.dat

27. The tidal theories fail to give the right period for large satellites (oceans ?) The spin-orbit synchronization weakens the action of torques due to planet tides. Only remaining effect: fast circularization

28. A new example. start: 2:1 ACR Tides on both star and planet Masses 0.82 Sun 8.2e-5 star 7.2e-4 star Time unit ~ 4 x 103 yrs t50323.dat

29. http://www.astro.iag.usp.br/~dinamica/usp-unc.htm @ArXiv: Astro-ph/0511xxx /0505169v2 /0404166 /0402335 /0301252 /0210577 Planet systems data (+ updates): See: http:// www.astro.iag.usp.br/~dinamica/exosys.htm

30. Data from: Ferraz-Mello et al (2005) [HD 82943], Laughlin et al (2005) [GJ 876], Vogt et al. (2005) [HD12831, HD 108871 and HD 37124], McArthur et al.(2004) [55 Cnc ], Correia et al. (2005) [HD 202206], Gozdziewski et al. (2005) [mu Ara = HD 160691], Santos et al. (2004) [HD 160691e], Mayor et al. (2004) [HD 169830], Fischer et al (2002) [HD 12661], Ford et al. (2005) [upsilon Andromedae], Konacki & Wolszczan (2003) [PSR 1257+12].