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

2. Why do we study the Dynamics of Extrasolar Planetary Systems ? To know how stable they are ! Ref: Brasil CoRoT week, Natal 2004

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 I II III

5. Class Ia – Planet pairs in Mean-Motion Resonance Star Period m.sin i a Period Eccentricity planets ratio (m_Jup) (AU) (days) HD 82943 1.99 1.7 0.75 219.50.39 c,b 1.8 1.18 436.20.15 GJ 876 2.020.597 0.13 30.38 0.218 c,b1.90 0.21 60.93 0.029 HD 128311 2.02 2.18 1.099 458.6 0.25 b,c 3.21 1.76 928.3 0.17 55 Cnc 2.990.78 0.11514.70.02 b,c(?) 0.22 0.2443.9 0.44 HD 202206 5.06 17.5 0.83 256.2 0.433 b,c 2.41 2.44 1296.8 0.28

6. GJ 876 (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. Ref: Ferraz-Mello et al. (ApJ 2005) The orbits of the least-squares solution are bound to a catastrophic event in less than 100,000 years.

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 Star(MS) Period m.sin i a Period Eccentricity planets ratio (m_Jup) (AU) (days) 47 UMa 2.64 2.92.1 1079.2 0.05 b,c(?) 1.14.0 2845.0 0 Planets Period Mass a Period Eccentricity ratio (m_Jup) (AU) (years) Jupiter 2.500 1.0 5.204 11.866 0.0489 Saturn 2.831 0.30 9.584 29.668 0.0571 Uranus 1.958 0.046 19.178 83.987 0.0468 Neptune 0.054 30.004 164.493 0.0112 Outer Solar System

12. Solar System with Saturn initialized on a grid of different initial conditions 50 Myr Collision Chaos Order Grid: 33x251 Ref: Michtchenko (unpub.) 2/1 7/3 5/2 8/3.

13. Star Period Mass a Period Eccentricity (PSR) ratio (m_Earth) (AU) (days) 1257+12 2.63 0.02 0.1925.262 -- 1.48 4.3 0.3666.5419 0.0186 3.9 0.4698.2114 0.0252 Class Ib – Low-eccentricity Near-resonant pairs Near Resonant Pulsar Planets

14. Grid: 21x101 Neighborhood of the 3 rd planet of pulsar B1257 +12 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) collision

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 e2=0.04 26x40 px cf TAM e1

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

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

21. (same example as before)

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

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

24. (same example as before)

25. SCALING : Adopted value of k 2 / Q ~ 2 x 10 -3 Actual values cf. Paetzold & Rauer, 2002 7 x 10 -8 < k 2 / Q < 2 x 10 -6 Hence, the scaling is in the range 10 3 to 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. Masses 0.82 Sun 8.2e-5 star 7.2e-4 star t50323.dat A new example. start: 2:1 ACR Tides on both star and planet Time unit ~ 4 x 10 3 yrs

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].