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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) Why do we study the Dynamics of Extrasolar Planetary Systems ? To know how stable they are ! Ref: Brasil CoRoT week, Natal 2004 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 Period ratio of consecutive planets in a system Period Ratio 100 III 10 II I 1 Class Ia – Planet pairs in Mean-Motion Resonance Star Period planets ratio HD 82943 1.99 c,b m.sin i (m_Jup) 1.7 1.8 a (AU) 0.75 1.18 Period Eccentricity (days) 219.5 0.39 436.2 0.15 GJ 876 c,b 2.02 0.597 1.90 0.13 0.21 30.38 60.93 0.218 0.029 HD 128311 2.02 b,c 55 Cnc 2.99 b,c(?) 2.18 3.21 0.78 0.22 1.099 1.76 0.115 0.24 458.6 928.3 14.7 43.9 0.25 0.17 0.02 0.44 HD 202206 5.06 b,c 17.5 2.41 0.83 2.44 256.2 1296.8 0.433 0.28 GJ 876 (0,0) apsidal corotation resonance SYMMETRIC APSIDAL COROTATIONS 0 (0,0) Ref: Beaugé et al., Lee and Peale Hadjidemetriou et al. 2002-2003-2004 HD 82943 M0=1.15 Msun m1=1.7 Mjup/sin i m2=1.8 Mjup/sin i MARS B C VENUS EARTH The orbits of the least-squares solution are bound to a catastrophic event in less than 100,000 years. SEMI-MAJOR AXIS (AU) 6 4 2 0 0 20000 40000 TIME (yr) 60000 Ref: Ferraz-Mello et al. (ApJ 2005) The planets of 47 UMa M 1= 2.9 M Jup M 2= 1.1 M Jup JÚPITER MARTE C B Class Ib – Low-eccentricity Near-resonant pairs Star(MS) planets 47 UMa b,c(?) Period ratio 2.64 m.sin i a (m_Jup) (AU) 2.9 2.1 1.1 4.0 Period (days) 1079.2 2845.0 Eccentricity Mass a Period (m_Jup) (AU) (years) 1.0 5.204 11.866 0.30 9.584 29.668 0.046 19.178 83.987 0.054 30.004 164.493 Eccentricity 0.05 0 Outer Solar System Planets Jupiter Saturn Uranus Neptune Period ratio 2.500 2.831 1.958 0.0489 0.0571 0.0468 0.0112 Solar System with Saturn initialized on a grid of different initial conditions 2/1 7/3 5/2 8/3 0.30 eccentricity 0.25 0.20 0.15 0.10 8.4 8.6 0 25 40 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4 semi-major axis (AU) Order 8.2 60 0.00 8.0 80 Chaos 50 Myr Collision 0.05 Grid: 33x251 Ref: Michtchenko (unpub.) Class Ib – Low-eccentricity Near-resonant pairs Near Resonant Pulsar Planets Star (PSR) 1257+12 Period ratio 2.63 1.48 Mass (m_Earth) 0.02 4.3 3.9 a (AU) 0.19 0.36 0.46 Period Eccentricity (days) 25.262 -66.5419 0.0186 98.2114 0.0252 Neighborhood of the 3rd planet of pulsar B1257 +12 ECCENTRICITY 0.2 0.1 11/8 0.0 0.44 collision 7/5 0.45 10/7 0.46 3/2 0.47 11/7 0.48 0.49 SEMI-MAJOR AXIS (AU) 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) One question: Is it possible to find a system of two close-in planets with period ratio close to 2.5? (Brasil CoRoT week, Natal 2004) Dynamical Map of the Neighborhood of the 5:2 MMR e1 e2=0.04 26x40 px cf TAM 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. INTERACTION WITH RESONANCES Consequences: Enhancement of eccentricities and inclinations, semi-major axis discontinuities, but no capture into the resonance. Example (highly hypothetical) --2:1-- ---- crossing Masses 0.82 Sun 1.1e-4 star 7.2e-4 star Time units ~ 2 x 10 4 to 5 x 10 5 years t41227.dat (same example as before) 3:1---- 5:2---- 2:1 7:4 --- (same example as before) One more realistic example Masses 0.82 Sun 1.1e-4 star 7.2e-4 star t41223.dat Time units ~ 2 x 10 4 to 5 x 10 5 years (same example as before) 3:1 ------ t23e (same example as before) 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 3 to 3 x 10 4 Synchronization (due to tides raised on the planet) Scaling ~ 10 3 t41231.dat 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 A new example. start: 2:1 ACR Tides on both star and planet t50323.dat Masses 0.82 Sun 8.2e-5 star 7.2e-4 star Time unit ~ 4 x 103 yrs http://www.astro.iag.usp.br/~dinamica/usp-unc.htm @ArXiv: Astro-ph/0511xxx /0404166 /0301252 /0505169v2 /0402335 /0210577 Planet systems data (+ updates): See: http:// www.astro.iag.usp.br/~dinamica/exosys.htm 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].