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:

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 I II III

Class Ia – Planet pairs in Mean-Motion Resonance Star Period m.sin i a Period Eccentricity planets ratio (m_Jup) (AU) (days) HD c,b GJ c,b HD b,c Cnc b,c(?) HD b,c

GJ 876 (0,  ) apsidal corotation resonance

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

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

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.

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

Class Ib – Low-eccentricity Near-resonant pairs Star(MS) Period m.sin i a Period Eccentricity planets ratio (m_Jup) (AU) (days) 47 UMa b,c(?) Planets Period Mass a Period Eccentricity ratio (m_Jup) (AU) (years) Jupiter Saturn Uranus Neptune Outer Solar System

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.

Star Period Mass a Period Eccentricity (PSR) ratio (m_Earth) (AU) (days) Class Ib – Low-eccentricity Near-resonant pairs Near Resonant Pulsar Planets

Grid: 21x101 Neighborhood of the 3 rd planet of pulsar B 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

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?

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

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: 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

(same example as before) 3: : :1 7:4 ---

(same example as before)

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

(same example as before) 3: t23e

(same example as before)

SCALING : Adopted value of k 2 / Q ~ 2 x Actual values cf. Paetzold & Rauer, x < k 2 / Q < 2 x 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

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

Astro-ph/0511xxx / v2 / / / / Planet systems data (+ updates): See:

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