C. Beaug

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USP-UNC team on Exoplanets
C. Beaugé (UNC) S. Ferraz-Mello (USP) T. A.
Michtchenko (USP)

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Why do we study the Dynamics of
Extrasolar Planetary Systems ? To know
how stable they are !
Ref Brasil CoRoT week, Natal 2004
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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
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Period ratio of consecutive planets in a system
III
II
I
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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 0.75 219.5 0.39 c,b 1.8 1.18 436.2 0.15
GJ 876 2.02 0.597 0.13 30.38 0.218 c,b 1.90 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 2.99 0.78 0.115 14.7 0.02 b,c(?) 0.22 0.24 43.9 0.44
HD 202206 5.06 17.5 0.83 256.2 0.433 b,c 2.41 2.44 1296.8 0.28
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GJ 876
(0,0) apsidal corotation resonance
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SYMMETRIC APSIDAL COROTATIONS
?????
(0,0)
Ref Beaugé et al., Lee and Peale Hadjidemetriou
et al. 2002-2003-2004
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M01.15 Msun m11.7 Mjup/sin i m21.8 Mjup/sin i
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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)
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The planets of 47 UMa
M 2.9 M M 1.1 M
1 Jup 2 Jup
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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 2.9 2.1 1079.2 0.05 b,c(?) 1.1 4.0 2845.0 0
Outer Solar System
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
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Solar System with Saturn initialized on a grid of
different initial conditions
2/1
7/3 5/2 8/3
.
50 Myr Collision Chaos Order
Grid 33x251 Ref Michtchenko (unpub.)
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Class Ib Low-eccentricity Near-resonant
pairs Near Resonant Pulsar Planets
Star Period Mass a Period Eccentricity (PSR) ratio (m_Earth) (AU) (days)
125712 2.63 0.02 0.19 25.262 -- 1.48 4.3 0.36 66.5419 0.0186 3.9 0.46 98.2114 0.0252


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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.
I90 degrees)
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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?
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Dynamical Map of the Neighborhood of the 52 MMR
e1
e20.04 26x40 px cf TAM
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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.
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INTERACTION WITH RESONANCES Consequences
Enhancement of eccentricities and inclinations,
semi-major axis discontinuities, but no
capture into the resonance.
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Example (highly hypothetical)
Masses 0.82 Sun 1.1e-4 star 7.2e-4 star
--21-- ---- crossing
Time units 2 x 10 4 to 5 x 10 5 years
t41227.dat
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(same example as before)
21 74 ---
31---- 52----
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(same example as before)
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One more realistic example
Masses 0.82 Sun 1.1e-4 star 7.2e-4 star
Time units 2 x 10 4 to 5 x 10 5 years
t41223.dat
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(same example as before)
31 ------
t23e
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(same example as before)
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SCALING Adopted value of k2 / Q 2 x
10-3 Actual values cf. Paetzold Rauer, 2002 7
x 10-8 lt k2 / Q lt 2 x 10-6
Hence, the scaling is in the range 10 3 to 3 x 10
4
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Synchronization (due to tides raised on the
planet)
Scaling 10 3
t41231.dat
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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
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A new example. start 21 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
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http//www.astro.iag.usp.br/dinamica/usp-unc.htm
_at_ArXiv Astro-ph/0511xxx /0505169v2
/0404166 /0402335
/0301252 /0210577

• Planet systems data ( updates) See
• http// www.astro.iag.usp.br/dinamica/exosys.htm

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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 125712.