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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].