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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
1
10
100
Perio
d R
atio
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 82943 1.99 1.7 0.75 219.5 0.39c,b 1.8 1.18 436.2 0.15
GJ 876 2.02 0.597 0.13 30.38 0.218c,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 0.02b,c(?) 0.22 0.24 43.9 0.44
HD 202206 5.06 17.5 0.83 256.2 0.433b,c 2.41 2.44 1296.8 0.28
GJ 876
(0,) apsidal corotation resonance
SYMMETRIC APSIDAL COROTATIONS
(0,0)
Ref: Beaugé et al., Lee and PealeHadjidemetriou et al.
2002-2003-2004
EARTH
MARSB
CVENUS
HD 82943
M0=1.15 Msun
m1=1.7 Mjup/sin im2=1.8 Mjup/sin i
0 20000 40000 60000TIME (yr)
0
2
4
6
SEMI-MAJ
OR A
XIS (A
U)
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.
JÚPITER
MARTE
BC
The planets of 47 UMa
M = 2.9 MM = 1.1 M1 Jup2 Jup
Class Ib – Low-eccentricity Near-resonant pairs
Star(MS) Period m.sin i a Period Eccentricityplanets ratio (m_Jup) (AU) (days)
47 UMa 2.64 2.9 2.1 1079.2 0.05b,c(?) 1.1 4.0 2845.0 0
Planets Period Mass a Period Eccentricity ratio (m_Jup) (AU) (years)
Jupiter 2.500 1.0 5.204 11.866 0.0489Saturn 2.831 0.30 9.584 29.668 0.0571Uranus 1.958 0.046 19.178 83.987 0.0468Neptune 0.054 30.004 164.493 0.0112
Outer Solar System
Solar System with Saturn initialized on a grid of different initial conditions
50 M
yr
Collis
ion
Ch
aos
Ord
er
025
40
60
80
Grid: 33x251Ref: Michtchenko (unpub.)
8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4
semi-major axis (AU)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
ecce
ntric
ity
2/1 7/3 5/2 8/3 .
Star Period Mass a Period Eccentricity(PSR) ratio (m_Earth) (AU) (days)
1257+12 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
Class Ib – Low-eccentricity Near-resonant pairsNear Resonant Pulsar Planets
0.44 0.45 0.46 0.47 0.48 0.49
SEMI-MAJOR AXIS (AU)
0.0
0.1
0.2
ECCE
NTRICITY
11/8 7/5 10/7 3/2 11/7
Grid: 21x101
Neighborhood of the 3rd planet of pulsar B1257 +12
Pulsar system initialized with planet C on a grid ofdifferent 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=0.04
26x40 pxcf 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)
--2:1-- ---- crossing
Time units ~ 2 x 10 4 to 5 x 10 5 yearst41227.dat
Masses0.82 Sun
1.1e-4 star7.2e-4 star
(same example as before)
3:1----
5:2----
2:1
7:4 ---
(same example as before)
One more realistic example
t41223.dat
Masses 0.82 Sun1.1e-4 star 7.2e-4 star
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 range10 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 rightperiod for large satellites (oceans ?)
The spin-orbit synchronization weakensthe action of torques due to planet tides.
Only remaining effect: fast circularization
Masses0.82 Sun
8.2e-5 star7.2e-4 star
t50323.dat
A new example.start: 2:1 ACRTides on both star and planet
Time unit ~ 4 x 103 yrs
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
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].
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