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].