based on the definition given by Kasting et al. (1993).

The Habitable Zone

Habitable ZoneHabitable Zone

Zone around a star where liquid water Zone around a star where liquid water can exist on the surface of a terrestial-can exist on the surface of a terrestial-like planetlike planet

This zone depends on:This zone depends on: the spectraltype , the mass , the age, …. of the the spectraltype , the mass , the age, …. of the

starstar the orbit of the planetthe orbit of the planet the mass, the composition, the atmosphere , the mass, the composition, the atmosphere ,

……of the planet……of the planet the parameters of other planets in this system the parameters of other planets in this system

(mass, orbit, …)(mass, orbit, …)

Types of Habitable Zones:

(1) hot-Jupiter type (2) Solar system type(3)+(4) giant planet type: habitable moon or trojan planet

Status of ObservationsStatus of Observations

164 Extra-solar planetary systems164 Extra-solar planetary systems

194 Planets near other solar-type 194 Planets near other solar-type starsstars

19 Mulitple planetary systems19 Mulitple planetary systems

21 Planets in binaries21 Planets in binaries

164 Extra-solar planetary systems164 Extra-solar planetary systems

194 Planets near other solar-type 194 Planets near other solar-type starsstars

19 Mulitple planetary systems19 Mulitple planetary systems

21 Planets in binaries21 Planets in binaries

Only 28% of the detected planets Only 28% of the detected planets have masses < 1 Jupitermasshave masses < 1 Jupitermass

About 33% of the planets are closer About 33% of the planets are closer to the host-star than Mercury to the to the host-star than Mercury to the SunSun

Nearly 60% have eccentricities > 0.2 Nearly 60% have eccentricities > 0.2 And even 40% have eccentricities > And even 40% have eccentricities >

0.30.3

Facts about Extra-Solar Facts about Extra-Solar Planetary Systems:Planetary Systems:

Distribution of the detected Extra-Solar Planets

Mercury Earth Mars Venus Jupit

er

BinariesBinaries

Single Star and Single Planetary SystemsSingle Star and Single Planetary Systems

Multi-planetary systemsMulti-planetary systems

.

Sources of uncertainty in parameter fits:Sources of uncertainty in parameter fits:

the orbital line-of-sight inclination the orbital line-of-sight inclination i is not known i is not known from radial velocities measurements we get only from radial velocities measurements we get only a lower limit for the planetary masses;a lower limit for the planetary masses;

the relative inclination the relative inclination iirr between planetary orbital between planetary orbital planes is usually unknown.planes is usually unknown.

Are the orbital parameters reliable -- using two body Are the orbital parameters reliable -- using two body keplerian fitskeplerian fits

(the strong dynamical interactions between planets)(the strong dynamical interactions between planets)

All these leave us a substantial available All these leave us a substantial available parameter space to be explored in order to parameter space to be explored in order to exclude the initial conditions which lead to exclude the initial conditions which lead to dynamically unstable configurations dynamically unstable configurations

Major catastrophe in less than 100000 years

0 20000 40000 60000TIME (yr)

0.00

4.00

8.00

SEMI-MAJ

OR A

XIS

(S. Ferraz-Mello, 2004)

Long-term numerical integration:

Stability-Criterion: No close encounters within the Hill‘ sphere

(i)Escape time(ii) Study of the eccentricity: maximum eccentricity

Chaos Indicators:

Fast Lyapunov

Indicator (FLI) C. Froeschle, R.Gonczi, E. Lega (1996)

Mean Exponential Growth factor of Nearby Orbits

(MEGNO)

Cincotta & Simo (2000)

Numerical Methods

Multi-planetarysystems

Classification of the known Classification of the known multi-planetary systems multi-planetary systems (S.Ferraz-Mello, 2005)(S.Ferraz-Mello, 2005)

Class Ia –>Class Ia –> Planets in mean motion Planets in mean motion resonance resonance (HD82943, (HD82943, Gliese876,HD128311,55Cnc,HD202206)Gliese876,HD128311,55Cnc,HD202206)

Class Ib Class Ib Low-eccentricity near- Low-eccentricity near-resonant planet pairs resonant planet pairs (47Uma)(47Uma)

Class IIClass II Non-resonant planets with Non-resonant planets with significant secular dynamics significant secular dynamics (55 Cnc, (55 Cnc, Ups And, HD12661, HD169830,HD37124, HD160691)Ups And, HD12661, HD169830,HD37124, HD160691)

Class IIIClass III Hierarchical planet pairs Hierarchical planet pairs (HD168443, HD74156,HD11964,HD38529,55Cnc)(HD168443, HD74156,HD11964,HD38529,55Cnc)

Class II III

Ia III Ia

III III II

Ia II III II II Ib

MMR

3:1

2:1

2:1

2:1

7:3/5:2

Gliese 876 HD82943 HD160691

Systems in 2:1 resonance

GJ876 b GJ876c HD82 b HD82 c HD160 b HD160 cA [AU]: 0.21 0.13 1.16 0.73 1.5 2.3 e: 0.1 0.27 0.41 0.54 0.31 0.8M .sin i: 1.89 0.56 1.63 0.88 1.7 1.0[M_jup]

S PPA A 1 212

P eriastra in the sam e d irection

S PPA A 1212

P eriastra in opposite d irections

Periastra in the same Periastra in the same directiondirection

S - PS - P11 - P - P22

S - AS - A11 - A - A22

AA11 - S - P - S - P22

PP11 - S - A - S - A22

Periastra in opposite Periastra in opposite directionsdirections

S - PS - P11 - A - A22

S - AS - A11- P- P22

PP11 - S – P - S – P22

AA11 - S – A - S – A22

Equivalent in pairs, Equivalent in pairs, depending on the depending on the resonanceresonance

HD82943

Aligned

Anti-aligned

HD160691 b HD160691 cA [AU]: 1.5 2.3 e: 0.31 0.8M .sin i: 1.7 1.0[M_jup]

Bois, E., Kiseleva-Eggleton, L., Rambaux, N.,Pilat-Lohinger, E., 2003, ApJ 598, 1312

MEGNO – Stability map

Stability condition: 2:1 mean motion resonance(exact location: a_c=2.381 AU)

Planet m sin i a e w Planet m sin i a e w P P

HD160691b 1.67 +/- 0.11 1.50 +/- 0.02 0.2 +/- 0.03 294 +/- HD160691b 1.67 +/- 0.11 1.50 +/- 0.02 0.2 +/- 0.03 294 +/- 9 645.5 +/- 3 9 645.5 +/- 3

c 3.1+/- 0.71 4.17+/- 0.07 0.57+/- 0.1 161 +/- c 3.1+/- 0.71 4.17+/- 0.07 0.57+/- 0.1 161 +/- 8 2986+/-308 2986+/-30

d 0.04405 0.09 0 (+0.02) 4+/- d 0.04405 0.09 0 (+0.02) 4+/- 2 9.55+/0.03 2 9.55+/0.03

Stability of thenew system HD160691

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

ec

Due to high eccentricitiesof the orbits and despiterelatively small semi-majoraxis, the relative distancesbetween the two planets may remain sufficiently large over the whole evolutionary time scale ofThe system.

It was shown by several authors It was shown by several authors ((e.g.e.g. Rivera & Lissauer 2000, Laughlin & Rivera & Lissauer 2000, Laughlin &

Chambers 2001, Chiang & Murray 2002; Lee & Chambers 2001, Chiang & Murray 2002; Lee & Peale 2002, 2003; Ji et al. 2003, 2004, Zhou & Peale 2002, 2003; Ji et al. 2003, 2004, Zhou & Sun 2003, Bois et al. 2003Sun 2003, Bois et al. 2003) )

that the orbits in almost all multi-planet that the orbits in almost all multi-planet systems systems

((except HD38529, HD168443,except HD38529, HD168443, HD74156HD74156) )

are locked in the are locked in the so-called so-called Apsidal Synchronous Precession

(ASP) meaning that the two orbital planes precess at meaning that the two orbital planes precess at

the same rate, i.e. the relative apsidal the same rate, i.e. the relative apsidal longitude longitude θθ3 3 of two planetary orbits of two planetary orbits librates librates about 0 (aligned topology) or about 0 (aligned topology) or ππ (anti-aligned (anti-aligned topology).topology).

, where

A suitable mechanism for compact A suitable mechanism for compact multi-planetary systemsmulti-planetary systems

Low order Mean Motion Resonance +Low order Mean Motion Resonance + Favorable relative initial orbital phases of Favorable relative initial orbital phases of

planets +planets + High planetary eccentricities, especially of High planetary eccentricities, especially of

the outer planet +the outer planet + Anti-aligned Apsidal Synchronous Anti-aligned Apsidal Synchronous

Precession Precession

==

NO close approaches between planets NO close approaches between planets =>=>

NO strong dynamical interactions => NO strong dynamical interactions =>

STABILITY over long evolutionary timescaleSTABILITY over long evolutionary timescale

Mstar = 1.05 MSun

HD 74156 bm sini = 1.6 Mjup

a = 0.28 AUe = 0.647

HD 74156 cm sin i= 8.2 Mjup

a = 3.82 AUe = 0.354

HD 74156• The orbital parameters were taken from the Geneva group of observers• Masses are Minimum Masses

e= e= 0.300.30

e=0.3e=0.355

e=0.4e=0.400

e=0.4e=0.455

HD 74156 bm = 1.86 MJup

a = 0.294 AUe = 0.635

HD 74156 cm = 6.42 MJup

a = 3.44 AUe = 0.561

New Data

HD 38529 HD 169830 HD 168443

Mstar = 1.39 MSun

HD 38529 bm = 0.78 MJup

a = 0.129 AUe = 0.29HD 38529 cm = 12.7 MJup

a = 3.68 AUe = 0.36

Mstar = 1.4 MSun

HD 169830 bm = 3.03 MJup

a = 0.82 AUe = 0.327HD 169830 cm = 2.51 MJup

a = 2.85 AUe = 0.0

Mstar = 1.01 MSun

HD 168443 bm = 7.73 MJup

a = 0.295 AUe = 0.53HD 168443 cm = 17.23 MJup

a = 2.9 AUe = 0.2

(in collaboration with Erdi and Sandor)

Unstable orbits2:1 1.3 AU 3:1 1 AUSR 0.8 – 0.9 AU4:1 0.82 AU

Stable orbitsBetween resonances

Terrestrial planet is possible!