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

Habitable Zone Zone around a star where liquid water can exist on the surface of a terrestial-like planet Zone around a star where liquid water can exist on the surface of a terrestial-like planet This zone depends on: This zone depends on: the spectraltype, the mass, the age, …. of the star the spectraltype, the mass, the age, …. of the star the orbit of the planet the orbit of the planet the mass, the composition, the atmosphere, ……of the planet the mass, the composition, the atmosphere, ……of the planet the parameters of other planets in this system (mass, orbit, …) the parameters of other planets in this system (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 Observations 164 Extra-solar planetary systems 164 Extra-solar planetary systems 194 Planets near other solar-type stars 194 Planets near other solar-type stars 19 Mulitple planetary systems 19 Mulitple planetary systems 21 Planets in binaries 21 Planets in binaries 164 Extra-solar planetary systems 164 Extra-solar planetary systems 194 Planets near other solar-type stars 194 Planets near other solar-type stars 19 Mulitple planetary systems 19 Mulitple planetary systems 21 Planets in binaries 21 Planets in binaries

Only 28% of the detected planets have masses < 1 Jupitermass Only 28% of the detected planets have masses < 1 Jupitermass About 33% of the planets are closer to the host-star than Mercury to the Sun About 33% of the planets are closer to the host-star than Mercury to the Sun Nearly 60% have eccentricities > 0.2 Nearly 60% have eccentricities > 0.2 And even 40% have eccentricities > 0.3 And even 40% have eccentricities > 0.3 Facts about Extra-Solar Planetary Systems:

Distribution of the detected Extra-Solar Planets Mercury Earth Mars Venus Jupiter

 Binaries  Single Star and Single Planetary Systems  Multi-planetary systems

.

Sources of uncertainty in parameter fits:  the orbital line-of-sight inclination 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 i r between planetary orbital planes is usually unknown.  Are the orbital parameters reliable -- using two body keplerian fits (the strong dynamical interactions between planets) (the strong dynamical interactions between planets) All these leave us a substantial available parameter space to be explored in order to exclude the initial conditions which lead to dynamically unstable configurations All these leave us a substantial available parameter space to be explored in order to exclude the initial conditions which lead to dynamically unstable configurations

Major catastrophe in less than years (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-planetary systems

Classification of the known multi- planetary systems (S.Ferraz-Mello, 2005) Class Ia –> Planets in mean motion resonance (HD82943, Gliese876,HD128311,55Cnc,HD202206) Class Ia –> Planets in mean motion resonance (HD82943, Gliese876,HD128311,55Cnc,HD202206) Class Ib  Low-eccentricity near-resonant planet pairs (47Uma) Class Ib  Low-eccentricity near-resonant planet pairs (47Uma) Class II  Non-resonant planets with significant secular dynamics (55 Cnc, Ups And, HD12661, HD169830,HD37124, HD160691) Class II  Non-resonant planets with significant secular dynamics (55 Cnc, Ups And, HD12661, HD169830,HD37124, HD160691) Class III  Hierarchical planet pairs (HD168443, HD74156,HD11964,HD38529,55Cnc) Class III  Hierarchical planet pairs (HD168443, HD74156,HD11964,HD38529,55Cnc)

Class II III Ia III Ia III II Ia II III II Ib MMR 3:1 2:1 7:3/5:2

Gliese 876HD82943HD Systems in 2:1 resonance GJ876 b GJ876c HD82 b HD82 c HD160 b HD160 c A [AU]: e: M.sin i: [M_jup]

Periastra in the same direction S - P 1 - P 2 S - A 1 - A 2 A 1 - S - P 2 P 1 - S - A 2 Periastra in opposite directions S - P 1 - A 2 S - A 1 - P 2 P 1 - S – P 2 A 1 - S – A 2 Equivalent in pairs, depending on the resonance

HD82943 Aligned Anti-aligned

HD b HD c A [AU]: e: M.sin i: [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 P Planet m sin i a e w P HD160691b / / / / /- 3 HD160691b / / / / /- 3 c 3.1+/ / / / /-30 c 3.1+/ / / / /-30 d (+0.02) 4+/ /0.03 d (+0.02) 4+/ /0.03

Stability of the new system HD160691

 c (deg) ~ ecec Due to high eccentricities of the orbits and despite relatively small semi-major axis, the relative distances between the two planets may remain sufficiently large over the whole evolutionary time scale of The system.

It was shown by several authors It was shown by several authors (e.g. Rivera & Lissauer 2000, Laughlin & Chambers 2001, Chiang & Murray 2002; Lee & Peale 2002, 2003; Ji et al. 2003, 2004, Zhou & Sun 2003, Bois et al. 2003) (e.g. Rivera & Lissauer 2000, Laughlin & Chambers 2001, Chiang & Murray 2002; Lee & Peale 2002, 2003; Ji et al. 2003, 2004, Zhou & Sun 2003, Bois et al. 2003) that the orbits in almost all multi-planet systems that the orbits in almost all multi-planet systems (except HD38529, HD168443, HD74156) (except HD38529, HD168443, HD74156) are locked in the so-called are locked in the so-called Apsidal Synchronous Precession (ASP) meaning that the two orbital planes precess at the same rate, i.e. the relative apsidal longitude θ 3 of two planetary orbits librates about 0 (aligned topology) or π (anti-aligned topology). meaning that the two orbital planes precess at the same rate, i.e. the relative apsidal longitude θ 3 of two planetary orbits librates about 0 (aligned topology) or π (anti-aligned topology)., where

A suitable mechanism for compact multi- planetary systems  Low order Mean Motion Resonance +  Favorable relative initial orbital phases of planets +  High planetary eccentricities, especially of the outer planet +  Anti-aligned Apsidal Synchronous Precession = NO close approaches between planets => NO strong dynamical interactions => STABILITY over long evolutionary timescale

M star = 1.05 M Sun HD b m sini = 1.6 M jup a = 0.28 AU e = HD c m sin i= 8.2 M jup a = 3.82 AU e = HD The orbital parameters were taken from the Geneva group of observers Masses are Minimum Masses

e= 0.30 e=0.35 e=0.40 e=0.45

HD b m = 1.86 M Jup a = AU e = HD c m = 6.42 M Jup a = 3.44 AU e = New Data

HD HD HD M star = 1.39 M Sun HD b m = 0.78 M Jup a = AU e = 0.29 HD c m = 12.7 M Jup a = 3.68 AU e = 0.36 M star = 1.4 M Sun HD b m = 3.03 M Jup a = 0.82 AU e = HD c m = 2.51 M Jup a = 2.85 AU e = 0.0 M star = 1.01 M Sun HD b m = 7.73 M Jup a = AU e = 0.53 HD c m = M Jup a = 2.9 AU e = 0.2 (in collaboration with Erdi and Sandor)

Unstable orbits 2:1 1.3 AU 3:1 1 AU SR 0.8 – 0.9 AU 4: AU Stable orbits Between resonances Terrestrial planet is possible!