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

1. The Habitable Zone based onthe definition given by Kasting et al. (1993).

2. Habitable Zone • Zone around a star where liquid water can exist on the surface of a terrestial-like planet • This zone depends on: • the spectraltype , the mass , the age, …. of the star • the orbit of the planet • the mass, the composition, the atmosphere , ……of the planet • the parameters of other planets in this system (mass, orbit, …)

3. Types of Habitable Zones: • hot-Jupiter type • Solar system type • +(4) giant planet type: habitable moon or trojan planet

4. Status of Observations • 164 Extra-solar planetary systems • 194 Planets near other solar-type stars • 19 Mulitple planetary systems • 21 Planets in binaries

5. Facts about Extra-Solar Planetary Systems: • 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 • Nearly 60% have eccentricities > 0.2 • And even 40% have eccentricities > 0.3

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

7. Multi-planetary systems • Binaries • Single Star and Single Planetary Systems

8. .

9. Sources of uncertainty in parameter fits: • the orbital line-of-sight inclination i is not known  from radial velocities measurements we get only a lower limit for the planetary masses; • the relative inclination irbetween planetary orbital planes is usually unknown. • Are the orbital parameters reliable -- using two body keplerian fits (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

10. Major catastrophe in less than 100000 years (S. Ferraz-Mello, 2004)

11. Numerical Methods Chaos Indicators: Fast Lyapunov Indicator (FLI) C. Froeschle,R.Gonczi, E. Lega (1996) Mean Exponential Growth factor of Nearby Orbits (MEGNO) Cincotta & Simo (2000) • Long-term numerical integration: • Stability-Criterion: • No close encounters within theHill‘ sphere • (i)Escape time • (ii) Study of the eccentricity:maximum eccentricity

12. Multi-planetary systems

13. Classification of the known multi-planetary systems (S.Ferraz-Mello, 2005) • Class Ia –> Planets in mean motion resonance (HD82943, Gliese876,HD128311,55Cnc,HD202206) • 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 IIIHierarchical planet pairs (HD168443, HD74156,HD11964,HD38529,55Cnc)

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

15. Systems in 2:1 resonance GJ876 b GJ876c HD82 b HD82 c HD160 b HD160 c A [AU]: 0.21 0.13 1.16 0.73 1.5 2.3 e: 0.1 0.27 0.41 0.54 0.31 0.8 M .sin i: 1.89 0.56 1.63 0.88 1.7 1.0 [M_jup] Gliese 876 HD82943 HD160691

16. Periastra in the same direction S - P1 - P2 S - A1 - A2 A1 - S - P2 P1 - S - A2 Periastra in opposite directions S - P1 - A2 S - A1- P2 P1 - S – P2 A1 - S – A2 Equivalent in pairs, depending on the resonance

17. HD82943 Aligned Anti-aligned

18. HD160691 b HD160691 c A [AU]: 1.5 2.3 e: 0.31 0.8 M .sin i: 1.7 1.0 [M_jup] MEGNO – Stability map Stability condition: 2:1 mean motion resonance (exact location: a_c=2.381 AU) Bois, E., Kiseleva-Eggleton, L., Rambaux, N., Pilat-Lohinger, E., 2003, ApJ 598, 1312

19. Planet m sin i a e w P HD160691b 1.67 +/- 0.11 1.50 +/- 0.02 0.2 +/- 0.03 294 +/- 9 645.5 +/- 3 c 3.1+/- 0.71 4.17+/- 0.07 0.57+/- 0.1 161 +/- 8 2986+/-30 d 0.04405 0.09 0 (+0.02) 4+/- 2 9.55+/0.03

20. Stability of thenew system HD160691

21. 360 ~ 0.9 wc (deg) 320 0.8 280 0.7 240 0.6 ec 200 0.5 160 0.4 120 0.3 80 0.2 40 0.1 0.0 0 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.

22. 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) that the orbits in almost all multi-planet systems (except HD38529, HD168443,HD74156) 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 θ3 of two planetary orbits librates about 0 (aligned topology) or π (anti-aligned topology). , where

24. 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

25. HD 74156 • The orbital parameters were taken from the • Geneva group of observers • Masses are Minimum Masses Mstar = 1.05 MSun HD 74156 b m sini = 1.6 Mjup a = 0.28 AU e = 0.647 HD 74156 c m sin i= 8.2 Mjup a = 3.82 AU e = 0.354

26. e= 0.30e=0.35e=0.40e=0.45

27. New Data HD 74156 b m = 1.86 MJup a = 0.294 AU e = 0.635 HD 74156 c m = 6.42 MJup a = 3.44 AU e = 0.561

28. (in collaboration with Erdi and Sandor) HD 38529 HD 169830 HD 168443 Mstar = 1.39 MSun HD 38529 b m = 0.78 MJup a = 0.129 AU e = 0.29 HD 38529 c m = 12.7 MJup a = 3.68 AU e = 0.36 Mstar = 1.4 MSun HD 169830 b m = 3.03 MJup a = 0.82 AU e = 0.327 HD 169830 c m = 2.51 MJup a = 2.85 AU e = 0.0 Mstar = 1.01 MSun HD 168443 b m = 7.73 MJup a = 0.295 AU e = 0.53 HD 168443 c m = 17.23 MJup a = 2.9 AU e = 0.2

29. Unstable orbits 2:1 1.3 AU 3:1 1 AU SR 0.8 – 0.9 AU 4:1 0.82 AU Stable orbits Between resonances Terrestrial planet is possible!