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

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

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**The Habitable Zone**based onthe definition given by Kasting et al. (1993).**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, …)**Types of Habitable Zones:**• hot-Jupiter type • Solar system type • +(4) giant planet type: habitable moon or trojan planet**Status of Observations**• 164 Extra-solar planetary systems • 194 Planets near other solar-type stars • 19 Mulitple planetary systems • 21 Planets in binaries**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**Distribution of the detected Extra-Solar Planets**Mercury Earth Mars Venus Jupiter**Multi-planetary systems**• Binaries • Single Star and Single 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 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**Major catastrophe in less than 100000 years**(S. Ferraz-Mello, 2004)**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**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 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 IIIHierarchical planet pairs (HD168443, HD74156,HD11964,HD38529,55Cnc)**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**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**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**HD82943**Aligned Anti-aligned**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**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**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.**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**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**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**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**(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**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!

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