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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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slide1

The Habitable Zone

based onthe

definition

given by

Kasting et al.

(1993).

slide2

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, …)
slide3

Types of Habitable Zones:

  • hot-Jupiter type
  • Solar system type
  • +(4) giant planet type: habitable moon or trojan planet
status of observations
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
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
slide7

Multi-planetary systems

  • Binaries
  • Single Star and Single Planetary Systems
sources of uncertainty in parameter fits
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

slide11

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
classification of the known multi planetary systems s ferraz mello 2005
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)
slide14

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

slide15

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

slide16

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

slide17

HD82943

Aligned

Anti-aligned

slide18

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

slide19
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

slide21

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.

slide22
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
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

slide25

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

slide27

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

slide28

(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

slide29

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!