Loading in 5 sec....

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

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

Download Presentation

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

Loading in 2 Seconds...

- 122 Views
- Uploaded on
- Presentation posted in: General

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

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

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

- 164 Extra-solar planetary systems
- 194 Planets near other solar-type stars
- 19 Mulitple planetary systems
- 21 Planets in binaries

- 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

.

- 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

- 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

- 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!