Stability of Stability of EarthlikeEarthlike Planets in the Planets in the Habitable Zones of five Extrasolar Habitable Zones of five Extrasolar

SystemsSystems

Renate ZechnerRenate Zechner

6th Alexander von Humboldt

Colloquium for Celestial Mechanics

Bad Hofgastein

23.03.2004

Stability of Stability of EarthlikeEarthlike Planets in the Planets in the Habitable Zones of five Extrasolar Habitable Zones of five Extrasolar

SystemsSystems

Gl 777 A HD 72659 Gl 614 47 Uma HD 4208

Stability of Stability of EarthlikeEarthlike Planets in the Planets in the Habitable Zones of five Extrasolar Habitable Zones of five Extrasolar

SystemsSystems

Chaos and Stability in Planetary Systems 1st September – 26th September 2003

Introduction

Extrasolar planetary systems (EPS) Distribution of a (for all EPS):

~0.02 to ~6.5 AU Habitable zone (HZ): ~0.7 to 1.5 AU

Liquid water + development of life

Our motivation Dynamical investigation to

determine stable regions Special role of resonances

Dynamical Investigations

Determination of the HZ according to the spectral type

Detailed analysis of the mean motion resonances (= MMR)

Dynamical models: restricted 3 (4) body problem Investigation of the full width of the HZ

with respect to the stability of possible planets Stability check of the orbits

Direct check of the maximum eccentricity Rényi entropy

Description ofthe Extrasolar Systems

Main characteristics of the 5 systems

Simulation Methods and Stability Analysis

Supercomputer with 128 processors Direct computation of orbits to assess stability

Lie-integration method Precise numerical integration scheme

with adaptive stepsize Initial conditions

Circular initial orbits Inclination: set to 0 Integration time of

1 million years

Simulation Methods and Stability Analysis

Analysis of stability Maximum eccentricity method (= MEM)

Straightforward check of the eccentricitiesExamination of the behavior of the eccentricity

along the planet‘s orbitUnstable orbit: e > 0.5 (= stability limit)

Rényi entropySensitive tool to show the

dynamical character of an orbitMeasure of the degree of chaoticity

Stability within Resonances

Investigation of resonances Initial conditions placed in the most relevant

MMRs (inside and outside the HZ) Check for stability in 8 different positions of

terrestrial planet (corresponding to M = 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°)

Jovian planet initially placed at the apoastron and periastron

Stability within Resonances

Example: HD 4208 Schematic view of the

stability of orbits in the resonances of 1st and 2nd order

Stable orbits close to the central star inside HZ

Stable orbits close to the Jovian planet for the initial conditions M=0° and M=180°

Stability within Resonances

Stability of orbits in the MMRs

HD 4208

Central star: G5 V with M ~ 1 M

Planet (2002): Almost circular orbit a = 1.67

HZ Jovian Planet

HD 4208

Results of 2 methods of analysis

MEM Entropy plot

Variable distance to the central star

Direct measure of the energy flux on the planet

Measure to determine how predictable an orbit is

Estimation by means of Recurrence Plots (RPs)

Both methods are complementary in their results

HD 4208

Results: Initial condition diagrams

MEM Entropy plot

HD 4208

Results: MEM Unstable orbits:

a > 1.3 AU Stable orbits from the 2:1

resonance on and with small e < 0.2

Habitability: eT < 0.2 Terrestrial planet in HZ

is possible!

Gl 777 A

Wide binary system with a very large separation of 3000 AU

Central star: G6 IV with 0.9 M

Planet (2003): Minimum mass = 1.33 MJ a = 4.8 AU Large eccentricity: e = 0.48 Possible region for additional planets is

confined to a < 2.4 AU

Gl 777 A

Main characteristics Region of habitability: 0.7 < a < 1.3 AU Nearly entire HZ is stable (ignoring large e)

Possible approach of the planet to the central starPosition of the HZ

Gl 777 A

Results: Initial condition diagrams

MEM Entropy plot

Gl 777 A

Results:

MEM 2 Features:

Strong vertical lines due to high order resonances

Unstable orbits due to high a and high e

Gl 777 A

Results:

Planet could survive long enough in the HZ with a < 1 AU

Terrestrial planet is possible!

Entropy plot

HD 72659

Central star: G0 V Jovian planet (2002):

a = 3.24 AU, e = 0.18 MMRs: 2.47 (3:2) to 1.11 AU (5:1) HZ: 5:1, 4:1 and 3:1

HD 72659

Results: MEM

Quite stable HZ Stable orbits

up to 3:1 (1.5 AU) for e < 0.2

Terrestrial planet is possible!

HD 72659

Comparison between both methods MEM Entropy plot

47 Uma

2 Jovian planets Outer planet (2002): large errors in the eccentricity Inner, more massive planet (1996): almost circular orbit

with small errors in the eccentricity

Almost all MMRs are inside the HZ Unstable system: einner > 0.12

47 Uma

Results of the MEM

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!

Gl 614

Central star: K0 V Planet:

4.89 MJ (massive!) a = 2.85 AU e = 0.38 (large!)

Gl 614

Results of the MEM

Unstable orbits: up to 6:1

Stable orbits:only for a < 0.7 AU

Exclude terrestrial planets within HZ!

Conclusion

Good chance for a planet HD 72659:

Very good candidate for hosting planets in HZ Gl 777 A

Nearly the entire HZ is stable 47 Uma

Stable regions inside HZ HD 4208

Planet could survive for sufficiently long time

No terrestrial planet Gl 614

Results exclude terrestrial planet with stable orbits

Stability of Terrestrial Planets in the Stability of Terrestrial Planets in the Habitable Zones of five Extrasolar Habitable Zones of five Extrasolar

SystemsSystems