stability of earthlike planets in the habitable zones of five extrasolar systems renate zechner 6 th...
Post on 15-Dec-2015
220 Views
Preview:
TRANSCRIPT
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
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°
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: 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:
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!
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
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
top related