Stability of Earthlike Planets in the Habitable Zones of five Extrasolar Systems Renate Zechner 6 th Alexander von Humboldt Colloquium for Celestial Mechanics Bad Hofgastein

Stability of Earthlike Planets in the Habitable Zones of five Extrasolar Systems  Gl 777 A  HD  Gl 614  47 Uma  HD 4208

Stability of Earthlike Planets in the Habitable Zones of five Extrasolar Systems Chaos and Stability in Planetary Systems 1 st September – 26 th 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 of the 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 eccentricities Examination of the behavior of the eccentricity along the planet‘s orbit Unstable orbit: e > 0.5 (= stability limit) Rényi entropy Sensitive tool to show the dynamical character of an orbit Measure 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 1 st and 2 nd 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: e T < 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 M J 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 star Position 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  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  Results: MEM Quite stable HZ Stable orbits up to 3:1 (1.5 AU) for e < 0.2 Terrestrial planet is possible!

HD  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: e inner > 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: AU  Stable orbits Between resonances  Terrestrial planet is possible!

Gl 614  Central star: K0 V  Planet: 4.89 M J (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 Habitable Zones of five Extrasolar Systems