Chaos and PlanetParticle Dynamics within the Habitable Zone of Extrasolar Planetary Systems

1
Chaos and Planet-Particle Dynamics within the
Habitable Zone of Extrasolar Planetary Systems
Some results from my masters thesis work

• - A qualitative comparative numerical stability
  study of HD4208 and HD70642

Tobias Cornelius Hinse Niels Bohr Institute,
Copenhagen
Supervisors Dr. U. G. Jørgensen and Dr. R.
Michelsen Collaboration partners Dr. S. Mikkola
(Tuorla Obsv., Finland), Dr. K. Gozdziewski
(Torin Obsv., Poland) and Dr. A. Erikson, Dr.
H. Rauer (DLR, Berlin).
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Planet formation theory and formation of
terrestrial planets
Planet formation by - accretion -
gravitational core collapse
Four stages of planet formation (accretion)
1. Initial stage Gravitational cloud
contraction. 2. Early stage Grain
growth and runaway accretion. 3. Middle
stage Oligarchic growth of protoplanets.
4. Late stage Gravitational perturbations
and crossing orbits.
References Kokubo and Ida (2002)
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Observations and Kepler elements of HD70642 and
HD4208
? Planets detected by the radial velocity
technique. ? References Vogt et al. (2001), ApJ
568, p.352 and Carter et al.
(2003), ApJ 594, p.L34. ? Stellar properties
HD4208 0.93 MSol, Teff 5572 K, G5V, 5 Gyrs.
HD70642 1.00 MSol, Teff 5670 K, G5, 4 Gyrs.
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Determining the habitable zone and orbit
constrains - I
? Habitable zone boundaries a) Initial (ZAMS)
habitable zone, b) current habitable zone
and c) continuous habitable zone. ? Boundaries,
din and dout, are determined by
interpolation from Kasting et al. (1993) Icarus,
101, p. 108 based on stellar age and Teff
. ? Simple back-of-the-envelope calculation -
considering a global-radiation energy
balance model yields
? Condition for habitability Liquid water.
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Determining the habitable zone and orbit
constrains - II
? Orbit confinement within a given annulus in
(a,e)- space and constrain equations ?
Pericenter distance a(1- e) ? Apocenter
distance a(1e)
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Numerical integration and the MEGNO indicator
? The hybrid mixed-variable (MVS)
symplectic algorithm is used as
implementet within the MERCURY6
integration package. (Chambers et al.
(1999)). ? Symplectic schemes have very good
conservation properties in energy and
angular momentum. ? Chaotic motion is detected
using MEGNO indicator.
For quasi-periodic (regular) dynamics, we have
For chaotic dynamics, we have
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Dynamical simulations and chaos analysis
results for HD4208 (MEGNO scans within (aTellus,
egiant) parameter space)
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Planet-particle dynamics for HD4208
Mass of HD4208b 1 Mjup Eccentricity 0.14
(upper limit)
41 31 52 21 85 32
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Conclusions and science application to SONG
?
The application of a MEGNO analysis proves useful
for obtaining a quick global (qualitative)
picture of the dynamics within the habitable
zone(s) for a given system under study.
?
MEGNO analysis and direct particle simulations
complement each other (cause and effect mean
motion resonance perturbations gt eccentricity
excitation !!!)
Giant planets on low eccentric, long period
orbits have an increased probability in harboring
terrestrial planets within the HZ The dynamics
of particles within HD70642 is more quiet
compared to HD4208 (chaos dominated).
?
Scientific application - SONG
Current work could help future search missions
for terrestrial (habitable) planets in known
exo-systems, by providing a mission targeting
list based on orbit stability analysis.
?
Numerical methods (symplectic n-body algorithms)
are available for dynamical studies of planetary
systems and for studying the formation of
terrestrial planets in general (frequency,
statistics of final orbital parameters).
?
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References (selected)
Stability studies (habitability of terrestial
planets in exo-systems) Rampino and Caldeira
(1994) Annu.Rev.Astr.Astrophy., vol. 32, p.
83. Gehman et al. (1996) Publ.Astr.Soc.Pac.,
vol. 108, p.1018. Wetherill (1996) Icarus,
vol. 119, p. 219. Jones et al. (2001) AA,
vol. 366, p.254. Jones and Sleep (2002) AA,
vol. 393, p.1015. Noble et al. (2002) ApJ,
vol. 572, p. 1024. Jones et al. (2003)
toed.conf. 625J Ashgari et al. (2004)
astro-ph 0403152v1 Symplectic algorithm and
MEGNO theory Chambers and Migliorini (1997)
BAAS 27-06-P. Chambers (1999) MNRAS, vol. 304,
p.793. Mikkola and Innanen (1999) CMDA vol.
74, p.59 Gozdziewski et al. (2001) AA,
vol.378, p.569 (and ref. therein). Habitable
zone and planet climate Kasting et al. (1993)
Icarus, vol.101, p.108 Forget and
Pierrehumbert (1997) Science, vol. 278, p.
1273. Gilmour and Sephton (2004) Book,
Cambridge Univ. Press.