J/ApJ/716/1336 Stability analysis of single-planet (Kopparapu+, 2010)
Stability analysis of single-planet systems and their habitable zones.
Kopparapu R.K., Barnes R.
<Astrophys. J., 716, 1336-1344 (2010)>
=2010ApJ...716.1336K 2010ApJ...716.1336K
ADC_Keywords: Planets ; Stars, masses
Keywords: methods: numerical - planetary systems
Abstract:
We study the dynamical stability of planetary systems consisting of
one hypothetical terrestrial-mass planet (1 or 10M{earth}) and one
massive planet (10M{earth}-10Mjup). We consider masses and orbits
that cover the range of observed planetary system architectures
(including non-zero initial eccentricities), determine the stability
limit through N-body simulations, and compare it to the analytic Hill
stability boundary. We show that for given masses and orbits of a
two-planet system, a single parameter, which can be calculated
analytically, describes the Lagrange stability boundary (no ejections
or exchanges) but diverges significantly from the Hill stability
boundary. However, we do find that the actual boundary is fractal, and
therefore we also identify a second parameter which demarcates the
transition from stable to unstable evolution. We show the portions of
the habitable zones (HZs) of ρ CrB, HD 164922, GJ 674, and HD 7924
that can support a terrestrial planet. These analyses clarify the
stability boundaries in exoplanetary systems and demonstrate that, for
most exoplanetary systems, numerical simulations of the stability of
potentially habitable planets are only necessary over a narrow region
of the parameter space. Finally, we also identify and provide a
catalog of known systems that can host terrestrial planets in their
HZs.
Description:
We used orbital parameters from the Exoplanet Data Explorer maintained
by the California Planet Survey consortium (http://exoplanets.org/)
and selected all 236 single-planet systems in this database with
masses in the range 10 Mjup-10M{earth} and e≤0.6.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table4.dat 71 236 Lagrange stable and unstable boundaries, and the
corresponding fraction of habitable zone stable
for terrestrial mass planets in known single
planet systems
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See also:
J/MNRAS/414/1278 : Eccentricities of transiting planets (Pont+, 2011)
J/other/Sci/330.653 : Detected planets in the Eta-Earth Survey (Howard+, 2010)
J/A+A/502/395 : WASP-11b (West+, 2009)
J/A+A/501/785 : Discovery and characterization of WASP-6b (Gillon+, 2009)
J/ApJ/706/785 : HAT-P-12 light curve (Hartman+, 2009)
J/A+A/424/L31 : Transiting exoplanet OGLE-TR-132b (Moutou+, 2004)
J/A+A/390/267 : The CORALIE survey for extrasolar planets VIII (Udry+, 2002)
http://exoplanets.org/ : Exoplanet orbit database home page
http://exoplanet.eu/ : The extrasolar planets encyclopaedia home page
Byte-by-byte Description of file: table4.dat
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Bytes Format Units Label Explanations
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1- 11 A11 --- Name System name
13- 18 F6.4 Mjup Mass Known planet mass in Jupiter masses
20- 26 F7.5 AU a Orbit semi-major axis
28- 31 F4.2 --- e Orbit eccentricity
33- 38 F6.4 --- 1tau-s 1M⊕ Lagrange stable boundary (1)
40- 45 F6.4 --- 1tau-u 1M⊕ Lagrange unstable boundary (1)
47- 51 F5.3 --- 1FHZ 1M⊕ Fraction of Habitable Zone (2)
53- 58 F6.4 --- 10tau-s 10M⊕ Lagrange stable boundary (1)
60- 65 F6.4 --- 10tau-u 10M⊕ Lagrange unstable boundary (1)
67- 71 F5.3 --- 10FHZ 10M⊕ Fraction of Habitable Zone (2)
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Note (1): According to Marchal & Bozis (1982CeMec..26..311M 1982CeMec..26..311M), a system is Hill
stable if the following inequality is satisfied:
-(2M/G2M3*)c2h>1+34/3(m1m2/m2/33(m1+m2)4/3)+...
where M is the total mass of the system, G is the gravitational
constant, M*=m1m2+m2m3+m3m1, c is the total angular momentum of the
system, h is the total energy, and m1, m2, and m3 are the masses of
the planets and the star, respectively. We call the left-hand side of
Equation (1) β and the right-hand side βcrit. If
β/βcrit>1, then a system is definitely Hill stable, if not
the Hill stability is unknown. In all the models, we assume that the
hypothetical additional planet is either 1M{earth} or 10M{earth}.
We designate a particular β/βcrit contour as τs
which is a conservative representation of the Lagrange stability
boundary. Similarly, we designate τu as the largest value of
β/βcrit for which all configurations are unstable. See
section 2 and 3 for further details.
Note (2): We have calculated this fraction for all single-planet systems in
the Exoplanet Data Explorer as of 2010 March 25. See section 4.5.
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History:
From electronic version of the journal
(End) Greg Schwarz [AAS], Emmanuelle Perret [CDS] 04-Jun-2012