stable planetary orbits in multiple planetary systems
DESCRIPTION
Stable planetary orbits in multiple planetary systems. Extrasolar Planets Systems with two or more Planets Habitable Zones HD 74156 The System Methods Initial Conditions Results Eccentricities Resonances HD 38529, HD 169830, HD 168443. Extrasolar Planets - PowerPoint PPT PresentationTRANSCRIPT
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Stable planetary orbits in multiple planetary systems
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• Extrasolar Planets• Systems with two or more Planets• Habitable Zones
• HD 74156• The System• Methods• Initial Conditions
• Results• Eccentricities• Resonances
• HD 38529, HD 169830, HD 168443
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Extrasolar Planets
•102 planetary systems•117 planets•13 multiple planetary systems•15 planetary systems in binaries
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Systems with two or more Planets
Star apl [AU] epl Mpl sin i [MJup] Ups And 0.059 0.012 0.69
0.829 0.28 1.19 2.53 0.27 3.75
HD 38529 0.129 0.29 0.78 3.68 0.36 12.7
55 Cnc 0.11 0.02 0.84 0.24? 0.34? 0.21? 5.9 0.16 4.05
Gliese 876 0.13 0.12 0.56 0.21 0.27 1.98
HD 74156 0.28 0.647 1.6 3.82 0.354 8.2
HD 168443 0.295 0.53 7.73 2.9 0.2 17.23
HD 37124 0.54 0.1 0.75 2.5 0.69 1.2
HD 82943 0.73 0.54 0.88 1.16 0.41 1.63
HD 169830 0.82 0.327 3.03 2.85 0.0 2.51
HD 12661 0.83 0.096 2.3 2.56 <0.1 1.57
HD 160691 1.5 0.31 1.7 2.3? 0.8? 1?
47 Uma 2.1 0.096 2.41 3.73 <0.1 0.76
Epsilon Eridani 3.3 0.608 0.86 40?? 0.3?? 0.1??
In collaboration with Prof. Erdi and his group from Budapest
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Habitable Zones
•Depends on the spectral type of the host star•Zones, where liquid water can exist•Planets have to stay on their orbits for a very long time•The eccentricity should not be higher than 0.2
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Mstar = 1.05 MSun
HD 74156 bm = 1.6 Mjup sin ia = 0.28 AUe = 0.647
HD 74156 cm = 8.2 Mjup sin ia = 3.82 AUe = 0.354
HD 74156• The orbital parameters were taken from the Geneva group of observers• Masses are Minimum Masses
Institute for Astronomy University of ViennaThe resonant region and the habitable zone
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Region between the resonances (habitable zone)
• Integration Methods• Numerical Integrations with the Lie-Series
• Initial Conditions• Restricted 4-body problem (star, 2 planets, massless test-planets)• Semimajor Axis: a = 0.6 to 1.4 AU• Eccentricities for the outer planet: e = 0.3, 0.35, 0.4, 0.45• Eccentricities for the inner planet: e = 0.5, ..., 0.7• Integration Time: 105 years
• Stability-Criterion• No close encounters within the Hill‘s sphere were allowed
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e = 0.3 e = 0.35
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e = 0.4 e = 0.45
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Resonances• Integration Method
• Numerical Integrations with the Lie-Series• The Fast Lyapunov Indicator (FLI) with a Bulirsch Stoer integrator
• Initial Conditions (Lie-Integrator)• Restricted 4-body problem (star, 2 planets, massless test-planets)• Inner Resonances with the outer planet• Outer Resonances with the inner planet• Mean Anomaly: 0°, 30°,..., 330°• Different mean anomalies of the known planets• Inclinations: i = 0°, 10°,..., 50° • Integration Time: 105 years
• Initial Conditions (FLI)•Different mean anomalies of the known planets•Semimajor axes: a = 0.7 and 1.3 AU
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•Stability-Criterion (Lie-Integrator)• No close encounters within the Hill‘s sphere were allowed
•Stability-Criterion (FLI)
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Inner Resonances with the outer planet: i = 0°
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FLI:a = 1.3 AU
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Outer Resonances with the inner planet: i = 0°
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FLI:a = 0.7 AU
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Inner Resonances with the outer planet: i = 20°
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Outer Resonances with the inner planet:i = 20°
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Inner Resonances with the outer planet: i = 50°
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Outer Resonances with the inner planet:i = 50°
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stable
0
5
10
15
20
25
30
0 20 40 60
Inclination
Inner Resonances
Outer Resonances
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HD 74156 bm = 1.86 MJup
a = 0.294 AUe = 0.635
HD 74156 cm = 6.42 MJup
a = 3.44 AUe = 0.561
New Data
Institute for Astronomy University of ViennaHD 38529 HD 169830 HD
168443
Mstar = 1.39 MSun
HD 38529 bm = 0.78 MJup
a = 0.129 AUe = 0.29HD 38529 cm = 12.7 MJup
a = 3.68 AUe = 0.36
Mstar = 1.4 MSun
HD 169830 bm = 3.03 MJup
a = 0.82 AUe = 0.327HD 169830 cm = 2.51 MJup
a = 2.85 AUe = 0.0
Mstar = 1.01 MSun
HD 168443 bm = 7.73 MJup
a = 0.295 AUe = 0.53HD 168443 cm = 17.23 MJup
a = 2.9 AUe = 0.2
Institute for Astronomy University of Vienna
Institute for Astronomy University of Vienna
Institute for Astronomy University of Vienna