StabilityStability ofof PlanetsPlanets inin BinaryBinary StarStar SystemsSystems
Ákos Bazsó in collaboration with: E. Pilat-Lohinger, D. Bancelin, B. Funk
ADG Group
Outline
Exoplanets in multiple star systems Secular perturbation theory Application: tight binary systems Summary + Outlook
About
NFN sub-project SP8 “Binary Star Systems and Habitability” Stand-alone project “Exoplanets: Architecture, Evolution and Habitability”
Basic dynamical types
S-type motion (“satellite”) around one star P-type motion (“planetary”) around both stars
Image: R. Schwarz
Exoplanets in multiple star systems
Observations: (Schwarz 2014, Binary Catalogue)
● 55 binary star systems with 81 planets ● 43 S-type + 12 P-type systems ● 10 multiple star systems with 10 planets
Example: γ Cep (Hatzes et al. 2003)
● RV measurements since 1981
● Indication for a “planet” (Campbell et al. 1988) ● Binary period ~57 yrs, planet period ~2.5 yrs
Multiplicity of stars
~45% of solar like stars (F6 – K3) with d < 25 pc in multiple star systems (Raghavan et al. 2010) Known exoplanet host stars:
single double triple+ source 77% 20% 3% Raghavan et al. (2006) 83% 15% 2% Mugrauer & Neuhäuser (2009) 88% 10% 2% Roell et al. (2012)
Exoplanet catalogues
The Extrasolar Planets Encyclopaedia http://exoplanet.eu Exoplanet Orbit Database http://exoplanets.org Open Exoplanet Catalogue http://www.openexoplanetcatalogue.com The Planetary Habitability Laboratory http://phl.upr.edu/home NASA Exoplanet Archive http://exoplanetarchive.ipac.caltech.edu Binary Catalogue of Exoplanets http://www.univie.ac.at/adg/schwarz/multiple.html Habitable Zone Gallery http://www.hzgallery.org
Binary Catalogue
Binary Catalogue of Exoplanets http://www.univie.ac.at/adg/schwarz/multiple.html
Dynamical stability
Stability limit for S-type planets Rabl & Dvorak (1988), Holman & Wiegert (1999), Pilat-Lohinger & Dvorak (2002) Parameters (a , e , μ) bin bin Outer limit at roughly max. ¼ of stellar separation (for μ = 0.5) Implications for planet formation → truncation of protoplanetary disk
Secular perturbation theory in a nutshell
Secular perturbation theory
“secular” = long time-scales: T sec ≫T rev min. 3 interacting massive bodies (m , m , m ) 0 1 2 gravitational perturbations lead to ... ● mean motion resonances (MMR) ● secular resonances (SR) resonance = integer ratio of 2 frequencies
f 1/f 2=p/q∈ℚ
Single star – single planet
two-body problem = indefinitely stable
Basic parameters
● Semi-major axis a ● Eccentricity e 0 < e < 1 ● Solar system planets: e ≤ 0.2
pericenter apocenter
Binary star system
precession of pericenter (and line of nodes) with time
Laplace-Lagrange linear theory
Developed for solar system (low mass-ratio) Limits = low eccentricity / inclination Objects = host star + 2 perturbers + massless test planet
Simple analytical formula (Murray & Dermott 1999) h(t)=e sin(g t+ϕ)+ A (g , g ,e )sin(g t+ϕ ) free ∑ j j j j j g = free (proper) secular frequency of test planet g = fundamental Eigenfrequencies of system j Free/forced eccentricity
Example 1: frequencies for planets
Example 2: asteroid main-belt
Image: Tsiganis (2008) Application
Binary star systems with separation a < 100 AU Typical setting:
● host star (“primary”) ● companion star (“secondary”) ● giant planet (Jupiter like) around primary ● stability of additional (terrestrial) planets ? Explanation for numerical results Semi-analytical method
● Determine secular frequency of giant planet ● Find intersection with analytical curve of free frequency
Aim of study
Investigated systems
Star 1 Star 2 Planet name Mass Spectral Mass Distance Ecc. Mass Distance Ecc. M Type M AU M AU sun sun jup GJ 3021 0.90 G6V 0.15 (?) 68 0.20 (?) 3.37 0.49 0.51
Gliese 86 0.83 K0V 0.49 19 0.40 4.01 0.11 0.05
94 Cet 1.34 F8V 0.20 (?) ≥ 100 (?) 0.20 (?) 1.68 1.42 0.30
HD 41004 0.70 K2V 0.15 (?) 23 0.20 (?) 2.54 1.64 0.20 (?)
τ Boo 1.30 F6IV 0.40 (?) 45 0.20 (?) 5.90 0.046 0.02
HD 177830 1.47 K0IV 0.23 97 0.20 (?) 1.49 1.22 ≈ 0.00
HD 196885 1.33 F8V 0.45 21 0.42 2.98 2.60 0.48
γ Cep 1.40 K1III 0.41 19 0.41 1.85 2.05 0.05
(?) = estimated values; minimum masses M sin(i) Selected systems
Star 1 Star 2 Planet name Mass Spectral Mass Distance Ecc. Mass Distance Ecc. M Type M AU M AU sun sun jup GJ 3021 0.90 G6V 0.15 68 0.20 3.37 0.49 0.51
Gliese 86 0.83 K0V 0.49 19 0.40 4.01 0.11 0.05
94 Cet 1.34 F8V 0.20 ≥ 100 0.20 1.68 1.42 0.30
HD 41004 0.70 K2V 0.15 23 0.20 2.54 1.64 0.20
τ Boo 1.30 F6IV 0.40 45 0.20 5.90 0.046 0.02
HD 177830 1.47 K0IV 0.23 97 0.20 1.49 1.22 ≈ 0.00
HD 196885 1.33 F8V 0.45 21 0.42 2.98 2.60 0.48
γ Cep 1.40 K1III 0.41 19 0.41 1.85 2.05 0.05
Numerical results for HD 41004
Image: E. Pilat-Lohinger
Why not the other systems ?
HD 1237
HD 41004
Dependence on secondary star 1
increasing a 2
Dependence on secondary star 2
increasing m 2
HD 196885
Outlook
Ongoing work Determine width of perturbation – dependence on parameters (mass, distance, eccentricity, …) Goals:
● Catalogue for observers ● Binary star systems allowing “unperturbed” habitable zone (small eccentricity)
That'sThat's allall folksfolks ...... References
Campbell, Walker & Yang (1988), ApJ 331, 902 Hatzes, Cochran, Endl et al. (2003), ApJ 599, 1383 Holman & Wiegert (1999), AJ 117, 621 Mugrauer & Neuhäuser (2009), A&A 494, 373 Murray & Dermott (1999), Solar System Dynamics, Cambridge Univ. Press Pilat-Lohinger & Dvorak (2002), CMDA 82, 143 Rabl & Dvorak (1988), A&A 191, 385 Raghavan, Henry, Mason et al. (2006), ApJ 646, 523 Raghavan, McAlister, Henry et al. (2010), ApJS 190, 1 Roell, Neuhäuser, Seifahrt & Mugrauer (2012), A&A 542, 92 Tsiganis (2008), Lecture Notes in Physics 729, 111, Springer