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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 systems Secular perturbation theory Application: tight binary systems Summary + Outlook

About

NFN sub-project SP8 “ Systems and Habitability” Stand-alone project “: Architecture, Evolution and Habitability”

Basic dynamical types

S-type motion (“”) around one star P-type motion (“planetary”) around both

Image: R. Schwarz

Exoplanets in multiple star systems

Observations: (Schwarz 2014, Binary Catalogue)

● 55 binary star systems with 81 ● 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 “” (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 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 Database http://exoplanets.org Open Exoplanet Catalogue http://www.openexoplanetcatalogue.com The 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

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

precession of pericenter (and line of nodes) with time

Laplace-Lagrange linear theory

Developed for (low -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”) ● ( 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 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 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