Stability Dynamics Habitability of Planets in Binary Systems

Stability Dynamics Habitability of Planets in Binary Systems

Facts and Questions: Binary and Multi-Star Systems in the Solar neighbourhood: >60% Do the gravitational perturbations allow planetary formation? (about 60 binary systems hosting planets) Information about the area of formation Long-term stability is of great interest search for habitable planets

Outline Types of planetary motion in binary star systems Stability of planetary motion Examples of planetary motion in tight binaries Habitable planets in binaries? Solar System in a wide binary (Innanen et al. 1997)

S-Typ Planetary motion in binaries:

Trojans type motion Near L4 and L5 L 4 and L 5 (stable for µ < 1:25) are at the third vertex of an equilateral triangle (Sun-Jupiter-Asteroid)

Studies by : Harrington (1977) Graziani & Black (1981) and Black (1982) planar case: No serious threat to the long-term stability if the star is at a distance > 5 x planetary distance inclined case: at high ibinary the planetary orbits becomes unstable Kozai mechanism Pendleton & Black (1983)

Some General Numerical Studies of planetary motion in binary systems: Dvorak R.(1984 and 1986) Rabl & Dvorak R. (1988) Dvorak R., Froeschle C. & Froeschle Ch. (1989) Holman M. & Wiegert P. (1999) Pilat-Lohinger E. & Dvorak R. (2002) Szenkovits F. & Mako Z. (2008)

Stability analysis Initial Conditions: abinary =1 AU ebinary=[0,.0.9] aplanet=[0.1, 0.9] eplanet=[0, 0.9] i, Ώ,ω, = 0 M= 0,90,180,270

Numerical Methods: Long-term numerical integration: Stability-Criterion: No close encounters within the Hill sphere (i)escape time (ii) Study of the eccentricity: maximum eccentricity Chaos Indicators: Fast Lyapunov Indicator (FLI) C. Froeschle, R.Gonczi, E. Lega (1996) MEGNO RLI Helicity Angle Lyapunov Exponent

General Studies of S-type motion in binary systems: Dvorak R.(1984 and 1986) Rabl & Dvorak R. (1988) Dvorak R., Froeschle C. & Froeschle Ch. (1989) (200-500 periods) Holman M. & Wiegert P. (1999) (mass-ratios: 0.1-09, ebinary: 0 0.9; 10000 periods)

Pilat-Lohinger & Dvorak (2002): The Fast Lyapunov Indicator (FLI) (see Froeschle et al., CMDA 1997) distinguish between regular and chaotic motion ; length of the largest tangent vector: FLI(t) = sup_i v_i(t) i=1,...,n (n denotes the dimension of the phase space) chaotic orbits can be found very quickly because of the exponential growth of this vector in the chaotic region; For most chaotic orbits only a few number of primary revolutions is needed to determine the orbital behavior.

Stability analysis Initial Conditions: abinary =1 AU ebinary=[0,.0.9] aplanet=[0.1, 0.9] eplanet=[0, 0.9] i, Ώ,ω, = 0 M= 0,90,180,270

mass-ratio = 0.5

mass-ratio S-type motion e_binary 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.45 0.38 0.37 0.30 0.26 0.23 0.20 0.16 0.13 0.1 0.37 0.32 0.29 0.27 0.24 0.20 0.18 0.15 0.11 0.2 0.32 0.27 0.25 0.22 0.19 0.18 0.16 0.13 0.10 0.3 0.28 0.24 0.21 0.18 0.16 0.15 0.13 0.11 0.09 0.4 0.21 0.20 0.18 0.16 0.15 0.12 0.11 0.10 0.07 0.5 0.17 0.16 0.13 0.12 0.12 0.09 0.09 0.07 0.06 0.6 0.13 0.12 0.11 0.10 0.08 0.08 0.07 0.06 0.045 0.7 0.09 0.08 0.07 0.07 0.05 0.05 0.05 0.045 0.035 0.8 0.05 0.05 0.04 0.04 0.03 0.035 0.03 0.025 0.02 Stable zone (in units of length) of S-type motion for all computed mass-ratios and eccentricities of the binary. The given size for each (mu,e_binary) pair is the lower value of the studies by Holman &Wiegert (AJ,1999) and Pilat-Lohinger &Dvorak (CMDA, 2002)

planets in binaries

tight binary systems binary abinary [AU] ebinary M1/M2 Gliese86 22? 0.7/0.5 γ Cephei 20 0.44 1.6/0.4 HD41004 23? 0.7/0.4 HD188753 12.3 0.5 1.06/1.63 HD196885 25? 1.3/0.6

Examples of Planets in Tight Binary Systems: binary abinary [AU] ebinary m1 m2 [msun] Gliese86 ~22? 0.7 0.5 γ Cephei ~20 0.4 1.6 0.4 HD41004 ~23? 0.7 0.4 Gliese86 γ Cephei HD 41004 m sin i = 4 MJ a = 0.11AU e = 0.045 m sin i = 1.6 MJ a = 2.15 AU e = 0.11 0.2 m sin i = 2.3 MJ a = 1.3 AU ( 1.6 or 1.7) e = 0.39 +/- 0.17?

Influence of the eccentricity of the planet?

Influence of the eccentricity

mass-ratio = 0.2 γ Cephei : a_binary= 20 AU e_binary= 0.44 e_planet= 0.2 acrit = 0.18 SZ= 3.6 AU a_planet=2.15 AU Pilat-Lohinger & Dvorak, (CeMDA 2002)

The mass of the planet? Is the elliptic restricted three body problem a good model?

Circular Planetary Motion: -- Size of Stable Region e_bin RTP 1Jup 3Jup 5Jup 0 0.38 0.38 0.35 0.35 0.1 0.34 0.31 0.31 0.31 0.2 0. 30 0.24 0.24 0.24 0.3 0.24 0.21 0.21 0.21 0.4 0. 20 0.20 0.20 0.20 0.5 0.16 0.14 0.14 0.14

Elliptic Planetary Motion: e_bin 0.1 0.2 0.3 0.4 0.5 e_plan 0.0 0.31 0.24 0.22 0.21 0.14 0.1 0.31 0.24 0.22 0.19 0.14 0.2 0.28 0.24 0.18 0.16 0.14 0.3 0.26 0.24 0.19 0.15 0.13 0.4 0.25 0.21 0.16 0.13 0.11 0.5 0.19 0.16 0.14 0.12 0.09 Stable Region for a 5Jupiter-mass Planet

e_bin=0.4 e_plan RTBP 1Mj 3Mj 5Mj 8Mj 0.0 0.2 0 0.20 0.20 0.20 0.20 0.1 0.2 0 0.20 0.20 0.19 0.19 0.2 0.18 0.18 0.17 0.16 016 0.3 0.17 0.16 0.16 0.15 0.15 0.4 0.17 0.15 0.14 0.13 0.13 0.5 0.15 0.12 0.11 0.09 0.09

gamma Cephei a_bin ~ 20 AU, e_bin ~ 0.4 e_plan RTBP 1Mj 3Mj 5Mj 8Mj 0.0 4.0 4.0 4.0 4.0 4.0 0.1 4.0 4.0 4.0 3.8 3.8 0.2 3.8 3.6 3.4 3.2 3.2 0.3 3.4 3.6 3.2 3.0 3.0 0.4 3.4 3.0 2.8 2.6 2.6 0.5 3.0 2.4 2.2 1.8 1.8

mass-ratio = 0.2 γ Cephei a_bin = 22 AU e_bin = 0.44 a_p = 2 AU e_p=0.21 3.6AU a_bin=18.5au e_bin=0.36 a_p=2.13au e_p=0.12 3.2 AU

Stability limits mass-ratio border of stable motion Gamma Cephei: 0.2 3.2 3.8 AU HD41004 AB: 0.36 (e=0.39) 4.6 2.8 AU (e=0.5) 4.6 2.53AU Gliese 86: 0.42 close-in planet

γ Cephei mass-ratio = 0.2 abinary = 20 AU ebinary ~ 0.4 increase e γ Cep b : 0.11 0.5. Planet s eccentricity border of stable region [AU] 0.0 4.0 0.1 3.8 0.2 3.6 0.3 3.4 04 3.2 0.5 3.0

gamma Cephei

ebinary not known! binary abinary [AU] ebinary m1 m2 Gliese86 ~22? 0.7 0.5 γ Cephei ~20 0.4 1.6 0.4 HD41004 ~23? 0.7 0.4 HD 41004A: m sin i = 2.3 MJ a = 1.3 AU ( 1.6 or 1.7) e = 0.39 +/- 0.17?

HD41004 AB

Influence of the secondary on the planetary motion?

with secondary without secondary gammacep e_b=0.44 e_pl=0.209 HD41004 e_b=0.2 e_pl=0.22

Differences of the two planetary systems: semi-major axis of the planet eccentricity of the binary mass-ratio of the binary mass of the giant planet

different e_binary

different mass-ratio Gamma Cephei

Planet is close to the host-star: The region is mainly influenced by the mean motion resonances If the planet is closer to the secondary -> an arc-like structure of chaos appears which depends on: a_planet, e_binary, masses,

Habitable Zone Zone around a star where liquid water can exist on the surface of a terrestial-like planet This zone depends on: the spectraltype, the mass, the age,. of the star the orbit of the planet the mass, the composition, the atmosphere, of the planet the parameters of other planets in this system (mass, orbit, )

The Habitable Zone based on the definition given by Kasting et al. (1993).

Different HZs

Binary Star Configurations:

Different Binary Configurations

Insolation

Next Studies: Inclined planetary systems

stable motion in the HZ only for a < 0.7 AU the eccentricity of the binary ebin < 0.7 Results for HD41004A we have found two zones for habitable planets: for nearly circular planetary motion around 0.5 AU the eccentricity of the detected planet has to be < 0.36 for higher eccentric planetary motion around 0.6 AU the eccentricity of the detected planet has to be < 0.3 e fpl < 0.06 e fpl < 0.23 maximum eccentricity

gamma Cephei Primary and Secondary: m1 = 1.6 MS m2 = 0.4 MS a = 20AU e = 0.44 Planet: mp = 1.7 Mjup a = 2.15 AU e = 0.2

abinary=22 AU ebinary=0.7 Gliese 86

HZ of HD41004 A red: low ecc. blue: high ecc. 4:1 7:2 3:1 8:3

Region of nearly circular motion exists size and position depends on (i) a_giant planet (ii) e_giant planet (iii) m_giant planet No strong dependence on i (i<25) Stable circular motion for close-in planets Stable region around i=35 -

ebinary=0.2 : eplanet=0.1, 0.3 eplanet =0.2 : ebinary=0.1, 0.3

Innanen et al. (1997) : Solar System in a Wide Binary Star System