The dynamical evolution of exoplanet systems Melvyn B. Davies Department of Astronomy and Theoretical Physics Lund University
Today s Talk 1) Begin with our Solar System. 2) Then consider tightly-packed systems. 3) Interactions between planetary systems and other stars (in crowded birth environments).
Our Solar System
Eccentricity of Jupiter and Saturn Eccentricity of Earth
The Solar System appears to be stable.
Known multiple-planet systems (Lovis et al. 2010)
Kepler systems are also flat By considering the ratio of three, two and single-planet transits, one gets a limit on mutual inclinations. Lissauer et al 2011; Tremaine & Dong 2012; Johansen et al 2012; Fang & Margot 2012
Kepler Catalogue of Candidate Systems Very large catalogue of multiple planet systems found by Kepler through transits. From first 16 months of data: 84 triples, 245 doubles, and 1425 single transits
Making everything from 3p systems 10 2t3p/3t3p 8 6 4 2 0 0.0 Increasing inclination spread 4.0 3.0 2.0 5.0 6.0 7.0 8.0 Kepler 9.0 10.0 0 5 10 15 20 25 30 1t3p/3t3p Kepler sees more 1t than come from 3p (Johansen, Davies, Church & Holmelin 2012)
Tightly-packed systems
An unstable system containing three Jupiters 0.6 0.4 e 0.2 0 1.75 1.5 PLANET1.aei.0 using 1:2 PLANET2.aei.0 using 1:2 PLANET3.aei.0 using 1:2 1.25 a/au 1 0.75 0.5 0 2500 5000 t/yr see also: Quillen (2011)
Planets which eject other planets become eccentric
Instability time as a function of separation R hill,m Mk + M k+1 3M a k + a k+1 2 1/3 (after Chambers et al. 1996; Marzari & Weidenschilling 2002)
Do planets scatter or collide? 2 = Mp M 1 Rp Strong planet-planet interactions tend to lead to scatterings if V esc,p >V orb,p Strong planet-planet interactions tend to lead to collisions if V esc,p <V orb,p 11 < 30 < 64 Collisions can shape planetary systems: e.g. Kepler 36 a p ROCK vs ICE vs GAS
In Kepler zone many planetary systems are multiple but most hot Jupiters are single.
(Mustill, Davies & Johansen 2015)
Injecting planets in from further out can mess up inner system. 3p+J=np or J 3p+np=p? (Mustill, Davies & Johansen 2015; Mustill, Davies & Johansen in prep.) KEY IDEA: this connects the inner (Kepler zone) with the outer (RV) zone.
(Mustill, Davies & Johansen 2015)
Outer multiple planets Stellar binary companion BOTTOM LINE: can produce a reasonable number of hot Jupiters but not all single-planet systems. (Mustill, Davies & Johansen in prep.)
Do eccentric Jupiters imply death on Earth? 1 0.8 0.6 e 0.4 0.2 0 0.01 0.1 1 10 100 a/au
(Carrera, Davies & Johansen, in prep.)
(Carrera, Davies & Johansen, in prep.)
(Carrera, Davies & Johansen, in prep.)
Two kinds of planetary systems: Think of a planetary system containing a number of gas giants. Either: 1) Planetary system is self-unstable, leading to the ejection of giant planets, leaving others on eccentric orbits, (e.g. Rasio & Ford 1996; Juric & Tremaine 2008) OR 2) Planetary system is not self-unstable (rather like our own solar system). (e.g. Lovis et al 2010; Kepler Candidates)
KEY IDEA: Close encounters with other stars, or Exchange encounters which leave planetary systems in binaries can destabilise planetary systems, leaving planets on more bound and eccentric orbits. Such encounters can occur in dense birth environments.
Crowded Places The birth environments of planetary systems Orion nebula and Trapezium cluster (2MASS image)
Stellar encounter timescales Cross section is given by σ = πr 2 min 1 + 2G(M 1 + M 2 ) R min V 2 Timescale for a given star to undergo an encounter is 100 pc τ enc ' 3.3 10 7 3 V 10 3 AU yr n 1 km/s R min M Beware of the average: lumpiness can make a difference. M t (e.g. Malmberg et al. 2007; Davies et al. 2014)
Effects of close encounters Extremely close fly-by encounters may result in the direct ejection of planets. Other planets may remain bound but on tighter and more eccentric orbits. Even very small perturbations can sometimes lead to significant outcomes via planet-planet interactions within planetary systems.
The long term effect of fly-bys (within 100 AU) (Malmberg, Davies & Heggie, 2011)
The four gas giants 10 8 years after fly-by (rmin < 100 AU) (Malmberg, Davies & Heggie, 2011, see also Scharf & Menou 2009; Veras, Crepp & Ford 2009)
Effects of being in a binary If the planetary system and stellar binary are highly inclined, the Lidov-Kozai Mechanism will make the planetary orbits highly eccentric. Strong planet-planet scattering will then occur for multiple-planet systems. For high inclinations planets orbits may become extremely eccentric leading to tidal circularisation.
Evolution of a planet within a stellar binary i=60 degrees
Evolution of our solar system in a binary (Malmberg, Davies & Chambers, 2007; Malmberg & Davies, 2009)
Simulate cluster evolution Evolve clusters considering a range of sizes and masses. Place some stars in binaries whilst others are initially single. Trace stellar histories: log all the close encounters between two stars and binary/ single encounters. Consider both warm & smooth and cold & lumpy initial conditions. (Goodwin & Whitworth 2004; Parker et al 2011)
Cold & lumpy: D=1.6, Q=0.1
Fraction of solar-like stars suffering encounters for cluster containing 700 stars Close fly-by Binary earlier Binary today WS-10 ~0.10 ~0.05 ~0.03 CL-10 ~0.15 ~0.20 ~0.15 WS-all ~0.20 ~0.20 ~0.03 CL-all ~0.20 ~0.50 ~0.10 (Church, Davies & Bonnerot, in prep.) In other words: fly-bys and binary companions can make stable planetary systems unstable interestingly often.
1) Some planetary systems are stable. 2) Instability timescales vary enormously. 3) Multiplicity matters. Conclusions 4) Scattering can match observed eccentricities. 5) Flybys and binary companions can mess up a planetary system. 6) Encounters happen interestingly often in stellar birth environments and clusters.