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1) the Case for Stochastic Orbital Migration 2) Open Exoplanet Catalogue Institute for Advanced Study 1) The case for stochastic orbital migration 2) Open Exoplanet Catalogue Hanno Rein @ UoT St. George Campus, March 2013 Extra-solar planet census All discovered extra-solar planets 869 confirmed extra- solar planets • Super-Jupiters • (Hot) Jupiters • Neptunes • Super-Earths • Earth-like planets Open Exoplanet Catalogue (Rein 2012b) All multi-planetary systems 327 confirmed planets in multi-planetary systems • Multiple Jupiters • Densely packed systems of Neptunes and (Super)-Earths • 1 Solar System • Some systems are deep in resonance Open Exoplanet Catalogue (Rein 2012b) Radial velocity planets 80 RV planets 70 Cumulative period ] 60 ratio in multi- 10 jup [M planetary systems 2 50 + m 1 • Periods of systems with 40 massive planets tend to pile up near integer number of pairs 30 ratios 1 20 total planet mass m • Most prominent 10 features at 4:1, 3:1, 2:1, 0 3:2 1 1.33 1.5 2 3 4 5 6 7 8 9 period ratio 300 0.1 KOI planets 250 ] jup [M Rein, Payne, Veras & Ford (2012) 200 2 + m 1 150 number of pairs 100 total planet mass m 50 0 0.01 1 1.33 1.5 2 3 4 5 6 7 8 9 period ratio Kepler candidates 2740 planet candidates • Probing a different regime • Small mass planets • A lot of planets Open Exoplanet Catalogue (Rein 2012b) Kepler candidates with multiple planets Kepler multi-planetary systems • Small mass planets • Hierarchical systems • Densely packed • Not many are in resonance Open Exoplanet Catalogue (Rein 2012b) 80 RV planets 70 ] 60 10 jup [M 2 50 + m 1 40 number of pairs 30 1 20 total planet mass m Kepler's 10 transiting planet candidates 0 1 1.33 1.5 2 3 4 5 6 7 8 9 period ratio 300 0.1 KOI planets 250 • Period ratio ] jup distribution much [M 200 2 smoother for small + m mass planets 1 150 • Deficiencies near 4:3, number of pairs 3:2, 2:1 100 total planet mass m • Excess slightly outside 50 of the exact commensurability 0 0.01 1 1.33 1.5 2 3 4 5 6 7 8 9 period ratio Rein, Payne, Veras & Ford (2012) Stochastic orbital migration Migration - Type I • Low mass planets • No gap opening in disc • Migration rate is fast • Depends strongly on thermodynamics of the disc 2D hydro code Prometheus (Rein 2010) Migration - Type II • Massive planets (typically bigger than Saturn) • Opens a (clear) gap • Migration rate is slow • Follows viscous evolution of the disc 2D hydro code Prometheus (Rein 2010) How does a real protoplanetary disk look like? Image credit: NASA/JPL-Caltech Why think about stochastic migration? • Angular momentum transport • Magnetorotational instability (MRI) • Density perturbations interact gravitationally with planets • Stochastic forces lead to random walk • Large uncertainties in strength of forces Animation from Nelson & Papaloizou 2004 Random forces measured by Laughlin et al. 2004, Nelson 2005, Oischi et al. 2007 Random walk in all orbital parameters pericenter eccentricity semi-major axis time Rein & Papaloizou 2009 Analytic growth rates for 1 planet 0.01 Dt 2 [AU] 0.001 (∆a) =4 RMS a> 2 n < 0.0001 1 2 2.5 γDt 0.1 RMS (∆$) = > 2 2 2 < e n a 0.01 0.001 0.01 γDt RMS 2 0.001 e> (∆e) =2.5 < n2a2 0.0001 Simulations Analytic solution Analytic solution (=1) 10 100 1000 10000 100000 time [years] Rein & Papaloizou 2009, Adams et al 2009, Rein 2010 Analytic growth rates for 2 planets 2 (∆⇥1) 9γf 2 = 2 2 Dt (p + 1) a1⇤lf 2 5γs (∆(∆⌅)) = 2 2 2 Dt 4a1n1e1 Rein & Papaloizou 2009 Multi-planetary systems in mean motion resonance GJ876 Earth • Stability of multi-planetary systems depends strongly on diffusion coefficient • Most planetary systems are stable for entire disc lifetime Rein & Papaloizou 2009 The formation of Kepler-36 Kepler-36 c as seen from Kepler-36 b • Would appear 2.5 times the size of the Moon • Very close orbits, near a 7:6 resonance • Very different densities Formation of Kepler-36 2.8 • Migration rate and mass 106 ratio determine the final 2.6 resonance stable resonances 2.4 105 8:7 7:6 6:5 5:4 4:3 3:2 Higher order resonances 2.2 • require faster migration 2.0 rates 104 1.8 time [yrs] period ratio • Higher mass planets end up crossing of the 2:1 resonance 1.6 in lower order resonances 103 1.4 • Once in resonance, planets convergent migration 1.2 often stay there for the rest 102 of the disc lifetime 1.0 103 104 105 migration timescale [yrs] Pardekooper, Rein & Kley (in prep) Problem with Kepler-36 <1000 years Need extremely fast migration rate to capture into a high order resonance. Unrealistically fast. Planets are not large enough to migrate in Type III regime. Pardekooper, Rein & Kley (in prep) τa = 2000 yrs τa = 10000 yrs low order resonances low order resonances high order resonances 2.8 2.8 104 7:6 2.6 2.6 2.4 5:4 2.4 104 2.2 2.2 3:2 2.0 2.0 103 1.8 1.8 time [yrs] time [yrs] period ratio 3 period ratio crossing of the 2:1 resonance 1.6 10 crossing of the 2:1 resonance 1.6 1.4 1.4 102 convergent migration 1.2 convergent migration 1.2 1.0 1.0 Solution: Stochastic10-3 migration10-2 10-1 10-3 10-2 10-1 amplitude of stochastic forces [F0] amplitude of stochastic forces [F0] τa = 20000 yrs τa = 100000 yrs low order resonances high order resonances low order resonances high order resonances 2.8 2.8 105 2.6 2.6 4:3 4:3 2.4 2.4 105 2.2 2.2 3:2 3:2 104 2.0 2.0 1.8 1.8 time [yrs] time [yrs] period ratio 104 period ratio crossing of the 2:1 resonance 1.6 crossing of the 2:1 resonance 1.6 103 1.4 1.4 convergent migration 1.2 convergent migration 1.2 1.0 103 1.0 10-3 10-2 10-1 10-3 10-2 10-1 amplitude of stochastic forces [F0] amplitude of stochastic forces [F0] Pardekooper, Rein & Kley (in prep) A statistical analysis 80 RV planets 70 ] 60 10 jup [M 2 50 + m 1 40 number of pairs 30 1 20 total planet mass m Kepler's 10 transiting planet candidates 0 1 1.33 1.5 2 3 4 5 6 7 8 9 period ratio 300 0.1 KOI planets 250 • Period ratio ] jup distribution much [M 200 2 smoother for small + m mass planets 1 150 • Deficiencies near 4:3, number of pairs 3:2, 2:1 100 total planet mass m • Excess slightly outside 50 of the exact commensurability 0 0.01 1 1.33 1.5 2 3 4 5 6 7 8 9 period ratio Rein, Payne, Veras & Ford (2012) Testing stochastic migration: Method Architecture and masses from observed KOIs Placing planets in a MMSN, further out, further apart, randomizing all angles N-body simulation with migration forces Rein 2012 Testing stochastic migration: Advantages Comparison of Comparison of statistical quantities individual systems • Period ratio distribution • Especially interesting for • Eccentricity distribution multi-planetary systems • TTVs • Can create multiple realizations of each system No synthesis of a planet population required • Observed masses, architectures • Model independent Preliminary results 600 Observed KOI planets 4 -6 Migration τ =10 years, α=10 a 4 -5 Migration τ =10 years, α=10 500 a 400 300 300 number of pairs 200 250 100 200 1.9 2 2.1 0 1 1.33 1.5 2 3 4 5 6 7 8 9 period ratio Rein 2012 Future expansions Physical disk model Completeness • 1D hydrodynamic simulation • Include planets missed by Kepler • Coupled to N-body simulations GPU based integrators Other physical effects • Allows for much bigger samples • Tidal damping • Wider parameter space exploration • Evaporation Saturn’s Rings REBOUND • Code description paper published by A&A, Rein & Liu 2012 • Multi-purpose N-body code • Only public N-body code that can be used for granular dynamics Astronomy & Astrophysics manuscript no. paper c ESO 2011 October 20, 2011 • Written in C99, open source, GPL REBOUND: An open-source multi-purpose N-body code for collisional dynamics Hanno Rein 1 and Shang-Fei Liu 2,3 • 1 Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540 Freely available at e-mail: [email protected] 2 Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, P. R. China 3 Department of Astronomy, Peking University, Beijing 100871, P. R. China e-mail: [email protected] http://github.com/hannorein/rebound Submitted: 13 September 2011 ABSTRACT REBOUND is a new multi-purpose N-body code which is freely available under an open-source license. It was designed for collisional dynamics such as planetary rings but can also solve the classical N-body problem. It is highly modular and can be customized easily to work on a wide variety of di ↵erent problems in astrophysics and beyond. REBOUND comes with three symplectic integrators: leap-frog, the symplectic epicycle integrator (SEI) and a Wisdom-Holman mapping (WH). It supports open, periodic and shearing-sheet boundary conditions. REBOUND can use a Barnes-Hut tree to calculate both self- gravity and collisions. These modules are fully parallelized with MPI as well as OpenMP. The former makes use of a static domain decomposition and a distributed essential tree. Two new collision detection modules based on a plane-sweep algorithm are also implemented.
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