Planetesimal Migration and the Curious Trend in the Period Ratio Distribution of the Kepler Multis Sourav Chatterjee Eric B. Ford University of Florida April 5, 2013 University of Florida
Kepler multiple planets have a curious P-ratio distribution
Kepler multiple planets have a curious P-ratio distribution
Kepler multiple planets have a curious P-ratio distribution
Constraining planet formation history Gas-rich protoplanetary diskplanets form and migrate
Constraining planet formation history Gas disperses Gas-rich protoplanetary diskplanets form and migrate Planets and planetesimals interact and evolve
Constraining planet formation history Gas disperses Gas-rich protoplanetary diskplanets form and migrate Planets and planetesimals interact and evolve Planetary Systems
Constraining planet formation history Gas disperses Gas-rich protoplanetary diskplanets form and migrate Planets and planetesimals interact and evolve Observed Planetary Systems
Constraining planet formation history Gas disperses Gas-rich protoplanetary diskplanets form and migrate Planets and planetesimals interact and evolve Mon. Not. R. Astron. Soc. 427, L21 L24 (2012) doi:10.1111/j.1745-3933.2012.01337.x Period ratios in multiplanetary systems discovered by Kepler are consistent with planet migration Hanno Rein Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA Observed Planetary Systems
Constraining planet formation history Gas disperses Gas-rich protoplanetary diskplanets form and migrate Planets and planetesimals interact and evolve PLANETS NEAR MEAN-MOTION RESONANCES Cristobal Petrovich 1,RenuMalhotra 2,&ScottTremaine 3 Draft version November 27, 2012 Observed Planetary Systems
Constraining planet formation history Gas disperses The Astrophysical Journal Letters,756:L11(5pp),2012September1 C 2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A. doi:10.1088/2041-820 Gas-rich protoplanetary diskplanets form and migrate RESONANT REPULSION OF KEPLER PLANET PAIRS Yoram Lithwick 1,2 and Yanqin Wu 3 1 Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA 2 Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA 3 Department of Astronomy and Astrophysics, University of Toronto, Toronto, ON M5S 3H4, Canada Received 2012 April 11; accepted 2012 July 24; published 2012 August 9 ABSTRACT Planets and planetesimals interact and evolve Observed Planetary Systems
Constraining planet formation history Gas disperses Gas-rich protoplanetary diskplanets form and migrate Planetesimal migration: destroys MMR Planets and planetesimals interact and evolve planets remain close to the initial integer P-ratio Observed Planetary Systems
Simulation Set Up 1. Trapping into mean motion resonance (MMR) in a gasrich disk 2. Add a planetesimal disk with the trapped planets Readily unstable orbits are cleaned up by planets 10 3 planetesimal orbits are randomly chosen from the database of survived orbits 3. Trapped planets and massive planetesimal disk are evolved for 10 5 years 4. At the end of simulation we study e.g., a, e, ε = P2/P1-2 is calculated and compared with Kepler planet candidates (KPC)
Resonance Angles Simulation Set Up 1. Trapping into Mean Motion Resonance a Start with 2 planets near 2:1 MMR Planets migrate: ȧ = 10 6 AUyr 1 ė = 100ȧ (Lee & Peale 2002) ε P 2 /P 1 2 Planets get trapped into 2:1 MMR
Simulation Set Up 1. Trapping into mean motion resonance (MMR) in a gasrich disk 2. Add a planetesimal disk with the trapped planets Readily unstable orbits are cleaned up by planets 10 3 planetesimal orbits are randomly chosen from the database of survived orbits 3. Trapped planets and massive planetesimal disk are evolved for 10 5 years 4. At the end of simulation we study e.g., a, e, ε = P2/P1-2 is calculated and compared with Kepler planet candidates (KPC)
Simulation Set Up 2. Adding a Planetesimal Disk dn/da Planetesimals are initially added as test particles Disk models: dn da aα Disk includes 1:3 period of the inner planet to 3:1 from the outer planet orbits a (AU) R e a d i l y u n s t a b l e planetesimal orbits are removed by planets
Simulation Set Up 2. Adding a Planetesimal Disk dn/da Planetesimals are initially added as test particles Disk models: dn da aα Disk includes 1:3 period of the inner planet to 3:1 from the outer planet orbits a (AU) R e a d i l y u n s t a b l e planetesimal orbits are removed by planets
Simulation Set Up 1. Trapping into mean motion resonance (MMR) in a gasrich disk 2. Add a planetesimal disk with the trapped planets Readily unstable orbits are cleaned up by planets 10 3 planetesimal orbits are randomly chosen from the database of survived orbits 3. Trapped planets and massive planetesimal disk are evolved for 10 5 years 4. At the end of simulation we study e.g., a, e, ε = P2/P1-2 are calculated and compared with Kepler planet candidates (KPC)
Simulation Set Up 1. Trapping into mean motion resonance (MMR) in a gasrich disk 2. Add a planetesimal disk with the trapped planets Readily unstable orbits are cleaned up by planets 10 3 planetesimal orbits are randomly chosen from the database of survived orbits 3. Trapped planets and massive planetesimal disk are evolved for 10 5 years 4. At the end of simulation we study e.g., a, e, ε = P2/P1-2 are calculated and compared with Kepler planet candidates (KPC)
Properties Explored Mass ratio of the planets: M1/M2 = 0.1 to 10 Disk mass to planet mass ratio: Md/Mp = 0.1 to 1 Disk profile dn/da ~ a α : α = -2 to 2 3 Realizations for each model
Resonance Angles Example Evolution of Dynamical Quantities Readily unstable planetesimals removed a ε Planets are trapped in 2:1 MMR Planetesimal driven migration destroys MMR and increases ε
Results Planetesimal Disk Evolution dn/da a (AU)
Results: Md/Mp and ε
Results: Md/Mp and ε ε i s s t r o n g l y dependent on Md/Mp. Only a small fraction of systems show ε < 0. For Md/Mp sufficiently small (~0.1), ε always remains small. For larger Md/Mp large ranges of ε values are possible depending on α and M1/M2.
Results: Distribution: 0.01 ε 0.1; M1/M2 = 0.1 Md/Mp vs α for a given M1/M2 can potentially constrain planetesimal disk properties after gas dispersal for KPCs with good TTV data
Summary and Conclusions For large ranges in planet and planetesimal disk properties planetesimal driven migration can destroy MMRs if Md/Mp is sufficiently high. Planetesimal migration often moves systems far from MMR for highly negative α and low values of M1/M2. Planetesimal migration can create systems similar to the near resonant KPCs if Md/Mp > 0.1 and M1 > M2 for a large range in α. This model naturally explains why near-resonant giant planets have small ε. This model can potentially constrain Md and α given Mp, M1/M2, and ε.
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