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Modelling the Resonant System HD128311

Modelling the Resonant System HD128311. Zs. Sándor 1,2 and W. Kley 2 1. Department of Astronomy Eötvös University, Budapest 2. Institut für Astronomie und Astrophysik Abt. Computational Physics, Universität Tübingen. Motivation.

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Modelling the Resonant System HD128311

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  1. Modelling the Resonant System HD128311 Zs. Sándor1,2 and W. Kley2 1. Department of Astronomy Eötvös University, Budapest 2. Institut für Astronomie und Astrophysik Abt. Computational Physics, Universität Tübingen

  2. Motivation Among the 19 multiplanet systems 1 / 3 are in low order MMR most prominent case for the 2:1 resonance: GJ 876 other cases: HD 82943, HD 128311 Capture into a low order MMR indicates that during the formation of these systems next to gravitation, dissipative forces has also worked resulting in decay of the semi – major axes Dissipative forces: disk – planet interaction Scenario of the planetary migration: possible answer to the question: why EPs are not where we imagined Modeling resonant EPSs provides more evidence of planetary migration Aim: explain the observed behaviour of HD 128311

  3. Characterization of the 2:1 MMR Resonant angles (2:1 resonance): q1 = 2l2 - l1 - w1 q2 = 2l2 - l1 - w2 Dq = q1 - q2 = w2 - w1 = Dw Apsidal corotation: Dq (Dw) librates around a mean value Slow (adiabatic) migration results in apsidal corotation

  4. Orbital solution for HD 128311 and its stability Vogt et al. (2005, ApJ 632, 638): new orbital solution for HD128311 the system is stable only if the giants are in the 2:1 resonance (other solutions are not stable) Peculiar behaviour of the eccentricities and the resonant angles: (i) large oscillations in the eccentricities and large amplitude libration ofθ1

  5. Orbital solution for HD 128311 and its stability (ii) circulation ofθ2andDw Thus, the giant planets in HD128311 are NOT in an apsidal corotation!

  6. Evolution of HD 128311 through adiabatic migration tool: numerical integration of the general three-body problem by applying non – conservative forces (BS, Radau integrators) initial configuration: a1 = 2 AU, a2 = 4 AU, e1 = e2= 0.0001 characteristics of migration: (damping only the outer planet) ta= 2x103years, K = 5, K =ta /te ta,te: e – folding times ofa2ande2, respectively relation between e – folding time and the damping rate:

  7. Evolution of HD 128311 through adiabatic migration In order to obtain the recent values of the semi – major axes and eccentricities we stopped migration between t1 = 2x103 and t2 = 3x103 years applying a linear decrease law. This corresponds to a smooth dispersal of the protoplanetary disk. behaviour ofa1anda2 behaviour ofe1ande2

  8. Evolution of HD 128311 through adiabatic migration behaviour of the resonant anglesθ1 and Dw Good agreement with HD calculations! Clearly, the present behaviour of HD128311 is NOT the result of an above migration scenario.

  9. Mixed evolutionary scenarios for HD 128311 I. Fast migration and sudden dispersal the inner part of the protoplanetary disk Physical background: There is a thick and dense disk with sharp inner border, the disk’s inner material is evaporated by the star. The outer planet migrates inward fast and reaches the disk’s inner border. This results in a strong – kicking – perturbation for the system, and the eccentricities begin to oscillate similar to the present case. ta = 5x102 years, K=10.

  10. Mixed evolutionary scenarios for HD 128311 I. Fast migration and sudden dispersal the inner part of the protoplanetary disk Behaviour of the eccentricities:

  11. Mixed evolutionary scenarios for HD 128311 I. Fast migration and sudden dispersal the inner part of the protoplanetary disk Behaviour of the resonant angles θ1 and Dw:

  12. Mixed evolutionary scenarios for HD 128311 II. Planet – planet scattering Idea: Modelling the multiplanet system Ups And by Ford et al. (2005) Two cases are considered: (i) close to the star a small planet orbits in the system (10 MEarth) the two giants approach their present position by migration (ii) the two giants are in a deep 2:1 resonance (apsidal corotation) a small planet migrates inward in the remnant of the protoplanetary disk

  13. Mixed evolutionary scenarios for HD 128311 II. Planet – planet scattering Results: case (i) Behaviour of the eccentricities of the giant planets:

  14. Mixed evolutionary scenarios for HD 128311 II. Planet – planet scattering Results: case (i) Behaviour of the resonant angles θ1 and Dw:

  15. Mixed evolutionary scenarios for HD 128311 II. Planet – planet scattering Results: case (ii) Behaviour of the eccentricities of the giant planets:

  16. Mixed evolutionary scenarios for HD 128311 II. Planet – planet scattering Results: case (ii) Behaviour of the resonant angles θ1 and Dw:

  17. Conclusion The present behaviour of HD 128311 could be the result of a mixed evolutionary scenario: - fast migration + sudden dispersal of the protoplanetary disk - migration + planet – planet scattering

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