1. 1 Determining the internal structure of extrasolar planets, and the phenomenon of retrograde planetary orbits Rosemary Mardling School of Mathematical Sciences Monash University

2. 2 Binary stars and apsidal motion double-line eclipsing binary - all parameters known except k 2 (1)

3. 3 Binary stars and apsidal motion This method of determining k 2 involves measuring the change in something… Claret & Gimenez 1993

4. 4 planets and apsidal motion k 2 is now called the LOVE NUMBER (= twice apsidal motion constant) Circularization timescale ~ 10 8 yr; age ~ 5 Gyr  b = 181±46 o __ error MUCH bigger than change per year b

5. 5 Tidal evolution of (isolated) binaries and short-period planets The minimum-energy state of a binary system (or star + planet) is: circular orbit rotational frequencies = orbital frequency spin axes aligned with orbit normal ??Definition of short-period planet -- circularization timescale less than the age of the system

6. 6 Tidal evolution of short-period planets with companions Many short-period planets have non-zero eccentricities AND anomolously large radii (eg. e = 0.05, R p = 1.4 Jupiter radii) Bodenheimer, Lin & Mardling (2001) propose that they have undetected companion planets Mardling (2007): a fixed-point theory for tidal evolution of short-period planets with companions (coplanar) - developed to understand inflated planets Batygin, Bodenheimer & Laughlin (2009) use this to deduce information about the internal structure of HAT-P-13b CAN MEASURE k 2 DIRECTLY (no need to wait for change in anything)

7. 7 Fixed-point theory of tidal evolution of planets with companions COPLANAR theory (Mardling 2007)

8. 8 Fixed-point theory of tidal evolution of planets with companions COPLANAR theory

9. 9 Fixed-point theory of tidal evolution of planets with companions

10. 10 Fixed-point theory of tidal evolution of planets with companions all parameters known except

11. 11 Fixed-point theory of tidal evolution of planets with companions

12. 12 Fixed-point theory of tidal evolution of planets with companions System evolves to doubly circular state on timescale much longer than age of system Real Q-value at least 1000 times larger …. evolution at least 1000times slower HD209458

13. 13 Fixed-point theory of tidal evolution of planets with companions Equilibrium eccentricity substantial if: large (there are interesting exceptions) not too small large HAT-P-13:

14. 14 The HAT-P-13 system data from Bakos et al 2009 HATNet transit discovery (CfA) Keck followup spectroscopy KeplerCam followup photometry

15. 15 The HAT-P-13 system Batygin et al: use fixed-point theory to determine and hence This in turn tells us whether or not the planet has a core. Measured value of (Spitzer will improve data in Dec)

16. 16 The HAT-P-13 system Given m b, R b, T eff, find m core, L tide from grid of models k b, Q b  k b /L tide, e b (eq) best fit

17. 17 However… A system with such a high outer eccentricity is highly unlikely to be COPLANAR! The high eccentricity of planet c may have been produced during a scattering event: Once upon a time there existed a planet d…..

18. 18 Scenario for the origin of the HAT-P-13 system a d =2.9 AU, m d =12 M J, Q b = 10 minimum separation 10 a b when e c ~ 0.67 MODEL 1: e d =0.17

19. 19 Scenario for the origin of the HAT-P-13 system MODEL 1: e d =0.17

20. 20 Scenario for the origin of the HAT-P-13 system MODEL 1: e d =0.17 i bc i *c

21. 21 Variable stellar obliquity

22. 22 Slightly different initial conditions produce a significantly different system… e d =0.17001 a d =2.9 AU, m d =12 M J, Q b = 10 minimum separation 6 a b when e c ~ 0.8

23. 23 Scenario 2 for the origin of the HAT-P-13 system e d =0.17001 a d =2.9 AU, m d =12 M J, Q b = 10 minimum separation 6 a b when e c ~ 0.8

24. 24 Scenarios for the origin of the HAT-P-13 system MODEL 1: e d =0.17MODEL 2: e d =0.17001

25. 25 Determining planetary structure in tidally relaxed inclined systems Fixed point replaced by limit cycle Mardling, in prep

26. 26 The mean eccentricity depends on the mutual inclination…

27. 27 Now a forced dynamical system - no fixed point solutions, only limit cycles  b is the argument of periastron

28. 28 It is only possible to determine k b if the mutual inclination is small… Mirror image for retrograde systems ( i b > 130 o )

29. 29 Kozai oscillations + tidal damping prevent 55 o < i <125 o High relative inclinations

30. 30 High relative inclinations kozai

31. 31 Kozai oscillations + tidal damping prevent 55 o < i <125 o Prediction: HAT-P-13b and c will not have a mutual inclination in this range Mutual inclination can be estimated via transit-timing variations (TTVs) (Nesvorny 2009) If stellar obliquity rel to planet b i *b > 55 o stellar obliquity rel to planet c i *c > i *b -55 o Stellar obliquity measured via the Rossiter-McLaughlin effect High relative inclinations

32. 32 retrograde planetary orbits 2009: two transiting exoplanet systems discovered to have retrograde orbits: 1.HAT-P-7b (Hungarian Automated Telescopes : CfA) 2.WASP-17b (Wide Angle Search for Planets: UK consortium)

33. 33 Transit spectroscopy: the Rossiter-McLaughlin effect  > 0  < 0  = 0

34. 34 Transit spectroscopy: the Rossiter-McLaughlin effect HD 209458 Signature of aligned stellar spin - consistent with planet migration model for short-period planets 11/13 like this Winn et al 2005

35. 35 Transit spectroscopy: the Rossiter-McLaughlin effect prograde retrograde

36. (v max =200 m/s) = sky-projected stellar obliquity rel to orbit normal of planet b

37. 37 discovery paper: (Magellan proposal with Bayliss & Sackett)

38. 38 Scenario for the origin of highly oblique systems with severely inflated planets