Determining the internal structure of extrasolar planets, and

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

2. double-line eclipsing binary - all parameters known except k2(1) Binary stars and apsidal motion

3. Binary stars and apsidal motion Claret & Gimenez 1993 This method of determining k2 involves measuring the change in something…

4. planets and apsidal motion b k2 is now called the LOVE NUMBER (= twice apsidal motion constant) Circularization timescale ~ 108 yr; age ~ 5 Gyr b = 181±46o __ error MUCH bigger than change per year

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. Tidal evolution of short-period planets with companions • Many short-period planets have non-zero eccentricities AND anomolously • large radii (eg. e = 0.05, Rp = 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 k2 DIRECTLY (no need to wait for change in anything)

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

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

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

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

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

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

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

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

16. The HAT-P-13 system best fit Given mb, Rb, Teff, find mcore, Ltide from grid of models kb, Qb kb/Ltide, eb(eq)

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. Scenario for the origin of the HAT-P-13 system MODEL 1: ed=0.17 ad=2.9 AU, md=12 MJ, Qb = 10 minimum separation 10 ab when ec ~ 0.67

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

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

21. Variable stellar obliquity

22. Slightly different initial conditions produce a significantly different system… ed=0.17001 ad=2.9 AU, md=12 MJ, Qb = 10 minimum separation 6 ab when ec ~ 0.8

23. Scenario 2 for the origin of the HAT-P-13 system ed=0.17001 ad=2.9 AU, md=12 MJ, Qb = 10 minimum separation 6 ab when ec ~ 0.8

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

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

26. The mean eccentricity depends on the mutual inclination…

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

28. It is only possible to determine kbif the mutual inclination is small… Mirror image for retrograde systems ( ib > 130o )

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

30. High relative inclinations kozai

31. High relative inclinations Kozai oscillations + tidal damping prevent 55o < i<125o 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 > 55o stellar obliquity rel to planet c i*c > i*b-55o Stellar obliquity measured via the Rossiter-McLaughlin effect

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

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

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

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

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

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

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