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

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

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

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

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

21 Variable stellar obliquity

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

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

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

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

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 k b if the mutual inclination is small… Mirror image for retrograde systems ( i b > 130 o )

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

30 High relative inclinations kozai

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

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

35 Transit spectroscopy: the Rossiter-McLaughlin effect prograde retrograde

(v max =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