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Determining the internal structure of extrasolar planets, and the phenomenon of retrograde planetary orbits

Rosemary Mardling

School of Mathematical SciencesMonash University

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Binary stars and apsidal motion

double-line eclipsing binary- all parameters known except k2

(1)

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Binary stars and apsidal motion

This method of determining k2 involves measuring the change in something…

Claret & Gimenez 1993

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planets and apsidal motion

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

b

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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

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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)

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Fixed-point theory of tidal evolution of planets with companions

COPLANAR theory(Mardling 2007)

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Fixed-point theory of tidal evolution of planets with companions

COPLANAR theory

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Fixed-point theory of tidal evolution of planets with companions

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Fixed-point theory of tidal evolution of planets with companions

all parameters known except

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γ

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Fixed-point theory of tidal evolution of planets with companions

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Fixed-point theory of tidal evolution of planets with companions

System evolvesto doubly circularstate on timescalemuch longer thanage of system

Real Q-value at least 1000 times larger ….evolution at least1000times slower

HD209458

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Fixed-point theory of tidal evolution of planets with companions

Equilibrium eccentricity substantial if:

• large (there are interesting exceptions)

• not too small

• large

€

ec

HAT-P-13:

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The HAT-P-13 system

data from Bakos et al 2009

HATNet transit discovery (CfA)

Keck followup spectroscopy

KeplerCam followup photometry

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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.

€

γ

Measured value of (Spitzer will improve data in Dec)

€

kb

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The HAT-P-13 system

Given mb, Rb, Teff, find mcore, Ltide from grid of models kb, Qb kb/Ltide, eb(eq)

best fit

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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…..

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Scenario for the origin of the HAT-P-13 system

ad=2.9 AU, md=12 MJ, Qb = 10 minimum separation 10 ab when ec ~ 0.67

MODEL 1: ed=0.17

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Scenario for the origin of the HAT-P-13 systemMODEL 1: ed=0.17

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Scenario for the origin of the HAT-P-13 systemMODEL 1: ed=0.17

ibc

i*c

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Variable stellar obliquity

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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

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Scenario 2 for the origin of the HAT-P-13 systemed=0.17001

ad=2.9 AU, md=12 MJ, Qb = 10 minimum separation 6 ab

when ec ~ 0.8

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Scenarios for the origin of the HAT-P-13 system

MODEL 1: ed=0.17 MODEL 2: ed=0.17001

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Determining planetary structure in tidally relaxed inclined systems

Fixed pointreplaced bylimit cycle

Mardling, in prep

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The mean eccentricity depends on the mutual inclination…

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Now a forced dynamical system - no fixed point solutions, only limit cycles

b is the argument of periastron

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It is only possible to determine kb if the mutual inclination is small…

Mirror image for retrograde systems ( ib > 130o )

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Kozai oscillations + tidal damping prevent 55o < i <125o

High relative inclinations

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High relative inclinations

kozai

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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

High relative inclinations

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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)

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Transit spectroscopy: the Rossiter-McLaughlin effect

> 0 < 0 = 0

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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

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Transit spectroscopy: the Rossiter-McLaughlin effect

prograd

e

retr

ogra

de

(vmax=200 m/s)

= sky-projected stellar obliquity rel to orbit normal of planet b

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discovery paper:

(Magellan proposal with Bayliss & Sackett)

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