Tidal Dynamics of Transiting Exoplanets

Dan Fabrycky

UC Santa Cruz

13 Oct 2010

Photo: Stefen Seip, apod/ap040611

At: The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution

Tidal Dynamics of Transiting Exoplanets

Why tides?

Cumming+08

Hot Jupiters are a Sub-class

Why transits?1) mp, Rp, (ap/R*) 2) /

Period (days)

Mas

s [M

J]

Dynamics not foreseen?{Spin-orbitmigration (Queloz+2000)

TTV/TDV (Miralda-Escude 2002)

Tidal consumption (Sasselov 2003)

Pont et al. 2010

• Historic perspective: disk migration is destructive (Goldreich & Tremaine 1980, Ward 1997)

• Stop it near the star? (Lin et al. 1996)

That gives >10x too many hot Jupiters (Ida talk)

• Solution: Disk migration does not produce most hot Jupiters.

Disk migration?

Cumming+08

Alternative: tidal dissipation

Rasio & Ford 1996, Wu & Murray 2003,

Matsumura, Peale, & Rasio 2010

Kozai Movie

QuickTime™ and a decompressor

are needed to see this picture.

But will tidal heating destroy the planet?

Disruption possible (Et>Eb) for

Maximum tidal input:

Planet binding energy:

work in progress with Doug Lin & Tsevi Mazeh

Circularization with Overflow…In Words

• Dynamics slowly lowers the periapse• Circularization takes hundreds of orbits• The planet inflates slowly to the Roche Lobe

• It overflows gently through L1 while circularizing

• Transfer of angular momentum raises periapse

In equations

• Energy conservation

• A.M. conservation

• Roche-Lobe filling

In a picture

Circularization with Overflow

• Allows the survival of tidally migrating/inflating planets

• May explain Mp-P correlation (Mazeh et al. 2005 relation):

Lower mass planets

less binding energy

overflow more back away from the star further

• This model is doomed to succeed.

Inclination expectations

remain aligned

get misaligned

Inclination to stellar equator?

• Disk migration

• Kozai cycles with tidal

friction

• Planet-planet scattering with

tidal friction

Fabrycky & Tremaine 07Wu+07

Nagasawa+08

e.g., Cresswell+07

Also, resonant-pumping (Yu & Tremaine 01, Thommes & Lissauer 03)

Inclination expectations

Comparison to Observations

Kozai

Planet-PlanetScattering

observations(Triaud+10)

New Correlations

• Host’s convective zone mass

• Tidal torque

Winn, Fabrycky, Albrecht, Johnson 2010 (see also Schlaufman 2010)

Clear and Present Danger:Planetary Consumption

• Tidal calculations assuming only the convective envelope feels torque from the planet.

• The planet can realign the star’s observable photosphere.

• The photosphere is not spun-up, due to magnetic braking.

• The planet is doomed.

Let’s look to Astrophysics

Radiative-Convective Decoupling

• Decoupling was predicted theoretically (Pinsonneault+1987)

• Observed stellar rotation periods as a function of age suggest decoupling (e.g., Irwin & Bouvier 2009)

• BUT: Coupling apparently observed in the Sun

Howe 2009, from helioseismology

[

10-4 r

ad/s

]

r/Rstar

Conclusions

• Fundamental indicators of hot Jupiter formation:– The pile-up and the mass-period relation within it– Spin-orbit alignment statistics and correlations

• Circularization from high eccentricity is likely the dominant channel.

• Tides in the star might damp obliquities, but it is time to entertain a variety of ideas.

Theory of Secular Resonance

frequency g

frequency

i

HD 80606:

Secular Resonance during Kozai cycles with tidal friction