Tidal Dynamics of Transiting Exoplanets Dan Fabrycky UC Santa Cruz 13 Oct 2010 Photo: Stefen Seip, apod/ap 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) m p, R p, (a p /R * ) 2)  / Period (days) Mass [M J ]  Dynamics not foreseen? { Spin-orbit  migration (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

But will tidal heating destroy the planet? Disruption possible (E t >E b ) 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 L 1 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 M p -P correlation (Mazeh et al 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 07 Wu+07 Nagasawa+08 e.g., Cresswell+07 Also, resonant-pumping (Yu & Tremaine 01, Thommes & Lissauer 03) Inclination expectations

Comparison to Observations Kozai Planet-Planet Scattering 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 rad/s] r/R star

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