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Tidal Dynamics of Transiting Exoplanets

Tidal Dynamics of Transiting Exoplanets. Tidal Dynamics of Transiting Exoplanets. At: The Astrophysics of Planetary Systems: Formation, Structure , and Dynamical Evolution. Dan Fabrycky UC Santa Cruz 13 Oct 2010. Photo: Stefen Seip, apod/ap040611. Why tides?. Cumming+08.

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Tidal Dynamics of Transiting Exoplanets

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  1. Tidal Dynamics of Transiting Exoplanets Tidal Dynamics of Transiting Exoplanets At: The Astrophysics of Planetary Systems: Formation,Structure, and Dynamical Evolution Dan Fabrycky UC Santa Cruz 13 Oct 2010 Photo: Stefen Seip, apod/ap040611

  2. Why tides? Cumming+08 Hot Jupiters are a Sub-class

  3. Mass [MJ] Period (days) Why transits? 1) mp, Rp, (ap/R*) 2)  /  Pont et al. 2010 { Spin-orbitmigration (Queloz+2000) TTV/TDV (Miralda-Escude 2002) Tidal consumption (Sasselov 2003) Dynamics not foreseen?

  4. Cumming+08 Disk migration? • 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.

  5. Alternative: tidal dissipation Rasio & Ford 1996, Wu & Murray 2003, Matsumura, Peale, & Rasio 2010

  6. Kozai Movie

  7. Disruption possible (Et>Eb) for But will tidal heating destroy the planet? Maximum tidal input: Planet binding energy: work in progress with Doug Lin & Tsevi Mazeh

  8. 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

  9. In equations • Energy conservation • A.M. conservation • Roche-Lobe filling

  10. In a picture

  11. 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.

  12. Inclination expectations Inclination to stellar equator? get misaligned remain aligned

  13. Inclination expectations e.g., Cresswell+07 • Disk migration • Kozai cycles with tidal friction • Planet-planet scattering with tidal friction Fabrycky & Tremaine 07 Wu+07 Nagasawa+08 Also, resonant-pumping (Yu & Tremaine 01, Thommes & Lissauer 03)

  14. Comparison to Observations Kozai Planet-Planet Scattering observations (Triaud+10)

  15. New Correlations Winn, Fabrycky, Albrecht, Johnson 2010 (see also Schlaufman 2010) • Host’s convective zone mass • Tidal torque

  16. 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.

  17. Let’s look to Astrophysics

  18. Howe 2009, from helioseismology Radiative-Convective Decoupling  [10-4 rad/s] • 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 r/Rstar

  19. 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.

  20. Theory of Secular Resonance frequency g frequency 

  21. Secular Resonance during Kozai cycles with tidal friction  i HD 80606: 

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