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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

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
Why tides?


Hot Jupiters are a Sub-class

Why transits

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?

Disk migration


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.

Alternative tidal dissipation
Alternative: tidal dissipation

Rasio & Ford 1996, Wu & Murray 2003,

Matsumura, Peale, & Rasio 2010

But will tidal heating destroy the planet

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

Circularization with overflow in words
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

In equations

  • Energy conservation

  • A.M. conservation

  • Roche-Lobe filling

Circularization with overflow
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
Inclination expectations

Inclination to stellar equator?

get misaligned

remain aligned

Inclination expectations1
Inclination expectations

e.g., Cresswell+07

  • Disk migration

  • Kozai cycles with tidal friction

  • Planet-planet scattering with tidal friction

Fabrycky & Tremaine 07



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

Comparison to observations
Comparison to Observations






New correlations
New Correlations

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

  • Host’s convective zone mass

  • Tidal torque

Clear and present danger planetary consumption
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.

Radiative convective decoupling

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



  • 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

Theory of Secular Resonance

frequency g

frequency 