Tidal Influence on Orbital Dynamics

1. Tidal Influence on Orbital Dynamics Dan Fabrycky (dfabrycky@cfa.harvard.edu) 4 Feb, 2010 Collaborators: Scott Tremaine Eric Johnson Jeremy Goodman Josh Winn Photo: Stefen Seip, apod/ap040611

2. Orbital Distribution Inclination to stellar equator? get misaligned remain aligned Cumming+08 Hot Jupiters are a Sub-class

3. Lorb Dissipating the energy of the tidal bulge: In the star’s tidal gravitational field: Lorb The spin vector precesses about the orbit normal A prolate tidal bulge is raised, which tracks the star’s position the spinning planet drags prolate bulge “downstream” • i) Parallelization; || ≈105 yr • ii) Spin synchronization; s=||/2 • iii) Eccentricity damping;≈109 yr Spin-orbit evolution Hot Jupiters are spinning, gaseous bodies with oblate rotational bulges While i, ii, or iii are ongoing, tidal heat is generated in the planet

4. Cassini States • Now suppose the orbital angular momentum (Lorb) precesses due to a stellar rotational bulge or another planet that is non-coplanar • Then: tidal damping on timescale || produces a stable equilibrium obliquity th 0, called a Cassini state. J Lorb I ? orbit precession rate spin precession rate

5. J Lorb I ? Moon’s spin Lunation: Cassini's Laws Protate = Porbit constant , Lorb , and J are coplanar

6. Lorb Settling into Cassini state 2 Oblique Pseudo-synch (Levrard et al. 2007)

7. Lorb Breaking of Cassini state 2 Tidal heating ends [Gyr]

8. ‘606 Laughlin +09 Naef+01

9.  Planets in Binaries i pericenter   ~40 systems known • On long timescales (secular approx.): • Semimajor axis a is conserved • e oscillates dramatically if icrit<i<180- icrit • icrit=cos-1[(3/5)1/2]=39.2 •  and  both vary as well • Orbital inclination relative to stellar equator (a.k.a. stellar obliquity): • varies for distant planets • constant for hot Jupiters

10. Citations to Kozai 1962, a paper on asteroids Kozai Cycles Holman, Touma, Tremaine 1997, on 16 Cyg B

11. Kozai Cycles with Tidal Friction HD 80606b: • Adding… • tidal effects: • time-shifted eq’m bulges • spins: • rotational oblateness • GR precession • Equations from: • Eggleton & Kiseleva-Eggleton, 2001

12.  Theory of Secular Resonance frequency g frequency 

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

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

15. Do Tides Realign the Star? Barker & Ogilvie 2009 Only if the planet is in the run-away process of being tidally consumed.

16. Gaudi & Winn 2006   Winn et al. 2006 HD189733b towards observer Measuring stellar obliquity

17. Spin-orbit observations… (excluding WASP-3b: =1510°; Kepler-8b:=-275°)

18. 1-f f E=1.1x10-5 E=34  distributions  = 39 +9-6 Two migration mechanisms? Fabrycky & Winn 2009 = 0.19+0.18-0.07

19. Topics • Spin states stabilized dynamically • Origin of hot Jupiters • Spin-orbit misalignment • Didn’t touch on: • Tides and mean-motion resonances • Theory (Terquem & Papaloizou 2007) • 55 Cnc b-c (Novak et al. 2003) • HD 40307 (Lin et al. in prep) • Tides and apsidal alignment • Mardling 2007, 2010 • Batygin et al. 2009ab - particular systems

20. Eggleton equations hin qin ein Dissipative: Non-Dissipative: …