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  1. Spin-Orbit Misalignment in Planetary Systemsand Magnetic Star -- Disk Interaction Dong Lai Cornell University ESO IAU “Astrophysics of Planetary Systems”, Torino, Italy, Oct.14, 2010

  2. Solar System Orientation of planet’s orbital plane ecliptic plane Sun’s equator Murcury 7.005 3.38 Venus 3.394 3.86 Earth 0 7.15 Mars 1.850 5.65 Jupiter 1.303 6.09 Saturn 2.489 5.51 Uranus 0.773 6.48 Neptune 1.770 6.43 All major planets lie in the same plane (within 2 deg), which is inclinded to the Sun’s equator by 7 deg.

  3. S*-Lp misalignment in Exoplanetary Systems: Importance of few-body interactions 1. Kozai + Tide migration by a distant star/planet (e.g., Eggleton et al. 2001; Wu & Murray 2003; Fabrycky & Tremaine 2007) Companion? Produce the observed distribution of period (and a_p)? 2. Planet-planet scattering (including internal Kozai) + Tide (e.g., Chatterjee et al. 2008; Juric & Tremaine 2008; Nagasawa et al 2008) Produce the observed distribution of period? Initial conditions? (need 3 giant planets in “compact” configuration?)

  4. This Talk: Take-home message Magnetic interaction between a protostar and its disk can (not always) push the stellar spin away from the disk axis • ==> 1. Protoplanetary disks do not have to be aligned with stellar spin 2. Before few-body interaction starts, the planet’s orbit axis may already be misaligned with stellar spin. DL, Francois Foucart (Cornell) & Doug Lin (2010) Foucart & DL (2010)

  5. Physical Origin of the Magnetic Interaction Torques between Star and Disk

  6. Magnetic Star - Disk Interaction: Basic Picture Magnetic star

  7. Magnetic Star - Disk Interaction: Physical Processes Magnetic field reconnects and penetrates the inner region of disk Field lines linking star and disk are twisted --> toroidal field --> field inflation Reconnection of inflated fields restore linkage

  8. Romanova, Long, et al. 2010

  9. My claim: In general, there are magnetic torques which tend to make the inner disk (before disruption) -- warp -- precess on timescale >> dynamical time (rotation/orbital period) Consider two limiting cases in general geometry…

  10. Perfect conducting disk: Torque on disk (per unit area): Averaging over stellar rotation: Precessional Torque

  11. Poorly-conducting disk: Torque on disk (per unit area): Averaging over stellar rotation: Warping torque threads the disk

  12. Recap: Magnetic precessional torque and warping torque on disk (per area) (Instability)

  13. So, magnetic toques from the star want to make the inner disk warp and precess… But disk will want to resist it by internal stresses (viscosity or bending wave propagation)

  14. Steady-state Disk Warp: Foucart & DL 2010 For most disk/star parameters, the disk warp is small

  15. What is happening to the stellar spin direction? (Is there secular change to the spin direction?) A hierarchy of time scales: (1) Orbital period of inner disk, spin period ==> short… Averaged out already (2) Warp growth time and precession period of inner disk (3) Viscous evolution time for disk warp (4) Timescale to change the spin (longest!)

  16. A hierarchy of time scales: (1) Orbital period of inner disk, spin period (days) ==> short… Averaged out already (2) Warp growth time and precession period of inner disk (3) Disk warp evolution time: e.g., due to viscosity (4) Timescale to change the spin (longest!)

  17. Back-reaction torque on the stellar spin… (for small warps --> flat disk)

  18. What does magnetic warping torque do?

  19. What does magnetic warping torque do?

  20. Including other torques…

  21. Evolution of the stellar spin

  22. Evolution of the stellar spin “weak” warping “strong” warping

  23. Including disk warp… Foucart & DL 2010

  24. Evolution of the stellar spin “weak” warping “strong” warping

  25. The 90 degree barrier: Starting form small angle, cannot evolve into retrograde if outer disk orientation is fixed

  26. The 90 degree barrier: Starting form small angle, cannot evolve into retrograde if outer disk orientation is fixed Possible to produce retrograde systems: (1) the outer disk changes direction (due to external perturber?)

  27. Possible to produce retrograde systems: (2) The initial condition is retrograde? e.g., disk formation in turbulent star forming clouds (Bate et al. 2010)

  28. Possible to produce retrograde systems: (2) The initial condition is retrograde? e.g., disk formation is turbulent star forming clouds (Bate et al. 2010) Note: Even in this scenario, the magnetic warping torque is important (without it, the stellar spin would align with the disk axis…)

  29. Distribution of stellar obliquity as a function of time (starting from random distribution) No (or “weak”) magnetic warping torque: 0 90 180

  30. Distribution of stellar obliquity as a function of time (starting from random distribution) With (“strong”) magnetic warping torque

  31. How to test this? • Measuring spin-orbit angles for systems with 2 transiting planets e.g., Kepler-9: 2 transiting planets • Measuring the orientation of stellar spin and disk • Young star and disk (with jets)? (Jerome Bouvier) • MS stars with debris disks?

  32. Watson et al 2010 Greaves et al. 1998 CSO and Spitzer (MIPS) image Backman et al 2009 Consistent with face-on (Stepelfeldt 2010)

  33. This Talk: Take-home message Magnetic interaction between a protostar and its disk can (not always) push the stellar spin away from the disk axis • ==> 1. Protoplanetary disks do not have to be aligned with stellar spin 2. Before few-body interaction starts, the planet’s orbit axis may already be misaligned with stellar spin. DL, Francois Foucart (Cornell) & Doug Lin (2010) Foucart & DL (2010)