spin-orbit misalignment in planetary systems and magnetic star -- disk interaction iau astrophysics...
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Spin-Orbit Misalignment in Planetary Systemsand Magnetic Star -- Disk Interaction
IAU “Astrophysics of Planetary Systems”, Torino, Italy, Oct.14, 2010
Dong Lai Cornell University
ESO
Solar System
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
Orientation of planet’s orbital plane
All major planets lie in the same plane (within 2 deg), which is inclinded to the Sun’s equator by 7 deg.
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?)
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
DL, Francois Foucart (Cornell) & Doug Lin (2010)Foucart & DL (2010)
==>1. Protoplanetary disks do not have to be aligned with stellar spin2. Before few-body interaction starts, the planet’s orbit axis may already be misaligned with stellar spin.
Physical Origin of the Magnetic Interaction Torques between Star and Disk
Magnetic Star - Disk Interaction: Basic Picture
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Magnetic star
Magnetic Star - Disk Interaction: Physical Processes
Magnetic field reconnects and penetrates the inner region of diskField lines linking star and disk are twisted --> toroidal field --> field inflationReconnection of inflated fields restore linkage
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Romanova, Long, et al. 2010
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My claim:In general, there are magnetic torques which tendto make the inner disk (before disruption) -- warp -- precesson timescale >> dynamical time (rotation/orbital period)
Consider two limiting cases in general geometry…
Perfect conducting disk:
Torque on disk (per unit area):Averaging over stellar rotation: Precessional
Torque
Poorly-conducting disk:
threads the disk
Torque on disk (per unit area):Averaging over stellar rotation:
Warping torque
Recap:Magnetic precessional torque and warping torque on disk (per area)
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(Instability)
So, magnetic toques from the star want to make the innerdisk warp and precess…
But disk will want to resist it by internal stresses (viscosity or bending wave propagation)
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Steady-state Disk Warp:
Foucart & DL 2010
For most disk/star parameters, the disk warp is small
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!)
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!)
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Back-reaction torque on the stellar spin…(for small warps --> flat disk)
What does magnetic warping torque do?
What does magnetic warping torque do?
Including other torques…
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Evolution of the stellar spin
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Evolution of the stellar spin
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“weak” warping
“strong” warping
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Foucart & DL 2010
Including disk warp…
Evolution of the stellar spin
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“weak” warping
“strong” warping
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The 90 degree barrier: Starting form small angle, cannot evolve into retrograde if outer disk orientation is fixed
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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?)
Possible to produce retrograde systems:
(2) The initial condition is retrograde?
e.g., disk formation in turbulent star forming clouds (Bate et al. 2010)
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…)
Distribution of stellar obliquity as a function of time (starting from random distribution)
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0 90 180
No (or “weak”) magnetic warping torque:
Distribution of stellar obliquity as a function of time (starting from random distribution)
With (“strong”) magnetic warping torque
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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?
Watson et al 2010
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Greaves et al. 1998
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CSO and Spitzer(MIPS) imageBackman et al 2009
Consistent with face-on (Stepelfeldt 2010)
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
DL, Francois Foucart (Cornell) & Doug Lin (2010)Foucart & DL (2010)
==>1. Protoplanetary disks do not have to be aligned with stellar spin2. Before few-body interaction starts, the planet’s orbit axis may already be misaligned with stellar spin.