spin-orbit misalignment in planetary systems and magnetic star -- disk interaction iau astrophysics...

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



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)





(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)







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?

Including other torques…



Evolution of the stellar spin








“weak” warping

“strong” warping



Foucart & DL 2010

Including disk warp…






“weak” warping

“strong” warping



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



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)



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



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



Greaves et al. 1998







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.

spin-orbit misalignment in planetary systems and magnetic star -- disk interaction iau astrophysics...

Documents

disk warp slide

disk axis slide

disk torque

flat disk slide

stellar spin slide

disk formation

small slide

inner disk warp