Spin-Orbit Misalignment in Planetary Systems and Magnetic Star -- Disk Interaction IAU Astrophysics of Planetary Systems, Torino, Italy, Oct.14, 2010 Dong.

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.