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Spin-Orbit Misalignment in Planetary Systems and Magnetic Star -- Disk Interaction

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Title: Magnetic Star - Disk Interactions: Warped Disks & Misaligned Planets (NSs) (& Boundary Layers) Author: Dong Lai Last modified by: Dong Lai – PowerPoint PPT presentation

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Title: Spin-Orbit Misalignment in Planetary Systems and Magnetic Star -- Disk Interaction


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 planets orbital plane
ecliptic plane Suns equator Murcury 7.0
05 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 Suns 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
  • gt
  • 1. Protoplanetary disks do not have to be aligned
    with
  • stellar spin
  • 2. Before few-body interaction starts, the
    planets 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 --gt toroidal field --gt 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 gtgt 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 gt 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) gt
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 --gt 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
  • gt
  • 1. Protoplanetary disks do not have to be aligned
    with
  • stellar spin
  • 2. Before few-body interaction starts, the
    planets orbit
  • axis may already be misaligned with stellar
    spin.

DL, Francois Foucart (Cornell) Doug Lin
(2010) Foucart DL (2010)
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