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Saving Planetary Systems:
the Role of Dead Zones
Ralph Pudritz, Soko Matsumura (McMaster
University),
& Ed Thommes (CITA)
AAS 208, Calgary
Migration can acconunt for orbits of massive extrasolar planets
– all within 5 AU
Migration occurs by tidal interaction between planet and disk:
 Type I: migration without gap opening –
planet swallowed within 1 Myr.
 Type II: migration after gap opening –
planet locked to disk and migrates
at rate dictated by inner disk – again lost quickly
Why do planetary systems survive it?

Absence of disk turbulence in “dead zone” in central disk
significantly slows planetary migration (Matsumura, Pudritz,
& Thommes 2006: MPT06). Can even reverse it.
Dead Zone (low viscosity region in a disk)
Dead Zone (Gammie, 1998):
- Magnetic turbulence is
inactive in poorly ionized
regions of the disk: so the disk’s
viscosity is very low there.
magnetic
field
Cosm ic rays
X-rays
RA elements
Dead Zone
- The DZ stretches out to about
13 Astronomical Units (1AU =
Earth-Sun difference).
Eg. Matsumura & Pudritz 2006
(MNRAS)
Ionization:
X-rays from star
cosmic rays
radioactive elements
heating from central star
Gap opens in a disk
when
Protoplanet
Tidal Torque ~
Tidal Torque
Disk
Viscous Torque
Disk
Viscous Torque
Level of magnetic
turbulence
responsible for the
“viscosity”  of the
gas
M planet
M star
 
Gap-opening masses of Planets
Gap-opening mass [MJ]
100
10
Jupiter
1
Uranus or
0.1
Neptune
0.01
Earth
0.001
0.0001
0.01
0.1
1
Disk Radius [AU]
10
100
Dead Zones and Planet Migration (MPT 06)
1. eg. Type I migration (before gapopening)
→ 10 MEarth (< MUranus)
Dead Zone
Star
Protoplanet
Numerical Technique:
We use a hybrid numerical code combining N-body
symplectic integrator SYMBA (Duncan et al 1998)
with evolution equation for gas (Thommes 2005)
- Allows us to follow evolution of planet and disk for
disk lifetime: 3 – 10 Million years.
10 ME: Type I migration (No Gap-opening)
=10-2
20
Dead
Zone
10
=10-2
30
Disk Radius [AU]
Disk Radius [AU]
30
20
10
=10-5
0
0 2×106 4×106 6×106 8×106 107
0
0 2×106 4×106 6×106 8×106 107
Time [years]
Time [years]
(w/o Dead Zone)
(w/ Dead Zone)
If planet forms within the DZ:
halt migration of terrestrial planets by opening a gap in the
DZ
10 M_E planet started in
dead zone; Left 2 million
yrs Viscosity:
 dz  10 5 ;  SS  10 2
Type II migration of Jupiter mass planet
30
=10-3
20
Dead
Zone
10
Disk Radius [AU]
Disk Radius [AU]
30
=10-3
20
10
=10-5
0
0 2×106 4×106 6×106 8×106 107
0
0 2×106 4×106 6×106 8×106 107
Time [years]
Time [years]
(w/o Dead Zone)
(w/ Dead Zone)

Migration of
a Jovian
planet over
10 Myr.
- Note extent
of gap
opened by
planet once
inside dead
zone.
- Planet
started at 20
AU settles
into orbit at
4AU after 10
Myr
10 ME opens
gap at 3.5
AU in
dead zone
Also:
1 ME opens
gap near
0.1 AU
Percentage of planets that migrate and stop within 5 AU

Assume uniform
distribution of
disks with
temperatures
(1AU) between
150 and 450 K;
and lifetimes
between 1 – 10
Million yrs
 Observe 5-20% of
stars with planets
in this regime: arises if disk
viscosity < 0.0001
Percent of planetary systems with planets
migrating inside 5AU
Summary:
Earth mass planets, that start migration
outside of DZ, are reflected to larger radii
 Earth mass planets that are formed inside
DZ halt migration because they can open a
gap in the disk (eg. Earth mass at around
0.1 AU).
 Massive planets open gaps, but their Type
II migration very slow in low viscosity DZ
 If viscosity parameter is < 0.0001, can
account for observed frequency of 5-20%
of stellar systems with planets inside 5AU
