Dead zones and Dead zones and the growth ofthe growth ofgiant planetsgiant planets

Ralph PudritzRalph Pudritz(McMaster University)(McMaster University)

Soko MatsumuraSoko Matsumura(Ph.D. McMaster; PDF Northwestern) (Ph.D. McMaster; PDF Northwestern)

Ed ThommesEd Thommes(CITA: Norwestern)(CITA: Norwestern)

OutlineOutline

1. Planet formation – disks and gaps1. Planet formation – disks and gaps

2. Dead zones (DZs) 2. Dead zones (DZs)

3. Gap opening masses in disks with DZs3. Gap opening masses in disks with DZs

4. Dead zones and planetary migration – step 14. Dead zones and planetary migration – step 1

The PointThe Point: Dead zones (=no MRI turbulence) : Dead zones (=no MRI turbulence) expected from first principles – they shape expected from first principles – they shape both planetary masses + halt planetary both planetary masses + halt planetary migration migration

Extrasolar Planets: Extrasolar Planets:

Several thousands Several thousands of solar type stars of solar type stars surveyed – 5 – 20% surveyed – 5 – 20% have planets within have planets within 5 AU.5 AU.

More than 200 now More than 200 now knownknown

Question:Question: what what halted migration in halted migration in (some?) systems?(some?) systems?

Gas Accretion & Gap-formation

HH 30 (from HST)

Flared, gaseous, dusty disk

http://www.astro.psu.edu/users/niel/astro1/slideshows/class43/slides-43.html

Protoplanet

Protoplanetary disks – from

cores to planets

1. Planet Formation – Disks and Gaps1. Planet Formation – Disks and Gaps

Giant planet formation; two mechanisms under intense Giant planet formation; two mechanisms under intense investigation:investigation:

1. 1. Core accretion modelCore accretion model…. Coagulation of …. Coagulation of

planetesimals that when exceeding 10 Earth masses, planetesimals that when exceeding 10 Earth masses, gravitationally captures gaseous envelope (eg. gravitationally captures gaseous envelope (eg. Bodenheimer & Pollack 1986)Bodenheimer & Pollack 1986)

2. 2. Gravitational instability modelGravitational instability model …. GI in Toomre …. GI in Toomre unstable disk produces Jovian mass objects in one go unstable disk produces Jovian mass objects in one go (eg. Boss 1998).(eg. Boss 1998).

For either 1 or 2 – For either 1 or 2 – final mass determined by “gap final mass determined by “gap opening”opening” in face of disk “viscosity”. in face of disk “viscosity”.

Protoplanet

Tidal Torque

Viscous Torque

Disk

Disk

Gap opens in a disk when

Tidal Torque ~

Viscous Torque

When planets start to appear…

Gap-opening masses of a Planet

- Gap-opening mass ~ Final mass of a planet - Two competing forces (Tidal vs Viscous) - Smaller gap-opening masses in an inviscid disk

Need to know - disk flaring (h/a) - viscosity

),(3

23

a

hQF

a

h

M

M

Star

Planet

(In an inviscid disk)

Rafikov (2002)

5

40

a

h

M

M

Star

Planet (In a viscous disk)

Lin & Papaloizou (1993)

Disk Radius a [AU]

Disk pressure scale height h [AU]

(Matsumura & Pudritz 2005, ApJL; 2006, MNRAS)

Chiang and Goldreich (1997)

Submm Infrared Optical

Disk structure – reprocessing stellar radiation

Radiative resprocessing: hydrostatic equilibrium disk

models

1: Disk Surface Tds

2: Disk Interior Ti

- Most promising source of viscosity: Magneto-rotational instability (MRI) turbulence (Balbus & Hawley, 1991) Dead Zone: where MRI is inactive (Gammie 1996) -> In sufficiently poorly ionized region, Ohmic dissipation damps out MRI

MRI active region: Disk is well-ionized -> MRI turbulence - Larger gap-opening mass for larger viscosity

2. Dead Zones

Ionization: X-rays cosmic rays radioactive elements thermal collisions of alkali ions

Dead Zones (no turbulence region in central disk)

X-rays

Dead Zone

Cosmic rays magnetic field

RA elements

Recombination: metal ions molecular ions grains

Dead Zone (Gammie, 1998):

- Ionization rate is very low

- Magneto-rotational instability (MRI) turbulence is inactive

- .. So disk’s viscosity is low there

3. Dead Zones in Chiang-Goldreich models

Disk Radius [AU] 0.01 0.1 1 10 100

100

10

1

0.1

0.01

0.001

0.0001

Dis

k H

eigh

t [A

U]

~ 13 AU

Our dead zones include entire pressure scale

height h of colder mid-plane (also

include critical column density

ratio for excitation of

motion at midplane by

turbulence in envelope).(Matsumura & Pudritz; 2005, 2006)

Gap-opening masses of Planets

Disk Radius [AU] 0.01 0.1 1 10 100

100

10

1

0.1

0.01

0.001

0.0001

Gap

-ope

ning

mas

s [

MJ]

Jupiter

Uranus or

Neptune

Earth

Even a terrestrial mass planet opens a gap in a DZ!!

4. Dead zones and planetary migration – step 1

1. eg. Type I migration (before gap-opening)

→ 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.

(Matsumura, Pudritz, & Thommes 2006)

Planetary migration: planet – disk interaction Planetary migration: planet – disk interaction (eg. Ward 1997)(eg. Ward 1997)

Planet exerts tidal torque at Lindblad Planet exerts tidal torque at Lindblad resonances in disk. resonances in disk.

This excites spiral density waves - propagate This excites spiral density waves - propagate away from resonances + spread angular away from resonances + spread angular momentum throughout diskmomentum throughout disk

PROBLEM: Migration too efficient… lose PROBLEM: Migration too efficient… lose planets in a million years!planets in a million years!

QUESTIONQUESTION: What saves planetary systems?: What saves planetary systems?

10 ME: Type I migration (No Gap-opening)

30

20

10

0

Dis

k R

adiu

s [A

U]

0 2×106 4×106 6×106 8×106 107

Time [years](w/o Dead Zone)

=10-5

30

20

10

0

Dis

k R

adiu

s [A

U]

0 2×106 4×106 6×106 8×106 107

Time [years](w/ Dead Zone)

Dead Zone

=10-2=10-2

Evolution of disk column density during gap openingEvolution of disk column density during gap opening

.10;10;10;10 7654 yrt

Note pile up of

material at outer edge of

dead zone. This

denstiy gradient deflects

migration of outer

light planets.

If planet forms within the DZ:If planet forms within the DZ:halt migration of terrestrial planets by opening a gap in the halt migration of terrestrial planets by opening a gap in the

DZDZ

10 M_E planet started in dead zone; Left 2 million yrs Viscosity:

25 10;10 SSdz

Type II migration (After Gap-opening)

30

20

10

0

Dis

k R

adiu

s [A

U]

0 2×106 4×106 6×106 8×106 107

Time [years](w/o Dead Zone)

30

20

10

0

Dis

k R

adiu

s [A

U]

0 2×106 4×106 6×106 8×106 107

Time [years]

(w/ Dead Zone)

=10-3 =10-3

=10-5

Dead Zone

Migration of Migration of a Jovian a Jovian planet over planet over 10 Myr.10 Myr.

- Note extent Note extent of gap of gap opened by opened by planet once planet once inside dead inside dead zone. (But zone. (But see Soko’s see Soko’s following following talk)talk)

- Planet Planet started at started at 20 AU 20 AU settles into settles into orbit at 4AU orbit at 4AU after 10 Myrafter 10 Myr

10 M10 MEE opens opens

gap at 3.5 gap at 3.5 AU in dead AU in dead zonezone

Also:Also:

1 M1 MEE opens opens

gap near 0.1 gap near 0.1 AU AU

- Look for - Look for this…this…

SummarySummary DZs are inescapableDZs are inescapable – (physics of MRI + high – (physics of MRI + high

column density of protostellar disks)column density of protostellar disks) DZs -> sharp radius beyond whichDZs -> sharp radius beyond which massive planets form (initially beyond 10 AU)massive planets form (initially beyond 10 AU) DZs -> terrestrial planets open gaps within DZs -> terrestrial planets open gaps within

them –> halt rapid loss of terrestrial planet them –> halt rapid loss of terrestrial planet cores…. hope for Kepler mission?cores…. hope for Kepler mission?

Outer edge of DZ – very interesting place for Outer edge of DZ – very interesting place for GI instabilities? GI instabilities?

QuestionQuestion: how do planets accrete as they : how do planets accrete as they

migrate in evolving disks? See Soko’s talk….migrate in evolving disks? See Soko’s talk….