Dead zones and the growth of giant planets

1. Dead zones and the growth ofgiant planets Ralph Pudritz (McMaster University) Soko Matsumura (Ph.D. McMaster; PDF Northwestern) Ed Thommes (CITA: Norwestern)

2. Outline 1. Planet formation – disks and gaps 2. Dead zones (DZs) 3. Gap opening masses in disks with DZs 4. Dead zones and planetary migration – step 1 The Point: Dead zones (=no MRI turbulence) expected from first principles – they shape both planetary masses + halt planetary migration

3. Extrasolar Planets: • Several thousands of solar type stars surveyed – 5 – 20% have planets within 5 AU. • More than 200 now known • Question: what halted migration in (some?) systems?

4. Flared, gaseous, dusty disk HH 30 (from HST) Protoplanetary disks – from cores to planets Gas Accretion & Gap-formation Protoplanet http://www.astro.psu.edu/users/niel/astro1/slideshows/class43/slides-43.html

5. 1. Planet Formation – Disks and Gaps • Giant planet formation; two mechanisms under intense investigation: 1. Core accretion model…. Coagulation of planetesimals that when exceeding 10 Earth masses, gravitationally captures gaseous envelope (eg. Bodenheimer & Pollack 1986) 2. Gravitational instability model …. GI in Toomre unstable disk produces Jovian mass objects in one go (eg. Boss 1998). • For either 1 or 2 – final mass determined by “gap opening” in face of disk “viscosity”.

6. When planets start to appear… Gap opens in a disk when Tidal Torque ~ Viscous Torque Protoplanet Tidal Torque Disk Viscous Torque Disk

7. Gap-opening masses of a Planet (In an inviscid disk) Rafikov (2002) (In a viscous disk) Disk pressure scale height h [AU] Lin & Papaloizou (1993) Disk Radius a [AU] (Matsumura & Pudritz 2005, ApJL; 2006, MNRAS) - 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

8. Disk structure – reprocessing stellar radiation Submm Infrared Optical Radiative resprocessing: hydrostatic equilibrium disk models 1: Disk Surface Tds 2: Disk Interior Ti Chiang and Goldreich (1997)

9. 2. Dead Zones - 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

10. Dead Zones (no turbulence region in central disk) Dead Zone (Gammie, 1998): - Ionization rate is very low - Magneto-rotational instability (MRI) turbulence is inactive - .. So disk’s viscosity is low there Ionization: X-rays cosmic rays radioactive elements thermal collisions of alkali ions Recombination: metal ions molecular ions grains

11. 3. Dead Zones in Chiang-Goldreich models 100 10 1 Disk Height [AU] 0.1 0.01 0.001 0.0001 0.01 0.1 1 10 100 Disk Radius [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). ~ 13 AU (Matsumura & Pudritz; 2005, 2006)

12. Gap-opening masses of Planets 100 10 1 Gap-opening mass [MJ] 0.1 0.01 0.001 0.0001 0.01 0.1 1 10 100 Disk Radius [AU] Jupiter Uranus or Neptune Earth Even a terrestrial mass planet opens a gap in a DZ!!

13. 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)

14. Planetary migration: planet – disk interaction (eg. Ward 1997) • Planet exerts tidal torque at Lindblad resonances in disk. • This excites spiral density waves - propagate away from resonances + spread angular momentum throughout disk • PROBLEM: Migration too efficient… lose planets in a million years! • QUESTION: What saves planetary systems?

15. 10 ME: Type I migration (No Gap-opening) 30 30 20 20 Dead Zone Disk Radius [AU] Disk Radius [AU] 10 10 0 0 0 2×106 4×106 6×106 8×106 107 0 2×106 4×106 6×106 8×106 107 Time [years] Time [years] (w/o Dead Zone) (w/ Dead Zone) =10-2 =10-2 =10-5

16. Evolution of disk column density during gap opening Note pile up of material at outer edge of dead zone. This denstiy gradient deflects migration of outer light planets.

17. 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:

18. Type II migration (After Gap-opening) 30 30 20 20 Dead Zone Disk Radius [AU] Disk Radius [AU] 10 10 0 0 0 2×106 4×106 6×106 8×106 107 0 2×106 4×106 6×106 8×106 107 Time [years] Time [years] (w/o Dead Zone) (w/ Dead Zone) =10-3 =10-3 =10-5

19. Migration of a Jovian planet over 10 Myr. • Note extent of gap opened by planet once inside dead zone. (But see Soko’s following talk) • Planet started at 20 AU settles into orbit at 4AU after 10 Myr

20. 10 ME opens gap at 3.5 AU in dead zone Also: 1 ME opens gap near 0.1 AU - Look for this…

21. Summary • DZs are inescapable – (physics of MRI + high column density of protostellar disks) • DZs -> sharp radius beyond which massive planets form (initially beyond 10 AU) • DZs -> terrestrial planets open gaps within them –> halt rapid loss of terrestrial planet cores…. hope for Kepler mission? • Outer edge of DZ – very interesting place for GI instabilities? Question: how do planets accrete as they migrate in evolving disks? See Soko’s talk….