lec13_28oct2011

Jovian planet formation. Core-accretion or gravitational instability?

Ge/Ay133

Properties of the Jovian Planets in the Solar System P  r2 for H2-He I/MR2=0.4 for a uniform sphere I/MR2=0.26 for P  r2

The radius-mass relationship and M.o.I. are used to infer the presence of primordial cores of 10-30 Mearth.

11-13

Caveat! Core mass estimate based on high pressure EOS:

[preferred EOS]

OK for Saturn, but…

[envelope]

Saumon & Guillot 2004 core mass constraints based on EOS

…very large extrapolations & uncertainties for Jupiter! (need better high P,T measurements, very difficult)

dubious EOS? Previously favored. Currently preferred EOS (Boriskov et al. 2005)

[envelope]

Saumon & Guillot (2004) core mass constraints based on EOS

Theory of nucleated instability: Cores in Jovian planets are almost certainly primordial, and the fact that all such objects in the solar system radiate more energy than they receive means they started hot. This has led to the development of the core-accretion model in which gas accretes onto cores built along the lines discussed in Lec. #12. Dense core

rH

~Isothermal

Ambient solar nebula

Photosphere Adiabatic envelope

Hill Sphere

Theory of nucleated instability: How do we analyze this situation? The extent of the envelope is determined via hydrostatic equilibrium. Key is the temperature profile, which is established by the radiative transfer equations below. L is the luminosity, K is the mass opacity coefficient.

Dense core

rH Ambient solar nebula

Photosphere Adiabatic envelope

Hill Sphere

The minimum luminosity that needs to be radiated is that which balances any ongoing accretion (equation at left). From this the mass/density properties of the envelope can be estimated:

Dense core

rH

Thus we need to solve for the density structure to get the envelope mass, which means we need to know the temperature profile.

Photosphere Adiabatic envelope

Hill Sphere

Solving the radiative transfer equations yields (for the envelope): Ideal gas

Dense core

rH

Photosphere Adiabatic envelope

Clearly the value of K is critical. Gas can only contribute a small fraction of the overall opacity, and so the dust grain or ice content in the envelope must be known, or assumed... Hill Sphere

How massive does the core need to be for the atmosphere to collapse? f~K in cm2/g Setting dMc/dMt=0 gives (a  m4)

Dense core

Adiabatic envelope

Photosphere

Stevenson 1982, Pl. Sp. Sci. 30, 755

The gas/dust ratio in the envelope is also critical for TIME SCALES! (determines how rapidly the envelope can cool)

ISM/50

Lissauer 2001, Nature 409, 23

ISM dust/gas

Smaller core

The most recent simulations include dust grain/heavy element settling in the envelope ratio in the envelope to give ~2-3 Myr times:

ISM/50

Lissauer et al. 2009, arXiv:0810.

ISM dust/gas

Smaller core

If the gas inflow is coherent, lots of angular momentum is involved:

G2/rd3 ~ GMp/rd2 where G is the specific ang. mom. and rd is the (protoplanet) disk radius. Equating this to the orbital specific ang. momentum gives, roughly G ~ rH2W/4 or rd~20rplanet

What might such a protoplanetary disk tell us about the formation of satellites? For a detailed recent review, see: Estrada, P.R. et al. 2009, arXiv:0809.1419

Properties of the inner moons of Jupiter: 1000 T(K) Hydrated silicates

500

Water ice

250

Solar nebula (buffer)

125

Ammonia-Water Hydrate

r

10 Io Europa 3.5 3.1 Anhydrous silicates

20 Ganymede 1.92

Hydrated 60/40 rock/ice silicates (initially)

30 Callisto 1.78

RJ g cm-3

50/50 rock/ice

Saturn picture not so clear, but Titan’s location may explain large volatile content.

Comparison of protosolar versus protoplanetary disks: Property

Protoplanetary Disk

Size (central body units) Mass (central body units) Typical Temperature

~20 ≥0.05 ~200 K (but up to 2000 K) Vertical optical depth ~100 (gas alone) ~10,000 (with dust) Mass surface density (g/cm2) ~105 (gas) ~103 (solids) Gas density (g/cm3) 10-4 – 10-6 Gas pressure (bars) ~1 Viscous spreading time ≥100 yr Cooling time ~10 4 – 106 yr

vs.

Protosolar Disk ~10 3 – 104 0.05-0.1 ~200 K (but up to >1000 K) 1.5 AU. • If M dwarfs have disks massive enough to undergo disk instability, then their gas giant protoplanets orbiting outside ~1.5 AU will be photoevaporated down to super-Earth mass, for M dwarfs in regions of high-mass star formation. • In low-mass star formation regions (e.g., Taurus), their gas giant protoplanets will survive to become gas giant planets.

Giant Planet Census: Host Star Metallicity • Correlation of short-period Jupiters with stellar metallicity is usually attributed to formation by core accretion • RV searches are beginning to find planets around low [Fe/H] dwarfs (HD 155358: [Fe/H] = -0.68 has two planets with masses of 0.5 and 0.9 MJup, Cochran et al. 2007; HD 171028: [Fe/H] = -0.49 has one with 1.8 MJup, Santos et al. 2007) • Most M dwarfs with known planets (GJ 176, GJ 876, GJ 317, GJ 436, GJ 581) have metallicities less than solar: [Fe/H] = -0.1, -0.12, -0.23, -0.32, and –0.33, while only GJ 849 has [Fe/H] = +0.16 (Butler et al. 2006) • Short-period SuperEarths do not correlate with the host star’s [Fe/H] (Mayor 2007) • Low [Fe/H] giant stars have more (long-period) gas giants than high [Fe/H] giant stars (Hatzes 2007) • M4 globular cluster has [Fe/H] ~ -1.5, yet pulsar B1620-26 has a giant planet with a mass ~ 2.5 MJup (Sigurdsson et al. 2003) • Core accretion cannot work as [Fe/H] drops to low values

Mayer et al. (2007) 3D SPH with radiative transfer, convection, fragmentation

m= 2.4 3000

m= 3.0 6000

Fragments for higher mean molecular weight and larger radiating surface area

m= 2.4 4000

m= 2.7 4000

Core Accretion Mechanism • •

• • • •

•

Pro: Leads to large core mass, as in Saturn Higher metallicity may speed growth of core Based on process of collisional accumulation, the same as for the terrestrial planets Does not require external UV flux to make ice giants, so works in Taurus HD 149026: 70 Earth-mass core plus 40 Earth-mass gaseous envelope? Formed by collision between two giant planets (Ikoma et al. 2006)? Failed cores naturally result

• Con: • Jupiter’s core mass is too small? • If gas disks dissipate before critical core mass reached  “failed Jupiters” result • Difficult to form gas giant planets for M dwarfs, low metallicity stars (e.g., M4), or rapidly (CoKu Tau/4?) • Loss of growing cores by Type I migration? • Needs disk mass high enough to be ~ gravitationally unstable • No in situ ice giant formation?

Disk Instability Mechanism • •

• •

• • •

•

Pro: Can explain core masses, bulk compositions, and radial ordering of gas and ice giant planets in Solar System Requires disk mass no more than that assumed by core accretion Forms gas giants in either metal-rich or metal-poor disks (M4) Clumps form quickly (CoKu Tau/4?) even in short-lived disks Works for M dwarf primaries Sidesteps Type I (and III) orbital migration danger Works in Taurus or Orion, implying Solar System analogues are common

• Con: • Requires efficient cooling of midplane (e.g., convection), coupled with efficient cooling from the surface of the disk: subject of work in progress • Clump survival uncertain: need for models with detailed disk thermodynamics and higher spatial resolution (e.g., AMR) • Requires large UV dose to make ice giant planets – in Taurus would make only gas giant planets