Ge/Ay133

Jovian planet formation. Core-accretion or gravitational instability?

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

Properties of the Jovian Planets in the Solar System

P for H2-He

I/MR2=0.4 for a uniform sphereI/MR2=0.26 for P 2

11-13

Saumon & Guillot 2004 core mass constraints based on EOS

[preferred EOS]

[envelope]

Caveat! Core mass estimate based on high pressure EOS:

OK for Saturn, but…

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

dubious EOS? Previously favored.

Currently preferred EOS (Boriskov et al. 2005)

[envelope]

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

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.

Hill Sphere

Photosphere

Dense core

Adiabatic envelope

Ambient solar nebula~Isothermal

rH

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.

Hill Sphere

Photosphere

Dense core

Adiabatic envelope

Ambient solar nebula

rH

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:

Hill Sphere

Photosphere

Dense core

Adiabatic envelope

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

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

Hill Sphere

Photosphere

Dense core

Adiabatic envelope

rH

Ideal gas

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...

How massive does the core need to be for the atmosphere to collapse?

Photosphere

Dense core

Adiabatic envelope

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

f~K in cm2/g

Setting dMc/dMt=0 gives (

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

ISM/50 ISM dust/gas Smaller core

Lissauer 2001, Nature 409, 23

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 ISM dust/gas Smaller core

Lissauer et al. 2009, arXiv:0810.

rd3 ~ GMp/rd

2

where G is the specific ang. mom.and rd is the (protoplanet) disk radius.Equating this to the orbital specificang. momentum gives, roughly

~ rH2/4 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

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

Properties of the inner moons of Jupiter:

10 20 30 RJ

Io Europa Ganymede Callisto 3.5 3.1 1.92 1.78 g cm-3

Anhydrous Hydrated 60/40 rock/ice 50/50 rock/ice silicates silicates (initially)

Hydrated silicates

Water ice

Ammonia-Water Hydrate125

250

500

1000

T(K)

Solar nebula (buffer)

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

Property Protoplanetary Disk Protosolar DiskSize (central body units) ~20 ~103 – 104

Mass (central body units) ≥0.05 0.05-0.1Typical Temperature ~200 K ~200 K (but up to 2000 K) (but up to >1000 K)Vertical optical depth ~100 (gas alone) <<1 (gas alone) ~10,000 (with dust) ~100 (with dust)Mass surface density (g/cm2) ~105 (gas) 102-103 (gas) ~103 (solids) 1-10 (solids)Gas density (g/cm3) 10-4 – 10-6 10-10 – 10-12

Gas pressure (bars) ~1 ~10-6

Viscous spreading time ≥100 yr ~105 – 106 yrCooling time ~104 – 106 yr ~100 – 104 yr

Comparison of protosolar versus protoplanetary disks:

vs.

Giant Planet Formation: Theory vs. Observations

Giant Planet Formation: Theory vs. Observations

The Formation of Planetary Systems

Heretic’s Approach to Solar System

FormationFForm

Alan P. BossCarnegie Institution of Washington

Molecules, Microbes and the Interstellar MediumGeophysical Laboratory’s Wes FestCarnegie Institution of Washington

October 26, 2007

Outline: Conventional scenario for Solar System formation:

•region of low mass star formation (Taurus)

•collisional accumulation of terrestrial planets

•formation of giant planets by core accretion

Heretical scenario for Solar System formation:

•region of high mass star formation (Orion, Carina)

•collisional accumulation of terrestrial planets

•formation of giant planets by disk instability

Observational tests to discriminate between these two formation mechanisms for giant planets?

3

Extrasolar Gas Giant Planet Census: Frequency

* Approximately 15% of nearby G dwarfs have gas giant planets with relatively short orbital periods – hot and warm Jupiters (Hatzes 2004)

* Approximately 25% of nearby G dwarfs appear to have gas giant planets with even longer orbital periods – Solar System analogues (Hatzes 2004)

* Hence as many as 40% of nearby G dwarfs appear to have gas giant planets inside about 10 AU (Hatzes 2004)

* Approximately 20% of FGK dwarfs have giant planets with orbital distances less than 20 AU (Marcy 2007)

* More massive stars (up to 1.9 Msun) have more gas giant planets than lower mass dwarfs (Marcy 2007)

* Using either set of statistics, gas giant planet formation mechanism must be relatively efficient and robust

Cieza et al. 2006 SST survey: ~65% of disks gone in < 1 Myr

Compact, massive disks are susceptible to clumping:

1.0 Msun protostarwith a 20 AU radius disk ofmass 0.09 Msun

Gravitational Instabilities (GIs) in disks, can rapid planet formation result?

Boss (2003) disk instability model after 429 yrs, 30 AU radius

GI clumps form rapidly, the key questions about planet formation are whether such clumps can cool efficiently enough to continue their contraction or whether they “bounce” and thus dissipate… Much like envelope collapse in core- accretion models. This approach is FAST, however, but needs compact & massive disks.

Inaba, Wetherill, & Ikoma (2003) core accretion model

Critical mass for onset of gas accretion

* first model which included effects of planetesimal fragmentation and loss by orbital migration as wellas capture by protoplanet’s gasenvelope* 21 Earth-mass core forms at 5.2 AU in 3.8 Myr* no Saturn formed* disk mass = 0.08 solar masses

Helled et al. 2006

Time in units of 105 yrs

Time in units of 105 yrs

log radius/RJupiter

accreted mass

~36 MEarth

GI models can generate substantial heavy element cores, if there is substantial dust settling before the instabilities lead to collapse.

A new paradigm for forming the giant planets rapidly:

Marginally gravitationally-unstable protoplanetary disk forms four or more giant gaseous protoplanets within about 1000 years, each with masses of about 1/3 to 1 Jupiter-masses

Dust grains coagulate and sediment to centers of the protoplanets, forming solid cores on similar time scale, with core masses of no more than about 6 Earth-masses per Jupiter-mass of gas and dust (Z=0.02)

Disk gas beyond Saturn’s orbit is removed in a million years by ultraviolet radiation from a nearby massive star (Orion, Carina, …)

Continued…

Outermost protoplanets are exposed to FUV/EUV radiation, which photoevaporates most of their envelope gas in about a million years or less

Outermost planets’ gas removal leads to roughly 15-Earth-mass solid cores with thin gas envelopes: Uranus, Neptune

Innermost protoplanet is sheltered by disk H gas gravitationally bound to solar-mass protosun and so does not lose any gas: Jupiter

Protoplanet at transitional gas-loss radius loses only a portion of its gas envelope: Saturn

Terrestrial planet region largely unaffected by UV flux [TPF/Darwin targets]

Discovery space with latest discoveries addedDiscovery space with planets around M (K?) dwarf stars highlighted

GJ 876

GJ 436

OGLE-2005-BLG-390

GJ 581

OGLE-2003-BLG-235OGLE-2005-BLG-071

GJ 876

GJ 876

OGLE-2005-BLG-169

OGLE-2006-BLG-109b,c

GJ 317GJ 849

GJ 176

Laughlin et al. 2004 core accretion models

1.0 Msun

0.4 Msuncore

coretotal

total

* gas giantsrarely form by core accretionaround M dwarfs:process too slow

0.5 solarmass starwith a 20 AU radius

disk after 215 yrs (Boss 2006)

Sufficiently massive disks around low mass stars do show GIs:

Jupiter and/or super Earth formation around K stars?

Heretical Explanation for Long-Period Super-Earths

• Most stars form in regions of high-mass star formation (e.g., Orion, Carina) where their protoplanetary disks can be photoevaporated away by nearby O stars.

• Photoevaporation converts gas giant protoplanets into ice giants if the protoplanet orbits outside a critical radius, which depends on the mass of the host star.

• For solar-mass stars, the critical radius is > 5 AU, while for a 0.3 MSun M dwarf star, the critical radius is > 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

Fragments for higher mean molecular weight and larger radiating surface area

= 2.43000

= 2.74000

= 2.44000

= 3.06000

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