1. Ge/Ay133 Jovian planet formation. Core-accretion
or gravitational instability?
Ge/Ay133

2. 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 Mearth.
11-13

3. Caveat! Core mass estimate based on high pressure EOS:
[preferred EOS]
[envelope]
OK for Saturn, but…
Saumon & Guillot 2004 core mass constraints based on EOS

4. …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

5. 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
Ambient solar nebula
~Isothermal
Photosphere
Adiabatic envelope
Hill Sphere

6. 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

7. 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

8. Solving the radiative transfer equations yields (for the envelope):
Ideal gas
Dense core rH
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...
Photosphere
Adiabatic envelope
Hill Sphere

9. 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

10. The gas/dust ratio in the envelope is also critical for TIME SCALES!
(determines how rapidly the envelope can cool)
ISM/ ISM dust/gas Smaller
core
Lissauer 2001, Nature 409, 23

11. The most recent simulations include dust grain/heavy element settling in the envelope ratio in the envelope to give ~2-3 Myr times:
ISM/ ISM dust/gas Smaller
core
Lissauer et al. 2009, arXiv:0810.

12. 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:

13. Properties of the inner moons of Jupiter:
1000
T(K)
500
Hydrated silicates
Water ice
250
Solar nebula
(buffer)
125
Ammonia-Water Hydrate RJ
Io Europa Ganymede Callisto
r g cm-3
Anhydrous Hydrated /40 rock/ice /50 rock/ice
silicates silicates (initially)
Saturn picture not so clear, but Titan’s location may explain large volatile content.

14. Comparison of protosolar versus protoplanetary disks:
Property Protoplanetary Disk Protosolar Disk
Size (central body units) ~ ~103 – 104
Mass (central body units) ≥
Typical 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) (gas)
~103 (solids) (solids)
Gas density (g/cm3) – – 10-12
Gas pressure (bars) ~ ~10-6
Viscous spreading time ≥100 yr ~105 – 106 yr
Cooling time ~104 – 106 yr ~100 – 104 yr
vs.

15. Hard to explain these planets w/core accretion:
Marois et al. (2008)
Kalas et al. (2008)
Initial systems consistent w/discovery space:
Young(ish) stars w/debris disks
Planets at fairly large radii (24/38/68 & 115 AU)
Are there ways to make Jovian planets near 100 AU?

16. Giant Planet Formation: Theory vs. Observations
The Formation of Planetary Systems
Heretic’s Approach to Solar System FormationFForm
Alan P. Boss
Carnegie Institution of Washington
Molecules, Microbes and the Interstellar Medium
Geophysical Laboratory’s Wes Fest
Carnegie Institution of Washington
October 26, 2007

17. 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)
formation of giant planets by disk instability
Observational tests to discriminate between these two formation mechanisms for giant planets? 3

18. 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

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

20. Gravitational Instabilities (GIs) in disks, can rapid planet formation result?
Compact, massive disks are susceptible to clumping:
1.0 Msun
protostar
with a 20 AU
radius disk of
mass 0.09 Msun

21. 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.

22. 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 well
as capture by
protoplanet’s gas
envelope
* 21 Earth-mass core
forms at 5.2 AU in
3.8 Myr
* no Saturn formed
* disk mass = 0.08
solar masses

23. Helled et al. 2006 accreted mass log radius/RJupiter ~36 MEarth
Time in units of 105 yrs
GI models can generate substantial heavy element cores, if there is substantial dust settling before the instabilities lead to collapse.
Time in units of 105 yrs

26. 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…

27. 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]

28. Discovery space with planets around M (K?) dwarf stars highlighted
Discovery space with latest discoveries added
GJ 876
OGLE-2003-BLG-235
OGLE-2005-BLG-071
GJ 317
GJ 849
GJ 876
OGLE-2006-BLG-109b,c
GJ 436
GJ 581
GJ 176
OGLE-2005-BLG-169
GJ 876
OGLE-2005-BLG-390

29. Laughlin et al. 2004 core accretion models
* gas giants
rarely form
by core accretion
around M dwarfs:
process too slow
1.0 Msun
total
core
0.4 Msun
total
core

30. Sufficiently massive disks around low mass stars do show GIs:
0.5 solar
mass star
with a 20 AU radius disk after 215 yrs (Boss 2006)
Jupiter and/or super Earth formation around K stars?

31. 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.

32. 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 : [Fe/H] = has two planets with masses of 0.5 and 0.9 MJup, Cochran et al. 2007; HD : [Fe/H] = 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] = , -0.12, -0.23, -0.32, and –0.33, while only GJ 849 has [Fe/H] = (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 B 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

33. Mayer et al. (2007) 3D SPH with radiative transfer, convection, fragmentation
= 2.4
3000
= 3.0
6000
Fragments for higher mean molecular weight and larger radiating surface area
= 2.4
4000
= 2.7
4000

34. Core Accretion Mechanism
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?
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 : 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

35. 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