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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 (gas alone)
~100 (with dust)
102-103 (gas)
1-10 (solids)
-10
10 – 10-12
~10-6
~10 5 – 106 yr
~100 – 104 yr
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?
Giant Planet Formation:
Theory vs. Observations
Alan P. Boss
The Formation
of
Carnegie Institution of Washington
Planetary Systems
Heretic’s Approach to
Solar System
FormationFForm
Molecules,
Microbes and the Interstellar Medium
Geophysical Laboratory’s Wes Fest
Carnegie 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
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
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 coreaccretion 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 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
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
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
added
Discovery space
with planets
around
M (K?)
dwarf stars
highlighted
GJ 876
GJ 317
GJ 849
GJ 876
OGLE-2003-BLG-235
OGLE-2005-BLG-071
OGLE-2006-BLG-109b,c
GJ 436 GJ 581
GJ 176
GJ 876
OGLE-2005-BLG-169
OGLE-2005-BLG-390
Laughlin et al. 2004 core accretion models
1.0 Msun
total
core
* gas giants
rarely form
by core accretion
around M dwarfs:
process too slow
0.4 Msun
total
core
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?
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
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