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巨大惑星の解剖学：
内部構造・熱進化から起源へ (第1部)
堀 安範

国立天文台 理論研究部© Cassini, NASA

© JUNO, NASA

第13回 森羅万象学校『木星を解剖する – 巨大ガス惑星の腹のうちと誕生の謎』

2013年 3月26日-28日＠北海道 支笏湖

LETTERS

PUBLISHED ONLINE: 21 APRIL 2013 | DOI: 10.1038/NGEO1791
LETTERS200a

α = 10¬2.5
α = 10¬3ò¢ýöRPÈ£ç¤ÀìRP¶Ĕ

100

Adiabatic
0.01

0.1

1

a

α = 10¬3ó¦êę α = 10

¬1.5
100
95

¬2.5

Adiabatic¬2.09085
0.01
4.0

0.00014.2

0.1 4.4

4.6

Age (Gyr)
Age (Gyr)

0.001

0.01

Adiabatic
1
4.8

0.1

5.0

1

98
Effective temperature (K)

105

3
0.01

b

α = 10¬3.5

¬2.5

100

10

¬1.0110

MLC = 0.5 M

150

Age (Gyr)α=b 10¬3.5
115
100

200

10

96
94
92

2

1

90
88
4.0

4.2

10

Age (Gyr)
Figure 2 | Cooling sequences of Saturn models
with layered convection.
Figure 3 | Impact of the sizeb
115 a, Effective (T ; solid curves) and intrinsic (T ; dashed curves)cooling sequence. a, Effective
int
eff
Figure1 | Evolutionof the totalinternal
energy+ Eth + Erot ) withtot ⌘ Egreference
temperature(see Methods)
evolutionin timefor the(Eadiabatic
curves) temperature evolutio
3(black) andthreemodels.
models with(↵ = 10 2.5to, 10thethree scenarios with layered c
110timemodel
for various
SaturnThelayered
solid convection
curve corresponds
3.5 from dark to light red). b, Zoom on present era. Dots show theand10reference adiabatic model. The long dashed, dashed and dotted curves darker
are to lighter red curves: oobserved
effective
temperature.
At
early
ages,
the
effective
temperatureofpresent
throughout the gaseo
2.5
3
3.5
models with layered convection with ↵ = 10
, 10 and 10,
105models with layered convection is lower owing to inefficient convection.
where M is the total mass ofrespectively. Owing to the reduced intrinsic luminosity caused by layered
After a few hundred million years, these models become brighter owing to
only the inner 50% of the env
convection,
more
slowlykeepstate.
the memory of their100
the releasetheseof themodels
excess ofcool
energystoredfrom andthe initial(MLC ⇡ 0.5 M; ↵ = 2 ⇥ 10 4 ),initial energetic state much longer.
between 0.5 and 0.7 M (MLC
layeredconvectionisfavouredoverhomogeneous
doublediffusive95
17 (Supplementary Information). However, the question
convection
gradients. In planets, however, this latter quantity is not a time
free occurs before Saturn
remains
whetherlayeredconvection
canalso
explainthepresentyieldsparameteris imposed by the (measured) energy flux to be a larger luminosity
90 luminositybutof the giant planets.
if the size of the convect

Effective temperature (K)÷PþrýöRPÈ£

Effective temperature (K)äĆòÓPÚċN¡­

α = 10¬3.5

α = 10¬2.5
α = 10¬3

Effective temperature (K)As the giant planets of our Solar System continue to cooland contract, they radiate more energy than they receivefrom the Sun. A giant planet’s cooling rate, luminosity andtemperature at a given age can be determined using thefirst and second principles of thermodynamics. Measurementsof Saturn’s infrared luminosity, however, reveal that Saturnis significantly brighter than predicted for its age1,2 . This
excess luminosity has been attributed to the immiscibilityof helium in Saturn’s hydrogen-rich envelope, which leads
to rains of helium-rich droplets3–8 . Existing calculationsof Saturn’s evolution, however, suggest that the energy
released by helium rains might be insufficient to resolveb
the luminosity puzzle9 . Here we demonstrate, using semianalytical models of planetary thermal evolution, that thecooling of Saturn’s interior is significantly slower in thepresence of layered convection generated—like in Earth’s
oceans—by a compositional gradient. We find that layered
convection can explain Saturn’s present luminosity for awide range of initial energy configurations without invoking
any additional energy source. Our findings suggest that theinterior structure, composition and thermal evolution of giant
planets in our Solar System and beyond may be more complex
than the conventional approximation of giant planets as
homogeneous adiabatic bodies.

150

Effective temperature (K)200

Total energy Etot (1035 J)§B
wn¨\£KYSX-RB³pgTOVa
Effective temperature (K)Jérémy Leconte1,2 * and Gilles Chabrier2,3

Effective temperature (K)Layered convection as the origin of Saturn’s
luminosity anomaly LETTERS
150

300

Effective temperature (K)aNATUREtransported in the planet. It can be shown that this flux is too high

巨大惑星の内部構造と熱進化の基礎知識

太陽系の巨大惑星~ 10 REarth~ 4 REarthfrom Wikipedia

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質量と半径の関係
0 K状態方程式（熱圧なし）
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Ba P] 

1

0.1

10
10+3

10+2
0.1
1
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Fig. from Chabrier+ (2009)
FIGURE 2. Mass-radius relationship from from the stellar to the planetary regime. The (black) solidýöand short-dash lines correspond to models with solar composition, for two isochrones. The (blue) longdahs line corresponds to an object with a Z = 10% mass fraction of heavy elements (from [5]). The
observationally-determined values of Hat-P-2b and Corot-3b are indicated.

1
1

the observations do confirm the theroretical predictions, providing confidence in thedescription of the internal physics characteristic of the cool, dense, partially degenerate
objects known as "substellar objects". A detailed composition of Hat-P-2b has been
derived in Baraffe et al.(2008) [5]. Models are shown in Fig. 2 for two different internal
compositions: one, with a solar abundance of heavy elements, corresponds to solarmetallicity BDs,for two isochrones, whereas the other one, with a 5-times solar metalenrichment, corresponds to massive gaseous planets. Assuming that (i) the theoretical
MRR is accurate, (ii) the observational error bars on the radius are reliable, the second
importantin Fig. 2
2 result illustrated
3
4 is that, given the age inferred for the system, ∼ 2-3
Gyr [3], Hat-P-2b is too dense to be a BD. This in turns shows that planets can form
up to at least 9 Jupiter masses, a result of prime importance for constraining models ofplanet formation. Although such a mass is still compatible with planet formation models
based on the core-accretion scenario [37], an alternative possibility for the formation ofsuch high-mass, short-period planets is collisions between less massive planets (see §6of [5]). Interestingly, although Corot-3b is compatible with this object being a BD with

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=

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Γ~50

Figurefromdiagram
Guillotfor&hydrogen
Gautierwith(2009)
Figure5: Phase
the main phase transitions occurring in the fluidor gas phase. The temperature-pressure profiles for Jupiter, Saturn, Uranus, Neptune, and the

`Y

氷＋岩石

core

core
0
0

0
400 LhN_
0200
Pad(t0) [bar]200
Pad(t0) [bar]

巨大惑星内部の水/氷

2.5

400

-2

-1
log

Figure 2. Cooling curves and internal structure of models with water envelope+rock core. All models are adjusted to have Rp (t0 ) = 2
core mass. (a) Core mass (solid line) and mass shell where water in the envelope enters the plasma phase (dashed line) of present time stpressures 5 bar ! Pad (t0 ) ! 400 bar. Single interior models run vertically. The gray shaded areas are a guide to the eye for the allowed P
with the thermal evolution (in panel (c)). (b) Same as (a) but radius coordinate. Numbers at models highlighted by filled circles are press
in K. (c) Evolution of radius of structure models IIa (dashed) and IIb (solid), see Table 1. Circles indicate those profiles during evolution

H2O “ice” の相図

(

海

Temperature [K]王星of water. Here we consider the case othe radiative atmosphere4)&(5 and in the aplasma10000
class III models) as parameterized by theionic fluid
Figure 4(a) shows
the change of the I:R
6000
40.&*5
The water to core mass ratio rises mode
super
4000
ionic
passes 1×(I:R)# at Z1 = 0.95, and thenmolecular fluid
values found for class II models. This2000
weakly on the choice of Pad (t0 ).
For class III models, the resulting H
ice X
GJ1214b
the planet (see Figure 4(a)) is about 2–
1000
case of an H/He layer on top of a wat
vapour600
maximum for Z1 ≈ 0.80 (the core mass?
ice VIIrequiring a high metallicity, and also Z
liquid300
We find a planetary H/He mass fractio@üÔÝjbn
ice II-VI
ice I
400 bar as in Figures 4(a) and (b), and sl
20 mbar 1 bar
1 kbar
1 Mbar 100 Mbar
up to 7% (colder envelopes reduce the cPressurecolder present time interior would takecool. For the cooling curve calculations w
Figure 3. Water phase diagram for 20 mbar < P < 100 Mbar and GJ 1214b
water
envelope+rockcore models
with Kramm+
Pad (t0 ) = 100
bar ApJ)(orange dash-dotted)
Figurefrom Nettelmann,
Fortney,(2011,
Z1 = 0.85, which gives an H/He mas
and 300 bar (red dash-dotted). The Neptune profile (blue dash-dotted) is adopted
maximum value but also a core mass b
16000

LhN_

重力モーメントの感度

The Astrophysical Journal, 726:15 (7pp), 2011 January 1
Jupiter

4

Contribution functions

J4`YOHVÂQØB7

J2

2
J0
1
core
0
0.0

0.2

0.4
0.6
Normalized Mean Radius β

0.8

1.0

Neptune4

Óðö ªðö

J6
Contribution functions

3

2. INTERIOR MODEL: FINDING RADIAL PROFILES OF`YOHVÂT
DENSITY AND PRESSURE

J4
J2

2

1

0
0.0

ËĎB7

J0

core

0.2

0.4
0.6
Normalized Mean Radius β

0.8

and Neptune that fit their measured gravitational fields arederived using Monte Carlo searches (Marley et al. 1995; Podolak
et al. 2000). This approach is free of preconceived notions aboutplanetary structure and composition and is not limited by theEOSs of assumed materials. Once the density profiles that fit thegravitational coefficients are found, conclusions regarding their
possible compositions can be inferred using theoretical EOSs
(Marley et al. 1995).
In this paper, we apply the method previously used in ourmodels of Saturn (Anderson & Schubert 2007; Helled et al.
2009a) to derive continuous radial density and pressure profiles
that fit the mass, radius, and gravitational moments of Uranus
and Neptune. The use of a smooth function for the densitywith no discontinuities allows us to test whether Uranus and
Neptune could have interiors with no density (and composition)
discontinuities. Section 2 summarizes the models and results. In
Section 3, we use physical equation of state tables to infer whatthese density distributions imply about the internal compositionof Uranus and Neptune. Conclusions are discussed in Section 4.

®ö Îö

J6
3

Helled et al.

1.0

Figure 1. Normalized integrands of the gravitational moments (contributionof Jupiter (top)and Neptune (bottom).
The values
are normalized
Figuresfunctions)from Helled,
Anderson,
Podolak+
2011.
ApJ tomake the area under each curve equal unity. J0 is equivalent to the planetary
mass. The range of possible core sizes is indicated. Here, core designates a

The procedure used to derive the interior model is described indetail in Anderson & Schubert (2007) and Helled et al. (2009a).
The method is briefly summarized below.
The gravitational field of a rotating planet is given by
!
%
∞ # $
"
2n
GM
a
1
U=
J2n P2n (cos θ ) + ω2 r 2 sin2 θ,
1−
r
r
2
n=1

(1)

where (r, θ, φ) are spherical polar coordinates, G is the gravitational constant, M is the total planetary mass, and ω is the angularLhN_

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®ö

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10

20

30

40

0

10

[qhp:guP°³ûîÄá"¿Ùá#
Figures from Saumon & Guillot (2004, ApJ)

LhN_

海王星型惑星の内部

and Space Science 77 (2013) 143–151

5000-5.5-3
3.6-0.2556

1.2

0.7

0.3
0.2
0.1
0

4700
5.1
3.6
2.9
0.2555

Neptune6000-7~0 ~inf0.25570.1

0.05 146
4500
5.0
3.7
2.7
0.2554

N. Nettelmann et al. / Planetary and Space Science 77 (2013) 143–151

5700
6.4-1.2
11.5-0.2557

0.6

outer envelope metallicity Z1

0.4

Z1

OUTER-Envelope-Metallicity

0.3

0.5

Outer-envelope
H+He+”ice”
Inner-envelope“ice”+H+He

5200
8.3-0.524
0.25570.01

0.5
Neptune

0.4

0.15

0.1

5200-5.5-3.7
2.8-0.2409

0.2

0.4
6600-8.0
Uranus~0-0.2411

N1

0.12

0.1

Z2

0

Uranus

0.9

0.1

0.05

0.08

6200-7.3-1.1
12.5-0.2416

0.8
0.9
inner envelope metallicity Z2

INNER-Envelope-Metallicity

0.3

5200
8.3-0.524
0.2557

1

0.1

0
1

4700
5.1
3.6
2.9
0.2555“rocky”-core

Neptune6000-7~0 ~inf0.2557

0.1

0.05
5700
6.4-1.2
11.5-0.2557

4500
5.0
3.7
2.7
0.2554@üÔÝjbn²
0.2

U1

5900-5.2-1
11-0.2295

1.2

0.7
0.3

0.5

0.7

0.3

5300-5.8-3.3
3.6

5000-5.5-3
3.6-0.2556

5700-8.9-0.4
39-0.2402

5700-6.5-2.7
4.5-0.2404

5300
6.2-1.5
0.3
8-0.2556

0.8

0.6

Z1

0.6

0.01

5300
6.2-1.5
8-0.2556

Uranus
0.15

0.12

0.8

Z2

0.9

1

Fig. 3. Same as Fig. 2 but using the modified shape and rotation data for Uranus
Fig. 3. Same as Fig. 2 but using the
shape
data
for Uranus
Fig. 2. modified
Heavy element massfraction in andthe outerrotationenvelope (Z ) andinner envelope(cyan) and Neptune (blue). Models U2, N2a, and N2b (Table 2) are highlighted by(Z ) of Uranus models (black) and Neptune models (grey) as labeled with theblack-filled, big circles. The boxes of Fig. 2 are also shown to facilitate the(cyan) and Neptune (blue). Models
U2,
N2a,
and
N2b
(Table2)
arehighlighted
byVoyager shape and rotation data. The solid lines frame the full set of solutions forcomparison. (For interpretation of the references to color in this figure caption,
Figurefrom
Nettelmann,
Helled,(2013,
PSS)
each planet.
Dashed linesFortney+
within the box of Neptune
models indicate
solutions of
the reader is referred to the web version of this article.)
black-filled, big circles. The boxesof Fig. 2 are also shown to facilitate thesame transition pressure in (Mbar) as labeled. Numbers at selected models (filled
circles) give T (K), P (Mbar), M ðM Þ, the ice-to-tock ratio I:R, and l. The dottedcomparison. (For interpretation ofthereferences to color in this figure caption,line is a guide to the eye for the solar metallicity Z ¼ 0:015.
Most obvious, the sets of solutions shift into opposite direc1

2

c

c

c

"

%

LhN_

巨大惑星の熱進化（重力収縮）
V
Yfhz

e lowest gravity,
d y-axes are thed Tint s are dotted.)

The Astrophysical Journal, 729:32 (14pp), 2011 March 1

e_ 

Fortney et al.

PQ"!

PQ"!

Figure 8. Radius evolution of the models of Jupiter and Saturn shown in Figure 7.
The black curves use the new model atmosphere grids presented in this work.
The red curves utilize the same interior structure and solar luminosity, but instead
use the Burrows et al. (1997) grid (see Fortney & Hubbard 2003).
(A color version of this figure is available in the online journal.)

MMTO6¡´e6d6G¯§±6y<G

dramatically super-adiabatic in the face of helium composition
gradients (Stevenson & Salpeter 1977a; Fortney & Hubbard2003).
The model calculations for Jupiter, which yield an age of
5.3 Gyr, rather than 4.6 Gyr, could have important implications
for the planet. Jupiter’s atmosphere is clearly depleted in helium,according to Galileo Entry Probe data (von Zahn et al. 1998),
which is a strong indication that helium phase separation has
occurred in this planet. Furthermore the atmosphere’s depletion

MMTO6½6h:8@G
Figures from Fortney, Ikoma, Nettelmann+ (2011, ApJ)

Figure 9. Thermal evol
models that feature threrock. The models are coday, and the evolution is
the formation of the sol
performed in the manneret al. (1975) model atm
atmospheres, but update
cooling times for both
EOSs as the dotted-cur
The thin solid red curve,
adjusting the current Tin(A color version of thisaffect the thermal ea set of evolution m& Macfarlane (198
calculations. The m

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ICARUS30, 305--310 (1977)m´i

ICARUS30, 305--310 (1977)

The Jovian Surface Condition and Cooling Rate
W. B. HUBBARD

The Jovian Surface Condition and Coo

Department of Planetary Sciences, Lunar and Planetary Laboratory,
University of Arizona, Tucson, Arizona 85721

W. B. HUBBARD

太陽照射なし● 太陽照射あり(変化)○ 太陽照射あり(一定)Received April 6, 1976; revised June 2, 1976
Department of Planetary Sciences, Lunar and Planetary
University of Arizona, Tucson, Arizona 8572
A theory which is almost fully analytic is used to investigate Jupiter's cooling rate. We findthat a simple model of contraction with adiabatic interior structure
gives a total
time
Received
Aprilcooling6, 1976;
revised June 2, 197
to the present which is in good agreement with the age of the solar system. The interplay
between the surface condition and the cooling rate is exhibited and discussed. The current rate
A theorytowhichis almost fully
is used to investigate Jupitof change of the effective temperature is calculatedbe -1°K/0.145
X 10analytic
a yr. Discrepancies
thatJovian
a simplemodelof contraction
with adiabatic interior structurewith fully numerical investigations of theage andcooling
rate are noted.

観測値



Z°&"

Figure from Hubbard, Guillot, Marley+ (1999, P&SS)

to the present which is in good agreement with the age of the sol
between the surface condition and the cooling rate is exhibited and d
I. INTRODUCTION
The
present paper
reportstotheof changeaboutof the 10%.
effective
temperature
is calculatedbe -1°K/0.14
ofindependentcalculationsof JovianH u b b a r d (1968) showed t h a t thewith
in-fullyresult
numerical investigations of the Jovian
age and cooling rat

trinsic thermal radiation from Jupiter cooling using the thermodynamics of M C I V
with an analytic representation
could be attributed, in order of magnitude, I.together
INTRODUCTION
about 10%. The
to Kelvin contraction-cooling of a de- of the same surface condition used by
H u b tbhaartd GPGO.
(1968) Because
showed thet hcalculationsa t the in-are result
almost of indepen
generate hydrogen fluid body. Sincecoolingtrinsic havethermalradiation
p i t e rnumerical, using theentirely
analytic fromrather J uthan
paper, a n u m b e r of investigations
togetherwith abe ofattributed,
in orderworker
of magnitude,
any interested
can reproducethea t t e m p t e d to s t u d y the thermalcould
history
of
the
same
su
to
Kelvincontraction-coolingofadeJupiter quantitatively. The most elaborate results and observe the impact of varying
G
P
G
O
.
Becausedifferent
parametersonthecoolingtime
generatehydrogen
fluid
body.
Since
t
h
a
t
calculations available to date are those ofentirely
calculations are havepublishedhere analyti
Graboske et al. (1975; henceforth,
GPGO).
paper,
a n uscale.
m b e r Theseof investigations
the thermal
shortfall history
in the coolinginterested
G P G O found t h a t a solar-compositiona t t e m p t e d tobecauses t u d y theof a n ytimeof Jupiter The
foundmostby elaborate
G P G O is notcon- and obse
results
object of Jovian mass would evolve
Jupiterfrom
quantitatively.
firmed. Thetodiscrepancies
betweentime
an initially gaseous and luminous
state to available
different
paramecalculations
date are thoseof thescalesof thepresent GPGO).
investigation
andThese calc
a state resembling the present Graboske
Jupiter in et al.
scale.
(1975;
henceforth,a time period of 2.6 X 109 yr.G PThethoset h aoft GaP Gsolar-composition
O are produced almost
en- the sho
becauseG O disfoundcrepancy between this coolingobject
time andtirely mass
duringwould
the late,degenerateofof Jupiterfounof Jovianevolvefrom phasethe expected age of Jupiter, roughly cooling; we have not carried outfirmed.
inde- The discan initially gaseous and luminous state to
4.5 X 10 ~ yr, was a t t r i b u t e d to possible pendent calculations for the early, nona state resembling the present Jupiter in scales of the pinaccuracies in constituent physics, in-

単純な一様・対流モデルで木星の年齢を説明できる

Conven&onal)Evolu&on)Models)with)State4of4the4art)Input)Physics
Fortney, Ikoma, Nettelmann, Guillot, & Marley (2011, ApJ)
理論進化曲線（全対流・重力収縮モデル）

Log 惑星放射量 [太陽=1]

The Astrophysical Journal, 729:32 (14pp), 2011 March 1

®ö

ªðö
Óðö

Fort

(),*+
understanding the cooling of the planets will likely cowork on the EOS of
planetary materials.
V\R
J.J.F. acknowledges the support of NASA OuteP]Q_Z'C^/;-*.
Research Program grant NNX08AU31G and the Alfre:7"HJ5SE Foundation. M.S.M. gratefully acknowledges the infl

Jim Pollack, who was in the planning phases of a sim
at the time of his untimely passing. Our atmosphericis strongly influenced by his work. Referee Gilles
AD<F"LZO9GV\provided valuable comments that improved the draft.

?W3Y

Îö

時間 [年]

Figure 15. Luminosity of the giant planets as a function of age. Observed
values (Pearl & Conrath 1991) are shown as black dots. The values for Uranus
and Neptune nearly overlap. Estimates at young ages are highly uncertain, anddepend strongly on the details of the formation process, especially for Uranus

REFERENCES

IW9GR$%#!8&

Ackerman, A. S., & Marley, M. S. 2001, ApJ, 556, 872
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KUW9GR$%#!`
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Baraffe, I., Chabrier, G., & Barman, T. 2010, Rep. Prog. Phys., 73,
Baraffe, I., Chabrier, G., Barman, T. S., Allard, F., & Hausc
2003, A&A, 402, 701
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Burrows, A., Sudarsky, D., & Hubbard, W. B. 2003, ApJ, 594, 545

土星が明るすぎる問題

土星の「明るい」問題の解決案
KT^
t

 {z%'NB*14-Q\®öOËSK6ÎöPº(áEÅNB
MBCñāëMÖ{LAV
Hubbard & Stevenson (1984)
Fortney & Hubbard (2003,2004)

I^
73

MH~^%'<ZpeXC
[qhp:gE°³ûOĈWKBVMBCyMÖ{LAV
Leconte & Chabrier (2013)

H-Heの分離：大気中のHe含有量■ H-Heの不混和 (He沈降) (Stevenson & Salpeter,1977)(1) 大気中(P ≦ 10bar)のHe枯渇 (原始太陽系星雲：Y = 0.27)

H

He

木星：Y = 0.231 ← Galileo NMS (Von Zahn+00; Niemann+00)
土星：Y = 0.17-0.24 ← Voyager IRIS/RMS(Conrath & Gautier,2000)
Y = 0.13 ← Cassini CIRS (Gautier+06)

輝度温度 (K)110

土星 (赤道付近~7°S)

100[He/H2] = 0.16
[He/H2] = 0.11
[He/H2] = 0.08
[He/H2] = 0.034
Cassini CIRS

電波掩蔽観測90(Fouchet+09)

80
100

200

300
400
波数 (cm-1)

500

600

alZdµå8ćĉWbZ?6eCI

He分離によるエネルギー解放
No. 2, 2004434
@l¡=n±z
PHASE SEPARATION IN GIANT PLANETS

1041

J.J. Fortney, N. Nettelmann]£H¶7:²yj

Fig. 5 Evolutionary models of
Saturn including helium phaseseparation, adapted from Fortneyand Hubbard (2004). “HDW”
uses the H/He phase diagram of
Hubbard and Dewitt (1985),
which allows immiscible helium
to redissolve at higher pressuresand hotter temperatures in theliquid metallic hydrogen.
“MPfaff” is an ad-hoc phase
diagram that forces immiscible
helium to rain down to Saturn’scoreUWai

Fig. 2.—Our current understanding of the high–pressure phase diagram of hydrogen. Regions of liquid molecular hydrogen (H2) and liquid metallic hydrogen(Hþ ) are shown at high temperatures and their solid counterparts at much lower temperatures. The curve marked ‘‘PPT?’’ is a possible transition from liquid H2 toliquid Hþ , as calculated by Saumon et al. (1995). The solid line marked 50% shows, from the theory of Ross (1998), where liquid H2 should be 50% dissociated.
Laser shock data points from Collins et al. (1998) are shown as a dash-dotted line. The reverberation shock data of Nellis et al. (1999) are shown as plus signs (fordeuterium) and asterisks (for hydrogen). The large black dot indicates the highest pressure that the conductivity of H2 has been measured, which seems to indicate
H2 may be 10% dissociated at this point (Nellis et al. 1999). The calculated region of helium immiscibility from Hubbard & Dewitt (1985) and Stevenson (1975) islabeled HDW/S. The lines marked Y ¼ 0:27 and Y ¼ 0:21 mark the immiscibility boundaries for these two compositions. The parallel lines labeled ‘‘Pfaff.’’ show
the helium immiscibility region as calculated by Pfaffenzeller et al. (1995). Again, the upper boundary is for Y ¼ 0:27 and the lower for 0.21, although they are notlabeled to avoid clutter. The current internal adiabats of Jupiter and Saturn are shown as heavy lines, while the dashed extensions show the pressure range within
their cores. Also shown in a heavy line is the adiabat of a hypothetical coreless 0.15MJ planet at an age of 4.5 Gyr. The parallel lines marked ‘‘P1’’ between the
Jupiter and Saturn adiabats is the ad hoc immiscibility region from Paper I. The immiscibility lines are defined to be exactly parallel to the adiabats. The arrow near
P1 is meant to indicate that the immiscibility curves continue at this slope to higher pressures.

Hubbard & DeWitt (1985); Stevenson (1975)%KTXUWai«wÛ

calculated the first evolutionary models that coupled high–pressure phase diagrams of hydrogen-helium mixtures and agrid of radiative atmosphere models for giant planets. A
variety of Saturn evolutionary models were calculated that
included helium phase separation. The main findings ofPaper I were as follows. The phase diagram of Hubbard &Dewitt (1985), which is essentially the same as that of
Stevenson (1975), is inapplicable to the interiors of Jupiterand Saturn, if helium phase separation is Saturn’s only additional energy source. These phase diagrams predict that A
from equation (1) is a decreasing function of pressure. As
Figure 3 shows, this phase diagram prolongs Saturn’s cooling
0.8 Gyr, even in the most favorable circumstance that all

Pfaffenzeller+ (1995)

energy to be released and still match the relatively high(Yatmos ¼ 0:18 0:25) helium abundance.
In Paper I, an ad hoc phase diagram was created that wasessentially a modification of the phase diagram calculated by
Pfaffenzeller et al. (1995). (Pfaffenzeller et al. 1995 find aphase diagram in which A from eq. [1] is an increasing
function of pressure.) To simplify the evolution of the planets,
the ad hoc phase diagram was constructed such that helium
immiscibility region runs exactly parallel to the planets’ internal adiabats. Therefore, there is no region for the helium
droplets to redissolve in the liquid metallic hydrogen. This
causes helium that phase-separates to rain all the way down to theplanet’s heavy element core. Consequently, all hydrogen/helium%

i²r65@F¤cNJ
gravitational potential energy. In light of the new first principles calculations of H/He phase
diagrams (Lorenzen
et al. 2009; Morales
et al. 2009), thermal evolution models of Jupiter
~D>o3=3G9?6kFigure from Fortney & Hubbard(2004, ApJ)
and Saturn should now be revisited.

Wb

ヘリウム不混和領域
PHYSICAL REVIEW B 84, 235109 (2011)

D REDMER

.6

elium
Also
Mott

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METALLIZATION IN HYDROGEN-HELIUM MIXTURES

PH

present work
Morales 2009

gH-H (r)

8000

iter
p
u
J

1

0

1

1.5
1
0.5
0

6000

gHe-He (r)

n
Satur

4000

3
2
1
0
1

2000

CP

H melting line

0FIG. 6. (Color) Snapshot of a simulation for x = 1/3, ! =4 g/cm3 , T = 6000 K, and P ≈ 20 Mbar visualized with the VMD
program (Ref. 72). Shown are the ions (small spheres) and isosurfacesof the specific particle density for ni = 0.5/Å3 . Blue: helium; red:hydrogen.

elting lin
He meliquid-liquid

V. DIRECT SIMULATION OF DEMIXING

0

1

2

3

Pressure [Mbar]

gH-He(r)Temperature [K]02

4

To study the effect of demixing directly, i.e., without using

5 the ideal entropy of mixing or thermodynamic integration,

we have performed simulations with 2048 electrons for x =1/3, i.e., 1024 hydrogen atoms and 512 helium atoms, at aconstant density of ! = 4 g/cm3 and temperatures between
6000 and 12 000 K. With this high (and demanding) particle
number it was possible to see demixing effects directly inside
the simulation box. A typical snapshot of such a simulation at
6000 K, i.e., inside the demixing region, is shown in Fig. 6. We
can identify helium-rich (blue) and helium-poor (red) regions.
Note that we did not prepare a demixed state but started from ahomogeneously mixed one and then let the system equilibrate.
After a simulation time of ∼1 ps (a few thousand time steps)
the demixing could be seen clearly and was stable until the endof the simulation (a further 3-ps simulation time). At higher
temperatures the demixing effect decreases.

0.5

0FIG. 7. (Color online) R
He, and H-He at ! = 4 g/c
12 000 K.

With increasing tempera
droplet decreases, andvanished, in agreement w
as derived from thermody
finite-size effects might s
at the moment not suitab
entropy of mixing approx

E@J8FDOSPRFIG. 5. (Color online) Demixing region (yellow/light gray area)
for a helium fraction of x = 0.086 in comparison with the isentropes;l`]:>'(black)of Lorenzen,
Jupiter (Ref.
2) (solidline)(2011,
and Saturn
Figuresfrom
Holst,& Redmer
PRB) (dashed line). The
filled circles are the calculated data from Fig. 4 and Ref. 22, and the1

0.8

土星の「明るい」問題の解決案
KT^
t

 {z%'NB*14-Q\®öOËSK6ÎöPº(áEÅNB
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Hubbard & Stevenson (1984)
Fortney & Hubbard (2003,2004)

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73

MH~^%'<ZpeXC
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Leconte & Chabrier (2013)

Wb

Z?6eCI

組成非一様エンベロープの対流条件
Schwarzschild)不安定条件

d ln Td ln P

Ledoux)安定条件

d ln T<<d ln Padd ln Td ln P!: 平均分子量,:UAB;E

+
ad
ln
ln T

d ln µd ln P
,
P,µ

ln
ln µ

P,T

jf^

Overturning
convection

R Ρ"1'1

J. Leconte and G. Chabrier: A new vision of giant planet interiors=¾Ê>
Layeredconvection

R Ρ"1'Rmin"1

Figure from Leconte & Chabrier (2012. A&A)
d ln µTurbulent
diffusion

StablesystemFig. 1. Stability diagram
presenting a destabilizing
gradient
and a stabilizin
d ln
µ
Α
&Μ
"1 1 Μ
d lndient,P
as a function of in
R Ρ R#T addlnTΑT &dT ln"&(decreasing Rρ ). The ud ln Pd ln P ad"1 Pr ( 1ity Ledoux criterion coRΡ 'Pr ( Τ
R−1
ρ ! 1.

of mean molecular weight (µ), ∇µ ≡ d ln P . The actual dynamical

while well defined thermo/compositional layers sta

Wb

Z?6eCI

準対流モデル
Leconte.&.Chabrier.(2012).の半解析的モデル
A&A 540, A20 (2012)
165K
2-4 Z

135K
2-8 Z

SaturnJupiter

8-12 Z
19000-30000K
0-0.5M

11-25Z
11500-42000K
10-21MRocks+Ices

Fig. 2. Schematic representation of the interiors of Jupiter and Saturn, according to the present study, and of layered convection, with the resulting
compositional and thermal radial profiles. The abundance of metals is constant within the well mixed convective cells of size l, and undergoes asteep variation within the diffusive interfaces of thermal size δT (gray regions). Thanks to this steep gradient, these interfaces are stable against
convection and energy and matter are transported therein by diffusive processes. Because the size of these layers is very small compared with thesize of the planet, the mean thermal and compositional gradients (!∇T # and !∇µ #) can be used in good approximation to infer the planet’s overall
structure.

8.Parameterized.convec<on
8.層のサイズと数を仮定
8.進化において層構造は常に維持されると仮定

In a laboratory or a numerical experiment, the efficiency ofthe convection is characterized by the thermal Nusselt number,

Figure from Leconte & Chabrier (2012. A&A)
NuT ≡Ftot − Fdad,

(7)

Krishnamurti (1995) tend to show that this exponent could belower, and as low as a = 0.2. On the other hand, for homogeneous Rayleigh-Bénard convection (without boundaries),
Garaud et al. (2010) show that the regime predicted by the mix-

Wb

準対流熱進化モデル

LETTERS

Effective temperature (K)

200

b

150

150

α = 10¬2.5
α = 10¬3

α = 10¬3.5

α = 10¬3a

α = 10¬3.5

100
0.01

Adiabatic
0.1
1
10
*$%#!
Age (Gyr) $" ##

100
95
90
85

4.0

4.2

4.4

0.01
4.6

4.8

5.0

Age (Gyr)

Figure 2 | Cooling sequences of Saturn models with layered convection.
a, Effective (Teff ; solid curves) and intrinsic (Tint ; dashed curves)
temperature (see Methods) evolution in time for the adiabatic reference
model (black) and three models with layered convection (↵ = 10 2.5 , 10 3
and 10 3.5 from dark to light red). b, Zoom on present era. Dots show theobserved effective temperature. At early ages, the effective temperature ofmodels with layered convection is lower owing to inefficient convection.
After a few hundred million years, these models become brighter owing to
the release of the excess of energy stored from the initial state.

bature (K)

115

110

layered convection is favoured over homogeneous double diffusive
convection (Supplementary Information). However, the question
remains whether layered convection can also explain the present
luminosity of the giant planets.
To answer this question, we have computed the thermal

MLC = 0.5 M

150
100

MLC = 0.2 M

0.1

1

b

98
96
94

10

ó¦jbn
(α=1) Adiabatic

92
90

0.1

88
4.0

4.2

Age (Gyr)

4.4

1

4.6

4.8

MLC = 0.5 M

5.0

10

100

yjcq_´5\qe®~
¿hF3

0.01

Age (Gyr)

Figure 3 | Impact of the size of the layered convection zone on Saturn’scooling sequence. a, Effective (Teff ; solid curves) and intrinsic (Tint ; dashedcurves) temperature evolution for the adiabatic model (black curve) andthree scenarios with layered convection. b, Zoom on the present era. Fromdarker to lighter red curves: our baseline scenario with layered convection
present throughout the gaseous envelope of the planet (MLC = 0.8 M,
where M is the total mass of the planet; ↵ = 2 ⇥ 10 3 ), a scenario where
only the inner 50% of the envelope exhibits layered convection(MLC ⇡ 0.5 M; ↵ = 2 ⇥ 10 4 ), a case with a layered convection shell
between 0.5 and 0.7 M (MLC ⇡ 0.2 M; ↵ = 10 4 ).

time occurs before Saturn’s present age so that layered convection
Figure from Leconte & Chabrier (2013.
Nat. Geo)yields a larger luminosity at 4.6 Gyr. As shown in Figs 2 and 3,

105

A

200
yjdqu½?DF150²@¼¿º3

MLC = 0.8 M

Age (Gyr)(layer thickness)(scale height)

105

200

Adiabatic

0.01

Effective temperature (K)

110

300

300

~\C<E,-s(

NATURE GEOSCIENCE DOI: 10.1038/NGEO1791

100

115

Effective temperature (K)a

α = 10¬2.5

Effective temperature (K)aNATURE GEO

if the size of the convective layers is about 2–3 ⇥ 10 3 pressure
scale heights, this process properly leads to the present observedb98
ature (K)

(,/(0$120(Effective
temperature (K)200
LETTERS

Effective temperature (K)aZ?6eCI

96

Wb

Z?6eCI

準対流：内部組成推定への影響
J. Leconte and G. Chabrier: A new vision of giant planet interiors°j:iqcPñāëMÖ{HV´

Numberof Layers

SaturnLower
convection
efficiency

25

Core mass !M! "

105

20

10

Core
Total

102

`YNG®öLT°~M
Envelope
Core
Total
Ö{HV

10
Lower
convection
efficiency

00Jupiter
10

20

30

40

50

Jupiter
SaturnAmount of heavy elements (M⊕ )Homogeneous model
36
4.7
3.9
25.6
40
30.3
Semiconvective models
41–63.5
10–36
0–0.5
10–21
41–63
26–50

ę°³ûP}×
Envelope35

ęĂ[qhp:gRegion104

15ĀßÒéÉPØ

Table 3. Heavy element content for Jupiter and Saturn inferred from thevarious models consistent with the observational constraints within thequoted observational uncertainties.

60

70

Metal mass in the envelope !M! "Fig. 7. Mass range of heavy elements in the core (Mc ) and in the envelope(MZ,envLeconte) consistent
all observational
constraints,
for different
Figure from& withChabrier2012. A&A
540, A20
numbers of layers, for Jupiter (bottom right) and Saturn (upper left).
The open dots at the upper left of each region correspond to the homo-`YÃèjbnMĘė9on the coolingof these planets, and of giant planets in general,
remains to be explored. This requires more cumbersome evolutionary 
calculations,for which initial conditions will be cru`YPĖã9
cial, as will be explored in a forthcoming study. Evolution will
add an additional constraint, namely that the planet cooling rates
yield the correct properties at the age of the solar system, which
will put more stringent constraints on the range of possible layer
sizes/numbers. Without going into such detailed calculations,however, the following points can be mentioned.
6.1. Merging of the layers

天王星が暗すぎる問題

&*+*+0

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1990年代の問題意識
2%%$0'$&$0+$-(  X»§

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

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water plasmagX`bCIcore

高圧氷層による対流の阻害00200Pad(t0) [bar]

core
0
0

400

P

Figure 2. Cooling curves and internal structure of models with water envelope+coremass. (a) Core mass (solid line) and mass shell where water in the envelope
JXRW.Q
pressures 5 bar ! Pad (t0 ) ! 400 bar. Single interior models run vertically. The grwith the thermal evolution (in panel (c)). (b) Same as (a) but radius coordinate. N
第一原理計算に基づく
in K. (c) Evolution of radius of structure
models IIa (dashed) and IIb (solid), see T
SXOV

(
4)&(5

40.&*5LI 16000

H2O “ice” の相図

plasma10000
ionic fluid‣固体(or(液体?
‣固体なら磁場はどうする？

Figure from Nettelmann+ (2011, ApJ)

super
ionic

4000
molecular fluid

1000
600

王
星

2000

GJ1214b
vapour

ice VIIliquid

300

ice X

海

超イオン((super,ionic)(層…-高圧氷＋自由プロトン

Temperature [K]

6000

ice I

20 mbar 1 bar?

ice II-VI

1 kbar

1 Mbar 100 Mbar

Pressure
Figure 3. Water phase diagram for 20 mbar < P < 100 Mbar and GJ 1214b

gure 7.
work.
nsteadgX`bCI

問題の変更

m´iFortney et al.

(),*+V\R 
P]Q_Z'C^/;-*.
:7"HJ5SEªðöÓðöx4E¾;:be&"

Figure 9. Thermal evolution models of Uranus (red) and Neptune (blue) for
models that feature three distinct homogeneous layers of H/He, fluid ices, androck. The models are constructed to match the Teff of both planets at the presentday, and the evolution is followed backward in time. The thick gray line indicatesthe formation of the solar system. The dashed curves are cooling calculations
performed
the mannerIkoma,of Hubbard& Macfarlane (1980),
use the Graboske
FigurefrominFortney,
Nettelmann+(2011,andApJ)
et al. (1975) model atmosphere grids. The dotted curves use the same model
atmospheres, but updated water and rock EOSs, which dramatically shorten the[ko
&w

gX`bCI放射への寄与の制限

48

N. Nettelmann et al. / Planetary and Space Science 77 (2013) 143–151

cooling time [Gyr]987

Uranus6

0.5

Neptune

5
4

f=0

3
0

0.2

0.4
0.5

f=0

0.2

0.6
0.4
cut-off mass [MU]

0.8  

0.3
1

the convective heat flux.
ratio F cond,ad =F conv % 0:02
flux along an adiabatic gwould have cooled down
convection (Podolak et al
ending of the stable incomparison, we have ap(model N2a). Neptune’s cthe innermost 20% of Ne

*1.0Sg)/4. Discussion and conc
4>E5&up2Zo

4.1. Bulk compositionZoxv+g. 6. Thermal evolution of Uranus (model U2, solid, cyan) assuming that theheat
4>E5&upzm

ux fromNettelmann,
the mass interior
the cut-offHelled, toFortney+(2013,mass
PSS)(x-axis) is limited to a fraction f ofe convective energy flux. For f¼ 0–0.4 and a cut-off mass of 0.45–0.85, a cooling

We had to make seve
Uranus and Neptune mogX`bCI

天王星と海王星の内部

and Space Science 77 (2013) 143–151

0.6

5000-5.5-3
3.6-0.2556

1.2

0.7

0.4

Z1

OUTER-Envelope-Metallicity

0.3

0.5

0.3
0.2
0.1
0

4700
5.1
3.6
2.9
0.2555Outer-envelope
H+He+”ice”
Inner-envelope“ice”+H+He

5200
8.3-0.524
0.2557

Neptune6000-7~0 ~inf0.25570.1“rocky”-core

0.05
5700
6.4-1.2
11.5-0.2557

4500
5.0
3.7
2.7
0.25540.01

5300
6.2-1.5
8-0.2556

Uranus
0.15
0.12

0.8

Z2

0.9

INNER-Envelope-Metallicity

1

.+
!,

Fig. 3. Same as Fig. 2 but using the modified shape and rotation data for Uranus(cyan) and Neptune (blue). Models U2, N2a, and N2b (Table 2) are highlighted by
Figurebig
from
Nettelmann,(2013,toPSS)
black-filled,
circles.
The boxes Helled,of Fig. 2Fortney+
are also shown
facilitate thecomparison. (For interpretation of the references to color in this figure caption,

gX`bCI

天王星の「暗い」問題の解決案g)+6}%'<Z|YýöÕÿOôÐHV}PÏÌÑ;ú.0Ċ<E

r7xm%'Kt
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Podolak & Helled (2012)

MH~^%'<ZpeXC
[qhp:gE°³ûOĈWKBVMBCyMÖ{LAV

氷惑星の二分性：巨大衝突
斜め衝突 (oblique collision)(Stevenson,1986;Podolak & Helled,2012)

天王星
外殻のみ加熱
内部は密度成層のまま横倒し
衛星系円盤の形成

正面衝突 (head-on collision)

海王星
高温＋一様な内部
衛星系円盤なし

alZdµå8ćĉgX`bCI

天王星の「暗い」問題の解決案g)+6}%'<Z|YýöÕÿOôÐHV}PÏÌÑ;ú.0Ċ<E

r7xm%'Kt
ùWI|ÇčMÖ{LAV
Podolak & Helled (2012)

MH~^%'<ZpeXC
[qhp:gE°³ûOĈWKBVMBCyMÖ{LAVgX`bCI

準対流熱進化モデル

LETTERS(,/(0$120(Effective
temperature (K)

200
150

a

yjdq
MLC = 0.5 Mu½?DF200²@¼¿º3

α = 10¬2.5
α = 10¬3

Effective temperature (K)a

α = 10¬3.5100
*$%#!
 $" ##(layer thickness)(scale height)
0.01

NATURE GEO

ö
300ð
A
Ó

ó¦jbn
(α=1) Adiabatic

0.1

1

10

ö

Î

110

Figure from Leconte & Chabrier (2013. Nat. Geo)

105

b

98
ature (K)ature (K)

115

100

yjcq_´5\qe®~¿hF3

Age (Gyr)

b

150

96



0.01

gX`bCI

天王星・海王星の自転軸と磁場
天王星/海王星
の磁場
[
47°

太陽

S





N 
 47°

N

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60°

S

S

N

N

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60°
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

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

0.23%gauss%RU3

0.13%gauss%RN3

60°

47°

0.3%RU

0.6%RNThe Astrophysical Journal, 733:2 (11pp), 2011 May 20

最適モデル（？）

Core Mass

1

Core Radius

1(a)molecular and dissociatedfluid water• /04)2 ""•  
1.0 Mbar
5750 Kr / Rpm / Mpmolecular and dissociatedfluid water

0.5

1.0
5350

water plasma

0.5• !
H2O"((*5or"/73-61')
core
core
•0  

0
0
200
400
0
200
P
P
(t
)
[bar]
(t
#H2O,4+(.
& ) [bar]2.9 Mbar
7150 K

water plasma

1.0
50

ad 0

2.93
6760

3
6

ad 0

or
#

Figure 2. Cooling curves and internal structure of models with water envelope+rock core. All mocore mass. (a) Core mass (solid line) and mass shell where water in the envelope enters the plasmapressures 5 bar ! Pad (t0 ) ! 400 bar. Single interior models run vertically. The gray shaded areas awith the thermal evolution (in panel (c)). (b) Same as (a) but radius coordinate. Numbers at modelin K. (c) Evolution of radius of structure models IIa (dashed) and IIb (solid), see Table 1. Circles inH2O

• /#"$'%

16000

plasma10000
ionic fluid

Temperature [K]

6000

super
ionic

4000
molecular fluid

2000
ice X

1000
600

vapour
ice VIIliquid300

ice I

20 mbar 1 bar?

ice II-VI

1 kbar

1 Mbar 100 Mbar

Pressure
Figure 3. Water phase diagram for 20 mbar < P < 100 Mbar and GJ 1214bof water.
the radiat
class III m
Figure 4(aThe water
passes 1×
values fou
weakly on
For clathe planecase of an
maximum
requiring
We find a
400 bar aup to 7%colder precool. For

系外惑星への応用

perspective is further supported by the slow
projected rotational velocity of HR 8799 [~40km sec−1S@(17)]; this is well below average foraDcb"
late-A and early-F type stars (30). If we assume
that it has a semimajor axis of 68 AU, a circular

巨大惑星の直接撮像
HR8799Picture from Keck Obs. / Figure from Marois+ (2008, Science)

(40 m
H
comp
nearsubst
perat
dwar
stars)
L dw
cool
(Fig.
brow
solut
are colutionyoun
nions
fainte
mem

Fig.
el at
locatepress
sured

aDcb"S@Hot)Start)or)Cold)Start?
546

MARLEY ET AL. Fig. 5.—Luminosity evolution of various

Luminosity (Sun=1)

Hot start model

solid and dotted lines are the standard baselin
Other line types are for 10 and 0.10 times theṀLim , and a case with higher nebular gas teHot)Start)➡)Disk)Instability)

for a 4MJ planet with a variety of inCold)Start)(expressed in units of kB /baryon) b➡)Core)Accre&on
more than spans the plausible initial

Cold start modelFig. 4.—Model radius, R, effective temperature, TeA , and luminosity, L, ofyoung Jupiters of various masses. Line types as in Fig. 2. Unlike Fig. 2, in this figFigure
Marleyet al. (2007, evolution
ApJ)
ure
time tfrom¼ 0 forthe core-accretionis chosen to be the last model of thecore-accretion calculation. There is thus an offset of 2.5–3 Myr, depending on mass,

we found that !HK / e!2:8S . Thus, stimate of S produce disproportionatel
ing rate. Large values of S yield fas
cooling rates led to the conventiona
forget their initial conditions. But s
implementation of the core-accretio
slower early cooling times and pla
For this reason, as we noted in x 2
fidence in the comparison between in
Fig. 5.—Luminosity evolution of various 2MJ cases discussed
for core-accreted planets of differensolid and dotted lines are the standard baseline core-accretion andOtherfromline types
are for other10 and 0.10
times the standard
limiting
each
relatively
littleinmain
ṀLim , and a case with higher nebular gas temperature, Tneb .
cretion shock and the mass accreti

?34C
q;3B5,

aDcb"S@

ホットジュピター：異常膨張
理論と観測の比較

惑星半径 [木星=1]

BURROWS ET AL.

Vol. 661

K='04)7Mbmd
!Y>$5Pk&J

Burrows+((2007)

年齢 [Gyr]

Figure from Burrows+ (2007, ApJ)

aDcb"

ホットジュピターの重元素
Miller & Fortney

Heavy'element'mass'in'planet''`bwNjrw
[Earth'mass]

gust 1

flux. Planetsd for a 1 MJ
ted; Fortney
e is not wellt fluxes. We
n the largest! 1000 K.

S@

Miller'&'Fortney'(2011)

 Hc`bwymass for
Figure 2. Stellar metallicity
and inferred planet heavy-element
exoplanets within our incident flux cut. The required heavy elements are from the“Average Case” in Table 1. (See the text.) Planets are numbered corresponding
to the entries in Table 1. The rarity of gas giants around metal-poor stars iswell established (Fischer & Valenti 2005). Using a least-squares fit, we find theStellar'metallicity'¦lt§¢¯§Cx|­AE

形成過程への示唆

[FR\"

Ol

木星型惑星のガス捕獲過程
80
60
40
20
0
0

NJ

岩石＋氷

[qhp:gÙá"¿ #100

ċêN¨

`Y

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Figure from Ikoma et al. (2000)*6352水素＋ヘリウムin250/
.('qL_a
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bunmilar
es of
Q=
re in
bles,
g the
>3
core

from
discs
their
rains
et al.
enko
eless
sents
grain
The
n icy
d like
rains

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巨大惑星の集積過程の現代的描像»­§· 
!&#©+·@Yv?DF¥¸ !
Envelope pollution of gas giants by icy planetesimals+·?DFYv¹µ+!"!3of gas contained inside the outer edge of the envelope, which isdefined by the smaller of the Bondi radius (RB ) and the Hill radius(RHill ):
!
"1/3
Mp
GMp
RB = 2 , RHill = ap
,
(11)
cs
3(Mp + M∗ )where cs is the sound speed, ap is the semimajor axis of the protoplanet, and M ∗ is the mass of the central star. In this paper, we
use ap = 5.2 au, M∗ = 1 M" , Tdisc = 150 K and ρ disc = 5.0 ×
10−11 g cm−3 , unless otherwise noted.
We assume that the energy release by planetesimals occurs in anarrow region on the top of the core (i.e., " acc = 0). This assumption seems to be incompatible with the situation that planetesimals
evaporate and deposit their kinetic energy before reaching the core.
However, such a simplification affects the results little, because theenergy deposition of planetesimals occurs mostly in the deep, convective envelope, the structure of which is insensitive to the locationof energy deposition inside it. On the other hand, we ignore in thisstudy the effect of the sinking of dissolved materials of icy planetesimals.
potential
energythe mass
sinking
Figure2. TheGravitational
critical core mass
(M crit) as a released
function byof thefracmaterials inmakes
a contribution
to envelope,the slowingoftionofofablated
heavy elements
the lower
layer of theZ h .down
The solid,gas accretion
ondot–dashed
to a protogas
giantcorrespondas pointed tooutthebyresults
Pollackforet Tal.
dashed,dotted andcurvesh =Whetherthe&energy
releasedby
thedouble
sinkingdot–dashedof ablated mate300,(1996).
500,from
1000
and
2000
K,
respectively.
The
curve isFiguresHori
Ikoma(2011,MNRAS)
effectively
in envelopes.
a wide region
on thethe calculations,
top of the core
the rials
resultoccursof wholly
polluted
In allwewhereassumeFigure 1. Schematic picture of the envelope polluted by icy planetesimals.
The envelope has a two-layer structure: the non-polluted (Z A ) and the polluted (Z h ) layers, where Z A and Z h are the mass fractions of heavy elements
for the disc gas and the mixture of the disc gas and icy planetesimals, respectively. The boundary between the upper and the lower layers is defined by
the homopause temperature (T h ). (A colour version of this figure is available
in the electronic edition of MNRAS.)x|­ºµ>¬vC©Ah:8@G27−1

in such a region, so that the upper envelope can also be enriched[FR\"

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100`YM[qhp:gP¤v

20
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Figures from Ikoma+ (2000, ApJ)) & Shiraishi+ (2008, ApJ)

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îÄË"®ö äĆ#]mo\gp:fā

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⬅ 高気圧に落下³û
Figure from Owen et al. (1999)

v,/#c" 8fTy

AA49CH03-Williams

ARI

14 July 2011

19:21

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n 06/26/12. For personal use only.

Accretion

温度

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b

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Evaporation
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~20K

~30K

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円盤の光蒸発d

EUV

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重元素
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[FR\"

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衛星の氷の形成温度

t§

"-)$
MUWL§(+'/12%#(+/12%#[FR\"S@

ホットジュピター大気の重元素_G[-*-L}
Owen+ (1999)

A;=8D?:&-G[k9@6=E

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2-/*31,

5G

8<9%n5G8<]#%ViTQ

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H2+H2O

Hubble Space Telescope
Swain, Vasisht, & Tinetti (2008, Nature)

:21

AR

AR233-EA33-17.tex

XMLPublishSM (2004/02/24)

P1: JRX

重力モーメントの限界
NJ

重力メーメンとの「感度」

GUILLOT]·^bÀ

1

0

Md`UC&BF=R #
]f|«
]·s­
~200GPa~6000K

0

0.2

0.4

0.6

0.8

中心からの距離/木星半径1Figure 4 Contributionof thelevel radii to the gravitational moments of Jupiter. J0
Fig: Guillot (2005,
AREPS)
is equivalent to the planet’s mass. The small discontinuities are caused by the following transitions, from left to right: core/envelope, helium rich/helium poor (metal$ the median radius for each moment.
<'
lic/molecular). Diamonds indicate

NJ KYSX-R¤c

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Table 1. Coupling between the masks, with value larger than 20%.
!=0
m=0
!=1
m=0
!=1
m=1
!=2
m=1

!=1
m = −198.0%!=2m = −197.0%!=2m = −297.0%!=3m = −2–96.4%!=2m=0–66.7%!=3m=0–72.1%!=3m=1–45.2%!=4m=1–56.6%!=2m=2–79.5%!=3m=2–77.0%!=3m=3–79.8%!=4m=3–78.2%!=3.(+/m = −1!=3m = −3–40.1%!=4m = −3–37.8%!=4m = −445.4%!=5m = −4
43.7%

Table 2. Frequencies and amplitudes of the peaks detected
H0 statistical test with 1% significance level.
ν
µHz
792
854
915
970
1011
1066
1094
1162
1245
1341
1410

Velocity
cm s−1
44.0
46.7
34.1
48.7
51.4
45.7
42.4
54.1
53.8
51.5
40.7

Error
cm s−1–6.2/+3.9–6.6/+4.2–4.8/+3.0–6.9/+4.4–7.2/+4.6–6.4/+4.1–6.0/+3.8–7.6/+4.8–7.6/+4.8–7.3/+4.6–5.7/+3.6「木震」波による内部探査–33.8%!=4m = −1–40.7%!=4m = −223.7%!=5m = −231.8%

木星表面の自由振動モード解析

ν
µHz
1478
1533
1615
1753
1939
2110
2535
2714
2837
2947
3071

Velocity
cm s−1
46.4
37.3
40.9
33.0
32.0
30.1
30.3
30.6
36.2
41.1
30.7

Erro
cm s−
–6.5/+–5.3/+–5.8/+–4.6/+–4.4/+–4.2/+–4.3/+–4.3/+–5.1/+–5.8/+–4.3/+

0Degree !

1
2
3
4
5
−5

−4

−3

−2

−1

0

1

2

3

4

5

Azimuthal order m
Gaulme, Schmider, Gay+ (2011, A&A)
Fig. 1. Representation of the projected spherical harmonics, as a function of degree ! and azimuthal order m, until degree ! = 5. The
masks used to filter the velocity maps are limited to 75% of the
Jovian diameter.

The fact that we observe a half harmonic in time rathe
only integer harmonics can be due either to a combination
window observing function with the modulation of nearby
lation modes or to a stochastic excitation of the modes. W
detect the presence of a peak at half the Jovian rotation
as would be expected from the rotational splitting of l =imuthal modes. The échelle diagram associated with thisspacing frequency ∆ν0 (Fig. 5) clearly shows two max
the ∼1000−1600 µHz range that are separated by half
155 µHz folding frequency. Furthermore, two secondary
ima of smaller amplitude mirror them in the 2500−300
domain.
To assess the significance of the observed signal, w
apply a null hypothesis (H0) statistical test to the peaks
fied in the power spectrum. We retain only peaks with a
icance level of 1% and remove all neighboring aliases
by the Earth’s rotational frequency (±11.6 µHz). Thisin the identification of 22 distinct local maxima betweeand 3100 µHz. Both amplitude and frequencies were mefrom the power spectrum rebinned over 11 points, to smoo¤cB}u6¥jHGm2F

series. The data set constitutes 27 946 measurements acquired
between April 2 at 23:48:14 (UT) and April 12 at 06:30:17 (UT),まとめ( ¦w/1¬a,¬[ 0²yjTNV@
k?B<

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