A bright hot spot on the stellar surface hidden during thefor an atmosphere of a planet occulting only 1.5% of the star.

theplanetary
magnetopause,
soexcluded.
that energetic
atoms
can thebe small
producedchargeexchangetransit is also
Such a hotneutral
spot would
have (ENAs)
to Althoughdistancein(8.5stellar radii)
between the planet
11
collisions
wind protons
theextended
contributebetween
about 15%stellarof the Lyman
a flux overand
1.5%of thestellar upper
and the neutral
star resultsatmospherein an extended Roche lobe with a limit at about

系外惑星の大気散逸と惑星組成・分布への影響

surface occulted by the planet, in contradiction with Lyman a 2.7 planetary radii (that is, 3.6 Jupiter radii), the filling up of thisinhomogeneities observed on the Sun10. Furthermore, this spot lobe gives a maximum absorption of about 10% during thewould have to be perfectly aligned with the planet throughout the planetary transit. Because a more important absorption is detected,
2010;
al. 2011a).
Fordirection,
illustrating
windwitha corresponds
atoms mustcoverinteraction
a larger area: a dropof 15%transit,Lammer
at the sameet
latitudeas the Earth’s
and withexpecteda hydrogenstellar
an occultation by
an objectof 4.3 Jupiterto
radii.
is clearly
peculiar narrow single-peaked
profile confined overthe Earth-size
In spectral to exoplanet,hydrogen-richupper atmosphere
of an
which
is exposed
a 5This
6Rochelimit as theoretically
predicted
region. It seems unlikelythat a stellar spot could satisfy allthese beyond the. Thus some
共同研究者：中本泰史(東工大理工),Lisa
Kaltenegger(MPIA,CfA)
times
higher EUV flux compared to the modern hydrogen
Sun, weatomsapplied,
Ekenbäck
et al. The spectral
conditions.
should as
escapefrom the planet.
absorption width shows independently that the atoms have large
velocities relative to the planet. Thus hydrogen atoms must be
Lyman-α transit of HD209458b (Vidal-Madjar et al., 2003)
escaping the planetary atmosphere.
We have built a particle simulation in which we assumed thathydrogen atoms are sensitive to the stellar radiation pressure

黒川 宏之 (名大理)hydrogen atoms

Lammer et al. (2012)のイメージ図

中心星の近傍系外惑星から大規模な大気散逸- メカニズムは？
- 惑星組成への影響は？
Figure 2 The HD209458 Lyman a profile observed with the G140M grating. The

inhomogeneities observed on the Sun10. Furthermore, this spot
would have to be perfectly aligned with the planet throughout thetransit, at the same latitude as the Earth’s direction, and with apeculiar narrow single-peaked profile confined over the In spectral
region. It seems unlikely that a stellar spot could satisfy all theseconditions.

lobe gives a maximum absorption of about 10% during theplanetary transit. Because a more important absorption is detected,hydrogen atoms must cover a larger area: a drop of 15% corresponds
to an occultation by an object of 4.3 Jupiter radii. This is clearly
beyond the Roche limit as theoretically predicted6. Thus somehydrogen atoms should escape from the planet. The spectral
absorption width shows independently that the atoms have large
velocities relative to the planet. Thus hydrogen atoms must be
Lyman-α transit of HD209458b (Vidal-Madjar et al., 2003)
escaping the planetary atmosphere.
We have built a particle simulation in which we assumed thathydrogenatoms are sensitive to the=stellar
radiation pressure
Lyman-α吸収の深さ15%4.3 木星半径

大気散逸の観測(cf. 可視光吸収 1.5%)→ヒル半径 3.6 木星半径を超えて水素が流出(Vidal-Madjar et al., 2003)

HD189733b (Lecavelier et al., 2010) ,55 Cnc b (Ehrenreich et al., 2012) で同様の検出→ 系外惑星の大気散逸は普遍的
C, O輝線でも~10%の吸収(Vidal-Madjar et al., 2004)→ 大規模な流体的散逸

Figure 2 The HD209458 Lyman a profile observed with the G140M grating. The
geocoronal emission has been subtracted; the propagated errors are consequently larger
in the central part of the profile, particularly in the Geo domain (see text). Dl represents
the spectral resolution. a, The thin line shows the average of the three observations
performed before the transits (exposures A1, B1 and C1); the thick line shows the average

Figure 3 Relative flux of Lyman a as a function of the HD209458’s system phase.
The averaged ratio of the flux is measured in the In (1,215.15–1,215.50 Å and 1,215.80–1,216.10 Å) and the Out (1,214.40–1,215.15 Å and 1,216.10–1,216.80 Å) domains inindividual exposures of the three observed transits of HD209458b. The central time of

A bright hot spot on the stellar surface hidden during the for an atmosphere of a planet occulting only 1.5% of the star.
planetary transit is also excluded. Such a hot spot would have to Although the small distance (8.5 stellar radii) between the planet
contribute about 15% of the Lyman a flux over 1.5% of the stellar and the star results in an extended Roche lobe11 with a limit at about
surface occulted by the planet, in contradiction with Lyman a 2.7 planetary radii (that is, 3.6 Jupiter radii), the filling up of thisinhomogeneities observed on the Sun10. Furthermore, this spot lobe gives a maximum absorption of about 10% during thewould have to be perfectly aligned with the planet throughout the planetary transit. Because a more important absorption is detected,
must covera larger model
area: a drop of 15% corresponds
transit, at the same latitude as the Earth’s direction,V.andwith &a A. hydrogen
Bourrier
Lecavelieratoms
des Etangs:
Evaporation
to an occultation(+by恒星風電荷交換)
an object of 4.3 Jupiter radii. This is clearly
peculiar narrow single-peaked
profile confined over the In spectral
EUV加熱による大気散逸+ 輻射圧加速region. It seems unlikely that a stellar spot could satisfy all these beyond the Roche limit as theoretically predicted6. Thus someet al.,2010;shouldBourrier& Lecavelier
Etangs,2013)
conditions. (Vidal-Madjar et al., 2003; Holmström et al., 2008; Ekenbäckhydrogenatoms
escapefrom thedes
planet.
The
spectralabsorption width shows independently that the atoms have large
velocities relative to the planet. Thus hydrogen atoms must be
Lyman-α transit of HD209458b (Vidal-Madjar et al., 2003)
escaping the planetary atmosphere.
We have built a particle simulation in which we assumed thathydrogen atoms are sensitive to the stellar radiation pressure

大気散逸メカニズム

No self−shieldingSelf−shielding

100 km s-1 , 青方偏移した吸収(cf. 熱速度 10 km s-1 at 104 K)

Bourrier & Lecavelier des Etangs (2013)より

109-11 g s-1 の大気散逸 (EUV駆動？)+ 輻射圧, 電荷交換による加速
Figure 2 The HD209458 Lyman a profile observed with the G140M grating. Theが観測と整合的

EUV加熱による熱的大気散逸
EUV加熱で10 9-11 g s-1の大気散逸率は実現可能(Lammer et al., 2003;Yelle, 2004,2006; Tian et al., 2005; García Muñoz, 2007, Murray-Clay et al., 2009; Guo 2011, 2013)

MURRAY-CLAY, CHIANG,&MURRAY
上層大気のエネルギー収支(Yelle, 2004)
大気散逸構造 (Murray-Clay et al.,1742009)
R.V. Yelle / Icarus 170 (2004) 167–179
log ρ (g/cm3)

8n

1.0

32
sonic point

1f+ = n+/nv (10 km/s)

10EUV =
n+6n0
adiabatic cooling(+ H3+ radiation)

0

τ=143
1

0.5
0.0

1Fig. 4. Heating rates and heating efficiencies in the reference model. The solid line represents the net heating rate in the atmosphe
0cooling rates by the processes indicated.
1恒星EUVが大気を加熱し、quence, most stellar EUV energy
absorbed by H escapes the2atmosphere and does not contribute to local heating. This+differs from recombination ofエネルギー律速の流体的散逸が起こる
H+
32 or H3 lower in the ther4 which returns chemical energy to the atmospheremosphere,
12
3
4
through the kinetic energy of the reactant products.
r/Rp

log τlog T (K)log n (cm ).

M = 3.3 x 1010 g/s

2r/Rp

3

Solution of the momentum equation reveals that the at-ure 1. Standard planetary wind model, which uses parameters inspired by大気散逸が惑星組成・分布に与える影響
EUVが大気散逸を引き起こす場合、恒星は初期にEUV光度が1-2桁大きいため、惑星組成に影響するほどの大気散逸が起こる(Valencia et al., 2010; Lopez et al., 2012; 黒川 & Kaltenegger, 2013; Owen & Wu, 2013; Lopez & Fortney, 2013; 黒川 & 中本 投稿中 など)

H/He大気の散逸を考慮したsuper Earthの惑星半径と

al, 775:105 (12pp), 2013 October 1

Kepler惑星候補天体の比較 (Owen & Wu, 2013)
Owen & Wu
98⊕

Radius [R ]765432101000
500
Equilibrium Temperature [K]Figure 5. Upper envelope of planet sizes as a function of equilibrium temperature. The open circles show the KOIs that are around solar-type stars(T∗ = 5200–6200 K) and are in multiple transiting systems. The black curves
are the theoretical final radii for planet models with initial masses of 20 M⊕ and10 M⊕ (dashed line), 12.5 M⊕ (solid line), and 15 M⊕ (dot-dashed line) rocky
cores. The dotted line corresponds to ∼30 M⊕ planets with 12.5 M⊕ cores. All(生駒 & 堀, 2012)
models here have an initial cooling time of 107 yr. The thin line shows the50% completeness limit calculated by Petigura et al. (2013), and extrapolated
to larger(Mordasinietandal.,smaller2012)separations (solid line and dashed line, respectively).
(A color version of this figure is available in the online journal.)

しかし、惑星組成・分布は形成過程とその後の大気散逸の両方の影響を受けている- Super EarthのH/He大気量は円盤温度、円盤散逸時間に依存- 固体質量に依存

どう区別するか？

恒星スペクトル型の違いを考慮した大気散逸進化
XUV光度の時間進化

XUV 光度 [erg s -1]

1031

F型星
G型星

1030

- 大気散逸に寄与する恒星XUV(X-ray +EUV)光度はK型星
1029

恒星スペクトル型によって数桁異なるM型星

恒星スペクトル型への依存性を調べることで、
1028

形成過程と大気散逸進化過程をJackson et al. (2012)に基づくXUV進化モデル

1027
107

108

時間 [年]

109

分離して議論できるはず
1010

研究目的
大気散逸を考慮した惑星組成の時間進化計算を恒星スペクトル型ごとに行い、観測と比較
惑星組成に対する形成過程と大気散逸の影響を分離して議論する (黒川, Kaltenegger, & 中本, 投稿準備中)

Super Earthの組成と分布Super Earthの質量-半径の観測と様々な組成に対する理論計算の比較
8データ点：観測

惑星半径 [地球半径]

7K18d実線：理論

HATP26b6

鉄, 岩石, 水(黒崎さん提供),5

水素 1, 10, 20, 30 %
K36c

3K11d

K11c

K11b

K18b
K36b
K10b

105K30b55Cnce
HD97658b

G1214b

K11f

20G3470b

K11e

4C7b

K18c

K20c

K20b

1015

惑星質量 [地球質量]

2025

Super Earthの質量・半径から組成を推定し、軌道半径分布を大気散逸計算の結果と比較

モデル構造計算
RXUV(p=1nbar)

進化計算
熱進化 + 大気散逸 (エネルギー律速)

放射平衡

3dMp
⌘⇡FXUV RXUV=dt
GMp Ktide (e.g., Lopez et al., 2012)

対流Rplanet

XUV光度の時間進化
Jackson et al. (2012)に基づくXUV進化モデル
1031

静水圧平衡
放射平衡 (灰色近似) or 対流 (断熱温度勾配)
状態方程式
水素大気 - Saumon et al. (1995)
固体コア - Wagner et al. (2011)
大気不透明度
水素大気 - Freedman et al. (2008)

XUV 光度 [erg s -1]

質量保存

F型星
G型星

1030

K型星
1029

M型星

1028
1027
107

108

時間 [年]

1091010Super Earthの進化計算の例
固体質量10MEarth, 大気質量10MEarthの質量進化(左)と半径進化(右)250.06 AU 0.08 AU0.1 AU 0.12 AU0.14 AU15

固体質量50107105

円盤散逸1060.06 AU 0.08 AU
0.1 AU 0.12 AU
0.14 AU

15Radius [RE ]Mass [ME ]201020固体半径108Age [year]

1091010

0106

107

108

Age [year]

軌道半径が大きいほど水素大気保持可能→ 受け取るXUV放射量が小さいため水素大気を保持できる閾値となる軌道半径が存在
初期~108年に大部分の散逸が終わる→ 中心星XUV光度のsaturation phase ~108年 などに起因観測される典型的な年齢~109-10年においては年齢に依存せず議論可能

1091010水素大気を保持できる/できない条件 (G型星)
100億年間で水素大気を失う軌道半径

固体質量 [地球質量]

2010

大気量 =
固体質量×1
大気量 =固体質量×0.1
大気量 =固体質量×0.01

水素大気なし10.01

水素大気あり0.1
軌道半径 [AU]・固体質量への依存性大きい
水素大気を失う軌道半径 固体質量-1・初期大気質量への依存性小さい
大気量が多いと惑星半径大きく大気散逸率大きい

1

中心星スペクトル型への依存性
100億年間で水素大気を失う軌道半径

固体質量 [地球質量]

2010

K型星

M型星

G型星

F型星

中心星軽い

中心星重い

初期大気量 =
固体質量 の場合
10.010.1
軌道半径 [AU]・軽い中心星ほどsuper Earthは水素大気保持
主にXUV光度の違いに起因
・固体質量への依存性はスペクトル型によらず同じ
水素大気を失う軌道半径 固体質量-11観測との比較：G型星
大気散逸で水素大気を失う軌道半径とSuper Earthの組成との比較

惑星質量 [地球質量]

20

K20c

K18d

K18c

10

岩石
水 or 薄い水素大気
厚い水素大気
K30b

K36c
K11d

K11e

K36b

理論

K20b

観測？
K10b

K18b
K11c

K11b

10.010.1
軌道半径 [AU]K11f

1

観測の示す惑星質量依存性は理論の予測より小さい？
ただしKepler-11c,fを除けば整合的

観測との比較：K型星
大気散逸で水素大気を失う軌道半径とSuper Earthの組成との比較
HATP26b

惑星質量 [地球質量]

201055Cnce
C7b

10.01

岩石
水 or 薄い水素大気
厚い水素大気HD97658b0.1
軌道半径 [AU]1

観測数は少ないが理論と観測は整合的

観測との比較：M型星
大気散逸で水素大気を失う軌道半径とSuper Earthの組成との比較
岩石
水 or 薄い水素大気
厚い水素大気

惑星質量 [地球質量]

20
G3470b

10G1214b

10.010.1
軌道半径 [AU]1

観測数は少ないが理論と観測は整合的惑星質量 [地球質量]

20K20c

K18d

K18c

10

岩石
水 or 薄い水素大気
厚い水素大気
K30b

K36c
K11d
K20b

K36b
K10b

2010K11f

・中心星が軽いほど小さい軌道半径でも水素大気保持0.1
軌道半径 [AU]
HATP26b55Cnce
C7b

HD97658b

理論：・質量依存性大：軌道半径 質量-1K11c

10.01

惑星質量 [地球質量]

G型星

K18b

K11b

1

観測との比較：岩石
水 or 薄い水素大気
厚い水素大気理論の予測より質量依存性小さい？ (G型星)
散逸律速メカニズムの遷移を考慮するとK型星

質量依存性は大きくはなるが小さくするのは難しい

ただしKepler-11c,fを除けばすべてのスペクトル型について整合的

10.010.1
軌道半径 [AU]1

可能性1- 大気散逸計算は絶対値として過大評価であり、岩石
水 or 薄い水素大気
厚い水素大気20
惑星質量 [地球質量]K11e

まとめと議論現在の分布は形成過程を反映

G3470b10M型星
G1214b可能性2- Kepler-11は例外的にXUV活動度が小さく、現在の分布は大気散逸を反映(XUV光度は同じスペクトル型でも一桁程度の多様性あり)

10.010.1軌道半径 [AU]1

惑星形成論への示唆
閾値となる軌道半径の内側(=スノーライン内側)に氷super Earth存在→ migrationを経験
閾値となる軌道半径の外側でH/He大気量にばらつき→ 形成過程でばらつきが生じる？

Formation phase: migration + gas capture (diversity of mass)

Evolution phase: atmospheric mass-loss

snow line ~ 1 AU

evaporation line ~ 0.1 AU