第9回：惑星大気2

地球惑星圏物理学 

第9回：惑星大気2

1

担当：黒川 宏之

小レポート課題解答

2

地球惑星圏物理学

2019

年度 期末レポート

大問 1

太陽系内の惑星・衛星には大気を持つものと持たないものが存在する。

ここではその理由を考察する。

問 1.1

惑星が大気を保持できる条件式は

(1)

式で与えられる。

λ ≡ GM

_p

m

_g

R

_p

k

_B

T

_s

> γ

γ − 1



(1)

M

_p

, R

_p

, m

_g

, T

_s はそれぞれ惑星質量、惑星半径、大気分子の質量、地表面 温度である。

λ

は大気分子の重力ポテンシャルエネルギーと熱エネルギー の比であり、エスケープ・パラメータと呼ばれる。

γ

はポリトロープ関係 式の指数であるが、ここでは大気分子の比熱比と等しいとする。

水星・金星・地球・月・火星の

5

つの天体に対して、大気を持たない場 合の地表面温度

(

平衡温度

)T

_eq 及び、窒素分子

(N

₂

)

大気を持つための地 表面温度の上限値

T

_s,max を求めよ。各惑星の太陽からの距離、惑星質量、

惑星半径等は表

1

を参照すること。また、簡単化のため惑星のアルベドは

0

とし、平衡温度は

(2)

式で与えられるものとする。

T

_eq

= 280

! a

1 AU

"

_−1/2

K (2)

ここで

a

は軌道半径である。

問 1.1 解答

(1)

式より、

T

_s,max

= γ − 1 γ

GM

_p

m

_g

R

_p

k

_B

(3)

(2), (3)

式より、

T

_eq と

T

_s,max を求めると表

1

のようになる。

天体 軌道長半径

[AU]

質量

[10

²⁴

kg]

半径

[km] T

_eq

[K ] T

_s,max

[K]

水星

0.39 0.33 2400 448 8900

金星

0.72 4.9 6100 330 52000

地球

1 6.0 6400 280 60000

月

1 0.073 1700 280 2800

火星

1.5 0.64 3400 230 12000

表

1:

各天体の物理量。

問 1.2

1

問

1.1

の

T

_eq と

T

_s,max の大小関係と各天体の大気の有無を比較すること

で、

(1)

式が惑星大気の有無と対応しているか調べよ。対応していない場 合、その理由を考察せよ。

問 1.2 解答

(

例

)

金星・地球・火星は大気保持条件を満たしており、実際に大気を 纏っている。水星・月は大気保持条件を満たしているが、大気を纏ってい ない。大気のもととなる揮発性元素に乏しい材料物質から形成された、も しくは形成後に大気散逸によって大気を失った可能性がある。

大問 2

地球と金星は軌道半径や質量が同程度であり、兄弟惑星と形容されるこ ともある。しかし、地球と比較して金星ははるかに厚い大気を持ち、その 結果として地表面温度には大きな隔たりがある。ここでは地球と金星の大 気の違いについて考察する。

問 2.1

静水圧平衡の式は次式で与えられる。

dp

dz = − ρg

 

(4)

ここで、

p

は圧力、

z

は地表からの高さ、

ρ

は密度、

g

は重力加速度であ る。

(4)

式を積分することで、惑星の地表大気圧

p

_s 及び重力加速度

g

と大 気の柱密度

! ρ dz (

単位地表面積上に存在する大気の質量

)

の関係式を導 くことができる。このことを利用し、惑星の大気質量

M

_atm が、

M

_atm

= 4π R

_p²

p

_s

g (5)

と書き表されることを示せ。ここで、

R

_p は惑星の半径である。ただし、

大気圏の厚みは惑星半径に比べて十分に小さいことから、大気圏において 重力は一定とし、曲率は無視できるものとする。

問 2.1 解答

式

(4)

を地表面から無限遠まで積分することで、次式を得る。

p(z = ∞ ) − p(z = 0) = − g

"

_∞

0

ρdz. (6)

ここで、

p(z = ∞ ) = 0

_、

p(z = 0) = p

_s、

!

₀^∞

ρdz × 4πR

²_p

= M

_{atm より、}

M

_atm

= 4πR

²_p

p

_s

g . (7)

問 2.2

2

3

宇宙空間に流出する惑星大気

真空紫外線で撮像された地球 (100-200 nm)

• 地球を取り囲んで広がる水素が太陽光 (Lyman-α) を散乱

• 地球大気起源の水素が流出している

• 大気散逸は惑星大気と表層環境進化の要因

Rairden et al. (1986)

大気散逸過程の分類

4

熱的散逸 :

大気成分がその熱エネルギーによって散逸

• Jeans’ escape ( ジーンズ散逸 )

• Hydrodynamic escape ( 流体力学的散逸 )

非熱的散逸 :

個々の粒子が光化学反応や太陽風との相互作用など で加速

• 光化学的散逸 (e.g. 光解離 , 解離性再結合 )

• スパッタリング …etc 天体衝突剥ぎ取り

太陽放射・太陽風

小惑星・彗星衝突

熱的散逸

5

ジーンズ散逸

流体力学的散逸

Catling & Kasting (2017)

速度分布関数 ( マクスウェル分布 )

速さ [km s

^-1

]

確率密度

二乗平均速度 脱出速度

宇宙空間へ流出

熱的散逸

6

Exobase に存在する水素原子の運動速度 ,

1

2 mv 2 = 3

2 kT

m: 質量 1.67×10

^-27

kg v: 平均速度

k: ボルツマン定数 1.38×10

^-23

J K

^-1

T: Exobase の温度 1000 K

v ' 5 km s 1

一方、地球からの脱出速度は

v esc = 11.2 km s 1

現在の地球大気からの熱的散逸

= ジーンズ散逸

ジーンズ散逸

流体力学的散逸

Catling & Kasting (2017)

上層大気には 太陽 UV によって電離した hot (fast) H + イオンが存在

The polar wind ポーラーウインド : 磁極からのイオン流出

Charge exchange (H-H + ) 電荷交換 :

Hot H + イオンが中性原子と電荷交換

高速の中性原子となって流出

現在の地球における水素散逸への寄与は

60-90% 電荷交換 , 10-40% ジーンズ散逸 , and 10-15% polar wind

非熱的散逸

7

系外惑星の大気散逸

8

Image credit: NASA/CXC/M. Weiss

恒星の近傍 (< 0.1 AU)を公転する巨大ガス惑星の大規模な大気散逸  地球の 10 2-4  倍の極端紫外線(<120 nm)と恒星風に晒されている

visits 2 and 3, whereas it is missing in visit 1. By contrast, the flux remains stable over the whole red-shifted wing of the line (Fig. 2b).

The decrease of the red-wing flux seen

⁶

during the post-transit phases of visit 1 is not reproduced during visits 2 and 3. The mean post-transit red-shifted signal is compatible with no detection at the 3s level.

Our combined analysis of X-ray and ultraviolet data (see Methods) shows that stellar magnetic activity cannot explain the observed decrease at Lyman-a. We propose that the asymmetric absorption is caused by the passage of a huge hydrogen cloud, surrounding and trailing the planet (Fig. 3). The planetary atmosphere is an obvious source for this hydrogen. To produce this extinction signature, we estimate that an ellipsoidal, optically thick cloud of neutral hydrogen should have a projected extension in the plan of the sky of

,12 stellar

radii (R

w<

0.44R

_[

) along the orbital path of the planet and

,2.5Rw

in the cross direction, well beyond the planet Roche lobe radius (0.37R

w

).

Since GJ 436b grazes the stellar disk during transit, we surmise that a central transit would have totally eclipsed the star. This could happen in the case of other red dwarfs exhibiting central transits from planets similar to GJ 436b. Future ultraviolet observations of systems similar to GJ 436 could potentially reveal total Lyman-a eclipses.

The radial velocity interval of the absorption signal constrains the dynamics of the hydrogen atoms and the three-dimensional structure of the exospheric cloud. The whole velocity range is in excess of the

planet escape velocity (,26 km s

²¹

at the planet surface), consistent with gas escaping from the planet. The acceleration mechanism of hydrogen atoms escaping from highly irradiated hot Jupiters is debated: after escaping the planets with initial velocities dominated by the orbital velocity (,100 km s

²¹

for GJ 436b in the host star reference frame), atoms are submitted to the stellar radiation pressure, interact with the stellar wind and are eventually ionized by stellar extreme ultraviolet (EUV; 10–91.2 nm) radiation. For strong lines such as Lyman-a, radiation pressure can overcome the stellar gravity, repel- ling the escaping atoms towards the observer and producing a blue- shifted signature. In one hot Jupiter (HD 189733b), the absorption

Flux (×10–14 erg cm–2 s–1 )

2.0

1.5

1.0

0.5

0

Flux (×10–14 erg cm–2 s–1 ) 5

4

3

2

1

0

H ^I Lyα blue wing

H I Lyα red wing

–4 –2 0 2 4 29.5 30.5

Time from mid-transit (h)

a

b

Figure 2 | Lyman-atransit light curves of GJ 436b. a,b, Data are from visit 1 (circles), visit 2 (stars), visit 3 (squares) and visit 0 (triangles). All uncertainties are 1s. a, The Lyman-a (Lya) line is integrated over [2120,240] km s²¹ and shows mean absorption signals with respect to the out-of-transit flux of 17.6 6 5.2% (pre-transit), 56.2 6 3.6% (in-transit) and 47.2 6 4.1% (post- transit). b, The line is integrated over [130,1200] km s²¹ and shows no notable absorption signals: 0.763.6% (pre-transit), 1.763.5% (in-transit) and 8.0 63.1% (post-transit). With a depth of 0.69%, the optical transit (thin black lines in a and b) is barely seen at this scale between its contact points (dotted lines in a and b). A synthetic light curve (green) calculated from the three- dimensional numerical simulation²⁰ is overplotted on the data in a.

–10 –5 0 5

–5 0 5

log[Column density (cm –2)] 14.4

14.0

13.6

13.2

12.8

12.4

12.0 Distance (R )

Distance (R )

Figure 3 | Particle simulation showing the comet-like exospheric cloud transiting the star, as seen from Earth. GJ 436b is the small black dot represented at mid-transit at 0.8521R_w (ref. 26) from the centre of the star, which is represented by the largest black circle. The dotted circle around the planet represents its equivalent Roche radius. The colour of simulation particles denotes the logarithm of the column density of the cloud. The transit of this simulated cloud gives rise to absorption over the blue wing of the Lyman-aline as shown spectrally in Extended Data Fig. 2 and by the synthetic light curve in Fig. 2a.

0 2 4

–6 –4 –2

–8 –14 –12 –10

–12 –10 –8 –6 –4

Doppler velocity (km s –1) 20 0 –20 –40 –60 –80 –100 –120

Distance (R )

Distance (R )

Figure 4 | Polar view of three-dimensional simulation representing a slice of the comet-like cloud coplanar with the line of sight. Hydrogen atom velocity and direction in the rest frame of the star are represented by arrows.

Particles are colour-coded as a function of their projected velocities on the line of sight (the dashed vertical line). Inset, zoom out of this image to the full spatial extent of the exospheric cloud (in blue). The planet orbit is shown to scale with the green ellipse and the star is represented with the yellow circle.

4 6 0 | N A T U R E | V O L 5 2 2 | 2 5 J U N E 2 0 1 5

RESEARCH LETTER

G2015 Macmillan Publishers Limited. All rights reserved

visits 2 and 3, whereas it is missing in visit 1. By contrast, the flux remains stable over the whole red-shifted wing of the line (Fig. 2b).

The decrease of the red-wing flux seen⁶during the post-transit phases of visit 1 is not reproduced during visits 2 and 3. The mean post-transit red-shifted signal is compatible with no detection at the 3s level.

Our combined analysis of X-ray and ultraviolet data (see Methods) shows that stellar magnetic activity cannot explain the observed decrease at Lyman-a. We propose that the asymmetric absorption is caused by the passage of a huge hydrogen cloud, surrounding and trailing the planet (Fig. 3). The planetary atmosphere is an obvious source for this hydrogen. To produce this extinction signature, we estimate that an ellipsoidal, optically thick cloud of neutral hydrogen should have a projected extension in the plan of the sky of ,12 stellar radii (Rw<0.44R_[) along the orbital path of the planet and,2.5Rwin the cross direction, well beyond the planet Roche lobe radius (0.37Rw).

Since GJ 436b grazes the stellar disk during transit, we surmise that a central transit would have totally eclipsed the star. This could happen in the case of other red dwarfs exhibiting central transits from planets similar to GJ 436b. Future ultraviolet observations of systems similar to GJ 436 could potentially reveal total Lyman-a eclipses.

The radial velocity interval of the absorption signal constrains the dynamics of the hydrogen atoms and the three-dimensional structure of the exospheric cloud. The whole velocity range is in excess of the

planet escape velocity (,26 km s²¹ at the planet surface), consistent with gas escaping from the planet. The acceleration mechanism of hydrogen atoms escaping from highly irradiated hot Jupiters is debated: after escaping the planets with initial velocities dominated by the orbital velocity (,100 km s²¹ for GJ 436b in the host star reference frame), atoms are submitted to the stellar radiation pressure, interact with the stellar wind and are eventually ionized by stellar extreme ultraviolet (EUV; 10–91.2 nm) radiation. For strong lines such as Lyman-a, radiation pressure can overcome the stellar gravity, repel- ling the escaping atoms towards the observer and producing a blue- shifted signature. In one hot Jupiter (HD 189733b), the absorption

Flux (×10–14 erg cm–2 s–1 ) 2.0

1.5

1.0

0.5

0

Flux (×10–14 erg cm–2 s–1 ) 5

4

3

2

1

0

H I Lyα blue wing

H I Lyα red wing

–4 –2 0 2 4 29.5 30.5

Time from mid-transit (h)

a

b

Figure 2 | ^Lyman-atransit light curves of GJ 436b. a,b, Data are from visit 1 (circles), visit 2 (stars), visit 3 (squares) and visit 0 (triangles). All uncertainties are 1s. a, The Lyman-a (Lya) line is integrated over [2120,240] km s²¹ and shows mean absorption signals with respect to the out-of-transit flux of 17.6 6 5.2% (pre-transit), 56.2 6 3.6% (in-transit) and 47.2 6 4.1% (post- transit). b, The line is integrated over [130,1200] km s²¹ and shows no notable absorption signals: 0.763.6% (pre-transit), 1.763.5% (in-transit) and 8.0 63.1% (post-transit). With a depth of 0.69%, the optical transit (thin black lines in a and b) is barely seen at this scale between its contact points (dotted lines in a and b). A synthetic light curve (green) calculated from the three- dimensional numerical simulation²⁰ is overplotted on the data in a.

–10 –5 0 5

–5 0 5

log[Column density (cm –2)] 14.4

14.0

13.6

13.2

12.8

12.4

12.0 Distance (R )

Distance (R )

Figure 3 | Particle simulation showing the comet-like exospheric cloud transiting the star, as seen from Earth. GJ 436b is the small black dot represented at mid-transit at 0.8521Rw (ref. 26) from the centre of the star, which is represented by the largest black circle. The dotted circle around the planet represents its equivalent Roche radius. The colour of simulation particles denotes the logarithm of the column density of the cloud. The transit of this simulated cloud gives rise to absorption over the blue wing of the Lyman-aline as shown spectrally in Extended Data Fig. 2 and by the synthetic light curve in Fig. 2a.

0 2 4

–6 –4 –2

–8 –14 –12 –10

–12 –10 –8 –6 –4

Doppler velocity (km s –1) 20 0 –20 –40 –60 –80 –100 –120

Distance (R )

Distance (R )

Figure 4 | Polar view of three-dimensional simulation representing a slice of the comet-like cloud coplanar with the line of sight. Hydrogen atom velocity and direction in the rest frame of the star are represented by arrows.

Particles are colour-coded as a function of their projected velocities on the line of sight (the dashed vertical line). Inset, zoom out of this image to the full spatial extent of the exospheric cloud (in blue). The planet orbit is shown to scale with the green ellipse and the star is represented with the yellow circle.

4 6 0 | N A T U R E | V O L 5 2 2 | 2 5 J U N E 2 0 1 5

RESEARCH LETTER

G2015 Macmillan Publishers Limited. All rights reserved

可視光

紫外線

Ehrenreich et al. (2015)

UV transit of GJ 436b

太陽活動の時間進化

9

2 Page 6 of 72 H. Lammer et al.

Fig. 1 Expected rotation-based EUV enhancement factor normalized to that of today’s solar level (after Tu et al. 2015). The dotted line corresponds to the EUV activity evolution enhancement of slowly rotating weakly active young solar-like stars. The solid line corresponds to a young Sun rotating moderately, while the dashed line represents the evolution of a fast rotating EUV active young solar-like star. The shaded areas mark the different geological eons on Earth and Mars

et al. 1993). This convergence is attributed to the feedback between the magnetic dynamo and angular momentum loss in a magnetized wind. The wide dispersion of

P rot for young stars instead reflects the initial conditions for rotation starting after the protostellar disk phase (e.g. Gallet and Bouvier 2013).

An evolutionary decay law for high-energy radiation, therefore, needs to account for the dispersion of rotation periods. Observationally, a wide distribution of L X in young clusters was in fact known from early cluster surveys (e.g. Stauffer et al. 1994).

A proper analysis of the problem was laid out in the work by Johnstone et al. (2015a, 2015b) and Tu et al. (2015) in which a solar-wind model was adapted to stars at different activity levels and different magnetic fluxes, fitting distributions of P rot in time from various clusters. Translating rotation to high-energy radiation, Tu et al.

(2015) reported the finding illustrated in Fig. 1. This figure shows that, depending on whether a solar analog starts out as a slow or fast rotator after the disk phase, the X- ray and EUV evolutionary tracks first diverge (a slow rotator rapidly decays with time while that of a fast rotator does not) and then converge again after several hundred Myr when the rotation periods converge. The nearly constant X-ray and EUV luminosity for fast (but spinning-down) rotators is due to the saturation effect.

The distribution of high-energy radiation is broadest in the range of a few tens to a few hundreds of Myr, precisely the range of interest for protoatmospheric loss, the formation of a secondary atmosphere, a crust and a liquid water ocean on Earth, and the earliest steps toward the formation of life. A proper study of atmospheric evolution, therefore, needs to account for the uncertainty of early stellar high-energy evolution.

To the present day, we do not know the evolutionary track in high-energy radiation the Sun has taken.

123

極端紫外線光度(現在=1)

恒星の年齢 [100万年]

冥王代 太古代

原生代

顕生代

誕生から数億年間、太陽系の惑星も大規模な大気散逸を経験した？

Lammer et al. (2018)

コールドトラップ

10

Catling & Kasting (2017)

成層圏

対流圏 中間圏 熱圏

ppmv = ×10

^-6

( 体積 ) 百万分率

対流圏で凝結するため、上層大気での水蒸気混合比は数 ppmv

⇒ 水蒸気の解離と大気散逸を防ぐ

コールド 

トラップ

拡散律速フラックス

11

対流圏で上昇気流が降雨することで、現在の地球からの  水素散逸率は小さく抑えられている (コールドトラップ)

dif ,i ' b i f i

H a ' 2.5 ⇥ 10 17 f T (H) m 2 s 1

均質圏界面から外気圏への拡散フラックス (= 水素散逸フラックス)

H

_a

: scale height of atmosphere b

_i

: binary di↵usion coefficient of i f

_i

: volume mixing ratio of I f

_T

(H) : total hydrogen mixing ratio f

_T

(H) = f

_H

+ 2f

_H2

+ 2f

_H2O

+ 4f

_CH4

+ . . .

i

スケールハイト 相互拡散係数 体積混合率

水素の総体積混合率

地球型惑星の比較

12

軌道半径 0.7 AU 1 AU 1.5 AU

地表面気圧 90 bar 1 bar 0.006 bar 大気主成分 CO

2

N

2

, O

2

CO

2

地表平均気温 735 K 288 K 210 K 全球平均水深 30 mm 2700 m >20 m

水の主な形態 水蒸気 液体の水 極冠の氷

金星の水の散逸

13

恒星に近いほど、大気中の水蒸気量が上昇 

地球ではコールドトラップが水の散逸を抑制   金星では散逸

成層圏の水蒸気混合比 (破線)

太陽光フラックス[地球=1]

地表面温度 [K] (実線)

暴走温室状態 急速な 

水素散逸 成層圏 

H2O

H2Oの  臨界温度 

現在の地球

現在の  金星 地表面温度 

Catling & Kasting (2017)

火星の水の痕跡

LETTERS

NATURE GEOSCIENCEDOI: 10.1038/NGEO891

MOLA elevation (km)

¬2.5 ¬1.8

B

A

1 km

¬2.0

A B

¬2.2

¬2.4

Elevation (km)

¬2.60 3 6

Distance (km)

Apex

(Max) Front

(Mean)

Bottom (Min) A

B Apex

Front

Max

Min Bottom

9 N

Mean

Figure 1|Data and methodology used for the analysis of the martian deltaic deposits.Left: Context image of a sedimentary deposit in Nepenthes Mensae (No 14 of Supplementary Table S1). The dots indicate the location of the available MOLA-shot measurements. Right: The topographic profile AB shows the morphometry of the deposit (left panel for location). The bottom schematic diagram illustrates the morphometric indicators used for the extraction of the elevation values for each delta. The error bar defines the maximum water level excursion; the black square corresponds to the delta front (mean water highstand). See the Methods section for explanations.

complete closure within and along the margins of the northern lowlands (Fig. 2 and Supplementary Fig. S2), delineating the boundary of the basin within which the deposits formed. The standard deviation (177 m) ofSis remarkably small if spread across the entire length of the global contour, comparable to the total variation of the terrestrial geoid (⇠200 m), and significantly smaller (up to one order of magnitude) than the dispersed values previously obtained for the elevations of Contact 1 (Arabia shoreline, Fig. 2c) and Contact 2 (Deuteronilus shoreline)³. Therefore, the deposits topographically connected to the site occupied by the putative ocean define the closest approximation of an equipotential surface as would be expected if they formed in a single large body of standing water encompassing the northern hemisphere of Mars.

Moreover, the S level is consistent with large portions of the

‘Arabia shoreline’ previously identified from geomorphologic and topographic analyses^1,4 (Fig. 2c) and is also close to its average value ( 2,499 m, compare the trendline of this contact with S in Fig. 2c). In particular, S is consistent with the previous observational evidence at (1) Terra Sirenum, (2) in the northern part of Tempe Terra, (3) along the circum-Chryse Planitia region, (4) within northern Arabia Terra and the fretted terrain regions of Deuteronilus Mensae and finally (5) across the crustal dichotomy along the Nepenthes and Aeolis Mensae regions and the surroundings of Gale crater (Fig. 2).

Notably, a further twelve deltas that formed in closed basins (green triangles in Fig. 2) fall within the error bars of the S level.

However, to include these deposits in the same group of the S level, thus totalling ⇠55% of the present global database, it must be assumed that a water table should have intersected the surface at this base level all over the planet. Indeed, the S level ( 2,540±177 m) is virtually the same as the 2,550 m elevation suggested by theoretical calculations for the global distribution of water during the Noachian⁴. Moreover, the latter value was derived from thermophysical properties of Mars with the assumption that water was saturating the crust and ponding in hydrostatic equilibrium on the surface of the planet⁴. Therefore, the analysis

of 29 sedimentary deposits (⇠55% of total deltas) supports this thermal-hydraulic reconstruction, implying that a vast ocean and large seas were present in the northern hemisphere and in Argyre and Hellas basins, respectively. Several groundwater-fed palaeolakes would have contemporarily emerged within a region of a few hundreds of kilometres wide upslope from the S ocean boundary and the crustal dichotomy and around the rim of Argyre and Hellas within craters deep enough to reach the S level (Fig. 2a and Supplementary Fig. S2). The palaeolakes would have been almost entirely concentrated in the topographically gradational zone of Arabia Terra, a province where sedimentary and morphological studies support the occurrence of palaeolakes^19,20 and indicate that putative spring deposits exist within craters²¹. Furthermore, an anomalous concentration of craters with extensive exposures of eroded layered sedimentary deposits^19–22 and other distinguishable spectral and elemental properties (including also an elevated hydrogen content) have been reported for Arabia Terra and interpreted to be the results of a past volatile-rich history^19–22. Similar layered sequences and other evidence suggestive of past lacustrine activity have also been suggested for Hellas and Argyre^4,22,23and increasingly reported during the past years also for craters along the rim of the main Hellas basin^24,25, thus making the case for the occurrence of a Noachian basin-wide sea within Hellas²³ and a series of surrounding palaeolakes within a range of elevations compatible with theS level^24,25. Finally, although the analysis of deltas cannot uniquely confirm the occurrence of large seas in Hellas and Argyre, if there was an ocean on the northern plains as a component of a martian global hydrosphere, water must have ponded also in these two basins⁴.

The reconstructed equipotential surface is also generally con- sistent with the distribution and terminations of martian valley networks⁸ excluding the region between 30 W and 60 E, that is, the topographically gradational zone of Arabia Terra (Fig. 2).

Arabia Terra is characterized by smooth elevation variations⁵ and it is possible that the S surface may mark a different level of the same ocean previously mapped here at slightly higher elevations

460 NATURE GEOSCIENCE| VOL 3|JULY 2010| www.nature.com/naturegeoscience

2014/11/12 Google

https:// .google.co.jp/maps/@34.6466597,136.5251989,7524m/data=!3m1!1e3 1/1

2014 Google, Da a SIO, NOAA, U.S. Na , NGA, GEBCO, Te aMe ic , 2014 Google, ZENRIN 500 m :

火星 地球

Di Achille & Hynek (2010) Nature

cemented and made up of rounded to subangular rock fragments larger than 2 mm in diameter in a finer-grained matrix of sand or silt).

Additional evidence for a fluvial interpreta- tion is the stratification at Hottah. Alternating pebble-rich and sand layers (Fig. 3C) indicate fluctuations within sediment transport that result in size sorting of the deposits. In bedload trans- port, the presence of sand mixed with fine peb- bles leads to a sorting instability within flows that produces shallow migrating bedforms (bedload sheets), resulting in fine-scale vertical variations in grain sorting (23), as observed at Hottah.

Alternative sediment transport mechanisms to water flows are inconsistent with the observed rock characteristics. For example, the well-developed rounding of the pebbles together with clast fabric, specifically the grain-to-grain contact and local imbrication, make mass transport as a debris flow unlikely. Likewise, pebble clusters and the rela- tively wide size range of pebbles within the de- posit are inconsistent with transport and deposition by wind. The largest grains mobilized by wind will move via creep driven by impacts from abun- dant saltating finer grains. On Mars, 1- to 2-mm grains are driven by creep, leading to formation of megaripples observed at both Mars Explora- tion Rover landing sites [e.g., (24)]. The result of this process is a relatively thin surface layer of uniformly sized clasts due to size-dependent down- wind (creep) migration rates, which differs in both geometry and the coarse grain size range (2 to 40 mm) within the martian conglomerates described here. The higher density of liquid fluids relative to air results in higher bed shear stress (and a buoyancy force on the particle), which can mobilize coarse sediment.

A number of factors influence the develop- ment of rounded clast perimeters in fluvial trans- port, including the original clast size, shape, and lithology, as well as the grain size of the bed material (21, 25). Sand commonly acts as an abrasive agent when transported with pebbles in fluvial systems, causing the coarser particles to round more rapidly (21, 22). The presence of coarse sand and rounded pebbles in the martian rocks is consistent with a highly abrasive flow.

For clasts of the same size, lithology is the major factor affecting the rate of downstream rounding [e.g., (25–27)]. On the basis of published data for pebbles in natural streams and fluvial abrasion experiments for a range of compositions [e.g., (25–27)], and assuming an initial angular pebble, we estimate a minimum transport distance of a few kilometers to produce a rounded pebble surface.

On Mars, the elastic collisions within the flow may have had lower energy due to the reduced gravity, resulting in lower abrasion rates and lon- ger transport distances to achieve similarly rounded pebbles. Overall, the rounded pebbles of apparently diverse lithology within the martian conglomerates are strong evidence for sustained fluvial transport.

The grain size distribution can be used to es- timate the critical shear stress for sediment mo- bility, and in turn the flow depth and mean velocity

assuming a water surface slope between 0.1 and 1% (17, 28–30) (tables S3 to S5). This range of slope values corresponds to the nearby alluvial fan slope (1%) and an approximate lower value (0.1%) for gravel-bedded streams [e.g., (31,32)].

For the clast size distributions observed in the three conglomerates, the minimal flow depth (suffi- cient to initiate motion) is 0.03 to 0.9 m and the corresponding average flow velocity is estimated to be 0.20 to 0.75 m/s. In all cases, the estimated Fig. 2. Comparison of pebbles at Link and a terrestrial analog site.(A) Link was imaged with the 100-mm Mastcam on sol 27 (17). (B) Rounded clasts of similar size and shape are observed in comparably sized distal alluvial fan deposits on Earth, such as this example from the Atacama Desert, Chile.

Fig. 3. Examples of sedimentary texture and fabric in the Hottah outcrop.(A) The Hottah outcrop has fractured and gently tilted (~30°) blocks, as seen in this mosaic of Mastcam images taken on sol 39 (17). (B) The perimeter of a well-rounded pebble protruding from the outcrop (upper black arrow, long axis ~3 cm) is smooth. White arrow points to parallel stratification. (C) In places, there are alternating protruding, pebble-rich layers (black arrows) and recessive layers. An example of a clast-supported pebble cluster is marked by the yellow circle. (D) Example of imbricated clasts.

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火星

Williams et al. (2013) Science

地球

数多くの火星探査 

- Mars Global Surveyor,  Curiosity, …   

水に関連した地形の発見 

- 渓谷, 三角州 

- 角の取れた小石, 堆積岩  現在の火星は寒冷 

平均気温 >0℃とするには 数気圧のCO 2 大気が必要

14

火星の三角州地形の分布

15

NATURE GEOSCIENCE DOI: 10.1038/NGEO891 LETTERS

60° S

Terra Sirenum Tempe Terra

Chryse Planitia

Arabia Terra

Denteronilus Mensae Nepenthes/Aeolis Mensae Tharsis

rise 30° S

0° 30° N 60° N

150° W

180° 120° W 90° W 60° W 30° W Xanthe Terra

Tharsis rise S

S

S

S S

Argyre Planitia

Arabia Terra

¬8,208 21,249

Ocean Land

S

S

MOLA elevation (m)

Hellas Planitia

0° 30° E 60° E

Amazonian Hesperian Noachian

90° E 120° E 150° E 180°

150° W

180° 120° W 90° W 60° W 30° W 0° 30° E 60° E 90° E 120° E 150° E 180°

MOLA elevation (km)

3 2

S0 S

S0

S 1

0

¬1 –2 –3 –4

–5–180 –120 –60 0

Longitude (°)

60 120 180

a

b

c

60° S 30° S 0° 30° N 60° N

Figure 2 | Topography, geology and distribution of valleys and deltas on Mars. a, Topography of Mars with superimposed deltas connected to the

northern plains (red squares) and in closed basins (green triangles and blue diamonds, see the Methods section). Some of the 52 deposits are located too close to each other and thus overlap at this map scale (see Supplementary Table S1 for the complete list of deposits); the white contour indicates the

equipotential surface S . b, Martian valley networks (black lines)

⁸

in relation to the three main geological epochs

^30,31

(main craters in yellow). c, Elevation of the deltas as a function of longitude and the equipotential surface S (red line) inferred by considering only open deltas (S0, red dashed line, indicates the mean highstand level of all of the 52 deltas); the error bars indicate the maximum water excursion for each delta. The grey dots represent elevation values extracted from the ‘Arabia shoreline’

⁴

and the black dashed line the linear trendline of these values.

NATURE GEOSCIENCE | VOL 3 | JULY 2010 | www.nature.com/naturegeoscience 461

Di Achille & Hynek (2010)

赤：北部低地に流入  青, 緑：盆地に流入

三角州は北部低地を取り囲むように存在   かつての海？

火星の気候変動

16

火星はかつて液体の水を保持できるほど温暖であった 

 現在と比較して大量の水と温室効果のある厚い大気が存在した

約 40 億年前 現在

非磁化惑星からの非熱的散逸

17

Carr and Head (2003) estimated the volume of a potential early martian water reservoir from a geomorphological anal- ysis of possible shorelines. The data suggest that the surface features can be explained by a primitive (post-Noachian) martian water ocean equivalent to a global layer with a depth of about 150 m (Carr and Head, 2003).

The absence of valleys in the younger areas of the north- ern hemisphere suggests that the liquid water presumably present during the Noachian epoch disappeared suddenly, before or during the end of the Late Heavy Bombardment about 3.8 Ga. Based on the calculation by Kass (2001) that an equivalent global water layer with a depth of about 50 m may have escaped to space since the Hesperian epoch (about 3.5 Ga), and assuming that an amount of water equivalent to a global ocean with a depth of about 20–30 m may still be retained in the present polar caps, Carr and Head (2003) es- timated a subsurface water reservoir to be equivalent to a global ocean with a depth of about 80 m, which may be trapped in volatile-rich deposits on the surface or in a groundwater system.

It is important to note that after the Noachian epoch the martian atmosphere was most likely not protected by a strong intrinsic magnetic field. Therefore, the solar wind plasma could interact directly with the upper atmosphere.

Later studies by Leblanc and Johnson (2002) and Lammer et al. (2003a) of the water loss since the Hesperian epoch, after the martian magnetic dynamo had ceased operating, indi- cated that the earlier water loss estimates of 30–80 m (e.g., Luhmann et al., 1992; Zhang et al., 1993a; Kass and Yung, 1995, 1996, 1999; Kass, 2001; Krasnopolsky and Feldman, 2001) may be overestimations. The water loss study by Lam- mer et al. (2003a) included thermal escape, ion pickup, dis- sociative recombination, and sputtering, and used data of solar proxies with different ages to reconstruct the Sun’s ra- diation and particle environment from the present time back to 3.5 Ga (Dorren and Guinan, 1994; Guinan and Ribas, 2002;

Wood et al., 2002; Ribas et al., 2005). They estimated a total loss of water equivalent to a global martian ocean with a depth of about 12 m over the past 3.5 billion years by as- suming the self-regulation mechanism between the loss of O and H, as postulated by McElroy and Donahue (1972).

However, as pointed out by Lammer et al. (2003a), some additional complex ionospheric processes, such as detached plasma clouds and cold ion outflow (Fig. 1), might also have contributed to the erosion of the atmosphere. The ejection of plasma clouds triggered by plasma instabilities or other pro- cesses at the ionopause transition region, which were ob- served at Venus (Brace et al., 1982) and studied by a number of authors (Wolff et al., 1980; Terada et al., 2002, 2004; Ar- shukova et al., 2004), should be considered an additional way by which heavy ions may have escaped from the martian ionosphere (Penz et al., 2004). Cold ion outflow from the ionosphere into the martian ionospheric plasma tail, due to momentum transfer from the solar wind plasma flow (e.g., Pérez-de-Tejada, 1992, 1998; Lundin et al., 1989, 1990, 1991, 2007, 2008a, 2008b; Terada et al., 2002, 2004), is another po- tentially important process. It would be logical to suggest that the cold ion outflow into the plasma tail could have been a very efficient loss process on Mars, because the same loss process was recently identified as one of the most efficient loss processes from the Venus atmosphere by ASPERA-4 ob- servations on board Venus Express (Barabash et al., 2007a).

Pérez-de-Tejada (1992) estimated that cold ion escape due to momentum transport effects may have removed an amount of water from Mars that would have been equiva- lent to a global ocean with a depth of about 10–30 m, de- pending on uncertainties in the solar wind parameters and the martian plasma environment in the past. Lammer et al.

(2003b) found, for moderate solar activity, a cold O^! ion out- flow loss rate from present-day Mars on the order of "10²⁵ s^#1, which is in agreement with the recently observed AS- PERA-3 ion escape rates into the plasma tail (Lundin et al., 2007, 2008a, 2008b). Assuming D/H isotopic constraints over the last 3.5 billion years, Lammer et al. (2003b) estimated a total water loss from Mars equivalent to a global ocean with a depth of about 14 m (minimum) to 34 m (maximum). To derive this estimate, they added together the loss rates due to O^! ion pickup (Lammer et al., 2003a), dissociative recom- bination loss of hot O* (Luhmann, 1997), O^! ion loss induced by plasma instabilities (Penz et al., 2004), and sputtering of O, CO, and CO₂ (Leblanc and Johnson, 2002). The main un- certainties in this estimate result from present uncertainties in the atmospheric and ionospheric parameters and the re- lated atmospheric escape rates due to plasma instabilities and cold ion outflow in the transition layer between the so- lar wind and the martian ionosphere. It should be noted that in previous estimations of cold ion outflow loss, Pérez-de- Tejada (1992) and Lammer et al. (2003b) assumed that the ions escaped through the entire 100% circular ring area around the terminator. Therefore, the estimated cold ion out- flow loss rates by these authors should be considered to be an upper limit.

An important question regarding the loss of the martian atmosphere and its initial water inventory involves the on- TERADA ET AL.

56

FIG. 1. Illustration of ion pickup, cold ion outflow, plasma clouds, and sputtering regions around Mars. The dashed line corresponds to the planetary obstacle (ionopause) and the solid line to the bow shock. !_i is the thickness of the ionos- phere at the terminator.

磁場を持たない惑星の場合、太陽風が 上層大気と相互作用することで大気散 逸を引き起こす ⇒ 火星の気候変動

イオンピックアップ :

上層大気中のイオンが太陽風磁場に よって流出

スパッタリング :

ピックアップイオンによって中性粒 子が叩き出される

コールドイオンフロー :

電離した大気の一部が流体的に散逸

Terada et al. (2009)

まとめ

大気散逸：惑星大気への宇宙空間の流出現象 

熱的散逸：Hydrodynamic escape, Jeans escape 

非熱的散逸：光化学的散逸, Ion pick-up, sputtering など  数十億年スケールでの惑星の表層環境・気候変動に関連 

例：金星・火星の水, 火星の大気

小レポート課題(7/12締切)

19

現在の地球からの水素散逸フラックスは約3.6 10 12 個/

m 2 /s  である。この水素の起源は海水である。過去40億年 間に渡って水素散逸フラックスが一定であった場合、失われ た海水の割合を求めよ(有効数字1桁)。H 2 Oのうち残った酸 素は地殻を酸化することで失われるとする。計算には地球 の半径  6.4 10 6   m,  水素原子質量  1.7 10 -27   kg,  海水の 総質量 1.4 10 21  kg を用いてよい。

下記問題を解き、計算過程も含めレポートにまとめて 

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