Takanori Sasaki (Tokyo Tech)

Amount of Water to be Habitable

・Inner edge of habitable zone

　runaway greenhouse limit: 0.84AU@present S.S.

[Kasting 1988; Nakajima et al. 1992]

・Outer edge of habitable zone

　Forming CO2 clouds: 1.37AU [Kasting 1993]

45367298�

� � &��

���� &��

;0.9AU� ;1.5AU�$%���

;110%����'��� ;50%�

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CO2/ ���

��!).��/�+�-,1!��*0/#(/��:�

from Kasting et al. (1993) "���� 436�

H.Z. for Ocean Planets

3 Types of Water Planets

“Land Planet” “Aqua Planet” “Ocean Planet”

unconnected lakeson a land

connected oceansand lands

an oceanwithout lands

H.Z. for Land Planets・Inner edge of habitable zone

　　Dry low latitude can emit above the “critical flux”

　　Runaway greenhouse limit of solar flux is larger

・Outer edge of habitable zone

　　Lower albedo by smaller area of ice and cloud

　　Freezing limit of solar flux is smaller

H.Z. is wider for “land planets” than “aqua planets”[Abe et al. 2011]

C.H.Z. for Various Planets

0.9-1.1AU[e.g., Kasting et al. 1993]

~0.73-1.3AU[Abe et al. 2011]

“Land Planet” “Aqua Planet” “Ocean Planet”

= the region in which liquid water can exist over the lifetime of a host star

- 結果 - - 初期海洋質量の影響 -・恒星：太陽質量　・恒星からの距離：0.75AU・惑星：地球質量　・初期海洋質量：0.001~2海洋質量　

1

0.1

10-2

10-3

初期海洋質量

[現在の地球の海洋質量で規格化]

0 2 4 6 8 10

0.15

進化せず

進化

時間 [Gyr]

- 結果 - - 初期海洋質量の影響 -・恒星：太陽質量　・恒星からの距離：0.75AU・惑星：地球質量　・初期海洋質量：0.001~2海洋質量　

1

0.1

10-2

10-3

初期海洋質量

[現在の地球の海洋質量で規格化]

0 2 4 6 8 10

0.15

進化せず

進化

時間 [Gyr]

- 結果 -

- 初期海洋質量の影響 -

・恒星：太陽質量　・恒星からの距離：0.75AU

・惑星：地球質量　・初期海洋質量：0.001~2海

洋質量　

1

0.1

10-2

10-3

初期海洋質量[現在の地球の海洋質量で規格化]

02

46

810

0.15

進化せず

進化

時間 [Gyr]

- 結果 -

- 初期海洋質量の影響 -

・恒星：太陽質量　・恒星からの距離：0.75AU

・惑星：地球質量　・初期海洋質量：0.001~2海

洋質量　

1

0.1

10-2

10-3

初期海洋質量[現在の地球の海洋質量で規格化]

02

46

810

0.15

進化せず

進化

時間 [Gyr]

Time [Gyr]

Initi

al o

cean

mas

s[E

arth

’s oc

ean

mas

s] runawaygreenhouse

habitable

[Kodama, Genda & Abe, in prep.]

Evolution of H.P.habitable

Earth-size＠0.75AU

Habitable Snowball Planets

L54 TAJIKA Vol. 680

Fig. 1.—Habitable zone (HZ) around main-sequence stars. The region withlight gray shading represents the HZ for the Earth-like ocean planet (Kastinget al. 1993; Mischna et al. 2000). The region with dark gray shading (denotedby “minimum HZ”) represents the HZ in the narrow sense (0.84 AU ! d !0.87 for p 1) which is defined here as the region between the runawayL/L0

greenhouse limit (Kasting 1988; Nakajima et al. 1992) and the orbit at whichthe effective temperature is 273 K for the planet with no greenhouse gas inthe atmosphere (! p 1) and A p 0.3. Solid curves represent the orbits atwhich the surface temperature is 273 K for the planet with some greenhousegases in the atmosphere (! ! 1) and A p 0.3. Filled circle represents thepresent condition for the Earth.

Fig. 2.—Heat flow and ice thickness. (a) Temporal variations of heat flowfor the terrestrial planets with masses of 0.1–10 obtained from calculationsM!

of thermal evolution of the planets with a parameterized convection model.(b) Temporal variations of ice thickness for the planets around the Sun withmasses of 0.1–10 at d p 1 and A p 0.62. It is assumed that there is noM!

greenhouse gas in the planetary atmosphere (! p 1) for 5 billion years withoutany supply of CO2 to the atmosphere in order to obtain an upper estimate ofthe ice thickness. Here, the luminosity increase due to the evolution of theSun as a main-sequence star (Gough 1981) is considered. The surface tem-perature of the planet therefore changes with time. The water depth is estimatedby assuming a water abundance the same as that of the Earth (0.023 wt.%)and no continental crust on the planetary surface (hence it provides a lowerestimate of the water depth).

For example, because hot-spot-type volcanism due to a rise ofmantle plumes would be the most common type of volcanismon the terrestrial planet (as seen on Venus, Mars, and Earth),there may be terrestrial planets without volcanism due to platetectonics. On such planets, the CO2 supply could be intermittentand insufficient for maintaining a warm climate. Also, theremay be terrestrial planets orbiting outside the HZ for the oceanplanet. These planets would be inevitably globally ice covered.On the analogy of the snowball glaciations, however, there isa possibility that liquid water exists beneath the surface iceshell even when the planetary surface is covered with ice.

In this study, theoretical constraints on terrestrial planets withliquid water underneath the surface ice shell are investigatedin order to understand characteristic features of a possible typeof terrestrial planet expected to be observed in extrasolar plan-etary systems in the future.

2. NUMERICAL RESULTS

In order to estimate variations of geothermal heat flow qfrom the interior through planetary evolution, thermal evolutionof the terrestrial planet with the same abundance of radiogenicheat sources (238U, 235U, 232Th, 40K) as those in the Earth’smantle is investigated by using a parameterized convectionmodel (Tajika & Matsui 1992) (Fig. 2a).

The heat flow for a planet with a mass of 0.1–10 at 4.6M!

billion years since the planetary formation is estimated to bein the range of 40–200 mW m (Fig. 2a), comparable to that!2

of the Earth at present (87 mW m ) (Stein 1995). These values!2

can be converted to an equilibrium ice thickness ( ), assum-DHing that the same amount of heat flow from the planetary in-terior is transferred through the surface ice shell by thermalconduction ( , where k is the thermal conductivityDH p kDT/qof ice and is the temperature difference between the surfaceDTand bottom of the ice).

We can see that if a planet at 1 AU around our Sun withthe same water abundance as that of the Earth (0.023 wt.%) isglobally glaciated, the heat flow on the planet with a mass 10.4M! would be large enough to sustain liquid water for the time-scale of planetary evolution (Fig. 2b). This means that liquidwater is generally stable on these planets even when the surfaceis covered with ice. Such a planet may be termed a “snowballplanet.” A Mars-sized planet (0.1 M!) is, however, too smallto keep the heat flow high enough to maintain liquid waterexcept during its earliest history (Fig. 2b).

The incident flux from the central star affects the surfacetemperature, hence the ice thickness. The effect is estimatedfor different values of luminosity of the central star and thesemimajor axis of the planetary orbit (Figs. 3 and 4). The resultssuggest that the ice thickness increases with distance from thecentral star because of a decrease in the incident flux. Theinternal ocean of the snowball Earth, for example, would sur-vive as far as AU from the Sun (for a water depth ofd " 4

Snowball planets could have an internal ocean with geothermal heat flow from the planetary interior

[Tajika 2008]

No. 1, 2008 SNOWBALL PLANETS L55

Fig. 3.—Limit of the planetary mass above which liquid water exists. (a)Ice thickness as a function of planetary mass and distance from the centralstar with the present luminosity of our Sun. Because of higher heat flow, icethickness is thinner for larger planets. (b) The water depth and the maximumice thickness as a function of planetary mass. The maximum ice thickness isdefined here as the ice thickness estimated by assuming the surface temperatureto be 0 K (hence assuming the maximum temperature gradient in the ice). Itis apparent that the internal ocean cannot freeze completely if the planetarymass is !4 , irrespective of the orbit and the luminosity of the central star.M!

Fig. 4.—Limit of the distance from the central star for the existence ofsubsurface liquid water. As the planetary mass increases, the ice thicknessdecreases while the water depth increases. Therefore, liquid water under theice shell may not freeze completely for a planet with a mass of 3.5 evenM!

when the distance from the central star is as far as 40 AU. The region withlight gray shading represents the HZ for an Earth-like ocean planet (see Fig.1).

!4000 m; Fig. 3a). Because larger planets have higher heatflow and larger amounts of water (Figs. 2a and 2b), the outerlimit is expected to be very distant (Fig. 3a).

In fact, because the ice thickness decreases with the planetarymass (Fig. 3a) while the water depth increases, the internalocean cannot freeze completely for planets with masses !4M! (Fig. 3b). This is because the heat flow is too large to betransported by heat conduction through the ice shell with thewhole ocean thickness, even if the surface temperature is aslow as 0 K. It is, therefore, almost certain that liquid waterexists on the super-Earth (Valencia et al. 2007) either on itssurface (as an ocean planet) or beneath the ice shell (as asnowball planet), except for those orbiting inside the runawaygreenhouse limit. As shown in Figure 4, the internal ocean ofthe snowball planet with a mass 13.5 M! is maintained evenat the orbit of the Edgeworth-Kuiper belt objects (40 AU). Itis, therefore, suggested that if the subsurface ocean on thesnowball planet could be habitable for life, life might well existfar outside the HZ for the traditional ocean planet.

3. DISCUSSION

On Earth, many extant clades of eukaryotic algae have sur-vived through the Neoproterozoic snowball glaciations. This

might imply that there was liquid water on the ice surface orwithin the photic zone (the upper !100 m of the ocean). Sucha condition may have resulted because (1) there were manyshallow hot springs around volcanic islands (Hoffman et al.1998; Hoffman & Schrag 2002), (2) there were regions withvery thin ice (! 30 m) through which sunlight penetrated andlife could have photosynthesized beneath the sea ice (McKay2000; Warren et al. 2002; Goodman & Pierrehumbert 2003;Pollard & Kasting 2005), (3) the equatorial oceans did notfreeze while the equatorial continents were covered with ice(Hyde et al. 2000), and/or (4) the ice surface could have meltedseasonally. These arguments might provide insight into hab-itability of the snowball planet.

On the snowball planet, accumulation of CO2 in the atmo-sphere through volcanic activities (Kirschvink 1992) wouldeventually melt the ice shell completely. If the volcanic fluxof CO2 is too low to sustain a warm climate, however, theplanet would soon freeze again. Global-scale melting and freez-ing may repeat on the snowball planet.

The timescale for the snowball-Earth events has been esti-mated from the timescale for CO2 to accumulate in the atmo-sphere due to volcanic CO2 supply to a level required for melt-ing of ice. This timescale is estimated to be on the order of

yr for the Neoproterozoic to yr for the Paleoproterozoic6 710 10snowball-Earth events (Caldeira & Kasting 1992; Hoffman etal. 1998; Kirschvink et al. 2000). Therefore, the total durationof the snowball glaciations would be a few percent of theEarth’s history. Sleep and Zahnle suggested that the early Earthmight have been globally glaciated owing to chemical weath-ering of ultramafic volcanics and impact ejecta for the first fewhundred million years (Sleep & Zahnle 2001; Zahnle 2006).Considering such a possibility, the total duration of the snow-ball glaciations may be at most 10% of the Earth’s history. Itwould be difficult for a distant observer to observe the globallyice-covered Earth.

There could be, however, extrasolar terrestrial planets moresusceptible to being globally ice covered than the Earth. For

No. 1, 2008 SNOWBALL PLANETS L55

Fig. 3.—Limit of the planetary mass above which liquid water exists. (a)Ice thickness as a function of planetary mass and distance from the centralstar with the present luminosity of our Sun. Because of higher heat flow, icethickness is thinner for larger planets. (b) The water depth and the maximumice thickness as a function of planetary mass. The maximum ice thickness isdefined here as the ice thickness estimated by assuming the surface temperatureto be 0 K (hence assuming the maximum temperature gradient in the ice). Itis apparent that the internal ocean cannot freeze completely if the planetarymass is !4 , irrespective of the orbit and the luminosity of the central star.M!

Fig. 4.—Limit of the distance from the central star for the existence ofsubsurface liquid water. As the planetary mass increases, the ice thicknessdecreases while the water depth increases. Therefore, liquid water under theice shell may not freeze completely for a planet with a mass of 3.5 evenM!

when the distance from the central star is as far as 40 AU. The region withlight gray shading represents the HZ for an Earth-like ocean planet (see Fig.1).

!4000 m; Fig. 3a). Because larger planets have higher heatflow and larger amounts of water (Figs. 2a and 2b), the outerlimit is expected to be very distant (Fig. 3a).

In fact, because the ice thickness decreases with the planetarymass (Fig. 3a) while the water depth increases, the internalocean cannot freeze completely for planets with masses !4M! (Fig. 3b). This is because the heat flow is too large to betransported by heat conduction through the ice shell with thewhole ocean thickness, even if the surface temperature is aslow as 0 K. It is, therefore, almost certain that liquid waterexists on the super-Earth (Valencia et al. 2007) either on itssurface (as an ocean planet) or beneath the ice shell (as asnowball planet), except for those orbiting inside the runawaygreenhouse limit. As shown in Figure 4, the internal ocean ofthe snowball planet with a mass 13.5 M! is maintained evenat the orbit of the Edgeworth-Kuiper belt objects (40 AU). Itis, therefore, suggested that if the subsurface ocean on thesnowball planet could be habitable for life, life might well existfar outside the HZ for the traditional ocean planet.

3. DISCUSSION

On Earth, many extant clades of eukaryotic algae have sur-vived through the Neoproterozoic snowball glaciations. This

might imply that there was liquid water on the ice surface orwithin the photic zone (the upper !100 m of the ocean). Sucha condition may have resulted because (1) there were manyshallow hot springs around volcanic islands (Hoffman et al.1998; Hoffman & Schrag 2002), (2) there were regions withvery thin ice (! 30 m) through which sunlight penetrated andlife could have photosynthesized beneath the sea ice (McKay2000; Warren et al. 2002; Goodman & Pierrehumbert 2003;Pollard & Kasting 2005), (3) the equatorial oceans did notfreeze while the equatorial continents were covered with ice(Hyde et al. 2000), and/or (4) the ice surface could have meltedseasonally. These arguments might provide insight into hab-itability of the snowball planet.

On the snowball planet, accumulation of CO2 in the atmo-sphere through volcanic activities (Kirschvink 1992) wouldeventually melt the ice shell completely. If the volcanic fluxof CO2 is too low to sustain a warm climate, however, theplanet would soon freeze again. Global-scale melting and freez-ing may repeat on the snowball planet.

The timescale for the snowball-Earth events has been esti-mated from the timescale for CO2 to accumulate in the atmo-sphere due to volcanic CO2 supply to a level required for melt-ing of ice. This timescale is estimated to be on the order of

yr for the Neoproterozoic to yr for the Paleoproterozoic6 710 10snowball-Earth events (Caldeira & Kasting 1992; Hoffman etal. 1998; Kirschvink et al. 2000). Therefore, the total durationof the snowball glaciations would be a few percent of theEarth’s history. Sleep and Zahnle suggested that the early Earthmight have been globally glaciated owing to chemical weath-ering of ultramafic volcanics and impact ejecta for the first fewhundred million years (Sleep & Zahnle 2001; Zahnle 2006).Considering such a possibility, the total duration of the snow-ball glaciations may be at most 10% of the Earth’s history. Itwould be difficult for a distant observer to observe the globallyice-covered Earth.

There could be, however, extrasolar terrestrial planets moresusceptible to being globally ice covered than the Earth. For

H.Z. for Snowball Planets

[Tajika 2008]

High-pressure Ice– 22 –

Fig. 3.— (a) Schematic phase diagram of H2O (gray lines), temperature gradient (black

lines), and H2O-rock boundaries (dashed lines). (b) Types of planets that have H2O on the

planetary surface. (c) Schematic view of the models to treat high-pressure ice.

– 22 –

Fig. 3.— (a) Schematic phase diagram of H2O (gray lines), temperature gradient (black

lines), and H2O-rock boundaries (dashed lines). (b) Types of planets that have H2O on the

planetary surface. (c) Schematic view of the models to treat high-pressure ice.

・High-pressure ices appear if the planet has larger

　amount of water than the Earth

・High-pressure ices are denser than liquid water

– 25 –

Fig. 6.— Conditions for a planet around a central star (E/E0 = 1) for (a) Msw/Msw0 = 1,

(b) Msw/Msw0 = 2, (c) Msw/Msw0 = 5, and (d) Msw/Msw0 = 10. Horizontal axis represents

the distance from the central star; vertical axis represents the planetary mass normalized by

Earth’s mass.

S.P. w/ High-pressure Ice

[Ueta & Sasaki, submitted to ApJ]

Mwater = 5 x 0.023 wt.%

– 22 –

Fig. 3.— (a) Schematic phase diagram of H2O (gray lines), temperature gradient (black

lines), and H2O-rock boundaries (dashed lines). (b) Types of planets that have H2O on the

planetary surface. (c) Schematic view of the models to treat high-pressure ice.

Habitable?

Europa

– 22 –

Fig. 3.— (a) Schematic phase diagram of H2O (gray lines), temperature gradient (black

lines), and H2O-rock boundaries (dashed lines). (b) Types of planets that have H2O on the

planetary surface. (c) Schematic view of the models to treat high-pressure ice.

Not Habitable?

Ganymede

- 結果 - - 初期海洋質量の影響 -・恒星：太陽質量　・恒星からの距離：0.75AU・惑星：地球質量　・初期海洋質量：0.001~2海洋質量　

1

0.1

10-2

10-3

初期海洋質量

[現在の地球の海洋質量で規格化]

0 2 4 6 8 10

0.15

進化せず

進化

時間 [Gyr]

- 結果 - - 初期海洋質量の影響 -・恒星：太陽質量　・恒星からの距離：0.75AU・惑星：地球質量　・初期海洋質量：0.001~2海洋質量　

1

0.1

10-2

10-3

初期海洋質量

[現在の地球の海洋質量で規格化]

0 2 4 6 8 10

0.15

進化せず

進化

時間 [Gyr]

- 結果 -

- 初期海洋質量の影響 -

・恒星：太陽質量　・恒星からの距離：0.75AU

・惑星：地球質量　・初期海洋質量：0.001~2海

洋質量　

1

0.1

10-2

10-3

初期海洋質量[現在の地球の海洋質量で規格化]

02

46

810

0.15

進化せず

進化

時間 [Gyr]

- 結果 -

- 初期海洋質量の影響 -

・恒星：太陽質量　・恒星からの距離：0.75AU

・惑星：地球質量　・初期海洋質量：0.001~2海

洋質量　

1

0.1

10-2

10-3

初期海洋質量[現在の地球の海洋質量で規格化]

02

46

810

0.15

進化せず

進化

時間 [Gyr]

– 25 –

Fig. 6.— Conditions for a planet around a central star (E/E0 = 1) for (a) Msw/Msw0 = 1,

(b) Msw/Msw0 = 2, (c) Msw/Msw0 = 5, and (d) Msw/Msw0 = 10. Horizontal axis represents

the distance from the central star; vertical axis represents the planetary mass normalized by

Earth’s mass.

Summary

Time [Gyr]

Initi

al o

cean

mas

s[E

arth

’s oc

ean

mas

s]

・Amount of water changes the range of H.Z.

・Too much water could prevent the habitability.

・How much water do they have? is a key question.