RAPID WATER LOSS CAN EXTEND THE LIFETIME OF PLANETARY HABITABILITY

The initial amount of water on terrestrial planets just after their formation is not known. We treat the initial amount of water as a parameter, i.e., we consider planets with various initial amounts of water. The amount of water on the surface of a planet would change through interaction with the planetary interior through processes such as subduction of hydrous minerals, outgassing of water at mid-ocean ridges and arcs, and so on. For the present Earth, the ingassing flux of water is estimated to be 5 × 10²²–1.1 × 10²³ mol Gyr⁻¹ (Rea & Ruff 1996; Javoy 1998), and the degassing flux of water is estimated to be 2.2 × 10²²–1.1 × 10²³ mol Gyr⁻¹ (Bounama et al. 2001; Hilton et al. 2002). Ingassing and outgassing fluxes in water appear to be in equilibrium on the present Earth. The difference between the ingassing and outgassing water fluxes is on the order of 10²² mol Gyr⁻¹. By comparison, once the rapid escape of water into space starts as the central star evolves, the escape flux of water vapor exceeds 10²³ mol Gyr⁻¹ (see Sections 3.1 and 3.2). For simplicity, we assume that the change in the total amount of water on a planet is attributed solely to the loss of water into space.

We assume that the amount of water decreases via the hydrodynamic escape of hydrogen molecules. The change in the amount of water is given by

$$\begin{eqnarray}&&\displaystyle \frac{{{dM}}_{{{\rm{H}}}_{2}{\rm{O}}}}{{dt}}={-\phi }_{\mathrm{esc}}\end{eqnarray} \tag{ 1 }$$

where ${M}_{{{\rm{H}}}_{2}{\rm{O}}}$ is the total amount of water and ${\phi }_{\mathrm{esc}}$ is the escape flux of molecular hydrogen. The escape process of hydrogen is described in Section 2.3.

The amount of water vapor in the atmosphere depends on the atmosphere model used. For the aqua planet and land planet modes, the amount of water vapor is estimated by using the one-dimensional (1D), cloud-free, radiative-convective atmospheric model developed by Abe & Matsui (1988) and using the results obtained by Abe et al. (2011), respectively. The amount of water on the surface can then be estimated by subtracting the amount of water in the atmosphere from the total amount of water on the planet. An aqua planet is considered to evolve into a land planet if the amounts of water in both reservoirs meet specific transition conditions, described in detail in Section 2.2.

Planetary albedo, which plays an important role in climate, depends on the properties of the planetary surface and atmosphere. In our numerical simulation, we fixed the albedo of the planetary surface at 0.3, which is typical of deserts. When the amount of water vapor increases due to warming caused by an increase in the luminosity of the central star, the atmosphere gets denser and light from the central star is scattered more efficiently. Therefore, we also consider the scattering albedo for an aqua planet. Since the scattering albedo is negligible for a land planet (if the effect of dust is not considered), we consider that the planetary albedo for a land planet to be 0.3.

Here, we assume that the planets have zero obliquity and eccentricity, with a mass and a radius equivalent to those of the Earth. In the planetary atmosphere, 1 bar of the present Earth's atmosphere is considered as the background atmosphere. Except for water vapor, no changes in atmospheric components were considered in this study. It is possible that the carbon cycle exists on Earth-like planets. The carbon cycle in the presence of liquid water provides a negative feedback on surface temperature that maintains a stable climate (Walker et al. 1981). However, in the case of a central star with high luminosity, the feedback breaks down because there is too little CO₂ in the atmosphere to affect changes in surface temperatures owing to efficient chemical erosion (rapid fixing of CO₂ as carbonate rock). Therefore, the evolution of the atmosphere is driven almost entirely by changes in the amount of water in the planetary atmosphere.

Abe et al. (2011) assumed that an aqua planet with the present Earth's ocean mass could evolve to land planet mode just before all of its water is lost, and before there was a rapid increase in surface temperatures due to the runaway greenhouse effect. Under such transition conditions, it is possible that a planet with a large amount of water in its atmosphere can evolve from an aqua planet to a land planet. However, if the planet has a large amount of water vapor in its atmosphere before the loss of water, then it may maintain a heated state during atmospheric escape. Under these conditions, such a planet may not evolve into a land planet, even if it loses most of the water on the surface. It is therefore necessary to consider the amount of water vapor in the planetary atmosphere. We therefore imposed several conditions on the amounts of water on the planetary surface and the amounts of water vapor in its atmosphere for the transition from an aqua planet to land planet mode.

However, one problem is that we do not know the amount of water vapor in an aqua planet's atmosphere just before the threshold for the runaway greenhouse effect is reached. In order to evolve into land planet mode, there should be an upper limit to the amount of water in the atmosphere; we treat this upper limit to the amount of water as a parameter, which we denote as M_cv and refer to as "the critical amount of vapor for the runaway greenhouse effect." From previous studies (Abe & Matsui 1988; Kasting 1988; Goldblatt et al. 2013; Kopparapu et al. 2013), it appears that when M_cv is expressed as a column it is equivalent to 1–10 m of precipitable water. In this paper, to illustrate typical results, an M_cv of 3 m was used for our standard model.

Another important parameter is the maximum amount of water that a land planet can have and still behave as a land planet. We consider the distribution of surface water from the results of Abe et al. (2011). Surface water on a land planet is typically located at latitudes above 60°, which corresponds to 10% of the entire planetary surface. According to percolation theory, for any given area, only half of that area is required to form a connected area. The maximum unconnected oceanic area is thus half of the area above 60° latitude, which corresponds to 5% of the entire planetary surface. If planetary topography is ignored, then the typical amount of water on a land planet is 5% of the present Earth's ocean mass. If a planet has more water, that water will extend equatorward of 60° latitude. Therefore, we assume that 5% of the present Earth's ocean mass on the planetary surface approximates the transition conditions that are required for the maximum amount of water required for an aqua planet to evolve into a land planet. We refer to this condition "the maximum liquid water mass for a land planet mode," which we denote as M_ml. If the amounts of water on the planetary surface and in the atmosphere meet these conditions, then the aqua planet can evolve into a land planet. We treat M_ml = 0.05 M_oc as our standard case, but we also treat M_ml as a parameter that varies from 0.01 to 0.1 M_oc, where M_oc is the amount of the present Earth's ocean (8.4 × 10²² moles). In Section 4.1, we discuss the evolution of an aqua planet under several transition conditions.

Escape is an important process in atmospheric evolution. In this study, we consider the hydrodynamic escape of hydrogen molecules because it is the fastest process of hydrogen escape and has the most potential to decrease the water reservoir of a planet. We will address two major bottlenecks to hydrogen molecular escape from the planetary atmosphere. The first is the energy source required to drive the escape of hydrogen molecules. The main source of energy for escape is EUV, usually defined by λ < 100 nm from the central star, which is directly absorbed by hydrogen molecules and atoms. When the escape flux is controlled by the EUV flux, the escape is said to be "energy-limited." The other major bottleneck is the diffusion of hydrogen-containing molecules through the background atmosphere to reach the altitudes where escape occurs. When escape is controlled by the diffusion of molecules through the upper atmosphere, then the escape is referred to as "diffusion-limited." We calculate escape fluxes in both modes and adopted the smaller one as the actual escape flux. Other possible bottlenecks, such as the photon-limited photochemistry that converts H₂O to H₂, magnetospheric drag, and radiative cooling by ions (e.g., ${{\rm{H}}}_{3}^{+}$) and molecules embedded in the outflowing wind, are less well established and will be neglected here.

The escape flux of the diffusion-limited escape mode depends on the total mixing ratio of hydrogen-containing species in the upper atmosphere (Walker 1977, p. 164). The diffusion-limited escape flux (ϕ_d ) of hydrogen molecules is given by

$$\begin{eqnarray}&&{\phi }_{{\rm{d}}}={f}_{{\rm{T}}}({{\rm{H}}}_{2})\displaystyle \frac{b({m}_{{\rm{a}}}-{m}_{{\rm{i}}})g}{{{kT}}_{\mathrm{str}}}\end{eqnarray} \tag{ 2 }$$

where f_T (H₂ ) is the total mixing ratio of hydrogen molecules in all forms at homopause (f_T (H₂) = f(H₂ O) + f(H₂) + 2 f (CH₄) + ⋯), T_str is the temperature in the stratosphere (T_str = 200 K), b is the binary diffusion coefficient between the background atmosphere and H₂ (b = 1.9 × 10¹⁹ (T_str/300 K)^0.75 cm⁻¹ s⁻¹ for H₂ in air), g is the acceleration due to gravity, k is Boltzmanns constant, and m_a and m_i are the average molecular masses of the background atmosphere and the molecular mass of hydrogen, respectively. We assumed that the major carrier of hydrogen is water vapor. Therefore, we adopt f_T (H₂) = f(H₂ O), where f(H₂O) is the mixing ratio of water vapor in the upper atmosphere.

An escape flux is limited by EUV flux if the planetary upper atmosphere is hydrogen-rich atmosphere. The energy-limited escape flux (ϕ_e) is given by Watson et al. (1981) as

$$\begin{eqnarray}&&{\phi }_{{\rm{e}}}=\displaystyle \frac{\epsilon {S}_{\mathrm{EUV}}{r}_{{\rm{p}}}}{{m}_{{\rm{i}}}{{GM}}_{{\rm{p}}}}\end{eqnarray} \tag{ 3 }$$

where is the escape efficiency, S_EUV is the EUV radiation flux, G is the gravitational constant, r_p is the radius of the planet, and M_p is the planetary mass. According to Watson et al. (1981), the escape efficiency ranges from 0.15 to 0.3; we adopted 0.15 as the escape efficiency. Since we used Earth-sized planets in this study, we used the Earth's radius and mass for r_p and M_p, respectively.

Atmospheric H₂O molecules are dissociated by UV radiation from the central star (via ${{\rm{H}}}_{2}{\rm{O}}+h\nu \to {\rm{H}}+\mathrm{OH}$) (e.g., Brinkmann 1969). Hydrogen molecules are transported to the upper atmosphere, where EUV radiation reaches, and are heated by such radiation. The resultant hydrogen molecules escape to space (e.g., Kasting et al. 1984). When hydrogen escapes, the oxygen left behind can build up in the planetary atmosphere. Because we assume diffusion-limited escape, oxygen does not escape. If an amount of water equivalent to the Earth's ocean mass escapes, approximately 240 bars of O₂ will remain (Kasting 1997). In this study, we assume that all of this oxygen is absorbed by the crust of the planet.

In order to estimate the escape flux of hydrogen molecules in the diffusion-limited escape mode, we need the mixing ratio of water vapor in the upper atmosphere. For the aqua planet mode, we estimate the mixing ratio of water vapor in the upper atmosphere as described by Abe & Matsui (1988). Figure 1 shows the mixing ratio of water vapor in the upper atmosphere as a function of the incident stellar radiation. It is very low until the cold trap region disappears. The escape flux of hydrogen molecules in the diffusion-limited escape mode is thus expected to be very low due to the very low mixing ratio of water vapor under these conditions. If an aqua planet receives incident solar flux from the central star that is sufficiently strong to eliminate the cold trap, the upper atmosphere will become humid and the escape of hydrogen molecules will be rapid.

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For the land planet mode, we estimate the mixing ratio of water vapor in the upper atmosphere using the results of Abe et al. (2011). The mixing ratio for a land planet also increases with the increasing luminosity of the central star. In a case where the insolation from the central star is above the threshold for the runaway greenhouse effect for a land planet, the upper atmosphere becomes humid and the escape of hydrogen is rapid (Figure 2).

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We consider the evolution of total luminosity and the EUV flux of a star because the escape flux of hydrogen molecules depends strongly on both. The total luminosity of a star increases over time. We treated the central star as a solar-type star. For the luminosity for a G-type star, we use the following expression given by Gough (1981):

$$\begin{eqnarray}&&S(t)={\left[1+\displaystyle \frac{2}{5}\left(1-\displaystyle \frac{t}{{t}_{\odot }}\right)\right]}^{-1}{S}_{\odot }\end{eqnarray} \tag{ 4 }$$

where S(t) is the incident stellar flux for a G-type star at 1 AU as a function of time, t is the time in Gyr,t_⊙ is the age of the Sun (t_⊙ = 4.5 Gyr), and S_⊙ is the solar constant (S_⊙ = 1366 W m⁻²).

Since the EUV flux for young stars is stronger than that for old stars, we employed the following expression of Lammer et al. (2009) for a G-type star:

$$\begin{eqnarray}{L}_{\mathrm{EUV}}=\left\{\begin{array}{lc}0.375{L}_{0}{t}^{-0.425} & (t\leqslant 0.6\;\mathrm{Gyr})\\ 0.19{L}_{0}{t}^{-1.69} & (t\gt 0.6\;\mathrm{Gyr})\end{array}\right.\end{eqnarray} \tag{ 5 }$$

where L_EUV is the luminosity of EUV in W s⁻¹, and L₀ = 10^22.35 W. The relation between the luminosity and the flux is given by S_EUV = L_EUV /4πa², where a is a distance from the central star to the planet in meters.

In this section, we examine typical results obtained by our numerical simulations describing the planetary evolution. Figure 3 shows the evolution of a planet with the present Earth's ocean at the beginning (M_ini = 1.0 M_oc) at a = 0.80 AU, where M_ini is the initial amount of water.

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As long as the luminosity of the central star is low (<3 Gyr), the mixing ratio of water vapor in the upper atmosphere remains low (Figure 3(a)). Consequently, the escape flux of water vapor in the diffusion-limited escape mode also remains extremely low (Figure 3(b)) and the amount of water on the surface hardly changes during this period (Figure 3(c)). The atmosphere gets wetter as the luminosity of the central star increases over time, and after 3 Gyr, the mixing ratio of water vapor in the upper atmosphere increases rapidly. The increase in the mixing ratio in the upper atmosphere enhances the escape flux of water vapor in the diffusion-limited escape mode and decreases the amount of water on the planet (Figure 3(c)). In this calculation, this planet does not satisfy the transition conditions from aqua planet mode to land planet mode because the amount of surface water exceeds the maximum water mass for land planet mode (0.05 M_oc) when the average column mass of atmospheric water vapor reaches M_cv (i.e., a depth of 3 m), which is the critical amount for the runaway greenhouse effect. Therefore, the planet remains in aqua planet mode until the onset of the runaway greenhouse effect, eventually evolving into the uninhabitable steam planet state. Over a period of approximately 0.1 Gyr, all of the water escapes into space and the planet finally evolves into a dry planet state.

Figure 4 shows the evolution of a planet with M_ini = 0. 1 M_oc and a = 0.8 AU. The difference between the cases shown in Figures 3 and 4 is the initial amount of water. The overall evolution of water is very similar to that shown in Figure 3 before t = 3.19 Gyr. However, when the amount of surface water decreases to M_ml = 0. 05 M_oc (i.e., the maximum water mass for the land planet mode), the average column mass of the atmospheric water vapor is less than the 3 m threshold for the runaway greenhouse effect in Figure 4(d). This planet therefore satisfies the requirements for a transition from aqua planet mode to land planet mode and can evolve into land planet mode. Once in land planet mode, the planet's atmosphere becomes dry (Figure 4(a)) and escape shuts off (Figure 4(b)). This planet can keep liquid water on its surface until the central star has become sufficiently bright enough to exceed the runaway threshold of a land planet (Figure 4(c)). When the planet receives insolation above this limit, the planet evolves into the steam planet state and then the dry planet state once it has lost its remaining water into space over about 0.17 Gyr.

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Whether or not an aqua planet can evolve into a land planet thus depends on the initial amount of water. Qualitatively, planets with small initial amounts of water can more easily evolve from the aqua planet mode to the land planet mode.

Here we examine the effect of the distance from the central star on planetary evolution. Figure 5 shows the evolution of a planet with M_ini = 0. 1 M_oc and a = 1.0 AU. In Figure 5(d), the amount of surface water remaining on the planet exceeds M_ml and the planet experiences the runaway greenhouse effect. This planet evolves into the steam planet state without passing through a land planet state. On the other hand, we have seen that a planet with the same initial amount of water at 0.8 AU can evolve from aqua planet mode to land planet mode (Figure 4). This evolution occurs because the planet closer to the central star evolves through the moist greenhouse stage when the star is younger, and the EUV flux and hydrogen escape flux are higher. Any planet near the central star will lose more water during the period of rapid escape of water vapor.

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The timing of the onset and duration of rapid escape of water vapor are the two key events that determine whether or not an aqua planet will evolve into a land planet. In the case of a planet that is located far away from its central star, the onset of rapid escape of water vapor occurs later when the star is older and its EUV flux is lower. It therefore takes more time for a more distant planet to lose its surface water; phrased another way, the more distant planet loses less water between the onset of the moist greenhouse effect and the onset of the runaway greenhouse effect for an aqua planet. Moreover, because the rate of stellar luminosity increases with time (see Equation (4)), more distant planets have less time to shed excess water before the onset of runaway greenhouse effect. As a result, it is more difficult for a distant planet to evolve into a land planet, and easier to evolve directly into a steam planet.

In the previous section, we showed several typical numerical results obtained for planetary evolution. We found that the initial amount of water (M_ini) and the distance from the central star (a) are important in determining whether or not an aqua planet can evolve into a land planet.

Figure 6 shows the maximum initial amount of water that is required for the transition from aqua planet mode to land planet mode as a function of the distance from the central star. In this figure, planets below the curve can evolve from aqua planet mode to land planet mode. Aqua planets close to a central star with small initial amounts of water can evolve into land planets, but aqua planets that are too far from a central star, or that are born with large amounts of water, evolve into steam planets without passing through the land planet stage.

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Planets with less than the maximum liquid water mass for land planets (M_ini < M_ml) remain in land planet mode from the beginning. In cases of planets with small orbits (a < 0.72 AU), all of the water evaporates and such planets are in the steam planet state from the beginning.

Here we discuss the inner edge of the HZ of solar-type stars based on our results. Figure 7 shows the evolution of planets with M_ini = 1.0 M_oc at various distances from the central star under the same transition conditions. For planets with M_ini = 1.0 M_oc, rapid escape of water occurs, but such planets cannot evolve into the land planet mode because they cannot lose enough water—they cannot get from 1.0 M_oc to M_ml—before encountering the runaway greenhouse threshold for aqua planets. Therefore, the boundary between the aqua planet mode and the steam planet state corresponds to the inner edge of the classical instantaneous HZ, proposed in Kasting et al. (1993; Figure 7).

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As in Figure 7, Figure 8 shows the time evolution of planets with M_ini = 0.1 M_oc. When located between 0.72 and 0.82 AU, such planets can evolve from the aqua planet mode to the land planet mode. Planets in the land planet mode remain habitable for an additional 2 Gyr before evolving into the steam planet state and then to the dry planet state due to increased luminosity of the central star.

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In both Figures 7 and 8, aqua planets closer than about 0.7 AU from the central star are in the steam planet state from the beginning. Such planets lose all of their water rapidly (over a few tens of million years) because the EUV flux at that time is very strong; such planets are called Type II terrestrial planets (Hamano et al. 2013).

Figure 9 shows the inner edge of the CHZ, which is defined here as the region where a planet has liquid water on its surface for more than 4.6 Gyr. We divided the CHZ into two types according to the initial amount of water. One type of CHZ refers to those regions on aqua planets that maintain water on their surface for more than 4.6 Gyr; this type corresponds to the CHZ proposed in Kasting et al. (1993) and is referred to here as a type I CHZ. The other type of CHZ refers to regions on land planets that maintain water on their surface for a total of more than 4.6 Gyr; this is referred to as a type II CHZ.

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In our model, planets with M_ini > 0.22 M_oc cannot evolve into land planets: such planets have a type I CHZ. On the other hand, planets with M_ini < 0.22 M_oc can evolve into land planets. However, planets with 0.19 M_oc < M_ini < 0.22 M_oc cannot maintain liquid water on their surface for 4.6 Gyr because the insolation on such planets exceeds the threshold of the runaway greenhouse effect. Planets with M_ini ≤ 0.19 M_oc have a type II CHZ.

Figure 9 shows that planets that begin with 0.09 M_oc < M_ini ≤ 0.19 M_oc have both type I and type II CHZs, but these two CHZs are not contiguous. However, planets with 0.05 M_oc < M_ini ≤ 0.09 M_oc also have both CHZs and they are contiguous. Planets with an initial water mass less than the maximum water mass for a land planet (M_ml = 0.05 M_oc) on their surface are in land planet mode from the beginning.

In previous sections, we showed results when M_cv, the critical water vapor amount for the runaway greenhouse, was taken as a global average of 3 m water depth equivalent and M_ml, the maximum liquid water mass for a land planet mode, was taken to be 0.05 M_oc. In this section, we investigate how the evolution from aqua planet mode to land planet mode changes when the transition conditions are altered.

Figure 10 shows the maximum M_ini required for a planet to evolve into a land planet for different values of M_cv. In these calculations, M_ml is fixed at 0.05 M_oc. If M_cv exceeds 3 m, then the maximum M_ini increases because the onset of the runaway greenhouse effect is delayed. For planets closer to the central star, the maximum M_ini is larger because the escape flux of water is larger before the onset of runaway greenhouse effect. However, if planets are too close to the central star, the maximum M_ini decreases and has a peak (see Figure 10). The amount of water that escapes is determined by the duration of the period of a rapid escape until the onset of the runaway greenhouse effect and the escape flux of water during this period. For planets that are very close to the central star, the runaway greenhouse effect occurs early and the duration of the period of rapid escape is short. Although the escape flux in the energy-limited escape mode is large, the rapid escape of water occurs in the diffusion-limited escape mode for these planets. Therefore, the total amount of escaped water hits a peak, which is shown by the maximum M_ini value in Figure 10. An aqua planet cannot evolve into a land planet when M_cv is 1 m (global average). In our model, the mixing ratio of water vapor in the upper atmosphere reached 10⁻³ when the column of water in the atmosphere is 1.9 m (global average). If M_cv is less than 1.9 m, then a planet in the aqua planet mode cannot lose enough water and it passes directly into the steam planet state.

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Our standard case takes M_ml = 0. 05 M_oc. This value of M_ml is dependent upon the planetary topography. Figure 11 shows the dependence of the maximum M_ini on M_ml for a planet evolving into a land planet. In this calculation, the value of M_cv is fixed at our standard value of 3 m. A smaller value for M_ml results in smaller maximum M_ini, but it is possible for aqua planets to evolve into land planets even if M_ml = 0.01 M_oc. However, an aqua planet cannot evolve into a land planet when M_cv is less than 1 m (see Figure 10). Therefore, the parameter M_cv has a greater impact on the evolution path to land planets than the parameter M_ml.

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We investigated the evolutionary paths of planets using a 1D, cloud-free, radiative–convective atmospheric model developed in the 1980s (Abe & Matsui 1988). The 1D atmospheric models have been improved by using more accurate opacity estimates for water vapor (Goldblatt et al. 2013; Kopparapu et al. 2013, 2014). The inner edge of the CHZ (defined by moist greenhouse effect) in Kopparapu et al. (2013) is 0.99 AU. In our model, the onset of the moist greenhouse effect is 1.39 S_⊙. Since the onset of the runaway greenhouse effect is dependent on the value of M_cv, when M_cv is set to 3 m, the onset of the runaway greenhouse effect is 1.40 S_⊙. In Kopparapu et al. (2013), the onsets of the moist and runaway greenhouse effects are 1.015 and 1.06 S_⊙, respectively. The timing of the onset of rapid water loss and the amount of water that escaped should therefore be different between our atmospheric model and their model. In order to investigate the evolution from an aqua planet into a land planet, we need the relationship between the incident solar flux and the amount of water vapor in the atmosphere, but it was not shown in previous papers. We therefore qualitatively compared our results to those of Kopparapu et al. (2013).

We estimated how much water escapes during the period from the onset of the moist greenhouse effect to the onset of the runaway greenhouse effect using the results from Kopparapu et al. (2013). To estimate the escaped water amount by Kopparapu et al. (2013), we presume that the mixing ratio of water vapor is 10⁻³, so that the escaped water amount during this period in the diffusion-limited escape mode is approximately 3 × 10²¹ moles (ca. 0.04 M_oc). The amount of escaped water under energy-limited escape mode conditions in the same period was estimated to be 10²³ moles (ca. 1.19 M_oc). The actual amount of escaped water falls between these estimates (i.e., between 3 × 10²¹ and 1 × 10²³ moles). In our model, planets that can evolve into land planets typically lose about 0.1 M_oc of water (see Section 3.3), which is comparable to, or less than, the estimates of Kopparapu et al. (2013). Kopparapu et al. (2013) indicate that planets at a < 0.84 AU are in the steam planet state. Thus, the region where aqua planets can evolve into land planets moves outward (about 0.1 AU) when the model of Kopparapu et al. (2013) is applied. The type II CHZ (see Figure 9), in which aqua planets evolve to land planets, also moves outward.

We assessed the effect of EUV flux on our results. The uncertainty associated with the EUV flux from the central star is large (e.g., Zahnle & Walker 1982; Lammer et al. 2009). Just before an aqua planet evolves into a land planet, water escapes rapidly in the energy-limited escape mode (see Figure 4(b)). If the EUV flux is larger than that used in our model, then the escape flux increases. However, since the escape flux is limited by the diffusion process, a larger EUV flux does not markedly affect our results. On the other hand, if the EUV flux is smaller than that used in our model, then the escape flux decreases. This makes it harder for aqua planets to evolve into land planets.

An important complication could be the evolution of the amount of CO₂ in the atmosphere. Since the carbon cycle on a land planet has not yet been investigated, we speculate possible effects of carbon cycle on a land planet climate in the following.

The amount of CO₂ in the atmosphere is governed by the balance between the degassing flux of CO₂ and the removal flux of CO₂ through chemical weathering. We expect the degassing flux of CO₂ to be smaller on a land planet than on an aqua planet because plate tectonics is likely to be less efficient on a water-poor mantle. Chemical weathering may be also less efficient on a land planet, because it occurs mainly in wet regions. If the former effect exceeds the latter, then the amount of CO₂ in the atmosphere should be smaller on a land planet than on an aqua planet. However, any decrease in the degassing flux would be difficult to estimate.

Therefore, it is not clear whether there would be more or less CO₂ on a land planet compared to an aqua planet. If the amount of CO₂ is balanced at a high value, then the period of habitability may be shorter than that estimated in our study because the greenhouse effect attributed to CO₂ may trigger the runaway greenhouse effect. On the other hand, if the CO₂ amount is balanced at a low value, the environment is cooler than our estimate. However, such an effect is likely minor, because the insolation is high enough to keep from the global freezing without CO₂ greenhouse effect. It should also be noted that a land planet is relatively resistant to global freezing (Abe et al. 2011). Even if ice caps appear, their size is regulated by the carbon cycle, because CO₂ removal through chemical weathering would be negligible in the ice-covered area. Under such a scenario, the lifetime of a habitable environment would likely be similar to that estimated in our study.

We have neglected the geologic water cycle by presuming that the fluxes of water into and out of the mantle are roughly in balance. This rough balance is likely to break down after an aqua planet has become a land planet, because the mantle may still be wet and outgassing may still be considerable, but the subduction of hydrous minerals is probably restricted to locations near the poles. Thus, water outgassing would be a potential hazard to the future habitability of the land planet over long timescales. However, while the aqua planet is losing its hydrogen in the moist greenhouse state, it is possible that the imbalance goes in the other direction, as the generally warm, wet climate of the moist greenhouse would likely promote weathering reactions and possibly promote the subduction of hydrous minerals. Thus, we believe it probable that the geologic water cycle would aid rather than subvert the transition of a suitable planet from aqua to land modes.

Stars of different spectral types evolve differently from the Sun. In particular, the luminosity evolution of stars of later spectral type (late G dwarfs, K dwarfs, and M dwarfs) is slower than in the Sun. These stars are fainter than the Sun and hence the HZ is closer to these stars than to the Sun. The ratio of EUV radiation to luminosity is about the same for K stars as for G stars, and the ratio is higher for most M stars (Lammer et al. 2009). Hence, these stars are at least as effective at driving hydrogen escape as a Sun-like star, and so we would expect similar or faster rates of hydrogen escape for an HZ planet around these other stars. The slower rate of luminosity evolution means that there is more time available for escape to take place before the moist greenhouse becomes a runaway greenhouse, and therefore we expect that late-type stars are more favorable to a planet making a continuously habitable transition from aqua state to land state. We will quantitatively investigate the evolution path from the aqua planet mode to the land planet mode for stars of different spectral types in a subsequent paper.