THE INNER EDGE OF THE HABITABLE ZONE FOR SYNCHRONOUSLY ROTATING PLANETS AROUND LOW-MASS STARS USING GENERAL CIRCULATION MODELS

Following Kepler's third law, the orbital period P is a function of orbital semimajor axis a and the stellar mass M_⋆:

$$\begin{eqnarray}&&P\;(\mathrm{years})={\left[\displaystyle \frac{a{(\mathrm{au})}^{3}}{{M}_{\star }/{M}_{\odot }}\right]}^{1/2}.\end{eqnarray} \tag{ 1 }$$

The stellar flux incident on a planet, F_P, compared to the flux on Earth (F_⊕) can be written as:

$$\begin{eqnarray}&&{F}_{P}/{F}_{\oplus }=\displaystyle \frac{{L}_{\star }/{L}_{\odot }}{{a}^{2}}\end{eqnarray} \tag{ 2 }$$

where L_⋆/L_⊙ is the luminosity of the star with respect to the bolometric luminosity of the Sun. Combining these two equations, the orbital period can be written as:

$$\begin{eqnarray}&&P\;(\mathrm{years})=\left[{\left(\displaystyle \frac{{L}_{\star }/{L}_{\odot }}{{F}_{P}/{F}_{\oplus }}\right)}^{3/4}\right]{[{M}_{\star }/{M}_{\odot }]}^{-1/2}.\end{eqnarray} \tag{ 3 }$$

This equation indicates that the orbital period of a planet in synchronous rotation can be calculated from the luminosity, mass and the incident flux, and it cannot be chosen irrespective of the stellar type. This result is obvious, and not new, but it has significant implications for where the inner edge of the HZ is located. Moreover, for a star with a fixed effective radiating temperature, T_eff, stellar luminosity depends on the metallicity of a star (Chabrier & Baraffe 2000; Dotter et al. 2008, see Figure 2(a)) because of changes in the opacity of the stellar atmosphere. So the HZ also varies as a function of stellar metallicity (Young et al. 2012). In this srudy, we used the Dartmouth stellar evolution database (Dotter et al. 2008)¹¹ to obtain L_⋆ and M_⋆ for both low ([Fe/H] = −0.5) and high ([Fe/H] = 0.3) metallicities, as a function of T_eff. For convenience, we parameterized the relationship between T_eff, M_⋆, and L_⋆ and provided the coefficients in Table 1 ¹² :

$$\begin{eqnarray}&&y=a+{bx}+{{cx}}^{2}+{{dx}}^{3}+{{ex}}^{4}+{{fx}}^{5}\end{eqnarray} \tag{ 4 }$$

Here, y can be either M_⋆/M_⊙ or L_⋆/L_⊙, and x is T_eff. These relations apply only for stars with 3300 ≤ T_eff ≤ 4500 K, as we are focused on low-mass stars which may have synchronously rotating planets near the inner edge of their HZs. The lower limit of 3300 K is based on the completeness of the Dartmouth model grid for our chosen parameters.

One can calculate a range of orbital periods using Equation (3), substituting the values for M_⋆/M_⊙ and L_⋆/L_⊙ obtained from Equation (4), assuming a given F_P/F_⊕.

For a 3400 K star, using Equation (4), the corresponding stellar luminosity and mass are 0.0049L_⊙ and 0.189M_⊙, respectively, for the low-metallicity case, 0.0204L_⊙ and 0.416M_⊙ for the high-metallicity case. A high metallicity star has a higher mean atmospheric opacity, so for a certain stellar mass and age, a given optical depth is higher in the atmosphere and therefore at a lower temperature (lower T_eff). To match the same T_eff as a lower metallicity star (as is done here), the higher metallicity star (at a given age) must be more massive, increasing the overall stellar energy output and therefore T_eff. If one assumes P = 60 days in Equation (3), the corresponding stellar fluxes are 0.165F_⊕ for [Fe/H] = −0.5, and 0.406F_⊕ for [Fe/H] = 0.3. These fluxes are much lower than the value used by Yang et al. (2014) at the inner HZ; indeed, they are substantially lower than that of present day Earth. Thus, a planet with P = 60 days around a T_eff = 3400 K is more likely to have a frozen surface than to be at the precipice of a runaway.

One can calculate a consistent orbital period from Equation (3), assuming an inner HZ flux of 1.626F_⊕ calculated from Yang et al. (2014) for a 3400 K star. Then, the orbital period that the planet should have is 10.79 days for [Fe/H] = −0.5, and 21.21 days for [Fe/H] = 0.3, both much shorter than the 60 days period assumed by Yang et al. (2014). We performed simulations at both of these orbital periods. For the 10.79 days period, the planet warms rapidly and no converged solution is found. By contrast, the 21.2 days case and the (unphysical) 60 days case remain climatologically stable (Figure 1). Both the 21.2 and 60 days simulations exhibit similar climatological characteristics, with planetary albedos of 0.54 and mean surface temperatures in the upper end of 270 K. While the 10.79 days case is not quite a "fast" rotator like Earth, the increased rotation rate alters dynamics such that some of the substellar cloud deck is advected to the anti-stellar side of the planet, lowering the planetary albedo, and causing the planet to become much warmer than in the slowly rotating cases.

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For slower rotation rates (P > 20 days), thick substellar clouds produce a large planetary albedo, which stabilizes the climate against strong solar radiation. However, as P approaches ∼10 days, the sub-stellar cloud decks begins to be smeared around the planet, resulting in a reduced albedo on the substellar hemisphere, and thus rapidly rising temperatures. The simulation with P = 10.79 days experiences numerical instability after only a few years, with a residual energy imbalance of >10 Wm⁻². While stable climates may lie beyond the numerical limits of our model, such atmospheres surely are excessively hot.

One can derive a range of orbital periods that is self-consistent with incident flux (Equation (3)), using the luminosities and masses from Table 1 for different [Fe/H]. Figure 2 shows the correct orbital periods calculated using Equation (3) that one should use, if one assumes an inner HZ flux F_P/F_⊕ from the slow-rotator equation of Yang et al. (2014) for different stars. Also shown are the P = 60 days periods assumed by Yang et al. (2014) (blue filled circles), and the results from our own simulations for a T_eff = 3400 K star using the correct orbital periods (10.8 and 21.2 days, blue cross and square, respectively) from Equation (3) to illustrate the differences. The unstable 10.8 days and the stable 21.2 days solutions indicate that, for this T_eff = 3400 K, the correct inner HZ limit should lie somewhere in between these two orbital periods.

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To determine an inner HZ limit that is self-consistent with the calculated orbital periods, we followed the procedure described below for each star with T_eff = 3300, 3700, 4000, 4500 K. The lower limit of 3300 K pushes across the edge of the Dartmouth model grid in some parameters, so we limit our simulations to values above this T_eff. We first calculated the appropriate values of L_⋆/L_⊙ and M_⋆/M_⊙ from Equation (4) for that T_eff, and then chose a range of F_P (in Wm⁻²) to calculate the corresponding orbital periods for these F_P. Then, we performed climate simulations at these P and F_P values using CAM, assuming synchronous rotation, BB spectral energy distribution (SED) from the star, and zero planetary obliquity. We assumed, as did Yang et al. (2014), that the last converged solution represents the inner edge of the HZ. The SEDs used in our models are given in Table 2.

In this section we discuss the large-scale atmospheric dynamics of synchronously rotating planets. We examine simulations with a stellar effective temperature of 3300 K at the correct orbital period of 9 days which is self-consistent with the assumed incident flux, and for the 60 days period, which is not self-consistent. As the planets are assumed to be synchronously rotating, such that the orbital period equals the period of rotation for the planet, we focus on the dynamical contribution toward the reduction in cloud cover caused by these differences in rotation rate.

Figure 3 shows the latitude-longitude contour plots for three simulations of planets around a T_eff = 3300 K star, centered on the substellar point. The first column uses a 60 days rotation period, as used by Yang et al. (2014), to define the inner edge of the HZ for slow rotators. The second and third columns show contour plots for stable simulations using physically consistent orbital period and solar insolation relationships for both high and low stellar metallicity cases, respectively. For each simulation, the incident flux, rotation rate, mean surface temperature and albedo are listed above each column. While the incident stellar flux is different for each case, the resultant global mean surface temperatures are roughly similar. The key difference between each case is the modification of the cloud albedo as a function of rotation rate. Reducing the rotation rate from 60 to 9 days, decreases the top-of-atmosphere (TOA) albedo by ∼25%.

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Vigorous convection occurs over the substellar point in each of the three cases. Column-integrated cloud water and cloud fractions are expectedly large, as substellar convection lofts water into the free troposphere, creating high upper atmosphere relative humidities and thick convective water clouds, much like in Earth's tropics today. However, the important differences lie in the details. As the rotation rate of the planet increases from 60 to 16.46 to 9 days for high and low metallicity stars, respectively, the beginnings of a dynamical regime change become evident. This dynamical transition has previously been found by other studies for both highly irradiated and cool planets of different rotation rates (Heng & Vogt 2011; Showman et al. 2013a; Carone et al. 2014; Kaspi & Showman 2015). While all cases maintain strong sub-stellar convection, gradually increasing the rotation produces a corresponding increase in the strength of the zonal winds (Figures 4, 5). Stronger upper level zonal winds begin to smear the clouds into a narrow equatorial band that can stretch around the entire planet. The 500 mb relative humidity (and thus water vapor) closely mirrors the distribution of clouds. The areal extent of clouds over the substellar hemisphere is reduced, most noticeably along the western flank of the sub-stellar point. Increased upper level winds advect clouds eastward, away from their formation region above the sub-stellar point. This reduces the overall fractional cloud cover on the sunlit side of the planet, decreasing the TOA albedo, and thereby warming the climate. Thus, with a 9 days rotation rate, it takes ∼26% less solar flux to maintain an equal global mean surface temperature compared to the 60 days rotation case.

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Note also that cloud fractions remain high (∼100%) on the anti-stellar side of the planet, despite there being little to no convective activity, nor cloud water. On the anti-stellar side, the complete absence of solar surface heating, combined with substellar-to-antistellar atmospheric heat redistribution aloft, creates strong inversions, similar in nature to those that occur during the polar night on Earth. Here, a uniform, thin ice fog extends from the surface up to the inversion cap near 800 mb across the entire night side of the planet. Cloud fractions are near unity, but the clouds contain exceedingly little water and interact only very weakly with the thermal emission from the planet.

Global average temperature and horizontal wind for T_eff = 3300 K low metallicity, 9 and 60 days simulations are shown in Figure 4. Surface temperature and winds are shown in the left column of Figure 4, with inflow along the equator and from the poles into the substellar point at the center. Upper atmosphere temperature and winds at the 200 hPa surface are shown in the right-hand column of Figure 4, with strong zonal westerly flow aloft in the 9 days case and much weaker turbulent flow in the 60 days case. Differences between these cases show up to 4 K of surface warming at the substellar point and more than 10 K along the equator when the rotation rate is increased. Warming of about 4 K also occurs aloft in a gyre near the antistellar point. This warming occurs as a result of a transition from the stabilizing cloud feedback described by Yang et al. (2013) to a banded cloud structure that allows a larger stellar flux incident on the surface. The direction and magnitude of surface winds are similar between the 9 and 60 days cases, but the pattern of winds aloft differs significantly, with the 9 days case displaying strong upper-level flow that generates a banded cloud structure.

This shift in upper level flow is also apparent in the time-averaged zonal mean zonal wind shown in Figure 5. The 9 days case shows strong westerly flow aloft at all latitudes, with two jets prominent at midlatitudes and weaker easterlies along the surface. By comparison, the 60 days case shows weaker westerly flow aloft only at tropical latitudes, with easterly jets in the upper atmosphere toward the poles and extremely weak surface winds. This weaker flow in the 60 days case provides part of the physical process by which a stabilizing cloud feedback can be maintained; however, the stronger flow when the rotation rate is increased to 9 days inhibits the maintenance of this cloud structure.

The mean zonal circulation (MZC) and mean vertical wind for these T3300 (i.e., T_eff = 3300 K simulations are shown in Figure 6. Rising motion with the MZC and upward vertical wind is apparent at the substellar point, with regions of sinking in the vicinity of the antistellar point. Both of these cases show that the MZC spans the full hemisphere from substellar to antistellar point, which is expected because the orbital periods of all our cases are greater than the critical period P_c where a dynamical regime shift would occur (Edson et al. 2011; Carone et al. 2014). The 60 days case shows a stronger zonal circulation than the 9 days case, with greater rising motion at the substellar point and sinking motion at the antistellar point. The symmetry of the MZC and associated rising motion in the 60 days case also suggests a symmetric formation for clouds aloft, while the asymmetry observed in the 9 days case corresponds to the formation of banded clouds.

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The cross-polar circulation is shown in Figure 7. This circulation pattern is obtained by subtracting the zonal mean from all zonal wind vectors (Joshi et al. 1997; Haqq-Misra & Kopparapu 2015), which helps to illustrate the complex three-dimensional patterns that form the general circulation of synchronous rotators. Both cases show flow across the pole at both the 800 hPa and 200 hPa surfaces, although the direction of this flow varies with each experiment. Both cases also display vortices near 0°–30° longitude that contribute to a unique circulation pattern not easily described by the MZC or the mean meridional circulation. This cross-polar circulation is stronger in the 9 days case, both an aloft and along the surface, while the 60 days case shows a relatively similar flow pattern but with a reduced magnitude. The increase in cross-polar flow when rotation rate changes from 60 to 9 days also provides a mechanism that would disrupt the formation of a stabilizing cloud feedback above the substellar point.

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Figure 8 shows our new inner HZ boundary for stars with 3300 K ≤ T_eff ≤ 4500 K. We show the limits for both low (red) and high (green) [Fe/H] cases. The red curve is farther away from the star because, for a given stellar T_eff, the low-metallicity star is brighter (see discussion below). For comparison, we also plotted the inner HZ limit from Yang et al. (2014) (blue) for their 60 days rotator case. These results indicate that the inner edge of the HZ is closer to the star than predicted by Yang et al. (2014) for 3700 K ≤ T_eff ≤ 4500 K. This is true for both the high and low [Fe/H] cases, though the difference between these two [Fe/H] is minimal. For stars with T_eff ≤ 3700 K, although the low and high [Fe/H] cases diverge dramatically from each other, with the high [Fe/H] case (green) staying closer to the Yang et al. (2014) inner edge limit (blue). We have also shown several currently confirmed exoplanets on this plot.

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The reason for this large divergence between the two stellar metallicity cases can be traced to the differences in the stars' luminosities and planetary rotation rates. Figure 8(a) illustrates this point. The difference between L_⋆/L_⊙ for [Fe/H] = 0.3 (blue) and −0.5 (red) is largest at lower T_eff, and that is precisely where we see the divergence in our inner HZ result. The difference in log[L_⋆/L_⊙] for the two metallicities is ≈30% at T_eff = 3300 K. To receive the same amount of incident F_P around a low luminosity star, a planet that is in synchronous rotation needs to be at a shorter P (fast rotator), according to Equation (3), compared to a high luminosity one. As discussed before, fast rotating planets have stronger Coriolis force, which tends to create more banded cloud formations that reduce the planetary albedo. Furthermore, stars with lower T_eff output more flux in the near-infrared (IR) part of the SED. As terrestrial planets at the inner edge of the HZ are expected to have increasing amounts of water vapor in their atmospheres, and as H₂O is a good near-IR absorber, a small increment in the stellar flux around these low T_eff stars would push the planet close to the runaway greenhouse limit. Hence, the inner edge of the HZ is further away around these cool stars.

For stellar effective temperatures greater than 3700 K, we find that the inner edge of the HZ occurs at stellar fluxes up to 20% larger than shown by Yang et al. (2014). This result was unexpected, as in this regime orbital periods in the HZ remain firmly within the slow-rotating regime, and there is little difference between our model and theirs in the mean state of the climate. In fact, for T_eff = 4500 K, we find self-consistent orbital periods at the inner edge of the HZ of 55.31 and 64.1 days for low- and high-metallicity stars, respectively, bracketing the 60 days value used in Yang et al. (2014). However, the differences can be traced to subtle differences in the model configuration. Yang et al. (2014) used CAM3, while here we use CAM4 with an improved numerical algorithm for deep convection. With this patch, CAM4 is able to remain numerically stable at hotter temperatures, while keeping a relatively long model timestep (1800 s). To better understand this difference, we repeated simulations for 4500 K stellar effective temperature star using CAM3 without any numerical improvement to the deep convection scheme, but with an exceedingly short model timestep (100 s) to improve numerical stability. When we do this, we find similar results to those found with CAM4 using a longer timestep. Thus, there is no actual conflict between the results shown here and those shown in Yang et al. (2014) for T_eff > 3700 K; rather, it is an issue of model configuration and numerical stability. This point highlights why model intercomparisons are of the utmost importance.

Computational and numerical limitations prevent current Earth-derivative 3D climate models from exploring the full runaway greenhouse process, through surface temperatures beyond the critical point and the vaporization of the entire oceans. This has led to the so-called "last converged solution" criteria being used as a proxy for the inner edge of the HZ (Wolf & Toon 2014; Yang et al. 2014). While at first glance this criteria appears unsatisfying, the last converged solution may nonetheless be diagnostic of an imminent climatic state transition. Using CAM4 to study Earth (a rapid rotator), Wolf & Toon (2014) first found the last converged solution to have a global mean surface temperature of ∼313 K. However, in a subsequent study, using the same model but with improved numerics, Wolf & Toon (2015) showed that their previous assumed last converged solution was actually hovering just below the threshold of an abrupt transition into a hotter climate state.

In Figure 9, we summarize the global mean climates of our last converged solutions as a function of the stellar effective temperature. There is a definite trend in the global mean surface temperature of the last converged solution, with the last stable temperatures being significantly lower around 3300 K stars compared to 4500 K stars. This trend is caused by the interaction of different SEDs with atmospheric water vapor. Changes to the TOA albedo also display a trend, in this case linked most tightly to the rotation rate of the planet due to the dynamical modulation of the cloud fields, as is discussed in Section 3.2. SED does affect atmospheric scattering, with planets around bluer stars scattering more of the incident sunlight than those around redder stars; however this effect is relatively small at the atmospheric temperatures and pressures we consider in this study. Here, the TOA albedo is dominated by the clouds rather than by atmospheric scattering. As the rotation rate (Figure 9) falls to ∼10 days, a steep reduction in the TOA albedo is observed.

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To gain more insight into the problem, we must also consider what happens immediately beyond the last converged solution: the so-called "first unstable" simulation. The first unstable simulation is defined as that with the smallest value for the solar insolation where the simulation fails due to numerical instability. Beyond the last converged solution, our test planet is moved closer to the star, and thus towards higher stellar fluxes and slightly shorter rotational periods. Here, dynamical differences due to the change in rotation rate are not important, as the rotation rate only changes by several percent between the last converged and the first unstable simulations. The key driver is the input of solar energy. In Figure 10 we show vertical profiles of temperature, convection, and clouds for the substellar region of the planet for the last converged and first unstable simulations around T_eff = 3300 and 4500 K high-metallicity stars. Note, we show only profiles (and the mean) from the substellar region (the region forming an ellipse bounded by ±30° latitude and longitude from the substellar point), as this is where convection and clouds most strongly influence the energy budget of slow-rotating aquaplanets. While converged simulations of course reach equilibrium conditions, unstable simulations fail well before reaching equilibrium. For the first unstable simulations shown in Figure 10, we take results averaged over the last 30 days of simulations immediately before the point of failure.

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Increased solar input drives the water vapor greenhouse feedback. Increased atmospheric water vapor leads to increased solar absorption aloft, and thus reduces the mean lapse rate, noticeably below about 800 mb in Figure 10. This causes the substellar atmosphere to trend towards convective stability, reducing convection emanating from the substellar boundary layer (Figures 10(b), (f)) and thus suppressing the formation of the ubiquitous substellar cloud deck (Figures 10(c), (d), (g), (h)). A similar mechanism for radiatively driven convective stabilization of the lower atmosphere was proposed for rapidly rotating planets (Wordsworth & Pierrehumbert 2013; Wolf & Toon 2015). Strong solar absorption in the near-IR water wapor bands can stabilize the lower atmosphere and prevent boundary layer convection from occurring. However, while rapidly rotating planets may maintain climatological stability beyond this transition, the transition appears catastrophic for strongly irradiated synchronous rotators. At the last converged solution, the substellar cloud deck protects synchronous rotators from incendiary warming under immense stellar fluxes. Thus, even a small dent in the substellar cloud shield lets in a tremendous amount of solar radiation, strongly destabilizing climate. Note that this bifurcation about last converged and first unstable simulations is also illustrated in Figure 1.

While the triggering of climatic instabilities in the model is caused by increases to the total stellar flux, the trend in the temperatures of the last converged solution are traceable to differences in stellar effective temperature and thus the SED. The last stable temperature is much lower around lower T_eff stars due to the fact that redder SED interacts much more strongly with near-IR water vapor absorption bands. Thus, strong solar heating and subsequent convective stabilization around the substellar point can occur with less water vapor in the atmosphere and thus at lower mean surface temperatures around redder stars compared with bluer stars. The bifurcation between the last converged and first unstable simulations is very pronounced around 3300 K stars (Figure 10). However, the apparent bifurcation becomes more subtle as one moves towards higher stellar effective temperatures. Nonetheless, even for the 4500 K case, one can still clearly see that the first unstable simulation has less substellar convection and clouds than the last converged solution. This result agrees with the assertion of Kopparapu et al. (2013), that planets around low mass stars may skip over the moist greenhouse phase completely and instead move straight to the runaway phase, owing to stronger interactions with water vapor near-IR bands. Thus, planets around bluer stars may have additional stable climate states near the inner edge boundary.

In Section 3.3 we established new limits to the inner edge of the HZ based on the last converged solutions for stable climates. This criterion is intentionally taken to compare with inner HZ results for slow rotators in Yang et al. (2014). In Section 3.4 we argue that the last converged solutions lie just below the threshold of an abrupt climatic transition towards hotter states, whereupon the substellar cloud deck weakens considerably and strong solar radiation then heats the planet. However, we have not yet considered the potential for significant water-loss from our modeled atmospheres. Notably, water-loss to space from a moist greenhouse is believed to be the more conservative estimate for inner edge of the HZ, and essentially a limit to habitability, occurring at a lower stellar flux (and thus further from the star) than does a runaway greenhouse.

At first glance, Figure 9 appears to indicate that our model atmospheres located nearest the inner edge of the HZ are probably too cold to experience significant water-loss to space, all being below  310 K. Note that the canonical value for the mean surface temperature marking the moist greenhouse water-loss limit is 340 K in 1D models (Kasting et al. 1993; Kopparapu et al. 2013), and was recently found be to  350 K using CAM4 to simulate Earth under high stellar fluxes (Wolf & Toon 2015). In Figure 11 we show the model top (i.e., 3 mb) water vapor mixing ratio and the lifetime of the ocean against water-loss, assuming an initial water inventory equal to 1 Earth ocean (1.4 × 10²⁴ g H₂O). We assume diffusion limited escape from the upper most model layer, following Hunten (1973). The solid red and solid blue lines in the Figure 11(b) are the estimated main sequence lifetimes for high and low metallicity stars respectively. Interestingly, for nearly all our simulations that define the IHZ, even those with seemingly little water vapor in their upper atmospheres, the lifetime to lose an Earth ocean is approximately equal to or shorter than the main sequence lifetime of the host star. Of course, for M stars this timescale remains much larger than the current age of the universe, and thus is of little practical use for determining habitability.

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However, synchronous rotators around late-K stars have significant water vapor near the model top and thus can have rapid water-loss rates. Our last converged solutions around stars with T_eff = 4500 K can lose an Earth ocean in less than 1 Gyr (red and blue diamonds in Figure 11(b), left-top). Thus these atmospheres may not be habitable under the more stringent water-loss criteria. The inner edge of the HZ defined by water-loss is thus likely at a lower stellar flux for late-K stars, compared with that illustrated in Figure 8. These atmospheres undergo rapid water-loss at a surprisingly low global mean surface temperature, between 295 and 310 K. We postulate that strong substellar convection may be more effective at pumping water vapor into the high atmosphere, compared to tropical convection on a rapidly rotating world. However, there is much more work left to be done. Here, our model uses a relatively low model top, with poor resolution of the stratosphere. Furthermore, Yang et al. (2014), using CAM3 with an identical vertical resolution, found much lower water vapor mixing ratios in the upper atmosphere for an early (wet) Venus around the Sun. Future planned work will utilize a higher model top, with significantly improved vertical resolution, and will study a wider range of stellar fluxes.

Several studies have argued that terrestrial planets within the HZs of M-dwarfs may not be habitable, either because they could be deficient in volatiles (Lissauer 2007) or form dry as a result of inefficient water delivery (Raymond et al. 2007), if they formed in situ. If the planets migrate from the outer parts of the system, they accumulate massive H and He envelopes. Whether they are able to shed most of their H-rich envelopes and potentially become "habitable evaporated cores" depends on the mass of the solid core and the X-ray/UV-driven escape (Luger et al. 2015). Recently, Luger & Barnes (2015) pointed out that due to the extended pre-main sequence phase of M-dwarfs (∼100 Myr, Baraffe et al. 2015), where the star is more luminous than its main sequence phase, terrestrial planets in the (current) HZs of M-dwarfs could have been in runaway greenhouse during the pre-main sequence phase and may therefore be uninhabitable. This prolonged runaway greenhouse state may have removed water from a planet's atmosphere through photolysis, and may dessicate the planet. As a by-product, if the surface of the planet is not an efficient oxygen sink, the resulting oxygen from the photolysis may accumulate and can potentially generate an abiotically produced bio-signature (Luger & Barnes 2015). However, based on the combined results from planetary population synthesis and atmospheric water-loss models, Tian & Ida (2015) suggest a bimodel distribution of water contents for terrestrial planets around low mass stars. Earth-like water endowments may be rare, but dune and deep ocean worlds may both be common. Thus, the extended pre-main sequence phase of M-dwarfs does not unequivocally rule out the existence of ocean planets.