All Figures

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{8091fig1.eps}\end{figure}$ Figure 1: The CO₂ and H₂O pressure and the mean surface temperature of a habitable planet as a function of the orbital distance. The diagram gives $P_{{\rm CO}_2}$ and P $_{{\rm H}_2{\rm O}}$ (left y-axis) and T_S (grey, right y-axis) of an Earth-like planet across the inner part of the HZ around the present Sun. At orbital distances larger than $\sim$ 0.98 AU, T_S is assumed to be fixed at 288 K (its current value on Earth) by the carbonate-silicate cycle, which is obviously an idealized picture. Beyond 1.3 AU, CO₂ condenses in the atmosphere and the required level of CO₂ depends on the coverage by CO₂-ice clouds. The pressure of H₂O and $T_{\rm s}$ in the inner HZ is calculated for a cloud-free atmosphere and 50% cloud cover and assuming a reservoir of water that contains (as on Earth) more than the equivalent of 220 bars of H₂O.
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In the text

$\begin{figure} \par\includegraphics[width=16.8cm,clip]{8091fig2.eps}\end{figure}$ Figure 2: Plots showing the effect of the stellar effective temperature on the albedo. The graphs represent the reflected irradiance at the substellar point of a planet subject to the irradiation from a Sun-like star with $T_{\rm eff}=5800$ K ( top) and from an M-type star with $T_{\rm eff}=3200$ K, similar to Gl 581 ( bottom). In this illustration, both stars are assumed to radiate as black bodies. The graphs give the spectral irradiance of a planet receiving an integrated stellar flux of 1360 W m^-2 ( left) and 1500 W m^-2 ( right). The shaded curves with black-body shape give the irradiance of an airless planet with a fixed surface albedo of 0.15. The non-shaded spectra show the irradiance computed with Phoenix (Paillet 2006) when a cloud-free atmosphere is added. The current Earth atmosphere is shown on the left and a N₂-H₂O atmosphere with $T_{\rm s}=360$ K, $P_{\rm s}=1.3$ bar and $P_{\rm w}=0.5$ bar on the right. This illustrates the increase in the reflected energy with the stellar effective temperature.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{8091fig3.eps}\end{figure}$ Figure 3: The orbital region that remains continuously habitable during at least 5 Gyr as a function of the stellar mass. The darker area is defined by the empirical "early Mars'' and "recent Venus'' criteria. The light grey region gives the theoretical inner (runaway greenhouse) and outer limits with 50% cloudiness, with H₂O and CO₂ clouds, respectively. The dotted boundaries correspond to the extreme theoretical limits, found with a 100% cloud cover. The dashed line indicates the distance at which a 1 $M_{\oplus }$ planet on a circular orbit becomes tidally locked in less than 1 Gyr.
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In the text

$\begin{figure} \par\includegraphics[width=13.4cm,clip]{8091fig4.eps}\end{figure}$ Figure 4: Diagrams depicting the HZ around the Sun and Gliese 581. The grey areas indicate the theoretical inner edge for different fractional cloud covers. The width of each inner edge is defined by the runaway greenhouse and water loss limits. The thick lines give the inner and outer boundaries of the "empirical'' HZ, based on the non-habitability of Venus for the last 1 Gyr and the apparent habitability of Mars 4 Gyr ago. The dashed line gives the outermost theoretical limit of the HZ, found with a 100% CO₂ cloud cover. The upper diagram shows the limits computed for the Sun's properties. The lower diagram shows the limits computed for a 3700 K M-type star and scaled to the stellar luminosity of Gl 581 (for which $T_{\rm eff}=3200$ K). The limits marked with the symbol * are simply scaled to the luminosity and are thus slightly closer to the star - they are shown here because the wavelength dependency of the albedo has been explicitly computed only for thick and cloud-free H₂O- and CO₂-rich atmospheres. The albedo should be less sensitive to the stellar effective temperature in the presence of clouds. For the eccentric solution found by Udry et al. (2007), the orbits are confined within the grey bars about the marked planet locations.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{8091fig5.eps}\end{figure}$ Figure 5: Evolution of the ratio between the X-ray and bolometric luminosities as a function of age for stars of different masses. The solid lines represent semi-empirical laws, while symbols give observed values for G (+), K (*) and M ( $\diamond$ ) stars. The dashed line gives the upper limit for the value of $\log (L_{\rm X}/L_{\rm bol})$ in the case of Gl 581, for which there is no ROSAT detection.
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In the text