Abstract
Habitable conditions are important environmental indicators of extrasolar planet. One important habitability con-dition is stability of liquid water for geological timescale. Tajika and Matsui (1990)(1) show stabilization of the sur-face temperature by carbon cycle against the increase of solar radiation with Sun's evolution. Kasting et al.(1993)(2) obtain the range of orbital radii for the continuously habitable planets con-sidering both the carbon cycle and the runaway greenhouse effect.
The atmospheric temperature depends on the incident energy flux and the greenhouse effect in the atmosphere. The amount of carbon dioxide, which is an important greenhouse gas, in the atmos-phere depends on the balance between fluxes of degassing and fixation as car-bonates. Hence, the large degassing flux results in strong greenhouse effect, and warm environment. The degassing rate depends on thermal history, which is dependent on the planetary size. Thus, planetary radius affects the evolution of the atmospheric temperature. However, the size dependence of the habitability condition is not well discussed yet.
Here, we investigate the planetary size dependence of the stability of liq-uid water over geological time scale by examining the length of the period while the surface temperature is kept above freezing. Since the solar flux in-creases with the Sun's evolution, the degassing rate of CO2 required for keep-ing the surface temperature decreases with time. On the other hand, owing to planetary cooling, the degassing rate decreases with time. Thus, on a rapidly cooling planet, namely a small planet, the degassing rate decreases below the critical value that is required for keeping the surface temperature. In the fol-lowing, we define the "lifetime" of a habitable planet as the period while the surface temperature is kept above a certain reference temperature. For sim-plicity, we assume that the atmospheric and the surface temperatures are the same. We consider 3 reference surface temperatures: 15C which is annually and globally averaged temperature on the present Earth, 5C, and the standard tem-perature 25C . Using simple expressions of the thermal evolution and degassing rate, the greenhouse warming, and the carbonate formation rate, we investigate the dependence of the lifetime of plan-ets on the planetary size and orbital radius.
As the result, lifetime has a linearly relation to planetary radius. And the dependence of lifetime on incident en-ergy flux is stronger than the linear relation. We investigate requirements for stability of liquid water during 4.5 billion years. Planetary radius is larger than the Mars-size for the re-quirements and orbital radius is smaller than 1.12AU when planetary radius is Mars-size. The model in this time has a large uncertainty. And we estimate the requirements without considering temper-ature distribution from north to south and the other greenhouse effect like de-pendance of CO2 column abundance in the atmosphere. The next step is to clarify the effect of these factors on the life-time of the planet.
(1)Tajika, E. and Matsui, T.(1990):The evolution of the terrestrial environ-ments. In "Origin of the Earth"(Newsoms, M. E. and Jones. H. eds.), Oxford Univ. Press, pp.347-370
(2)Kasting, J. F., Whitmire, D. P., Reynolds, R. T.(1993):Habitable Zones a-round Main Sequence Stars, Icarus, 101, 108-128, 1993
