Potsdam Institute for Climate Impact Research (PIK), Telegrafenberg, P.O. Box 60 12 03, 14412 Potsdam, Germany.
A general modelling scheme for assessing the suitability for life on any Earth-like extrasolar planet is presented. This approach is based on an integrated Earth system analysis in order to calculate the habitable zone in main-sequence-star planetary systems. A new attempt by Lineweaver (2001) to estimate the formation rate of Earth-like planets over cosmological time scales is applied to calculate the average number of habitable planets in the Milky Way as a function of time. The combination of this results with our estimations of extrasolar habitable zones yields the average number of habitable planets over cosmological time scales. We find that there was a maximum number of habitable planets at the time of Earth's origin.
One prominent and still open question is whether life exist on other planets. Recent progress in astronomical measurement techniques has confirmed the existence of a multitude of extrasolar planets. Up to now nearly 100 planets have been observed around solar-type stars, where most of them are giant planets (see the exasolar planet catalog from the "The Extrasolar Planets Encyclopaedia"). The ultimate quest of extrasolar planet research is to identify Earth-like planets located in the habitable zone of their host stars. The habitable zone (HZ) is defined a s the region around a star within which a planet might enjoy moderate surface temperatures required for higher life forms. At present time, however, the detect ion of such Earth-like planets is still beyond technical feasibility. Therefore we are restricted to theoretical considerations in order to estimate the number of habitable Earth-like planets which could principally harbour life. The knowledge of two factors is crucial for this attempt. On the one hand it is necessary y to know the planet formation rate (PFR) of Earth-like planets, on the other hand the probability that the planet formed is habitable has to be assessed. Recent results of Lineweaver (2001) can be used to calculate PFR as a function of cosmological time. The extent of HZs for different types of main-sequence stars has been determined by different authors (e.g., Kasting et al., 1993; Forget and Pierrehumbert, 1997). In the following we apply our definition of habitability (Franck et al., 2000a, 2000b), that does not just depend on the parameters of the central star, but also on the properties of the planetary geodynamics. The calculation of the HZ for different central star masses allows us to determine the probability that an Earth-like planet is habitable. Finally it is possible to estimate the number of habitable planets in the Milky Way.
To estimate the planet formation rate, PFR, of Earth-like planets in the Milky Way an approach by Lineweaver (2001) has been followed- The PFR is derived from the star formation rate and star metallicity as an ingredient for the formation of Earth-like planets. The relation between metallicity and the probability of forming Earth-like planets is a so-called Goldilocks problem: if the metallicity is too low, there is not enough material to build Earth-like planets; if the metallicity is too high, there is a high probability of forming hot Jupiters. Taking all these effects into account, one can derive the time-dependent PFR. In Fig. 1 we show the PFR recalculated from Lineweaver (2001) and rescaled to the present star formation rate in the Milky Way of about one solar mass per year.
Fig. 1: Earth-like planet formation rate PFR (Lineweaver, 2001) of the Milky Way.
The number of Earth-like planets, P(t), can be calculated from the PFR with the help of a convolution integral. It depends on the probability that an Earth-like planet is in the habitable zone around a central star with mass M. In previous studies climatic constraints, e.g. the presence of liquid water at the planetary surface, have been used to assess the habitability of terrestrial planets around different t types of stars (Kasting et al., 1993). Our method (Franck et al., 2000b defines additional constraints: first, habitability is linked to photosynthetic activity and second, habitability is strongly influenced by the "geodynamics" of the Earth-like planet. To estimate these constraints for the determination of the inner and outer boundaries of the HZ we use our Earth system model (Franck et al, 2000a).
Fig. 2: Global carbon cycle regulating the global temperature on Earth.
It couples the increasing central star luminosity, the silicate-rock weathering rate, and the global energy balance to estimate the partial pressure of atmospheric carbon dioxide, the mean global surface temperature, and the biological productivity as function s of time (see Fig. 3). It resembles the idea of Lovelock (1989) about the Earth as an self-regulating system ("Gaia" hypothesis).
Fig. 3: Integrated Earth system model. The arrows indicate different forcings and feedback mechanisms.
The results for the estimation of the HZ of the solar system via the geodynamic model are summarised in Fig. 4, where we have plotted the width and position of the HZ for three different points in time (past, present, future). In about 500 Myr the inner boundary reaches the Earth distance from the Sun (R=1 AU) and the biosphere ceases to exist. The outer boundary, decreases in a strongly non-linear way.
Fig. 4: Habitable zone (green shading) for the solar system at three different time steps. The orbits of the three terrestrial planets, Venus, Earth and Mars are shown. The solid green line describes the evolution of the inner and outer boundary of the HZ.
In Fig. 5 the width and position of the HZ is plotted for three different central star masses, M=0.8, 1.0, 1.2 Ms over time, where Ms is one solar mass. First we can find that the width and the position of the HZ depend strongly on the mass of the central star. Furthermore, up to about 3.5 Gyr of cogenetic stellar and planetary evolution the outer boundary of the HZ is steadily increasing as a result of increasing central-star luminosity. After this point, the continental area has grown to such a size that weathering is very effective in bringing CO2 out of the atmosphere and decreasing the outer boundary of the HZ which finally joins the inner one. For 1.2 Ms central stars life would be limited to 4.9 Gyr after starting cogenetic evolution because the central star leaves the main sequence and becomes a red giant. For 0.8 and 1.0 Ms central stars this limitation appears up to 6.5 Gyr after starting cogenetic evolution because continental growth and decline in spreading rate force atmospheric CO2 content below 10-5 bar.
Fig. 5: Graphs of the width and position of the HZ derived from the geodynamic model for three different stellar masses M (0.8, 1.0, 1.2 Ms. tmax is the maximum life span of the biosphere limited by geodynamic effects. tH indicates the hydrogen burning time on the main sequence limiting the life span of more massive stars (Franck et al., 2001).
The result for the calculation of the number of habitable planets in the Milky Way is shown in Fig. 6.
Fig. 6: The number of habitable planets P(t) as a function of cosmological time for the Milky Way. The vertical dashed lines denote the time of Earth's origin and the present time, respectively.
P(t) has a distinct maximum at 8.5 Gyr after Big Bang. This is just before Earth's origin (t=8.8 Gyr). This supports the idea that interstellar panspermia (see, e.g., Weber and Greenberg, 1985; Horneck et al., 2001) might have caused a kick start to the processes by which life originated on Earth (von Bloh et al., 2002): there is palaegeochemical evidence of a very early appearance of life on Earth leaving not more than 1 Gyr for the emergence of life.
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