2. When a star leaves the main sequence to turn into a red giant, there clearly re- mains no HZ for an Earth-like planet. This limitation is relevant for stellar masses in the range between 1.1 and 2.2 M s . 3. In the stellar mass range between 0.6 and 1.1 M s the maximum life span of the biosphere is determined exclusively by planetary geodynamics, which is inde-
54 S. Franck et al. pendent (in a first approximation, but see limiting effect 4) from R . So we ob- tain the limitation t < t max . 4. There have been discussions about the habitability of tidally locked planets. We take this complication into account and indicate the domain, where an Earth- like planet on a circular orbit experiences tidal locking. That domain consists of the set of ( M,t ) couples which generate an outer HZ boundary below the tidal- locking radius. This limitation is relevant for M <0.6 M s . As an illustration we depict the HZ for R = 2 AU in Fig. 3.3. 3.3 Conclusions The question, whether an Earth-like planet discovered outside the solar system may accommodate life, can be answered with the help of Figs. 3.2 and 3.3 if the mass and age of the central star as well as the planet‘s orbit are known. This is only the present state of the art in theoretical modeling of HZ. There are of course a lot prerequisites for such calculations that have been summarized recently by Lissauer . Fig. 3.3 Shape of the HZ (dark grey) in the mass-time plane for an Earth-like planet with photo- synthesis at distance R = 2 AU from the central star. The potential overall domain for accommo- dating the HZ of planets at some arbitrary distance is limited by a number of R -independent factors that are explained in the text. (Figure slightly changed from Franck et al. , copyright by the American Geophysical Union).