3 Discussion

In Fig. 3, we examine the predicted synthetic spectra based on the model photospheres, which are essentially the same with those discussed before (Tsuji 1978) except that the photosphere is now assumed to be spherically symmetric rather than plane-parallel. Also, the opacity data are largely updated by the use of the HITEMP linelist, whose loggf values agree with those by Schwenke & Partridge (1997) within 0.05dex. The weak absorption features in the models of $T_{\rm eff}$ between 4000 and 3400K are due to high excitation tails of the CO fundamental bands whose band origin is at 4.6$\mu$m. H₂O features appear first in the model of $T_{\rm eff} = 3300$K and strengthen in the model of $T_{\rm eff} = 3200$K. On the other hand, $T_{\rm eff}$'s of the early M giant stars (M0-M3.5) are between 3600 and 4000K as shown in Table 1. However, H₂O features can never be predicted from the models of $T_{\rm eff} = 3600 {-} 4000$K. Does this imply that our classical model photospheres are so useless?

It is true that model photospheres of cool stars are not yet perfect. However, stellar photospheres can be relatively well modeled based on few ad-hoc assumptions except possibly for the treatments of convection and turbulence, and there is no reason why cool stars are exception only if molecular opacities are properly taken into account. In fact, the present model photospheres of red giant stars have been tested by the fact that the empirical effective temperature scale and the predicted one based on our models show reasonable agreement as noted in Sect.1. We believe that the photosphere of red giant stars can be modeled at least approximately within the framework of the so-called classical assumptions and that the model photospheres of cool stars cannot be so wrong as to not able to predict the major molecular features originating in the photosphere. However, we should notice that the stellar atmosphere, which represents all the observable outer layers, could not necessarily be represented by the model photosphere. In other words, it should still be possible that some new component remains unrecognized in the atmosphere of red giant stars beside the known ones including the photosphere, chromosphere and wind.

One possibility may be to assume the presence of large starspots, but such large starspots should give noticeable effects on other observables such as the spectral energy distributions, spectra, variabilities, activities etc. However, we know little evidence for such effects in the normal red giant stars. Another possibility is to assume that the red giant stars are veiled by a cloud of water vapor. In fact, we found clear evidence for such a case in the M supergiant star $\mu$ Cep (M2Ia) by detecting the H₂O 6.3$\mu$m bands in emission on the ISO spectrum (Tsuji 2000) and by confirming the 1.4 and 1.9$\mu$m bands in absorption on the Stratoscope data (Tsuji 2000). In another M supergiant star $\alpha$ Ori, the H₂O 6.3$\mu$m bands appear in absorption (Tsuji 2000) and also absorption lines due to the H₂O pure-rotation transitions were detected by the high resolution ground-based spectroscopy (Jennings & Sada 1998). The nature of water in the red giant stars is rather similar to that in the red supergiant stars (e.g. $T_{\rm ex} \approx 1500$K in the both cases), and we propose that the similar model of a rather warm molecular sphere (MOLsphere) as for supergiants should be applied to the normal red giant stars.

In this connection, it is interesting that the molecular cloud referred to as "CO-mosphere'' was found recently in the Sun by detecting CO emission beyond the solar limb (Solanski et al. 1994). Thus, the presence of the rather warm molecular sphere (MOLsphere) may be a common phenomenon in late-type stars including the Sun, red giants and supergiants, and we hope that future detailed studies of the MOLsphere as well as of the CO-mosphere will clarify the physical basis of such a phenomenon. Also, high excited water gas around very cool (super)giants has been known from water masers for a long time (Knowles et al. 1969). But it now turns out that such warm water gas already exists in the late K and early M giants even though H₂O masers are not observed. This fact implies that the cradle for maser activity may have already been germinating in K and M giant stars.

So far, the presence of the hot chromosphere ( $T \approx 10^{4}$K) is known in K and M giant stars but no evidence for the solar-type corona (Linsky & Haisch 1979). On the other hand, steady stellar wind already starts in K giant stars (Reimers 1977), but the origin of the wind is unknown yet. Recently, high sensitive infrared survey with the ISO (ISOGAL) revealed that efficient dust formation already starts in red giant stars with weak mass-loss rates (Omont et al. 1999). An interesting possibility is that the outer part of the MOLsphere is cool enough for dust to form, and this may explain why dust formation starts in the red giant stage prior to the AGB phase. Further, dust formed this way may be pushed outward by the radiation pressure and thus may explain the onset of the wind. This is of course not a solution to the origin of the dust and/or of the wind so long as the origin of the MOLsphere is unknown. But now it appears that the atmosphere of red giant stars is composed of the newly recognized MOLsphere in addition to the previously known photosphere, chromosphere and wind. With this new component, a more unified picture and self-consistent theory for the atmospheric structure of red giant stars could be developed.