The circumstellar dust envelopes of red giant stars. I - M giant stars with the 10-micron silicate emission band

Spherical dust envelope models of red giant stars are constructed by solving the radiative transfer equations of the generalized two-stream Eddington approximation. The IRAS observations of M giant stars which show the 10-micron silicate emission band in IRAS LRS spectra are explained by the models with the dirty silicate grains with K proportional to lambda exp -1.5 for lambda greather than 28 microns. Under the assumption of steady mass flow in the envelope, this model analysis gives the following conclusions: (1) the strength of the silicate emission peak at 10 microns is a good indicator of the mass loss rate of the star, (2) no stars with the 10-microns silicate emission feature are observed in the range of mass loss rate smaller than 7 x 10 to the -8th solar mass/yr, and (3) the characteristic time of the mass loss process of M stars does not exceed a few 10,000 years.