Theoretical studies of the infrared emission from circumstellar dust shells: the infrared characteristics of circumstellar silicates and the mass-loss rate of oxygen-rich late-type giants

We have modeled the infrared emission of spherically symmetric, circumstellar dust shells with the aim of deriving the infrared absorption properties of circumstellar silicate grains and the mass-loss rates of the central stars. As a basis for our numerical studies, a simple semianalytical formula has been derived that illustrates the essential characteristics of the infrared emission of such dust shells. A numerical radiative transfer program has been developed and applied to dust shells around oxygen-rich late-type giants. Free parameters in such models include the absorption properties and density distribution of the dust. An approximate, analytical expression is derived for the density distribution of circumstellar dust driven outward by radiation pressure from a central source. A large grid of models has been calculated to study the influence of the free parameters on the emergent spectrum. These results form the basis for a comparison with near-infrared observations. Observational studies have revealed a correlation between the near-infrared color temperature, Tc, and the strength of the 10 micrometers emission or absorption feature, A10. This relationship, which essentially measures the near-infrared optical depth in terms of the 10 micrometers optical depth, is discussed. Theoretical A10-Tc relations have been calculated and compared to the observations. The results show that this relation is a sensitive way to determine the ratio of the near-infrared to 10 micrometers absorption efficiency of circumstellar silicates. These results as well as previous studies show that the near-infrared absorption efficiency of circumstellar silicate grains is much higher than expected from terrestrial minerals. We suggest that this enhanced absorption is due to the presence of ferrous iron (Fe2+) color centers dissolved in the circumstellar silicates. By using the derived value for the ratio of the near-infrared to 10 micrometers absorption efficiency, the observed A10-Tc relation can be calibrated in terms of the total dust column density of the circumstellar shell and thus the mass-loss rate of late-type giants can easily be derived. Detailed models have been made of the infrared emission of three well-studied Miras: R Cas, IRC 10011, and OH 26.5+0.6, with the emphasis on the shape of the 10 micrometers emission or absorption feature. The results show that the intrinsic shape of the 10 micrometers resonance varies from a very broad feature in R Cas to a relatively narrower feature in OH 26.5+0.6, with IRC 10011 somewhere in between. Possible origins of this variation are discussed. The mass-loss rates from these objects are calculated to be 3 x 10(-7), 2 x 10(-5), and 2 x 10(-4) M Sun yr-1 for R Cas, IRC 10011, and OH 26.5+0.6, respectively. These results are compared to other determinations in the literature.