We present a detailed, self-consistent model of the radiatively driven winds which couples the radiative transfer and hydrodynamics equations. The circumstellar envelope, which consists of gas and dust, is described as a two-component fluid to account for relative drifts. The radiative transfer equation is treated in the moment form.

Our results show that steady-state outflows driven by radiation pressure on dust grains adequately describe the surroundings of late-type stars. Thanks to scaling properties, both the dynamics and the radiative transfer are fully characterized by , the flux averaged optical depth of wind. The region of parameter space where radiation pressure can support a given mass-loss rate is identified, and it shows that radiatively driven winds can explain the highest mass-loss rates observed to date. A new procedure to derive mass-loss rates from the observational data is introduced, and its results agree with other determinations. Theoretical predictions for the dust emission are in good agreement with observations. Observed spectra are associated with different and various grain materials, and a new method to determine from infrared observations is presented. We show that analysis of infrared spectral signatures provides constraints on the grains chemical composition and find that, in carbonaceous grains, the abundance of SiC grains is limited to 20-30%. Similarly, in mixtures of astronomical silicate and crystalline olivine, the abundance of olivine is limited to 20-30%.

We have devised a simple model showing howfields of broken clouds cause average photon path lengths to be grater than those predicted by homogeneous radiative transfer calculations of cloud/atmosphere ensemble with similar albedos, especially under and within the cloud layer. This one-sided bias is a contribution to the anomalous absorption. This model has been described by us previously and is reviewed here for clarity. We illustrate the model quantitatively with a numerical stochastic radiative transfer calculation. More than half the anomaly is explained, for the parameters used in the numerical example.

For dust heated only by the radiation field we show that the resulting spectral shape does not depend on the spatial dimensions of the underlying source and envelope. The only parameters that specify the radiative transfer are the overall optical depth and, unlike for plan-parallel geometry, the functional form of the dust spatial distribution. The properties of the central source enter only through its spectral shape and are not important at the infrared wavelengths considered here. Consequently, for a given dust chemical composition, the resulting spectrum is fully determined by the dust spatial distribution and overall optical depth. This conclusion is of great importance since objects of different nature are expected to have different dust spatial distributions, dependent mainly on whether the envelope is collapsing onto or expanding away from the central source. Thus, detailed radiative transfer modeling can provide efficient methods to determine the amount of dust, its chemical composition and the nature of the object which emitted the observed spectrum.

Our models show that observations obtained by the Infrared Astronomical Satellite (IRAS) can indeed be interpreted in terms of the overall optical depth and dust spatial distributions. Preliminary comparison with results obtained for some sources by other methods verify the basic premises and show that reliable classification of all sources observed by IRAS is feasible.