5. Discussion and conclusions
Concerning the nature of these synthetic IRAS colours calculated from self-consistent models of dust-driven winds, several points need to be emphasized. First, in contrast to scalable models (e.g. Ivezi & Elitzur 1995) where e.g. the condensation temperature and the properties of the dust grains have to be specified or where the relation of important quantities like mass loss rates and outflow velocities to fundamental stellar parameters is uncertain due to simplifying assumptions and adjustable parameters of the models, we can calculate the entire dynamical structure of the outflow depending only on fundamental stellar parameters. Secondly, while the outer structure of the stellar mass loss visible in the colour can be represented by time-integrated properties the results of our dynamical models show that the fluxes generated much closer to the star are strongly influenced by short time dynamical phenomena like pulsations, shocks and time-dependent dust formation.
Comparing our self-consistent models with mass loss estimates like (e.g. Ivezi & Elitzur 1995)
reveals a number of basic differences. Here denotes the flux-weighted optical depth and the spatially integrated ratio between gravitational and radiative acceleration. In our models we have not assumed a certain condensation point but calculated the extended zone where dust particles condense and grow to their final sizes. It is difficult to define an appropriate inner boundary for the spatial integration. The value of clearly depends on this point and approaches unity as the boundary is shifted inwards. Furthermore the formula given above is derived for stationary outflows driven by radiation pressure neglecting the momentum input by stellar pulsations. Hence, our LPV models are not consistent with this kind of relation and we obtain negative values of for certain models. As demonstrated in Höfner & Dorfi (1997) the outflow velocities of the models show a good correlation with a quantity which characterizes the strength of radiation pressure on dust relative to gravitation whereas no such correlation is found for the mass loss rate or .
We want to express a general warning that fitting the observed quantities by an assumed stationary outflow can lead to severe problems because the variations in the fluxes occurring during a pulsational cycle are then extrapolated through the whole circumstellar envelope up to several thousand stellar radii. At large distances the stellar outflow becomes more and more stationary but the inner part of the wind zone is totally dominated by the time-dependence of the dust formation process. Hence, within a few photospheric radii the density, temperature and velocity structure is completely different from a stationary solution. Using stationary models may therefore result in relations between quantities characterizing the outflow (like mass loss rates and outflow velocities or dust-to-gas ratios) and intrinsic stellar properties (luminosity, mass, chemical abundances, etc.) which are seriously wrong.
Based on the IRAS observations it has been pointed out earlier (van der Veen & Habing 1988) that the location of an object in the IRAS two colour diagram represents basically the mass loss rate. Our theoretical models of dust driven winds support this conclusion and show that the specific stellar conditions (luminosity, stellar mass, carbon-to-oxygen ratio, etc.) causing a certain mass loss cannot be easily extracted from such a diagram because the mass loss rate depends on the stellar parameters in a complicated, non-unique way.
Concerning the simulations of detached shells and dust grains containing SiC we have demonstrated how the structure and composition of the dust envelope affects the position in this IRAS diagram.
© European Southern Observatory (ESO) 1997
Online publication: May 26, 1998