2001A&A...368..969S

Using a detailed radiative transfer analysis, combined with an energy balance equation for the gas, we have performed extensive modelling of circumstellar CO radio line emission from a large sample of optically bright carbon stars, originally observed by Olofsson et al. (1993ApJS...87..267O). Some new observational results are presented here. We determine some of the basic parameters that characterize circumstellar envelopes (CSEs), e.g., the stellar mass loss rate, the gas expansion velocity, and the kinetic temperature structure of the gas. Assuming a spherically symmetric CSE with a smooth gas density distribution, created by a continuous mass loss, which expands with a constant velocity we are able to model reasonably well 61 of our 69 sample stars. The derived mass loss rates depend crucially on the assumptions in the circumstellar model, of which some can be constrained if enough observational data exist. Therefore, a reliable mass loss rate determination for an individual star requires, in addition to a detailed radiative transfer analysis, good observational constraints in the form of multi-line observations and radial brightness distributions. In our analysis we use the results of a model for the photodissociation of circumstellar CO by Mamon et al. (1988ApJ...328..797M). This leads to model fits to observed radial brightness profiles that are, in general, very good, but there are also a few cases with clear deviations, which suggest departures from a simple r^–2 density law. The derived mass loss rates span almost four orders of magnitude, from ∼5x10^–9M_☉/yr up to ∼2x10^–5M_☉/yr, with the median mass loss rate being ∼3x10^–7M_☉/yr. We estimate that the mass loss rates are typically accurate to ∼50% within the adopted circumstellar model. The physical conditions prevailing in the CSEs vary considerably over such a large range of mass loss rates. Among other things, it appears that the dust-to-gas mass ratio and/or the dust properties change with the mass loss rate. We find that the mass loss rate and the gas expansion velocity are well correlated, and that both of them clearly depend on the pulsational period and (with larger scatter) the stellar luminosity. Moreover, the mass loss rate correlates weakly with the stellar effective temperature, in the sense that the cooler stars tend to have higher mass loss rates, but there seems to be no correlation with the stellar C/O-ratio. We conclude that the mass loss rate increases with increased regular pulsation and/or luminosity, and that the expansion velocity increases as an effect of increasing mass loss rate (for low mass loss rates) and luminosity. Five, of the remaining eight, sample stars have detached CSEs in the form of geometrically thin CO shells. The present mass loss rates and shell masses of these sources are estimated. Finally, in three cases we encounter problems using our model. For two of these sources there are indications of significant departures from overall spherical symmetry of the CSEs. Carbon stars on the AGB are probably important in returning processed gas to the ISM. We estimate that carbon stars of the type considered here annually return ∼0.05M_☉ of gas to the Galaxy, but more extreme carbon stars may contribute an order of magnitude more. However, as for the total carbon budget of the Galaxy, carbon stars appear to be of only minor importance.