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 .
( ApJS , 87 , 267 ) .
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 .
( 1988 ) .
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 \sim 5 \times 10 ^ { -9 } M _ { \sun } yr ^ { -1 } up to \sim 2 \times 10 ^ { -5 } M _ { \sun } yr ^ { -1 } , with the median mass loss rate being 2.8 \times 10 ^ { -7 } M _ { \sun } yr ^ { -1 } .
We estimate that the mass loss rates are typically accurate to \sim 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 \sim 0.05 M _ { \sun } 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 .