Dust Shells Around Carbon Mira Variables

The spectral energy distributions and mid-infrared spectra of 44 carbon Mira variables are fitted using a dust radiative transfer model. The periods cover the entire range observed for carbon Miras. The luminosities are calculated from a period-luminosity relation. Parameters derived are the distance, the dust mass loss rate and the ratio of silicon carbide to amorphous carbon dust. The total mass loss rate is derived from a modified relation between the photon momentum (L/c) and the momentum in the wind (M υ∞). Mass loss rates between 1 × 10−8 and 4 × 10−5 M⊙ yr−1 are found. We find good correlations between mass loss rate and pulsation period, and mass loss rate and luminosity. The dust-to-gas ratio appears to be almost constant up to periods of about 500 days, corresponding to about 7900 L⊙, and then to increase by a factor of 5 towards longer periods and higher luminosities. A comparison is made with radiation-hydrodynamical calculations including dust formation. The mass loss rates predicted by these models are consistent with those derived in this paper. The main discrepancy is in the predicted expansion velocities for models with luminosities below ∼5000 L⊙. The radiation-hydrodynamical calculations predict expansion velocities which are significantly too large. This is related to the fact that these models need to be calculated with a large C/O ratio to get an outflow in the first place. This is contrary to observations. It indicates that a principle physical ingredient in these radiation-hydrodynamical calculations is still missing. Possibly the winds are ‘clumpy’ which may lead to dust formation on a local scale, or there is an additional outwards directed force, possibly radiation pressure on molecules.