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 pulsation periods of these stars cover the entire range observed for carbon Miras. The luminosities are derived from a period-luminosity relation. Parameters derived are the distance, the temperature of the dust at the inner radius, 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 transfer rate (L/c) and the momentum transfer rate of the wind (Ṁv∞). 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 (log Ṁ = 4.08 log P - 16.54), and between mass-loss rate and luminosity (log Ṁ = 3.94 log L - 20.79). These relations are not independent, as we assumed a P-L relation. If we had assumed a constant luminosity for all stars, there still would be a significant relation between Ṁ and P. The dust-to-gas ratio appears to be almost constant up to periods of about 500 d, 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. Such a large C/O ratio is contrary to observational evidence. It indicates that a principal 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.