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 ((M) over dot v(infinity)). Mass-loss rates between 1 x 10(-8) and 4 x 10(-5) M. yr(-1) are found. We find good correlations between mass-loss rate and pulsation period (log (M) over dot = 4.08 log P-16.54), and between mass-loss rate and luminosity (log (M) over dot = 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 (M) over dot 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 similar to 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.