The mass-loss return from evolved stars to the Large Magellanic Cloud III. Dust properties for carbon-rich asymptotic giant branch stars

We present a radiative transfer model for the circumstellar dust shell around a Large Magellanic Cloud (LMC) long-period variable (LPV) previously studied as part of the Optical Gravitational Lensing Experiment (OGLE) survey of the LMC. OGLE LMC LPV 28579 (SAGE J051306.40-690946.3) is a carbon-rich asymptotic giant branch (AGB) star for which we have Spitzer broadband photometry and spectra from the SAGE and SAGE-Spec programs along with broadband UBVIJHK(s) photometry. By modeling this source, we obtain a baseline set of dust properties to be used in the construction of a grid of models for carbon stars. We reproduce the spectral energy distribution of the source using a mixture of amorphous carbon and silicon carbide with 15% SiC by mass. The grain sizes are distributed according to the KMH model, with gamma = 3.5, a(min) = 0.01 mu m and a(0) = 1.0 mu m. The best-fit model produces an optical depth of 0.28 for the dust shell at the peak of the SiC feature (11.3 mu m), with an inner radius of about 1430 R-circle dot or 4.4 times the stellar radius. The temperature at this inner radius is 1310 K. Assuming an expansion velocity of 10 km s(-1), we obtain a dust mass-loss rate of 2.5 x 10(-9) M-circle dot yr(-1). We calculate a 15% variation in this mass-loss rate by testing the sensitivity of the fit to variation in the input parameters. We also present a simple model for the molecular gas in the extended atmosphere that could give rise to the 13.7 mu m feature seen in the spectrum. We find that a combination of CO and C2H2 gas at an excitation temperature of about 1000 K and column densities of 3 x 10(21) cm(-2) and 10(19) cm(-2) respectively are able to reproduce the observations. Given that the excitation temperature is close to the temperature of the dust at the inner radius, most of the molecular contribution probably arises from this region. The luminosity corresponding to the first epoch of SAGE observations is 6580 L-circle dot. For an effective temperature of about 3000 K, this implies a stellar mass of 1.5-2 M-circle dot and an age of 1-2.5 Gyr for OGLE LMC LPV 28579. We calculate a gas mass-loss rate of 5.0 x 10(-7) M-circle dot yr(-1) assuming a gas: dust ratio of 200. This number is comparable to the gas mass-loss rates estimated from the period, color and 8 mu m flux of the source.