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 2Dust model for the dust shell around a LMC long-period variable (LPV) previously studied as part of the OGLE survey. OGLE LMC LPV 28579 (SAGE J051306.40-690946.3) is a carbon-rich asymptotic giant branch (AGB) star for which we have photometry and spectra from the Spitzer SAGE and SAGE-Spec programs along with 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 its spectral energy distribution using a mixture of AmC and SiC (15% by mass). The grain sizes are distributed according to the KMH model. The best-fit model has an optical depth of 0.28 for the shell at the peak of the SiC feature, with R_in~1430 R_sun or 4.4 R_star. 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 2.5x10^-9 M_sun yr-1. We calculate a 15% variation in this rate by testing the fit sensitivity against variation in 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 C_2H_2 gas at an excitation temperature of about 1000 K and column densities of 3x10^21 cm^-2 and 10^19 cm^-2 respectively are able to reproduce the observations. Given that the excitation temperature is close to T_dust(R_in), most of the molecular contribution probably arises from the inner shell region. The luminosity corresponding to the first epoch of SAGE observations is 6580 L_sun. For an effective temperature of about 3000 K, this implies a stellar mass of 1.5-2 M_sun and an age of 1-2.5 Gyr. For a gas:dust ratio of 200, we obtain a gas mass-loss rate of 5.0x10^-7 M_sun yr^-1, consistent with the gas mass-loss rates estimated from the period, color and 8 \mu m flux of the source.