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

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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 UBVIJHKₛ 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 Rᵢn 1430 Rₛun or 4.4 Rₛtar. 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 Mₛun 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 μm 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 3x10²1 cm-2 and 10¹9 cm-2 respectively are able to reproduce the observations. Given that the excitation temperature is close to Tdust(Rᵢn), most of the molecular contribution probably arises from the inner shell region. The luminosity corresponding to the first epoch of SAGE observations is 6580 Lₛun. For an effective temperature of about 3000 K, this implies a stellar mass of 1.5-2 Mₛun 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 Mₛun yr-1, consistent with the gas mass-loss rates estimated from the period, color and 8 μm flux of the source.