The mass-loss return from evolved stars to the Large Magellanic Cloud - V. The GRAMS carbon-star model grid

The total dust return rate from AGB and RSG star outflows is an important constraint to galactic chemical evolution models. However, this requires detailed radiative transfer (RT) modeling of individual stars, which becomes impractical for large data sets. Another approach is to select the best-fit spectral energy distribution (SED) from a grid of dust shell models, allowing for a faster determination of the luminosities and mass-loss rates for entire samples. We have developed the Grid of RSG and AGB ModelS (GRAMS) to measure the mass-loss return from evolved stars. The models span the range of stellar, dust shell and grain properties relevant to evolved stars. In this paper we present the carbon-star grid and compare our results with data of Large Magellanic Cloud (LMC) carbon stars from the SAGE and SAGE-Spec programs. We generate spherically symmetric dust shell models using the 2Dust code, with hydrostatic models for the central stars. We explore five values of the inner radius R_in of the dust shell (1.5, 3, 4.5, 7 and 12 R_star). We use amorphous carbon dust mixed with 10% silicon carbide by mass. The grain sizes follows a KMH distribution. The models span 26 values of 11.3 um optical depth, ranging from 0.001 to 4. For each model, 2Dust calculates the output SED from 0.2 to 200 um. Over 12,000 models have dust temperatures below 1800 K. The GRAMS synthetic photometry is in good agreement with SAGE photometry for LMC carbon-rich and extreme AGB star candidates, as well as spectroscopically confirmed carbon stars from the SAGE-Spec study. Our models reproduce the IRAC colors of most of the extreme AGB star candidates, consistent with the expectation that a majority of these enshrouded stars have carbon-rich dust. Finally, we fit the SEDs of some well-studied carbon stars and compare the resulting luminosities and mass-loss rates with those from previous studies.