We develop an approximate analytical solution for the transfer of line-averaged radiation in the hydrogen recombination lines for the ionized cavity and molecular shell of a spherically symmetric planetary nebula. The scattering problem is treated as
a perturbation, using a mean intensity derived from a scattering-free solution. The analytical function was fitted to Halpha and Hbeta data from the planetary nebula NGC6537. The position of the maximum in the intensity profile produced consistent values for the radius of the cavity as a fraction of the radius of the dusty nebula: 0.21 for Halpha and 0.20 for Hbeta. Recovered optical depths were broadly consistent with observed optical extinction in the nebula, but the range of fit parameters in this case is evidence for a clumpy distribution of dust.
Using Spitzer IRAC and MIPS observations of the Large Magellanic Cloud, we have identified 13 objects that have extremely red mid-IR colors. Follow-up Spitzer IRS observations of seven of these sources reveal varying amounts of SiC and C2H2 absorptio
n as well as the presence of a broad MgS feature in at least two cases, indicating that these are extreme carbon stars. Preliminary estimates find these objects have luminosities of 4-11x10^3 Lsol and preliminary model fitting gives mass-loss rates between 4x10^-5 and 2x10^-4 Msol/yr, higher than any known carbon-rich AGB star in the LMC. These spectral and physical properties require careful reconsideration of dust condensation and mass-loss processes for carbon stars in low metallicity environments.
