Molecule and dust emission at the beginnings and ends of stellar evolution

A combination of photoionization and photodissociation region codes is used to model planetary nebulae and the Crab Nebula supernova remnant, to explain the observed molecular emission. The inclusion of ionizing ultraviolet flux is necessary to reproduce the observed H2 emission and the trend in OH+ detections with central star temperature in PNe. The highest observed H2 line strengths may require an additional heating mechanism, such as shocks. The observed ArH+ and OH+ line strengths in the Crab Nebula, and the lack of [C I] emission, are explained by high values of the cosmic ray ionization rate, appropriate for the environment. Models with extinctions similar to observed dusty globules can also reproduce the H2 and fine structure line emission from the Crab. The thermal dust emission from grains heated by the synchrotron radiation field and by particle collisions is calculated under conditions appropriate for the Cassiopeia A supernova remnant. The observed spectral energy distribution requires ~0.6 Msun of silicate dust, primarily in the unshocked ejecta. Other dust species cannot comprise a significant fraction of the total dust mass. Gas-to-dust ratios for each gas component show that the condensation efficiency in the ejecta is high, and dust located in clumps is protected from destruction by the reverse shock. Gravitational collapses of prestellar cores are approximated analytically, and used to model the evolution of the molecular abundances with time and radius. It is shown that the mode of collapse has observable consequences for many important molecules - CO profiles observed in cores appear to differ significantly from those predicted by collapse via ambipolar diffusion. The potential of this method to decrease the required computing time is shown by creating a grid of models with varying input parameters, and the effects of these changes discussed