The Structure of the Homunculus. II. Modeling the physical conditions in Eta Car's molecular shell

We present models that reproduce the observed double-shell structure of the Homunculus Nebula around eta Carinae, including the stratification of infrared H2 and [FeII] emission seen in data obtained with the Phoenix spectrograph on Gemini South, as well as the corresponding stratified grain temperature seen in thermal-infrared data. Tuning the model to match the observed shell thickness allows us to determine the threshold density which permits survival of H2. An average hydrogen density of n_H=(0.5-1)x10^7 cm-3 in the outer zone is required to allow H2 to exist at all latitudes in the nebula, and for Fe+ to recombine. This gives independent confirmation of the very large mass of the Homunculus, indicating a total of roughly 15--35 Msun (although we note reasons why the lower end of this range is favored). At the interface between the atomic and molecular zones, we predict a sharp drop in the dust temperature, in agreement with the bimodal dust color temperatures observed in the two zones. In the outer molecular shell, the dust temperature drops to nearly the blackbody temperature, and becomes independent of grain size because of self-shielding at shorter UV wavelengths and increased heating at longer wavelengths. This relaxes constraints on large grain sizes suggested by near-blackbody color temperatures. Finally, from the strength of infrared [FeII] emission in the inner shell we find that the gas-phase Fe abundance is roughly solar. This is astonishing in such a dusty object, where one normally expects gaseous iron to be depleted by two orders of magnitude