  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.
