  The temperature and ionization of SN 1987A is modeled between 200 and 2000
days in its nebular phase, using a time-dependent model. We include all
important elements, as well as the primary composition zones in the supernova.
The energy input is provided by radioactive decay of Co-56, Co-57, and Ti-44.
The thermalization of the resulting gamma-rays and positrons is calculated by
solving the Spencer-Fano equation. Both the ionization and the individual level
populations are calculated time-dependently. Adiabatic cooling is included in
the energy equation. Charge transfer is important for determining the
ionization and is included with available and estimated rates. Full, multilevel
atoms are used for the observationally important ions. As input models to the
calculations we use explosion models for SN 1987A calculated by Woosley et al
and Nomoto et al. The most important result in this paper refers to the
evolution of the temperature and ionization of the various abundance zones. The
metal-rich core undergoes a thermal instability, often referred to as the
IR-catastrophe, at 600 - 1000 days. The hydrogen-rich zones evolve
adiabatically after 500 - 800 days, while in the helium region both adiabatic
cooling and line cooling are of equal importance after ~1000 days. Freeze-out
of the recombination is important in the hydrogen and helium zones. Concomitant
with the IR-catastrophe, the bulk of the emission shifts from optical and
near-IR lines to the mid- and far-IR. After the IR-catastrophe, the cooling is
mainly due to far-IR lines and adiabatic expansion. Dust cooling is likely to
be important in the zones where dust forms. We find that the dust condensation
temperatures occur later than ~500 days in the oxygen-rich zones, and the most
favorable zone for dust condensation is the iron core.
