  Recent Suzaku X-ray spectra of SNR 3C 397 indicate enhanced stable iron-group
element abundances of Ni, Mn, Cr, and Fe. Seeking to address key questions
about the progenitor and explosion mechanism of 3C 397, we compute
nucleosynthetic yields from a suite of multidimensional hydrodynamics models in
the near-Chandrasekhar mass, single-degenerate paradigm for supernova Type Ia.
Varying the progenitor white dwarf internal structure, composition, ignition,
and explosion mechanism, we find the best match to the observed iron-peak
elements of 3C 397 are dense (central density $\ge$ 6$\times$10$^{9}$ g
cm$^{-3}$), low-carbon white dwarfs that undergo a weak, centrally-ignited
deflagration, followed by a subsequent detonation. The amount of $^{56}$Ni
produced is consistent with a normal or bright normal supernova Type Ia. A pure
deflagration of a centrally-ignited, low central density ($\simeq$
2$\times$10$^{9}$ g cm$^{-3}$) progenitor white dwarf, frequently considered in
the literature, is also found to produce good agreement with 3C 397
nucleosynthetic yields, but leads to a subluminous SN Ia event, in conflict
with X-ray linewidth data. Additionally, in contrast to prior work which
suggested a large super-solar metallicity for the white dwarf progenitor for
SNR 3C 397, we find satisfactory agreement for solar and sub-solar metallicity
progenitors. We discuss a range of implications our results have for the
single-degenerate channel.
