  Extremely luminous, super-Chandrasekhar (SC) Type Ia Supernovae (SNe Ia) are
as yet an unexplained phenomenon. We analyse a well-observed SN of this class,
SN 2009dc, by modelling its photospheric spectra with a spectral synthesis
code, using the technique of 'Abundance Tomography'. We present spectral models
based on different density profiles, corresponding to different explosion
scenarios, and discuss their consistency. First, we use a density structure of
a simulated explosion of a 2 M_sun rotating C-O white dwarf (WD), which is
often proposed as a possibility to explain SC SNe Ia. Then, we test a density
profile empirically inferred from the evolution of line velocities
(blueshifts). This model may be interpreted as a core-collapse SN with an
ejecta mass ~ 3 M_sun. Finally, we calculate spectra assuming an interaction
scenario. In such a scenario, SN 2009dc would be a standard WD explosion with a
normal intrinsic luminosity, and this luminosity would be augmented by
interaction of the ejecta with a H-/He-poor circumstellar medium. We find that
no model tested easily explains SN 2009dc. With the 2 M_sun WD model, our
abundance analysis predicts small amounts of burning products in the
intermediate-/high-velocity ejecta (v > 9000 km/s). However, in the original
explosion simulations, where the nuclear energy release per unit mass is large,
burned material is present at high v. This contradiction can only be resolved
if asymmetries strongly affect the radiative transfer or if C-O WDs with masses
significantly above 2 M_sun exist. In a core-collapse scenario, low velocities
of Fe-group elements are expected, but the abundance stratification in SN
2009dc seems 'SN Ia-like'. The interaction-based model looks promising, and we
have some speculations on possible progenitor configurations. However,
radiation-hydro simulations will be needed to judge whether this scenario is
realistic at all.
