  The observed sub-class of "superluminous" Type Ia supernovae lacks a
convincing theoretical explanation. If the emission of such objects were
powered exclusively by radioactive decay of 56Ni formed in the explosion, a
progenitor mass close to or even above the Chandrasekhar limit for a
non-rotating white dwarf star would be required. Masses significantly exceeding
this limit can be supported by differential rotation. We, therefore, explore
explosions and predict observables for various scenarios resulting from
differentially rotating carbon-oxygen white dwarfs close to their respective
limit of stability. Specifically, we have investigated a prompt detonation
model, detonations following an initial deflagration phase ("delayed
detonation" models), and a pure deflagration model. In postprocessing steps, we
performed nucleosynthesis and three-dimensional radiative transfer
calculations, that allow us, for the first time, to consistently derive
synthetic observables from our models. We find that all explosion scenarios
involving detonations produce very bright events. The observables predicted for
them, however, are inconsistent with any known subclass of Type Ia supernovae.
Pure deflagrations resemble 2002cx-like supernovae and may contribute to this
class. We discuss implications of our findings for the explosion mechanism and
for the existence of differentially rotating white dwarfs as supernova
progenitors.
