  Context: Superluminous type Ia supernovae (SNe Ia) may be explained by
super-Chandrasekhar-mass explosions of rapidly rotating white dwarfs (WDs). In
a preceding paper, we showed that the deflagration scenario applied to rapidly
rotating WDs generates explosions that cannot explain the majority of SNe Ia.
Aims: Rotation of the progenitor star allows super-Chandrasekhar-mass WDs to
form that have a shallower density stratification. We use simple estimates of
the production of intermediate and iron group elements in pure detonations of
rapidly rotating WDs to assess their viability in explaining rare SNe Ia.
Methods: We numerically construct WDs in hydrostatic equilibrium that rotate
according to a variety of rotation laws. The explosion products are estimated
by considering the density stratification and by evaluating the result of
hydrodynamics simulations. Results: We show that a significant amount of
intermediate mass elements is produced for theoretically motivated rotation
laws, even for prompt detonations of WDs. Conclusions: Rapidly rotating WDs
that detonate may provide an explanation of rare superluminous SNe Ia in terms
of both burning species and explosion kinematics.
