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Abridged. In the double detonation scenario for Type Ia supernovae (SNe Ia) adetonation initiates in a shell of He-rich material accreted from a companionstar by a sub-Chandrasekhar-mass White Dwarf (WD). This shell detonation drivesa shock front into the carbon-oxygen (C/O) WD that triggers a secondarydetonation in the core. The core detonation results in a complete disruption ofthe WD. Earlier studies concluded that this scenario has difficulties inaccounting for the observed properties of SNe Ia since the explosion ejecta aresurrounded by the products of explosive He burning in the shell. Recently, itwas proposed that detonations might be possible for much less massive He shellsthan previously assumed. Moreover, it was shown that even detonations of theseminimum He shell masses robustly trigger detonations of the C/O core. Here wepresent time-dependent multi-wavelength radiative transfer calculations formodels with minimum He shell mass and derive synthetic observables for both theoptical and {\gamma}-ray spectral regions. These differ strongly from thosefound in earlier simulations of sub-Chandrasekhar-mass explosions in which moremassive He shells were considered. Our models predict light curves which coverboth the range of brightnesses and the rise and decline times of observed SNeIa. However, their colours and spectra do not match the observations. Inparticular, their B-V colours are generally too red. We show that thisdiscrepancy is mainly due to the composition of the burning products of the Heshell of our models which contain significant amounts of Ti and Cr. Using a toymodel, we also show that the burning products of the He shell depend cruciallyon its initial composition. This leads us to conclude that good agreementbetween sub-Chandrasekhar-mass explosions and observed SNe Ia may still befeasible but further study of the shell properties is required.

Double-detonation sub-Chandrasekhar supernovae: synthetic observables for minimum helium shell mass models