Models for the spectra and the light curve, in the photospheric as well as in the late nebular phase, are used to infer the properties of the very radio-bright, broad-lined type IIb Supernova 2003bg. Consistent fits to the light curve and the spectral evolution are obtained with an explosion that ejected ~ 4 M_sun of material with a kinetic energy of ~ 5 10^51 erg. A thin layer of hydrogen, comprising ~ 0.05 M_sun, is inferred to be present in the ejecta at the highest velocities (v >~ 9000 km/s), while a thicker helium layer, comprising ~ 1.25 M_sun, was ejected at velocities between 6500 and 9000 km/s. At lower velocities, heavier elements are present, including ~ 0.2 M_sun of 56Ni that shape the light curve and the late-time nebular spectra. These values suggest that the progenitor star had a mass of ~ 20-25 M_sun (comparable to, but maybe somewhat smaller than that of the progenitor of the XRF/SN 2008D). The rather broad-lined early spectra are the result of the presence of a small amount of material (~ 0.03 M_sun) at velocities > 0.1 c, which carries ~ 10 % of the explosion kinetic energy. No clear signatures of a highly aspherical explosion are detected.
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