Abstract | The calculated monochromatic (B and V) light curves of a set of Type Ia supernova models are compared with the observed monochromatic light curves of 13 Type Ia supernovae (SNIa). The set consists of 11 Type Ia supernova models including deflagrations, detonations, delayed detonations, pulsating delayed detonations and tamped detonations. The theoretical light curves have been calculated using our recently developed light curve model. The model incorporates a detailed equation of state with an elaborate treatment of the ionization balance, an implicit grey LTE radiation transport scheme based on the moment equations, a total energy equation for the gas and the radiation field, expansion opacities, and a Monte Carlo gamma-ray deposition scheme. To evolve the structure of the underlying explosion models homologous expansion is assumed. We find that fast rising light curves (e.g., SN 1972E, SN 1981B and SN 1986G) can be reproduced best by delayed detonation models, and that slowly rising (t_max_ >~ 17 days) light curves (e.g., SN 1984A and SN 1990N) cannot be reproduced by standard detonation, deflagration or delayed detonation models. In order to obtain an acceptable agreement with observations for slowly rising light curves explosion models are required where the C/O white dwarf is surrounded by an unburnt extended envelope of typically 0.2 to 0.4 M_sun_. Our interpretation of the light curves is also favoured from the expansion velocities observed in the spectra of the slowly rising SNIa. Based on a comparison of theoretical light curves and observational data, the distances of the parent galaxies have been determined. We show that SNe Ia allow for a measurement of the value of the Hubble constant provided individual fits are used and if they are located at distances larger than 15 Mpc, because only then they are in the "Hubble" flow. Taking this restriction into account a Hubble constant of H = 66 +/- 10 km/(secMpc) can be derived within a 2σ error. |