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Abstract

Observational properties of our series of models are discussed, in particular, the relation between the absolute brightness, postmaximum decline rates, the colors at several moments of time, etc. All models with a ⁵⁶Ni production larger than ≈0.4 M_sun produce light curves of similar brightness. The influence of the cosmological redshift on the light curves and on the correction for interstellar reddening is discussed.

Based on data rectification of the standard deviation, a quantitative procedure to fit the observations has been used to determine the free parameters, i.e., the distance, the reddening, and the time of the explosion. Fast-rising light curves (e.g., SN 1981B and SN 1994D) can be reproduced by delayed detonation models or deflagration models similar to W7. Slowly rising (t_max >= 16 days) light curves (e.g., SN 1984A and SN 1990N) cannot be reproduced by standard detonation, deflagration, or delayed detonation models. To obtain an acceptable agreement with observations, models are required in which the C/O white dwarf is surrounded by an unburned extended envelope of typically 0.2-0.4 M_sun which may either be preexisting or produced during the explosion. Our interpretation of the light curves is also supported by the photospheric expansion velocities. Mainly due to the fast increase of the y radiation produced by the outer ⁵⁶Ni, the postmaximum decline of helium detonations tends to be faster compared to observations of normal bright SN Ia's.

Strongly subluminous SN Ia's can be understood in the framework of pulsating delayed detonations, both from the absolute brightness and the colors. Alternatively, subluminosity can be produced within the scenario of helium detonations in low-mass white dwarfs of about 0.6-0.8 M_sun if the explosion occurs when rather little helium has been accreted. However, even subluminous helium detonation models are very blue at maximum light owing to heating in the outer layers, and brighter models show a fast postmaximum decline, in contradiction to the observations.

We find evidence for a correlation between the type of host galaxy and the explosion mechanism. In spiral galaxies, about the same amount of prompt explosions (delayed detonations and W7) and pulsating delayed detonations seems to occur. In contrast, in ellipticals, the latter type is strongly favored. This difference may provide a hint about the stellar evolution of the progenitors.

Based on a comparison of theoretical light curves and observational data, the distances of the parent galaxies are determined independently from secondary distance indicators. A comparison with theoretical models allows for a consistent determination of the interstellar reddening and the cosmological redshift For the example of SN 1988U, we show the need for a simultaneous use of both spectral and light curve data if the data set is incomplete. Based on the models, SN Ia's allow for a measurement of the value of the Hubble constant H₀. H₀ is found to be 67±9 km s^-1 Mpc^-1 within a 95% probability for distances up to 1.3 Gpc. SN 1988U at 1.3 Gpc is consistent with a deceleration parameter q₀ of 0.7±0.5 (1 sigma).

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