Maximum Brightness and Post-Maximum Decline of Light Curves of SN~Ia: A Comparison of Theory and Observations

We compare the observed correlations between the maximum brightness, postmaximum decline rate and color at maximum light of Type Ia supernovae (SN Ia) with model predictions. The observations are based on a total of 40 SN Ia with 29 SN of the Calan Tololo Supernova Search and 11 local SN which cover a range of 2 mag in the absolute visual brightness. The observed correlations are not tight, one dimensional relations. Supernovae with the same postmaximum decline or the same color have a spread in visual magnitude of about 0.7 mag. The dispersion in the color-magnitude relation may result from uncertainties in the distance determinations or the interstellar reddening within the host galaxy. The dispersion in the decline rate-magnitude relation suggests that an intrinsic spread in the supernova properties exists that cannot be accounted for by any single relation between visual brightness and postmaximum decline. Theoretical correlations are derived from a grid of models which encompasses delayed detonations, pulsating delayed detonations, the merging scenario and helium detonations. We find that the observed correlations can be understood in terms of explosions of Chandrasekhar mass white dwarfs. Our models show an intrinsic spread in the relations of about 0.5 mag in the maximum brightness and about 0.1 mag in the B-V color. Our study provides strong evidence against the mechanism of helium detonation for subluminous, red SN Ia.