Light and Color Curve Properties of Type Ia Supernovae: Theory Versus Observations

We study the optical light curve (LC) relations of Type Ia supernovae (SNe Ia) for their use in cosmology using high-quality photometry published by the Carnegie Supernova Project (CSP-I). We revisit the classical luminosity decline rate (Δm ₁₅) relation and the Lira relation, as well as investigate the time evolution of the (B - V) color and B(B - V), which serves as the basis of the color-stretch relation and Color-MAgnitude Intercept Calibrations (CMAGIC). Our analysis is based on explosion and radiation transport simulations for spherically symmetric delayed-detonation models (DDT) producing normal-bright and subluminous SNe Ia. Empirical LC relations can be understood as having the same physical underpinnings, i.e., opacities, ionization balances in the photosphere, and radioactive energy deposition changing with time from below to above the photosphere. Some three to four weeks past maximum, the photosphere recedes to ⁵⁶Ni-rich layers of similar density structure, leading to a similar color evolution. An important secondary parameter is the central density ρ _c of the WD because at higher densities, more electron-capture elements are produced at the expense of ⁵⁶Ni production. This results in a Δm ₁₅ spread of 0.1 mag in normal-bright and 0.7 mag in subluminous SNe Ia and ≈0.2 mag in the Lira relation. We show why color-magnitude diagrams emphasize the transition between physical regimes and enable the construction of templates that depend mostly on Δm ₁₅ with little dispersion in both the CSP-I sample and our DDT models. This allows intrinsic SN Ia variations to be separated from the interstellar reddening characterized by E(B - V) and R _B. Invoking different scenarios causes a wide spread in empirical relations, which may suggest one dominant scenario.