Spectral luminosity indicators in Type Ia supernovae. Understanding the (Si ii) line-strength ratio and beyond

Type Ia supernovae (SNe Ia) are good distance indicators because the shape of their light curves, which can be measured independently of distance, varies smoothly with luminosity. This suggests that SNe Ia are a single family of events. Similar correlations are observed between luminosity and spectral properties. In particular, the ratio of the strengths of the Si iiλ5972 and λ6355 lines, known as (Si ii), was suggested as a potential luminosity indicator. Here, the physical reasons for the observed correlation are investigated. A Monte Carlo code is used to construct a sequence of synthetic spectra resembling those of SNe with different luminosities near B maximum. The influence of abundances and of ionization and excitation conditions on the synthetic spectral features is investigated. The ratio (Si ii) depends essentially on the strength of Si iiλ5972, because Si iiλ6355 is saturated. In less luminous objects, Si iiλ5972 is stronger because of a rapidly increasing Si ii/Si iii ratio. Thus, the correlation between (Si ii) and luminosity is the effect of ionization balance. The Si iiλ5972 line itself may be the best spectroscopic luminosity indicator for SNe Ia, but all indicators discussed show scatter which may be related to abundance distributions.