Type Ia supernovae have two physical width-luminosity relations and they favour sub-Chandrasekhar and direct collision models - I. Bolometric

While the width-luminosity relation (WLR) among Type Ia supernovae (slower is brighter) has been extensively studied, its physical basis has not been convincingly identified. In particular, the 'width' has not been quantitatively linked yet to a physical time-scale. We demonstrate that there are two robust fundamental time-scales that (1) can be calculated based on integral quantities of the ejecta, with little dependence on radiation transfer modelling and (2) can be inferred from observations. The first is the gamma-ray escape time t 0, which determines the long-term evolution of the bolometric light curve and is studied in this Paper I. The second is the recombination time of 56 Fe and 56 Co, which sets the long-term colour evolution of the emitted light and is studied inPaper II. Here we show that the gamma-ray escape time t 0 can be derived with ∼ 15 per cent accuracy from bolometric observations based on first principles. When applied to a sample of supernovae, the observed values of t 0 span a narrow range of 30-45 d for the wide range of observed 56 Ni masses 0.1M⊙≤M56 Ni≤ 1 M⊙. This narrow range of the gamma-ray escape time across the range of luminosities (a trivial WLR) is consistent with central detonations and direct collisions of sub-Chandrasekhar mass white dwarfs (WDs) but not with delayed detonation models for explosions of Chandrasekhar mass WDs, which are therefore disfavoured as the primary channel for the population of Type Ia supernovae. Computer codes for extracting t 0 from observations and models and for calculating gamma-ray transfer in 1D-3D are provided.