We present numerical solutions of the 2D relativistic hydrodynamics equations describing the deceleration and expansion of highly relativistic conical jets, of opening angles 0.05 ≤ θ 0 ≤ 0.2, propagating into a medium of uniform density. Jet evolution is followed from a collimated relativistic outflow through to the quasi-spherical non-relativistic phase. We show that relativistic sideways expansion becomes significant beyond the radius r θ at which the expansion Lorentz factor drops to θ −1 0 . This is consistent with simple analytic estimates, which predict faster sideways expansion than has been claimed based on earlier numerical modeling. For t > t s = r θ /c the emission of radiation from the jet blast wave is similar to that of a spherical blast wave carrying the same energy. Thus, the total (calorimetric) energy of GRB blast waves may be estimated with only a small fractional error based on t > t s observations.

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 modeling 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 color evolution of the emitted light and is studied in Paper II. Here we show that the gamma-ray escape time t 0 can be derived with ∼ 15% 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 days for the wide range of observed 56 Ni masses 0.1M ⊙ M56 Ni 1M ⊙ . 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 disfavored 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.

Type Ia supernovae (SNe Ia) are likely the thermonuclear explosions of carbon-oxygen (CO) white-dwarf (WD) stars, but their progenitor systems remain elusive. Recent studies have suggested that a propagating detonation within a thin helium shell surrounding a sub-Chandrasekhar mass CO core can subsequently trigger a detonation within the core (the double-detonation model, DDM). The outcome of this explosion is similar to a central ignition of a sub-Chandrasekhar mass CO WD (SCD). While SCD is consistent with some observational properties of SNe Ia, several computational challenges prohibit a robust comparison to the observations. We focus on the observed t0 − MNi56 relation, where t0 (the γ-rays’ escape time from the ejecta) is positively correlated with MNi56 (the synthesized 56Ni mass). We apply our recently developed numerical scheme to calculate SCD and show that the calculated t0 − MNi56 relation, which does not require radiation transfer calculations, converges to an accuracy of a few percent. We find a clear tension between our calculations and the observed t0 − MNi56 relation. SCD predicts an anti-correlation between t0 and MNi56, with t0 ≈ 30 day for luminous (MNi56 ≳ 0.5 M⊙) SNe Ia, while the observed t0 is in the range of 35 − 45 day. We show that this tension is larger than the uncertainty of the results, and that it exists in all previous studies of the problem. Our results hint that more complicated models are required, but we argue that DDM is unlikely to resolve the tension with the observations.