Off-centre ignition of sub-Chandrasekhar white dwarfs does not resolve the tension with the observed $t_0$-$M_{\mathrm{N}\mathrm{i}56}$ relation of type Ia supernovae

Type Ia supernovae (SNe Ia) are likely the thermonuclear explosions of carbon-oxygen (CO) white-dwarf (WD) stars, but the exact nature of their progenitor systems remains uncertain. 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 resulting explosion resembles a central ignition of a sub-Chandrasekhar mass CO WD (SCD), which is known to be in tension with the observed $t_0$-$M_{\mathrm{N}\mathrm{i}56}$ relation, where $t_0$ (the $\gamma$-rays’ escape time from the ejecta) is positively correlated with $M_{\mathrm{N}\mathrm{i}56}$ (the synthesized ${}^{56}$Ni mass). SCD predicts an anticorrelation between $t_0$ and $M_{\mathrm{N}\mathrm{i}56}$, with $t_0\approx 30\text{day}$ for luminous ($M_{\mathrm{N}\mathrm{i}56}\gtrsim 0.5M_{\odot }$) SNe Ia, while the observed $t_0$ is in the range of 35-45 day. In this study, we apply our recently developed numerical scheme to calculate in 2D the impact of off-centre ignition in sub-Chandrasekhar mass CO WD, aiming to better emulate the behaviour expected in the DDM scenario. Our calculations of the $t_0$-$M_{\mathrm{N}\mathrm{i}56}$ relation, which do not require radiation transfer calculations, achieve convergence to within a few per cent with a numerical resolution of $\sim 1\mathrm{k}\mathrm{m}$. We find that the results only slightly depend on the ignition location, mirroring the SCD model, and consequently, the discrepancy with the observed $t_0$-$M_{\mathrm{N}\mathrm{i}56}$ relation remains unresolved.