Sub-Chandrasekhar-mass detonations are in tension with the observed $t_0-M_\text{Ni56}$ relation of type Ia supernovae

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 $t_0-M_\text{Ni56}$ relation, where $t_0$ (the $\gamma$-rays' escape time from the ejecta) is positively correlated with $M_\text{Ni56}$ (the synthesized $^{56}$Ni mass). We apply our recently developed numerical scheme to calculate SCD and show that the calculated $t_0-M_\text{Ni56}$ 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 $t_0-M_\text{Ni56}$ relation. SCD predicts an anti-correlation between $t_0$ and $M_\text{Ni56}$, with $t_0\approx30\,\textrm{day}$ for luminous ($M_\text{Ni56}\gtrsim0.5\,M_{\odot}$) SNe Ia, while the observed $t_0$ is in the range of $35-45\,\textrm{day}$. 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.