  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.
