Confronting double-detonation sub-Chandrasekhar models with the low-luminosity suppression 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. Recently, Sharon & Kushnir used The Zwicky Transient Facility Bright Transient Survey to construct a synthesized ⁵⁶Ni mass, M_Ni56, distribution of SNe Ia. They found that the rate of low-luminosity ($M_\text{Ni56}\approx 0.15\, \mathrm{M}_{\odot }$) SNe Ia is lower by a factor of ~10 than the more common $M_\text{Ni56}\approx 0.7\, \mathrm{M}_{\odot }$ events. We here show that in order for the double-detonation model (DDM, in which a propagating thermonuclear detonation wave, TNDW, within a thin helium shell surrounding a sub-Chandrasekhar mass CO core triggers a TNDW within the core) to explain this low-luminosity suppression, the probability of a low-mass ($\approx 0.85\, \mathrm{M}_{\odot }$) WD explosion should be ~100-fold lower than that of a high-mass ($\approx 1.05\, \mathrm{M}_{\odot }$) WD. One possible explanation is that the ignition of low-mass CO cores is somehow suppressed. We use accurate one-dimensional numerical simulations to show that if a TNDW is able to propagate within the helium shell, then the ignition within the CO core is guaranteed (resolved here for the first time in a full-star simulation), even for $0.7\, \mathrm{M}_{\odot }$ WDs, providing no natural explanation for the low-luminosity suppression. DDM could explain the low-luminosity suppression if the mass distribution of primary WDs in close binaries is dramatically different from the field distribution; if the Helium shell ignition probability is suppressed for low-mass WDs; or if multidimensional perturbations significantly change our results.