On the type Ia supernovae 2007on and 2011iv: Evidence for Chandrasekhar-mass explosions at the faint end of the luminosity-width relationship

Radiative transfer models of two transitional type Ia supernova (SNe Ia) have been produced using the abundance stratification technique. These two objects --designated SN 2007on and SN 2011iv-- both exploded in the same galaxy, NGC 1404, which allows for a direct comparison. SN 2007on synthesised 0.25 $M_{\odot}$ of $^{56}$Ni and was less luminous than SN 2011iv, which produced 0.31 $M_{\odot}$ of $^{56}$Ni. SN 2007on had a lower central density ($\rho_{c}$) and higher explosion energy ($E_{\rm kin}$ $\sim 1.3\pm$0.3$\times10^{51}$erg) than SN 2011iv, and it produced less nuclear statistical equilibrium (NSE) elements (0.06 $M_{\odot}$). Whereas, SN 2011iv had a larger $\rho_{c}$, which increased the electron capture rate in the lowest velocity regions, and produced 0.35 $M_{\odot}$ of stable NSE elements. SN 2011iv had an explosion energy of $E_{\rm kin}$ $\sim 0.9 \pm$0.2$\times10^{51}$erg. Both objects had an ejecta mass consistent with the Chandrasekhar mass (Ch-mass), and their observational properties are well described by predictions from delayed-detonation explosion models. Within this framework, comparison to the sub-luminous SN 1986G indicates SN 2011iv and SN 1986G have different transition densities ($\rho_{tr}$) but similar $\rho_{c}$. Whereas, SN 1986G and SN 2007on had a similar $\rho_{tr}$ but different $\rho_{c}$. Finally, we examine the colour-stretch parameter $s_{BV}$ vs. $L_{max}$ relation and determine that the bulk of SNe Ia (including the sub-luminous ones) are consistent with Ch-mass delayed-detonation explosions, where the main parameter driving the diversity is $\rho_{tr}$. We also find $\rho_{c}$ to be driving the second order scatter observed at the faint end of the luminosity-width relationship.