Constraints on the density distribution of type Ia supernovae ejecta inferred from late-time light-curve flattening

The finite time, $\tau_{\rm dep}$, over which positrons from $\beta^{+}$ decays of $^{56}$Co deposit energy in type Ia supernovae ejecta lead, in case the positrons are trapped, to a slower decay of the bolometric luminosity compared to an exponential decline. Significant light-curve flattening is obtained when the ejecta density drops below the value for which $\tau_{\rm dep}$ equals the $^{56}$Co life-time. We provide a simple method to accurately describe this "delayed deposition" effect, which is straightforward to use for analysis of observed light curves. We find that the ejecta heating is dominated by delayed deposition typically from 600 to 1200~day, and only later by longer lived isotopes $^{57}$Co and $^{55}$Fe decay (assuming solar abundance). For the relatively narrow $^{56}$Ni velocity distributions of commonly studied explosion models, the modification of the light curve depends mainly on the $^{56}$Ni mass-weighted average density, $\langle \rho \rangle t^{3}$. Accurate late-time bolometric light curves, which may be obtained with JWST far-infrared (far-IR) measurements, will thus enable to discriminate between explosion models by determining $\langle \rho \rangle t^3$ (and the $^{57}$Co and $^{55}$Fe abundances). The flattening of light curves inferred from recent observations, which is uncertain due to the lack of far-IR data, is readily explained by delayed deposition in models with $\langle \rho\rangle t^{3} \approx 0.2\,M_{\odot}\,(10^{4}\, \textrm{km}\,\textrm{s}^{-1})^{-3}$, and does not imply supersolar $^{57}$Co and $^{55}$Fe abundances.