Constraining Type Ia Supernova Progenitor Scenarios with Extremely Late-time Photometry of Supernova SN 2013aa

We present Hubble Space Telescope observations and photometric measurements of the Type Ia supernova (SN Ia) SN 2013aa 1500 days after explosion. At this epoch, the luminosity is primarily dictated by the amounts of radioactive ${}^{57}\textrm{Co}$ and ${}^{55}\textrm{Fe}$, while at earlier epochs, the luminosity depends on the amount of radioactive ${}^{56}\textrm{Co}$. The ratio of odd-numbered to even-numbered isotopes depends significantly on the density of the progenitor white dwarf during the SN explosion, which, in turn, depends on the details of the progenitor system at the time of ignition. From a comprehensive analysis of the entire light curve of SN 2013aa, we measure a $M({}^{57}\textrm{Co})/M({}^{56}\textrm{Co})$ ratio of $0.02^{+0.01}_{-0.02}$, which indicates a relatively low central density for the progenitor white dwarf at the time of explosion, consistent with double-degenerate progenitor channels. We estimate $M({}^{56}\textrm{Ni}) = 0.732 \pm 0.151\:\mathrm{M_{\odot}}$, and place an upper limit on the abundance of ${}^{55}\textrm{Fe}$. A recent study reported a possible correlation between $M({}^{57}\textrm{Co})/M({}^{56}\textrm{Co})$ and stretch for four SNe Ia. SN 2013aa, however, does not fit this trend, indicating either SN 2013aa is an extreme outlier or the correlation does not hold up with a larger sample. The $M({}^{57}\textrm{Co})/M({}^{56}\textrm{Co})$ measured for the expanded sample of SNe Ia with photometry at extremely late times has a much larger range than that of explosion models, perhaps limiting conclusions about SN Ia progenitors drawn from extremely late-time photometry.