empirical metallicity estimates in @Gallazzi:2005df. In decreasing the initial stellar metallicity from $Z=0.03$ to 0.004, roughly the range spanned in Fig. \[Iarate\], @Umeda:1998ij determined that an additional $\sim 0.05-0.15\,M_\odot$ is added to the CO remnant at fixed initial mass (see their Fig. 6).

Fig. 8 of @Umeda:1998ij displays the relative number of SN Ia progenitors obtained from their stellar evolution model as a function of metallicity after integrating over a Salpeter IMF from a lower initial stellar mass (which varies with $Z$) corresponding to fixed final WD mass to an upper mass at which point ONeMg WDs were expected to be produced (varying with $Z$ from $\sim 7-8.5\, M_\odot$). Using a threshold WD mass of $0.85\,M_\odot$ yields a dependence on the rate with metallicity that can be approximately parametrized as $$N_{\rm Ia}(Z) \propto \left(Z+0.003\right)^{-0.5}
\label{umfit}$$ over the range $Z=0.004-0.03$. Using a lower threshold mass of $0.7\,M_\odot$ yields a slightly weaker dependence, due to the larger mass range, of approximately $$N_{\rm Ia}(Z) \propto \left(Z+0.0015\right)^{-0.3}.
\label{umfit2}$$ To derive galactic rates, we again use a SN Ia rate for each galaxy $\propto \Delta t^{-\gamma}$ and scale directly to the @Umeda:1998ij results, normalizing these relations to unity at $Z=0.025$, the metallicity of a characteristic 