Binaries drive high Type Ia supernova rates in dwarf galaxies

The scaling of the specific Type Ia supernova (SN Ia) rate with host galaxy stellar mass $\dot{N}_\text{Ia} / M_\star \sim M_\star^{-0.3}$ as measured in ASAS-SN and DES strongly suggests that the number of SNe Ia produced by a stellar population depends inversely on its metallicity. We estimate the strength of the required metallicity dependence by combining the average star formation histories (SFHs) of galaxies as a function of their stellar mass with the mass-metallicity relation (MZR) for galaxies and common parametrizations for the SN Ia delay-time distribution. The differences in SFHs can account for only $\sim$30% of the increase in the specific SN Ia rate between stellar masses of $M_\star = 10^{10}$ and $10^{7.2} M_\odot$. We find that an additional metallicity dependence of approximately $\sim$Z$^{-0.5}$ is required to explain the observed scaling. This scaling matches the metallicity dependence of the close binary fraction observed in APOGEE, suggesting that the enhanced SN Ia rate in low-mass galaxies can be explained by a combination of their more extended SFHs and a higher binary fraction due to their lower metallicities. Due to the shape of the MZR, only galaxies below $M_\star \approx 3\times10^9 M_\odot$ are significantly affected by the metallicity-dependent SN Ia rates. The $\dot{N}_\text{Ia} / M_\star \sim M_\star^{-0.3}$ scaling becomes shallower with increasing redshift, dropping by factor of $\sim$2 at $10^{7.2} M_\odot$ between $z = 0$ and $1$ with our $\sim$$Z^{-0.5}$ scaling. With metallicity-independent rates, this decrease is a factor of $\sim$3. We discuss the implications of metallicity-dependent SN Ia rates for one-zone models of galactic chemical evolution.