Environmental Dependence of Type Ia Supernova Luminosities from a Sample
  without a Local-Global Difference in Host Star Formation
  It is now established that there is a dependence of the luminosity of type Ia
supernovae (SNe Ia) on environment: SNe Ia in young, star-forming, metal-poor
stellar populations appear fainter after light-curve shape corrections than
those in older, passive, metal-rich environments. This is accounted for in
cosmological studies using a global property of the SN host galaxy, typically
the host galaxy stellar mass. However, recent low-redshift studies suggest that
this effect manifests itself most strongly when using the local star-formation
rate (SFR) at the SN location, rather than the global SFR or stellar mass of
the host galaxy. At high-redshift, such local SFRs are difficult to determine;
here, we show that an equivalent 'local' correction can be made by restricting
the SN Ia sample in globally star-forming host galaxies to a low-mass host
galaxy subset ($\le10^{10} M_{\odot}$). Comparing this sample of SNe Ia (in
locally star-forming environments) to those in locally passive host galaxies,
we find that SNe Ia in locally star-forming environments are $0.081\pm0.018$
mag fainter ($4.5\sigma$), consistent with the result reported by Rigault et
al. (2015), but our conclusion is based on a sample ~5 times larger over a
wider redshift range. This is a larger difference than when splitting the SN Ia
sample based on global host galaxy SFR or host galaxy stellar mass. This method
can be used in ongoing and future high-redshift SN surveys, where local SN Ia
environments are difficult to determine.
