Should Type Ia Supernova Distances Be Corrected for Their Local Environments

Recent analyses suggest that distance residuals measured from Type Ia supernovae (SNe Ia) are correlated with local host galaxy properties within a few kpc of the SN explosion. However, the well-established correlation with the global properties of the host galaxy is nearly as significant, with a shift of 0.06 mag across a low to high mass boundary (the mass step). Here, we investigate whether the stellar masses and rest-frame $u - g$ colors of regions within 1.5 kpc of the SN Ia explosion site are significantly better correlated with SN distance measurements than global properties or properties measured at random locations in SN hosts. With the Foundation and Pantheon datasets, we measure host properties using 271 SNe Ia at $z 2 \sigma$ and we conservatively estimate a systematic shift in H$_0$ measurements of -0.13 km s$^{-1}$ Mpc$^{-1}$ with an additional uncertainty of 0.13 km s$^{-1}$ Mpc$^{-1}$, $\sim$10% of the present uncertainty.