[O <scp>ii</scp>] as an effective indicator of the dependence between the standardized luminosities of Type Ia supernovae and the properties of their host galaxies

ABSTRACT We have obtained Integral Field Unit (IFU) spectra of 75 Type Ia supernova (SN Ia) host galaxies from the Foundation Supernova Survey to search for correlations between the properties of individual galaxies and SN Hubble residuals. After standard corrections for light-curve width and SN colour have been applied, we find correlations between Hubble residuals and the equivalent width (EW) of the [${\rm O\, {\small II}}$] $\lambda \lambda$3727, 3729 doublet (2.3$\sigma$), an indicator of the specific star formation rate. When splitting our sample by SN colour, we find no colour dependence impacting the correlation between EW[${\rm O\, {\small II}}$] and Hubble residual. However, when splitting by colour, we reveal a correlation between the Hubble residuals of blue SNe Ia and the Balmer decrement (2.2$\sigma$), an indicator of dust attenuation. These correlations remain after applying a mass-step correction, suggesting that the mass-step correction does not fully account for the limitations of the colour correction used to standardize SNe Ia. Rather than a mass correction, we apply a correction to SNe from star-forming galaxies based on their measurable EW[${\rm O\, {\small II}}$]. We find that this correction also removes the host galaxy mass-step, while also greatly reducing the significance of the correlation with the Balmer decrement for blue SNe Ia. We find that correcting for EW[${\rm O\, {\small II}}$], in addition to or in place of the mass-step, may further reduce the scatter in the Hubble diagram.