[O II] as an Effective Indicator of the Dependence Between the Standardised Luminosities of Type Ia Supernovae and the Properties of their Host Galaxies

We have obtained IFU spectra of 75 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 of the [O II] $\lambda\lambda$ 3727, 3729 doublet (2.3$\sigma$), an indicator of the specific star formation rate (sSFR). When splitting our sample by SN colour, we find no colour dependence impacting the correlation between EW[O 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 standardise SNe Ia. Rather than a mass correction, we apply a correction to SNe from star forming galaxies based on their measurable EW[O 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[O II], in addition to or in place of the mass-step, may further reduce the scatter in the Hubble diagram.