Calibrating the Absolute Magnitude of Type Ia Supernovae in Nearby Galaxies using [OII] and Implications for H₀

The present state of cosmology is facing a crisis where there is a fundamental disagreement in measurements of the Hubble constant ($H_{0}$), with significant tension between the early and late universe methods. Type Ia supernovae (SNe Ia) are important to measuring $H_{0}$ through the astronomical distance ladder. However, there remains potential to better standardise SN Ia light curves by using known dependencies on host galaxy properties after the standard light curve width and colour corrections have been applied to the peak SN Ia luminosities. To explore this, we use the 5-year photometrically identified SNe Ia sample obtained by the Dark Energy Survey, along with host galaxy spectra obtained by the Australian Dark Energy Survey. Using host galaxy spectroscopy, we find a significant trend with the equivalent width (EW) of the [OII] $\lambda\lambda$ 3727, 29 doublet, a proxy for specific star formation rate, and Hubble residuals. We find that the correlation with [OII] EW is a powerful alternative to the commonly used mass step after initial light curve corrections. Applying this [OII] EW correction to 20 SNe Ia in calibrator galaxies observed with WiFeS, we examined the impact on SN Ia absolute magnitudes and $H_{0}$. Our [OII] EW corrections result in $H_{0}$ values ranging between 73.04 to 73.51 $\mathrm{km} \mathrm{s}^{-1} \mathrm{Mpc}^{-1}$, with a combined statistical and systematic uncertainty of $\sim$1.31 $\mathrm{km} \mathrm{s}^{-1} \mathrm{Mpc}^{-1}$. However, even with this additional correction, the impact of host galaxy properties in standardising SNe Ia appears limited in reducing the current tension ($\sim$5$\sigma$) with the CMB result for $H_{0}$.