Characterizing the Roman Grism Redshift Efficiency of Type Ia Supernova Host Galaxies for the High-latitude Time-domain Survey

The High-latitude Time-domain Survey (HLTDS) for the Nancy Grace Roman Space Telescope (Roman) will discover thousands of high-redshift Type Ia supernovae (SNe Ia) to set generation-defining cosmological constraints on dark energy. To construct the Roman SN Hubble diagram, a strategy to obtain redshifts must be determined. While the nominal HLTDS will use only the Roman prism, in this work, we consider the utility of the Roman grism observations from overlap with the High-latitude Wide-area Survey for SN Ia cosmology. We determine a galaxy grism redshift recovery rate by simulating dispersed grism images and measuring redshifts with the Grizli software, obtaining an H-band 50% redshift recovery at magnitude 20.61 and 90% recovery at magnitude 19.27. To estimate the total number of spectroscopic redshifts expected for Roman SN cosmology, we also consider a Roman prism SN redshift efficiency and a ground-based telescope redshift efficiency for host galaxies. We apply these redshift efficiencies to SN Ia catalog-level simulations and predict that ∼6800 SNe will have an SN or host spectroscopic redshift. Second, we evaluate the size of potential systematics related to modeling the grism redshift efficiency by considering the impact of additional dependences on stellar mass and host-galaxy color. We estimate the largest potential size of this systematic to be 0.0066 ± 0.002 and −0.0266 ± 0.0079, roughly 42.9% and 49.6% of the statistical uncertainty, for w0 and wa, respectively. Lastly, we consider the effects of assuming different redshift sources on the optimization of the HLTDS survey strategy by measuring relative changes to the dark energy figure of merit.