Evaluating and Optimizing a Slitless Prism for Nancy Grace Roman Space Telescope SN Cosmology

This work presents a set of studies addressing the use of the low-dispersion slitless prism on Roman for SN spectroscopy as part of the Roman High Latitude Time Domain Survey (HLTDS). We find SN spectral energy distributions including prism data carry more information than imaging alone at fixed total observing time, improving redshift measurements and sub-typing of SNe. The Roman field of view will typically include ~ 10 SNe Ia at observable redshifts at a range of phases (the multiplexing of host galaxies is much greater as they are always present), building up SN spectral time series without targeted observations. We show that fitting these time series extracts more information than stacking the data over all the phases, resulting in a large improvement in precision for SN Ia subclassification measurements. A prism on Roman thus significantly enhances scientific opportunities for the mission, and is particularly important for the Roman SN cosmology program to provide the systematics-controlled measurement that is a focus of the Roman dark energy mission. Optimizing the prism parameters, we conclude that the blue cutoff should be set as blue as the prism image quality allows (~ 7500A), the red cutoff should be set to ~ 18000A to minimize thermal background, and the two-pixel dispersion should be >~ 70.