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

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