Ly$\alpha$ at Cosmic Dawn with a Simulated Roman Grism Deep Field

The slitless grism on the Nancy Grace Roman Space Telescope will enable deep near-infrared spectroscopy over a wide field of view. We demonstrate Roman's capability to detect Ly$\alpha$ galaxies at $z>7$ using a multi-position-angle (PA) observational strategy. We simulate Roman grism data using a realistic foreground scene from the COSMOS field. We also input fake Ly$\alpha$ galaxies spanning redshift z=7.5-10.5 and a line-flux range of interest. We show how a novel data cube search technique -- CUBGRISM -- originally developed for GALEX can be applied to Roman grism data to produce a Ly$\alpha$ flux-limited sample without the need for continuum detections. We investigate the impact of altering the number of independent PAs and exposure time. A deep Roman grism survey with 25 PAs and a total exposure time of $70$hrs can achieve Ly$\alpha$ line depths comparable to the deepest $z=7$ narrow-band surveys ($L_{{\rm{Ly}}\alpha}\gtrsim10^{43}$erg s$^{-1}$). Assuming a null result, where the opacity of the intergalactic medium (IGM) remains unchanged from $z\sim7$, this level of sensitivity will detect $\sim400$ deg$^{-2}$ Ly$\alpha$ emitters from $z=7.25-8.75$. A decline from this expected number density is the signature of an increasing neutral hydrogen fraction and the onset of reionization. Our simulations indicate that a deep Roman grism survey has the ability to measure the timing and magnitude of this decline, allowing us to infer the ionization state of the IGM and helping us to distinguish between models of reionization.