An Ultra Deep Field survey with WFIRST

Studying the formation and evolution of galaxies at the earliest cosmic times, and their role in reionization, requires the deepest imaging possible. Ultra-deep surveys like the HUDF and HFF have pushed to mag \mAB$\,\sim\,$30, revealing galaxies at the faint end of the LF to $z$$\,\sim\,$9$\,-\,$11 and constraining their role in reionization. However, a key limitation of these fields is their size, only a few arcminutes (less than a Mpc at these redshifts), too small to probe large-scale environments or clustering properties of these galaxies, crucial for advancing our understanding of reionization. Achieving HUDF-quality depth over areas $\sim$100 times larger becomes possible with a mission like the Wide Field Infrared Survey Telescope (WFIRST), a 2.4-m telescope with similar optical properties to HST, with a field of view of $\sim$1000 arcmin$^2$, $\sim$100$\times$ the area of the HST/ACS HUDF. This whitepaper motivates an Ultra-Deep Field survey with WFIRST, covering $\sim$100$\,-\,$300$\times$ the area of the HUDF, or up to $\sim$1 deg$^2$, to \mAB$\,\sim\,$30, potentially revealing thousands of galaxies and AGN at the faint end of the LF, at or beyond $z$\,$\sim$\,9$\,-\,$10 in the epoch of reionization, and tracing their LSS environments, dramatically increasing the discovery potential at these redshifts. (Note: This paper is a somewhat expanded version of one that was submitted as input to the Astro2020 Decadal Survey, with this version including an Appendix (which exceeded the Astro2020 page limits), describing how the science drivers for a WFIRST Ultra Deep Field might map into a notional observing program, including the filters used and exposure times needed to achieve these depths.)