We present simulations from the new Figuring Out Gas & Galaxies in Enzo (FOGGIE) project. In contrast to most extant simulations of galaxy formation, which concentrate computational resources on galactic disks and spheroids with fluid and particle elements of fixed mass, the FOGGIE simulations focus on extreme spatial and mass resolution in the circumgalactic medium (CGM) surrounding galaxies. Using the Enzo code and a new refinement scheme, FOGGIE reaches spatial resolutions of 381 comoving $h^{-1}$ pc and resolves extremely low masses ($lesssim 1$--$100$ Msun out to 100 comoving $h^{-1}$ kpc from the central halo. At these resolutions, cloud and filament-like structures giving rise to simulated absorption are smaller, and better resolved, than the same structures simulated with standard density-dependent refinement. Most of the simulated absorption arises in identifiable and well-resolved structures with masses $lesssim 10^4$ Msun, well below the mass resolution of typical zoom simulations. However, integrated quantities such as mass surface density and ionic covering fractions change at only the $lesssim 30$% level as resolution is varied. This relatively small changes in projected quantities---even when the sizes and distribution of absorbing clouds change dramatically---indicate that commonly used observables provide only weak constraints on the physical structure of the underlying gas. Comparing the simulated absorption features to the KODIAQ (Keck Observatory Database of Ionized Absorption toward Quasars) survey of $z sim2$--$3.5$ Lyman limit systems, we show that high-resolution FOGGIE runs better resolve the internal kinematic structure of detected absorption, and better match the observed distribution of absorber properties. These results indicate that CGM resolution is key in properly testing simulations of galaxy evolution with circumgalactic observations.
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