The standard cosmological model ($Lambda$CDM) predicts the existence of the cosmic web: a distribution of matter into sheets and filaments connecting massive halos. However, observational evidence has been elusive due to the low surface brightness of the filaments. Recent deep MUSE/VLT data and upcoming observations offer a promising avenue for Ly$alpha$ detection, motivating the development of modern theoretical predictions. We use hydrodynamical cosmological simulations run with the AREPO code to investigate the potential detectability of large-scale filaments, excluding contributions from the halos embedded in them. We focus on filaments connecting massive ($M_{200c}sim(1-3)times10^{12} M_odot$) halos at z=3, and compare different simulation resolutions, feedback levels, and mock-image pixel sizes. We find increasing simulation resolution does not substantially improve detectability notwithstanding the intrinsic enhancement of internal filament structure. By contrast, for a MUSE integration of 31 hours, including feedback increases the detectable area by a factor of $simeq$5.5 on average compared with simulations without feedback, implying that even the non-bound components of the filaments have substantial sensitivity to feedback. Degrading the image resolution from the native MUSE scale of (0.2)$^2$ per pixel to (5.3)$^2$ apertures has the strongest effect, increasing the detectable area by a median factor of $simeq$200 and is most effective when the size of the pixel roughly matches the width of the filament. Finally, we find the majority of Ly$alpha$ emission is due to electron impact collisional excitations, as opposed to radiative recombination.
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