Galactic outflows are critical to our understanding of galaxy formation and evolution. However the details of the underlying feedback process remain unclear. We compare Ly$alpha$ observations of the circumgalactic medium (CGM) of Lyman Break Galaxies (LBGs) with mock observations of their simulated CGM. We use cosmological hydrodynamical `zoom-in simulations of an LBG which contains strong, momentum-driven galactic outflows. Simulation snapshots at $z=2.2$ and $z=2.65$ are used, corresponding to the available observational data. The simulation is post-processed with the radiative transfer code textsc{crash} to account for the impact of ionising photons on hydrogen gas surrounding the simulated LBG. We generate mock absorption line maps for comparison with data derived from observed close galaxy-galaxy pairs. We perform calculations of Ly$alpha$ photons scattering through the CGM with our newly developed Monte-Carlo code textsc{slaf}, and compare to observations of diffuse Ly$alpha$ halos around LBGs. Our fiducial galactic outflow model comes closer to reproducing currently observed characteristics of the CGM in Ly$alpha$ than a reference inefficient feedback model used for comparison. Nevertheless, our fiducial model still struggles to reproduce the observed data of the inner CGM (at impact parameter $b<30$kpc). Our results suggest that galactic outflows affect Ly$alpha$ absorption and emission around galaxies mostly at impact parameters $b<50$ kpc, while cold accretion flows dominate at larger distances. We discuss the implications of this result, and underline the potential constraining power of CGM observations - in emission and absorption - on galactic outflow models.
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