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Galaxy formation depends critically on the physical state of gas in thecircumgalactic medium (CGM) and its interface with the intergalactic medium(IGM), determined by the complex interplay between inflows from the IGM andoutflows from supernovae or AGN feedback. The average Lyman-alpha (Ly-a)absorption profile around galactic halos represents a powerful tool to probetheir gaseous environments. We compare predictions from Illustris and Nyxhydrodynamical simulations with the observed absorption around foregroundquasars, damped Ly-a systems, and Lyman-break galaxies. We show how large-scaleBOSS and small-scale quasar pair measurements can be combined to preciselyconstrain the absorption profile over three decades in transverse distance20kpc$\lesssim b\lesssim$20Mpc. Far from galaxies $\gtrsim2$Mpc, thesimulations converge to the same profile and provide a reasonable match to theobservations. This asymptotic agreement arises because the $\Lambda$CDM modelsuccessfully describes the ambient IGM, and represents a critical advantage ofstudying the mean absorption profile. However, significant differences betweenthe simulations, and between simulations and observations are present on scales20kpc$\lesssim b\lesssim$2Mpc, illustrating the challenges of accuratelymodeling and resolving galaxy formation physics. It is noteworthy that thesedifferences are observed as far out as $\sim2$Mpc, indicating that the`sphere-of-influence' of galaxies could extend to approximately $\sim7$ timesthe halo virial radius ($\sim100$kpc). Current observations are very precise onthese scales and can thus strongly discriminate between different galaxyformation models. We demonstrate that the Ly-a absorption profile is primarilysensitive to the underlying temperature-density relationship of diffuse gasaround galaxies, and argue that it thus provides a fundamental test of galaxyformation models.

A Fundamental Test for Galaxy Formation Models: Matching the Lyman-$\alpha$ Absorption Profiles of Galactic Halos over Three Decades in Distance