The circumgalactic medium (CGM) encodes signatures of the galaxy-formation process, including the interaction of galactic outflows driven by stellar and supermassive black hole (SMBH) feedback with the gaseous halo. Moving beyond spherically symmetric radial profiles, we study the textit{angular} dependence of CGM properties around $z=0$ massive galaxies in the IllustrisTNG simulations. We characterize the angular signal of density, temperature, and metallicity of the CGM as a function of galaxy stellar mass, halo mass, distance, and SMBH mass, via stacking. TNG predicts that the CGM is anisotropic in its thermodynamical properties and chemical content over a large mass range, $M_*sim10^{10-11.5}M_odot$. Along the minor axis directions, gas density is diluted, whereas temperature and metallicity are enhanced. These feedback-induced anisotropies in the CGM have a magnitude of $0.1-0.3$ dex, extend out to the halo virial radius, and peak at Milky Way-like masses, $M_*sim10^{10.8}M_odot$. In TNG, this mass scale corresponds to the onset of efficient SMBH feedback and the production of strong outflows. By comparing the anisotropic signals predicted by TNG versus other simulations -- Illustris and EAGLE -- we find that each simulation produces distinct signatures and mass dependencies, implying that this phenomenon is sensitive to the underlying physical models. Finally, we explore X-ray emission as an observable of this CGM anistropy, finding that future X-ray observations, including the eROSITA all-sky survey, will be able to detect and characterize this signal, particularly in terms of an angular modulation of the X-ray hardness.
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