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EIGER IV: The cool 10$^4$K circumgalactic environment of high-$z$ galaxies reveals remarkably efficient IGM enrichment

We report new observations of the cool diffuse gas around 29, $2.3<z<6.3$ galaxies, using deep JWST/NIRCam slitless grism spectroscopy around the sightline to the quasar J0100+2802. The galaxies span a stellar mass range of $7.1 \leq \log M_{*}/M_{sun} \leq 10.7$, and star-formation rates of $-0.1 < \log \; SFR/M_{sun}yr^{-1} \; <2.3$. We find galaxies for seven MgII absorption systems within 300 kpc of the quasar sightline. The MgII radial absorption profile falls off sharply with radii, with most of the absorption extending out to 2-3$R_{200}$ of the host galaxies. Six out of seven MgII absorption systems are detected around galaxies with $\log M_{*}/M_{sun} >$9. MgII absorption kinematics are shifted from the systemic redshift of host galaxies with a median absolute velocity of 135 km/s and standard deviation of 85 km/s. The high kinematic offset and large radial separation ($R> 1.3 R_{200}$), suggest that five out of the seven MgII absorption systems are gravitationally not bound to the galaxies. In contrast, most cool circumgalactic media at $z<1$ are gravitationally bound. The high incidence of unbound MgII gas in this work suggests that towards the end of reionization, galaxy halos are in a state of remarkable disequilibrium, and are highly efficient in enriching the intergalactic medium. Two strongest MgII absorption systems are detected at $z\sim$ 4.22 and 4.5, the former associated with a merging galaxy system and the latter associated with three kinematically close galaxies. Both these galaxies reside in local galaxy over-densities, indicating the presence of cool MgII absorption in two "proto-groups" at $z>4$.