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We use hydrodynamic cosmological simulations to predict correlations between Lyα forest absorption and the galaxy distribution at redshift z 3. The probability distribution function (PDF) of Lyα flux decrements shifts systematically toward higher values in the vicinity of galaxies, reflecting the overdense environments in which these galaxies reside. The predicted signal remains strong in spectra smoothed over 50-200 km s-1, allowing tests with moderate-resolution quasar spectra. The strong bias of high-redshift galaxies toward high-density regions imprints a clear signature on the flux PDF, but the predictions are not sensitive to galaxy baryon mass or star formation rate, and they are similar for galaxies and dark matter halos. The dependence of the flux PDF on galaxy proximity is sensitive to redshift determination errors, with rms errors of 150-300 km s-1 substantially weakening the predicted trends. On larger scales, the mean galaxy overdensity in a cube of 5 or 10 h-1 Mpc (comoving) is strongly correlated with the mean Lyα flux decrement on a line of sight through the cube center. The slope of the correlation is ~3 times steeper for galaxies than for dark matter as a result of galaxy bias. The predicted large-scale correlation is in qualitative agreement with recently reported observational results. However, observations also show a drop in the average absorption in the immediate vicinity of galaxies, which our models do not predict even if we allow the galaxies or active galactic nuclei within them to be ionizing sources. This decreased absorption could be a signature of galaxy feedback on the surrounding intergalactic medium, perhaps via galactic winds. We find that a simplified "wind" model that eliminates neutral hydrogen in spheres around the galaxies can marginally explain the data. However, because peculiar velocities allow gas at large distances to produce saturated absorption at the galaxy redshift, these winds (or any other feedback mechanism) must extend to comoving radii of ~1.5 h-1 Mpc to reproduce the observations. We also discuss the possibility that extended Lyα emission from the target galaxies "fills in" the expected Lyα forest absorption at small angular separations.


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