In this paper, we use large-angle, nearby galaxy redshift surveys to investigate the relationship between the 81 low-redshift Lya absorbers in our HST/GHRS survey and galaxies, superclusters, and voids. In a subsample of 46 Lya absorbers located in regions where the February 8, 2000 CfA catalog is complete down to at least L* galaxies, the nearest galaxy neighbors range from 100kpc to >10 Mpc. Of these 46 absorbers, 8 are found in galaxy voids. After correcting for pathlength and sensitivity, we find that 22+-8% of the Lya absorbers lie in voids, which requires that at least some low-column density absorbers are not extended halos of individual bright galaxies. The number density of these clouds yields a baryon fraction of 4.5+-1.5% in voids. The stronger Lya absorbers (10^{13.2-15.4} cm^-2) cluster with galaxies more weakly than galaxies cluster with each other, while the weaker absorbers (10^{12.4-13.2} cm^-2) are more randomly distributed. The median distance from a low-z Lya absorber in our sample to its nearest galaxy neighbor (~500 kpc) is twice the median distance between bright galaxies in the same survey volume. This makes any purposed association between these Lya absorbers and individual galaxies problematic. The suggested correlation between Lya absorber equivalent width (W) and nearest-galaxy impact parameter does not extend to W<200mA, or to impact parameters >200kpc. Instead, we find statistical support for the contention that absorbers align with large-scale filaments of galaxies. While some strong (W>400mA) Lya absorbers may be gas in the extended gaseous halos of individual galaxies, much of the local Lya forest appears to be associated with the large-scale structures of galaxies and some with voids.
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