The Relationship Between Galaxies and Low Redshift Weak Lyman $\alpha$ Absorbers in the Directions of H1821+643 and PG1116+215

To study the nature of low z Lya absorbers in the spectra of QSOs, we have obtained high signal-to-noise UV spectra of H 1821+643 (z = 0.297) and PG 1116+215 (z = 0.177) with the GHRS on the HST. The spectra have minimum S/N of 70-100 and 3 sigma limiting equivalent widths of 50-75 mA. We detect 26 Lya lines with Wr > 50 mA toward H1821+643 and 13 toward PG1116+215, which implies a density of 102+/-16 lines per unit redshift. The two-point correlation function shows marginal evidence of clustering on ~500 km/s scales, but only if the weakest lines are excluded. We have also used the WIYN Observatory to measure galaxy redshifts in the ~1 degree fields centered on each QSO. We find 17 galaxy-absorber pairs within projected distances of 1 Mpc with velocity separations of 350 km/s or less. Monte Carlo simulations show that if the Lya lines are randomly distributed, the probability of observing this many close pairs is 3.6e-5. We find that all galaxies with projected distances of 600 kpc or less have associated Lya absorbers within 1000 km/s, and the majority of these galaxies have absorbers within 350 km/s. We also find that the Lya equivalent width is anticorrelated with the projected distance of the nearest galaxy out to at least 600 kpc, but this should be interpreted cautiously because there are potential selection biases. Statistical tests using the entire sample also indicate that the absorbers are not randomly distributed. We discuss the nature of the Lya absorbers in light of the new data