The relationship between galaxies and low-redshift weak Ly alpha absorbersin the directions of H1821+643 and PG 1116+215

To study the nature of low-z Ly alpha absorbers in the spectra of QSOs, we have obtained high signal-to-noise ratio (S/N) UV spectra of H1821+643 (z(e m) = 0.297) and PG 1116 + 215 (z(em) = 0.177) with the Goddard High-Resolut ion Spectrograph on the Hubble Space Telescope. The spectra have minimum S/ Ns of similar to 70-100 and 3 sigma limiting equivalent widths of 50-75 m A ngstrom at a resolution of similar to 150 km s(-1) Excluding lines within 3 000 km s(-1)of z(em), detect 26 Ly alpha lines with W-r >50 m Angstrom towa rd H1821 + 643 and 13 toward PG 1116+215 (comparable to the 13 Ly alpha lin es observed toward 3C 273 by Morris et al.), which implies a density of 102 +/- 16 lines per unit redshift for W-r > 50 m Angstrom and z(abs) < 0.28. The two-point velocity correlation function shows marginal evidence of clus tering of Ly alpha lines on similar to 500 km s(-1) scales, but only if the weakest lines are excluded. We have also used the Wisconsin-Indiana-Yale-N OAO (WIYN) Observatory to measure galaxy redshifts in the similar to 1 degr ees fields centered on each QSO in order to study the relationship between the Ly alpha absorbers and galaxies. We find 17 galaxy-absorber pairs withi n projected distances of 1 h(75)(-1) Mpc with velocity separations of 350 k m s(-1) or less. Monte Carlo simulations show that if the Ly alpha lines ar e randomly distributed, the probability of observing this many close pairs on the two sight lines is 3.6 x 10(-5). We find that all galaxies with proj ected distances rho less than or equal to 600 h(75)(-1) kpc from the QSO si ght lines have associated Ly alpha absorbers within 1000 km s(-1), and the majority of these galaxies have absorbers within 350 km s(-1). We also find that the Ly alpha equivalent width is anticorrelated with the projected di stance of the nearest galaxy out to at least rho approximate to 600 h(75)(- 1) kpc. For rho > 600h(75)(-1) kpc, we find galaxies that do not have assoc iated Ly alpha lines, but nevertheless the anticorrelation persists if we s elect galaxies with rho less than or similar to 2 h(75)(-1) Mpc that are wi thin 500 or 1000 km s(-1) of a Ly alpha absorber. This anticorrelation has a high significance but should be interpreted cautiously because there are potential selection biases that could lead to an artificial correlation. St atistical tests also show that the Ly alpha absorbers are not randomly dist ributed with respect to the galaxies. Splitting the sample into roughly equ al sets with W-r > 100 m Angstrom and W-r <100 m Angstrom shows that the we akest absorbers are not randomly distributed either. Comparison of the near est neighbor distances of the weaker and stronger absorbers suggests that t he weakest absorbers are less closely associated with galaxies, but the dif ference is not yet statistically significant. We find several galaxy groups that do not have clearly associated Ly alpha absorbers. However, given the projected distance of the nearest galaxy, we do not necessarily expect to find detectable Ly alpha lines in these groups based on the equivalent widt h-projected distance anticorrelation. Furthermore, we find several countere xamples of comparable galaxy groups that do have associated Ly alpha lines. As in previous studies, we find some Ly alpha absorbers in regions apparen tly devoid of galaxies, although this may be caused by the limited spatial extent and/or limited depth of the redshift survey. The equivalent width distributions of the absorbers apparently in voids and nonvoid absorbers are statistically indistinguishable, but the sample is s mall. We discuss the nature of the Ly alpha absorbers in light of the new d ata. The observations are consistent with the hypothesis that many of the l ow-redshift Ly alpha absorption lines with rest equivalent widths in the ra nge from 50 to similar to 500 m Angstrom trace the overall gas distribution s in the large-scale structures of galaxies rather than the gaseous halos o f individual galaxies. Other phenomena may also cause Ly alpha absorption l ines.