Requirements for investigating the connection between Lyman-alpha absorption clouds and the large-scale distribution of galaxies

We model the requirements on observational data that would allow an accurate determination of the degree of association between Lyman-alpha absorbers and peaks in the redshift distribution of galaxies (large-scale structures like clusters of galaxies). We compare simulated distributions of low-redshift Lyman-alpha absorption systems, constrained to be consistent with the distribution observed with HST, with the large-scale distribution of galaxies determined from pencil-beam redshift surveys. We estimate the amount of observational data required from catalogs of Lyman-alpha absorbers and galaxies to allow a statistically significant test of the association of absorbers with large-scale structures of galaxies. We find that for each line of sight observed for Ly alpha absorption lines (assuming that the entire redshift range out to z similar or equal to 0.4 is observable), redshifts must be obtained for at least similar to 18 galaxies brighter than M(B) = -18 and having redshifts between 0.2 and 0.4. Based on the redshift surveys used in this study, a search radius of similar to 10' from the quasar line of sight is required. This will ensure that all peaks in the galaxy redshift distribution are represented by at least one galaxy in the observed sample. If Lyman-alpha absorbers are intrinsically uncorrelated with galaxies, we find that about eight lines of sight must be observed to show that the distributions are different at the 95% confidence level. However, if a fraction of the Lyman-alpha absorbers are distributed with the peaks in the galaxy distribution, similar to 38 lines of sight must be mapped for the distribution of both Lyman-alpha absorbers and galaxies in order to determine the fraction of absorbers distributed with the peaks of the galaxy distribution to an accuracy of 10%.