TESTING COSMOLOGICAL MODELS WITH A LY-ALPHA FOREST STATISTIC - THE HIGH-END OF THE OPTICAL DEPTH DISTRIBUTION

We pay particular attention to the high end of the Ly alpha optical de pth distribution of a quasar spectrum. Based on the flux distribution (Miralda-Escude et al.), a simple yet seemingly cosmological model-dif ferentiating statistic, Delta(tau 0)-the cumulative probability of a q uasar spectrum with Ly alpha optical depth greater than a high-value t au(0)-is emphasized. It is shown that two different models-the cold da rk matter model with a cosmological constant and the mixed hot and col d dark matter model, both normalized to COBE and local galaxy cluster abundance-yield quite different values of Delta(tau 0): 0.13 for the f ormer versus 0.058 for the latter, for tau(0) = 3.0 at z = 3. Moreover , it is argued that Delta(tau 0) may be fairly robust to compute theor etically because it does not seem to depend sensitively on small varia tions of simulation parameters such as the radiation field, cooling, t he feedback process, radiative transfer, the resolution, and the simul ation volume within the plausible ranges of the concerned quantities. Furthermore, it is illustrated that Delta(tau 0) can be obtained suffi ciently accurately from currently available observed quasar spectra fo r tau(0) similar to 3.0-4.0, when observational noise is properly take n into account. We anticipate that analyses of observations of quasar Ly alpha absorption spectra over a range of redshift may be able to co nstrain the redshift evolution of the amplitude of the density fluctua tions on small-to-intermediate scales, therefore providing an independ ent constraint on Omega(0), Omega(0,HDM), and Lambda(0).