THE OPACITY OF THE Lya FOREST AND IMPLICATIONS FOR ) b AND THE IONIZING BACKGROUND1

We have measured the distribution function of the Nux decrement D \ 1 ( e~q caused by Lya forest absorption from intervening gas in the lines of sight to high-redshift QSOs from a sample of seven high- resolution QSO spectra obtained with the Keck telescope. The observed Nux decrement distribution function (FDDF) is compared with the FDDF from two simulations of the Lya forest: a "CDM model (with ) \ 0.4, " \ 0.6), computed with the Eulerian code of Cen & Ostriker, and a standard cold dark matter (SCDM) model (with ) \ 1), computed with the smoothed particle hydrodynamics code of Hern- quist et al. Good agreement is obtained between the shapes of the simulated and observed FDDFs for both simulations after -tting only one free parameter, which controls the mean Nux decrement. The dif- ference between the predicted FDDFs from the two simulations is small, and we show that it arises mostly from a di†erent temperature in the low-density gas (caused by di†erent assumptions that were made about the reionization history in the two simulations), rather than di†erences between the two cosmological models or numerical e†ects in the two codes, which use very di†erent computational methods. A measurement of the parameter (where ! is the H I ionization rate due to the ionizing k P ) b h3/! background) is obtained by requiring the mean Nux decrement in the simulations to agree with the observed one. Estimating the lower limit !( 7 )10~13 s~1 from the abundance of known QSOs, we derive a lower limit on the baryonic matter density, (0.017) for the "CDM (SCDM) model. ) b h2 ( 0.021 The di†erence between the lower limits inferred from the two models is again due to di†erent tem- peratures in the low-density gas. We give general analytical arguments for why this lower limit is unlikely to be reduced for any other models of structure formation by gravitational collapse that can explain the observed Lya forest. When combined with constraints from big bang nucleosynthesis, the large we infer is inconsistent with some recent D/H determinations (Rugers & Hogan), favoring a low ) b deuterium abundance as reported by Tytler, Fan & Burles. Adopting a -xed the measurement of k(z) ) b , allows a determination of the evolution of the ionizing radiation -eld with redshift. Our models predict an intensity that is approximately constant with redshift, which is in agreement with the assumption that the ionizing background is produced by known quasars for z \ 3, but requires additional sources of ionizing photons at higher redshift given the observed rapid decline of the quasar abundance. Subject headings: intergalactic medium E quasars: absorption lines E radiative transfer