Spectral analysis of the Ly alpha forest in a cold dark matter cosmology

We simulate the Ly alpha forest in a standard cold dark matter universe using a two-level hierarchical grid code to evolve the dark and baryonic matter components self-consistently. We solve the time-dependent ionization equations for hydrogen and helium, adopting Haardt & Madau's recent estimate for the meta-galactic UV radiation background. We compare our simulation results with the measured properties of the Ly alpha forest by constructing synthetic spectra and analyzing them using an antomated procedure to identify, deblend, and fit Voigt line profiles to the absorption features. The H 1 column density and Doppler parameter distributions that we obtain agree closely with those measured by the Keek Observatory's High Resolution Eschelle Spectrograph (HIRES) and earlier high spectral resolution observations over the column density range 10(12) cm(-2) < N-HI < 10(16) cm(-2). In particular, we End that a power-law column density distribution persists to the lowest values (similar to 10(12) cm(-2)) reported from the HIRES measurements, in agreement with the incompleteness-corrected observations. We are able to match the normalization of the column density distribution at the low end using the Haardt & Madau spectrum and a baryon density consistent with nucleosynthesis limits. We iind, however, a significant deficit of systems at higher column densities, N-HI greater than a few times 10(16) cm(-2). The deficit arises from a curvature in the column density distribution that may not be removed by an overall renormalization. We find evolution in the cloud number density and opacity comparable to the observed evolution, though growing somewhat too quickly at the highest redshifts. The evolution, however, is sensitive to the assumed UV radiation field, which becomes increasingly uncertain at higher redshifts (z > 3.5). We also compare with measured values of the intergalactic Ile II opacity. Our results require an He II. ionizing background lower than the Haardt & Madau estimate by a factor of 4, corresponding to a soft intrinsic QSO spectrum with alpha(Q) approximate to 1.8-2.