EVOLUTION OF STRUCTURE IN THE INTERGALACTIC MEDIUM AND THE NATURE OF THE LY-ALPHA FOREST

We have performed a detailed statistical study of the evolution of str ucture in a photoionized intergalactic medium (IGM) using analytical s imulations to extend the calculation into the mildly nonlinear density regime found to prevail at z = 3. Our work is based on a simple funda mental conjecture: that the probability distribution function of the d ensity of baryonic diffuse matter in the universe is described by a lo gnormal (LN) random field. The LN distribution has several attractive features and follows plausibly from the assumption of initial linear G aussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluct uations in a universe dominated by cold dark matter (CDM), we compute the behavior of the baryonic matter, which moves slowly toward minima in the dark matter potential on scales larger than the Jeans length. W e have computed two models that succeed in matching observations. One is a nonstandard CDM model with Omega = 1, h = 0.5, and Gamma = 0.3, a nd the other is a low-density flat model with a cosmological constant (LCDM), with Omega = 0.4, Omega(Lambda) = 0.6, and h = 0.65. In both m odels, the variance of the density distribution function grows with ti me, reaching unity at about z = 4, where the simulation yields spectra that closely resemble the Ly alpha forest absorption seen in the spec tra of high-z quasars. The calculations also successfully predict the observed properties of the Ly alpha forest clouds and their evolution from z = 4 down to at least z = 2, assuming a constant intensity for t he metagalactic UV background over this redshift range. However, in ou t. model the forest is not due to discrete clouds, but rather to fluct uations in a continuous intergalactic medium. At z = 3, typical clouds with measured neutral hydrogen column densities N-HI = 10(15.3), 10(1 3.5) and 10(11.5) cm(-2) correspond to fluctuations with mean total de nsities approximately 10, 1, and 0.1 times the universal mean baryon d ensity. Perhaps surprisingly, fluctuations whose amplitudes are less t han or equal to the mean density still appear as ''clouds'' because in our model more than 70% of the volume of the IGM at z = 3 is filled w ith gas at densities below the mean value. We find that the column den sity distribution of Ly alpha forest lines can be fitted to f(N-HI) pr oportional to N-HI(-beta) with beta = 1.46 in the range 12.5 < log N-H I < 14.5, matching recent Keck results. At somewhat higher column dens ities the distribution steepens, giving beta = 1.80 over the range 14. 0 < log N-HI < 15.5, matching earlier observations for these stronger lines. The normalization of the line numbers in our model also agrees with observations if the total baryon density is Omega(b) = 0.015 h(-2 ) and the ionizing background intensity is J(21) = 0.18. Alternatively , if J(21) = 0.5 as recently estimated for the background due to obser ved quasars at z = 2.5, then Omega(b) = 0.025 h(-2) yields the observe d number of Ly alpha lines and the observed mean opacity. The model pr edicts that about 80% of the baryons in the universe are associated wi th Ly alpha forest features with 13 < log N-HI < 15 at z = 3, while 10 % are in more diffuse gas with smaller column densities and 10% are in higher column density clouds and in collapsed structures, such as gal axies and quasars. Our model requires that absorbers at z = 3 with col umn densities higher than about 10(16) cm(-2)-Lyman limit systems and damped Ly alpha systems-represent a separate population that has colla psed out of the IGM. We find the number density of forest lines is dN/ dz = 75[(1 + z)/4](2.5) for lines with EW > 0.32 Angstrom, also in goo d agreement with observations. We fit Voigt profiles to our simulated lines and find a distribution of b parameters that matches that obtain ed from similar fits to real spectra. The effective opacity in the Ly alpha forest is found from the model to be tau(eff) = 0.26[(1 + z)/4]( 3.1), again in good agreement with observations. The exponents for the evolution of the number of lines and the effective opacity do not sim ply differ by 1.0, as in the standard cloud picture, owing to saturati on effects for the stronger lines. This also explains why the effectiv e opacity evolves more slowly than (1 + z)(4.5), which is expected for the Gunn-Peterson effect in a uniform medium with J = constant (and O mega = 1). We compare the spectral filling factor for our CDM and LCDM models with observations of the Ly alpha forest in HS 1700+64 and fin d good agreement. Similar calculations for a standard CDM model and a cold plus hot dark matter model fail to match the observed spectral fi lling factor function. We have also compared a number of predictions o f our analytical model with results of numerical hydrodynamical calcul ations (Miralda-Escude et al. 1996) and again find them to be in good agreement. The lognormal hypothesis, coupled with otherwise attractive CDM-dominated cosmological models, appears to provide a plausible and useful description of the distribution of photoionized intergalactic gas and provides a new estimate of the baryonic density of the univers e.