Evolution of Structure in the Intergalactic Medium and the Nature of the Lyα Forest

Abstract

We have performed a detailed statistical study of the evolution of structure in a photoionized intergalactic medium (IGM) using analytical simulations to extend the calculation into the mildly nonlinear density regime found to prevail at z = 3. Our work is based on a simple fundamental conjecture: that the probability distribution function of the density of baryonic diffuse matter in the universe is described by a lognormal (LN) random field. The LN distribution has several attractive features and follows plausibly from the assumption of initial linear Gaussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluctuations 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. We have computed two models that succeed in matching observations. One is a nonstandard CDM model with Ω = 1, h = 0.5, and Γ = 0.3, and the other is a low-density flat model with a cosmological constant (LCDM), with Ω = 0.4, Ω Λ = 0.6, and h = 0.65. In both models, the variance of the density distribution function grows with time, reaching unity at about z = 4, where the simulation yields spectra that closely resemble the Lyα forest absorption seen in the spectra of high- z quasars. The calculations also successfully predict the observed properties of the Lyα forest clouds and their evolution from z = 4 down to at least z = 2, assuming a constant intensity for the metagalactic UV background over this redshift range. However, in our model the forest is not due to discrete clouds, but rather to fluctuations in a continuous intergalactic medium. At z = 3, typical clouds with measured neutral hydrogen column densities N H I = 10 15.3 , 10 13.5 , and 10 11.5 cm -2 correspond to fluctuations with mean total densities approximately 10, 1, and 0.1 times the universal mean baryon density. Perhaps surprisingly, fluctuations whose amplitudes are less than 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 with gas at densities below the mean value. We find that the column density distribution of Lyα forest lines can be fitted to f ( N H I )∝ N H I , with β = 1.46 in the range 12.5 < log N H I < 14.5, matching recent Keck results. At somewhat higher column densities the distribution steepens, giving β = 1.80 over the range 14.0 < log N H I < 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 Ω 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 observed quasars at z = 2.5, then Ω b = 0.025 h -2 yields the observed number of Lyα lines and the observed mean opacity. The model predicts that about 80% of the baryons in the universe are associated with Lyα forest features with 13 < log N H I < 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 galaxies and quasars. Our model requires that absorbers at z = 3 with column densities higher than about 10 16 cm -2 —Lyman limit systems and damped Lyα systems—represent a separate population that has collapsed 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 Å, also in good agreement with observations. We fit Voigt profiles to our simulated lines and find a distribution of b parameters that matches that obtained from similar fits to real spectra. The effective opacity in the Lyα forest is found from the model to be τ 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 simply differ by 1.0, as in the standard cloud picture, owing to saturation effects for the stronger lines. This also explains why the effective 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 Ω = 1). We compare the spectral filling factor for our CDM and LCDM models with observations of the Lyα forest in HS 1700+64 and find good agreement. Similar calculations for a standard CDM model and a cold plus hot dark matter model fail to match the observed spectral filling factor function. We have also compared a number of predictions of our analytical model with results of numerical hydrodynamical calculations (Miralda-Escudé 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 intergalact