3. THE BARYON BUDGET AT z 3

There has been significant progress in understanding stellar populations at high redshift (e.g., Madau et al. 1996), but many issues remain open. It is fortunate for our purpose that stars are subdominant in the budget at the present epoch and likely are even less important at high redshift, so we can concentrate on the constraints on diffuse gas from quasar absorption line spectra.

The neutral hydrogen at z ~ 3 is predominantly in the high column density damped Lyman- absorbers (DLAs; Lanzetta, Wolfe, & Turnshek 1995 and references therein). The amount of neutral hydrogen in the DLAs increases with increasing redshift back to z ~ 2. Our adopted value for the the density parameter in this form at 2 < z < 3 is from Storrie-Lombardi, Irwin, & McMahon (1996):

(35)

The two estimates are for = 0 and = 1 respectively, and include the mass of the accompanying helium. Because these systems are optically thick to ionizing radiation there is no correction for an ionized fraction in the neutral gas. (The significant amount of mass in plasma in HII regions around young stars or in regions exposed to the intergalactic ionizing radiation are included in the forest component below). Equation (35) could be an underestimate if extinction by dust in the gas suppressed the selection of quasars behind high column density absorbers (Fall and Pei 1993) or an overestimate if gravitational lensing enhanced selection of lines of sight through dust-free, gas-rich absorbers.

Yet another uncertainty is the residency time of gas in DLAs. The large velocities in the DLAs (Prochaska & Wolfe 1997) indicate the cloud masses could be depleted by winds only if there were considerable energy input from supernovae. The more likely scenario is that the density parameter in DLAs is decreasing at z 2 because the HI is being converted into stars. The HI mass in DLAs at z = 3 is about half that in present-day stars (lines 1, 2, 3, and 9 in Table 3). That could mean there is a significant mass in stars in DLAs and other young galaxies at z = 3 and/or that intergalactic matter still is settling onto protogalaxies at z = 3. However, these issues do not affect the budget regarded as a snapshot of conditions at z = 3.

The dominant baryonic mass component is the Lyman- forest gas, detected by the trace neutral hydrogen in plasma that fills space as a froth at z = 3. The density can be estimated from CDM model simulations that give good fits to the observations taking into account the distributions of cloud shapes, sizes, flow velocities, and temperatures, although these estimates are still sensitive to the uncertain flux of ionizing radiation. Rauch et al. (1997) conclude that the baryon density parameter needed to correctly reproduce the statistical absorption (mostly due to clouds at HI surface density 10^{13 ± 1} cm^-2) is _HII h² > 0.017-0.021, depending on cosmological model. Weinberg et al. (1997) quote a lower limit of 0.0125h^-2. Zhang et al. (1997), including a self-consistent analysis of the ionizing spectrum, arrive at a range for h = 0.5 of 0.03< _b < 0.08, with about half of this in the forest clouds. Smaller densities may be possible however because the same absorption can be produced by a higher HI fraction, caused by higher density contrast and lower gas entropy (Wadsley and Bond 1996, Bond and Wadsley 1997). Because of the unresolved issues we assign the current estimates a ``B'' grade. We adopt in Table 3 the range given by Zhang et al. (1997), scaling by h^-3/2. For the lower limit we include not the total density but just that in the forest clouds; this is appropriate for consistency, since the simulations predict a larger fraction of cooled baryonic matter than we infer from observations.

Cool plasma between the forest clouds has lower density and hence a lower neutral fraction and very low HI Lyman- resonance optical depth. The amount of plasma in this form is best probed by measurements of resonance absorption by the most abundant absorbing ion, singly ionized helium (Jakobsen et al. 1994; Davidsen, Kriss, & Zheng 1996.) High resolution HST/GHRS quasar absorption line spectra of two quasars now permit the separation of the more diffuse component of the HeII resonance absorption from the component in the HI Lyman- forest clouds (Hogan, Anderson, & Rugers 1997, Reimers et al. 1997). The upper bound on intercloud gas density is derived based on the maximum permitted mean HeII Lyman- optical depth allowed after subtracting the minimal contribution from the detected HI Lyman- forest clouds, while adopting the hardest ionizing spectrum allowed by the data, with opposite assumptions leading to the lower bound. (Note that the upper bound is on photoionized cool gas; hot gas with thermally ionized helium is not constrained by absorption, but is even less plausible at z 3 than at zL 0.) These limits are consistent with predictions from numerical simulations of CDM models, in which most of the gas is clumped in redshift space by this time (Croft et al. 1997, Zhang et al. 1997, Bi and Davidsen 1997.) Although in principle the helium bounds are sound the present results are given a ``B'' grade because they are as yet based on only two quasars.