A Lower Bound on the Cosmic Baryon Density

We derive lower bounds on the cosmic baryon density from the requirement that the high-redshift intergalactic medium (IGM) contain enough neutral hydrogen to produce the observed Lyα absorption in quasar spectra. The key theoretical assumption that leads to these analytic bounds is that absorbing structures are no more extended in redshift space than they are in real space. This assumption might not hold if Lyα clouds are highly overdense and thermally broadened, but it is likely to hold in the gravitational instability picture for the Lyα forest suggested by cosmological simulations, independently of the details of the cosmological model. The other ingredients that enter these bounds are an estimate of (or lower limit to) the intensity of the photoionizing UV background from quasars, a temperature T ∼ 104 K for the “warm” photoionized IGM that produces most of the Lyα absorption, a value of the Hubble constant, and observational estimates of the mean Lyα flux decrement D or, for a more restrictive bound, the distribution function P (τ) of Lyα optical depths. With plausible estimates of the quasar UV background and D, the mean decrement bound implies a baryon density parameter Ωb ∼> 0.0125h −2, where h ≡ H0/100 km s −1 Mpc. With conservative values of the UV background intensity and D, the bound weakens to Ωb ∼> 0.005h −2, but the clustering of the absorbing gas that is required in order to reproduce the observed mean decrement with this baryon fraction is incompatible with other properties of quasar absorption spectra. A recent observational determination of P (τ) implies Ωb ∼> 0.0125h −2 even for a conservative estimate of the quasar UV background, and Ωb ∼> 0.018h −2 for a more reasonable estimate. These bounds are consistent with recent low estimates of the primordial deuterium-to-hydrogen ratio (D/H)P , which imply Ωb ≈ 0.025h −2 when combined with standard big bang nucleosynthesis. Since the bounds account only 1 Ohio State University, Department of Astronomy, Columbus, OH 43210; [email protected] 2 University of Pennsylvania, Department of Physics and Astronomy, Philadelphia, PA 19104; [email protected] University of California, Lick Observatory, Santa Cruz, CA 95064; [email protected] Presidential Faculty Fellow Department of Astronomy, University of Washington, Seattle, WA 98195