Connections between the cosmic baryon fraction, the extragalactic ionizing background, and Lyman break galaxies

We reassess constraints on the cosmological baryon density from observations of the mean decrement and power spectrum of the Lyα forest, taking into account uncertainties in all free parameters in the simplest gravitational instability model. The uncertainty is dominated by that of the photoionizing background, but incomplete knowledge of the thermal state of the intergalactic medium also contributes significantly to the error budget. While current estimates of the baryon fraction from the forest do prefer values that are somewhat higher than the big bang nucleosynthesis value of Ωb h2 = 0.02 ± 0.001, the discrepancy is at most about 3 σ. For instance, assuming the highest estimate of the ionizing background, as indicated by recent measurements of a large escape fraction from Lyman break galaxies by Steidel, Pettini, & Adelberger, we find Ωbh2 = 0.045 ± 0.008. A recent measurement of the ionizing background from the proximity effect by Scott et al., on the other hand, implies Ωbh2 = 0.03 ± 0.01. We provide an expression from which future likelihoods for Ωb h2 can be derived as measurements of the ionizing background improve—consistency among constraints from the forest, nucleosynthesis, and the microwave background will provide a powerful test of the gravitational instability model for the forest and for large-scale structure in general. We also develop a formalism that treats lower bounds on the baryon density in a statistical manner, which is appropriate if only a lower bound on the ionizing background is known. Finally, we discuss the implications of the escape fraction measurement for the age, structure, and stellar content of Lyman break galaxies. We show that the observed hard spectrum from Lyman break galaxies requires a very young age (less than about 1 million years) and/or a top-heavy initial mass function. We also build a model in which an extended (non-disk-like) gas distribution allows a large escape fraction.