Combining Wilkinson Microwave Anisotropy Probe and Sloan Digital Sky Survey Quasar Data on Reionization Constrains Cosmological Parameters and Star Formation Efficiency

We present constraints on cosmological and star formation parameters based on combining observations from the Wilkinson Microwave Anisotropy Probe (WMAP) and high-redshift quasars from the Sloan Digital Sky Survey (SDSS). We use a semianalytic model for reionization that takes into account a number of important physical processes both within collapsing halos (e.g., H₂ cooling) and in the intergalactic medium (e.g., H₂ cooling, Compton cooling, and photoionization heating). We find that the Gunn-Peterson absorption data provide tight constraints on the power spectrum at small scales in a manner analogous to that derived from the cluster mass function. Assuming that the efficiency of producing UV photons per baryon is constant, the constraint takes on the form σ₈Ω ≈ 0.33 in a flat, Λ-dominated universe with h = 0.72, n = 0.99, and Ω_bh² = 0.024. However, the calculated optical depth to electron scattering of τ_es ~ 0.06 is well below the value found by WMAP of 0.17 ± (0.04 ~ 0.07). Since the WMAP constraints on τ_es are somewhat degenerate with the value of the spectral index n, we then permit the primordial spectral index n to float and consider the 1 σ WMAP-only determination of Ω₀h² = 0.14 ± 0.02 (implying Ω₀ = 0.27 ± 0.04), while normalizing the power spectrum using WMAP. In addition, we allow the UV efficiency to be greater in the past. Combining the WMAP constraints with the quasar transmission data, our analysis then favors a model with τ_es = 0.11(Ω₀/0.27)^-1, n = 0.96(Ω₀/0.27)^-0.57, implying a WMAP normalization of σ₈ = 0.83(Ω₀/0.27)^0.53 (all at 95% confidence) and an effective UV efficiency that was at least ~10 times greater at z ≫ 6. The implied UV efficiency is not unreasonable for stars, spanning the range from 10^-5.5 to 10^-4. These results indicate that the quasar and WMAP observations are consistent. If future observations confirm an optical depth to electron scattering τ_es ~ 0.1, then it would appear that no more "exotic" sources of UV photons, such as miniquasars or active galactic nuclei, are necessary. However, unless one considers more radical sources of UV photons or alternative forms for the power spectrum of density fluctuations, one cannot achieve a value of τ_es ≳ 0.17 without violating some combination of constraints from quasar transmission data from z = 4 to 6 and WMAP measurements at large scales.