Combining WMAP and SDSS Quasar Data on Reionization Constrains Cosmological Parameters and the Star Formation Efficiency

We present constraints on cosmological and star formation parameters based on combining observations of the Wilkinson Microwave Anisotropy Probe (WMAP) and high-redshift quasars from the Sloan Digital Sky Survey (SDSS). We use a semi-analytic model for reionization (Chiu and Ostriker 2000) that takes into account a number of important physical processes both within collapsing halos and in the intergalactic medium. Assuming that the efficiency of producing UV photons per baryon is constant, we derive a constraint of the form sigma_8 Omega_0^0.5~0.33 in a flat, Lambda-dominated universe with h=0.72, n=0.99, and Omega_b h^2=0.024. However, the calculated optical depth to electron scattering of tau_es~0.06 is well below the value found by WMAP of 0.17+/-(0.04~0.07) (Spergel et al 2003). Since the WMAP constraints on tau_es are somewhat degenerate with the value of the spectral index n, we then permit the primordial spectral index n to float and fix Omega_0 h^2=0.14, while normalizing the power spectrum using WMAP. In addition, we allow the UV-efficiency to have time-dependence. Combining the WMAP constraints with the quasar transmission data, our analysis then favors a model with tau_es=0.11^{+0.02}_{-0.03}, n=0.96^{+0.02}_{-0.03}$, implying sigma_8=0.83^{+0.03}_{-0.05} (95% confidence), and an effective UV-efficiency that was at least ~10x greater at z >> 6. These results indicate that the quasar and WMAP observations are consistent. If future observations confirm an optical depth to electron scattering tau_es~0.1, then it would appear that no more "exotic" sources of UV-photons, such as mini-quasars or AGNs, are necessary; but our analysis indicates that a determination of tau_es>~0.17 would require a more radical solution.