Constraints on First-Light Ionizing Sources from Optical Depth of the   Cosmic Microwave Background
  We examine the constraints on high-redshift star formation, ultraviolet and X-ray pre-ionization, and the epoch of reionization at redshift z_r, inferred from the recent WMAP-5 measurement, tau_e = 0.084 +/- 0.016, of the electron scattering optical depth of the cosmic microwave background (CMB). Half of this scattering can be accounted for by the optical depth, tau_e = 0.04-0.05, of a fully ionized intergalactic medium (IGM) at z < z_GP = 6-7, consistent with Gunn-Peterson absorption in neutral hydrogen. The required additional optical depth, Delta-tau_e = 0.03 +/- 0.02 at z > z_GP, constrains the ionizing contributions of first light sources. WMAP-5 also measured a significant increase in small-scale power, which lowers the required efficiency of star formation and ionization from mini-halos. Early massive stars (UV radiation) and black holes (X-rays) can produce a partially ionized IGM, adding to the residual electrons left from incomplete recombination. Inaccuracies in computing the ionization history, x_e(z), and degeneracies in cosmological parameters (Omega_m, Omega_b, sigma_8, n_s) add systematic uncertainty to the measurement and modeling of $\tau_e$. From the additional optical depth from sources at z > z_GP, we limit the star-formation efficiency, the rate of ionizing photon production for Pop III and Pop II stars, and the photon escape fraction, using standard histories of baryon collapse, minihalo star formation, and black-hole X-ray preionization. 
J. Michael Shull and Aparna Venkatesan