The implications of Wilkinson Microwave Anisotropy Probe observations for population III star formation processes

In an earlier paper, we pointed out the strong likelihood for universal reionization to occur twice, giving rise to a much larger Thomson optical depth due to the intergalactic medium than that in the case of a single rapid reionization at z similar to 6. The latest Wilkinson Microwave Anisotropy Probe (WMAP) observations of Kogut et al. indicate that the universe indeed appears to have entered a significantly ionized state at a very high redshift. In light of this new development, we perform a more focused analysis of the Thomson optical depth in the context of the spatially flat, cosmological constant-dominated cold dark matter model (LambdaCDM) constrained by WMAP observations. While the current uncertainties of the observed Thomson optical depth are still relatively large, with tau(e) = 0.17 +/- 0.04 (68%), important implications for Population III (Pop III) star formation processes at high redshift can already be inferred. We are able to draw four conclusions: ( 1) In the absence of a top-heavy initial stellar mass function (IMF) for Pop III metal-free stars and without a dramatic upturn in the star formation efficiency and in the ionizing photon escape fraction at high redshift (z > 6), we find tau(e) less than or equal to 0.09. (2) With a top-heavy IMF for the Pop III metal-free stars, a plausible star formation efficiency, and an ionizing photon escape fraction less than or equal to20%, it is expected that taue less than or equal to 0.02, which could be raised to taue = 0.14, if the metal-enrichment efficiency of the intergalactic medium by Pop III stars is reduced by a factor of 5. (3) To reach tau(e) = 0.15-0.17 requires at least one of the following three conditions: the cosmological model power index n is positively tilted to n greater than or equal to 1.03, Pop III star formation in minihalos with molecular hydrogen cooling has an efficiency c(*) (H-2, III) > 0.01, or the ionizing photon escape fraction from Pop III galaxies is close to unity. The highest tau(e) that we have obtained is 0.24 for a WMAP-consistent LambdaCDM model with n = 1.03, a Pop III star formation efficiency of 1% for minihalos, and an ionizing photon escape fraction of 100% from Pop III galaxies. (4) For the WMAP-normalized running index LambdaCDM model, we obtain tau(e) with a Pop III star formation efficiency of 1% for minihalos and an ionizing photon escape fraction of 100% from Pop III galaxies. If the current observed value of the Thomson optical depth withstands future data, we will have strong observational evidence that Pop III stars are massive and that their formation efficiency may be much higher than current theoretical works suggest. Alternatively, there may be unknown, nonstellar ionizing sources at very high redshift.