A realistic determination of the error on the primordial helium abundance: Steps toward nonparametric nebular helium abundances

Using the WMAP determination of the baryon density, the standard model of big bang nucleosynthesis yields relatively precise predictions of the primordial light-element abundances. Currently there are two significantly different observational determinations of the primordial helium abundance, and if only statistical errors in ⁴He abundance determinations are considered, the discrepancies between the observational determinations and the value favored by the WMAP results are significant. Here we examine in detail some likely sources of systematic uncertainties that may resolve the differences between the two determinations. We conclude that the observational determination of the primordial helium abundance is completely limited by systematic errors and that these systematic errors have not been fully accounted for in any published observational determination of the primordial helium abundance. In principle, the observed metal-poor H ∥ region spectra should be analyzed in a nonparametric way, such that the H ∥ region physical conditions and the helium abundance are derived solely from the relative flux ratios of the helium and hydrogen emission lines. In practice, there are very few H n region spectra with the quality that allows this, so that most analyses depend on assumed ranges or relationships between physical parameters, resulting in parametric solutions with underestimated error bars. A representative result of our analysis yields Y_p, = 0.249 ± 0.009. We stress that the main result of the present work is the increase in the size of the uncertainty rather than the shift in the primordial value. Furthermore, given that most of the spectra analyzed to date do not significantly constrain the primordial helium abundance, we argue in favor of a range of allowed values of 0.232 ≤ Y _p ≤ 0.258. This easily allows for concordance between measurements of the baryon-to-photon ratio (η) from WMAP, deuterium abundances, and helium abundance (although the discrepancy with lithium remains).