A Realistic Determination of the Error on the Primordial Helium Abundance: Steps Toward Non-Parametric Nebular Helium Abundances

TL;DR

This work assesses the primordial helium abundance by explicitly modeling systematic uncertainties in nebular helium determinations from metal-poor H II regions. It introduces an updated non-parametric minimization framework that self-consistently derives $n$, $\\tau$, $a_{HeI}$, and $T$ from six He I lines, with Monte Carlo error propagation to quantify degeneracies and uncertainties. Re-analyses of IT98 and IT04 targets reveal that underlying absorption, radiative-transfer corrections, and temperature–density degeneracies induce larger, more model-dependent uncertainties than previously reported, leading to a broader allowed range for $Y_p$ (roughly $0.232 \le Y_p \le 0.258$). Regression of $Y$ vs metallicity yields $Y_p \approx 0.249-0.250$ with uncertainties of order $\\sim 0.01$, broadly consistent with the CMB-derived baryon density, and the study emphasizes the need for higher-quality data and more robust treatment of systematics to sharpen the primordial helium constraint.

Abstract

Currently there are two significantly different observational determinations of the primordial helium abundance, and, if only statistical errors in He4 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 which 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 HII region spectra should be analyzed in a non-parametric way, such that the HII 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 HII region spectra with the quality that allow 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 \pm 0.009. However, given that most of the spectra analyzed to date do not significantly constrain the primordial helium abundance, we argue in favor a range of allowed values of 0.232 le Y_p le 0.258. [abstract abridged]