Uncertainties in 4He abundance determinations in extragalactic HII regions

In order to provide a useful constraint on standard big bang nucleosynthesis predictions, the primordial helium abundance must be determined with an accuracy of a few percent. Here we investigate the estimation of errors in deriving and reporting nebular helium abundances from optical emission line spectra of H II regions. We first show that while an estimation of reddening and underlying stellar absorption in H Balmer emission lines can be made by solving for these quantities simultaneously, a minimization routine may underestimate the true errors in the solution due to the degeneracy of the sensitivities of the individual lines. We show that Monte Carlo modeling allows for a better estimate of the errors in underlying absorption and reddening which need to be propagated to all of the data. We emphasize that a comparison of the corrected Balmer line strengths relative to their theoretical values provides a robust test of the magnitude of their associated errors. We conduct a detailed examination of "self-consistent'' methods for determining not only the He-4 abundance from H I and He I emission line ratios, but also other physical parameters. We show that there are strong degeneracies in the sensitivity of the He-4 abundance to various physical parameters. Because of this, Monte Carlo simulations of the data are required to derive accurate estimates of both the He-4 abundance and the appropriate errors. Typically, we find that the uncertainties derived from the Monte-Carlo simulations are a factor of similar to2 larger than those obtained from a straight minimization procedure. This translates into a similar increase in the size of the uncertainty of the derived primordial abundance. For the first time, we demonstrate how to quantify the effects of stellar absorption underlying the He I emission lines (as opposed to assuming that the effects are negligible). We further show that He I lambda 4026 is a sensitive diagnostic of underlying He I absorption, and we recommend adding it to minimization methods. Finally, we demonstrate that solving for physical parameters via a minimization routine opens up the possibility of incorrect solutions if there are any systematic problems with even one observed He I emission line. (C) 2001 Published by Elsevier Science B.V.