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 4He 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 4He abundance to various physical parameters. Because of this, Monte Carlo simulations of the data are required to derive accurate estimates of both the 4He abundance and the appropriate errors. Typically, we find that the uncertainties derived from the Monte-Carlo simulations are a factor of ~2 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 λ4026 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.
Bibliographical noteFunding Information:
We would like to thank R. Kennicutt and B. Pagel for insightful comments on the manuscript. We also are pleased to thank R. Benjamin, D. Kunth, A. Peimbert, M. Peimbert, G. Shields, J. Shields, G. Steigman, E. Terlevich, R. Terlevich, and S. Viegas for informative and valuable discussions. The work of KAO is supported in part by DOE grant DE-FG02-94ER-40823. EDS is grateful for partial support from a NASA LTSARP grant No. NAGW-3189.
- Early universe
- Galaxies: abundances
- H II regions