We have pointed out a number of points in the analysis of optical spectra of nebulae that can lead to biased or inaccurate abundance results if not accounted for properly. We hope to draw attention to the treatment of the H I Balmer lines as a critically important step in an accurate abundance analysis.
Our inspection of self consistent minimization methods for determining helium abundances has revealed several things. In the perfect world when all of the uncertainties in the input data are under control, the 6 line method is best at solving for the physical input parameters and ultimately the He abundance. However, minimization routines should used with caution with a eye toward systematically biased observations. The key diagnostics are the values of the 2 in a straight minimization, and the results of the 3 line method. When the data are good the 2 per degree of freedom should be small, and the results of the 3, 5, and 6 line methods should be consistent. The latter methods should be more accurate and carry smaller error bars on the derived quantities. If either of these conditions are not met, then it is probably not advisable to use those data in a determination of the primordial He abundance. In any case, a Monte Carlo realization of the observations should be conducted to assess the true uncertainties in the resultant abundances.
While it may seem that, in some cases, the straight minimization gives a solution closer to the original input parameters than does the average Monte Carlo result, one must bear in mind that we have been using synthetic data with known values. By running the Monte Carlo on synthetic data we are modeling possible sets of observations consistent with the true physical description of the HII region. That is, each Monte Carlo minimization represents the result of a single possible observation. Running a Monte Carlo realization of real data allows an exploration of all of the possible suitable solutions allowed by the degeneracies in the sensitivities of the various He I lines to the different physical parameters.
Clearly the abundances used in estimating Yp are not observed but rather derived quantities. As we have seen, the derivation of the He abundance relies on several, a priori, unknown but physical input parameters. In this paper, we hope to have clarified the determination process, and quantified the uncertainties in the result. Thus, it may be premature to be arguing over the 3rd decimal place in Yp until a systematic treatment and Monte Carlo analysis of the data has been performed. Our purpose here is not to propose a minimum error for all nebular helium abundances nor to try to give a quantitative estimate of how a given analysis may result in a systematic bias in the derivation of Yp. Rather, we wish to promote a methodology for the analysis of all nebular HII region spectra in the pursuit of accurate He abundances. We emphasize the importance of reporting more information (the equivalent widths of all of the H I and He I emission lines, the 2 results for minimizations) and the use of Monte Carlo techniques for characterizing error terms. In the future, we will apply the recommended methods to both new observations and other observations reported in the literature.
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, M. Peimbert, G. Shields, J. Shields, G. Steigman, E. Terlevich, and R. Terlevich 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.