UMN-TH-1913/00, TPI-MINN-00/35
astro-ph/0007081

For a postscript version of the article, click here.

Abstract. Of the light element abundances capable of testing standard big bang nucleosynthesis, only ⁴ He is measured with an accuracy of a few percent. Thus, it is imperative to establish a comprehensive technique for determining ⁴ He abundances and reliable estimates of the true systematic uncertainties. Helium abundance determinations in H II regions are made from the observations of several distinct He I emission lines and their strengths relative to H I emission lines. With the general availability of large format, linear CCD detectors, the accuracy of relative emission line ratios has improved to the point where several terms in the error budget which were assumed to be negligible may now be important. Here we investigate the estimation of errors in deriving and reporting nebular helium abundances from optical emission line spectra.

We first investigate the analysis of the H Balmer emission lines. These lines can be used to determine the reddening of the spectrum, but underlying stellar absorption needs to be accounted for. Using a minimization routine, it is possible to solve simultaneously for both reddening and underlying absorption, but, due to the degeneracy of the sensitivities of the individual lines, a minimization routine may underestimate the true errors in the solution. 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. The magnitude of the ² in such a minimization is important in judging the reliability of the derived solution. We also point out that comparing corrected Balmer line ratios to their theoretical values provides a sensitive test of the propriety of the magnitude of the errors of reported emission line strengths.

The derived ⁴ He abundance depends on the H I and He I emissivities, the electron density, the electron temperature, the presence of underlying stellar absorption, and, in some cases, the optical depth in the He I emission lines. Certain He I emission lines depend sensitively on some of these quantities. Ideally, solutions in which all observable He I lines yield the same answer for the derived He abundance are favored. We examine several methods for such a "self-consistent" analysis to obtain the ⁴ He abundance in low metallicity HII regions, and attempt to make a thorough assessment of the uncertainties involved in such determinations. We demonstrate that solving for physical parameters via a minimization routine opens up the possibilities of incorrect solutions if there are any systematic problems with even one observed He I emission line. In many cases, minimizing with just three lines (5876, 4471, and 6678) is competitive with adding more lines into a minimization (and always provides a useful diagnostic). Underlying He I absorption can be important at the level of reported uncertainties, yet hard to detect. He I 4026 is shown to be a sensitive diagnostic of underlying He I absorption, and we recommend adding it in to minimization methods. We show that Monte-Carlo simulations are necessary to reliably determine the uncertainties in the physical parameters as well as the ⁴ He abundance determined in minimization routines. We also point out that the magnitude of the ² is important in judging the reliability of the derived solution and should be reported in addition to the derived helium abundance.

Table of Contents

• INTRODUCTION
• DETERMINATION OF PHYSICAL PARAMETERS
• Measurements of Relative Emission Line Strengths and Errors
• Determination of Reddening and Underlying H I Absorption from Balmer Lines
• Electron Temperature Determinations from Collisionally Excited Lines
• Electron Density Determinations from Collisionally Excited Lines
• CONVERTING INDIVIDUAL HE I LINES INTO HE/H ABUNDANCES
• He I and H I Emissivities
• Collisional Enhancement of He I Emission Lines
• The Effects of Underlying Stellar Absorption
• He I Optical Depth Effects
• Ionization Correction Factors
• SELF-CONSISTENT METHODS FOR EXTRACTING THE ⁴ He ABUNDANCE
• Using 3 Lines
• Using 5 Lines
• Using 6 Lines
• TEST CASES AND EXAMPLES
• Cases with no Systematic Errors
• Cases with Systematic Errors in I(λ3889)
• Cases with Systematic Errors in I(λ7065)
• DISCUSSION
• MONTE CARLO ESTIMATES OF REDDENING AND UNDERLYING BALMER ABSORPTION
• MONTE CARLO ESTIMATES OF REDDENING AND UNDERLYING BALMER ABSORPTION IN REAL OBSERVATIONS
• MONTE CARLO ESTIMATES OF SELF-CONSISTENT HELIUM LINE RATIOS
• REFERENCES