Mapping systematic errors in helium abundance determinations using Markov Chain Monte Carlo

Monte Carlo techniques have been used to evaluate the statistical and systematic uncertainties in the helium abundances derived from extragalactic H~II regions. The helium abundance is sensitive to several physical parameters associated with the H~II region. In this work, we introduce Markov Chain Monte Carlo (MCMC) methods to efficiently explore the parameter space and determine the helium abundance, the physical parameters, and the uncertainties derived from observations of metal poor nebulae. Experiments with synthetic data show that the MCMC method is superior to previous implementations (based on flux perturbation) in that it is not affected by biases due to non-physical parameter space. The MCMC analysis allows a detailed exploration of degeneracies, and, in particular, a false minimum that occurs at large values of optical depth in the He~I emission lines. We demonstrate that introducing the electron temperature derived from the [O~III] emission lines as a prior, in a very conservative manner, produces negligible bias and effectively eliminates the false minima occurring at large optical depth. We perform a frequentist analysis on data from several "high quality" systems. Likelihood plots illustrate degeneracies, asymmetries, and limits of the determination. In agreement with previous work, we find relatively large systematic errors, limiting the precision of the primordial helium abundance for currently available spectra.Comment: 25 pages, 11 figure

A New Approach to Systematic Uncertainties and Self-Consistency in Helium Abundance Determinations

Tests of big bang nucleosynthesis and early universe cosmology require precision measurements for helium abundance determinations. However, efforts to determine the primordial helium abundance via observations of metal poor H II regions have been limited by significant uncertainties. This work builds upon previous work by providing an updated and extended program in evaluating these uncertainties. Procedural consistency is achieved by integrating the hydrogen based reddening correction with the helium based abundance calculation, i.e., all physical parameters are solved for simultaneously. We include new atomic data for helium recombination and collisional emission based upon recent work by Porter et al. and wavelength dependent corrections to underlying absorption are investigated. The set of physical parameters has been expanded here to include the effects of neutral hydrogen collisional emission. Because of a degeneracy between the solutions for density and temperature, the precision of the helium abundance determinations is limited. Also, at lower temperatures (T \lesssim 13,000 K) the neutral hydrogen fraction is poorly constrained resulting in a larger uncertainty in the helium abundances. Thus the derived errors on the helium abundances for individual objects are larger than those typical of previous studies. The updated emissivities and neutral hydrogen correction generally raise the abundance. From a regression to zero metallicity, we find Y_p as 0.2561 \pm 0.0108, in broad agreement with the WMAP result. Tests with synthetic data show a potential for distinct improvement, via removal of underlying absorption, using higher resolution spectra. A small bias in the abundance determination can be reduced significantly and the calculated helium abundance error can be reduced by \sim 25%.Comment: 51 pages, 13 figure