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 (compared with the value inferred from BBN theory using the CMB determined value of the baryon density). 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. It is noted that H gamma and H delta allow better isolation of the collisional effects from the reddening. 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 less than or similar to 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. Seven previously analyzed, "high quality" H II region spectra are used for a primordial helium abundance determination. The updated emissivities and neutral hydrogen correction generally raise the abundance. From a regression to zero metallicity, we find Y-p as 0.2561 +/- 0.0108, in broad agreement with the WMAP result. Alternatively, a simple average of the data yields Y-p = 0.2566 +/- 0.0028. 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 similar to 25%.