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

TL;DR

The paper addresses the precision challenge of the primordial helium abundance from metal-poor H II regions by introducing a self-consistent framework that simultaneously solves hydrogen reddening and helium abundance corrections. It updates emissivities with new data, includes neutral hydrogen collisional emission, and tests a fully integrated χ² minimization over nine lines and seven physical parameters. The results show a general upward shift in helium abundance and broadened uncertainties due to degeneracies, yielding a primordial value around $Y_p ≈ 0.256$ with substantial systematic errors, broadly consistent with CMB-based determinations from the Wilkinson Microwave Anisotropy Probe. The study also demonstrates potential improvements from higher-resolution spectra and highlights remaining systematic obstacles that limit precision, guiding future observational and modeling efforts.

Abstract

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%.

Figures (13)

• Figure 1: Recent historical progression of the primordial helium mass fraction over the previous decade and comparison to the WMAP result pag92itl94oli97itl97it98izo99ppr00ti02ppl02lur03spe03it04os04spe06its07plp07wmap . A general increase in the primordial abundance is apparent. Note that, historically, the error bars are typically small relative to the differences between studies and with WMAP in particular.
• Figure 2: A plot of the derived helium abundance as a function of the temperature and density for a synthetically generated spectrum. Impressed on this diagram is a contour plot of $\chi^2$ versus density and temperature for the same spectrum. The synthetic model uses $n_{e} = 100~cm^{-3}$, $a_{He} = 1.0$ Å, $\tau = 1.0$, $T = 18,000$ K, and $y^{+}=0.08$. The extension of the $\chi^{2} = 2.3$ contour with a strong negative correlation highlights the degeneracy between density and temperature (note that for synthetic data $\chi^{2}_{min} = 0.0$). That the $\chi^{2}$ and abundance contours are nearly perpendicular demonstrates the impact of the degeneracy on the abundance determination ($\pm$5%).
• Figure 3: Monte Carlo plot of 1000 solutions based upon synthetic data taken from os01. The synthetic model is for $n_{e} = 100~cm^{-3}$, $a_{He} = 0.1$ Å, $\tau = 0.1$, and $T = 18,000$ K. The solid circle with error bars marks the original (direct) solution; while the solid square with error bars marks the average of the Monte Carlo solutions. Upon performing the Monte Carlo, the large range in density solutions (with a corresponding large range in temperature solutions), gives a much larger density uncertainty, resulting in a marked increase in the abundance uncertainty (1% to 3%).
• Figure 4: Comparison of the PFM emissivities, $\frac{E(H\beta)}{E(\lambda)}$, to those of BSS (at n$_e$ = 100 cm$^{-3}$). The BSS fits are the dashed lines while the PFM fits are solid. The progression is, left to right, top to bottom, by wavelength: $\lambda$3889, 4026, 4471, 5876, 6678, 7065. The PFM emissivities plotted here are the refit equations of equation \ref{['eq:UE']}; on this plot, the equations reported in PFM are within the line thickness of the refit equations.
• Figure 5: The PFM emissivities, $\frac{E(H\beta)}{E(\lambda)}$, plotted relative to those of BSS (at n$_e$ = 100 cm$^{-3}$). The newer fits deviate from the old by only several percent, but the relative shifts are clearly not the same for all six lines. The three strongest lines, $\lambda$4471, 5876, and 6678, show similar behavior, but 4026 is opposite, and 3889 and 7065 cross the zero deviation line.