An MCMC determination of the primordial helium abundance

TL;DR

The paper applies Markov Chain Monte Carlo (MCMC) methods to an eight-parameter nebular model to extract the primordial helium abundance $Y_p$ from metal-poor H II region spectra. It emphasizes data quality, notably the inclusion of the weak He I $\lambda4026$ line, and uses a $\chi^2$ goodness-of-fit criterion to curate a reliable final dataset. The analysis yields $Y_p = 0.2534 \pm 0.0083$ (via regression of $Y$ on metallicity $O/H$) in broad agreement with the WMAP value, illustrating the method's potential to tighten constraints with more high-quality spectra. The work advocates a rigorous, bias-reducing data selection pipeline and highlights pathways for future improvement, including higher-resolution spectra and additional diagnostic lines to better constrain underlying absorption and temperature degeneracies.

Abstract

Spectroscopic observations of the chemical abundances in metal-poor H II regions provide an independent method for estimating the primordial helium abundance. H II regions are described by several physical parameters such as electron density, electron temperature, and reddening, in addition to y, the ratio of helium to hydrogen. It had been customary to estimate or determine self-consistently these parameters to calculate y. Frequentist analyses of the parameter space have been shown to be successful in these determinations, and Markov Chain Monte Carlo (MCMC) techniques have proven to be very efficient in sampling this parameter space. Nevertheless, accurate determination of the primordial helium abundance from observations of H II regions is constrained by both systematic and statistical uncertainties. In an attempt to better reduce the latter, and better characterize the former, we apply MCMC methods to the large dataset recently compiled by Izotov, Thuan, & Stasinska (2007). To improve the reliability of the determination, a high quality dataset is needed. In pursuit of this, a variety of cuts are explored. The efficacy of the He I 4026 emission line as a constraint on the solutions is first examined, revealing the introduction of systematic bias through its absence. As a clear measure of the quality of the physical solution, a χ^2 analysis proves instrumental in the selection of data compatible with the theoretical model. In addition, the method also allows us to exclude systems for which parameter estimations are statistical outliers. As a result, the final selected dataset gains in reliability and exhibits improved consistency. Regression to zero metallicity yields Y_p = 0.2534 \pm 0.0083, in broad agreement with the WMAP result. The inclusion of more observations shows promise for further reducing the uncertainty, but more high quality spectra are required.

Figures (14)

• Figure 1: Histogram of the HeBCD sample of ITS07 in terms of the oxygen to hydrogen ratio, O/H.
• Figure 2: Histogram of the HeBCD sample of ITS07 in terms of the equivalent width of H$\beta$, W(H$\beta$).
• Figure 3: Plot of the helium abundance versus O/H for the entire sample. The black circles denote objects for which He I $\lambda$4026 is reported and was used to calculate $\chi^{2}$ and determine the best-fit solution, while the red squares mark objects for which He I $\lambda$4026 is not reported and is, therefore, excluded from their analysis. An upward bias in the value of y$^{+}$ is apparent in the distribution of points lacking He I $\lambda$4026.
• Figure 4: Histogram of best-fit $\chi^{2}$ for the 70 observations with He I $\lambda$4026 reported. 25 observations have $\chi^{2}<4$ (95.45% confidence level).
• Figure 5: $\chi^{2}$ versus the neutral to ionized hydrogen fraction, $\xi$, for Mrk 35 and Mrk 209. On the left, Mrk 35 exhibits an unphysical $\xi$ in contrast to the well determined value for Mrk 209, shown on the right, with the 68% confidence level marked. Mrk 35's $\xi$ likelihood plot corresponds to more than 99% of the hydrogen present being in the neutral state, an unphysical model for an H II region.