An MCMC determination of the primordial helium abundance

Abstract

Spectroscopic observations of the chemical abundances in metal-poor H II\nregions provide an independent method for estimating the primordial helium\nabundance. H II regions are described by several physical parameters such as\nelectron density, electron temperature, and reddening, in addition to y, the\nratio of helium to hydrogen. It had been customary to estimate or determine\nself-consistently these parameters to calculate y. Frequentist analyses of the\nparameter space have been shown to be successful in these determinations, and\nMarkov Chain Monte Carlo (MCMC) techniques have proven to be very efficient in\nsampling this parameter space. Nevertheless, accurate determination of the\nprimordial helium abundance from observations of H II regions is constrained by\nboth systematic and statistical uncertainties. In an attempt to better reduce\nthe latter, and better characterize the former, we apply MCMC methods to the\nlarge dataset recently compiled by Izotov, Thuan, & Stasinska (2007). To\nimprove the reliability of the determination, a high quality dataset is needed.\nIn pursuit of this, a variety of cuts are explored. The efficacy of the He I\n4026 emission line as a constraint on the solutions is first examined,\nrevealing the introduction of systematic bias through its absence. As a clear\nmeasure of the quality of the physical solution, a \\chi^2 analysis proves\ninstrumental in the selection of data compatible with the theoretical model. In\naddition, the method also allows us to exclude systems for which parameter\nestimations are statistical outliers. As a result, the final selected dataset\ngains in reliability and exhibits improved consistency. Regression to zero\nmetallicity yields Y_p = 0.2534 \\pm 0.0083, in broad agreement with the WMAP\nresult. The inclusion of more observations shows promise for further reducing\nthe uncertainty, but more high quality spectra are required.\n