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

Abstract

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