Systematic uncertainties in the determination of the primordial $^\mathsf{4}$He abundance

Abstract

The primordial helium abundance Y_p is commonly inferred from abundance determinations in low-metallicity extragalactic HII-regions. Such determinations may be subject to systematic uncertainties that are investigated here. Particular attention is paid to two effects: icf-corrections for ``imperfect'' ionization structure leading to significant amounts of (unobservable) neutral helium or hydrogen and ``tcf''-corrections due to non-uniform temperature. Model HII-regions with a large number of parameters are constructed and it is shown that required corrections are almost exclusively functions of two physical parameters: the number of helium- to hydrogen- ionizing photons in the illuminating continuum Q(He0)/Q(H0), and the ratio of width to radius delta r_S/r_S of the Stromgren sphere. For clouds of sufficient He-ionizing photons Q(He0)/Q(H0) >~ 0.15 and non-negligible width of the Stromgren sphere a significant overestimate of helium abundances may result. Such clouds show radiation softness parameters in the range -0.4 <~ log(eta) <~ 0.3 coincident with the range of eta in observed HII-regions. Existing data of HII-regions indeed seem to display a correlation which is consistent with a typical ~ 2-4% overestimate of helium abundances due to these effects. In case such an interpretation prevails, and in the absence of other compensating effects, a significant downward revision of Y_p may result. It is argued that caution should be exercised regarding the validity of commonly quoted error bars on Y_p.