On the abundance of primordial helium

We have used recent observations of helium-4, nitrogen, and oxygen from some four dozen, low-metallicity, extragalactic H II regions to define mean N vs. O, ⁴He vs. N, and ⁴He vs. O relations which are extrapolated to zero metallicity to determine the primordial ⁴He mass fraction Y_P. The data and various subsets of the data, selected on the basis of nitrogen and oxygen, are all consistent with Y^P = 0.232 ± 0.003. For the 2 σ (statistical) upper bound we find Y_P^{2 σ} ≤ 0.238. Estimating a 2% systematic uncertainty (σ_syst = ± 0.005) leads to a maximum upper bound to the primordial helium mass fraction: Y_P^MAX = Y_P^{2 σ} + σ_syst ≤ 0.243. We compare these upper bounds to Y_P with recent calculations of the predicted yield from big bang nucleosynthesis to derive upper bounds to the nucleon-to-photon ratio η(η₁₀ ≡ 10¹⁰_η) and the number of equivalent light (≲10 MeV) neutrino species. For Y_p ≤ 0.238 (0.243), we find η₁₀ ≤ 2.5(3.9) and N_v ≤ 2.7(3.1). If indeed Y_P ≤ 0.238, then BBN predicts enhanced production of deuterium and helium-3 which may be in conflict with the primordial abundances inferred from model-dependent (chemical evolution) extrapolations of solar system and interstellar observations. Better chemical evolution models and more data - especially D-absorption in the QSO Ly-α clouds - will be crucial to resolve this potential crisis for BBN. The larger upper bound, Y_P ≤ 0.243, is completely consistent with BBN which, now, bounds the universal density of nucleons ( for Hubble parameter 40 ≤ H_o ≤ 100 km s^-1 Mpc^-1 and cosmic background radiation temperature T = 2.726 ± 0.010) to lie in the range 0.01 ≤ Ω_BBN ≤ 0.09 (for H_o = 50 h₅₀ km s^-1 Mpc^-1, 0.04 ≤ Ω_BBN h₅₀² ≤ 0.06).