On the Abundance of Primordial Helium

We have used recent observations of helium-4, nitrogen and oxygen from some four dozen, low metallicity, extra-galactic HII regions to define mean $N$ versus $O$, $^4He$ versus $N$ and $^4He$ versus $O$ 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 $Y_P = 0.232 \pm 0.003$. For the 2$\sigma$ (statistical) upper bound we find $Y_P^{2\sigma} \le 0.238$. Estimating a 2\% systematic uncertainty $(\sigma _{syst} = \pm 0.005)$ leads to a maximum upper bound to the primordial helium mass fraction: $Y_P^{MAX} = Y_P^{2\sigma} + \sigma_{syst} \le 0.243$. 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 $\eta$ ($\eta_{10} \equiv 10^{10}\eta$) and the number of equivalent light (\lsim 10 MeV) neutrino species. For $Y_P \le 0.238$ ($0.243$), we find $\eta_{10} \le 2.5 (3.9)$ and $N_\nu \leq 2.7 (3.1)$. If indeed $Y_P \le 0.238$, 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-$\alpha$ clouds - will be crucial to resolve this potential crisis for BBN. The larger upper bound, $Y_P \leq 0.243$ is completely