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New Strong Line Abundance Diagnostics for \HII Regions: Effects of $κ$-Distributed Electron Energies and New Atomic Data

Recently, \citet{Nicholls12}, inspired by \emph{in situ} observations of solar system astrophysical plasmas, suggested that the electrons in \HII regions are characterised by a $κ$-distribution of electron energies rather than by a simple Maxwell-Boltzmann distribution. Here we have collected together the new atomic data within a modified photoionisation code to explore the effects of both the new atomic data and the $κ$-distribution on the strong-line techniques used to determine chemical abundances in \HII regions. By comparing the recombination temperatures ($T_{\rm rec}$) with the forbidden line temperatures ($T_{\rm FL}$) we conclude that $ κ\sim 20$. While representing only a mild deviation from equilibrium, this is sufficient to strongly influence abundances determined using methods which depend on measurements of the electron temperature from forbidden lines. We present a number of new emission line ratio diagnostics which cleanly separate the two parameters determining the optical spectrum of \HII regions - the ionisation parameter $q$ or $\cal{U}$ and the chemical abundance; 12+log(O/H). An automated code to extract these parameters is presented. Using the homogeneous dataset from \citet{vanZee98}, we find self-consistent results between all these different diagnostics. The systematic errors between different line ratio diagnostics are much smaller than was found in the earlier strong line work. Overall the effect of the $κ$-distribution on the strong line abundances derived solely on the basis of theoretical models is rather small.