The effects of clumping on derived abundances in H ii regions

We have compared Monte Carlo photoionization models of H  ii regions with a uniform density distribution with models with the same central stars and chemical compositions but with a three‐dimensional hierarchical density distribution consisting of clumps within clumps, on a four‐tier scheme. The purpose is to compare the abundances of He, N, O, Ne and S obtained by standard analyses (emission‐line strengths and measured mean temperatures from [O  iii ] and [N  ii ]) with the abundances in our models. We consider stellar temperatures in the range 37.5–45 kK and ionizing photon luminosities from 10 48 to 10 51 s −1 . Clumped models have different ionic abundances than uniform. For hot stars, (He 0 /H + ) is 2–3 per cent, much larger than with uniform models. This amount of He 0 is independent of metallicity and so impacts the determination of the primordial abundance of He. The total abundances of O, Ne and S obtained by the usual methods of analysis, using T ([O  iii ]) for high stages of ionization and T ([N  ii ]) for low, are about as accurate for clumped models as for uniform, and within ∼20 per cent of the true values. If T ([O  iii ]) is used for analysing all ions, the derived (O/H) is ∼40–60 per cent too large for cool stars but is good for hot stars. Uniform models have similar errors, so the clumping does not change the accuracy of abundance analysis. The physical causes of the ionic abundance errors are present in real nebulae. In clumped models, helium ionizing radiation from zones of high ionization (low He 0 and low ultraviolet opacity) can penetrate nearby regions near the edge of the ionized zone. This effect allows He 0 to absorb more stellar photons than in uniform or radially symmetrical geometries. In turn, these absorptions compete with O + , etc., for those energetic stellar photons.