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 3-D hierarchical clumps. We compare the abundances of He, N, O, Ne, and S obtained from emission line strengths and [O III] and [N II] temperatures to those in our models. We consider stellar temperatures in the range 37.5 -- 45kK and ionizing luminosities from 10^{48} to 10^{51} photons/s.   Clumped models have different ionic abundances than uniform. For hot stars, He^0/He^+ is 2 -- 3%, much larger than with uniform models. This amount of He I 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([OIII) for high stages of ionization and T([NII]) for low, are about as accurate for clumped models as for uniform and within about 20% of the true values. If T([OIII]) is used for analyzing all ions, the derived (O/H) is 40 to 60% 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 UV 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. 
John S. Mathis (1) and Kenneth Wood (2) ((1) The University of   Wisconsin-Madison, (2) University of St. Andrews)