Effects of photon escape on diagnostic diagrams for HII regions

In this article we first outline the mounting evidence that a significant fraction of the ionizing photons emitted by OB stars within H.. regions escape from their immediate surroundings, i.e from what is normally defined as the H.. region, and explain how an H.. region structure containing high density contrast inhomogeneities facilitates this escape. Next we describe sets of models containing inhomogeneities which are used to predict tracks in the commonly used diagnostic diagrams ( based on ratios of emission lines) whose only independent variable is the photon escape fraction,xi. We show that the tracks produced by the models in two of the most cited of these diagrams conform well to the distribution of observed data points, with the models containing optically thick inhomogeneities (CLUMPY models) yielding somewhat better agreement than those with optically thin inhomogeneities (FF models). We show how variations in the ionization parameter U, derived from emission line ratios, could be due to photon escape, such that for a given region from which 50% of its ionizing photons leak out we would derive the same value of U as for a region with no photon escape but with an input ionizing flux almost an order of magnitude higher. This effect will occur whether the individual inhomogeneities are optically thick or thin. Photon escape will also lead to a change in the derived value of the radiation hardness parameter, and this change differs significantly between models with optically thin and optically thick clumps. Using a rather wide range of assumptions about the filling factor of dense clumps we find, for a selected set of regions observed in M 51 by Diaz et al. (1991) an extreme limiting range of computed photon escape fractions between near zero and 90%, but with the most plausible values ranging between 30% and 50%. We show, using oxygen as the test element, that models with different assumptions about the gas inhomogeneity will tend to give variations in the abundance values derived from diagnostic diagrams, but do not claim here to have a fully developed set of diagnostic tools to improve abundance determinations made in this way. We do present an important step towards an eventual improvement in abundance determinations: the combination of line ratios with the absolute Ha luminosity of a given H.. region, which allows us to determine the photon escape fraction, and hence resolve the degeneracy between U and.. We use observational data of this type show that a large set of H II regions in M 101 observed by Cedres & Cepa (2002) all show significant photon escape with values of xi ranging up to 60% in the leakiest cases.