The effects of spatially distributed ionization sources on the temperature structure of HII regions

Spatially resolved studies of star-forming regions show that the assumption of spherical geometry is not realistic in most cases, with a major complication posed by the gas being ionized by multiple non-centrally located stars or star clusters. Geometrical effects including the spatial configuration of ionizing sources affect the temperature and ionization structure of these regions. We try to isolate the effects of multiple non-centrally located stars via the construction of 3D photoionization models using the 3D Monte Carlo photoionization code MOCASSIN with very simple gas density distributions, but various spatial configurations for the ionization sources. Our first aim is to study the resulting temperature structure of the gas and investigate the behaviour of temperature fluctuations within the ionized region. We show that geometry affects the temperature structures in our models differently according to metallicity. For the geometries and stellar populations considered in our study, at intermediate and high metallicities, models with ionizing sources distributed in the full volume, whose Stromgren spheres rarely overlap, show smaller temperature fluctuation than their central ionization counterparts, with fully overlapping concentric Stromgren spheres. The reverse is true at low metallicities. Finally, the true temperature fluctuations due to the stellar distribution (as opposed to the large-scale temperature gradients due to other gas properties) are small in all cases and not a significant cause of error in metallicity studies. Emission-line spectra from H II regions are often used to study the metallicity of star-forming regions, as well as providing a constraint for temperatures and luminosities of the ionizing sources. Empirical metallicity diagnostics must often be calibrated with the aid of photoionization models. However, most studies so far have been carried out by assuming spherical or plane-parallel geometries, with major limitations on allowed gas and dust density distributions and with the spatial distribution of multiple, non-centrally located ionizing sources not being accounted for. We compare integrated emission-line spectra from our models and quantify any systematic errors caused by the simplifying assumption of a single, central location for all ionizing sources. We find that the dependence of the metallicity indicators on the ionization parameter causes a clear bias due to the fact that models with a fully distributed configuration of stars always display lower ionization parameters than their fully concentrated counterparts. The errors found imply that the geometrical distribution of ionization sources may partly account for the large scatter in metallicities derived using model-calibrated empirical methods.