The effects of spatially distributed ionisation sources on the temperature structure of H II 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 ionised by multiple non-centrally located stars or star clusters. Geometrical effects including the spatial configuration of ionising sources affect the temperature and ionisation structure of these regions. We try to isolate the effects of multiple non-centrally located stars, via the construction of 3D photoionisation models using the 3D Monte Carlo photoionisation code MOCASSIN with very simple gas density distributions, but various spatial configurations for the ionisation sources. Our first aim is to study the resulting temperature structure of the gas and investigate the behaviour of temperature fluctuations within the ionised 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 ionising sources distributed in the full volume, whose Strömgren spheres rarely overlap, show smaller temperature fluctuation than their central ionisation counterparts, with fully overlapping concentric Strömgren 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 starforming regions, as well as providing a constraint for temperatures and luminosities of the ionising sources. Empirical metallicity diagnostics must often be calibrated with the aid of photoionisation 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 ionising 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 ionising sources. We find that the dependence of the metallicity indicators on the ionisation parameter causes a clear bias, due to the fact that models with a fully distributed configuration of stars always display lower ionisation parameters than their fully concentrated counterparts. The errors found imply that the geometrical distribution of ionisation sources may partly account for the large scatter in metallicities derived using model-calibrated empirical methods.