The origin of the ionization of the diffuse interstellar medium in spiral galaxies. II. Modelling the distribution of ionizing radiation in NGC 157

In this paper we make a quantitative study of the hypothesis that the diffuse H-alpha emitted from the discs of spiral galaxies owes its origin to the ionizing photons escaping from HII regions. We use the H-alpha measurements of the complete set of HII regions in the spiral NGC 157, for which an HI density map was available, to derive a family of models which predict the ionizing photon distribution in the disc of this galaxy. The predicted diffuse H-alpha surface brightness distributions from our models were compared with the observed distributions showing that, in general terms, the hypothesis of density bounding for the HII regions allows us to predict well the spatial distribution of the diffuse ionized gas. In the model yielding the best fit to the data, the regions of lower luminosity lose a constant fraction of their ionizing flux to their surroundings, while for HII region luminosities above a specific transition value the ionizing escape fraction is a rising function of the Ha luminosity.