The giant H II region NGC 588 as a benchmark for 2D photoionisation models

Aims. We use optical integral field spectroscopy and 8 mu m and 24 mu m mid-IR observations of the giant H II region NGC 588 in the disc of M33 as input and constraints for two-dimensional tailor-made photoionisation models under different geometrical approaches. We do this to explore the spatial distribution of gas and dust in the interstellar, ionised medium surrounding multiple massive stars. Methods. Two different geometrical approaches are followed for the modelling structure: i) Each spatial element of the emitting gas is studied individually using models, which assume that the ionisation structure is complete in each element, to look for azimuthal variations across gas and dust. ii) A single model is considered, and the two-dimensional structure of the gas and the dust are assumed to be due to the projection of an emitting sphere onto the sky. Results. The models in both assumptions reproduce the radial profiles of H beta surface brightness, the observed number of ionising photons, and the strong optical emission-line relative intensities. The first approach produces a constant-density, matter-bounded thin shell of variable thickness and dust-to-gas ratio, while the second gives place to a radiation-bounded, thick shell sphere of decreasing particle density. However, the radial profile of the 8 mu m/24 mu m IR ratio, depending on the gas and dust geometry, only fits well when the thick-shell model is used. The resulting dust-to-gas mass ratio, which was obtained empirically from the derived dust mass using data from Spitzer, also has a better fit using the thick-shell solution. In both approaches, models support the importance of the low surface-brightness positions on the integrated spectrum of the nebula, the chemical homogeneity, the ionisation-parameter radial decrease, and the robustness of strong-line methods to derive the equivalent effective temperature in extended regions. These results must be taken with care in view of the very low extinction values that are derived from the IR, as compared to that derived from the Balmer decrement. Besides, the IR can be possibly contaminated with the emission from a cloud of diffuse gas and dust above the plane of the galaxy detected at 250 mu m Herschel image.