HST/WFPC2 imaging analysis and cloudy modelling of the multiple-shell planetary nebulae NGC 3242, NGC 6826, and NGC 7662

We performed a detailed photometric analysis and photoionization modelling on three high-excitation multiple-shell planetary nebulae: NGC 3242, NGC 6826, and NGC 7662. Archival Hubble Space Telescope/Wide Field Planetary Camera 2 (HST/WFPC2) narrow band filter images were used to investigate shocked regions by two independent methods: using low-excitation ions (via H α/[N II] versus H α/[S II] extended diagnostic diagrams) and by means of high-excitation species looking for regions of enhanced [O III]/H α line ratios. Shocked region analysis via low-excitation ions shows that major deviations from the general inside to outside ionization trend correspond only to regions where fast low-ionization emission regions or low-ionization emission line structures are located. The reduction on the signal-to-noise ratio at the outskirts of the [O III]/H α ratio maps made us unable to unambiguously identified for an enhancement on the [O III]/H α line ratio as an indicator for shocks. For non-shocked regions, we performed a photoionization modelling using CLOUDY. Fittings to the [O III]- and H α-observed radial profiles lead us to constrain on the free parameters of the density laws and filling factors together to temperatures and luminosities for the CSPNe. Best-fitting models show a very well representation of the [O III] and H α emission. Discrepancies in the model fittings to the [N II] and [S II] profiles at NGC 6826 and NGC 3242 can be attributed in the former case, due to a contamination by the light of the CSPN and, in the latter case, either due to gas inhomogeneities within the clumps or to a leaking of ultraviolet radiation.