Planetary nebulae of the Large Magellanic Cloud II. The connection with the progenitors' properties

Context. The study of planetary nebulae (PNe) offers the opportunity to evaluate the efficiency of the dust production mechanism during the very late asymptotic giant branch (AGB) phases, which allows us to assess the role played by AGB stars as dust manufacturers. Aims. We studied the relationship between the properties of PNe, particularly the gas and dust content, and the mass and metallicity of the progenitor stars to understand how dust production works in the late AGB phases and to shed new light on the physical processes the stars and the material in their surroundings are subject to in the period between the departure from the AGB and the start of the PN phase. Methods. We considered a sample of nine PNe in the Large Magellanic Cloud, seven of which are characterised by the presence of carbonaceous dust and the remaining two the presence of silicates. For these stars, we estimated the masses and the metallicity of their progenitor stars. We combined results from stellar evolution and dust formation modelling with results from analyses of the spectral energy distribution to determine the relation between the dust and gas mass of the PNe considered and the mass and metallicity of the progenitors. Results. The physical properties of carbon-rich PNe are influenced by the mass of the progenitor star. Specifically, the dust-to-gas ratio in the nebula increases from 5 x 10(-4) to 6 x 10(-3 )as the progenitor star's mass increases from approximately 0.9-2 M-circle dot. This change is partly influenced by the effective temperature of the PNe, and it occurs because higher-mass carbon stars are more efficient at producing dust. Consequently, as the progenitor's mass increases, the gas mass of the PN decreases since the larger amounts of dust lead to greater effects from radiation pressure, which pushes the gas outwards. No meaningful conclusions can be drawn from the study of the PNe with silicate-type dust, because the subsample comprises two PNe only, one of which is almost dust-free.