We present a new synthetic model to follow the evolution of a planetary nebula ( PN ) and its central star , starting from the onset of AGB phase up to the white dwarf cooling sequence .
The model suitably combines various analytical prescriptions to account for different ( but inter-related ) aspects of planetary nebulae , such as : the dynamical evolution of the primary shell and surrounding ejecta , the photoionisation of H and He by the central star , the nebular emission of a few relevant optical lines ( e.g .
H \beta ; He ii \lambda 4686 ; [ O iii ] \lambda 5007 ) .
Particular effort has been put into the analytical description of dynamical effects such as the three-winds interaction and the shell thickening due to ionisation ( i.e .
the thin-shell approximation is relaxed ) , that are nowadays considered important aspects of the PN evolution .
Predictions of the synthetic model are tested by comparison with both findings of hydrodynamical calculations , and observations of Galactic PNe .
The sensitiveness of the results to the models parameters ( e.g .
transition time , mass of the central star , H-/He-burning tracks , etc . )
is also discussed .
We briefly illustrate the systematic differences that are expected in the luminosities and lifetimes of PNe with either H- or He-burning central stars , which result in different “ detection probabilities ” across the H-R diagram , in both H \beta and [ O iii ] \lambda 5007 lines .
Adopting reasonable values of the model parameters , we are able to reproduce , in a satisfactory way , many general properties of PNe , like the ionised mass–nebular radius relationship , the trends of a few main nebular line ratios , and the observed ranges of nebular shell thicknesses , electron densities , and expansion velocities .
The models naturally predict also the possible transitions from optically-thick to optically-thin configurations ( and vice versa ) .
In this context , our analysis indicates that the condition of optical thinness to the H continuum plays an important role in producing the observed “ Zanstra discrepancy ” between the temperatures determined from H or He ii lines , as well as it affects the mass-increasing part of the ionised mass-radius relation .
These predictions are supported by observational indications by Méndez et al .
( 1992 ) .
Another interesting result is that the change of slope in the electron density–nebular radius relation at R _ { ion } \sim 0.1 pc , pointed out by Phillips ( 1998 ) , is also displayed by the models and may be interpreted as the result of the progressive convergence of the PNe to the condition of constant ionised mass .
Finally we would like to remark that , thanks to its computational agility , our synthetic PN model is particularly suitable to population synthesis studies , and it represents the basic ground from which many future applications will be developed .