Planetary nebulae as tracers of galaxy stellar populations

We address the general problem of the luminosity-specific planetary nebula (PN) number, better known as the 'alpha' ratio, given by alpha=N-PN/L-gal, and its relationship with the age and metallicity of the parent stellar population. Our analysis relies on population synthesis models that account for simple stellar populations (SSPs), and more elaborate galaxy models covering the full star formation range of the different Hubble morphological types. This theoretical framework is compared with the updated census of the PN population in Local Group (LG) galaxies and external ellipticals in the Leo group, and the Virgo and Fornax clusters. The main conclusions of our study can be summarized as follows. (i) According to the post-asymptotic giant branch (AGB) stellar core mass, PN lifetime in a SSP is constrained by three relevant regimes, driven by the nuclear (M-core greater than or similar to 0.57 M-circle dot), dynamical (0.57 M-circle dot greater than or similar to M-core greater than or similar to 0.55 M-circle dot) and transition (0.55 M-circle dot greater than or similar to M-core greater than or similar to 0.52 M-circle dot) time-scales. The lower limit for M-core also sets the minimum mass for stars to reach the AGB thermal-pulsing phase and experience the PN event. (ii) Mass loss is the crucial mechanism to constrain the value of alpha, through the definition of the initial-to-final mass relation (IFMR). The Reimers mass-loss parametrization, calibrated on Pop II stars of Galactic globular clusters, poorly reproduces the observed value of alpha in late-type galaxies, while a better fit is obtained using the empirical IFMR derived from white dwarf observations in the Galaxy open clusters. (iii) The inferred PN lifetime for LG spirals and irregulars exceeds 10 000 yr, which suggests that M-core less than or similar to 0.65 M-circle dot cores dominate, throughout. (iv) The relative PN deficiency in elliptical galaxies, and the observed trend of alpha with galaxy optical colours, support the presence of a prevailing fraction of low-mass cores (M-core less than or similar to 0.55 M-circle dot) in the PN distribution and a reduced visibility time-scale for the nebulae as a consequence of the increased AGB transition time. The stellar component with M-core less than or similar to 0.52 M-circle dot, which overrides the PN phase, could provide an enhanced contribution to hotter HB and post-HB evolution, as directly observed in M 32 and the bulge of M 31. This implies that the most UV-enhanced ellipticals should also display the lowest values of alpha, as confirmed by the Virgo cluster early-type galaxy population. (v) Any blue-straggler population, invoked as progenitor of the M-core greater than or similar to 0.7 M-circle dot PNe in order to preserve the constancy of the bright luminosity-function cut-off magnitude in ellipticals, must be confined to a small fraction (a few per cent at most) of the whole galaxy PN population.