On the most luminous planetary nebulae of M31.

To study the progenitors of PNe at the tip of the Planetary Nebula Luminosity Function (PNLF), we obtained the deepest existing spectra of a sample of PNe in the galaxy M31. Precise chemical abundances allow us to confront the theoretical yields for Asymptotic Giant Branch (AGB) stellar masses and metallicities expected at the bright end of the PNLF. Central star masses of the sampled PNe provide direct information on the controversial origin of the universal cutoff of the PNLF. Using the 10.4m Gran Telescopio Canarias (GTC) optical spectra of nine bright M31 PNe were obtained: four of them at the tip of the PNLF, and the other five some 0.5 magnitudes fainter. A control sample of 21 PNe with previous GTC spectra from literature is also included. Their physical properties and chemical abundances (He, N, O, Ar, Ne and S) are analysed. The central star masses are estimated with Cloudy modelling using the most recent evolutionary tracks. The studied PNe show a remarkable uniformity in all their nebular properties, the brightest PNe showing relatively large electron densities. Stellar characteristics also span a narrow range: ${ = 4300 \pm 310, = 122000 \pm 10600 K}$ for the central stars of the four brightest PNe, and ${ = 3300 \pm 370, = 135000 \pm 26000 K}$ for those in the control set. This groups all the brightest PNe at the location of maximum temperature in the post-AGB tracks for stars with initial masses ${M = 1.5 M_{\odot}}$. These figures provide robust observational constraints about the stellar progenitors producing the PNLF cutoff in a star-forming galaxy such as M31, where a large range of initial masses is in principle available. Inconsistency is found, however, in the computed N/O abundance ratios of five nebulae, which are 1.5 to 3 times larger than predicted by the existing models for stars of these masses.