Planetary nebulae in

Context. The Gaia Early Data Release 3 (EDR3), published in December 2020, features improved photometry and astrometry compared to that published in the previous DR2 file and includes a substantially larger number of sources, of the order of 2000 million, making it a paradigm of big data astronomy. Many of the central stars of planetary nebulae (CSPNe) are inherently faint and difficult to identify within the field of the nebula itself. Gaia measurements may be relevant not only in identifying the ionising source of each nebula, but also in the study their physical and evolutionary properties. Aims. We demonstrate how Gaia data mining can effectively help to solve the issue of central star misidentification, a problem that has plagued the field since its origin. As we did for DR2, our objective is to present a catalogue of CSPNe with astrometric and photometric information in EDR3. From that catalogue, we selected a sample of stars with high-quality astrometric parameters, on which we carried out a more accurate analysis of CSPNe properties. Methods.GaiaGBP − GRP colours allow us to select the sources with sufficient temperatures to ionise the nebula. In order to estimate the real colour of a source, it is important to take into account interstellar extinction and, in the case of compact nebulae, nebular extinction when available. In addition, distances derived from EDR3 parallaxes (combined with consistent literature values) can be used to obtain nebular intrinsic properties from those observed. With this information, CSPNe can be plotted in an Hertzsprung-Russell diagram. From information on the spectral classification of the CS (from the literature) and evolutionary models for post-AGB stars, their evolutionary state can then be analysed. Furthermore, EDR3 high-quality astrometric data enable us to search for objects comoving with CSs in the field of each nebula by detecting sources with parallaxes and proper motions similar to those of the CS. Results. We present a catalogue of 2035 PNe with their corresponding CS identification from among Gaia EDR3 sources. We obtain the distances for those with known parallaxes in EDR3 (1725 PNe). In addition, for a sub-sample (405 PNe) with the most accurate distances, we obtain different nebular properties such as their Galactic distribution, radius, kinematic age, and morphology. Furthermore, for a set of 74 CSPNe, we present the evolutionary state (mass and age) derived from their luminosities and effective temperatures from evolutionary models. Finally, we highlight the detection of several wide binary CSPNe through an analysis of the EDR3 astrometric parameters, and we contribute to shedding some light on the relevance of close binarity in CSPNe