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Our goal is to morphologically classify the sources identified in the images of the J-PLUS early data release (EDR) into compact (stars) or extended (galaxies) using a suited Bayesian classifier. J-PLUS sources exhibit two distinct populations in the r-band magnitude vs. concentration plane, corresponding to compact and extended sources. We modelled the two-population distribution with a skewed Gaussian for compact objects and a log-normal function for the extended ones. The derived model and the number density prior based on J-PLUS EDR data were used to estimate the Bayesian probability of a source to be star or galaxy. This procedure was applied pointing-by-pointing to account for varying observing conditions and sky position. Finally, we combined the morphological information from g, r, and i broad bands in order to improve the classification of low signal-to-noise sources. The derived probabilities are used to compute the pointing-by-pointing number counts of stars and galaxies. The former increases as we approach to the Milky Way disk, and the latter are similar across the probed area. The comparison with SDSS in the common regions is satisfactory up to r ~ 21, with consistent numbers of stars and galaxies, and consistent distributions in concentration and (g - i) colour spaces. We implement a morphological star/galaxy classifier based on PDF analysis, providing meaningful probabilities for J-PLUS sources to one magnitude deeper (r ~ 21) than a classical boolean classification. These probabilities are suited for the statistical study of 150k stars and 101k galaxies with 15 < r < 21 present in the 31.7 deg2 of the J-PLUS EDR. In a future version of the classifier, we will include J-PLUS colour information from twelve photometric bands., Submitted to Astronomy and Astrophysics. 14 pages, 16 figures, 1 tables. Comments are welcome. All extra figures and the number counts files will be available with the paper in press

Context. From the approximately 3500 planetary nebulae (PNe) discovered in our Galaxy, only 14 are known to be members of the Galactic halo. Nevertheless, a systematic search for halo PNe has never been performed. Aims. In this study, we present new photometric diagnostic tools to identify compact PNe in the Galactic halo by making use of the novel 12-filter system projects, Javalambre Photometric Local Universe Survey (J-PLUS) and Southern-Photometric Local Universe Survey (S-PLUS). Methods. We reconstructed the Isaac Newton Telescope Photometric H alpha Survey of the Northern Galactic Plane diagnostic diagram and propose four new ones using (i) the J-PLUS and S-PLUS synthetic photometry for a grid of photo-ionisation models of halo PNe, (ii) several observed halo PNe, as well as (iii) a number of other emission-line objects that resemble PNe. All colour-colour diagnostic diagrams are validated using two known halo PNe observed by J-PLUS during the scientific verification phase and the first data release (DR1) of S-PLUS and the DR1 of J-PLUS. Results. By applying our criteria to the DR1s (similar to 1190 deg(2)), we identified one PN candidate. However, optical follow-up spectroscopy proved it to be a HII region belonging to the UGC 5272 galaxy. Here, we also discuss the PN and two HII galaxies recovered by these selection criteria. Finally, the cross-matching with the most updated PNe catalogue (HASH) helped us to highlight the potential of these surveys, since we recover all the known PNe in the observed area. Conclusions. The tools here proposed to identify PNe and separate them from their emission-line contaminants proved to be very efficient thanks to the combination of many colours, even when applied - like in the present work - to an automatic photometric search that is limited to compact PNe. © ESO 2020, The authors acknowledge anonymous referee for very insightful comments and for helping us to significantly improve our paper. We thank J.A. Caballero and R. Lopes de Oliveira for their useful comments and suggestions. L.A.G.S. acknowledges the support of CAPES-the Brazilian Federal Agency for Support and Evaluation of Graduate Education within the Ministry of Education of Brazil. D.R.G. thanks the partial support of CNPq (grant 304184/2016-0) and S.A. acknowledges CAPES for a fellowship from the National Postdoctoral Program (PNPD). L.G. was funded by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 839090. R.L.O. was partially supported by the Brazilian agency CNPq (PQ 302037/2015-2). This work is based on observations made with the JAST/T80 telescope at the Observatorio Astrofisico de Javalambre (OAJ), in Teruel, owned, managed and operated by the Centro de Estudios de Fisica del Cosmos de Aragon. Funding for the J-PLUS Project has been provided by the Governments of Spain and Aragon throug the Fondo de Inversiones de Teruel, the Spanish Ministry of Economy and Competitiveness (MINECO: under grants AYA2015-66211-C2-1-P, AYA2015-66211-C2-2, AYA2012-30789 and ICTS-2009-14), and European FEDER funding (FCDD10-4E-867, FCDD13-4E-2685). The Brazilian agencies FAPESP and the National Observatory of Brazil have also contributed to this project. We acknowledge the OAJ Data Processing and Archiving Unit (UPAD) for reducing and calibrating the OAJ data used in this work. This study used data collected at the T80-South, a new 0.826 m telescope carried out by S-PLUS project. The T80-South robotic telescope (Mendes de Oliveira et al. 2019) was founded as a partnership between the Sao Paulo Research Foundation (FAPESP), the Observatorio Nacional (ON), the Federal University of Sergipe (UFS) and the Federal University of Santa Catarina (UFSC), with important financial and practical contributions from other collaborating institutes in Brazil, Chile (Universidad de La Serena) and Spain (CEFCA). We want to thank to the S-PLUS team for the reducing and calibrating of the data. This research has made use of the HASH PN database at hashpn.space. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofisica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut fur Astrophysik Potsdam (AIP), Max-Planck-Institut fur Astronomie (MPIA Heidelberg), Max-Planck-Institut fur Astrophysik (MPA Garching), Max-Planck-Institut fur Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatario Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autonoma de Mexico, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.