Photometry and astrometry with JWST -- III. A NIRCam-Gaia DR3 analysis of the open cluster NGC 2506

In the third paper of this series aimed at developing the tools for analysing resolved stellar populations using the cameras on board of the James Webb Space Telescope (JWST), we present a detailed multi-band study of the 2 Gyr Galactic open cluster NGC 2506. We employ public calibration data-sets collected in multiple filters to: (i) derive improved effective Point Spread Functions (ePSFs) for ten NIRCam filters; (ii) extract high-precision photometry and astrometry for stars in the cluster, approaching the main-sequence (MS) lower mass of ~0.1 Msun; and (iii) take advantage of the synergy between JWST and Gaia DR3 to perform a comprehensive analysis of the cluster's global and local properties. We derived a MS binary fraction of ~57.5 %, extending the Gaia limit (~0.8 Msun) to lower masses (~0.4 Msun) with JWST. We conducted a study on the mass functions (MFs) of NGC 2506, mapping the mass segregation with Gaia data, and extending MFs to lower masses with the JWST field. We also combined information on the derived MFs to infer an estimate of the cluster present-day total mass. Lastly, we investigated the presence of white dwarfs (WDs) and identified a strong candidate. However, to firmly establish its cluster membership, as well as that of four other WD candidates and of the majority of faint low-mass MS stars, further JWST equally deep observations will be required. We make publicly available catalogues, atlases, and the improved ePSFs.