Exploring Galactic open clusters with Gaia: I. An examination in the first kiloparsec

Context. Since the first publication of the Gαία catalogue, a new view of our Galaxy has arrived. Its astrometric and photometric information has improved the precision of the physical parameters of open star clusters obtained from them. Aims. Using the Gaia Data Release 3 (DR3) catalogue, our aim was to find physical stellar members including faint stars for 370 Galactic open clusters located within 1 kpc. We also estimated the age, metallicity, distance modulus, and extinction of these clusters. Methods. We employed the HDBSCAN algorithm on both astrometric and photometric data to identify members in the open clusters. Subsequently, we refined the samples by eliminating outliers through the application of the Mahalanobis metric utilizing the χ² distribution at a confidence level of 95%. Furthermore, we characterized the stellar parameters with the PARSEC isochrones. Results. We obtained reliable star members for 370 open clusters with an average parallax error of σ_ϖ = 0.16 mas. We identified about ~40% more stars in these clusters compared to previous work using the Gaia DR2 catalogue, including faint stars as new members with G ≥ 17. Before the clustering application we corrected the parallax zero-point bias to avoid spatial distribution stretching that may affect clustering results. Our membership lists include merging stars identified by HDBSCAN with astrometry and photometry. We note that the use of photometry in clustering can recover up to 10% more stars in the fainter limit than clustering based on astrometry only; this combined with the selection of stars filtered out by quality cuts significantly reduces the number of stars with huge σ_ϖ. After clustering, we estimated age, Z, and A_V from the photometry of the membership lists. Conclusions. We carried out a search to extend the membership list for 370 open clusters mainly on the Galactic plane in a neighbourhood of 1 kpc. Our methodology provides a robust estimator for the identification of outliers and also extends the membership lists to fainter stars in most of the clusters. Our findings suggest the need to carefully identify spurious sources that may affect clustering results.