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In this work, starting from the well-accepted relations in literature, weintroduce a new formalism to compute the astrometric membership probabilitiesfor sources in star clusters, and we provide an application to the case of theopen cluster M 37. The novelty of our approach is a refined -- andmagnitude-dependent -- modelling of the parallax distribution of the fieldstars. We employ the here-derived list of members to estimate the cluster'smean systemic astrometric parameters, which are based on the most recent Gaia'scatalog (EDR3).

Astrometric star-cluster membership probability: application to the case of M 37 with Gaia EDR3