The selection function of the Gaia DR3 open cluster census

¹ Department of Astrophysics, University of Vienna, Türkenschanzstrasse 17, 1180 Wien, Austria
² Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
³ Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), Martí i Franquès, 1, 08028 Barcelona, Spain
⁴ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB), Martí i Franquès, 1, 08028 Barcelona, Spain
⁵ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels (Barcelona), Spain
⁶ INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
⁷ INAF, Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁸ Dipartimento di Fisica e Astronomia, Università di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 21 October 2025
Accepted: 9 January 2026

Abstract

Context. Open clusters are among the most useful and widespread tracers of Galactic structure. The completeness of the Galactic open cluster census, however, remains poorly understood.

Aims. For the first time ever, we aim to establish the selection function of an entire open cluster census, publishing our results as an open-source Python package for use by the community. Our work is valid for the Hunt & Reffert catalogue of clusters in Gaia DR3.

Methods. We developed and open sourced our cluster simulator from our first work. Then, we performed 80 590 injection and retrievals of simulated open clusters to test the Hunt & Reffert catalogue’s sensitivity. We fitted a logistic model of cluster detectability that only depends on a cluster’s number of stars, median parallax error, Gaia data density, and a user-specified significance threshold.

Results. We find that our simple model accurately predicts cluster detectability, with a 94.53% accuracy on our training data that is comparable to a machine-learning-based model with orders of magnitude more parameters. Our model itself offers numerous insights into why certain clusters are detected. We briefly used our model to show that cluster detectability depends on non-intuitive parameters, such as a cluster’s proper motion, and we show that even a modest 25 km/s boost to a cluster’s orbital speed can result in an almost 3× higher detection probability, depending on its position. In addition, we published our raw cluster injection and retrievals and cluster memberships, which could be used for a number of other science cases – such as estimating cluster-membership incompleteness.

Conclusions. Using our results, selection effect-corrected studies are now possible with the open cluster census. Our work will enable a number of brand new types of study, such as detailed comparisons between the Milky Way’s cluster census and recent extragalactic cluster samples.