Selection function Gaia DR3 open cluster census

Then, we performed 80590 injection and retrievals of simulated open clusters to test the Hunt & Reffert (2024A&A...686A..42H, Cat. J/A+A/686/A42) catalogue's sensitivity. We fit a logistic model of cluster detectability that depends only on a cluster's number of stars, median parallax error, Gaia data density, and a user-specified significance threshold.

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 on why certain clusters are detected. We briefly use 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 25km/s boost to a cluster's orbital speed can result in an almost 3 times higher detection probability, depending on its position.

In addition, we publish 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. 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.