The Present-Day Mass Function of Star Clusters in the Solar Neighborhood

Abstract: This work analyses the present-day mass function (PDMF) of 93~star clusters utilizing Gaia DR3 data, with membership determined by the StarGo machine learning algorithm. The impact of unresolved binary systems on mass estimation is rigorously assessed, adopting three mass ratio profiles for correction. The PDMF is characterized by the power-law index, $\alpha$, derived through a robust maximum likelihood method that avoids biases associated with data binning. The value of $\alpha$ for stars between the completeness limited mass of Gaia with a mean 0.3 $M_\odot$ for our cluster samples and 2 $M_\odot$, exhibits stability for clusters younger than 200 Myr, decreasing for older clusters, particularly when considering stars within the half-mass radius. The PDMF of these star clusters is consistent with a dynamically evolved Kroupa IMF via the loss of low-mass stars. Cluster morphology shows a correlation with $\alpha$, as $\alpha$ values exhibit a decreasing trend from filamentary to tidal-tail clusters, mirroring the sequence of increasing cluster age. The dependence of $\alpha$ on total cluster mass is weak, with a subtle increase for higher-mass clusters, especially outside the half-mass radius. We do not observe a correlation between $\alpha$ and the mean metallicity of the clusters. Younger clusters have lower metallicity compared to their older counterparts, which indicates that the older clusters might have migrated to the solar neighbourhood from the inner disk. A comparison with numerical models incorporating a black hole population suggests the need for observations of distant, older, massive open clusters to determine whether or not they contain black holes.