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

Abstract

This work analyzes the present-day mass function (PDMF) of 93 star clusters utilizing Gaia Data Release 3 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, α, derived through a robust maximum likelihood method that avoids biases associated with data binning. The value of α for stars between the completeness limited mass of Gaia (with a mean 0.3 M ⊙ for our cluster samples) and 2 M ⊙ 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 initial mass function via the loss of low-mass stars. Cluster morphology shows a correlation with α, as α values exhibit a decreasing trend from filamentary to tidal-tail clusters, mirroring the sequence of increasing cluster age. The dependence of α on the 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 α 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 neighborhood 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.

The Variation in the Galaxy-wide Initial Mass Function for Low-mass Stars: Modeling and Observational Insights

“…The IMF is often characterized as a power law at its massive end, gradually flattening toward the low-mass range. When scrutinizing stars with masses approximately near 0.5 M e , where a mass boundary for the IMF to change its slope cannot be precisely determined, a common practice involves adopting a single power law to represent the IMF's shape (e.g., Wyse et al 2002;Kalirai et al 2013;Gennaro et al 2018a;Li et al 2023;Pang et al 2024). To achieve this, we employ the Markov Chain Monte Carlo (MCMC) method.…”

“…Compared to studies of the galaxy-wide IMF, the IMF determinations for star clusters encounter additional obstacles due to completeness problems, mass segregation, and dynamical evolution of the star clusters with different ages and orbits within the MW. As a result, many star cluster studies focus on estimating the present-day mass function rather than the IMF (e.g., Pang et al 2024). Correcting for binary fractions, which vary among different clusters, and transitioning from the unresolved-system IMF to the single-star IMF ideally requires detailed N-body simulations of star clusters (Kroupa et al 2001).…”