How Star Clusters Grow Old: Modeling the Formation and Evolution of the Milky Way’s Stellar Families

In this eighth installment of the Milky Way Star Cluster (MWSC) survey, lead author J.H. Klos and collaborators explore how star clusters form and evolve over time in our galaxy. Star clusters, especially open clusters in the Milky Way, are groups of stars born from the same gas cloud. Their age and mass tell us about the history of the galaxy’s star formation. But these clusters don’t stay the same forever—they lose mass as they age, and eventually dissolve. The team’s goal is to build and test a model that explains how clusters change over time, and whether this matches what we actually observe in the sky.

Mapping the Age and Mass of Star Clusters

The study starts by using a large catalogue of open star clusters called MWSC, which includes 3,061 clusters, to look at how clusters are distributed by age and mass. Since not all clusters are equally easy to observe (especially the faint ones), the authors apply a correction to make sure their sample is representative. They focus on 2,227 clusters that fall within a well-defined completeness range, meaning these clusters are likely to give an accurate view of the broader population. Each cluster’s age and mass are plotted on a 2D plane, and uncertainties in those measurements are taken into account using a smoothing technique. This creates what the authors call the "Cluster Age-Mass Function" (CAMF)—a kind of heatmap showing how many clusters exist at different combinations of age and mass.

Building a Model of Cluster Evolution

To explain the patterns seen in the CAMF, the authors build a mathematical model that includes several ingredients: a constant rate at which clusters form, a two-part power law for the distribution of their starting masses, and a set of rules for how clusters lose mass over time. This mass loss happens in three phases: (1) early mass loss from stellar evolution, (2) a rapid loss called “violent relaxation” that occurs shortly after gas expulsion, and (3) a slower, steady loss due to gravitational effects from both internal dynamics and the Galaxy’s tidal forces. Each of these stages is modeled with its own equation.

Fitting the Model to Observations

With the model in place, the authors use statistical tools to adjust the model’s parameters until it best matches the observed CAMF. They test three methods: a traditional chi-squared statistic, the Kullback-Leibler divergence (which is more sensitive to rare features), and a maximum-likelihood estimate. All three approaches involve running simulations using a method called Markov Chain Monte Carlo (MCMC), which helps explore the huge space of possible parameter combinations.

What the Best Models Show

The Kullback-Leibler method turned out to produce the best match with the observed data, especially in the low-density parts of the age-mass plane. According to the best-fit model, clusters lose about 72% of their initial mass during the violent relaxation phase, which lasts around 5 million years. This early, intense loss helps explain why many young massive clusters seem to "disappear" quickly. The authors also find that the shape of the initial mass function is well constrained, and the data is consistent with a constant rate of cluster formation across the last several billion years. Interestingly, the observed age cap of about 5 billion years for most clusters suggests that even massive clusters eventually dissolve, though this effect can't be fully explained by initial mass limits alone.

Testing Against Other Data

To check the robustness of their findings, the authors apply their model to a separate cluster catalogue based on data from the Gaia space observatory. This new data set gives similar results, though with a slightly older average cluster age and more high-density regions. The comparison suggests that while the exact numbers may vary slightly, the overall trends and model assumptions hold up well.

Final Thoughts

This study supports the idea that the mass and age distribution of star clusters in the Milky Way can be explained using a relatively simple model—provided it includes a strong early mass-loss phase and accounts for observational uncertainties. While the model doesn’t perfectly capture every detail (like the sharp upper limit in cluster age), it brings us a step closer to understanding how these stellar families live and die in the galaxy. It also shows how powerful statistical modeling can be when paired with rich astronomical data sets.

Source: Klos