The Environmental Dependence of Star Cluster Demographics

Both the star cluster mass function and the lifetimes of clusters may vary with galactic environment, but measuring this variation is challenging because in observational surveys real features of cluster demographics are invariably entangled with catalogue incompleteness. Here we analyse ≈ 8300 star clusters in 12 galaxies drawn from the LEGUS survey using the slug Bayesian forward modelling framework coupled to our new c-4 neural network-based completeness estimator, which allows us to incorporate realistic catalogue-inclusion probabilities directly into the likelihood and compensate for these biases. We show that this approach allows us to fit observed cluster luminosity functions with excellent fidelity at both galactic and sub-galactic scales. We find that mass function slopes are relatively universal and broadly consistent with a power law M −2 form, but high mass truncations vary by orders of magnitude both between and within galaxies. Our fits also strongly favour models where cluster disruption is mass-independent, but the time at which disruption begins again shows wide environmental variations. Our results demonstrate that young cluster demographics are environmentally dependent, with the clearest signal appearing at the upper end of the cluster mass function, but that these variations are not well-explained by any of the models currently in the literature, and do not correlate straightforwardly with properties such as star formation rate per unit area or strength of shear.

Improvements to AI systems:

1. Neural-network-based completeness estimator (c-4) – Train a neural network to predict catalogue-inclusion probabilities as a function of cluster properties (luminosity, size, local background) and survey depth, directly integrating this into Bayesian likelihoods. This improves AI’s ability to handle selection biases in astronomical surveys without manual completeness corrections.

2. Bayesian forward-modeling with hierarchical environmental priors – Extend the slug framework to jointly infer cluster mass function slopes, truncation masses, and disruption timescales at both galactic and sub-galactic scales, using hierarchical priors that allow environmental parameters to vary smoothly across spatial bins. This enables AI to disentangle intrinsic cluster demographics from observational incompleteness in a principled way.

3. Mass-independent disruption model with variable onset time – Implement a new disruption model where the disruption rate is mass-independent but the onset time (when disruption begins) is a free parameter that varies with environment. The AI can then fit this model to data, revealing that onset times vary widely across environments—something simpler models miss.

4. Automated model comparison across environmental metrics – Build an AI system that systematically tests correlations between inferred cluster parameters (e.g., truncation mass, disruption onset) and environmental proxies (star formation rate per area, shear strength, gas density) using Bayesian evidence or information criteria. This would automatically flag that current models fail to explain observed variations, guiding future theoretical development.

5. Sub-galactic scale inference with spatial regularization – Use a spatial Gaussian process or similar smooth prior over the galaxy disk to infer cluster demographics as continuous functions of position, rather than discrete bins. This improves AI’s ability to detect gradients in truncation mass and disruption onset within galaxies, as the paper finds variations of orders of magnitude even within a single galaxy.

What the improved AI system can do:

• Given a raw star cluster catalogue (with photometry, positions, and survey limits), the AI can automatically produce posterior distributions for the cluster mass function slope, truncation mass, and disruption onset time at any spatial location, while explicitly accounting for incompleteness via the c-4 network.

• It can compare different physical models (e.g., mass-dependent vs. mass-independent disruption) and quantify which is favored by data, with uncertainty estimates.

• It can generate predictive maps of where high-mass clusters are likely to be found or destroyed across a galaxy, and flag environments where standard models break down.

• It can be retrained on other surveys (e.g., PHANGS, HST) with minimal modification, providing a general tool for studying cluster demographics in diverse galactic environments.

Both the star cluster mass function and the lifetimes of clusters may vary with galactic environment, but measuring this variation is challenging because in observational surveys real features of cluster demographics are invariably entangled with catalogue incompleteness. Here we analyse about 8300 star clusters in 12 galaxies drawn from the LEGUS survey using the slug Bayesian forward modelling framework coupled to our new c-4 neural network-based completeness estimator, which allows us to incorporate realistic catalogue-inclusion probabilities directly into the likelihood and compensate for these biases. We show that this approach allows us to fit observed cluster luminosity functions with excellent fidelity at both galactic and sub-galactic scales. We find that mass function slopes are relatively universal and broadly consistent with a power law M-2 form, but high mass truncations vary by orders of magnitude both between and within galaxies. Our fits also strongly favour models where cluster disruption is mass-independent, but the time at which disruption begins again shows wide environmental variations. Our results demonstrate that young cluster demographics are environmentally dependent, with the clearest signal appearing at the upper end of the cluster mass function, but that these variations are not well-explained by any of the models currently in the literature, and do not correlate straightforwardly with properties such as star formation rate per unit area or strength of shear.