Insights into the dependence of galaxy properties on the environment with explainable machine learning models

TL;DR

This study quantifies how galaxy properties depend on their surrounding environment using an interpretable neural-network framework trained on IllustrisTNG300 at $z=0$. By predicting $M_*$ and SFR from dark matter subhalo properties of both host and neighboring subhalos, and applying SHAP to separate environmental from assembly-history influences, the authors reveal a hierarchical, distance-based environmental impact. They find that $M_*$ is best predicted with information from the nearest neighbor alone, while SFR benefits from up to the third-nearest neighbor, with satellites generally more environmentally influenced than centrals and low-mass galaxies more affected than massive ones. These results provide actionable guidance for improving empirical and semi-analytic galaxy formation models by incorporating neighbor-dependent environmental effects that vary with galaxy type and mass.

Abstract

Galaxies reside within dark matter halos, but their properties are influenced not only by their halo properties but also by the surrounding environment. We construct an interpretable neural network framework to characterize the surrounding environment of galaxies and investigate the extent to which their properties are affected by neighboring galaxies in IllustrisTNG300 data ($z=0$). Our models predict galaxy properties (stellar mass and star formation rate) given dark matter subhalo properties of both host subhalo and of surrounding galaxies, which serve as an explainable, flexible galaxy-halo connection model. We find that prediction accuracy peaks when incorporating only the nearest neighboring galaxy for stellar mass prediction, while star formation rate prediction benefits from information from up to the third-nearest neighbor. We determine that environmental influence follows a clear hierarchical pattern, with the nearest neighbor providing the dominant contribution that diminishes rapidly with additional neighbors. We confirm that central and satellite galaxies, as well as different galaxy categories based on mass and star-forming activity, exhibit distinct environmental dependencies. Environmental dependence for low-mass galaxies ($\log(M_*/M_\odot) < 10$) shows 35-50% environmental contribution compared to just 8-30% for massive centrals, while satellite galaxies experience consistently stronger environmental effects than centrals across all populations. Furthermore, we find that the most significant attribute from neighboring subhalos for predicting target galaxy properties is its distance to the nearest neighboring galaxy. These quantitative results offer guidance for constructing more sophisticated empirical and semi-analytic models of galaxy formation that explicitly include environmental dependence as a function of galaxy type and mass.

Figures (20)

• Figure 1: All datasets used in this study are shown. To define the star-formation main sequence (MS; green solid line), kernel density estimation (KDE) is applied to the SFR–$M_*$ plane of the entire dataset, and principal component analysis (PCA) is performed on the top 1% highest-density region. The green dashed and dash-dotted lines indicate deviations of $\pm1$ dex and $\pm0.5$ dex from the MS, respectively.
• Figure 2: Test set example. Main sequence (MS) derived by Fig. \ref{['Fig:MS']}. The colors of the plot are indicative of different galaxy types.
• Figure 3: Schematic illustration of the definition of the surrounding environment. The parameter $N$ takes values $0 \sim 10$, $15$, $20$, $25$, and $30$, where $N = 0$ indicates the absence of any environmental information.
• Figure 4: Distribution of coefficient of determination ($R^2$) values for models with varying numbers of neighboring galaxies. Each distribution is generated through 100 bootstrap tests, with median values displayed above each violin plot. The one-neighbor model demonstrates the highest median $R^2$ for $M_*$ predictions (top), while the three-neighbors model yields the highest median $R^2$ for SFR predictions (bottom).
• Figure 5: Comparison of $M_*$ predictions for central (left) and satellite galaxies (right) with and without environmental information. Top panel: Blue and red points represent median values in each mass bin for models with (one-neighbor model) and without environmental information, respectively. Error bars indicate 16th and 84th percentile ranges. Dashed lines indicate perfect one-to-one relationships. Bottom panel: Difference in mean absolute error (MAE), i.e., difference in model prediction accuracy, between predictions without and with environmental information as a function of $M_*$ (calculated as $\mathrm{MAE}_{\mathrm{without}} - \mathrm{MAE}_{\mathrm{with}}$ at each bin). Positive values indicate improved performance with environmental information. Horizontal dashed lines mark $\Delta \mathrm{MAE} = 0$. Overall MAE and $R^2$ values for each model are displayed in top panels. Each bin contains at least 10 galaxies to ensure statistical reliability.