Connection between galaxy morphology and dark-matter halo structure II: predicting disk structure from dark-matter halo properties

TL;DR

This study establishes a quantitative link between dark-matter halo properties and detailed disk morphology using the TNG50 simulation, comparing full hydrodynamic runs with matched dark-matter-only runs. By measuring 37 halo properties and applying Random Forests, SHAP, and Symbolic Regression, it demonstrates that halo structure and assembly history strongly predict disk size and thickness, with inner-halo dynamics playing a crucial role in hydro runs. The work yields compact SR-based prescriptions that map halo features to disk properties, outperforming previous analytic relations and offering practical tools for galaxy-halo modeling in semi-analytic frameworks. It also reveals baryonic effects as the primary source of the disk–Einasto index connection and highlights mass and redshift dependencies in disk compactness and thickness, with clear implications for how disks grow and thicken across cosmic time.

Abstract

We investigate how galactic disk structures connect to the detailed properties of their host dark-matter halos using the TNG50 simulation. From the hydrodynamic and matched dark-matter-only runs, we measure a comprehensive list of halo properties describing density structure, angular momentum, shape, assembly history, and environment. Using the morphological decomposition developed in Paper I, we quantify the sizes, scale heights, and mass fractions of the disk components for galaxies at $0 \le z \le 4$. Random Forest (RF) regression shows halo properties alone predict disk size and thickness with high accuracy, while Symbolic Regression (SR) provides compact empirical relations with slightly lower accuracy. Disk height is consistently easier to predict than disk size, and lower-mass halos yield higher accuracy than massive halos. Predictions based on halo properties measured in the full-physics hydro simulations outperform those based on the matched dark-matter-only halos, reflecting the imprint of baryonic restructuring on the inner halo. SHAP analysis reveals that the most informative halo parameters include concentration, Einasto shape, global and inner spin, and recent mass accretion, though their importance varies across disk properties. We show that correlations between disk size and the density-profile shape arise primarily from disk-induced modification of the inner halo, rather than a primordial connection. Finally, we point out that disks become more extended with respect to their host halos at higher redshift in low-mass halos, while massive high-redshift halos show the opposite trend. We provide SR-based prescriptions that accurately map halo properties to disk structures, offering practical tools for galaxy-halo modeling.

Figures (18)

• Figure 1: Analysis pipeline, which contains three parts: measurements (gray), machine-learning training (green), and output evaluation (red). The corresponding sections, figures, tables and equations are indicated by blue texts.
• Figure 2: Performance of the regression models for global galaxy properties in the TNG50 simulation, and the scaling relations predicted by the symbolic-regression (SR) models. The global galaxy properties shown are stellar mass ( top), SFR ( middle), and half-stellar-mass radius ( bottom). Left: Comparison of RF (contours) and SR (dashed curves with 16–84% ranges) predictions against test data, using measurements from the hydro (blue) and DMO (red) runs. Performance is evaluated with MAE, $R^2$, and RMSE. Middle: SHAP scores that indicate the relative contributions of the top 10 RF features, with blue (left axis) and red (right axis) labels corresponding to the hydro and DMO results, respectively. Error bars show the 16–84% ranges. Feature categories are indicated by the color of the text boxes: mass (black), density profile (green), angular momentum or trivial shape (purple), and environment (gray). Right: Scaling relations predicted by SR, where cyan and red curves show median relations for hydro halos and DMO halos, respectively, at $z=0$ (solid) and $z=4$ (dashed). Gray and black squares show the corresponding medians measured directly from the hydro simulation at $z=0$ and $z=4$. Shaded regions and error bars denote 16–84% ranges. The sample in the SFR row includes only star-forming galaxies. For clarity, the $z=4$ relations in the $M_{\star}$–$M_{\rm vir}$ panel are shifted horizontally by 1.5 dex.
• Figure 3: Performance of regression models for disk compactness, $R_{\rm 1/2,Disk}/R_{\rm vir}$, and the most predictive halo properties -- for galaxies with significant disk components ($f_{\rm Disk} > 0.3$). Formatting follows Fig. \ref{['fig:validation']}. Columns correspond to different halo mass ranges: all ( left), low-mass ($10^{10.6}M_\odot \leq M_{\rm vir} < 10^{11.6}M_\odot$, middle), and high-mass ($M_{\rm vir} \geq 10^{11.6}M_\odot$, right).
• Figure 4: Performance of regression models for disk thickness, $Z_{\rm 1/2,Disk}/R_{\rm vir}$, for galaxies with significant disk components ($f_{\rm Disk} > 0.3$). Formatting follows Fig. \ref{['fig:validation']}. Columns correspond to different halo mass ranges: all (left), low-mass ($10^{10.6} \leq M_{\rm vir}/M_\odot < 10^{11.6}$, middle), and high-mass ($M_{\rm vir}/M_\odot \geq 10^{11.6}$, right).
• Figure 5: Performance of regression models for disk mass fraction, $f_{\rm Disk}$, for galaxies with significant disk components ($f_{\rm Disk} > 0.3$). Formatting follows Fig. \ref{['fig:validation']}.