IllustrisTNG50 angular momentum maps: tracing the morpho-kinematic evolution of galaxies

Technical Summary: IllustrisTNG50 Angular Momentum Maps: Tracing the Morpho-Kinematic Evolution of Galaxies

Problem and Motivation
While modern cosmological simulations successfully reproduce the global scaling relation between total stellar specific angular momentum ($j_\star$) and total stellar mass ($M_\star$), known as the Fall relation, reproducing this global relation alone is insufficient to fully understand the coupling between galaxy evolution and angular momentum acquisition. Observations of late-type galaxies have recently revealed an unexpected morpho-kinematic diversity within galactic discs, characterized by distinct spatial distributions of stellar specific angular momentum surface density (sAMSD). This diversity suggests that angular momentum is redistributed into specific substructures ($j_\star$-substructures) that do not always align with traditional morphological classifications. The primary objective of this study is to quantify and understand this morpho-kinematic diversity within cosmological hydrodynamic simulations, specifically testing whether the $j_\star$-substructures identified in observations (Pacheco-Arias et al. 2026, hereafter PA26) are reproduced in the IllustrisTNG50 simulation suite.

Methodology
The authors analyzed a sample of approximately 8,000 stellar discs from the IllustrisTNG50 MW/M31 subsample, spanning redshifts $0 \le z \le 3.5$ and stellar masses $10^{9.5} \le M_\star \le 10^{11.2} M_\odot$. The sample was constructed by tracking SubHalos from the MW/M31 catalogue back in time, selecting only those hosting stable, rotationally supported discs ($V/\sigma \ge 0.5$) with sufficient spatial resolution ($R_{max} \ge 7$ kpc) and low counter-rotation ($f_{CR} \le 0.20$).

The core methodology involved:

1. sAMSD Map Construction: Calculating the stellar specific angular momentum ($j_{\star,k}$) for individual particles and projecting the surface density ($\iota_\star = dj_\star/dS$) onto a regular grid ($500$ pc pixels), smoothed with a Gaussian kernel matching the stellar softening length ($\epsilon_\star \approx 300$ pc).
2. Morpho-Kinematic Metrics: Four metrics were defined to quantify $j_\star$-substructures:
   • $C_{2D}$: A 2D correlation coefficient measuring the resemblance of the sAMSD map to a Freeman disc model (indicative of $j_\star$-rings).
   • $a_{max}^1$: The maximum normalized amplitude of the $m=1$ Fourier mode (quantifying asymmetry/$j_\star$-irregularities).
   • $a_{max}^2$: The maximum normalized amplitude of the $m=2$ Fourier mode (quantifying bi-symmetry).
   • $R_{max}^2$: The radial extent fraction where the $m=2$ mode peaks (distinguishing between centrally concentrated bars and extended spirals).
3. Classification: A Gaussian Mixture Model (GMM) with four fully covariant components was applied to the four-dimensional parameter space ($C_{2D}, a_{max}^1, a_{max}^2, R_{max}^2$). This probabilistic approach assigned each galaxy a posterior probability of belonging to one of four identified $j_\star$-types: $j_\star$-irregular, $j_\star$-spiral, $j_\star$-ring, and $j_\star$-bar.

Key Results

• Morpho-Kinematic Diversity: The TNG50 simulations exhibit a morpho-kinematic diversity similar to observations. The stellar discs store and redistribute angular momentum predominantly in the four identified $j_\star$-substructures.
• Evolutionary Sequence: A canonical evolutionary pathway was identified based on the mean redshifts of each class and Markov transition probabilities:
  • $j_\star$-irregular ($\bar{z} = 0.91$) $\rightarrow$ $j_\star$-spiral ($\bar{z} = 0.76$) $\rightarrow$ $j_\star$-ring ($\bar{z} = 0.62$) $\rightarrow$ $j_\star$-bar ($\bar{z} = 0.39$).
  • $j_\star$-irregulars and $j_\star$-spirals act as transitional states, while $j_\star$-rings and $j_\star$-bars act as dynamical attractors; once formed, rings and bars tend to persist.
• Physical Drivers:
  • Gas Fraction ($f_{gas}$): This is the primary driver separating the classes. High $f_{gas}$ favors $j_\star$-irregulars and $j_\star$-spirals, while low $f_{gas}$ favors $j_\star$-rings and $j_\star$-bars.
  • Rotation Support ($V/\sigma$): Once $f_{gas}$ is fixed, high $V/\sigma$ favors $j_\star$-spirals in gas-rich systems and $j_\star$-rings in gas-poor systems.
  • Environment: At $z=0$, no strong correlations were found between the morpho-kinematic metrics and the local cosmic web environment (density, distance to filaments/nodes) or the alignment of the angular momentum vector with filaments.
• $j_\star$-$M_\star$ Diagram: Galaxies cluster in distinct regions of the $j_\star$-$M_\star$ plane depending on their $j_\star$-type. The best-fit Fall relation for the sample yields a slope $\alpha = 0.80 \pm 0.01$, steeper than some previous TNG50 studies due to the kinematic selection ($V/\sigma \ge 0.5$) which excludes dispersion-dominated systems.

Significance and Conclusions
The paper establishes a canonical pathway for the redistribution of angular momentum within secularly evolving discs in TNG50. The study demonstrates that the $j_\star$-substructure classification provides a framework that integrates dynamical and morphological information more effectively than traditional morphology alone, as $j_\star$-substructures do not always coincide with morphological counterparts (e.g., a morphological bar does not necessarily imply a $j_\star$-bar).

The results suggest that gas accretion and stellar feedback are the primary physical processes driving angular momentum redistribution. The observed prevalence of $j_\star$-rings and $j_\star$-bars at $z=0$ is attributed to the sample selection criteria (favoring stable discs) and the lack of efficient regulatory mechanisms for bar destruction in the TNG50 simulation physics. The authors note the absence of $j_\star$-clumps in the simulation, likely due to resolution limits, and the overabundance of $j_\star$-bars, suggesting a need for refined feedback processes in future simulation iterations. Ultimately, the sAMSD analysis links variations in stellar dynamics to mass redistribution, offering a tool to reconstruct comprehensive galactic evolutionary histories that extends beyond standard kinematic indicators.