NIHAO-UHD Cosmological Simulation

• The simulation models Milky Way-mass galaxy formation using ultra-high resolution hydrodynamics and advanced gas physics, enabling precise chemodynamical tracking.
• It incorporates full orbital tracing and chemical enrichment prescriptions to reveal energy–abundance correlations during major merger events.
• Results challenge traditional merger-induced heating by showing that Splash stars emerge from intrinsic turbulent disk dynamics rather than abrupt dynamical heating.

The NIHAO-UHD cosmological simulations are a suite of ultra–high definition zoom-in hydrodynamical simulations within a cosmological context, designed to model the formation and evolution of Milky Way–mass galaxies and their satellite populations. They are built upon the NIHAO (Numerical Investigation of Hundred Astrophysical Objects) framework and employ high mass and spatial resolution, advanced gas physics (including metal-line cooling and turbulent diffusion), and detailed chemical enrichment prescriptions for a range of elements, tracing the chemodynamical evolution of simulated galaxies across cosmic time. The unique combination of cosmological realism, fine temporal and spatial sampling, and full element tracking enables detailed exploration of dynamical and chemical memory through major merger events, the structure of stellar disks, and the origins of key galactic populations such as Splash and accreted halo stars.

1. Simulation Architecture and Advancements

The NIHAO-UHD simulations leverage the GASOLINE2 code with sub-grid turbulent diffusion and star formation prescriptions following Stinson et al. (2006, 2013). They resolve Milky Way–like galaxies in a ΛCDM cosmology with approximately $5 \times 10^6$ star particles and force softening $<$100 pc, ensuring reliable gravitational and hydrodynamical modeling down to $\lesssim1\%$ of the virial radius. Multiple chemical elements (H, He, C, N, O, Mg, Al, Si, Mn, Fe, etc.) are followed on a solar abundance scale. Spatial coordinates are typically referenced as:

$R_\mathrm{3D} = \sqrt{x^2 + y^2 + z^2}$

while specific Newtonian energy is defined as:

$$E = \frac{1}{2}(v_x^2 + v_y^2 + v_z^2) + \phi(x, y, z)$$

where $\vec{v}$ and $\phi$ are the local velocity and potential. Orbital actions ($J_R$, $J_\phi$, $J_z$) are computed using a multipole expansion and the Stäckel fudge method via the agama package, facilitating kinematic segregation of stellar populations.

2. Chemodynamical Memory and Major Mergers

Recent work utilizing the NIHAO-UHD suite demonstrates that past major merger events encode long-lived chemodynamical memory within the host galaxy (Buder et al., 13 Oct 2025). By tracking the birth location, age, and present-day orbit for individual accreted stars during a 1:5 mass-ratio merger ($\sim$8–10 Gyr ago), a clear correlation emerges:

• Stars born in the progenitor's central core are both more tightly bound (lower orbital energy) and more chemically enriched ([Fe/H], [$\alpha$/Fe]) than stars from its outskirts.
• Energy–abundance correlations persist across the merger, supported by median trends in planes such as [Al/Fe] vs. [Mg/Mn].
• Birth radii, present-day binding energy, and orbital actions collectively form a "golden thread" (Editor's term) that connects spatial and temporal memory throughout violent assembly.
• The observed non-linear abundance–energy relations (less linear than in idealized models [Skuladottir et al. 2025]) imply complex star formation and mixing histories within the progenitor, yet retain robust signatures at the high-metallicity end.

Methodologically, phase-space selections based solely on integrals-of-motion ($E$, $L_z$, $J_R$) tend to miss a substantial fraction of the most enriched (lowest–energy) core stars, biasing reconstructed progenitor metallicity distribution functions toward lower values. Simultaneous chemical tagging or birth-position tracing within the simulation circumvents this issue.

3. Splash Population: Heating versus Born-Hot Formation

The origin of "Splash" stars—stellar populations with disk-like chemistry and halo-like kinematics—has been a point of major debate. NIHAO-UHD analysis (Buder et al., 23 Oct 2025) finds:

• Splash-like stars (selected by [Fe/H] and azimuthal velocity, $V_\varphi$) are exclusively in situ and show chemical properties continuous with the thick disk.
• Birth and present-day positions show only minimal displacement:

$$\Delta R = R_\mathrm{now} - R_\mathrm{birth} \qquad \Delta Z = Z_\mathrm{now} - Z_\mathrm{birth} \approx \text{small}$$

indicating little evidence for abrupt heating ("splashing") during the merger.

• The $V_\varphi$ distribution is broad and positively skewed, not bimodal and not strongly negative as would be expected for heated stars. The best-fit skewed normal is:

$V_\varphi = 73_{-59}^{+74}\, \mathrm{km\,s^{-1}}$

• The transition to a rotation-supported thin disk only arises during or after the merger as inflowing, lower-angular-momentum gas is assimilated and star formation shifts toward higher-angular-momentum orbits.

This signals that the observed "Splash" population may instead reflect intrinsic kinematic diversity in a turbulent thick protodisk, not violent merger-induced heating, and that the spin-up of the disk is a post-merger process.

4. Elemental Abundance Planes and Reconstruction Biases

Examination of diagnostic abundance planes ([Al/Fe] vs. [Mg/Mn], and others) reveals:

• Non-linear median trends across bins of binding energy—core stars are more chemically enriched, outskirts more metal-poor.
• These relations agree qualitatively with observational analyses [Skuladottir et al. 2025], but the simulation highlights curvature and complexity at intermediate metallicity, with best agreement at the highest [Fe/H].
• Integrals-of-motion selections typically undersample the chemically enriched core, potentially biasing mass–metallicity reconstructions for accreted satellites by missing dense, metal-rich populations that overlap dynamically with the host disk.

For accurate progenitor inference, selection strategies must combine kinematic, chemical, and positional information.

5. Methodological Innovations and Limitations

The simulations demonstrate the advantages of combining full orbital tracing with individual chemical histories. Calculations employ explicit kinematic definitions, such as:

• Full action computation for each star
• Energy–abundance correlation analysis in energy bins
• "Golden thread" visualizations linking birth spatial overdensities with present-day phase-space

Nevertheless, interpretation of observed samples may systematically miss highly bound, enriched accreted stars without chemical tagging. Additionally, the NIHAO-UHD suite models Milky Way analogues with relatively quiescent late-time merger histories; variations in gas accretion or additional feedback mechanisms may further modulate chemodynamical imprints.

6. Implications for Galactic Archaeology

The NIHAO-UHD results have significant implications:

• The present-day Milky Way retains spatial and chemical signatures of its merger history—chemodynamical memory is robust against phase-mixing and survives across several Gyr (Buder et al., 13 Oct 2025).
• Reinterpretation of Splash stars as "born hot" with minimal additional dynamical heating alters understanding of the early disk and the mechanisms that lead to its kinematic structure (Buder et al., 23 Oct 2025).
• Selection bias in progenitor reconstruction affects mass–metallicity inference for merger events, motivating combined kinematic–chemical selection in both simulations and observations.
• Continued ultra-high resolution simulations with expanded merger and feedback scenarios are critical for quantifying the full diversity of chemodynamical histories in spiral galaxy analogues.

The suite thus provides a powerful framework for testing and refining models of Galactic structure and for interpreting the signatures left by hierarchical assembly in the Milky Way and similar galaxies.