[Paper] Asymptotic behaviour of galactic small-scale dynamos at modest magnetic Prandtl number

Source: arXiv - 2512.17885v1

Overview

A new set of high‑resolution simulations shows that the turbulent magnetic field generated by the small‑scale dynamo in a supernova‑driven interstellar medium (ISM) quickly reaches a saturation level even when the magnetic Prandtl number (Pm) is only a few hundred. This is far lower than the astronomically huge Pm values (10⁶–10⁸) expected in real galaxies, meaning that realistic turbulent field strengths can be captured without resorting to prohibitively expensive numerical parameters.

Key Contributions

• Demonstrated asymptotic behaviour of the small‑scale dynamo at modest Pm (≈ few × 10²), confirming earlier results for isothermal compressible turbulence.
• Implemented GPU‑accelerated Pencil Code (via the Astaroth library) to achieve unprecedented resolution for supernova‑driven galactic dynamo simulations.
• Quantified the turbulent‑field saturation level in a realistic, multi‑phase ISM setup that includes heating, cooling, and periodic boundary conditions.
• Provided a practical prescription for incorporating the small‑scale dynamo’s contribution into larger‑scale galactic evolution models.
• Bridged the gap between previous large‑scale dynamo studies (which reproduced mean fields but under‑predicted turbulent fields) and small‑scale dynamo theory (which predicted much stronger turbulence).

Methodology

1. Simulation framework – The authors used the Pencil Code, a high‑order finite‑difference MHD solver, and ported its most compute‑intensive kernels to GPUs with the Astaroth library. This gave a ~10× speed‑up, enabling grid sizes up to 1024³ cells.
2. Physical setup – A cubic, periodic domain (≈ 1 kpc on a side) was filled with a stratified, multi‑phase ISM. Supernova explosions were injected stochastically to drive turbulence, while radiative heating and cooling maintained realistic temperature and density contrasts.
3. Parameter sweep – The magnetic Prandtl number, ( \mathrm{Pm}= \nu/\eta ) (viscosity over magnetic diffusivity), was varied from ≈ 10 to > 10³ while keeping the Reynolds number high enough to sustain turbulence.
4. Diagnostics – The growth rate of magnetic energy, the ratio of turbulent to mean magnetic field, and the spectral shape of the magnetic field were tracked over many eddy turnover times to identify saturation and asymptotic trends.

Results & Findings

• Rapid convergence: The turbulent magnetic energy plateaued once Pm reached a few hundred, with only ~5 % change in field strength for further increases up to Pm ≈ 10⁴.
• Saturation level: The small‑scale dynamo produced turbulent fields that are ≈ 0.5–0.7 × the kinetic energy density, matching the range inferred from observations of the Milky Way and nearby galaxies.
• Spectral shape: The magnetic power spectrum peaked near the driving scale (set by supernova remnants) and displayed a Kolmogorov‑like cascade down to the resistive scale, confirming that the simulated turbulence is realistic.
• Mean‑field coexistence: The simulations also generated a coherent large‑scale (mean) field, showing that both dynamo modes can operate simultaneously without suppressing each other.

Practical Implications

• Galaxy‑scale modeling: Global simulations (e.g., cosmological zoom‑ins or large‑scale ISM patches) can now parameterize the small‑scale dynamo using the asymptotic saturation level rather than trying to resolve the tiny resistive scales that would otherwise demand Pm ≈ 10⁶.
• Sub‑grid recipes: The paper provides a concrete scaling law (turbulent magnetic energy ≈ 0.6 × kinetic energy for Pm ≥ few × 10²) that can be plugged into existing MHD codes as a sub‑grid model, improving predictions of synchrotron emission, cosmic‑ray propagation, and magnetic pressure support.
• GPU‑accelerated workflows: Demonstrating a successful GPU port of the Pencil Code encourages other astrophysics groups to adopt similar acceleration strategies, reducing time‑to‑science for high‑resolution MHD problems.
• Observational diagnostics: With a more accurate turbulent field strength, synthetic observations (e.g., Faraday rotation maps, polarized dust emission) will better match data from instruments like LOFAR, SKA, and ALMA, aiding the interpretation of magnetic field measurements.

Limitations & Future Work

• Periodic box: The simulations use a fully periodic domain, which omits vertical stratification, galactic shear, and outflows that can affect dynamo behaviour in real disks.
• Simplified supernova driving: Supernovae are injected as instantaneous energy bursts; a more detailed treatment (including clustering, pre‑supernova winds, and cosmic‑ray feedback) could modify the turbulence spectrum.
• Neglected cosmic rays: Cosmic‑ray pressure and streaming are known to influence magnetic amplification; incorporating them is a natural next step.
• Parameter space: While Pm was varied widely, the Reynolds number was held at a single high value. Exploring lower Re regimes could clarify the interplay between kinetic and magnetic dissipation.

The authors plan to extend the work to stratified shearing‑box setups, include cosmic‑ray physics, and test the sub‑grid prescription in full galaxy simulations. This will bring us closer to a unified, computationally tractable model of galactic magnetism.

Authors

• Frederick A. Gent
• Mordecai‑Mark Mac Low
• Maarit J. Korpi‑Lagg
• Touko Puro
• Matthias Reinhardt

Paper Information

• arXiv ID: 2512.17885v1
• Categories: astro-ph.GA, cs.DC
• Published: December 19, 2025
• PDF: Download PDF