Non-Gaussian Magnetic Structures in the Small-Scale Turbulent Dynamo

TL;DR

The paper investigates the 3D morphology of magnetic fields produced by the small-scale turbulent dynamo in the ISM using Minkowski functionals across a range of Mach numbers $\mathcal{M}$ from $0.1$ to $10$. It compares non-Gaussian dynamo-generated fields in both the kinematic and saturated stages to Gaussian random fields with identical power spectra, revealing persistent non-Gaussian morphology. The results show that dynamo fields are significantly non-Gaussian in all regimes, with saturation reducing curvature and increasing connectivity, and the degree of non-Gaussianity peaking near $\mathcal{M}\approx 5$ before diminishing at $\mathcal{M}=10$, highlighting a regime-dependent saturation mechanism. The study provides a quantitative framework for relating 3D magnetic-field morphology to density fluctuations and Lorentz-force back-reaction, offering a robust basis for interpreting projected 2D polarization observations from current and upcoming ISM surveys.

Abstract

The small-scale turbulent dynamo is a key mechanism for amplifying galactic magnetic fields, yet the resulting field morphology remains poorly understood. Using 3D driven turbulence simulations across a range of compressibilities, characterised by Mach number, and Minkowski functionals, we quantitatively investigate the morphology of magnetic fields generated by the small-scale turbulent dynamo in both the exponentially growing kinematic stage and the statistically steady saturated stage. In both stages and across all Mach numbers, we find that the magnetic field departs significantly from a Gaussian random field. Magnetic structures are statistically less curved and more interconnected in the saturated stage than in the kinematic stage, with these morphological differences decreasing as compressibility increases. Our work provides a quantitative description of how density fluctuations in turbulence and the back-reaction of amplified magnetic fields via the Lorentz force together shape complex, non-Gaussian magnetic structures and offers a valuable framework for comparing simulations with polarisation observations.

Figures (3)

• Figure 1: Excursion sets of the $x$-component of the magnetic field for $b_x/{b_{\rm rms}} > 1.2$ for $\mathcal{M} =0.1$ (a, b) and $10$ (c, d) simulations in their corresponding kinematic ($\rm Kin$; a, c) and saturated ($\rm Sat$; b, d) stages. The magnetic structures are significantly different between the $\rm Kin$ and $\rm Sat$ cases for $\mathcal{M} =0.1$, and such differences are less pronounced for $\mathcal{M} =10$.
• Figure 2: Minkowski functionals ($V_0, V_1, V_2,$ and $V_3$) as a function of the threshold, $b_i / {b_{\rm rms}}$, for simulated magnetic fields (solid lines) and their Gaussianised versions with the same power spectra ($\rm GRF$, dashed lines) in the kinematic ($\rm Kin$) and saturated ($\rm Sat$) stages for $\mathcal{M} = 0.1$ (a-d) and $\mathcal{M} = 10$ (e-h) simulations.
• Figure 3: Comparison of $V_2$ (a-d; quantifying the mean curvature) and $V_3$ (e-h; quantifying the connectedness of the structures) for the $\rm Kin$ and $\rm Sat$ stages at $\mathcal{M} = 0.1$ (a, e), $2$ (b, f), $5$ (c, g), and $10$ (d, h), which further highlights the morphological changes due to the turbulent dynamo saturation across Mach numbers.