Fluctuation dynamos in supersonic turbulence at ${\rm Pm} \gtrsim 1$

TL;DR

This study probes fluctuation dynamos in highly compressible, supersonic turbulence with ${M_{rms}} \approx 11$ across ${Pm}=1$ to 10 using high-resolution 3D MHD simulations. It shows that dynamo growth and saturation strengthen with increasing ${Pm}$, with kinematic growth rates rising from ${\gamma \approx 0.42}$ to ${\gamma \approx 0.93}$ and higher saturation levels at ${Pm}=10$; density–magnetic-field coupling weakens in the nonlinear regime, reflected in decreasing ${r_p(\rho,B)}$ especially at high ${Pm}$. The analysis reveals a robust, ${Pm}$-independent ratio ${\ell^V_{int}}/{\ell^M_{int}} \approx 3.4$, while the ratio ${\ell_\nu}/{\ell_\eta}$ grows with ${Pm}$, indicating increasing separation of viscous and resistive scales. Spectral analyses show enhanced small-scale magnetic energy and greater solenoidal action at high ${Pm}$, with RM coherence scales of about ${1/4}$ to ${1/3}$ of the forcing scale, implying potential contributions to observed Faraday rotation in turbulent, gas-rich young disk galaxies. Collectively, the results illuminate how compressibility and magnetic diffusivity shape fluctuation dynamos and their observable magnetic signatures in astrophysical plasmas.

Abstract

Fluctuation dynamos provide a robust mechanism for amplifying weak seed magnetic fields in turbulent astrophysical plasmas. However, their behaviour in the highly compressible regimes characteristic of the interstellar medium remains incompletely understood. Using high-resolution 3D magnetohydrodynamic simulations of supersonic turbulence with rms Mach number $\mathcal{M}_{\rm rms} \approx 11$, we explore fluctuation dynamos across magnetic Prandtl numbers ${\rm Pm} = 1-10$. At ${\rm Pm}=1$, dynamo growth is slower and saturates at lower magnetic-to-kinetic energy ratios, with amplification in the kinematic phase dominated by compression rather than line stretching. In contrast, at ${\rm Pm}=10$, vortical stretching emerges as the dominant mechanism, yielding faster growth, higher saturation levels, and stronger suppression of density--magnetic field correlations by magnetic pressure. This transition is reflected in the correlation coefficient between density and magnetic field strength, which is strongly positive at ${\rm Pm}=1$ but decreases significantly at higher ${\rm Pm}$. Across all runs, the ratio of velocity-to-magnetic integral scales is $\sim 3.4$, in the saturated phase, independent of ${\rm Pm}$, while the ratio of viscous to resistive dissipation scales increases with the increase in ${\rm Pm}$. Synthetic Faraday rotation measures reveal coherence lengths of $\sim$one-fourth to one-third of the forcing scale across the range of ${\rm Pm}$ explored. Using these coherence scales, we discuss the potential contribution of fluctuation dynamos to Faraday rotation expected from turbulent, gas-rich young disk galaxies.

Figures (7)

• Figure 1: 2D slices in the $x-z$ plane at $y=0.5$ from Pm1 (top row) and Pm10 (bottom row) in the saturated phase. The left panels show logarithmic density contrasts, $\log(\rho/\langle\rho\rangle)$ with the color scale ranging from low-density voids (green) to highly dense structures (red and yellow). The right panels display the logarithmic values of the normalized field strength, $\log(B/{B_{\rm rms}})$, with a blue-to-red color scale depicting regions of low-to-high field strengths. The arrows of equal length represent the directions of the in-plane magnetic field vectors.
• Figure 2: Evolution of $\mathcal{M}_{\rm rms}$ (top) and $E_{\rm m}/E_{\rm k}$ (bottom) with $t/{t_{\rm ed}}$ for Pm1 (blue dashed), Pm5 (red dotted) and Pm10 (black solid). While $\mathcal{M}_{\rm rms} \approx 11$ in the steady state, the growth rates in the kinematic phase and the saturation level of $E_{\rm m}/E_{\rm k}$ are strongly dependent on the $\rm Pm$, with higher values producing faster exponential growth and higher saturation levels. The annotated slopes indicate the growth rates in the kinematic phases.
• Figure 3: Evolution of the Pearson correlation coefficient $r_{p}(\rho, B)$ with $t/{t_{\rm ed}}$ for Pm1 (blue asterisks), Pm5 (black squares), and Pm10 (red triangles). Starting from a strong positive correlation, $r_{p}(\rho,B)$ drops as the dynamo evolves from the kinematic to saturated phase. The decrease in $r_{p}(\rho, B)$ is strongly dependent on $\rm Pm$, with the $\rm Pm = 10$ run decreasing by $\approx 52\%$ from its value in the kinematic phase.
• Figure 4: Evolution of $r_{p}(\rho, B)$ for Pm1 (top), Pm5 (middle), and Pm10 (bottom) in different ranges of $B/{B_{\rm rms}}$. The solid black line shows the evolution over the full range of magnetic field strengths similar to Fig. \ref{['fig:corr_m11_diffpm']}. The blue open triangles represent $r_{p}(\rho,B)$ in regions where $B/{B_{\rm rms}} \leq 1$, while green asterisks denote correlations in regions with $B/{B_{\rm rms}} > 1$.
• Figure 5: Kinetic $K(k,t)$ and magnetic $M(k,t)$ energy spectra for Pm1 and Pm10 at fixed ${\rm Rm}$. Panels (a) and (b) show the time evolution of $K(k,t)$ (solid black lines) and $M(k,t)$ (dotted orange lines) as functions of wavenumber $k/k_{\rm min}$ for $\rm Pm = 1$ and $\rm Pm =10$, respectively. Panel (c) shows the time-averaged ratio of solenoidal to compressive components of the kinetic energy spectrum, $K_{\rm sol}(k)/K_{\rm comp}(k)$, for both runs in the saturated phase of the dynamo. Higher $\rm Pm$ leads to a relatively larger solenoidal energy fraction at intermediate and small scales and enhances magnetic energy at small scales compared to the $\rm Pm = 1$ case. The thin vertical at $k/k_{\rm min} = 2$ is the turbulence driving scale, where $k_{\rm min} = 2\pi\,L^{-1}$ is the smallest wavenumber in the box. The $K(k,t)$ shown here are density-weighted velocity spectra ($\sqrt{{\langle \rho\rangle}}\hbox{\boldmath $U$} {}$). Since ${\langle \rho\rangle} \approx 1$ in our simulation volume, the weighting does not affect the spectral slopes.