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

TL;DR

This work investigates the asymptotic behavior of the galactic small-scale dynamo (SSD) using high-resolution, SN-driven MHD simulations in a periodic, 256 pc box with GPU-accelerated Pencil Code. By distinguishing explicit magnetic diffusivity from numerical diffusion and probing a range of resolutions, the authors show the SSD saturates at a modest magnetic Prandtl number ($Pm$ on the order of $10$–$100$), with the saturation level around $e_s \approx 0.05\, e_K$ and a Kazantsev-like spectrum ($e_B(k) \propto k^{3/2}$) in the kinematic phase. The findings imply that the turbulent magnetic field produced by the SSD can be represented in global galactic models (e.g., via subgrid or input fields) despite ISM $Pm$ being many orders of magnitude larger, and that the SSD reaches its asymptotic strength on short timescales ($\sim$1–2 Myr). These results provide a practical framework for incorporating SSD-driven turbulence into large-scale simulations of galaxy formation and evolution.

Abstract

Magnetic fields are critical at many scales to galactic dynamics and structure, including multiphase pressure balance, dust processing, and star formation. Dynamo action determines their dynamical structure and strength. Simulations of combined large- and small-scale dynamos have successfully developed mean fields with strength and topology consistent with observations but with turbulent fields much weaker than observed, while simulations of small-scale dynamos with parameters relevant to the interstellar medium yield turbulent fields an order of magnitude below the values observed or expected theoretically. We use the Pencil Code accelerated on GPUs with Astaroth to perform high-resolution simulations of a supernova-driven galactic dynamo including heating and cooling in a periodic domain. Our models show that the strength of the turbulent field produced by the small-scale dynamo approaches an asymptote at only modest magnetic Prandtl numbers. This allows us to use these models to suggest the essential characteristics of this constituent of the magnetic field for inclusion in global galactic models. The asymptotic limit occurs already at magnetic Prandtl number of only a few hundred, many orders of magnitude below physical values in the the interstellar medium and consistent with previous findings for isothermal compressible flows.

Figures (3)

• Figure 1: Magnetic energy spectra $e_{\rm B}(k)$ compensated by the Kazantsev scaling $k^{3/2}$ and normalized by their compensated maximum for (a) Models N128, (b) N256 and (c) N512 using different values of the magnetic diffusivity $\eta$ in$~ {\rm kpc}~ {\rm km~s}^{-1}$ as listed in the legends. Insets zoom in near the start of the inertial range to highlight deviations from the curve for $\eta=0$.
• Figure 2: Magnetic energy spectra $e_{\rm B}(k)$ normalized by $e_{\rm B}(k_f)$ at a typical SN forcing wavenumber $k_f = 125 \hbox{kpc}^{-1}$ at a given Pm for models listed in the legends. The $k^{3/2}$ Kazantsev scaling is indicated upper left (dotted dark blue).
• Figure 3: Magnetic energy $e_{\rm B}$ normalised by time-averaged turbulent kinetic energy ${\overline{e_{\rm K}}}$ for grid (a)$512^3$(b), $1024^3$(c), $2048^3$ and (d)$4096^3$. See the legends for Pm and $e_{\rm s}$ from an average over the latest 2.5% of simulation time. Markers are shown at the time of SN explosions. Note that the time scales are dramatically smaller at higher resolution.