Fundamental MHD scales -- II: the kinematic phase of the supersonic small-scale dynamo

Understand

Many astrophysical small-scale dynamos (SSDs) amplify weak magnetic fields via highly compressible, supersonic turbulence, but established SSD theories have overlooked these compressible effects.

• To address this, we perform visco-resistive SSD simulations across a range of sonic Mach numbers ($\mathcal{M}$), hydrodynamic Reynolds numbers ($\mathrm{Re}$), and magnetic Prandtl numbers ($\mathrm{Pm}$).
• We develop robust methods to measure kinetic and magnetic energy dissipation scales ($\ell_\nu$ and $\ell_\eta$) and the scale of strongest magnetic fields ($\ell_\mathrm{p}$) during the kinematic phase.
• We demonstrate that $\ell_\nu/\ell_\eta \sim \mathrm{Pm}^{1/2}$ is a universal feature for $\mathrm{Pm} \geq 1$ SSDs, regardless of $\mathcal{M}$ or $\mathrm{Re}$.