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

Neco Kriel; James R. Beattie; Christoph Federrath; Mark R. Krumholz; Justin Kin Jun Hew

doi:10.1093/mnras/staf188

paper

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

arXiv:2310.17036 · doi:10.1093/mnras/staf188

Abstract

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 ( $M$ ), hydrodynamic Reynolds numbers ( $Re$ ), and magnetic Prandtl numbers ( $Pm$ ). We develop robust methods to measure kinetic and magnetic energy dissipation scales ( $ℓ_{ν}$ and $ℓ_{η}$ ) and the scale of strongest magnetic fields ( $ℓ_{p}$ ) during the kinematic phase. We demonstrate that $ℓ_{ν} / ℓ_{η} \sim Pm^{1/2}$ is a universal feature for $Pm \geq 1$ SSDs, regardless of $M$ or $Re$ . Incompressible SSDs (either $M \leq 1$ or $Re < Re crit \approx 100$ ) concentrate magnetic energy at $ℓ_{p} \sim ℓ_{η}$ with inversely correlated field strength and curvature. However, for compressible SSDs ( $M > 1$ and $Re > Re crit$ ), shocks concentrate magnetic energy in large structures with $ℓ_{p} \sim (ℓ_{turb} / ℓ_{shock})^{1/3} ℓ_{η} ≫ ℓ_{η}$ , where $ℓ_{shock}$ is the characteristic shock width, and $ℓ_{turb}$ is the outer scale of the turbulent field. In this regime, magnetic field-line curvature becomes nearly independent of field strength. These results have implications for galaxy mergers and cosmic ray transport models in the interstellar medium.

30 pages, 15 figures, dataset available from MNRAS

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

Abstract

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