Fundamental MHD scales -- II: the kinematic phase of the supersonic small-scale dynamo
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| Format: | Preprint |
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2023
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| _version_ | 1866929707989073920 |
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| author | Kriel, Neco Beattie, James R. Federrath, Christoph Krumholz, Mark R. Hew, Justin Kin Jun |
| author_facet | Kriel, Neco Beattie, James R. Federrath, Christoph Krumholz, Mark R. Hew, Justin Kin Jun |
| contents | 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 ($\ell_ν$ and $\ell_η$) and the scale of strongest magnetic fields ($\ell_\mathrm{p}$) during the kinematic phase. We demonstrate that $\ell_ν/\ell_η\sim \mathrm{Pm}^{1/2}$ is a universal feature for $\mathrm{Pm} \geq 1$ SSDs, regardless of $\mathcal{M}$ or $\mathrm{Re}$. Incompressible SSDs (either $\mathcal{M} \leq 1$ or $\mathrm{Re} < \mathrm{Re}\mathrm{crit} \approx 100$) concentrate magnetic energy at $\ell_\mathrm{p} \sim \ell_η$ with inversely correlated field strength and curvature. However, for compressible SSDs ($\mathcal{M} > 1$ and $\mathrm{Re} > \mathrm{Re}\mathrm{crit}$), shocks concentrate magnetic energy in large structures with $\ell_\mathrm{p} \sim (\ell_\mathrm{turb} / \ell_\mathrm{shock})^{1/3} \ell_η\gg \ell_η$, where $\ell_\mathrm{shock}$ is the characteristic shock width, and $\ell_\mathrm{turb}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17036 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fundamental MHD scales -- II: the kinematic phase of the supersonic small-scale dynamo Kriel, Neco Beattie, James R. Federrath, Christoph Krumholz, Mark R. Hew, Justin Kin Jun Astrophysics of Galaxies High Energy Astrophysical Phenomena Fluid Dynamics Plasma Physics 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 ($\ell_ν$ and $\ell_η$) and the scale of strongest magnetic fields ($\ell_\mathrm{p}$) during the kinematic phase. We demonstrate that $\ell_ν/\ell_η\sim \mathrm{Pm}^{1/2}$ is a universal feature for $\mathrm{Pm} \geq 1$ SSDs, regardless of $\mathcal{M}$ or $\mathrm{Re}$. Incompressible SSDs (either $\mathcal{M} \leq 1$ or $\mathrm{Re} < \mathrm{Re}\mathrm{crit} \approx 100$) concentrate magnetic energy at $\ell_\mathrm{p} \sim \ell_η$ with inversely correlated field strength and curvature. However, for compressible SSDs ($\mathcal{M} > 1$ and $\mathrm{Re} > \mathrm{Re}\mathrm{crit}$), shocks concentrate magnetic energy in large structures with $\ell_\mathrm{p} \sim (\ell_\mathrm{turb} / \ell_\mathrm{shock})^{1/3} \ell_η\gg \ell_η$, where $\ell_\mathrm{shock}$ is the characteristic shock width, and $\ell_\mathrm{turb}$ 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. |
| title | Fundamental MHD scales -- II: the kinematic phase of the supersonic small-scale dynamo |
| topic | Astrophysics of Galaxies High Energy Astrophysical Phenomena Fluid Dynamics Plasma Physics |
| url | https://arxiv.org/abs/2310.17036 |