Small-scale dynamos on the solar surface: dependence on magnetic Prandtl number

TL;DR

This study investigates the conditions under which small-scale dynamo action occurs on the solar surface using realistic 3D MHD simulations, focusing on the critical magnetic Prandtl number and its implications for astrophysical environments.

Contribution

It demonstrates the sensitivity of small-scale dynamo action to the magnetic Prandtl number and identifies a critical value dependent on numerical resolution, advancing understanding of solar surface magnetism.

Findings

Dynamo action disappears below a critical Pm of about 1 at 3.5 km grid spacing.

The critical Pm increases with coarser grid resolution.

Uncertainty remains whether small-scale dynamo operates in the astrophysical regime where Pm<<1.

Abstract

The question of possible small-scale dynamo action in the surface layers of the Sun is revisited with realistic 3D MHD simulations. As in other MHD problems, dynamo action is found to be a sensitive function of the magnetic Prandtl number ${\rm P_{\rm m} }=\nu/\eta$; it disappears below a critical value ${\rm P_{\rm c}}$ which is a function of the numerical resolution. At a grid spacing of 3.5 km, ${\rm P_{\rm c}}$ based on the hyperdiffusivities implemented in the code (STAGGER) is $\approx 1$, increasing with increasing grid spacing. As in other settings, it remains uncertain whether small scale dynamo action is present in the astrophysical limit where ${\rm P_{\rm m} }<<1$ and magnetic Reynolds number ${\rm R_m}\gg 1$. The question is discussed in the context of the strong effect that external stray fields are observed to have in generating and maintaining dynamo action in other numerical and laboratory systems, and in connection with the type-II hypertransient behavior of dynamo action observed in the absence of such external fields.