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

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
e-mail: irina@mpa-garching.mpg.de
² Kiepenheuer Institute for Solar Physics, Schöneckstraße 6, 79104 Freiburg im Breisgau, Germany

Received: 28 February 2014
Accepted: 9 April 2015

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 P_m = ν/η; it disappears below a critical value P_c which is a function of the numerical resolution. At a grid spacing of 3.5 km, P_c based on the hyperdiffusivities implemented in the code (STAGGER) is ≈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 P_m ≪ 1 and magnetic Reynolds number R_m ≫ 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.