Numerical simulations of quiet Sun magnetism: On the contribution from a small-scale dynamo

TL;DR

This paper uses radiative MHD simulations to investigate the origin, distribution, and strength of magnetic fields in the quiet Sun, revealing the importance of small-scale dynamo processes and the role of domain size and resolution.

Contribution

It provides new insights into the magnetic energy distribution and flux concentrations in the quiet Sun, emphasizing the significance of small-scale dynamo action and the effects of simulation parameters.

Findings

50% of magnetic energy at b51 level is from fields <500 G

Flux concentrations >1 kG require mean vertical field >30-40 G

Most of the convection zone is magnetized near equipartition

Abstract

We present a series of radiative MHD simulations addressing the origin and distribution of mixed polarity magnetic field in the solar photosphere. To this end we consider numerical simulations that cover the uppermost 2-6 Mm of the solar convection zone and we explore scales ranging from 2 km to 25 Mm. We study how the strength and distribution of magnetic field in the photosphere and subsurface layers depend on resolution, domain size and boundary conditions. We find that 50% of the magnetic energy at the \tau=1 level comes from field with the less than 500 G strength and that 50% of the energy resides on scales smaller than about 100 km. While probability distribution functions are essentially independent of resolution, properly describing the spectral energy distribution requires grid spacings of 8 km or smaller. The formation of flux concentrations in the photosphere exceeding 1 kG requires a mean vertical field strength greater than 30-40 G at \tau=1. The filling factor of kG flux concentrations increases with overall domain size as magnetic field becomes organized by larger, longer lived flow structures. A solution with a mean vertical field strength of around 85 G at \tau=1 requires a subsurface RMS field strength increasing with depth at the same rate as the equipartition field strength. We consider this an upper limit for the quiet Sun field strength, which implies that most of the convection zone is magnetized close to equipartition. We discuss these findings in view of recent high-resolution spectropolarimetric observations of quiet Sun magnetism.