Connecting mean-field theory with dynamo simulations

TL;DR

This paper reviews how mean-field dynamo theory connects with advanced 3D simulations of magnetic fields, validating the theory through comparisons with realistic models of solar and stellar magnetism.

Contribution

It provides a comprehensive overview of the links between mean-field models and dynamo simulations, highlighting recent advances and remaining challenges.

Findings

Successful validation of mean-field models against simulations

Identification of turbulent transport coefficients from simulations

Summary of challenges in mean-field interpretation

Abstract

Mean-field dynamo theory, describing the evolution of large-scale magnetic fields, has been the mainstay of theoretical interpretation of magnetism in astrophysical objects such as the Sun for several decades. More recently, three-dimensional magnetohydrodynamic simulations have reached a level of fidelity where they capture dynamo action self-consistently on local and global scales without resorting to parametrization of unresolved scales. Recent global simulations also capture many of the observed characteristics of solar and stellar large-scale magnetic fields and cycles. Successful explanation of the results of such simulations with corresponding mean-field models is a crucial validation step for mean-field dynamo theory. Here the connections between mean-field theory and current dynamo simulations are reviewed. These connections range from the numerical computation of turbulent transport coefficients to mean-field models of simulations, and their relevance to the solar dynamo. Finally, the most notable successes and current challenges in mean-field theoretical interpretations of simulations are summarized.