Simple Scaling Relationships for Stellar Dynamos

TL;DR

This paper explores simple scaling laws for stellar dynamos, comparing theoretical models with numerical simulations to understand the relationship between magnetic and kinetic energies in stellar magnetic fields.

Contribution

It introduces and compares three dynamo scaling models, including a new one based on buoyancy and ohmic dissipation, validated against convective dynamo simulations.

Findings

Scaling relationships match simulation data across Rossby numbers

Magnetostrophic and inertia-inclusive models provide complementary insights

Derived scaling law effectively predicts magnetic energy in stellar dynamos

Abstract

This paper provides a brief overview of dynamo scaling relationships for the degree of equipartition between magnetic and kinetic energies. Three basic approaches are adopted to explore these scaling relationships, with a first look at two simple models: one assuming magnetostrophy and another that includes the effects of inertia. Next, a third scaling relationship is derived that utilizes the assumptions that the dynamo possesses two integral spatial scales and that it is driven by the balance of buoyancy work and ohmic dissipation as studied in Davidson 2013. The results of which are then compared to a suite of convective dynamo simulations that possess a fully convective domain with a weak density stratification and that captured the behavior of the resulting dynamo for a range of convective Rossby numbers (Augustson et al. 2016).