Toward 2D Dynamo Models Calibrated by Global 3D Relativistic Accretion Disk Simulations

TL;DR

This paper investigates how to improve 2D black hole accretion disk models by calibrating dynamo effects using 3D relativistic simulations, aiming to incorporate non-axisymmetric turbulence feedback.

Contribution

It introduces new methods to estimate dynamo parameters from 3D simulations and evaluates different closure models for mean-field dynamo effects.

Findings

Dynamo models based solely on local variables are insufficient.

Global, covariant models show promise but are not yet satisfactory.

Non-axisymmetric turbulence significantly influences mean magnetic fields.

Abstract

Two-dimensional models assuming axisymmetry are an economical way to explore the long-term evolution of black hole accretion disks, but they are only realistic if the feedback of the nonaxisymmetric turbulence on the mean momentum and magnetic fields is incorporated. Dynamo terms added to the 2D induction equation should be calibrated to 3D MHD simulations. For generality, the dynamo tensors should be calibrated as functions of local variables rather than explicit functions of spatial coordinates in a particular basis. In this paper, we study the feedback of non-axisymmetric features on the 2D mean fields using a global 3D, relativistic, Cartesian simulation from the IllinoisGRMHD code. We introduce new methods for estimating overall dynamo alpha and turbulent diffusivity effects as well as measures of the dominance of non-axisymmetric components of energies and fluxes within the disk interior. We attempt closure models of the dynamo EMF using least squares fitting, considering both models where coefficient tensors are functions of space and more global, covariant models. None of these models are judged satisfactory, but we are able to draw conclusions on what sorts of generalizations are and are not promising.