Extension of the MURaM radiative MHD code for coronal simulations

TL;DR

This paper introduces an extended version of the MURaM radiative MHD code capable of simulating the solar corona from the convection zone, incorporating coronal physics and efficient numerical methods for realistic, long-term solar atmosphere modeling.

Contribution

The authors developed and validated a new MURaM code version that includes coronal physics and semi-relativistic MHD, enabling explicit, long-duration solar corona simulations.

Findings

Coronal heating is mainly due to viscous dissipation owing to high magnetic Prandtl number.

Reasonable simulations are achievable with a reduced speed of light just above maximum sound speed.

The code can simulate days-long flux emergence events with explicit time steps around 0.1 seconds.

Abstract

We present a new version of the MURaM radiative MHD code that allows for simulations spanning from the upper convection zone into the solar corona. We implemented the relevant coronal physics in terms of optically thin radiative loss, field aligned heat conduction and an equilibrium ionization equation of state. We artificially limit the coronal Alfv{\'e}n and heat conduction speeds to computationally manageable values using an approximation to semi-relativistic MHD with an artificially reduced speed of light (Boris correction). We present example solutions ranging from quiet to active Sun in order to verify the validity of our approach. We quantify the role of numerical diffusivity for the effective coronal heating. We find that the (numerical) magnetic Prandtl number determines the ratio of resistive to viscous heating and that owing to the very large magnetic Prandtl number of the solar corona, heating is expected to happen predominantly through viscous dissipation. We find that reasonable solutions can be obtained with values of the reduced speed of light just marginally larger than the maximum sound speed. Overall this leads to a fully explicit code that can compute the time evolution of the solar corona in response to photospheric driving using numerical time steps not much smaller than $0.1$ seconds. Numerical simulations of the coronal response to flux emergence covering a time span of a few days are well within reach using this approach.