A resolution criterion based on characteristic timescales for MHD simulations of molecular clouds

TL;DR

This paper examines how numerical magnetic diffusion affects MHD simulations of molecular clouds, proposing a resolution criterion based on characteristic timescales to ensure physical accuracy.

Contribution

It introduces a new resolution criterion for MHD simulations that accounts for numerical magnetic diffusion by comparing diffusion times to physical process timescales.

Findings

Higher resolution simulations avoid artificial collapse.

Numerical magnetic diffusion can be quantified through current-sheet simulations.

A resolution criterion based on diffusion times improves simulation reliability.

Abstract

We investigate the effect of numerical magnetic diffusion in magnetohydrodynamic simulations of magnetically supported molecular clouds. To this end, we have performed numerical studies on adaptive mesh isothermal simulations of marginally sub-critical molecular clouds. We find that simulations with low and intermediate resolutions collapse, contrary to what is theoretically expected. However, the simulation with the highest numerical resolution oscillates around an equilibrium state without collapsing. In order to quantify the numerical diffusion of the magnetic field, we ran a second suit of current-sheet simulations in which the numerical magnetic diffusion coefficient can be directly measured, and computed the corresponding diffusion times at various numerical resolutions. On this basis, we propose a criterion for the resolution of magnetic fields in MHD simulations based on requiring that the diffusion time to be larger than the characteristic timescale of the physical process responsible for the dynamic evolution of the structure.