The stress-pressure relationship in simulations of MRI-induced turbulence

TL;DR

This study investigates how MRI-induced turbulent stresses depend on gas pressure in simulations, revealing a stronger relationship than previously thought and highlighting issues with numerical convergence and the influence of imposed magnetic flux.

Contribution

The paper demonstrates that the stress-pressure relationship in MRI turbulence is stronger than earlier reports suggested, emphasizing the importance of physical diffusivities and box size in simulations.

Findings

Stress proportional to P^{0.5} without physical diffusion

Stress approaches P^{0.9} with physical diffusivities

Numerical convergence issues affect stress-pressure relationship

Abstract

We determine how MRI-turbulent stresses depend on gas pressure via a suite of unstratified shearing box simulations. Earlier numerical work reported only a very weak dependence at best, results that call into question the canonical alpha-disk model and the thermal stability results that follow from it. Our simulations, in contrast, exhibit a stronger relationship, and show that previous work was box-size limited: turbulent `eddies' were artificially restricted by the numerical domain rather than by the scale height. Zero-net-flux runs without physical diffusion coefficients yield a stress proportional to $P^{0.5}$, where P is pressure. The stresses are also proportional to the grid length and hence remain numerically unconverged. The same runs with physical diffusivities, however, give a result closer to an alpha-disk: the stress is proportional to $P^{0.9}$. Net-flux simulations without explicit diffusion exhibit stresses proportional to $P^{0.5}$, but stronger imposed fields weaken this correlation. In summary, compressibility is important for the saturation of the MRI, but the exact stress-pressure relationship is difficult to ascertain in local simulations because of numerical convergence issues and the influence of any imposed flux. As a consequence, the interpretation of thermal stability behaviour in local simulations is a problematic enterprise.