The stress–pressure relationship in simulations of MRI-induced turbulence
We determine how MRI (magnetorotational instability)-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 α-disc 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 scaleheight. 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 α-disc: the stress is ∝P^0.9. Net-flux simulations without explicit diffusion exhibit stresses ∝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.