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

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Ross, J 
Latter, HN 
Guilet, J 

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 P0.5, 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 P0.9. Net-flux simulations without explicit diffusion exhibit stresses proportional to P0.5, 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.

accretion, accretion discs, MHD, turbulence
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Monthly Notices of the Royal Astronomical Society
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Oxford University Press (OUP)
Science and Technology Facilities Council (ST/L000636/1)
Science and Technology Facilities Council (ST/K501906/1)
Some of the simulations were run on the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility ( This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the UK National E-Infrastructure run. JR and HNL are partially funded by STFC grants ST/L000636/1 and ST/K501906/1. JG acknowledges support from the Max-Planck-Princeton Center for Plasma Physics.