Erratum: On characterizing non-locality and anisotropy for the magnetorotational instability

Abstract

The extent to which angular momentum transport in accretion discs is primarily local or nonlocal and what determines this is an important avenue of study for understanding accretion engines. Taking a step along this path, we analyse simulations of the magnetorotational instability (MRI) by calculating energy and stress power spectra in stratified isothermal shearing box simulations in several new ways. We divide our boxes in two regions, disc and corona wherethediscistheMRIunstableregionandcoronaisthemagneticallydominatedregion.We calculate the fractional power in different quantities, including magnetic energy and Maxwell stresses and find that they are dominated by contributions from the lowest wave numbers. This is even more dramatic for the corona than the disc, suggesting that transport in the corona regionisdominatedbylargerstructuresthanthedisc.Bycalculatingaveragedpowerspectrain one direction of k space at a time, we also show that the MRI turbulence is strongly anisotropic on large scales when analysed by this method, but isotropic on small scales. Although the shearing box itself is meant to represent a local section of an accretion disc, the fact that the stress and energy are dominated by the largest scales highlights that the locality is not captured within the box. This helps to quantify the intuitive importance of global simulations for addressing the question of locality of transport, for which similar analyses can be performed.