On characterizing nonlocality and anisotropy for the magnetorotational
  instability
  The extent to which angular momentum transport in accretion discs is
primarily local or non-local and what determines this is an important avenue of
study for understanding accretion engines. Taking a step along this path, we
analyze 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 where the disc is the MRI unstable region and corona is the magnetically
dominated region. 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 region is
dominated by larger structures than the disc. By calculating averaged power
spectra in one direction of $k$ space at a time, we also show that the MRI
turbulence is strongly anisotropic on large scales when analyzed 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.
