The angular momentum transport by standard MRI in quasi-Kepler cylindric Taylor-Couette flows

TL;DR

This study investigates how nonaxisymmetric magnetorotational instability modes in Taylor-Couette flows influence angular momentum transport, revealing dependencies on magnetic field strength and mode number, with implications for accretion disk dynamics.

Contribution

It provides new insights into the excitation conditions and transport properties of nonaxisymmetric MRI modes in quasi-Keplerian flows, challenging previous assumptions about MRI decay at low magnetic Prandtl numbers.

Findings

Nonaxisymmetric modes require higher rotation rates for excitation.

Positive angular momentum transport depends linearly on Lundquist number.

MRI does not decay at low magnetic Prandtl numbers as previously thought.

Abstract

The instability of a quasi-Kepler flow in dissipative Taylor-Couette systems under the presence of an homogeneous axial magnetic field is considered with focus to the excitation of nonaxisymmetric modes and the resulting angular momentum transport. The excitation of nonaxisymmetric modes requires higher rotation rates than the excitation of the axisymmetric mode and this the more the higher the azimuthal mode number m. We find that the weak-field branch in the instability map of the nonaxisymmetric modes has always a positive slope (in opposition to the axisymmetric modes) so that for given magnetic field the modes with m>0 always have an upper limit of the supercritical Reynolds number. In order to excite a nonaxisymmetric mode at 1 AU in a Kepler disk a minimum field strength of about 1 Gauss is necessary. For weaker magnetic field the nonaxisymmetric modes decay. The angular momentum transport of the nonaxisymmetric modes is always positive and depends linearly on the Lundquist number of the background field. The molecular viscosity and the basic rotation rate do not influence the related {\alpha}-parameter. We did not find any indication that the MRI decays for small magnetic Prandtl number as found by use of shearing-box codes. At 1 AU in a Kepler disk and a field strength of about 1 Gauss the {\alpha} proves to be (only) of order 0.005.