The Super-Alfvénic Rotational Instability in accretion disks about black holes

Abstract

The theory of instability of accretion disks about black holes, neutron stars or protoplanets, is revisited by means of the recent method of the Spectral Web. The cylindrical accretion disk differential equation is shown to be governed by the forward and backward Doppler-shifted continuous Alfvén spectra Ω ± A ≡ mΩ ± ω A , where ω A is the static Alfvén frequency. It is crucial to take non-axisymmetry (m = 0) and super-Alfvénic rotation of the Doppler frames (|mΩ|A and Ω − A then overlap, ejecting a plethora of Super-Alfvénic Rotational Instabilities (SARIs). Indepth analysis for small inhomogeneity shows that the two Alfvén singularities reduce the extent of the modes to sizes much smaller than the width of the accretion disk. Generalization for large inhomogeneity leads to the completely unprecedented result that, for mode numbers |k| |m|, any complex ω in a wide neighborhood of the real axis is an approximate 'eigenvalue'. The difference with genuine eigenmodes is that the amount of complementary energy to excite the modes is tiny, |W com | ≤ c, with c the machine accuracy of the computation. This yields a multitude of two-dimensional continua of quasi-discrete modes: quasi-continuum SARIs. We conjecture that the onset of 3D turbulence in magnetized accretion disks is governed, not by the excitation of discrete axisymmetric Magneto-Rotational Instabilities, but by the excitation of modes from these two-dimensional continua of quasidiscrete non-axisymmetric Super-Alfvénic Rotational Instabilities.

A non-local magneto-curvature instability in a differentially rotating disk

“…Localized nonaxisymmetric MRI mode structures were found to be confined between the Alfvénic resonant points (where the magnitude of the Doppler-shifted wave frequency is equal to Alfvén frequency (Matsumoto & Tajima 1995). In cylindrical shear flows (Ogilvie & Pringle 1996) and in the compressible limit (Goedbloed & Keppens 2022), it was shown that forward and backward overlapping of these Alfvén continua results in discrete localized nonaxisymmetric modes at large axial and azimuthal mode numbers. The question arises whether in a real domain with spatial curvature, global non-axisymmetric modes with real frequencies can persist.…”