The Super-Alfvenic Rotational Instability in Accretion Disks about Black Holes

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 Alfven spectra Omega(+/-)(A) m Omega +/- omega(A), where omega(A) is the static Alfven frequency. It is crucial to take nonaxisymmetry (m not equal 0) and super-Alfvenic rotation of the Doppler frames (vertical bar m Omega vertical bar >> vertical bar omega(A)vertical bar) into account. The continua Omega(+)(A) and Omega(-)(A) then overlap, ejecting a plethora of super-Alfvenic rotational instabilities (SARIs). In-depth analysis for small inhomogeneity shows that the two Alfven 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 vertical bar k vertical bar >> vertical bar m vertical bar any complex omega 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, vertical bar W-com vertical bar <= 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 magnetorotational instabilities but by the excitation of modes from these two-dimensional continua of quasi-discrete nonaxisymmetric SARIs.

Automated summary

The theory of instability of accretion disks about black holes, neutron stars, or protoplanets is revisited using the method of the Spectral Web. The study shows that the cylindrical accretion disk differential equation is governed by the forward and backward Doppler-shifted continuous Alfven spectra. The analysis considers the nonaxisymmetry and super-Alfvenic rotation of the Doppler frames, leading to the discovery of super-Alfvenic rotational instabilities. It is conjectured that 3D turbulence in magnetized accretion disks is governed by the excitation of modes from two-dimensional continua of quasi-discrete nonaxisymmetric SARIs.