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

The theory of instability accretion disks about black holes, neutron stars or proto-planets, is revisited by means the recent method Spectral Web. cylindrical disk differential equation shown to be governed forward and backward Doppler-shifted continuous Alfv\'en spectra $\Omega_{\rm A}^\pm \equiv m \Omega \pm \omega_{\rm A}$, where $\omega_{\rm A}$ static frequency. It crucial take non-axisymmetry ($m \ne 0$) super-Alfv\'enic rotation Doppler frames ($|m\Omega| \gg |\omega_{\rm A}|$) into account. continua A}^+$ A}^-$ then overlap, ejecting a plethora Super-Alfv\'enic Rotational Instabilities (SARIs). In-depth analysis for small inhomogeneity shows that two singularities reduce extent modes sizes much smaller than width disk. Generalization large leads completely unprecedented result that, mode numbers $|k| |m|$, any complex $\omega$ in wide neighborhood real axis an approximate `eigenvalue'. difference with genuine eigenmodes amount complementary energy excite tiny, $|W_{\rm com}| \le c$, $c$ machine accuracy computation. This yields multitude two-dimensional quasi-discrete modes: quasi-continuum SARIs. We conjecture onset 3D turbulence magnetized governed, not excitation discrete axisymmetric Magneto-Rotational Instabilities, but from these non-axisymmetric Instabilities.