Robustly Unstable Eigenmodes of the Magnetoshearing Instability in Accretion Disks

The stability of nonaxisymmetric perturbations in differentially rotatingastrophysical accretion disks is analyzed by fully incorporating the propertiesof shear flows. We verify the presence of discrete unstable eigenmodes withcomplex and pure imaginary eigenvalues, without any artificial disk edgeboundaries, unlike Ogilvie & Pringle(1996)'s claim. By developing themathematical theory of a non-self-adjoint system, we investigate the nonlocalbehavior of eigenmodes in the vicinity of Alfven singularities atomega_D=omega_A, where omega_D is the Doppler-shifted wave frequency andomega_A=k_// v_A is the Alfven frequency. The structure of the spectrum ofdiscrete eigenmodes is discussed and the magnetic field and wavenumberdependence of the growth rate are obtained. Exponentially growing modes arepresent even in a region where the local dispersion relation theory claims tohave stable eigenvalues. The velocity field created by an eigenmode isobtained, which explains the anomalous angular momentum transport in thenonlinear stage of this stability.