The Absolutely Unstable Discrete Eigenmodes in the Magneto-rotational Instability in an Accretion Disk

Details The Absolutely Unstable Discrete Eigenmodes in the Magneto-rotational Instability in an Accretion Disk The Absolutely Unstable Discrete Eigenmodes in the Magneto-rotational Instability in an Accretion Disk

Sep 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999aas...19411507n&link_type=abstract

American Astronomical Society Meeting 194, #115.07

Astronomy and Astrophysics

Astronomy

Scientific paper

Recent years a revived interest has been directed at the magneto- rotational instability(Velikhov, Chandrasekhar, Balbus-Hawley). This is because of its possibility of explaining the magnetic viscosity of accretion disks. Matsumoto & Tajima [1] showed the absolute instability eigenmode structure of this mode. Ogilvie & Pringle [2] cast a doubt about the nature of the discrete eigenmodes and their stability. We examine the non-axisymmetric unstable modes proposed by Matsumoto & Tajima [1], which are not influenced by the disk edge boundaries and grow exponentially in time, and prove that these modes are descrete and do not vanish by phase-mixing, in contrary to what Ogilvie & Pringle [2] pointed out. Basic propaties of the modes are examined analytically, and eigenvalues are calculated numerically with higher accuracy. We also prove the existence of continuum modes that are distinct from the discrete modes; the continuum modes have singularity at the Alfven resonance points. Angular momentum transfer is then explained by the superposition of the unstable modes that are confined between the Alfven singularities. [1] Matsumoto R., Tajima T., 1995, ApJ, 445, 767 [2] Ogilvie G. I., Pringle J. E., 1996, MNRAS, 279, 152

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