Origins, Structure, and Inflows of m=1 Modes in Quasi-Keplerian Disks
  Simulations show eccentric disks (m=1 modes) forming around quasi-Keplerian
potentials, a topic of interest for fueling quasars, forming super-massive BHs,
planet formation and migration, explaining the origin and properties of nuclear
eccentric stellar disks like that in M31, and driving the formation of the
obscuring AGN torus. We consider the global, linear normal m=1 modes in
collisionless disks, without the restriction that the disk mass be negligible
relative to the central (Keplerian) mass. We derive their structure and key
resonance features, and show how they arise, propagate inwards, and drive both
inflow/outflow and eccentricities in the disk. We compare with hydrodynamic
simulations of such disks around a super-massive BH, with star formation, gas
cooling, and feedback. We derive the dependence of the normal mode structure on
disk structure, mass profiles, and thickness, and mode pattern speeds and
growth rates. We show that, if the disk at some radii has mass of >~10% the
central point mass, the modes are linearly unstable and are self-generating.
They arise as 'fast modes' with pattern speed of order the local angular
velocity at these radii. The characteristic global normal modes have pattern
speeds comparable to the linear growth rate, of order (G*M_0*R_0^{-3})^{1/2},
where M_0 is the central mass and R_{0} is the radius where the enclosed disk
mass ~M_{0}. They propagate inwards by exciting eccentricities towards smaller
and smaller radii, until at small radii these are 'slow modes.' With moderate
amplitude, the global normal modes can lead to shocks and significant gas
inflows at near-Eddington rates at all radii inside several ~R_0.
