Eccentricity of masing disks in Active Galactic Nuclei
  Observations of Keplerian disks of masers in NCG 4258 and other Seyfert galaxies can be used to obtain geometric distance estimates and derive the Hubble constant. The ultimate precision of such measurements could be limited by uncertainties in the disk geometry. Using a time-dependent linear theory model, we study the evolution of a thin initially eccentric disk under conditions appropriate to sub-pc scales in Active Galactic Nuclei. The evolution is controlled by a combination of differential precession driven by the disk potential and propagating eccentricity waves that are damped by viscosity. A simple estimate yields a circularization timescale of approximately 10 Myr at 0.1 pc. Numerical solutions for the eccentricity evolution confirm that damping commences on this timescale, but show that the subsequent decay rate of the eccentricity depends upon the uncertain strength of viscous damping of eccentricity. If eccentricity waves are important further decay of the eccentricity can be slow, with full circularization requiring up to 50 Myr for disks at radii of 0.1 pc to 0.2 pc. Observationally, this implies that it is plausible that enough time has elapsed for the eccentricity of masing disks to have been substantially damped, but that it may not be justified to assume vanishing eccentricity. We predict that during the damping phase the pericenter of the eccentric orbits describes a moderately tightly wound spiral with radius. 
Philip J. Armitage