On Estimating the Mass of Keplerian Accretion Disks in H2O Maser Galaxies

H2O maser disks with Keplerian rotation in active galactic nuclei offer a clean way to determine accurate black hole mass and the Hubble constant. An important assumption made in using a Keplerian H2O maser disk for measuring the black hole mass and the Hubble constant is that the disk mass is negligible compared to the black hole mass. To test this assumption, a simple and useful model can be found in Hure et al. (2011). In this work, the authors apply a linear disk model to a position-dynamical mass diagram and re-analyze position-velocity data from H2O maser disks associated with active galactic nuclei. They claim that a maser disk with nearly perfect Keplerian rotation could have disk mass comparable to the black hole mass. This would imply that ignoring the effects of disk self-gravity can lead to large systematic errors in the measurement of black hole mass and the Hubble constant. We examine their methods and find that their large estimated disk masses of Keplerian disks are likely the result of their use of projected instead of 3-dimensional position and velocity information. To place better constraints on the disk masses of Keplerian maser systems, we incorporate disk self-gravity into a 3-dimensional Bayesian modelling program for maser disks and also evaluate constraints based on the physical conditions for disks which support water maser emission. We find that there is little evidence that disk masses are dynamically important at the ~<1% level compared to the black holes.