Accelerations of Water Masers in NGC4258
  The water masers in NGC4258 delineate the structure and dynamics of a sub-parsec-diameter accretion disk around a supermassive black hole. We report acceleration measurements for 12 systemic-velocity spectral features and 19 high-velocity spectral features, using a total of 25 epochs of observations from Effelsberg (5 epochs), the VLA (15 epochs), and the VLBA (5 epochs) spanning the years 1994 to 1997. The measured accelerations of the systemic-velocity features are between 7.5 and 10.4 km/s/yr, and there is no evidence for a dip in the spectrum at the systemic velocity. Such a dip has been attributed in the past to an absorbing layer of non-inverted H2O (Watson & Wallin 1994; Maoz & McKee 1998). The accelerations of the high-velocity features, measured here for the first time, range from -0.77 to 0.38 km/s/yr.   From the line-of-sight accelerations and velocities, we infer the positions of these high-velocity masers with a simple edge-on disk model. The resulting positions fall between -13.6 and 9.3 degrees in azimuth (measured from the midline, the diameter perpendicular to the line of sight). A model that suggests a spiral shock origin of the masers (Maoz & McKee 1998), in which changes in maser velocity are due to the outward motion of the shock wave, predicts apparent accelerations of -0.05 times theta_p/2.5 degrees km/s/yr, where theta_p is the pitch angle of the spiral arms. Our data are not consistent with these predictions. We also discuss the physical properties of the high-velocity masers. Most notably, the strongest high-velocity masers lie near the midline, where the velocity gradient is smallest, thereby providing the longest amplification path lengths. (Abridged) 
A. E. Bragg, L. J. Greenhill, J. M. Moran, and C. Henkel