Accelerations of water masers in NGC 4258

The water masers in NGC 4258 delineate the structure and dynamics of a subp arsec-diameter accretion disk around a supermassive black hole. Very Long B aseline Array (VLBA) observations provide precise information about the pos itions in the plane of the sky and the three-dimensional velocity vectors f or the maser emission, but the positions along the line of sight must be in ferred from models. Previous measurements placed an upper limit on the acce lerations of the high-velocity spectral features of 1 km s(-1) yr(-1), sugg esting that they are located near the midline (the diameter perpendicular t o the line of sight), where they would have exactly zero acceleration. From similar measurements, the accelerations of the systemic velocity spectral features have been estimated to be about 9 km s(-1) yr(-1), indicating that they lie toward the front of the disk where the acceleration vector points directly away from the line of sight. We report acceleration measurements for 12 systemic velocity spectral features and 19 high-velocity spectral fe atures using a total of 25 epochs of observations from Effelsberg (five epo chs), the Very Large Array (15 epochs), and the VLBA (five epochs) spanning the years 1994-1997. The measured accelerations of the systemic velocity f eatures are between 7.5 and 10.4 km s(-1) yr(-1), and there is no evidence for a dip in the spectrum at the systemic velocity. Such a dip has been att ributed in the past to an absorbing layer of noninverted H2O. The accelerat ions of the high-velocity features, measured here for the first time, range from -0.77 to 0.38 km s(-1) yr-'. From the line-of-sight accelerations and velocities, we infer the positions of these high-velocity masers with a si mple edge-on disk model The resulting positions fall. between -13 degrees 6 and 9 degrees 3 in azimuth (measured from the midline). A model that sugge sts a spiral shock origin of the masers, in which changes in maser velocity are due to the outward motion of the shock wave, predicts apparent acceler ations of -0.05(theta(p)/2 degrees 5) km s(-1) yr(-1), where theta(p) is th e pitch angle of the spiral arms. Our data are not consistent with these pr edictions. We also discuss the physical properties of the high-velocity mas ers. Most notably, the strongest high-velocity masers lie near the midline, where the velocity gradient is smallest, thereby providing the longest amp lification path lengths.