The water masers in NGC4258 delineate the structure and dynamics of a sub-parsec-diameter accretion disk around a supermassive black hole .
VLBA observations provide precise information about the positions in the plane of the sky and the three-dimensional velocity vectors for the maser emission , but the positions along the line of sight must be inferred from models .
Previous measurements placed an upper limit on the accelerations of the high-velocity spectral features of 1 km s ^ { -1 } yr ^ { -1 } , suggesting that they are located near the midline ( the diameter perpendicular to 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 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 ^ { -1 } yr ^ { -1 } 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 H _ { 2 } O ( 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 ^ { -1 } yr ^ { -1 } .
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 ^ { \circ } and 9.3 ^ { \circ } in azimuth ( measured from the midline ) .
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 ( \theta _ { p } / 2.5 ^ { \circ } ) km s ^ { -1 } yr ^ { -1 } , 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 .