Accelerations of Water Masers in NGC 4258

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Abstract
The water masers in NGC 4258 delineate the structure and dynamics of a subparsec-diameter accretion disk around a supermassive black hole. Very Long Baseline Array (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 (five epochs), the Very Large Array (15 epochs), and the VLBA (five epochs) spanning the years 1994-1997. 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 noninverted H2O. 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 -136 and 93 in azimuth (measured from the midline). A model that suggests 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 accelerations of -0.05(θp/25) km s-1 yr-1, where θp 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.

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