Astrometric VLBI observations of H$_2$O masers in an extreme OH/IR star candidate NSV17351
Results of astrometric very long baseline interferometry (VLBI) observations towards an extreme OH/IR star candidate NSV17351 are presented. We used the VERA (VLBI Exploration of Radio Astrometry) VLBI array to observe 22\,GHz H$_2$O masers of NSV17351. We derived an annual parallax of 0.247$\pm$0.035 mas which corresponds to a distance of 4.05$\pm$0.59 kpc. By averaging the proper motions of 15 maser spots, we obtained the systemic proper motion of NSV17351 to be ($\mu_{\alpha}\cos{\delta}, \mu_{\delta}$)$^{\mathrm{avg}}$ $=$ ($-$1.19 $\pm$ 0.11, 1.30 $\pm$ 0.19) mas\,yr$^{-1}$. The maser spots spread out over a region of 20 mas $\times$ 30 mas, which can be converted to a spatial distribution of $\sim$80 au $\times$ $\sim$120 au at the source distance. Internal motions of the maser spots suggest an outward moving maser region with respect to the estimated position of the central star. From single dish monitoring of the H$_2$O maser emission, we estimate the pulsation period of NSV17351 to be 1122$\pm$24 days. This is the first report of the periodic activity of NSV17351, indicating that NSV17351 could have a mass of $\sim$4\,M$_{\odot}$. We confirmed that the time variation of H$_2$O masers can be used as a period estimator of variable OH/IR stars. Furthermore, by inspecting dozens of double-peaked H$_2$O maser spectra from the last 40 years, we detected a long-term acceleration in the radial velocity of the circumstellar matter to be $0.17\pm0.03$ km\,s$^{-1}$\,yr$^{-1}$ Finally, we determined the position and kinematics of NSV17351 in the Milky Way Galaxy and found that NSV17351 is located in an interarm region between the Outer and Perseus arms. We note that astrometric VLBI observations towards extreme OH/IR stars are useful samples for studies of the Galactic dynamics.