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The Distance and Size of the Red Hypergiant NML Cyg from VLBA and VLA Astrometry

We have measured the annual parallax and proper motion of NML Cyg from multiple epoch VLBA observations of the circulstellar H2O and SiO masers. The measured parallax of NML Cyg is 0.620+/-0.047 mas, corresponding to a distance of 1.61+/-0.12 kpc. The measured proper motion of NML Cyg is mu_x = -1.55+/-0.42 mas/yr eastward and mu_y= -4.59+/-0.41 mas/yr northward. Both Both the distance and proper motion are consistent with that of Cyg OB2, within their joint uncertainty, confirming their association. Taking into consideration molecular absorption signatures seen toward NML Cyg, we suggest that NML Cyg lies on the far side of the Cyg OB2 association. The stellar luminosity revised with our distance brings NML Cyg significantly below the empirical luminosity limit for a red supergiant. Using the VLA observation the radio photosphere and the SiO maser as a phase reference, we partially resolve the radio photosphere of NML Cyg at 43 GHz and find its diameter is about 44 mas, suggesting an optical stellar diameter of 22 mas, if the size of radio photosphere is 2 times the optical photosphere. Based on the position of circumstellar SiO masers relative to the radio photosphere, we estimate the absolute position of NML Cyg at epoch 2008.868 to be R.A. = 20h46m25.5382s +/- 0.0010s, Decl. = 40d06'59.379" +/- 0.015". The peculiar motions of NML Cyg, the average of stars in Cyg OB2, and four other star-forming regions rules out that an expanding "Stroemgren sphere" centered on Cyg OB2 is responsible for the kinematics of the Cygnus X region.