Fundamental Parameters of the Milky Way Galaxy Based on VLBI Astrometry

We present analyses to determine the fundamental parameters of the Galaxy based on VLBI astrometry of 52 Galactic maser sources obtained with VERA, VLBA, and EVN. We model the Galaxy's structure with a set of parameters, including the Galaxy center distance $ R_0$ , the angular rotation velocity at the LSR $ \Omega_0$ , the mean peculiar motion of the sources with respect to Galactic rotation ( $ U_{\rm src}$ , $ V_{\rm src}$ , $ W_{\rm src}$ ), the rotation-curve shape index, and the $ V$ component of the Solar peculiar motions, $ V_\odot $ . Based on a Markov chain Monte-Carlo method, we find that the Galaxy center distance is constrained at a 5% level to be $ R_0$ $ =$ 8.05 $ \pm$ 0.45 kpc, where the error bar includes both statistical and systematic errors. We also find that the two components of the source peculiar motion $ U_{\rm src}$ and $ W_{\rm src}$ are fairly small compared to the Galactic rotation velocity, being $ U_{\rm src}$ $ =$ 1.0 $ \pm$ 1.5 km s $ ^{-1}$ and $ W_{\rm src}$ $ =$ $-$ 1.4 $ \pm$ 1.2 km s $ ^{-1}$ . Also, the rotation curve shape is found to be basically flat between Galacto-centric radii of 4 and 13 kpc. On the other hand, we find a linear relation between $ V_{\rm src}$ and $ V_\odot $ as $ V_{\rm src}$ $ =$ $ V_\odot $ $-$ 19 ( $ \pm$ 2) km s $ ^{-1}$ , suggesting that the value of $ V_{\rm src}$ is fully dependent on the adopted value of $ V_\odot $ . Regarding the rotation speed in the vicinity of the Sun, we also find a strong correlation between $ \Omega_0$ and $ V_\odot $ . We find that the angular velocity of the Sun, $ \Omega_{\odot}$ , which is defined as $ \Omega_\odot$ $ \equiv$ $ \Omega_0$ $ +$ $ V_\odot/R_0$ , can be well constrained with the best estimate of $ \Omega_\odot$ $ =$ 31.09 $ \pm$ 0.78 km s $ ^{-1}$ kpc $ ^{-1}$ . This corresponds to $ \Theta_0$ $ =$ 238 $ \pm$ 14 km s $ ^{-1}$ if one adopts the above value of $ R_0$ and recent determination of $ V_\odot $ $ \sim$ 12 km s $ ^{-1}$ .