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VLBI Astrometry of AGB Variables with VERA -- A Mira Type Variable T Lepus

We conducted phase referencing VLBI observations of the Mira variable T~Lepus (T~Lep) using VERA, from 2003 to 2006. The distance to the source was determined from its annual parallax which was measured to be 3.06$\pm$0.04 mas, corresponding to a distance of 327$\pm$4\,pc. Our observations revealed the distribution and internal kinematics of H$_2$O masers in T~Lep, and we derived a source systemic motions of 14.60$\pm$0.50 mas yr$^{-1}$ and $-$35.43$\pm$0.79 mas yr$^{-1}$ in right ascension and declination, respectively. We also determined a LSR velocity of $V_\mathrm{LSR}^{\ast} = -$27.63 km s$^{-1}$. Comparison of our result with an image recently obtained from the VLTI infrared interferometer reveals a linear scale picture of the circumstellar structure of T~Lep. Analysis of the source systemic motion in the Galacto-centric coordinate frame indicates a large peculiar motion, which is consistent with the general characteristics of AGB stars. This source makes a contribution to the calibration of the period-luminosity relation of Galactic Mira variables. From the compilation of data for nearby Mira variables found in the literature, whose distances were derived from astrometric VLBI observations, we have calibrated the Galactic Mira period-luminosity relation to a high degree of accuracy.