We present the very long baseline interferometry H _ { 2 } O maser monitoring observations of the red supergiant , PZ Cas , at 12 epochs from 2006 April to 2008 May .
We fitted maser motions to a simple model composed of a common annual parallax and linear motions of the individual masers .
The maser motions with the parallax subtracted were well modeled by a combination of a common stellar proper motion and a radial expansion motion of the circumstellar envelope .
We obtained an annual parallax of 0.356 \pm 0.026 mas and a stellar proper motion of \mu ^ { * } _ { \alpha } \cos { \delta } = -3.7 \pm 0.2 and \mu ^ { * } _ { \delta } = -2.0 \pm 0.3 mas yr ^ { -1 } eastward and northward , respectively .
The annual parallax corresponds to a trigonometric parallax of 2.81 ~ { } ^ { +0.22 } _ { -0.19 } kpc .
By rescaling the luminosity of PZ Cas in any previous studies using our trigonometric parallax , we estimated the location of PZ Cas on a Hertzsprung-Russell diagram and found that it approaches a theoretically evolutionary track around an initial mass of \sim 25 M _ { \odot } .
The sky position and the distance to PZ Cas are consistent with the OB association , Cas OB5 , which is located in a molecular gas super shell .
The proper motion of PZ Cas is close to that of the OB stars and other red supergiants in Cas OB5 measured by the Hipparcos satellite .
We derived the peculiar motion of PZ Cas of U _ { \mathrm { s } } = 22.8 \pm 1.5 , V _ { \mathrm { s } } = 7.1 \pm 4.4 , and W _ { \mathrm { s } } = -5.7 \pm 4.4 km s ^ { -1 } .
This peculiar motion has rather a large U _ { \mathrm { s } } component , unlike those of near high-mass star-forming regions with negatively large V _ { \mathrm { s } } motions .
The uniform proper motions of the Cas OB5 member stars suggest random motions of giant molecular clouds moving into local potential minima in a time-dependent spiral arm , rather than a velocity field caused by the spiral arm density wave .