  Umbral dots (UDs) were observed in a stable sunspot in NOAA 10944 by the
Hinode Solar Optical Telescope on 2007 March 1. The observation program
consisted of blue continuum images and spectropolarimetric profiles of Fe I 630
nm line. An automatic detection algorithm for UDs was applied to the 2-hour
continuous blue continuum images, and using the obtained data, the lifetime,
size, and proper motion of UDs were calculated. The magnetic structure of the
sunspot was derived through the inversion of the spectropolarimetric profiles.
  We calculated the correlations between UD's parameters (size, lifetime,
occurrence rate, proper motion) and magnetic fields (field strength,
inclination, azimuth), and obtained the following results: (1) Both the
lifetime and size of UDs are almost constant regardless of the magnetic field
strength at their emergence site. (2) The speed of UDs increases as the field
inclination angle at their emergence site gets larger. (3) The direction of
movement of UDs is nearly parallel to the direction of the horizontal component
of magnetic field in the region with strongly inclined field, while UDs in the
region with weakly inclined field show virtually no proper motion.
  Our results describe the basic properties of magnetoconvection in sunspots.
We will discuss our results in comparison to recent MHD simulations by
Schussler & Vogler (2006) and Rempel et al. (2009).
