  This work aims to constrain the physical nature of umbral dots (UDs) using
high-resolution spectropolarimetry. Full Stokes spectra recorded by the
spectropolarimeter on Hinode of 51 UDs in a sunspot close to the disk center
are analyzed. The height dependence of the temperature, magnetic field vector,
and line-of-sight velocity across each UD is obtained from an inversion of the
Stokes vectors of the two FeI lines at 630 nm. No difference is found at higher
altitudes (-3 <= log(tau) <= -2) between the UDs and the diffuse umbral
background. Below that level the difference rapidly increases, so that at the
continuum formation level (log(tau) = 0) we find on average a temperature
enhancement of 570 K, a magnetic field weakening of 510 G, and upflows of 800
m/s for peripheral UDs, whereas central UDs display an excess temperature of on
average 550 K, a field weakening of 480 G, and no significant upflows. The
results for, in particular, the peripheral UDs, including cuts of magnetic
vector and velocity through them, look remarkably similar to the output of
recent radiation MHD simulations. They strongly suggest that UDs are produced
by convective upwellings.
