  Realistic 3D radiative MHD simulations reveal the magneto-convective
processes underlying the formation of the photospheric fine structure of
sunspots, including penumbral filaments and umbral dots. Here we provide
results from a statistical analysis of simulated umbral dots and compare them
with reports from high-resolution observations. A multi-level segmentation and
tracking algorithm has been used to isolate the bright structures in synthetic
bolometric and continuum brightness images. Areas, brightness, and lifetimes of
the resulting set of umbral dots are found to be correlated: larger umbral dots
tend to be brighter and live longer. The magnetic field strength and velocity
structure of umbral dots on surfaces of constant optical depth in the continuum
at 630 nm indicate that the strong field reduction and high velocities in the
upper parts of the upflow plumes underlying umbral dots are largely hidden from
spectro-polarimetric observations. The properties of the simulated umbral dots
are generally consistent with the results of recent high-resolution
observations. However, the observed population of small, short-lived umbral
dots is not reproduced by the simulations, possibly owing to insufficient
spatial resolution.
