  A new Stokes inversion technique that greatly reduces the effect of the
spatial point spread function of the telescope is used to constrain the
physical properties of umbral dots (UDs). The depth-dependent inversion of the
Stokes parameters from a sunspot umbra recorded with Hinode SOT/SP revealed
significant temperature enhancements and magnetic field weakenings in the core
of the UDs in deep photospheric layers. Additionally, we found upflows of
around 960 m/s in peripheral UDs (i.e., UDs close to the penumbra) and
$\approx$ 600 m/s in central UDs. For the first time, we also detected
systematic downflows for distances larger than 200 km from the UD center that
balance the upflowing mass flux. In the upper photosphere, we found almost no
difference between the UDs and their diffuse umbral background.
