  We study the velocity structure of penumbral filaments in the deep
photosphere to obtain direct evidence for the convective nature of sunspot
penumbrae. A sunspot was observed at high spatial resolution with the 1-m
Swedish Solar Telescope in the deep photospheric C I 5380 {\AA} absorption
line. The Multi-Object Multi-Frame Blind Deconvolution (MOMFBD) method is used
for image restoration and straylight is filtered out. We report here the
discovery of clear redshifts in the C I 5380 {\AA} line at multiple locations
in sunspot penumbral filaments. For example, bright head of filaments show
larger concentrated blueshift and are surrounded by darker, redshifted regions,
suggestive of overturning convection. Elongated downflow lanes are also located
beside bright penumbral fibrils. Our results provide the strongest evidence yet
for the presence of overturning convection in penumbral filaments and highlight
the need to observe the deepest layers of the penumbra in order to uncover the
energy transport processes taking place there.
