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.
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