Context : The thermal structure of the penumbra below its visible surface ( i.e. , \tau _ { 5 } \geq 1 ) has important implications for our present understanding of sunspots and their penumbrae : their brightness and energy transport , mode conversion of magneto-acoustic waves , sunspot seismology , and so forth .

Aims : We aim at determining the thermal stratification in the layers immediately beneath the visible surface of the penumbra : \tau _ { 5 } \in [ 1 , 3 ] ( \approx 70 - 80 km below the visible continuum-forming layer )

Methods : We analyzed spectropolarimetric data ( i.e. , Stokes profiles ) in three Fe i lines located at 1565 nm observed with the GRIS instrument attached to the 1.5-meter solar telescope GREGOR .
The data are corrected for the smearing effects of wide-angle scattered light and then subjected to an inversion code for the radiative transfer equation in order to retrieve , among others , the temperature as a function of optical depth T ( \tau _ { 5 } ) .

Results : We find that the temperature gradient below the visible surface of the penumbra is smaller than in the quiet Sun .
This implies that in the region \tau _ { 5 } \geq 1 the penumbral temperature diverges from that of the quiet Sun .
The same result is obtained when focusing only on the thermal structure below the surface of bright penumbral filaments .
We interpret these results as evidence of a thick penumbra , whereby the magnetopause is not located near its visible surface .
In addition , we find that the temperature gradient in bright penumbral filaments is lower than in granules .
This can be explained in terms of the limited expansion of a hot upflow inside a penumbral filament relative to a granular upflow , as magnetic pressure and tension forces from the surrounding penumbral magnetic field hinder an expansion like this .

Conclusions :