Coordinates on the disk of Betelgeuse and polarized spectra in the case of one bright spot. In the left of the figure a cartoon of the stellar disk shows the polar coordinates for three bright spots at the same χ but at different μ. Accross each spot the arrow shows both the orientation and relative polarization expected. Around the disk the dashed arrows show the definition of the Stokes parameters Q,U. In the right-hand part of the figure, the leftmost two plots show Stokes Q (top) and U (bottom) for the three spots as they would be seen in a resolved stellar disk. The two rightmost plots show what would be observed with Narval and the radial velocity scale is shifted to the HRV of Betelgeuse. See Sect. 5.3 for a complete description.