The height of convective plumes in the red supergiant $\mu$ Cep

International audienceAims. We seek to understand convection in red supergiants and the mechanisms that trigger the mass loss from cool evolved stars. Methods. Linear spectropolarimetry of the atomic lines of the spectrum of $\mu$ Cep reveals information well outside the wavelength range expected from previous models. This is interpreted as structures in expansion that are visible in the front hemisphere and sometimes also in the back hemisphere. We model the plasma distribution together with its associated velocities through an inversion algorithm to fit the observed linear polarization. Results. We find that supposing the existence of plasma beyond the limb rising high enough to be visible above it can explain the observed linear polarization signatures as well as their evolution in time. From this we are able to infer the geometric heights of the convective plumes and establish that this hot plasma rises to at least 1.1 R*. Conclusions. $\mu$ Cep appears to be in an active phase in which plasma rises often above 1.1 R* . We generalize this result to all red supergiants in a similarly evolved stage, which at certain epochs may easily send plasma to greater heights, as $\mu$ Cep appears to be doing at present. Plasma rising to such heights can easily escape the stellar gravity