Abstract
Aims. We assess the ability to image the photosphere of red supergiants and, in particular Betelgeuse, through the modelling of the observed linear polarization in atomic spectral lines. We also aim to analyse the resulting images over time, to measure the size and dynamics of the convective structures in these stars.Methods. Rayleigh scattering polarizes the continuum and spectral lines depolarize it. This depolarization is seen as a linear polarization signal parallel to the radial direction on the stellar disk. Integrated over the disk, it would result in a null signal, except if brightness asymmetries/inhomogeneities are present. This is the basic concept behind our imaging technique. Through several tests and comparisons, we have tried to assess and extend its validity, and to determine what can be learnt unambiguously through it.Results. The several tests and comparisons performed prove that our technique reliably retrieves the salient brightness structures in the photosphere of Betelgeuse, and should be relevant to other red supergiants. For Betelgeuse, we demonstrate that these structures we infer are convective cells, with a characteristic size of more than 60% of the stellar radius. We also derive the characteristic upflow and downflow speeds, 22 and 10 km s−1, respectively. We find weak magnetic fields concentrated in the downflow lanes in between granules, similar to the quiet sun magnetism. We follow those convective structures in time. Changes happen on timescales of 1 week, but individual structures can be tracked over 4 yr of observations.Conclusions. The measured characteristics of the convection in Betelgeuse confirm the predictions of numerical simulations in both the strong, supersonic upflows and the size of the convective cells. They also concur in the presence of weak magnetic fields that are completely dominated by the convective flows and constrained to the dark lanes of down-flowing plasma.