Surface imaging of cool evolved stars in the era of the ELT M. Wittkowski1 A. Chiavassa2 S. Höfner3 J. B. Climent4 1 ESO 2 Université Côte d’Azur, Nice, France 3 Uppsala University, Sweden 4 Universitat de València Cool evolved stars are the main source of chemical enrichment of the interstellar medium. Understanding their mass loss offers a unique opportunity to study the cycle of matter. We discuss interferometric studies and their comparison to latest state-of-the-art dynamic model atmospheres. They show broad agreement for asymptotic giant branch stars. For red supergiants, however, current models cannot explain observed extensions by far, pointing to missing physical processes in their models, and uncertainties in our general understanding of mass loss. We present ongoing imaging and time-series observations that may provide the strongest constraint and may help to identify missing dynamic processes. VLTI studies will remain the highest spatial resolution observations at ESO into the ELT era, complemented by ALMA observations. We discuss crucial improvements in both instrumental and operational areas for surface imaging of cool evolved stars in the era of the ELT. Introduction Low-to-intermediate mass asymptotic giant branch (AGB) stars and massive red supergiants (RSGs) are cool evolved stars with low effective temperatures between about 2500 K and 4000 K, and together spanning a huge range of luminosities of log L/Lsun between about 3 and 6. They experience a mass loss rate of up to about 10-5 to 10-4 Msun/year, precipitating the return of material to the interstellar medium. The mass-loss process is thought to be triggered by a levitation of the atmosphere to radii where dust can form, and radiative acceleration on dust grains dragging along the gas (e.g., Höfner and Olofsson 2018). However, some details of this process are surprisingly little understood, in particular for red supergiants, for which current models of pulsation and convection alone cannot elevate the atmosphere to observed extensions (Arroyo-Torres et al. 2015). Other processes may need to be included, such as radiative acceleration on Doppler-shifted molecular lines (Josselin & Plez 2007), magnetic fields and Alfén waves (e.g., Thirumalai & Heyl 2012, Airapetian et al. 2010), rotation (e.g., Vlemmings et al. 2018), or giant hot spots (e.g., Montarges et al. 2016, Vlemmings et al. 2017). The mass-loss is initiated on top of the convective photosphere of these sources, a crucial region that we need to image and study for a representative sample covering the large parameter space, to understand the physical mechanisms that elevate the atmosphere and drive the mass loss, by comparison to theoretical simulations. Current stage A decade of comparisons of mostly single-epoch spectro-interferometry at individual baselines to dynamic model atmospheres for AGB and RSG stars showed that both classes of evolved stars observationally show similarly extended molecular layers that can be fairly well reproduced by 1D pulsation dynamic models and with 3D models of convection for AGB stars (e.g., Wittkowski et al. 2016), but that by far cannot be reproduced by current 1D or 3D dynamic models of RSG stars (Arroyo- Torres et al. 2015). Interferometry now succeeds in imaging stellar surfaces and their environments, allowing us to compare reconstructed images and 3D simulations of convection in terms of contrast and morphology. Figs. 1-3 show as examples our work based on the PIONIER instrument in the near-IR H band for the the carbon AGB star R Scl (Wittkowski et al. 2017a), and the RSGs V766 Cen (Wittkowski et al. 2017b) and V602 Car (Climent et al., in prep.). All image reconstructions show a complex structure within the stellar disk. The image reconstruction of R Scl shows a complex structure and a dominant spot with large contrast