The effect of winds on atmospheric layers of red supergiants I. Modelling for interferometric observations

Red supergiants (RSGs) are evolved massive stars in a stage preceding core-collapse supernova. The physical processes that trigger mass loss in their atmospheres are still not fully understood. Based on observations of $\alpha$ Ori, a new semi-empirical method to add a wind to hydrostatic model atmospheres of RSGs was recently developed. We use this method of adding a wind to a MARCS model atmosphere to compute synthetic observables, comparing the model to spatially resolved interferometric observations. We present a case study to model published data of HD 95687 and V602 Car obtained with VLTI/AMBER. We compute model intensities, spectra and visibilities for different mass-loss rates using the radiative transfer code Turbospectrum. The models are convolved to match the different spectral resolutions of the VLTI instruments, studying a wavelength range of $1.8-5\,\mathrm{\mu m}$ corresponding to the $K$, $L$ and $M$-bands for GRAVITY and MATISSE data. We compare the model spectra and visibilities with the published VLTI/AMBER data. The synthetic visibilities reproduce observed drops in the CO, SiO, and water layers that are not shown in visibilities based on MARCS models alone. For the case studies, we find that adding a wind to MARCS with simple radiative equilibrium dramatically improves the agreement with the visibilities and the spectra. Our results reproduce observed extended atmospheres up to several stellar radii. This paper shows the potential of our model to describe extended atmospheres in RSGs: it can reproduce the shapes of the spectra and visibilities with better accuracy in the CO and water lines than previous models. The method can be extended to other wavelength bands for both spectroscopic and interferometric data. We provide temperature and density stratifications that succeed for the first time in reproducing observed interferometric properties of RSG atmospheres.