D. Jadlovský, M. Wittkowski, A. Chiavassa, K. Kravchenko, B. Freytag, S. Höfner, J. Krtička, C. Paladini, G. Rau, M. Brož, T. Granzer, M. Weber

The mass-loss process of red supergiant (RSG) and asymptotic giant branch (AGB) stars and its relation to variability is poorly constrained. We study two evolved stars, the Mira-type AGB star R Car and the extreme RSG VX Sgr. Our sample comprises 54 VLTI-GRAVITY snapshots taken over 7 years, being the largest VLTI time-series dataset to date. We determine the angular diameter as a function of time. The radii of the photosphere ($R_{\star}$) and atomic atmospheric layers are variable and relate to the light curve with phase shifts, showing a maximum radius near visual brightness minima. The more extended CO layers show longer, irregular periods and maximum extensions of $\sim 1.3-1.7 \: R_{\star}$ for R Car, and of $\sim 1.5-2.2 \: R_{\star}$ for VX Sgr. Comparison with CO5BOLD simulations revealed a similar behavior. Furthermore, during 2020-2021, VX Sgr exhibited an extreme mass-loss event similar to that of Betelgeuse, preceded by two strong shocks and culminating with the extreme expansion of H$_2$O and CO layers, both up to $\sim 2.2 \: R_{\star}$. During this event, we detected Brackett $γ$ and Balmer emission lines, both of which are signatures of a shock propagating through the atmosphere. The Mira R Car showed a photospheric radius $R_{\star} = 280 \pm 25 \: \rm R_\odot$, with a fundamental mode (FM) pulsation amplitude $\sim13 \%$ of $R_{\star} $. During its active cycle, the RSG VX Sgr showed $R_{\star} = 1556 \pm 110 \: \rm R_\odot$ with FM amplitude $ \sim13 \%$ of $R_{\star} $, the same as R Car. During its quiescent cycle, it showed $R_{\star}= 1456 \pm 108 \: \rm R_\odot$ and low-amplitude pulsations near the first overtone, only $\sim4 \%$ of $R_{\star} $. This supports a steady mass loss for Miras related to stable, large-amplitude FM pulsation, whereas the mass-loss process for RSGs may be dominated by extreme events connected to changes in the pulsation mode.