VLTI-GRAVITY measurements of cool evolved stars. II. Pulsation properties and mass-loss process of the Mira star R Car and the red supergiant VX Sgr

The mass-loss process of red supergiant (RSG) and asymptotic giant branch (AGB) stars and its relation to variability are poorly constrained. We aim to study the photosphere and near-surface atmospheric structure, where the mass-loss is initiated. For this purpose, we studied two oxygen-rich evolved stars: the Mira-type AGB star R Car and the RSG VX Sgr. We used the VLTI-GRAVITY instrument operating in the near-infrared K-band. Our sample comprises 54 VLTI-GRAVITY snapshots (18 R Car, 36 VX Sgr) taken over about 7 years, making it the largest VLTI time series dataset to date. We determined the angular diameter as a function of time for the continuum (photosphere) and selected atomic and molecular bands, i. e. , lines of and as well as bands of H₂O and CO. Furthermore, we compared the variability and atmospheric structure to state-of-the-art radiative-hydrodynamics CO5BOLD 3D simulations. Ti i Sc i The radii of photosphere (R_⋆) and extended atmospheric layers are variable and relate to the light curve with phase shifts. The near-photospheric layers show a maximum radius near visual brightness minima (ϕ_ ̊m vis ∼ 0. 4-0. 6). Inner atomic (, ) and molecular (H₂O) layers are further phase-shifted by Δϕ_ Ti i Sc i ̊m vis ∼ 0. 05. The more extended CO layers show longer, irregular periods and maximum extensions of ∼ 1. 3-1. 7: R_⋆ for R Car and of ∼ 1. 5-2. 2: R_⋆ for VX Sgr. Comparison with synthetic interferometric data of an AGB model based on several pulsation cycles in CO5BOLD simulations revealed a similar behavior. The photosphere shows regular pulsations, but with maximum diameters preceding minimum brightness ̊m vis < 0. 5). The H₂O layer showed a much weaker extension compared to our observations, while CO showed a good agreement. Furthermore, during the 2020-2021 season, 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 H₂O and CO layers, both up to ∼ 2. 2: R_⋆. Unexpectedly, during this event, we also detected Brackett γ in interferometric data as well as strong Balmer emission in optical spectra, both of which are also signatures of a shock propagating through the atmosphere. The Mira R Car showed an estimated photospheric radius of R_⋆ = 280 ± 25: ̊m R_⊙, with a regular fundamental mode (FM) pulsation amplitude of sim13 % of R_⋆. During its active cycle, the extreme RSG VX Sgr showed R_⋆ = 1556 ± 110: ̊m R_⊙, with an FM pulsation amplitude of % of R_⋆, the same as R Car. During its quiescent cycle, it showed a smaller value, R_⋆= 1456 ± 108: ̊m R_⊙, and low-amplitude pulsations near the first overtone (O1), only sim4 % of R_⋆. This supports a steady mass-loss process for Mira stars 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 from low-amplitude O1 to large-amplitude FM pulsations.