VLTI/AMBER spectro-interferometry of the late-type supergiants V766 Cen (=HR 5171 A), sigma Oph, BM Sco, and HD 206859

Aims. We add four warmer late-type supergiants to our previous spectro-interferometric studies of red giants and supergiants. Methods. We measure the near-continuum angular diameter, derive fundamental parameters, discuss the evolutionary stage, and study extended atmospheric atomic and molecular layers. Results. V766 Cen (=HR 5171 A) is found to be a high-luminosity (log L/L-circle dot = 5.8 +/- 0.4) source of effective temperature 4290 +/- 760K and radius 1490 +/- 540 R-circle dot, located in the Hertzsprung-Russell (HR) diagram close to both the Hayashi limit and Eddington limit; this source is consistent with a 40 M-circle dot evolutionary track without rotation and current mass 27-36 M-circle dot. V766 Cen exhibits Na I in emission arising from a shell of radius 1.5 R-Phot and a photocenter displacement of about 0.1 R-Phot. It shows strong extended molecular (CO) layers and a dusty circumstellar background component. The other three sources are found to have lower luminosities of about log L/L-circle dot = 3.4-3.5, corresponding to 5-9 M-circle dot evolutionary tracks. They cover effective temperatures of 3900K to 5300K and radii of 60-120 R-circle dot. They do not show extended molecular layers as observed for higher luminosity RSGs of our sample. BM Sco shows an unusually strong contribution by an over-resolved circumstellar dust component. Conclusions. V766 Cen is a red supergiant located close to the Hayashi limit instead of a yellow hypergiant already evolving back toward warmer effective temperatures as discussed in the literature. Our observations of the Na I line and the extended molecular layers suggest an optically thick pseudo-photosphere at about 1.5 R-Phot at the onset of the wind. The stars sigma Oph, BM Sco, and HD 206859 are more likely high-mass red giants instead of RSGs as implied by their luminosity class Ib. This leaves us with an unsampled locus in the HR diagram corresponding to luminosities log L/L-circle dot similar to 3.8-4.8 or masses 10-13 M-circle dot, possibly corresponding to the mass region where stars explode as (type II-P) supernovae during the red supergiant stage. With V766 Cen, we now confirm that our previously found relation of increasing strength of extended molecular layers with increasing luminosities extends to double our previous luminosities and up to the Eddington limit. This might further point to steadily increasing radiative winds with increasing luminosity.