The pre- versus post-main sequence evolutionary phase of B[e] stars

Context. Many galactic B[e] stars suffer from improper distance determinations, which make it difficult to distinguish between a pre- and post-main sequence evolutionary phase on the basis of luminosity arguments. In addition, these stars have opaque circumstellar material, obscuring the central star, so that no detailed surface abundance studies can be performed. Aims. Instead of studying the surface abundances as a tracer of the evolutionary phase, we propose a different indicator for the supergiant status of a B[e] star, based on the enrichment of its circumstellar matter by 13C, and detectable via its 13CO band emission in the K band spectra. Methods. Based on stellar evolution models, we calculate the variation of the 12C/13C isotopic surface abundance ratio during the evolution of non-rotating stars with different initial masses. For different values of the 12C/13C ratio we then compute synthetic first-overtone vibration-rotational band spectra from both the 12CO and 13CO molecule at different spectral resolutions. We further discuss the influence of stellar rotation on the variation of the surface 12C/13C ratio and on the possibility of 13CO band detection. Results. The surface 12C/13C isotope ratio is found to decrease strongly during the post-main sequence evolution of non-rotating stars, from its interstellar value of about 70 to a value of about 15–20 for stars with initial masses higher than 7 $M_{\odot}$, and to a value of less than 5 for stars with initial masses higher than 25 $M_{\odot}$. We find that detectable 13CO band head emission is produced for isotope ratios 12C/$^{13}{\rm C}\la 20$, and can most easily be detected with a spectral resolution of $R\sim 1500 \ldots 3000$. For the rotating stellar models, the drop in 12C/13C already occurs for all stars with $M_{\rm in} \ga 9~M_{\odot}$ during the main-sequence evolution. The detection of 13CO band head emission in such mid-resolution K band spectra of a B[e] star thus favours an evolved rather than a young nature of the object