The evolutionary phase of B [ e ] stars is difficult to establish due to the un certainties in their fundamental parameters .
For instance , possible classifications for the Galactic B [ e ] star MWC 137 include pre-main-sequence and post-main-sequence phases , with a large range in luminosity .
Our goal is to clarify the evolutionary stage of this peculiar object , and to study the CO molecular component of its circumstellar medium .
To this purpose , we modeled the CO molecular bands using high-resolution K -band spectra .
We find that MWC 137 is surrounded by a detached cool ( T = 1900 \pm 100 K ) and dense ( N = ( 3 \pm 1 ) \times 10 ^ { 21 } cm ^ { -2 } ) ring of CO gas orbiting the star with a rotational velocity , projected to the line of sight , of 84 \pm 2 km s ^ { -1 } .
We also find that the molecular gas is enriched in the isotope 13 C , excluding the classification of the star as a Herbig Be .
The observed isotopic abundance ratio ( \mathrm { \textsuperscript { 12 } C / \textsuperscript { 13 } C } = 25 \pm 2 ) derived from our modeling is compatible with a proto-PN , main-sequence or supergiant evolutionary phase .
However , based on some observable characteristics of MWC 137 , we propose that the supergiant scenario seems to be the most plausible .
Hence , we suggest that MWC 137 could be in an extremely short-lived phase , evolving from a B [ e ] supergiant to a blue supergiant with a bipolar ring nebula .