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The Galactic B[e] supergiant MWC 137 is surrounded by a large-scale opticalnebula. To shed light on the physical conditions and kinematics of the nebula,we analyze the optical forbidden emission lines [NII] 6548,6583 and [SII]6716,6731 in long-slit spectra taken with ALFOSC at the Nordic OpticalTelescope. The radial velocities display a complex behavior but, in general,the northern nebular features are predominantly approaching while the southernones are mostly receding. The electron density shows strong variations acrossthe nebula with values spreading from about zero to ~800 cm$^{-3}$. Higherdensities are found closer to MWC~137 and in regions of intense emission,whereas in regions with high radial velocities the density decreasessignificantly. We also observe the entire nebula in the two [SII] lines withthe scanning Fabry-Perot interferometer attached to the 6-m telescope of theSpecial Astrophysical Observatory. These data reveal a new bow-shaped featureat PA = 225-245 and a distance 80" from MWC 137. A new H$\alpha$ image has beentaken with the Danish 1.54-m telescope on La Silla. No expansion or changes inthe nebular morphology appear within 18.1 years. We derive a mass of 37 (+9/-5)solar masses and an age of $4.7\pm0.8$ Myr for MWC 137. Furthermore, we detecta period of 1.93 d in the time series photometry collected with the TESSsatellite, which could suggest stellar pulsations. Other, low-frequencyvariability is seen as well. Whether these signals are caused by internalgravity waves in the early-type star or by variability in the wind andcircumstellar matter currently cannot be distinguished.

Resolving the circumstellar environment of the Galactic B[e] supergiant star MWC 137. II. Nebular kinematics and stellar variability