Resolving the circumstellar environment of the Galactic B[e] supergiant
  star MWC 137. II. Nebular kinematics and stellar variability
  The Galactic B[e] supergiant MWC 137 is surrounded by a large-scale optical
nebula. 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 Optical
Telescope. The radial velocities display a complex behavior but, in general,
the northern nebular features are predominantly approaching while the southern
ones are mostly receding. The electron density shows strong variations across
the nebula with values spreading from about zero to ~800 cm$^{-3}$. Higher
densities are found closer to MWC~137 and in regions of intense emission,
whereas in regions with high radial velocities the density decreases
significantly. We also observe the entire nebula in the two [SII] lines with
the scanning Fabry-Perot interferometer attached to the 6-m telescope of the
Special Astrophysical Observatory. These data reveal a new bow-shaped feature
at PA = 225-245 and a distance 80" from MWC 137. A new H$\alpha$ image has been
taken with the Danish 1.54-m telescope on La Silla. No expansion or changes in
the 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 detect
a period of 1.93 d in the time series photometry collected with the TESS
satellite, which could suggest stellar pulsations. Other, low-frequency
variability is seen as well. Whether these signals are caused by internal
gravity waves in the early-type star or by variability in the wind and
circumstellar matter currently cannot be distinguished.
