[en] Many magnetic structures in the solar atmosphere evolve rather slowly, so they can be assumed as (quasi-)static or (quasi-)stationary and represented via magnetohydrostatic (MHS) or stationary magnetohydrodynamic (MHD) equilibria, respectively. While exact 3D solutions would be desired, they are extremely difficult to find in stationary MHD. We construct solutions with magnetic and flow vector fields that have three components depending on all three coordinates. We show that the noncanonical transformation method produces quasi-3D solutions of stationary MHD by mapping 2D or 2.5D MHS equilibria to corresponding stationary MHD states, that is, states that display the same field-line structure as the original MHS equilibria. These stationary MHD states exist on magnetic flux surfaces of the original 2D MHS states. Although the flux surfaces and therefore also the equilibria have a 2D character, these stationary MHD states depend on all three coordinates and display highly complex currents. The existence of geometrically complex 3D currents within symmetric field-line structures provides the basis for efficient dissipation of the magnetic energy in the solar corona by ohmic heating. We also discuss the possibility of maintaining an important subset of nonlinear MHS states, namely force-free fields, by stationary flows. We find that force-free fields with nonlinear flows only arise under severe restrictions of the field-line geometry and of the magnetic flux density distribution.

[en] 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 [N ii] λ λ 6548,6583 and [S ii] λ λ 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 [S ii] 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 P.A. = 225°–245° and a distance 80″ from MWC 137. A new Hα 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 yr. We derive a mass of ${37}_{-<!--\; ???\; -->5}^{+9}{M}_{\odot <!--\; ???\; -->}$ and an age of 4.7 ± 0.8 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.

[en] Massive stars typically undergo short-lived post-main-sequence evolutionary phases with strong mass loss and occasional mass eruptions. Many of such massive stars in transition phases have been identified based on their dusty envelopes. The ejected material often veils the stellar photospheres so that the central stars cannot be assigned proper spectral types and evolutionary stages. The infrared spectral range has proved to be ideal for the classification of evolved massive stars and for the characterization of their environments. To improve our knowledge on the central stars of four such dust-enshrouded objects, [GKF 2010] MN 83, [GKF 2010] MN 108, [GKF 2010] MN 109, and [GKF 2010] MN 112, we collect and present their first medium-resolution K-band spectra in the 2.3–2.47 μm region and discuss the location of the stars in the JHK color–color diagram. We find that the emission-line spectra of both MN 83 and MN 112 show characteristics typically seen in luminous blue variable (LBV) stars. In addition, we propose that the presence and strength of the newly reported Mg ii lines might be used as a new complementary criterion to identify LBV candidates. The spectra of the other two objects imply that MN 108 is an O-type supergiant, whereas MN 109 could be an LBV candidate in its active phase. We derive lower limits for the reddening toward the stars and find that three of all dereddened fall into the region of confirmed LBVs.

[en] The Galactic object MWC 137 has been suggested to belong to the group of B[e] supergiants. However, with its large-scale optical bipolar ring nebula and high-velocity jet and knots, it is a rather atypical representative of this class. We performed multiwavelength observations spreading from the optical to the radio regimes. Based on optical imaging and long-slit spectroscopic data, we found that the northern parts of the large-scale nebula are predominantly blueshifted, while the southern regions appear mostly redshifted. We developed a geometrical model consisting of two double cones. Although various observational features can be approximated with such a scenario, the observed velocity pattern is more complex. Using near-infrared integral-field unit spectroscopy, we studied the hot molecular gas in the vicinity of the star. The emission from the hot CO gas arises in a small-scale disk revolving around the star on Keplerian orbits. Although the disk itself cannot be spatially resolved, its emission is reflected by the dust arranged in arc-like structures and the clumps surrounding MWC 137 on small scales. In the radio regime, we mapped the cold molecular gas in the outskirts of the optical nebula. We found that large amounts of cool molecular gas and warm dust embrace the optical nebula in the east, south, and west. No cold gas or dust was detected in the north and northwestern regions. Despite the new insights into the nebula kinematics gained from our studies, the real formation scenario of the large-scale nebula remains an open issue.